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astro-ph0607512

i

in this paper , we present a detailed study of the evolution in the color density relation at @xmath0 . using a sample of galaxies drawn from the deep2 galaxy redshift survey , we estimate the local overdensity about each galaxy according to the projected @xmath36nearest neighbor surface density . from this , we measure the evolution of the red fraction with environment across time . our principal results are as follows : * we find that the color density relation observed locally still exists at @xmath1 ; the fraction of galaxies on the red sequence increases with local galaxy overdensity to nearly the redshift limits of the deep2 survey . * at all epochs probed @xmath194 , we find there exists a population of red , morphologically early type galaxies residing in the the most underdense environments . * the color density relation evolves with redshift , growing weaker with lookback time such that at @xmath4 there is no detectable dependence of galaxy color on local environment in the deep2 sample . * our results support a picture in which the red sequence grew preferentially in dense environments ( i.e. , galaxy groups ) at @xmath195 . clearly , the local environment plays an important role in `` nurturing '' galaxies , establishing the existence of correlations such as the morphology density and color density relation over cosmic time . the strength of evolutionary trends suggests that the correlations observed locally do not appear to have been imprinted ( by `` nature '' ) upon the galaxy population during their epoch of formation . * our findings imply that there should be little color dependence in the clustering of @xmath5 galaxies at @xmath4 . this work was supported in part by nsf grants ast0071048 ast0071198 , ast0507428 , ast0507483 . j.a.n . and a.l.c . acknowledge support by nasa through hubble fellowship grants hst hf01165.01a and hst hf01182.01a , respectively , awarded by the space telescope science institute , which is operated by aura inc . under nasa contract nas 526555 . s.m.f . would like to acknowledge the support of a visiting miller professorship at uc m.c.c . would like to thank greg wirth and all of the keck observatory staff for their help in the acquisition of the keck / deimos data . in addition , the authors thank olga cucciati , chris marinoni , and the vvds team for helpful discussions related to this work , for review of an early version of this text , and for providing their data points for comparison . we also thank the referee , felipe menanteau , for his insightful comments and suggestions for improving this work . we also wish to recognize and acknowledge the highly significant cultural role and reverence that the summit of mauna kea has always had within the indigenous hawaiian community . it is a privilege to be given the opportunity to conduct observations from this mountain .

we find that the fraction of galaxies on the red sequence depends strongly on local environment out to , being larger in regions of greater galaxy density . at all epochs probed , we also find a small population of red , morphologically early type galaxies residing in regions of low measured overdensity . the strength of the observed evolutionary trends at suggests that the correlations observed locally , such as the morphology density and color density relations , are the result of environment driven mechanisms ( i.e. , `` nurture '' ) and do not appear to have been imprinted ( by `` nature '' ) upon the galaxy population during their epoch of formation .

using a sample of 19,464 galaxies drawn from the deep2 galaxy redshift survey , we study the relationship between galaxy color and environment at . we find that the fraction of galaxies on the red sequence depends strongly on local environment out to , being larger in regions of greater galaxy density . at all epochs probed , we also find a small population of red , morphologically early type galaxies residing in regions of low measured overdensity . the observed correlations between the red fraction and local overdensity are highly significant , with the trend at detected at a greater than level . over the entire redshift regime studied , we find that the color density relation evolves continuously , with red galaxies more strongly favoring overdense regions at low relative to their red sequence counterparts at high redshift . at , the red fraction only weakly correlates with overdensity , implying that any color dependence to the clustering of galaxies at that epoch must be small . our findings add weight to existing evidence that the build up of galaxies on the red sequence has occurred preferentially in overdense environments ( i.e. , galaxy groups ) at . furthermore , we identify the epoch at which typical galaxies began quenching and moved onto the red sequence in significant number . the strength of the observed evolutionary trends at suggests that the correlations observed locally , such as the morphology density and color density relations , are the result of environment driven mechanisms ( i.e. , `` nurture '' ) and do not appear to have been imprinted ( by `` nature '' ) upon the galaxy population during their epoch of formation .

1109.2671

i

one of the fundamental assumptions underpinning modern theories of galaxy formation is that galaxies form and evolve in massive virialised haloes of dark matter @xcite . characterising the properties of these haloes is an important problem , both theoretically and observationally , and its study has been one of the main objectives of cosmological @xmath0-body simulations over the last two decades . the majority of these simulations have modeled halo formation and evolution in a purely cold dark matter ( cdm ) universe ( cf . * ? ? ? * ) , with the focus primarily on their equilibrium structure ( cf . various studies have revealed that cdm haloes in dynamical equilibrium are triaxial structures ( e.g. * ? ? ? * ) supported by velocity dispersion rather than rotation ( e.g. * ? ? ? * ) , with mass profiles that are divergent down to the smallest resolvable radius ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) and an abundance of substructure ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? the qualification that a halo is in dynamical equilibrium is a particularly important one when seeking to characterise the structure and kinematics of simulated haloes in cosmological simulations . previous studies have shown that dynamically unrelaxed haloes tend to have lower central densities ( see , for example , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) and higher velocity dispersions ( see , for example , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) than their dynamically relaxed counterparts . this means that a dynamically unrelaxed halo is likely to have a measurably lower concentration @xmath8 and higher spin parameter @xmath9 than its dynamically relaxed counterpart ( see , for example , * ? ? ? * ; * ? ? ? * ) , and so care must be taken to avoid contaminating halo samples with dynamically unrelaxed systems when measuring , for example , spin distributions ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) and the correlation of halo mass and concentration @xmath10 ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? yet haloes do not exist in isolation , and the degree to which they are dynamically relaxed or unrelaxed bears the imprint of both their environment and their recent mass assembly and merging history . as previous studies have shown , dynamically unrelaxed haloes tend to have suffered one or more recent significant mergers ( e.g. * ? ? ? * ; * ? ? ? for this reason , it is common practice to use dynamical state and recent merging history interchangeably , with the understanding implicit that unrelaxed haloes are ones that have suffered one or more recent major mergers . however , it is important to establish this practice on a more quantitative footing and to assess how well a halo s dynamical state and its recent mass assembly history correlate . this is because of the need to identify robustly haloes that are in dynamical equilibrium or indeed disequilibrium in cosmological simulations for further discussion . ] . the goal of this paper is to quantify this relationship using a statistical sample of haloes drawn from cosmological @xmath0-body simulations of the cdm model . the cdm model is the ideal testbed for this study because of the fundamental role merging plays in halo mass assembly ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and because we expect massive haloes , which on average form later than their less massive counterparts , to have more violent recent merging histories . such an undertaking has practical implications . for example , if we want to robustly characterise the predicted variation of , say , concentration @xmath8 with virial mass @xmath4 on galaxy group and cluster mass scales ( @xmath11 ) , then it is essential that we can identify relaxed systems in a robust fashion . should we use mass assembly histories directly and select only haloes that have quiescent recent merging histories , or are commonly used measures that estimate dynamical state based on material within the halo s virial radius @xmath12 adequate ? this is particularly important for comparison with observations that provide crucial tests of the theory , such as the analysis the @xmath13 relation for groups and clusters drawn from the sloan digital sky survey by @xcite . in this paper , we examine how a halo s mass assembly history and dynamical state varies with its virial mass @xmath4 and its formation redshift , and adopt simple measures to characterise a halo s recent mass assembly and merging history namely , the fraction of mass assembled ( @xmath14 ) ; the rate of change of mass with redshift @xmath15 ; and the most significant merger @xmath16 . we compare these with two measures of the halo s dynamical state the virial ratio @xmath17 where @xmath18 and @xmath19 are the kinetic and gravitational potential energies of halo material ( cf . * ? ? ? * ; * ? ? ? * ) , and the centre - of - mass offset @xmath20 where @xmath21 and @xmath22 are the centres of density and mass of halo material and @xmath12 is the halo s virial radius ( cf . * ? ? ? * ; * ? ? ? * ; * ? ? ? previous studies have shown that both @xmath1 and @xmath2 increase in the aftermath of a major merger ( e.g. * ? ? ? * ; * ? ? ? * ) , and we will clarify precisely how they relate to a halo s mass assembly and merging activity in general . we note that our work develops earlier ideas presented in @xcite , in which we investigated the relationship between halo mass @xmath4 and spin @xmath9 , and it complements that of @xcite , who address related but distinct issues in their critique of the application of the virial theorem ( cf . [ ssec : virial_theorem ] ) to simulated high redshift dark matter haloes . + the layout of the paper is as follows . in [ sec : sims ] , we describe our approach to making initial conditions ; finding and analysing dark matter haloes in evolved outputs ; constructing merger trees of our dark matter haloes ; and our criteria for defining our halo sample . in [ sec : hierarchical ] , we examine the relationship between a halo s virial mass @xmath4 , its formation time @xmath3 and measures of its mass accretion and merging history . in [ sec : equilibrium ] , we present commonly used measures for assessing the dynamical state of a dark matter halo the virial ratio @xmath23 ( cf . [ ssec : virial_theorem ] ) and the centre - of - mass offset @xmath24 ( cf . [ ssec : centre_of_mass_offset ] ) and investigate how these measures correlate with @xmath4 and @xmath3 . in [ sec : linking_mass_assembly_and_dynamical_state ] we combine the insights from the previous two sections and show how a halo s dynamical state depends on its recent mass accretion and merging history . finally , we summarise our results in [ sec : summary ] and comment on the implications of our findings for both observational studies and galaxy formation modeling .

finally , we assess our results in the context of previous studies , and consider their observational implications . [ firstpage ] methods :-body simulations galaxies : formation galaxies : haloes cosmology : theory dark matter large - scale structure of universe

using a statistical sample of dark matter haloes drawn from a suite of cosmological-body simulations of the cold dark matter ( cdm ) model , we quantify the impact of a simulated halo s mass accretion and merging history on two commonly used measures of its dynamical state , the virial ratio and the centre of mass offset . quantifying this relationship is important because the degree to which a halo is dynamically equilibrated will influence the reliability with which we can measure characteristic equilibrium properties of the structure and kinematics of a population of haloes . we begin by verifying that a halo s formation redshift correlates with its virial mass and we show that the fraction of its recently accreted mass and the likelihood of it having experienced a recent major merger increases with increasing and decreasing . we then show that both and increase with increasing and decreasing , which implies that massive recently formed haloes are more likely to be dynamically unrelaxed than their less massive and older counterparts . our analysis shows that both and are good indicators of a halo s dynamical state , showing strong positive correlations with recent mass accretion and merging activity , but we argue that provides a more robust and better defined measure of dynamical state for use in cosmological-body simulations at . we find that is sufficient to pick out dynamically relaxed haloes at=0 . finally , we assess our results in the context of previous studies , and consider their observational implications . [ firstpage ] methods :-body simulations galaxies : formation galaxies : haloes cosmology : theory dark matter large - scale structure of universe

1109.2671

i

the aim of this paper has been to quantify the impact of a dark matter halo s mass accretion and merging history on two measures of dynamical state that are commonly used in cosmological @xmath0-body simulations , namely the virial ratio @xmath23 ( cf . * ? ? ? * ) and the centre - of - mass offset @xmath272 ( cf . * ? ? ? * ; * ? ? ? * ; * ? ? ? the virial ratio @xmath1 derives from the virial theorem and and the expectation is that @xmath185 for dynamically equilibrated haloes . the centre - of - mass offset @xmath2 can be regarded as a substructure statistic @xcite that provides a convenient measure of how strongly a halo deviates from smoothness and spherical symmetry . we expect a halo s dynamical state and its mass assembly history to correlate closely . understanding how is important because the degree to which a halo is dynamically equilibrated affects the reliability with which we can measure characteristic properties of its structure , such as the concentration parameter @xmath8 ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and kinematics , such as the spin parameter @xmath9 ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? for this reason , it is desirable to establish quantitatively how well they correlate and to assess how @xmath1 and @xmath2 can help us to characterise how quiescent or violent a halo s recent mass assembly history has been . our key results are that @xmath1 and @xmath2 show strong positive correlations with each other ( cf . figure [ fig : deltar_vs_eta ] ) as @xmath1 increases for a halo , so too does @xmath2 and that both are useful indicators of a halo s mass recent mass accretion and merging history . for example , @xmath1 and @xmath2 correlate strongly with @xmath16 , which measures the significance of a halo s recent merging activity ; haloes with @xmath273 ( cf . figure [ fig : virial_ratio_versus_deltamax ] ) and @xmath6 ( cf . figure [ fig : deltar_vs_mah ] ) will have quiescent recent mass assembly histories they are unlikely to have suffered mergers with mass ratios greater than 1:10 over the last few dynamical times . in contrast , interpreting the corrected virial ratio @xmath192=@xmath274 , where @xmath210 is the surface pressure energy , is problematic ( at least insofar as we have implemented it here , which follows the prescription of @xcite and has been applied in @xcite and @xcite ) . in principle , @xmath192 should account for the approximation that is made when we define a halo to be a spherical overdensity of @xmath57 times the critical density at a particular redshift . as we noted in [ sec : sims ] , haloes are more complex structures than this simple working definition gives them credit for , and by defining the halo s extent by the virial radius @xmath12 the likelihood is that material that belongs to the halo will be neglected . by correcting the virial ratio @xmath1 for what is effectively a truncation of the true halo , the corrected virial ratio @xmath192 takes account of the `` missing '' kinetic energy . however , our results imply that the correction itself ( the surface pressure energy @xmath181 ) is sensitive to a halo s merging history , and that it increases with increasing @xmath16 ( cf . figure [ fig : virial_ratio_versus_deltamax ] ) . for this reason we would caution against the use of @xmath192 to identify dynamically relaxed haloes , at least in the form that is currently used . interestingly , we find that systems with violent recent mass assembly histories ( most significant merger with a mass ratio @xmath275 between @xmath276 ) have values of @xmath1 and @xmath2 ( as measured at @xmath7=0 ) that peak at @xmath277 , which corresponds to a timescale of @xmath263 ( cf . figure [ fig : time_dep_dynstate ] ) . this is consistent with the earlier analysis of @xcite , who found that the velocity dispersion @xmath265 of material within the virial radius which is linked to the virial ratio @xmath1 peaks on first closest approach of the merging sub - halo with the centre of the more massive host halo . this should occur on a timescale of @xmath266 , after which @xmath265 and @xmath1 should dampen away . similar arguments can be made for @xmath2 . we note that these arguments can be made in a statistical sense , but if we look at the merging histories of individual haloes , the behaviour of @xmath1 and @xmath2 is much more complex , and as we demonstrate a simple timescale for their response to a major merger is difficult to define ( cf . figure [ fig : dynstate_merge_tree ] ) . we shall return to this topic in future work . + what is the significance of these results ? structure formation proceeds hierarchically in the cdm model and so we expect to find correlations between virial mass @xmath4 and formation redshift @xmath3 ( cf . figure [ fig : mass_versus_zform ] ) , which in turn result in positive correlations between @xmath4/@xmath3 and @xmath1/@xmath2 . ( cf . figures [ fig : virial_ratio_measures ] and [ fig : deltar_measures ] ) . this means that more massive haloes and those that formed more recently are also those that are least dynamically equilibrated , a fact that we should be mindful of when characterising the halo mass dependence of halo properties that are sensitive to dynamical state ( e.g. @xmath8 and @xmath9 ) . it s worth noting that the correlation between @xmath4 and @xmath1 is stronger than the correlation between @xmath4 and @xmath2 ; the median @xmath1 rises sharply with @xmath4 and there is no overlap between the width of the distributions of @xmath1 is the lowest and highest mass bins . in contrast , the median @xmath2 in the highest mass bin lies in the high-@xmath2 tail of the lowest mass bin . this is interesting because @xmath1 as it is usually calculated depends on @xmath19 , which is sensitive to the precise boundary of the halo . correcting for the surface pressure term does not appear to help , as we point out indeed , the surface pressure term itself correlates with merging activity . this points towards an ambiguity in the use of @xmath1 as we note , it rarely if ever satisfies @xmath1=1 . we discuss this point in a forthcoming paper , but we note that even in ideal situations , what one computes for @xmath1 depends on @xmath12 ( cf . * ; * ? ? ? * ) and so applying a flat cut based on a threshold in @xmath1 alone risks omitting massive haloes that might otherwise be considered dynamically equilibrated . for this reason we advocate the use of @xmath2 in cosmological @xmath0-body simulations as a more robust measure of a halo s dynamical state ; its calculation is computationally inexpensive , it is well defined as a quantity to measure , and its interpretation is both clear and straightforward . we find that @xmath278 , which corresponds to a @xmath279 , should be sufficient to pick out the most dynamically relaxed haloes in a simulation volume at @xmath7=0 . + although our focus has been fixed firmly on haloes in cosmological simulations , we note that our results have observational implications . whether or not an observed system for example , a galaxy cluster is in dynamical equilibrium will affect estimates of its dynamical mass if we assume a luminous tracer population that is in dynamical equilibrium ( e.g. * ? ? ? similarly , studies that seek to reconstruct a galaxy cluster s recent merging history tend to use signatures of disequilibrium ( e.g. * ? ? ? the most obvious measure of disequilibrium is the centre of mass offset @xmath2 , or its projected variant . although a more careful study in which we mock observe our haloes ( and a seeded galaxy population ) is needed , our results suggest that @xmath2 could be used to infer the redshift of the last major merger ( cf . figures [ fig : deltar_vs_mah ] and figure [ fig : deltar_measures ] , although care must be taken as figure [ fig : dynstate_merge_tree ] reveals ) . observationally , this would require measurement of , for example , projected displacements between gas and dark matter from gravitational lensing and x - ray studies . we note that @xcite have already tested this idea using idealised hydrodynamical simulations of mergers between galaxy clusters and found that the centroid offset between x - ray and projected mass maps captures the dynamical state of galaxy clusters well , but it is interesting to extend this idea using cosmological hydrodynamical simulations of galaxy groups and clusters . this will form the basis of future work .

using a statistical sample of dark matter haloes drawn from a suite of cosmological-body simulations of the cold dark matter ( cdm ) model , we quantify the impact of a simulated halo s mass accretion and merging history on two commonly used measures of its dynamical state , the virial ratio and the centre of mass offset . quantifying this relationship is important because the degree to which a halo is dynamically equilibrated will influence the reliability with which we can measure characteristic equilibrium properties of the structure and kinematics of a population of haloes . our analysis shows that both and are good indicators of a halo s dynamical state , showing strong positive correlations with recent mass accretion and merging activity , but we argue that provides a more robust and better defined measure of dynamical state for use in cosmological-body simulations at . we find that is sufficient to pick out dynamically relaxed haloes at=0 .

using a statistical sample of dark matter haloes drawn from a suite of cosmological-body simulations of the cold dark matter ( cdm ) model , we quantify the impact of a simulated halo s mass accretion and merging history on two commonly used measures of its dynamical state , the virial ratio and the centre of mass offset . quantifying this relationship is important because the degree to which a halo is dynamically equilibrated will influence the reliability with which we can measure characteristic equilibrium properties of the structure and kinematics of a population of haloes . we begin by verifying that a halo s formation redshift correlates with its virial mass and we show that the fraction of its recently accreted mass and the likelihood of it having experienced a recent major merger increases with increasing and decreasing . we then show that both and increase with increasing and decreasing , which implies that massive recently formed haloes are more likely to be dynamically unrelaxed than their less massive and older counterparts . our analysis shows that both and are good indicators of a halo s dynamical state , showing strong positive correlations with recent mass accretion and merging activity , but we argue that provides a more robust and better defined measure of dynamical state for use in cosmological-body simulations at . we find that is sufficient to pick out dynamically relaxed haloes at=0 . finally , we assess our results in the context of previous studies , and consider their observational implications . [ firstpage ] methods :-body simulations galaxies : formation galaxies : haloes cosmology : theory dark matter large - scale structure of universe

1205.3332

c

a detailed study of the numerical impact of kinematic power corrections goes beyond the tasks of this paper . this study has to be done at the level of cross sections , taking into account finite@xmath0 and target mass effects to kinematic ( e.g. phase space ) factors @xcite and including the interference with the bethe heitler process . since the corrections to helicity amplitudes are calculated in this work for the simplified model case of a scalar target only , such a complete analysis is probably not warranted at this stage . in this section we present numerical estimates for the kinematic power corrections to the imaginary part of the helicity - conserving dvcs amplitude , eq . ( [ ima++ ] ) , which gives the largest contribution to the cross section . to this end we use a model for the gpd @xmath359 corresponding to the @xmath360 ansatz from ref . it is based on the so - called single dd description which is defined by the `` gauge '' fixing condition @xmath361 imposed on the dds @xmath188 and @xmath189 in eq . ( [ dd1 ] ) , see ref . @xcite for more details . it is assumed that the dd @xmath188 takes a factorized form @xmath362 here @xmath363 is a ( quark ) parton distribution which we take as @xmath364 and @xmath365 the function @xmath366 satisfies the normalization condition @xmath367 . note that we use @xmath368 which is a standard approximation for the proton target , because this is case that is interesting phenomenologically . for the pion one expects @xmath369 . we assume that the dd ( [ singledd ] ) depends on @xmath0 through the corresponding dependence of the regge trajectory @xmath370 and in addition involves a multiplicative factor @xmath371 ( see e.g. ref . @xcite ) . the imaginary part of the amplitude ( [ ima++ ] ) involves @xmath183 in the region @xmath358 only . in this region one obtains a compact expression @xcite @xmath372 e^{bt},\end{aligned}\ ] ] where @xmath373 and @xmath374 . we consider the following ratios : @xmath375 where @xmath376 is the leading - order leading - twist result . note that the @xmath371 factor in the gpd cancels between the numerator and the denominator so that it is irrelevant for our purposes . the ratios @xmath377 still depend on @xmath0 , however , because of the non - factorizable @xmath0-dependence of the gpd through the regge trajectory . in fig . [ figure1 ] we show @xmath378 as a function of @xmath51 in the interval @xmath379 for @xmath380 ( which also corresponds to a factorizable @xmath0 dependence of the gpd ) and for the values @xmath381 and @xmath382 gev@xmath12 . the same is shown in fig . [ figure2 ] for the coefficient @xmath383 . [ cc][cc]@xmath378 [ cc][cc][0.9]@xmath384 [ cc][cc][0.9]@xmath385 [ cc][cc][0.9]@xmath386 [ cc][cc][0.9]@xmath387 [ cc][cc][0.9]@xmath388 [ cc][cc]@xmath51 in the range @xmath389 for different values of @xmath0 . the curves correspond to @xmath390.,title="fig:",width=321 ] [ cc][cc]@xmath383 [ bc][tc][0.9]@xmath384 [ cc][cc][0.9]@xmath385 [ cc][cc][0.9]@xmath386 [ cc][cc][0.9]@xmath387 [ cc][cc][0.9]@xmath388 [ cc][cc]@xmath51 in the range @xmath389 for different values of @xmath0 . the curves correspond to @xmath390.,title="fig:",width=321 ] one sees that in the whole kinematic range @xmath391 so that the target mass correction to the imaginary part of the amplitude is almost negligible . the finite-@xmath0 correction is , on the other hand , quite sizable . one has to have in mind that magnitude of the finite-@xmath0 correction depends on the definition of the skewedness parameter . using @xmath348 ( [ xib ] ) as a kinematic variable in the leading - order expression results in a redefinition of the kinematic correction , which acquires a stronger @xmath51 dependence but does not become smaller . for the particular case of the minimal allowed value of the momentum transfer @xmath392 we find @xmath393 which holds with a good accuracy in a broad interval of @xmath51 and @xmath198 . to summarize , in this paper we have presented the first complete calculation of kinematic power corrections to the helicity amplitudes of deeply - virtual compton scattering to the twist - four accuracy for a study case of a ( pseudo)scalar target . our main result is that both finite@xmath0 , @xmath1 , and target mass , @xmath2 , twist - four kinematic power corrections turn out to be factorizable , at least to the leading order in the strong coupling . our numerical estimates using a certain simple model of the generalized parton distribution suggests that target mass contributions to helicity amplitudes are very small , but the finite@xmath0 effects , on the contrary , rather significant in all kinematic regions of interest . the similar calculation for the dvcs from a nucleon is in progress and the results will be published separately .

using the formalism developed in we carry out the first complete calculation of kinematic power corrections to the helicity amplitudes of deeply - virtual compton scattering to the twist - four accuracy for a study case of a ( pseudo)scalar target . our main result is that both finite , , and target mass , , twist - four kinematic power corrections turn out to be factorizable , at least to the leading order in the strong coupling . the structure of these corrections is discussed and a short model study of their numerical impact is presented

using the formalism developed in we carry out the first complete calculation of kinematic power corrections to the helicity amplitudes of deeply - virtual compton scattering to the twist - four accuracy for a study case of a ( pseudo)scalar target . our main result is that both finite , , and target mass , , twist - four kinematic power corrections turn out to be factorizable , at least to the leading order in the strong coupling . the structure of these corrections is discussed and a short model study of their numerical impact is presented

astro-ph0405525

m

the high photon rate during grb021206 introduces numerous accidental coincidences . their rate can be determined from fig . [ fig : dtplot ] . we use the accidental coincidences with @xmath59b@xmath21s @xmath60 @xmath61b@xmath21s ( so - called `` time shifted coincidences '' ) and interpolate them around @xmath62 ( see fig . [ fig : dtplot ] ) . the time differences @xmath63 used to estimate the number of accidentals should on the one hand be higher than the longest readout time of the events , i.e. , longer than a few b@xmath21s . on the other hand , it should be smaller than the shortest time scale of variability in the grb light curve . the total number of coincidences ( @xmath64 ) as well as the number of accidental coincidences ( @xmath65 ) can be determined for any time interval , leading to time dependent functions @xmath66 and @xmath67 . the number @xmath67 is proportional to the square of the total count rate , and therefore shows a strong time variation . some of the real coincidences observed during the grb are induced by various background components . we call this number @xmath68 . it could show a rotation angle dependent time variation and can be estimated by interpolation of the data before and after the grb : @xmath69 where @xmath70 denotes a time bin before and @xmath71 a time bin after the grb , with equal rotation angle of rhessi as at time @xmath72 . the remaining number of coincidences , namely @xmath73 are called `` compton scattering candidates '' and includes the real compton scattering events . a closer look at all the close detector pairs that fulfill the energy cut ( [ e0_cut ] ) , the kinematical cut ( [ e_special ] ) , and and the @xmath52-cut ( [ dt_cut ] ) shows that many of them are part of a multiple coincidence ( 3 or more detector segments firing at the same time ) . it often happens that a photon undergoes a forward compton scattering in a front segment before being compton scattered in the rear segment into a neighboring detector . in other cases , several detectors observe a signal . this is relatively more often the case before and after the grb . multiple coincidences can be caused by nuclear reactions , bremsstrahlung , or pair / photon cascades originating from the passage of high energy cosmic rays through the spacecraft . none of these multiple coincidences contribute to a polarization signal . we therefore do not accept them . we identify multiple coincidences by looking at all accepted coincidences . let @xmath74 be the time of a coincidence , more exactly , the earlier time of the two events involved . two coincidences are members of a multiple coincidence if @xmath75b@xmath21s . all coincidences that fulfill this condition are rejected ( so - called `` no - multiples cut '' ) . however , members of multiple coincidences are also members of time shifted coincidences used to determine the number of accidental coincidences . in order to obtain the correct number of accidental coincidences , we clean the initial event list from members of multiple coincidences . we then search again for real and time shifted coincidences . in order to search for a polarization signal we first note that all close detector pairs can naturally be grouped into four scattering directions ( see fig . [ fig : dets ] ) , each separated by @xmath76 . according to a rhessi - fixed coordinate system , we call these directions the @xmath77 direction , the @xmath76 direction , the @xmath18 direction , and the @xmath78 direction . the true pair angles , measured from detector center to detector center , vary slightly . the mean deviation from the nominal value is @xmath79 with a maximum of @xmath80 . this is much less then the width of scattering angles accepted by a detector pair , which is of the order @xmath81 . assuming that polarized photons at a time @xmath82 were scattered preferentially in the @xmath78 direction , then , one eighth of a satellite rotation later , they would be scattered preferentially in the @xmath18-direction . after another rotation by @xmath76 , they would be scattered in the @xmath76-direction , and so on . we determine the number of compton scattering candidates for the 4 scattering directions and call them @xmath83 , with @xmath84 \ { 0 , 45 , 90 , 135 } . for a grb with a strongly varying light curve , such as grb021206 , the @xmath85 are strongly correlated with the light curve . let @xmath86 be the normalized coincidence light curves , @xmath87 where the sums are over the entire time interval used for polarization analysis ( typically one or more full rotations , e.g. eq . ( [ t0_cut ] ) ) . we can then define the following asymmetries : @xmath88 for an _ unpolarized _ grb , we make the plausible assumption that the @xmath85 are approximately proportional to each other , i.e. we assume that there exists a time dependent function @xmath89 and factors @xmath90 such that we can write @xmath91 . the factors @xmath90 take into account the efficiencies of the four scattering directions , while @xmath89 is closely related to the light curve of the grb . in that case , the asymmetries ( [ eq : asym ] ) are always zero ( within statistical errors ) . in the case of a _ polarized _ grb , an additional sinusoidal time dependence is introduced : @xmath92 the observation of a non - zero modulation amplitude @xmath93 would be an indication of a grb polarization . simulations show that @xmath93 is of order @xmath94 for a @xmath24% polarized grb . the expected periodicity of the modulation is @xmath95 . the absolute phase @xmath96 is unknown , and the relative phase shifts are fixed at @xmath97 , @xmath98 , @xmath99 , and @xmath100 . from eqs . ( [ eq : norm_cs_ltc])-([eq : ltc_mod ] ) , we obtain @xmath101 the definition of the asymmetries @xmath102 and @xmath103 uses only data . by making a fit , the best values for the observable modulation amplitude @xmath93 and the phase @xmath96 can be determined . in order to obtain the real polarization degree of a grb , @xmath93 should be compared with @xmath104 obtained from the simulation of a 100% polarized grb , analyzed the same way . the standard rhessi software provides energy deconvolution routines , using simulated response functions , but only for solar photons . therefore we have rerun the simulation code , but for off - axis photons . all essential parts of the satellite are built into a mass model using the geant3.21 particle tracking code @xcite . the model provides an exact description of the ge spectrometer and its adjacent elements , e.g. graded - z shielding , detector electronics and cryo - cooler . other components and structures that are positioned at larger distances from the ge detectors , maintain their mass and composition while some approximations were made for their geometry ( e.g. simplified shapes ) and internal arrangement ( e.g. using material of mean density and z - number ) . the total mass of the spacecraft is 291@xmath13 kg , including 131@xmath13 kg of scientific payload . especially for photons that arrive at an angle of less than @xmath105 with respect to the sun s direction ( as was the case for grb021206 ) , the mass distribution on the equipment deck affects the light curves and spectra . the most relevant components responsible for such effects are the solid state recorder at @xmath78 above ( i.e. sun side of ) the equipment deck , the cryo - cooler power converter at @xmath106 ( above the equipment deck ) , the idpu at @xmath76 ( below the equipment deck ) , and the battery cells at @xmath107 ( below the equipment deck ) , see fig . [ fig : hessi ] ( or @xcite , fig.10 ) . they all weigh of the order 10@xmath13 kg . using the mass model of the spacecraft and the spectrometer , the rhessi response function can be generated . for this purpose the spacecraft model in the geant code is illuminated by a parallel flux of gamma rays with a predefined energy spectrum and direction . all primary particles , like scattered photons , as well as secondary particles , like recoil electrons , are traced . finally , the energy deposition in each germanium detector segment is stored . photon polarization is not included in geant3 . we wrote specific routines to fully include photon polarization , using the same formalism as in the geant4 extension packet for low energy compton scattering @xcite . the momentum vector of the scattered photon and its polarization direction were generated in accordance with the klein - nishina formula taking into account its initial polarization . in order to analyze the simulated data with the same program as the real data , the output of the geant - code was prepared to look like real data . the effects of the readout electronics were simulated by delaying the front segment events by 1.6@xmath108s and the events in detector 2 by 2.6@xmath108s ( see end of section [ sec : coinc ] ) . next , the time was converted into integers ( in units of b@xmath21s ) and the energy was converted into channels . the rear segment decimation was simulated by accepting rear segment events with energy channel @xmath109 only if @xmath110 . we also added events as cosmic induced background . in order to obtain good statistics , we simulated the grb lasting over many rotations ( typically 10 to 40 ) . a very high photon rate per rotation would introduce a very high accidental coincidence rate .

this was challenged by a subsequent reanalysis . we perform simulations to obtain the instrument s polarimetric sensitivity , and these simulations include photon polarization . for grb021206 , we formally find a linear polarization degree of% , concluding that the data quality is insufficient to constrain the polarization degree in this case .

using the rhessi satellite as a compton polarimeter , a recent study claimed that the prompt emission of grb021206 was almost fully linearly polarized . this was challenged by a subsequent reanalysis . we present an novel approach , applying our method to the same data . we identify compton scattering candidates by carefully filtering events in energy , time , and scattering geometry . our polarization search is based on time dependent scattering rates in perpendicular directions , thus optimally excluding systematic errors . we perform simulations to obtain the instrument s polarimetric sensitivity , and these simulations include photon polarization . for grb021206 , we formally find a linear polarization degree of% , concluding that the data quality is insufficient to constrain the polarization degree in this case . we further applied our analysis to grb030519b and found again a null result .

astro-ph0512474

c

in the light of the new metallicity estimates outlined in the previous section , we discuss three possible ucd formation channels : 1 . unusually bright gcs . nuclei of de , ns . 3 . young massive star clusters created in violent star - forming events . + 1 . bright gcs : the brightest fornax ucd ( ucd 3 ) can not be defined as a gc , given its very high luminosity ( @xmath48 -13.4 mag ) and large half - light radius @xmath11 of 30 pc ( drinkwater et al . @xcite ) . surface brightness profile fitting even revealed a second exponential component of @xmath49 60 pc ( drinkwater et al . indeed , ucd 3 is the only ucd that is marginally resolved on ground - based images ( see hilker et al . @xcite and mieske et al . furthermore , fornax ucds are more extended around the cluster center , more numerous than expected from the extrapolation of a gaussian gclf and slightly offset in radial velocity with respect to the gcs ( mieske et al . the significances of these differences are all of the order 2@xmath13 . the strongest distinguishing feature is the metallicity difference between ucds ( @xmath6 ) and gcs ( @xmath10 mag ) found in the present paper , significant at 3.7@xmath13 . note , however , that this only implies that fornax ucds do not belong to the _ metal - poor _ , i.e. blue population of gcs . the mean metallicity of the fornax ucds is close to ( yet slightly lower than ) the typical value found for the metal - rich , red peak of the gc distribution ( e.g. peng et al . @xcite , kissler - patig et al . @xcite ) of about -0.6 to -0.3 dex . also their mean color of @xmath50 @xmath8 0.02 is identical to the red peak of ngc 1399 s bimodal gc color distribution ( gebhardt & kissler - patig ( @xcite ) . that is : the question `` can one explain ( some ) ucds as bright gcs ? '' must in the fornax cluster case be specified as : `` can the red bulge gcs extend to much higher masses / luminosities than the blue gcs ? '' . a possibility is that the most massive metal - rich star clusters preferentially form by the merging of several single , already massive clusters in the course of violent gas - rich merger events ( fellhauer & kroupa @xcite ) . this is an attractive scenario if one assumes that indeed galaxy - galaxy mergers were the main creation channel for the entire metal - rich gc bulge population of gcs ( e.g. rhode & zepf @xcite , li et al . this is opposed to the idea that both metal - poor and metal - rich gcs formed in single , monolithic collapse - like , subsequent episodes ( e.g. forbes et al . @xcite , harris & pudritz @xcite ) . in the latter case one might expect a less violent , more homogeneous star formation , not necessarily leading to the creation of super - massive gcs . kravtsov & gnedin @xcite find in their simulations on gcs formation that the maximum globular cluster mass in a given region strongly correlates with the local average star formation rate . on the observational side , larsen @xcite correspondingly found that the maximum mass of young massive clusters in spiral galaxies scales with local star formation rate . this implies that the most massive gcs are created in the most violent merger events . kravtsov & gnedin also show that the mass of the most massive gc built in a dm halo correlates with this dm halo s mass , although with a large dispersion , due to the varying star formation conditions within the halo . according to formula ( 8) of their paper , gcs as massive as the ucds ( 1 - 5@xmath2010@xmath51m@xmath5 ) must have progenitor haloes of @xmath3 5@xmath2010@xmath52m@xmath5 . this is only a few percent of ngc 1399 s dm halo mass ( @xmath53 , see richtler et al . therefore one may at face value not even require to merge _ several _ massive gcs to end up with _ one single _ . however , a strong argument against the identity ucds = bright single gcs comes from a size comparison : the five brightest fornax ucds have king half - light radii @xmath11 between 15 and 30 pc ( drinkwater et al . the typical @xmath11 of globular clusters is only @xmath543 pc ( jordn et al . @xcite ) over several orders of magnitude in mass , and even the most massive gcs are not expected to exceed radii of about 5 - 7 pc ( kravtsov & gnedin @xcite ) . the size distribution of ucds vs. gcs deserves some more detailed investigation : in fig . [ size ] we plot @xmath11 vs. luminosity for those compact objects that were imaged in the acs fornax cluster survey ( jordn @xcite and jordn et al . in preparation ) . all of them are imaged in two acs pointings . we include the data points for the five brightest ucds from drinkwater et al . @xcite and also plot the data points for all objects detected in the two acs pointings . note that the bulk of sources with @xmath55 mag are gcs , having the typical @xmath11 values around 3 pc ( jordn et al . @xcite , mclaughlin @xcite ) . the fact that they have a luminosity independent mean size is a physical effect , and not due to the resolution limit of the camera . at the distance of fornax , 3 pc subtend 0.03@xmath21 , or 0.6 wfc pixels . as shown in jordn et al . @xcite , the resolution limit regarding @xmath11 measurements is 0.25 wfc pixels ( @xmath31pc at virgo / fornax ) , which is substantially lower ( see also fig . [ size ] ) . it is very remarkable that the luminosity of the metallicity break corresponding to @xmath2 mag coincides exactly with the luminosity brighter than which there is a clear up - turn in the size - luminosity distribution of fornax compact objects . brighter than @xmath12 mag one enters the regime where size scales with mass / luminosity , while fainter than that , size is independent of mass / luminosity . this strengthens the separation occurring at @xmath12 mag between a ) metal - rich objects at brighter magnitudes whose size scales with luminosity the ucds and b ) more metal - poor objects at fainter luminosities with luminosity independent sizes the gcs . this luminosity limit corresponds to about 3@xmath56 , assuming an average m / l ratio of 3 ( drinkwater et al . note that @xmath57 centauri , the largest star cluster of the milky way , has a mass of about this value ( meylan & mayor @xcite , pryor & meylan @xcite ) . furthermore , this is also the mass which hasegan et al . @xcite propose to mark the transition between gcs and ucds . a possible clue to the up - turn in the size - luminosity distribution are the findings of fellhauer & kroupa @xcite and bekki et al . @xcite : super - clusters consisting of several single clusters that merged together will be significantly more extended than the average progenitor cluster . that is , they will deviate towards larger sizes from the constant mass - size relation of globular clusters . the corresponding effect in the fundamental plane ( drinkwater et al . @xcite , kissler - patig et al . @xcite , bastian et al . @xcite , maraston et al . @xcite ) has been found for the brightest and most massive young massive clusters and ucds , which do not follow the steep m-@xmath13 relation defined by gcs , but rather the extrapolation of the faber - jackson relation . this supports the hypothesis that ucds are successors of merged super - clusters , as opposed to being single super - massive gcs . the possibility of young massive clusters in the present universe as examples of `` early '' ucds will be discussed further in point 3 . nuclei : ucds in fornax are significantly more metal - rich and redder than nuclei of existing de , ns , with no indications for a significant age difference ( see previous section ) . if ucds are stripped nuclei , they were stripped of their gas and parts of their dark matter halo a long time ago ( see bekki et al . consequently they have had no opportunity of self - enrichment and star formation since the time of their stripping . in comparison to still existing nuclei that are embedded in a deep potential well with the principal possibility of further star formation events , one would therefore expect equal or lower metallicities and higher integrated ages for `` naked '' nuclei ( see also sect . [ intro ] , mieske et al . @xcite and jones et al . we find significantly higher metallicities , but can not tightly constrain the age difference . the large metallicity difference is not consistent with the stripping scenario as the major creation channel for ucds in fornax . we have outlined in sect . [ compnuclei ] that the metallicity difference between nuclei and ucds is slightly larger than predicted from their color difference of 0.10 to 0.15 mag . if one allows for age differences between ucds and nuclei to account for this `` deficit '' in color difference , one would require that ucds be younger than nuclei . this goes into the opposite direction of what would be expected in the stripping scenario . one conceivable way of explaining the metallicity difference between surviving `` embedded '' nuclei and ucds is that tidal stripping selects the most metal - rich de , ns . that is not pure speculation , since in some galaxy clusters , galaxy metallicities have been shown to increase towards the cluster center ( e.g. carter et al . @xcite for coma , ezawa et al . @xcite for awm 7 ) . this can lead to a selection bias because tidal stripping should affect only those de , ns that orbit close to the cluster center ( bekki et al . @xcite ) . however , the amplitude of the metallicity gradients found in the cited studies is only of the order of 0.2 - 0.3 dex over the entire radial cluster range . that is not sufficient to explain the difference of @xmath3 0.80 dex between ucds and nuclei found by us . furthermore , lotz et al . @xcite do not find any radial color gradient for fornax cluster dwarf elliptical galaxies , making a strong stripping selection bias unlikely . note that the ucds discovered in the virgo cluster exhibit slightly different properties , more consistent with the stripping scenario : the ucd candidates detected in the virgo cluster survey ( ct et al . @xcite ) based on their larger sizes than average gcs ( hasegan et al . @xcite ) are significantly bluer than the fornax ucds ( see also jones et al . @xcite ) . they are almost as blue as the blue peak of m87 s gc color distribution ( peng et al . @xcite ) and are consistent with the colors of virgo de , n nuclei ( ct et al . @xcite ) . in agreement with this finding , evstigneeva et al . @xcite report line index estimates for virgo ucds in which they are found to be old and metal _ poor_. for some of the virgo ucds , hasegan et al . @xcite report high m / l ratios between 6 and 9 , which in case of virial equilibrium requires some component of dark matter . those authors suggested a high m / l ratio as a bona - fide criterion to tell ucds from ordinary gcs . hasegan et al . @xcite find that the two ucd candidates with highest m / l ratios are the most metal - poor ones , strengthening the need for dark matter . in contrast , the fornax ucds have lower m / l ratios between between 2 and 4 ( drinkwater et al . @xcite ) and higher metallicities . this makes the scenario of ucds as successors of nuclei of dark matter dominated de , ns more likely for virgo than for fornax . the concluding remark we draw from this is : for the fornax ucds , the de , n stripping seems a less important formation channel , while for the virgo ucds the stripping scenario may be the preferred channel . young massive clusters ( ymcs ) : motivated by the difficulties of the stripping scenario to explain the fornax ucd metallicities , we discuss the hypothesis that ucds are successors of young massive clusters created in violent star - forming events . this hypothesis is closely related to the scenario of fellhauer & kroupa ( @xcite and @xcite ) that ucds may be merged super - clusters created in such mergers ( see also point 1 ) . one example for a possible future ucd is the ymc w3 in the star forming galaxy ngc 7252 ( maraston et al . @xcite ) with a mass of @xmath3 10@xmath58 m@xmath5 whose fundamental plane parameters place it in the region of ucds / m32 when passively aged several gyrs . fellhauer & kroupa @xcite show that w3 may have formed through the merging of several dozen massive single star clusters . bastian et al . @xcite and kissler - patig et al . @xcite find that also other ymcs populate the same fundamental plane region as the ucds . [ fe_v_nucl ] shows the location of w3 in the luminosity - metallicity diagram if aged passively to 10 and 13 gyrs , respectively . starting points are its present observed absolute magnitude @xmath5916.2 mag , an assumed age of 300 myr and assumed metallicities of z=0.4z@xmath60 and z=1.0z@xmath60 ( hilker et al . in preparation , maraston et al . w3 is located close to the regime of the brightest fornax cluster ucds , shifted slightly to higher metallicities . note that bastian et al . @xcite also found metallicities of z@xmath610.5z@xmath60 for several other young and massive star cluster complexes in the antenna galaxies ( ngc 4038/4039 ) . that is an indication that some of the fornax ucds may have been created in an early violent merger event similar to those occurring with ngc 7252 or the antennas , but in a lower metallicity environment . the very small number of ucds can be explained by the fact that only a small fraction of the cluster complexes observed today appears to be gravitationally bound ( e.g. fall et al . @xcite , bastian et al . that is , only very few of the complexes will survive over gyr time scales . fall et al . @xcite argue that while between 20% and 100% of all stars form in clusters , the fraction of surviving clusters over a hubble time is between 10@xmath62 and 10@xmath63 of the total stellar mass . for comparison , the total absolute brightness of all compact objects in fornax with @xmath6 mag is @xmath64 mag , about 6 mag or a factor of 250 fainter than ngc 1399 s absolute brightness of @xmath65 mag ( hilker et al . this is consistent with the fractional stellar mass range for surviving clusters as estimated by fall et al . and still leaves sufficient space for the main body of the fainter globular clusters . it is important to stress that in order to create a consistent link between ymcs and ucds in terms of metallicity , one would have to know the properties of an w3-like object created about 10 gyrs ago and then interpolate up to the present . star formation in the early universe was certainly not less intense than it is now , and mergers also happened more often than now . if the molecular clouds out of which early ymcs formed consisted of pre - processed material , one could have formed moderately metal - rich ymcs with fornax ucd metallicity , i.e. about 1/2 to 1/4 of the metallicities derived for present ymcs , relatively early in the universe . note that the cm trend amongst the fornax ucds / bright gcs ( see sect . [ cmrel ] ) may be explained with the ymc scenario : statistically , the more massive ymcs originate from more massive progenitor galaxies and more intense star - bursts ( see e.g. elmegreen et al . @xcite ) and might therefore also be more metal - enriched . + to finish the discussion , we consider in how far global differences between the fornax and virgo clusters are expected to influence the occurence of the two competing ucd formation channels . this may help to explain why properties of virgo ucds fit better the stripping scenario , while fornax ucds are more consistent with aged ymcs . the fornax cluster has a two times higher central galaxy density and a two times lower velocity dispersion than the virgo cluster ( drinkwater et al . @xcite , mieske et al . @xcite , richtler et al . @xcite , ferguson @xcite ) . since the galaxy merger rate in cluster environments has the approximate dependence @xmath66 ( makino & hut @xcite ) , one expects a much higher rate of galaxy mergers in fornax than in virgo . this qualitative difference should also hold at the time of the most violent galaxy mergers and hence ymc formation , even if both clusters were still in their early phase of evolution and had not yet settled into virial equilibrium . if the tidal stripping scenario and the fading of ymcs created in violent galaxy mergers are competing ucd formation channels , the probability of the ymc channel is therefore higher for fornax than for virgo . this fits to the observed properties of fornax and virgo ucds . to what extent is the stripping scenario influenced by the different cluster properties ? because of the higher mass of virgo and its correspondingly deeper potential well as compared to fornax , bekki et al . @xcite predict the number of ucds in virgo created by stripping de , ns to be about a factor of three higher than in fornax . given that the numbers of ucds in virgo and fornax ( jones et al . @xcite and drinkwater et al . @xcite ) do not differ by such a large factor , a plausible interpretation that fits to the observed ucd properties is that the population of fornax ucds is fueled by an additional formation channel . [ discussion ]

various formation channels for the puzzling ultra - compact dwarf galaxies ( ucds ) have been proposed in the last few years . it is noted that in contrast to that , the properties of virgo ucds are more consistent with the stripping scenario , suggesting that _ different _ ucd formation channels may dominate in either cluster .

various formation channels for the puzzling ultra - compact dwarf galaxies ( ucds ) have been proposed in the last few years . to better judge on some of the competing scenarios , we present spectroscopic [ fe / h ] estimates for a sample of 26 compact objects in the central region of the fornax cluster , covering the magnitude range of ucds and bright globular clusters ( or mag ) . we find a break in the metallicity distribution of compact objects at mag ( 3 m ) : for mag the mean metallicity is [ fe / h].62 0.05 dex , 0.56 0.15 dex higher than the value of.18 0.15 dex found for mag . this metallicity break is accompanied by a change in the size - luminosity relation for compact objects , as deduced from hst - imaging : for mag , scales with luminosity , while for mag , is almost luminosity - independent . in our study we therefore assume a limiting absolute magnitude of mag between ucds and globular clusters . the mean metallicity of five fornax de , n nuclei included in our study is about 0.8 dex lower than that of the ucds , a difference significant at the 4.5 level . this difference is marginally higher than expected from a comparison of their colors , indicating that ucds are younger than or at most coeval to de , n nuclei . because of the large metallicity discrepancy between ucds and nuclei we disfavor the hypothesis that most of the fornax ucds are the remnant nuclei of tidally stripped de , ns . our metallicity estimates for ucds are closer to but slightly below those derived for young massive clusters ( ymcs ) of comparable masses . we therefore favor a scenario where most ucds in fornax are successors of merged ymcs produced in the course of violent galaxy - galaxy mergers . it is noted that in contrast to that , the properties of virgo ucds are more consistent with the stripping scenario , suggesting that _ different _ ucd formation channels may dominate in either cluster .

astro-ph0512474

i

we have presented spectroscopic [ fe / h ] estimates for a sample of 26 compact objects in the central fornax cluster , spanning the luminosity range @xmath0 ( @xmath1 ) mag . our sample includes ucds at the bright end and is dominated by gcs at the faint end . we furthermore present [ fe / h ] measurements for the nuclear regions of five fornax de , ns . a. the mean metallicity of bright compact objects ( @xmath6 mag ) is [ fe / h]@xmath70.62 @xmath8 0.05 dex , which is 0.56 @xmath8 0.15 dex higher than the mean metallicity of @xmath91.18 @xmath8 0.15 dex for faint compact objects ( @xmath10 mag ) . the difference is significant at the 3.7@xmath13 level . this metallicity break at @xmath12 mag ( @xmath67 ) is accompanied by a change in the size - luminosity relation for compact objects , as deduced from acs - imaging : for @xmath6 mag , @xmath11 scales with luminosity , while for @xmath10 mag , @xmath11 is luminosity - independent and of typical value for gcs . due to these characteristic features in the metallicity and size distribution , we identify compact objects with @xmath6 mag as ucds and those with @xmath10 mag as gcs . the metallicity difference between ucds and gcs is consistent with their color difference in @xmath14 under the assumption of coeval populations . b. the mean metallicity of the five investigated de , n nuclear regions is [ fe / h]@xmath71.38 @xmath8 0.15 dex , which is 0.75 @xmath8 0.17 dex lower than that of the ucds , a difference significant at 4.5@xmath13 . from the balance of two counteracting observational biases , we expect the mean metallicity of the actual nuclei to be about 0.1 - 0.2 dex lower , increasing the disagreement with the ucds to at least 0.8 dex . the metallicity difference between ucds and nuclei is slightly higher but still marginally consistent with that expected from their color difference . this implies that ucds are coeval with or slightly younger than the nuclei . we find our metallicity estimates for ucds close to but slightly below those derived for young massive clusters ( ymcs ) . although the fornax ucds match the metallicity and color of the red , metal - rich peak of the gc distribution , they are unlikely to be single , super - massive gcs due to their larger average sizes . their sizes are more consistent with those predicted for merged super - clusters . \3 . we propose that most fornax ucds are successors of merged ymcs produced in earlier star formation bursts in the course of gas rich galaxy - galaxy mergers . in contrast , for the virgo cluster we suggest that the stripping scenario is the more important ucd formation channel . four facts favor this distinction of formation channels : a ) the virgo ucds are - in contrast to the fornax ucds - on average metal - poor and of comparable color to de , n nuclei . b ) some virgo ucds possess high m / l ratios that may require dark matter , while fornax ucds have lower m / l ratios . c ) the fornax cluster has a higher current galaxy merger rate than virgo , favoring the ymc scenario . d ) the virgo cluster has a higher mass and deeper potential well , favoring the tidal stripping scenario . + in the future , increasing the available sample of fornax compact objects by a factor of two to three may allow us to check whether there is a _ continuous trend _ in metallicity with luminosity , as suggested from the color distribution . this will give important clues on the detailled formation histories of the fornax ucds . furthermore , one must increase the baseline for environmental comparisons of ucd properties by surveying galaxy clusters with a broad variety of intrinsic properties such as merger history , total mass and density . we owe thanks to the staff at las campanas observatory for their assistance in carrying out the observations and gus oemler for making the cosmos package publicly available . we would like to thank the acsfcs team for granting use of the data shown in fig . [ size ] in advance of publication . we also thank pat ct for useful discussions . sm acknowledges support by dfg project hi 855/1 . li was supported by fondap `` center for astrophysics '' . bassino , l. p. , muzzio , j. c. , & rabolli , m. 1994 , apj , 431 , 634 bastian , n. , gieles , m. , efremov , y. n. , lamers , h.j.g.l.m . 2005a , a&a in press , astro - ph/0508110 bastian , n. , emsellem , e. , kissler - patig , m. , maraston , c. 2005b , a&a in press , astro - ph/0509249 bastian , n. , saglia , r. , goudfrooij , p. et al . 2005c , submitted to a&a bekki , k. , couch , w.j . , drinkwater , m.j . , shioya , y. , 2003 , mnras , 344 , 399 bekki , k. , couch , w.j . , drinkwater , m.j . , shioya , y. , 2004 , apjl , 610 , 13 brodie j.p . , huchra j.p . , 1991 , apj 379 , 157 bruzual , g. , charlot , s. 2003 , mnras , 344 , 1000 carter , d. , mobasher , b. , bridges , t. et al . 2002 , apj , 567 , 772 ct , p. , blakeslee , j. p. , ferrarese , l. et al . 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( vcs team ) 2005 , submitted to apj couture , j. , harris , w. e. , & allwright , j. w. b. 1990 , apjs , 73 , 671 de propris , r. , phillipps , s. , drinkwater , m. j. , gregg , m. d. , jones , j. b. , evstigneeva , e. , bekki , k. 2005 , apj , 623l , 105 dirsch , b. , richtler , t. , geisler , d. et al . 2003 , aj , 125 . , 1908 dirsch , b. , richtler , t. , geisler , d. et al . 2004 , aj , 127 , 2114 drinkwater m.j . , jones j.b . , gregg m.d . , phillipps s. , 2000 , pasa 17 , 227 drinkwater m.j . , gregg m.d . , colless , m. , 2001 , apj , 548l , 139 drinkwater , m.j . , gregg , m.d . , hilker , m. et al . , 2003 , nature , 423 , 519 elmegreen , b.g . , kaufman , m. , & thomasson , m. 1993 , apj , 412 , 90 evstigneeva , e.a . , gregg , m.d . , drinkwater , m. j. 2005 , to appear in the proceedings of the iauc198 `` near - field cosmology with dwarf elliptical galaxies '' , h. jerjen & b. binggeli ( eds . ) , astro - ph/0504289 ezawa , h. , fukazawa , y. , makishima , k. , ohashi , t. , takahara , f. , xu , h. , yamasaki , n. y. 1997 , apj , 490l , 33 fall , m.s . , chandar , r. , whitmore , b.c . 2005 , apj letters in press , astro - ph/0509293 fellhauer , m. , kroupa , p. , 2002 , mnras , 330 , 642 fellhauer , m. ; kroupa , p. , 2005 , mnras , 359 , 223 ferguson h.c . , sandage a. , 1989 , apj 346 , 53 forbes , d. a. , brodie , j. p. , grillmair , c. j. 1997 , aj , 113 , 1652 gebhardt , k. , kissler - patig , m. , 1999 , aj , 118 , 1526 harris , w. e. , pudritz , r. e. 1994 , apj , 429 , 177 hasegan , m. , jordn , a. , ct , p. et al . ( vcs team ) 2005 , apj , 627 , 203 held e.v . , mould j.r . , 1994 , aj 107 , 1307 hilker , m. , infante , l. , vieira , g. , kissler - patig , m. , & richtler , t. 1999 , a&as , 134 , 75 hilker , m. , mieske , s. , & infante , l. 2003 , a&al , 397 , l9 jones , j.b . , drinkwater , m.j . , jurek , r. et al . 2005 , aj in press , astro - ph/0509120 jordn , a. , ct , p. , blakeslee , j. et al . 2005a , apj in press , astro - ph/0508219 jordn et al . 2005b , in iau colloq . 198 , near - field cosmology with dwarf elliptical galaxies , ed . h. jerjen and b. binggeli ( cambridge : cambridge university press ) , in press . karick , a. , drinkwater , m.j . , gregg , m.d . 2003 , mnras , 344 , 188 kissler - patig , m. , kohle , s. , hilker , m. , richtler , t. , infante , l. , & quintana , h. 1997 , a&a , 319 , 470 kissler - patig , m. , brodie , j. p. , schroder , l. l. , forbes , d. a. , grillmair , c. j. , huchra , j. p. 1998 , aj , 115 , 105 kissler - patig , m. , jordn , a. , bastian , n. 2005 , submitted to a&a kravtsov , a. v. , gnedin , o. y. 2005 , apj , 623 , 650 kundu , a. , & whitmore , b. c. 1998 , aj , 116 , 2841larsen , s.s . 2002 , aj , 124 , 1393 li , y. , mac low , m. , klessen , r. s. 2004 , apj , 614l , 29 lotz , j. m. , miller , b. w. , ferguson , h. c. 2004 , apj , 613 , 262 makino , j. , hut , p. 1997 , apj , 481 , 83 maraston , c. , bastian , n. , saglia , r.p . , kissler - patig , m. , schweizer , f. , goudfrooij , p. 2004 , a&a , 416 , 467 mclaughlin , d.e . 2000 , apj , 539 , 618 meylan , g. , mayor , m. 1986 , a&a , 166 , 122 mieske , s. , hilker , m. , infante , l. , 2002 , a&a , 383 , 832 mieske , s. , hilker , m. , infante , l. 2004a , a&a , 418 , 445 mieske , s. , infante , l. , bentez , n. , et al . ( acs gto team ) , 2004b , aj , 128 , 1529 mieske , s. , infante , l. , hilker , m. et al . 2005a , a&a , 430l , 25 mieske , s. , hilker , m. , infante , l. 2005b , to appear in the proceedings of the iauc198 `` near - field cosmology with dwarf elliptical galaxies '' , h. jerjen & b. binggeli ( eds . ) , astro - ph/0505187 peng , e. , jordn , a. , ct , p. et al . ( vcs team ) 2005 , apj in press , astro - ph/0509654 phillipps s. , drinkwater m.j . , gregg m.d . , jones j.b . , 2001 , apj 560 , 201 pryor , c. , meylan , g. 1993 , aspc , 50 , 357 puzia , t. h. , saglia , r. p. , kissler - patig , m. , maraston , c. , greggio , l. , renzini , a. , ortolani , s. 2002 , a&a , 395 , 45 rakos k. , schombert j. , maitzen h.m . , prugovecki s. , odell a. , 2001 , aj 121 , 1974 richtler , t. , dirsch , b. , gebhardt , k. et al . 2004 , aj , 127 , 2094 rhode , k. l. , zepf , s. e. 2004 , aj , 127 , 302 schlegel , d.j . , finkbeiner , d.p . , & davis , m. 1998 , apj , 500 , 525 trager , s.c . , worthey , g. , faber , s.m . , burstein , d. , gonzalez , j.j . 1998 , apjs , 116 , 1 zinn , r. , west , m.j . 1984 , apjs , 55 , 45 lccccccc fcos 1 - 2053 & 3:38:54.05 & -35:33:33.8 & 18.06 & 1.18 & -0.52 @xmath8 0.11 & 2.46 @xmath8 0.09 & 0.136 @xmath8 0.022 + fcos 2 - 2143 & 3:38:05.04 & -35:24:09.7 & 18.93 & 1.14 & -0.69 @xmath8 0.21 & 2.32 @xmath8 0.05 & 0.084 @xmath8 0.014 + fcos 1 - 2083 & 3:39:35.90 & -35:28:24.2 & 19.12 & 1.12 & -0.85 @xmath8 0.29 & 2.86 @xmath8 0.12 & 0.051 @xmath8 0.023 + fcos 2 - 2111 & 3:38:06.29 & -35:28:58.8 & 19.23 & 1.12 & -0.90 @xmath8 0.33 & & 0.511 @xmath8 0.016 + fcos 1 - 021 & 3:38:41.96 & -35:33:12.9 & 19.70 & 1.16 & -0.58 @xmath8 0.15 & 2.05 @xmath8 0.07 & 0.108 @xmath8 0.020 + fcos 3 - 2004 & 3:39:20.50 & -35:19:14.2 & 19.73 & 1.21 & -0.49 @xmath8 0.04 & 2.02 @xmath8 0.13 & 0.178 @xmath8 0.036 + fcos 0 - 2031 & 3:38:28.97 & -35:22:55.9 & 19.87 & 1.11 & -0.38 @xmath8 0.05 & 2.43 @xmath8 0.09 & 0.210 @xmath8 0.022 + fcos 2 - 2153 & 3:38:06.48 & -35:23:03.8 & 20.04 & 1.06 & -0.70 @xmath8 0.21 & 2.46 @xmath8 0.10 & 0.079 @xmath8 0.023 + fcos 0 - 2066 & 3:38:23.23 & -35:20:00.6 & 20.09 & 1.10 & -0.61 @xmath8 0.14 & 2.61 @xmath8 0.15 & 0.108 @xmath8 0.031 + fcos 1 - 060 & 3:39:17.66 & -35:25:30.0 & 20.19 & 1.25 & -0.59 @xmath8 0.12 & 1.86 @xmath8 0.10 & 0.136 @xmath8 0.029 + fcos 0 - 2024 & 3:38:16.51 & -35:26:19.3 & 20.32 & 0.72 & -0.52 @xmath8 0.10 & 1.93 @xmath8 0.11 & 0.266 @xmath8 0.034 + fcos 0 - 2007 & 3:38:54.67 & -35:29:44.2 & 20.54 & 0.89 & -1.00 @xmath8 0.21 & 2.81 @xmath8 0.21 & 0.174 @xmath8 0.042 + fcos 2 - 2165 & 3:37:28.22 & -35:21:23.0 & 20.57 & 0.95 & -0.40 @xmath8 0.05 & & 0.176 @xmath8 0.031 + fcos 0 - 2023 & 3:38:12.70 & -35:28:57.0 & 20.66 & 1.09 & -1.13 @xmath8 0.14 & 3.49 @xmath8 0.15 & 0.067 @xmath8 0.025 + fcos 0 - 2069 & 3:38:26.71 & -35:30:07.2 & 20.67 & 0.97 & -1.50 @xmath8 0.20 & 1.56 @xmath8 0.14 & 0.027 @xmath8 0.046 + fcos 1 - 058 & 3:38:39.39 & -35:27:06.4 & 20.67 & 1.02 & -0.74 @xmath8 0.25 & 2.07 @xmath8 0.13 & 0.065 @xmath8 0.034 + fcos 0 - 2072 & 3:38:32.06 & -35:28:12.7 & 20.71 & 1.14 & -0.50 @xmath8 0.08 & 2.88 @xmath8 0.27 & 0.148 @xmath8 0.047 + fcos 2 - 2072 & 3:38:14.69 & -35:33:40.7 & 20.72 & 0.89 & -0.60 @xmath8 0.10 & 2.69 @xmath8 0.19 & 0.127 @xmath8 0.040 + fcos 0 - 2041 & 3:38:44.11 & -35:19:01.6 & 20.73 & 1.30 & -1.32 @xmath8 0.25 & 3.33 @xmath8 0.33 & 0.052 @xmath8 0.051 + fcos 0 - 2032 & 3:38:30.22 & -35:21:31.0 & 20.80 & 0.84 & -1.75 @xmath8 0.30 & 3.14 @xmath8 0.68 & 0.055 @xmath8 0.129 + fcos 2 - 086 & 3:37:46.77 & -35:34:41.7 & 20.81 & 0.90 & -0.66 @xmath8 0.17 & 3.05 @xmath8 0.23 & 0.242 @xmath8 0.041 + fcos 1 - 2115 & 3:38:49.18 & -35:21:42.1 & 20.85 & 1.20 & -1.26 @xmath8 0.25 & 2.50 @xmath8 0.18 & 0.491 @xmath8 0.039 + fcos 2 - 089 & 3:38:14.02 & -35:29:43.0 & 20.87 & 1.06 & -2.00 @xmath8 0.36 & & 0.015 @xmath8 0.044 + fcos 0 - 2074 & 3:38:35.66 & -35:27:15.5 & 20.91 & 1.04 & -2.25 @xmath8 0.27 & 2.17 @xmath8 0.12 & -0.006 @xmath8 0.033 + fcos 2 - 2100 & 3:38:00.17 & -35:30:08.3 & 20.94 & 1.05 & -0.91 @xmath8 0.24 & 1.91 @xmath8 0.16 & 0.069 @xmath8 0.046 + fcos 0 - 2092 & 3:39:05.02 & -35:26:53.9 & 20.96 & 1.13 & -1.66 @xmath8 0.38 & 1.59 @xmath8 0.14 & -0.006 @xmath8 0.047 +

to better judge on some of the competing scenarios , we present spectroscopic [ fe / h ] estimates for a sample of 26 compact objects in the central region of the fornax cluster , covering the magnitude range of ucds and bright globular clusters ( or mag ) . we find a break in the metallicity distribution of compact objects at mag ( 3 m ) : for mag the mean metallicity is [ fe / h].62 0.05 dex , 0.56 0.15 dex higher than the value of.18 0.15 dex found for mag . this metallicity break is accompanied by a change in the size - luminosity relation for compact objects , as deduced from hst - imaging : for mag , scales with luminosity , while for mag , is almost luminosity - independent . in our study the mean metallicity of five fornax de , n nuclei included in our study is about 0.8 dex lower than that of the ucds , a difference significant at the 4.5 level . because of the large metallicity discrepancy between ucds and nuclei we disfavor the hypothesis that most of the fornax ucds are the remnant nuclei of tidally stripped de , ns . our metallicity estimates for ucds are closer to but slightly below those derived for young massive clusters ( ymcs ) of comparable masses . we therefore favor a scenario where most ucds in fornax are successors of merged ymcs produced in the course of violent galaxy - galaxy mergers .

various formation channels for the puzzling ultra - compact dwarf galaxies ( ucds ) have been proposed in the last few years . to better judge on some of the competing scenarios , we present spectroscopic [ fe / h ] estimates for a sample of 26 compact objects in the central region of the fornax cluster , covering the magnitude range of ucds and bright globular clusters ( or mag ) . we find a break in the metallicity distribution of compact objects at mag ( 3 m ) : for mag the mean metallicity is [ fe / h].62 0.05 dex , 0.56 0.15 dex higher than the value of.18 0.15 dex found for mag . this metallicity break is accompanied by a change in the size - luminosity relation for compact objects , as deduced from hst - imaging : for mag , scales with luminosity , while for mag , is almost luminosity - independent . in our study we therefore assume a limiting absolute magnitude of mag between ucds and globular clusters . the mean metallicity of five fornax de , n nuclei included in our study is about 0.8 dex lower than that of the ucds , a difference significant at the 4.5 level . this difference is marginally higher than expected from a comparison of their colors , indicating that ucds are younger than or at most coeval to de , n nuclei . because of the large metallicity discrepancy between ucds and nuclei we disfavor the hypothesis that most of the fornax ucds are the remnant nuclei of tidally stripped de , ns . our metallicity estimates for ucds are closer to but slightly below those derived for young massive clusters ( ymcs ) of comparable masses . we therefore favor a scenario where most ucds in fornax are successors of merged ymcs produced in the course of violent galaxy - galaxy mergers . it is noted that in contrast to that , the properties of virgo ucds are more consistent with the stripping scenario , suggesting that _ different _ ucd formation channels may dominate in either cluster .

astro-ph9803139

i

from the fact that @xmath2 when normalised to the stellar mass of a galaxy @xmath2 the specific globular cluster ( * gc * ) frequency @xmath6 is a factor of @xmath7 higher in ellipticals than in spirals , zepf & ashman ( 1993 ) predict that if elliptical galaxies are formed from one major spiral @xmath2 spiral merger the number of gcs formed during the merger- induced starburst should be of the same order of magnitude as the number of gcs present in the progenitor galaxies . the high burst strengths and star formation ( * sf * ) efficiencies in massive gas - rich spiral @xmath2 spiral mergers and in ir - ultraluminous galaxies led to expect the formation of star clusters so tightly bound that they are able to survive as gcs ( fritze @xmath2 v. alvensleben & gerhard 1994 ) . fritze @xmath2 v. alvensleben & gerhard ( 1994 ) predicted the metallicity range of stars and star clusters formed in massive gas - rich ( i.e. late type ) spiral@xmath2spiral mergers on the basis of the ism abundances of the progenitor galaxies to be @xmath8 or @xmath9 } \lta -0.2 $ ] . in many interacting galaxies and merger remnants , bright blue knots have by now been observed ( cf . e.g. lutz 1991 , holtzman 1992 , whitmore 1993 , hunter 1994 , oconnell 1994 , 1995 , conti & vacca 1994 , borne 1996 , meurer 1995 ) . these bright blue knots , of course , immediately raised the question as to their identity : are these young star clusters ( * ysc * ) @xmath2 or , at least , some of them @xmath2 the progenitors of gcs ? and , if the latter were true , how many of them are typically formed in a merger ? how many will be able to survive in the tidal field of two massive interacting spirals ? can such a higher metallicity subpopulation be identified in gc systems ( hereafter * gcs * ) around merger remnants and perhaps even around normal ellipticals ? could the metallicity distribution of a gcs give information about the origin of its parent galaxy ( cf . zepf & ashman 1993 ) ? or should all of these bright blue knots be open clusters / ob associations ( van den bergh 1995 ) most of which will disperse within few gyr ? the discussion of the nature of these yscs is focussed on two aspects , their effective radii r@xmath10 and their luminosity function . in mergers at distances of the antennae or ngc 7252 , effective radii as measured on wfpc1 images are clearly overestimated . however , it has been shown that for ysc systems close enough the mean effective radii do readily fall within the range of gc radii ( meurer 1995 ) . our focus in this paper is the luminosity and colour evolution of the ysc population in the antennae and , in particular , the future evolution of the ysc s lf . in a previous paper , we model the evolution of star clusters for different initial metallicities in terms of broad band colours and stellar metallicity indices . we find important colour differences for clusters of various metallicities , already at young ages , and showed that once the stellar metallicity is known , rather precise age dating becomes possible . comparison with young star clusters in ngc 7252 ( whitmore 1993 ) , the two brightest of which have spectroscopy available ( schweizer & seitzer 1993 ) , confirmed a metallicity of @xmath11 predicted from our global starburst modelling in this sc @xmath2 sc merger remnant . the mean age of the young star cluster population was shown to agree well with the global burst age of @xmath12 gyr , and ages derived from solar metallicity models would differ by a factor @xmath7 ( see fritze @xmath2 v. alvensleben & burkert 1995 for details ) . observationally , the best case by now to study the lf of yscs are the antennae with more than 700 young star clusters detected by whitmore & schweizer ( 1995 , hereafter * ws95 * ) , a number large enough to allow for a statistical analysis . in this paper , we will examine the lf of the young star cluster system in the antennae . it seems clear that not all bright knots in the ngc 4038/39 system with its still ongoing starburst will probably be gcs , in particular those with large effective radii r@xmath10 might rather be open clusters or associations . therefore , after age dating the clusters in sect . 2 . , we subdivide whitmore & schweizer s young star cluster sample into two subsamples containing the small knots and the more extended systems , respectively ( sect . 3 . ) . in a first step , we assume a uniform age for the ysc population and we model the evolution of the yscs lf over a hubble time and compare to lfs of the milky way s and other nearby galaxies gcss ( sect.4 . ) . in an ongoing starburst like in the antennae , the age spread among the yscs may not be negligible ( see also meurer 1995 ) . to examine the age spread effects on the lf we determe individual ages for all star clusters from their ( v - i ) colour and discuss the star clusters age distribution in sect . we calculate the resulting individual fading for all clusters in sect . 6 . alternative possibilities to subdivide the ysc sample and their consequences are discussed in sect . . the of a young gcs may not only change by fading but also by dynamical effects as e.g. stellar mass loss within the cluster and/or tidal interaction of a cluster with the galactic potential . for gc populations in non - interacting galaxies , these effects were studied by chernoff & weinberg ( 1990 ) , their results are largely confirmed by the independent and more realistic approach of fukushige & heggie ( 1995 ) . in a recent paper vesperini ( 1997 ) shows that in the milky way potential an initial log - normal mas distribution represents a quasi - equilibrium state that allows to preserve both its shape and parameters during a hubble time of dynamical evolution , even though up to 70 % of the initial cluster population get disrupted . in case of the antennae , i.e. in a still uncompleted merger with its gravitational potential being highly variable both in space and in time , however , external dynamical effects seem extremely difficult to model . referring ysc luminosities to a common age allows to recover the mass function of the ysc system when combined with model we discuss the possible influence of dynamical effects in sect . 8 . and point out the possibility to observationally approach these dynamical effects by intercomparing star cluster populations in interacting galaxies and merger remnants of various ages . 9 . summarizes our conclusions . the spatial distribution of the yscs @xmath2 and of their properties as derived here @xmath2 will be discussed in a forthcoming paper .

this allows us to compare their luminosity function ( * lf * ) , evolved over a hubble time , to lfs observed for the milky way s and other galaxies star cluster systems . since effective radii we also follow the colour evolution of the young star clusters over a hubble time and compare to observations on the milky way and other galaxies gc systems . for an ongoing starburst like the one in the ngc we find that if age spread effects are properly accounted for the lf of the entire young star cluster population , and in particular that of the brighter subsample , after a hubble time is in good agreement with the average gauss - shaped lf of globular cluster systems having a turn - over at mag and mag .

we analyse the population of bright star clusters in the interacting galaxy pair ngc 4038/39 detected with hst wfpc1 by whitmore & schweizer ( 1995 ) . making use of our spectrophotometric evolutionary synthesis models for various initial metallicities we derive the ages of these star clusters and calculate their future luminosity evolution . this allows us to compare their luminosity function ( * lf * ) , evolved over a hubble time , to lfs observed for the milky way s and other galaxies star cluster systems . since effective radii are difficult to determine due to crowding of the clusters , the shape of the lf after a hubble time may help decide whether the young clusters are young globular clusters ( * gc * ) or rather open clusters / ob associations . we find an intriguing difference in the shapes of the lfs if we subdivide the cluster population into subsamples with small and large effective radii . while the lf for the extended clusters looks exponential , that for clusters with small effective radii clearly shows a turn - over brighter than the completeness limit . for other possible subdivisions as to luminosity or colour no comparable differences are found . evolving , in a first step , the lf from a common mean age of the young clusters of 0.2 gyr to an assumed age of 12 gyr , the lf for the subsample of clusters with small effective radii seems compatible with a gaussian gclf with typical parameters m and except for some overpopulation of the faint bins . these faintest bins , however , are suspected to be subject to the strongest depopulation through effects of dynamical evolution not included in our models . we also follow the colour evolution of the young star clusters over a hubble time and compare to observations on the milky way and other galaxies gc systems . for an ongoing starburst like the one in the ngc 4038/39 system age spread effects among the young star cluster population may not be negligible . in a second step , we therefore account for age spread effects , instead of using a mean age for the young cluster population , and this drastically changes the time evolution of the lf , confirming meurer s ( 1995 ) conjecture . we find that if age spread effects are properly accounted for the lf of the entire young star cluster population , and in particular that of the brighter subsample , after a hubble time is in good agreement with the average gauss - shaped lf of globular cluster systems having a turn - over at mag and mag . the age distribution shows that the brightest globular clusters from the interacting galaxies original population are also observed . they make up the bulk of the red subpopulation with ( vi) . their effective radii do not significantly differ from those of the young star cluster population , neither on average nor in their distribution . we discuss the influence of metallicity , the effects of an inhomogeneous internal dust distribution , as well as the possible influence of internal through stellar mass loss and external dynamical effects on the secular evolution of the lf . referring ysc luminosities to a uniform age and combining with model m / l , we recover the intrinsic mass distribution of the ysc system . it is gaussian in shape to good approximation thus representing a quasi - equilibrium distribution that according to vesperini s ( 1997 ) dynamical modelling for the milky way gc system will * not * be altered in shape over a hubble time of dynamical evolution , allthough a substantial number of clusters will be destroyed . we briefly compare the young star cluster population of the antennae to the older one in the merger remnant ngc 7252 and point out that the intercomparison of young cluster populations in an age sequence of interacting and merged galaxies may become an interesting approach to study in detail the role of external dynamical effects .

astro-ph9803139

c

here we compare average properties of the red ( @xmath144 ) and blue ( @xmath145 ) star cluster subsamples . we argued that the red subsample may mainly consist of the brightest of the original spirals gcs while we expect the blue subsample to contain some mixture of young open clusters , associations and globular clusters . table 2 summarises average quantities of the two subsamples with @xmath146 and @xmath147 . for 164 clusters , no @xmath15 observations are available . it is seen that the 69 red clusters populate an area within ngc 4038/39 somewhat more extended than the 481 blue ones . if dust were somehow concentrated to the center , the redder subsample should be less affected by dust than the bluer one , thus increasing the colour difference . plotted separately as projected on the sky , the blue yscs and the red gcs show very different spatial distributions . while the blue clusters tightly trace the tidal structure as seen on ws95 s hst image of the antennae , the red clusters show a more spherically symmetric distribution as expected for the original gc population . the redder clusters are fainter by @xmath148 mag with a scatter slightly smaller that the blue ones . if the difference in @xmath149 of 1 mag were due to stronger than average internal dust reddening the red clusters should be fainter than the blue ones by as much as 1.7 mag , on average . their @xmath150 corresponds to ages from 4 @xmath2 15 gyr for z=0.01 and from 1 @xmath2 10 gyr for z=0.04 , respectively , clusters with @xmath151 in our models do not reach colours as red as @xmath152 until 15 gyr , values @xmath153 is not even reached by our model clusters with @xmath154 . so we suspect , that these very red clusters are affected by stronger than average dust reddening . the average @xmath155 of the bluer clusters is bluer by 1 mag than that of the redder ones with a larger scatter and indicates a mean age of @xmath156 yr with a range from @xmath157 to @xmath158 yr for z = 0.01 . the mean dereddened luminosity of the red subsample is @xmath159 , so it is only the brightest of the really old gcs from the parent galaxies of the merging system , which are seen in the red subsample . from our models , the age difference between the subsamples corresponds to a fading by @xmath160 mag if they have the same metallicity and of 4.6 mag if the redder ones have @xmath132 . if the redder ones are older and fainter , however , only the very brightest of them can be observed , so that their mean brightness is overestimated . on the other hand , this difference may aresult if chances to survive a hubble time were larger for brighter and more massive clusters ( cf . sect.8 ) . the mean effective radius of the red subsample is slightly smaller than that of the bluer clusters . if they are really old this can be understood in terms of a preferential destruction of large r@xmath10 clusters strong enough to overcome the increase in r@xmath10 caused by internal stellar mass loss ( @xmath161 in r@xmath10 ) and mass loss through tidal stripping ( cf . sect . the difference in r@xmath10 is surprisingly small , however , in view of our expectation that the old star cluster population should consist of gcs while the blue and young star population might comprise open clusters and ob associations , as well . the distribution of effective radii of the ysc subsample has a clear maximum around 8 pc with a tail extending to @xmath162 pc , that of the old gc sample is somewhat flatter but otherwise very similar . the breakdown of the age distribution into clusters with small and large @xmath72 in figs 5b and 5c shows that while of the 201 clusters with @xmath163 pc 11% belong to the old and 89% to the young population , the respective fractions are 13% and 87% for the 349 clusters with @xmath164 pc . it is clear that the old objects must almost all be globulars , even those with @xmath164 pc , except for a small number of very old open clusters as reported for the milky way by friel ( 1995 ) . among the old gc population the number ratio of objects with @xmath163 pc to those with @xmath164 pc is 23/46 while among the ysc population it is 178/303 . this corresponds to a fraction of objects with @xmath163 pc of 33% among the old gc population , while this fraction amounts to 37% in the ysc population . * to summarize * , the red old gc population is slightly more extended than the population of young blue star cluster forming in the merger - induced starburst in the antennae . while the blue yscs trace the tidal structure , the red clusters rather show a spherically symmetric distribution . interestingly , the mean as well as the distribution of * effective radii are not significantly different for the bright end of the old gc population and for the less than 1 gyr old young star cluster population * which might be expected to also comprise an unknown fraction of open clusters and ob associations together with young gcs . in figs . 7a and b , we present the lfs of the yscs ( age @xmath165 gyr ) with @xmath163 pc and @xmath164 pc , respectively , both differentially aged to 12 gyr . no significant difference comparable to the one discussed in sect . 4 is visible any more . strikingly and at variance with our simplified analysis in sect . 4 . , * both the differentially aged lfs of subsamples with r@xmath36 pc and r@xmath69 pc now do show a turnover at m@xmath130 mag * , as seen in figs . 7a , b. pc and * ( 7b ) * clusters with r@xmath69 pc.,title="fig : " ] pc and * ( 7b ) * clusters with r@xmath69 pc.,title="fig : " ] so , while no doubt some open clusters may be among the ysc population , preferentially within the large @xmath72 subsample , it might well be that the bulk of the ysc population are young gcs . there is another plausible criterion to subdivide the ysc sample of ws95 into a subclass that might be expected to contain a significant number of young gcs as opposed to the rest of the sample that could possibly be dominated by open clusters and associations , and this is luminosity . one might conjecture that the most luminous objects might be young globulars while the fainter ones could also be open clusters / associations . to explore this hypothesis we subdivide the ysc sample of ws95 into subsamples of bright and faint clusters with a limiting @xmath166 , corresponding to a dereddened @xmath167 . table 3 presents the average properties of the faint and bright subsamples . our choice of the limiting magnitude makes both subsamples contain comparable numbers of objects . the fainter clusters , on average , seem to have larger galactocentric distances . it is not clear , however , if this is a real effect or due to the fact that low luminosity clusters are harder to detect near the center . the mean v @xmath2 magnitude of the faint subsample is @xmath168 mag lower than the @xmath169 of the brighter ones , the rms scatter is less than half that of the brighter ones . faint clusters are redder by 0.3 mag in @xmath15 . unfortunately , no @xmath23 colours are available for the faint subpopulation . it should be noted that the differences in v and @xmath15 can not be explained by reddening differences but may be understood in terms of age differences ( see below ) . finally , the mean effective radius of the fainter subpopulation is smaller by @xmath117 pc and the rms scatter is smaller , too , than the respective values of the bright subsample . all differences between the bright and faint subsamples increase if we chose a brighter limiting magnitude for our subdivision . the bright clusters have a mean age of their young population of @xmath170 yr , younger by almost a factor of 2 than that of @xmath171 yr for the fainter ones . in the age distribution of the bright subsample the vast majority of clusters is young , only 24/331 are 3 @xmath2 12 gyr old . the age distribution of the faint clusters shows 45/219 clusters to be old ( 3 @xmath2 12 gyr ) and 175/219 to be young ( 0 @xmath2 3 gyr ) . in sect . 5 , we argued that because of inhomogeneous metal and dust distributions probably most clusters with ages @xmath165 gyr are as young as @xmath172 yr and most clusters with ages @xmath173 gyr are as old as 12 gyr . after differentially aging all clusters from their present individual ages to an assumed final age of 12 gyr , however , the brighter subsample will keep a brighter final luminosity @xmath174 mag than the fainter subsample which will end up with @xmath175 mag . as shown in fig . 8 , after 12 gyr , the lf for the bright subsample clearly shows a turn - over definitely brighter than the completeness limit and does closely resemble the gaussian lf of gcs with typical parameters @xmath176 mag , @xmath177 mag rather than the exponentially increasing lf of open clusters . the fact that this turn - over is slightly brighter than the one we expect on the basis of our metal prediction @xmath2 if it is true @xmath2 might indicate that a limiting magnitude @xmath178 is still so bright as to exclude part of the young gc population . the lf of the faint clusters contains an important fraction of @xmath87 gyr old clusters . if these are left aside when the lf is evolved over a hubble time , we again observe a turn - over , however only slightly before the completeness limit is reached , i.e. at @xmath179 mag . mag differentially aged to 12 gyr . overplotted is a gaussian with @xmath180 mag , @xmath177 mag , normalised to the number of yscs in the histogram . ] * to summarise : * the faint cluster subsample contains a @xmath181% proportion of @xmath87 gyr old gcs , it is a little less concentrated to the center on average than the bright subsample . it has marginally smaller @xmath182 than the bright one . unless errors of the effective radii are systematically different for the bright and faint subsamples , the larger @xmath183 of the bright sample seem to reflect an initial correlation of larger radii for higher luminosity clusters that overcomes the age effect of increasing the radius due to mass loss . the lf of the subsample of clusters brighter than @xmath167 mag evolved over 12 gyr closely agrees with a typical gc system s lf ( @xmath3 mag , @xmath177 mag ) , provided age spread effects are properly accounted for . all the data discussed here were taken by ws95 with hst wfpc1 , i.e. before the refurbishment mission . the antennae are close enough to even identify the brightest members of the original gc population on these aberrated images . ws95 expect reobservations with wfpc2 to go deeper by 2@xmath23 mag . if this is true and the completeness limit can really be pushed down that far we might be able to observe beyond the turn - over of the original gc population . then both the old gc population and the ysc population can directly be compared . it would be very interesting to have spectroscopy for some of the clusters to settle their metallicity range and to allow for better age - dating . at the same time , ysc spectra will provide information about the local dust distribution and , if spectral resolution allows , also about the kinematics of the ysc system . the very youngest star clusters will give us the chance to directly study the upper imf .

are difficult to determine due to crowding of the clusters , the shape of the lf after a hubble time may help decide whether the young clusters are young globular clusters ( * gc * ) or rather open clusters / ob associations . the age distribution shows that the brightest globular clusters from the interacting galaxies original population are also observed . their effective radii do not significantly differ from those of the young star cluster population , neither on average nor in their distribution .

we analyse the population of bright star clusters in the interacting galaxy pair ngc 4038/39 detected with hst wfpc1 by whitmore & schweizer ( 1995 ) . making use of our spectrophotometric evolutionary synthesis models for various initial metallicities we derive the ages of these star clusters and calculate their future luminosity evolution . this allows us to compare their luminosity function ( * lf * ) , evolved over a hubble time , to lfs observed for the milky way s and other galaxies star cluster systems . since effective radii are difficult to determine due to crowding of the clusters , the shape of the lf after a hubble time may help decide whether the young clusters are young globular clusters ( * gc * ) or rather open clusters / ob associations . we find an intriguing difference in the shapes of the lfs if we subdivide the cluster population into subsamples with small and large effective radii . while the lf for the extended clusters looks exponential , that for clusters with small effective radii clearly shows a turn - over brighter than the completeness limit . for other possible subdivisions as to luminosity or colour no comparable differences are found . evolving , in a first step , the lf from a common mean age of the young clusters of 0.2 gyr to an assumed age of 12 gyr , the lf for the subsample of clusters with small effective radii seems compatible with a gaussian gclf with typical parameters m and except for some overpopulation of the faint bins . these faintest bins , however , are suspected to be subject to the strongest depopulation through effects of dynamical evolution not included in our models . we also follow the colour evolution of the young star clusters over a hubble time and compare to observations on the milky way and other galaxies gc systems . for an ongoing starburst like the one in the ngc 4038/39 system age spread effects among the young star cluster population may not be negligible . in a second step , we therefore account for age spread effects , instead of using a mean age for the young cluster population , and this drastically changes the time evolution of the lf , confirming meurer s ( 1995 ) conjecture . we find that if age spread effects are properly accounted for the lf of the entire young star cluster population , and in particular that of the brighter subsample , after a hubble time is in good agreement with the average gauss - shaped lf of globular cluster systems having a turn - over at mag and mag . the age distribution shows that the brightest globular clusters from the interacting galaxies original population are also observed . they make up the bulk of the red subpopulation with ( vi) . their effective radii do not significantly differ from those of the young star cluster population , neither on average nor in their distribution . we discuss the influence of metallicity , the effects of an inhomogeneous internal dust distribution , as well as the possible influence of internal through stellar mass loss and external dynamical effects on the secular evolution of the lf . referring ysc luminosities to a uniform age and combining with model m / l , we recover the intrinsic mass distribution of the ysc system . it is gaussian in shape to good approximation thus representing a quasi - equilibrium distribution that according to vesperini s ( 1997 ) dynamical modelling for the milky way gc system will * not * be altered in shape over a hubble time of dynamical evolution , allthough a substantial number of clusters will be destroyed . we briefly compare the young star cluster population of the antennae to the older one in the merger remnant ngc 7252 and point out that the intercomparison of young cluster populations in an age sequence of interacting and merged galaxies may become an interesting approach to study in detail the role of external dynamical effects .

astro-ph9803139

c

using our method of evolutionary synthesis for various metallicities we present a first analysis of ws95 s wfpc1 data on bright star clusters in the ongoing merger - induced starburst in ngc 4038/39 . assuming a metallicity z @xmath199 on the basis of the progenitor spirals ism properties and applying a uniform reddening as given by ws95 we age - date the bright cluster population from their ( v@xmath2i ) colors and , as far as available , also from their ( u@xmath2v ) . it turns out that in addition to a large population of young clusters with a mean age of @xmath47 yr ( consistent with the dynamical time since pericenter ) part of the original spirals old gc population is also observed . a key question with far - reaching consequences as to the origin of elliptical galaxies is whether there are a significant fraction of young gcs among the ysc population . two basic properties discriminate open clusters / ob associations from gcs in our galaxy and others : the concentration parameter c = log ( @xmath200 ) and the lf which , in contrast to that for an open cluster system , is gaussian for * old * gcss . tidal radii and , consequently , concentration parameters not being accessible to observations in distant galaxies we examine the lfs of cluster subsamples with large and small effective radii . in a first step , using a common mean age for all young clusters and a corresponding uniform fading to an age of @xmath87 gyr we find that while the lf for extended clusters at 12 gyr is definitely not gaussian , that for the low r@xmath201 clusters may well contain a gaussian (= gc ) subcomponent together with a strong overpopulation of the faint bins , which themselves , however , might be expected to be severely depopulated over a hubble time by dynamical effects not included in our models . since for an ongoing starburst the age spread among yscs may be of the same order as their ages , age spread effects are expected to reshape the lf . clusters from the bright end tend to be younger on average and fade more than clusters from the faint end . we therefore , in a second step , model the individual fading consistent with individual ages of the yscs as derived from their @xmath15 and @xmath23 colours , and we follow the lf changing its shape over a hubble time . surprisingly , accounting for these age spread effcets , we find the final lfs of large * and * small r@xmath202 cluster subsamples not to be significantly different any more . instead , the lf of * all * yscs evolved to a common age of 12 gyr is well compatible with a `` normal '' gclf . its turn - over occurs at @xmath203 mag , i.e. slightly fainter than the average value @xmath204 mag for 16 galaxies . this difference is readily explained in terms of a higher metallicity of the secondary cluster population . strikingly , neither the mean nor the distribution of effective radii is significantly different for the old gc sample and for the ysc sample . on the basis of these wfpc1 data we tentatively conclude that the bulk of the ysc population detected in the antennae might well be young gcs and that the open clusters / associations probably also present among the yscs do not seem to systematically differ from young gcs in terms of r@xmath202 . we are looking foreward to repeat this kind of analysis on wfpc2 data which may reach close to the old gcs s turn - over , reveal a number of fainter young objects , and will allow for more precise and definite conclusions . dynamical effects that eventually might further reshape the lf over a hubble time are discussed . referring the yscs luminosities to a uniform age allows to recover the intrinsic mass function of the ysc system . this mass function seems to be log - normal which , according to vesperini ( 1997 ) , represents a quasi - equilibrium distribution that is going to be preserved in shape though not in number of clusters over a hubble time of dynamical evolution . dynamical effects , however , are extremely difficult to model in detail in an ongoing merger . comparison of ysc populations in mergers / starbursts of various ages seems a promising tool in an attempt to understand these effects from an observational side . _ acknowledgements . _ i am deeply indebted to b. whitmore & f. schweizer for valuable discussions , encouragement and for sending us their star cluster data in machine readable form . i am grateful to ken freeman , tom richtler , and andreas burkert for interesting discussions on dynamical aspects . i wish to thank prof . appenzeller and all the collegues from the landessternwarte heidelberg for their warm hospitality during a 3 months stay , when this projected was begun . my deep thanks go to the referee , g. meurer , for his very detailed and constructive suggestions that greatly improved the paper . i gratefully acknowledge financial support from the sfb galaxienentwicklung in heidelberg and through a habilitationsstipendium from the deutsche forschungsgemeinschaft under grant fr 916/2 - 1 in gttingen . holtzman , j. a. , faber , s. m. , shaya , e. j. , lauer , t. r. , groth , e. j. , hunter , d. a. , baum , w. a. , ewald , s. p. , hester , j. j. , light , r. m. , lynds , c. r. , oneil , e. j. , westphal , j. a. , 1992 , aj * 103 * , 691

we analyse the population of bright star clusters in the interacting galaxy pair ngc 4038/39 detected with hst wfpc1 by whitmore & schweizer ( 1995 ) . making use of our spectrophotometric evolutionary synthesis models for various initial metallicities we derive the ages of these star clusters and calculate their future luminosity evolution . we find an intriguing difference in the shapes of the lfs if we subdivide the cluster population into subsamples with small and large effective radii . while the lf for the extended clusters looks exponential , that for clusters with small effective radii clearly shows a turn - over brighter than the completeness limit . for other possible subdivisions as to luminosity or colour evolving , in a first step , the lf from a common mean age of the young clusters of 0.2 gyr to an assumed age of 12 gyr , the lf for the subsample of clusters with small effective radii seems compatible with a gaussian gclf with typical parameters m and except for some overpopulation of the faint bins . these faintest bins , however , are suspected to be subject to the strongest depopulation through effects of dynamical evolution not included in our models . m / l , we recover the intrinsic mass distribution of the ysc system . it is gaussian in shape to good approximation thus representing a quasi - equilibrium distribution that according to vesperini s ( 1997 ) dynamical modelling for the milky way gc system will * not * be altered in shape over a hubble time of dynamical evolution , allthough a substantial number of clusters will be destroyed .

we analyse the population of bright star clusters in the interacting galaxy pair ngc 4038/39 detected with hst wfpc1 by whitmore & schweizer ( 1995 ) . making use of our spectrophotometric evolutionary synthesis models for various initial metallicities we derive the ages of these star clusters and calculate their future luminosity evolution . this allows us to compare their luminosity function ( * lf * ) , evolved over a hubble time , to lfs observed for the milky way s and other galaxies star cluster systems . since effective radii are difficult to determine due to crowding of the clusters , the shape of the lf after a hubble time may help decide whether the young clusters are young globular clusters ( * gc * ) or rather open clusters / ob associations . we find an intriguing difference in the shapes of the lfs if we subdivide the cluster population into subsamples with small and large effective radii . while the lf for the extended clusters looks exponential , that for clusters with small effective radii clearly shows a turn - over brighter than the completeness limit . for other possible subdivisions as to luminosity or colour no comparable differences are found . evolving , in a first step , the lf from a common mean age of the young clusters of 0.2 gyr to an assumed age of 12 gyr , the lf for the subsample of clusters with small effective radii seems compatible with a gaussian gclf with typical parameters m and except for some overpopulation of the faint bins . these faintest bins , however , are suspected to be subject to the strongest depopulation through effects of dynamical evolution not included in our models . we also follow the colour evolution of the young star clusters over a hubble time and compare to observations on the milky way and other galaxies gc systems . for an ongoing starburst like the one in the ngc 4038/39 system age spread effects among the young star cluster population may not be negligible . in a second step , we therefore account for age spread effects , instead of using a mean age for the young cluster population , and this drastically changes the time evolution of the lf , confirming meurer s ( 1995 ) conjecture . we find that if age spread effects are properly accounted for the lf of the entire young star cluster population , and in particular that of the brighter subsample , after a hubble time is in good agreement with the average gauss - shaped lf of globular cluster systems having a turn - over at mag and mag . the age distribution shows that the brightest globular clusters from the interacting galaxies original population are also observed . they make up the bulk of the red subpopulation with ( vi) . their effective radii do not significantly differ from those of the young star cluster population , neither on average nor in their distribution . we discuss the influence of metallicity , the effects of an inhomogeneous internal dust distribution , as well as the possible influence of internal through stellar mass loss and external dynamical effects on the secular evolution of the lf . referring ysc luminosities to a uniform age and combining with model m / l , we recover the intrinsic mass distribution of the ysc system . it is gaussian in shape to good approximation thus representing a quasi - equilibrium distribution that according to vesperini s ( 1997 ) dynamical modelling for the milky way gc system will * not * be altered in shape over a hubble time of dynamical evolution , allthough a substantial number of clusters will be destroyed . we briefly compare the young star cluster population of the antennae to the older one in the merger remnant ngc 7252 and point out that the intercomparison of young cluster populations in an age sequence of interacting and merged galaxies may become an interesting approach to study in detail the role of external dynamical effects .

1103.4283

r

( 130,90)(0,0 ) ( 0,50)(50,50)5 ( 50,50)(100,100)5 ( 50,50)(100,0)5 ( -15,48)@xmath128 ( 105,98)@xmath55 ( 105,-2)@xmath129 + at leading order the mssm higgs boson decays into squark - antisquark pairs are described by the diagram shown in fig . [ fg : lodia ] . the corresponding partial decay width reads as @xmath130 ^ 2 \sqrt{\lambda_{ij}}\ ] ] with the two - body phase - space function @xmath131 while higgs boson decays into squarks of the first two generations are generally suppressed , higgs decays into sbottoms and stops develop sizable branching ratios , whenever they are kinematically possible @xcite . in particular scenarios their branching ratios can reach a level of 8090% @xcite . ( 130,90)(0,0 ) ( 0,50)(50,50)5 ( 50,50)(100,100)5 ( 50,50)(100,0)5 ( 50,50)(30,-45,45)35 ( -15,48)@xmath128 ( 105,98)@xmath55 ( 105,-2)@xmath129 ( 90,48)@xmath56 ( 130,120)(-20,0 ) ( 0,50)(50,50)5 ( 75,75)(100,100)5 ( 75,25)(100,0)5 ( 50,50)(75,75 ) ( 50,50)(30,-45,45 ) ( 50,50)(30,-45,45)35 ( 75,25)(50,50 ) ( -15,48)@xmath128 ( 105,98)@xmath55 ( 105,-2)@xmath129 ( 55,65)@xmath57 ( 55,30)@xmath57 ( 90,48)@xmath58 ( -35,48)@xmath52 ( 115,48)@xmath52 ( 130,120)(-40,0 ) ( 0,50)(20,50)5 ( 50,50)(100,100)5 ( 50,50)(100,0)5 ( 35,50)(15,0,360)5 ( -15,48)@xmath128 ( 105,98)@xmath55 ( 105,-2)@xmath129 ( 30,70)@xmath55 + ( 130,120)(0,0 ) ( 0,50)(50,50)5 ( 50,50)(100,100)5 ( 50,50)(100,0)5 ( 75,75)(8,15)(45)0.5 ( -15,48)@xmath128 ( 105,98)@xmath55 ( 105,-2)@xmath129 ( -40,48)@xmath52 ( 115,48)@xmath52 ( 130,120)(-20,0 ) ( 0,50)(50,50)5 ( 50,50)(100,100)5 ( 50,50)(100,0)5 ( 75,25)(8,15)(-45)0.5 ( -15,48)@xmath128 ( 105,98)@xmath55 ( 105,-2)@xmath129 + ( 130,100)(0,0 ) ( 0,50)(50,50)5 ( 50,50)(100,100)5 ( 50,50)(100,0)5 ( 65,65)(100,65)33 ( -15,48)@xmath128 ( 105,98)@xmath55 ( 105,63)@xmath56 ( 105,-2)@xmath129 ( 130,90)(-20,0 ) ( 0,50)(50,50)5 ( 50,50)(100,100)5 ( 50,50)(100,0)5 ( 65,35)(100,35)33 ( -15,48)@xmath128 ( 105,98)@xmath55 ( 105,33)@xmath56 ( 105,-2)@xmath129 + the susy qcd corrections at nlo have been calculated in refs . @xcite . however , the analytical results will be repeated in this section in our notation and for the investigation of calculational details once consistent input parameters at nlo are included in the theoretical analysis . the susy qcd corrections consist of one - loop virtual corrections , mediated by the feynman diagrams depicted in fig . [ fg : nlodiav ] , supplemented by the renormalization of the mass , coupling and wave function parameters involved , and real corrections due to gluon bremsstrahlung , see fig . [ fg : nlodiar ] . we have performed the loop and phase - space integration within dimensional regularization in @xmath132 dimensions so that ultraviolet and infrared singularities appear as poles in @xmath133 . the infrared singularities cancel after adding the real and virtual corrections . the ultraviolet poles disappear after adding the corresponding counter terms which will be discussed in detail in the following , since they have to correspond to the schemes in which the squark masses , mixing angles and couplings are defined . the wave - function counter terms @xmath134 are determined by normalizing the residues of the diagonalized squark propagators to unity . the explicit calculation of the diagrams of fig . [ fg : sqself ] leads to the expressions @xmath135 b'_0(m_{\tilde q_i}^2;m_{{\tilde{g}}},m_q ) \right\ } \ , , \end{aligned}\ ] ] where the derivative of the two - point function is defined as @xmath136 throughout our calculation in this section the quark mass @xmath112 is defined as @xmath137 of eq . ( [ eq : deltab ] ) for decays into sbottom pairs and as @xmath138 of eq . ( [ eq : tmass ] ) for decays into stops . the mixing angle is renormalized by the anti - hermitian counter term of eq . ( [ eq : sqmixct ] ) . the trilinear couplings @xmath139 ( @xmath140 ) are defined in the @xmath22 scheme at the scale @xmath105 which is identical to the running couplings in the @xmath25 definition at nlo . thus , the counter term of @xmath139 can be cast into the form @xmath141 the quark mass counter term @xmath142 is given by @xmath143 with the top and bottom mass counter terms @xmath144 of eq . ( [ eq : dmq ] ) with @xmath145 . the calculation of the diagrams of fig . [ fg : nlodiav ] for the virtual corrections and those of fig . [ fg : nlodiar ] for the real corrections leads to the final result after renormalization , @xmath146 + c^\phi_{ct } + c^\phi_{real } \nonumber \\ c^\phi_1 & = & b_0(m_{\tilde q_i}^2;0,m_{\tilde q_i } ) + b_0(m_{\tilde q_j}^2;0,m_{\tilde q_j } ) - b_0(m_\phi^2 ; m_{\tilde q_i } , m_{\tilde q_j } ) \nonumber \\ & & - 2(m_\phi^2-m_{\tilde q_i}^2-m_{\tilde q_j}^2 ) c_0(m_{\tilde q_i}^2,m_\phi^2,m_{\tilde q_j}^2;0,m_{\tilde q_i},m_{\tilde q_j } ) \nonumber \\ c^{h , h}_2 & = & \frac{g_q^{h , h}}{g_{\tilde q_i\tilde q_j}^{h , h } } \left\ { \delta_{ij } m_q^2 \left [ b_0(m_{\tilde q_i}^2;m_{{\tilde{g}}},m_q ) + b_0(m_{\tilde q_j}^2;m_{{\tilde{g}}},m_q ) + 2b_0(m_{h , h}^2;m_q , m_q ) \right . \nonumber \\ & & \left . + ( 2m_{{\tilde{g}}}^2 + 2m_q^2-m_{\tilde q_i}^2-m_{\tilde q_j}^2 ) c_0(m_{\tilde q_i}^2,m_{h , h}^2,m_{\tilde q_j}^2;m_{{\tilde{g } } } , m_q , m_q ) \right ] \right . \nonumber \\ & & + { \cal r}_{ij } m_{{\tilde{g}}}m_q \left [ ( m_{h , h}^2 - 4m_q^2 ) c_0(m_{\tilde q_i}^2,m_{h , h}^2,m_{\tilde q_j}^2;m_{{\tilde{g } } } , m_q , m_q ) \right . \nonumber \\ & & \left . -b_0(m_{\tilde q_i}^2;m_{{\tilde{g}}},m_q ) - b_0(m_{\tilde q_j}^2;m_{{\tilde{g}}},m_q ) \right ] \right\ } \nonumber \\ c^a_2 & = & \frac{g_q^a}{g_{\tilde q_i\tilde q_j}^a } \left\ { m_q^2 \sin 2\theta_q \left [ b_0(m_{\tilde q_i}^2;m_{{\tilde{g}}},m_q ) - b_0(m_{\tilde q_j}^2;m_{{\tilde{g}}},m_q ) \right . \right . \nonumber \\ & & \left . + ( m_{\tilde q_i}^2-m_{\tilde q_j}^2 ) c_0(m_{\tilde q_i}^2,m_a^2,m_{\tilde q_j}^2;m_{{\tilde{g } } } , m_q , m_q ) \right ] \right . \nonumber \\ & & \left . -(-1)^i m_{{\tilde{g}}}m_q \left [ m_a^2 c_0(m_{\tilde q_i}^2,m_a^2,m_{\tilde q_j}^2;m_{{\tilde{g } } } , m_q , m_q ) \right . \nonumber \\ & & \left . -b_0(m_{\tilde q_i}^2;m_{{\tilde{g}}},m_q ) - b_0(m_{\tilde q_j}^2;m_{{\tilde{g}}},m_q ) \right ] \right\ } \nonumber \\ c^{h , h}_3 & = & -\frac{{\cal s}_{ik } g^{h , h}_{\tilde q_k\tilde q_l } { \cal s}_{lj}}{g_{\tilde q_i\tilde q_j}^{h , h } } b_0(m_{h , h}^2;m_{\tilde q_k } , m_{\tilde q_l } ) \nonumber \\ c^a_3 & = & b_0(m_a^2;m_{\tilde q_i } , m_{\tilde q_j } ) \nonumber \\ \frac{\alpha_s}{\pi } c^{h , h}_{ct } & = & \delta z_{ii}+\delta z_{jj } + \frac{2}{g_{\tilde q_i\tilde q_j}^{h , h } } \left [ \frac{\partial g^{h , h}_{\tilde q_i\tilde q_j}}{\partial m_q } \delta m_q + \frac{\partial g^{h , h}_{\tilde q_i\tilde q_j}}{\partial a_q } \delta \bar a_q + { \cal t}_{ij } \delta\theta_q \right ] \nonumber \\ \frac{\alpha_s}{\pi } c^a_{ct } & = & \delta z_{ii}+\delta z_{jj } + \frac{2}{g_{\tilde q_i\tilde q_j}^a } \left [ \frac{\partial g^a_{\tilde q_i\tilde q_j}}{\partial m_q } \delta m_q + \frac{\partial g^a_{\tilde q_i\tilde q_j}}{\partial a_q } \delta \bar a_q \right ] \nonumber \\ c^\phi_{real } & = & c_f \gamma(1+\epsilon ) \left ( \frac{4\pi\bar\mu^2}{m_\phi^2}\right)^\epsilon \left\ { \frac{1-\rho_i-\rho_j}{2\beta } \left [ \frac{\log x_0}{\epsilon } + \log x_0 \log\frac{\rho_i\rho_j x_0}{\beta^4 } \right . . \nonumber \\ & & \left . \left . - \frac{1}{2 } \log^2 x_1 - \frac{1}{2 } \log^2 x_2 + 4 li_2\left(\frac{1-x_0}{-x_0}\right ) - 2 li_2(1-x_1 ) - 2 li_2(1-x_2 ) \right ] \right . \nonumber \\ & & \left . + \frac{1}{\epsilon } + \log\frac{\rho_i\rho_j}{\beta^4 } + 4 - \frac{1+\rho_i+\rho_j}{2\beta } \log x_0 + \frac{\rho_i\log x_1 + \rho_j\log x_2}{\beta}\right\ } \ , , \label{eq : cphi}\end{aligned}\ ] ] where in @xmath147 we used the abbreviations @xmath148 with the two - body phase - space function @xmath149 of eq . ( [ eq : lambda ] ) and @xmath150 with @xmath151 . the two mixing matrices @xmath152 and @xmath153 used in the coefficients @xmath154 and @xmath155 are given by @xmath156 the three - point function @xmath157 is defined as @xcite @xmath158[(k+p_1)^2-m_2 ^ 2][(k+p_{12})^2-m_3 ^ 2]}\ ] ] with @xmath159 . the finite remainders of the mixing angle renormalization at the external squark legs can be cast into the form of the matrix @xmath160 multiplied by the finite shift @xmath161 which includes the corresponding anti - hermitian counter term @xmath162 of the mixing angle as given in eq . ( [ eq : sqmixct ] ) . in eq . ( [ eq : deltath ] ) the singularity for @xmath163 is cancelled by the anti - hermitian counter term . finally the derivatives of the squark couplings @xmath164 to the higgs bosons are given by @xmath165 the results for the coefficients @xmath166 are ultraviolet and infrared finite after all individual contributions are added up since our renormalized mixing angles fulfill the relation @xmath167 consistently . the scale of @xmath26 in eq.([eq : cphi ] ) is identified with the renormalization scale everywhere apart from the @xmath27 term within the effective bottom mass of eq . ( [ eq : deltab ] ) . it should be noted that our final results do not contain any leading @xmath24-enhanced corrections of the @xmath27-type anymore due to our scheme choices of the effective masses and couplings at nlo . due to this property the problems of a naive renormalization program have been solved consistently leading to moderate radiative corrections to the higgs decay widths into squark - antisquark pairs as will be shown explicitly in the next section . by using power counting arguments along the lines of ref . @xcite it can be shown that our approach resums all leading terms of @xmath168 so that the residual ho corrections are free of these leading terms . in the current eigenstate basis there are three sources of terms proportional to @xmath24 : _ ( i ) _ the higgs couplings to squarks and quarks as in table [ tb : hcoup ] and eq . ( [ eq : hsbsbcoup ] ) which drop out in the relative corrections ; _ ( ii ) _ off - diagonal mass insertions in the sbottom propagators which are power - suppressed by @xmath169 due to the kln theorem and the @xmath169 structure of these insertions ; ( iii ) potential @xmath24-enhancements of the counter terms . the @xmath22 renormalization of @xmath0 as in eq . ( [ eq : daqp ] ) does not involve any @xmath24 enhanced corrections as can also be inferred from the beta functions of the rges for the trilinear couplings up to three - loop order @xcite . the @xmath24 enhancement of the bottom - mass counter term entering the corresponding bottom yukawa couplings involved in the higgs couplings to bottom quarks and the sbottom mass matrix is explicitly absorbed in the effective bottom mass of eq . ( [ eq : deltab ] ) which contains the corresponding threshold correction @xmath27 in resummed form @xcite . therefore the counter terms @xmath170 and @xmath171 are free of @xmath24 enhanced corrections at all orders up to terms which are suppressed by @xmath169 . close to the threshold @xmath172 the nlo susy qcd corrections develop coulomb singularities , @xmath173 which agrees with the usual sommerfeld rescattering correction factor @xcite . these singularities for @xmath174 can be regularized by taking into account the finite decay widths of the squarks . moreover , these coulomb factors can be resummed systematically . both effects are expected to be relevant close to threshold , but are beyond the scope of this paper . on the other hand far above the threshold @xmath175 the nlo corrections approach the asymptotic limit @xmath176 \right . \nonumber \\ & & \left . \hspace*{0.5 cm } + 2\frac{m_s}{g_{\tilde q_i\tilde q_j}^\phi } \frac{\partial g_{\tilde q_i\tilde q_j}^\phi}{\partial a_q } \left [ -\log\frac{\mu_r^2}{m_s^2 } + \frac{1}{4 } \log^2\frac{m_\phi^2}{m_s^2 } + \frac{\zeta_2}{2 } - 2 \right ] + \delta_\phi \right\ } \nonumber \\ \delta_{h , h } & = & \left [ \frac{m_q}{g_{\tilde q_i\tilde q_j}^\phi } \frac{\partial g_{\tilde q_i\tilde q_j}^\phi}{\partial m_q } - 1 \right ] \left [ \log\frac{m_\phi^2}{m_s^2 } - 2 \right ] + \frac{g^\phi_q m_q^2}{g_{\tilde q_i\tilde q_j}^{h , h } } \delta_{ij } \log\frac{m_\phi^2}{m_s^2 } \nonumber \\ & & + ~{\cal t}_{ij}~\frac{m_q}{m_s } \frac{\cos 2\theta_q}{g_{\tilde q_i\tilde q_j}^\phi } \left [ 1-\frac{1}{2}\log\frac{m_s^2}{m_q^2 } \right ] \nonumber \\ \delta_a & = & 0 \ , , \label{eq : largemh}\end{aligned}\ ] ] where we have identified all supersymmetric masses , @xmath177 , and neglected the quark mass against the other masses . the term @xmath178 is given by @xmath179 thus confirming the absence of large corrections of @xmath180 to the on - shell quark and squark mass as well as the mixing angle counter terms as in eq . ( [ eq : sqmixct1 ] ) and renormalizes the quark mass on - shell , large corrections of @xmath181 emerge for the partial higgs decay widths into squarks . ] . the asymptotic result far above the threshold develops a double logarithmic contribution in the second square bracket of eq . ( [ eq : largemh ] ) which originates from the second diagram of fig . [ fg : nlodiav ] in the sudakov limit . it can not be absorbed in an appropriate choice of the renormalization scale @xmath105 but will cancel against the corresponding double logarithm of gluino radiation in association with quark - squark pairs in the large higgs mass limit which has not been taken into account in this work . in the following we will identify @xmath105 with the corresponding higgs mass @xmath182 as the central scale choice .

in particular the treatment of potentially large higher - order corrections originating from the soft susy breaking parameters , the trilinear higgs coupling to sbottoms , and , the higgsino mass parameter , is investigated . the remaining theoretical uncertainties including the susy - qcd corrections are analyzed quantitatively .

we analyze neutral higgs boson decays into squark pairs in the minimal supersymmetric extension of the standard model and improve previous analyses . in particular the treatment of potentially large higher - order corrections originating from the soft susy breaking parameters , the trilinear higgs coupling to sbottoms , and , the higgsino mass parameter , is investigated . the remaining theoretical uncertainties including the susy - qcd corrections are analyzed quantitatively . -1.0 cm psi pr1101 neutral higgs boson decays to squark pairs reanalyzed e. accomando , g. chachamis , f. fugel , m. spira and m. walser _ university of southampton , theory group , southampton so17 1bj , united kingdom + paul scherrer institut , ch-5232 villigen psi , switzerland + institute for theoretical physics , eth zrich , ch8093 zrich , switzerland _

1103.4283

r

the numerical analysis of the neutral higgs boson decays into stop and sbottom pairs is performed for two mssm scenarios , one close to the one of ref . @xcite where we lifted the gluino and squark masses of the first two generations beyond the mass bounds from the lhc @xcite , and a second scenario with large susy - breaking masses and large mixing in the stop sector as representative cases : @xmath183 where @xmath184 and @xmath185 denote the squark and slepton mass parameters of the first two generations . the results of this work have been implemented in the program hdecay @xcite which calculates the mssm higgs decay widths and branching ratios including the relevant higher - order corrections @xcite . we use the rg - improved two - loop expressions for the higgs masses and couplings of ref . @xcite which yield predictions for the higgs boson masses that agree with the diagrammatic calculations of ref . @xcite within 34% in general . thus the leading one- and two - loop corrections have been included in the higgs masses and the effective mixing angle @xmath16 . consistency of our scheme with the scheme and scale choices of ref . @xcite requires the evolution of our sbottom parameters @xmath186 and @xmath187 to the scale @xmath188 and the stop parameters @xmath189 and @xmath190 to the scale @xmath191 since the scales @xmath23 and @xmath192 are of similar order of magnitude we neglect resummation effects so that the relations are given by and @xmath193 are not equal , because they are evaluated for different scales @xmath194 and @xmath195 . we have modified the calculation of ref . @xcite to account for these differences consistently . ] @xmath196 \right\ } \log\frac{q_b^2}{q_0 ^ 2 } \nonumber \\ \overline{m}^2_{\tilde b_r}(q_b ) & = & \overline{m}^2_{\tilde b_l}(q_0 ) + \left\ { - c_f \frac{\alpha_s(q_0)}{\pi } m_3 ^ 2(q_0 ) + \frac{\alpha_b}{4\pi } x_b \right\ } \log\frac{q_b^2}{q_0 ^ 2 } \nonumber \\ \bar a_t(q_t ) & = & \bar a_t(q_0 ) + \left\ { c_f \frac{\alpha_s(q_0)}{\pi } m_3(q_0 ) + \frac{\alpha_t}{4\pi } \bar a_t(q_0 ) + \frac{3}{2 } \frac{\alpha_b}{\pi } \bar a_b(q_0 ) \right\ } \log\frac{q_t^2}{q_0 ^ 2 } \nonumber \\ \overline{m}^2_{\tilde t_l}(q_t ) & = & \overline{m}^2_{\tilde t_l}(q_0 ) + \left\ { - c_f \frac{\alpha_s(q_0)}{\pi } m_3 ^ 2(q_0 ) + \frac{1}{4 } \left [ \frac{\alpha_t}{\pi } x_t + \frac{\alpha_b}{\pi } x_b \right ] \right\ } \log\frac{q_t^2}{q_0 ^ 2 } \nonumber \\ \overline{m}^2_{\tilde t_r}(q_t ) & = & \overline{m}^2_{\tilde t_l}(q_0 ) + \left\ { - c_f \frac{\alpha_s(q_0)}{\pi } m_3 ^ 2(q_0 ) + \frac{\alpha_t}{4\pi } x_t \right\ } \log\frac{q_t^2}{q_0 ^ 2 } \label{eq : transform}\end{aligned}\ ] ] with the abbreviations @xmath197 and the soft susy - breaking higgs mass parameters @xmath198 the top pole mass has been taken as @xmath199 gev , while the bottom quark pole mass has been chosen to be @xmath200 gev , which corresponds to a @xmath22 mass @xmath201 gev . the strong coupling constant has been normalized to @xmath202 which corresponds to the qcd scale @xmath203 mev for 5 active flavours . the related susy qcd scale @xmath122 of eq . ( [ eq : als_susy ] ) amounts to @xmath204 kev in scenario a and @xmath205 kev in scenario b. the @xmath22 masses involved in the scales @xmath206 can be derived as @xmath207 gev and @xmath208 gev while the @xmath22 gluino mass at the input scale @xmath23 amounts to @xmath209 tev in scenario a and @xmath210 tev in scenario b. the squark masses in the two scenarios amount in particular to @xmath211 where @xmath212 and @xmath213 denote the up- and down - type squark masses of the first two generations . in fig . [ fg : vienna_t ] we display the results for the partial decay widths of the heavy neutral higgs particles into stop pairs and the relative corrections in scenario a. since the stops are moderately heavy all decay modes are kinematically allowed for higgs masses above about 560 gev . the partial decay widths range at the few gev level and turn out to be similar for all higgs bosons above the corresponding thresholds except the scalar higgs decay widths into non - diagonal stop pairs which are smaller . apart from the coulomb singularities at threshold the susy qcd corrections are of moderate size in our scheme . ( 100,500)(0,0 ) ( 40.0,120.0 ) ( 40.0,-135.0 ) similar results have been obtained for the neutral higgs boson decay widths into sbottom pairs as shown in fig . [ fg : vienna_b ] . the moderate size of the full susy qcd corrections confirms the proper absorption of the @xmath27 terms as in eq . ( [ eq : deltab ] ) . if the trilinear coupling @xmath0 and the bottom quark mass @xmath214 would be renormalized in the on - shell scheme the susy qcd corrections would increase the lo results by more than an order of magnitude so that the result in the on - shell scheme becomes totally unreliable @xcite . the partial widths of the non - diagonal higgs decays @xmath215 are small , since the mixing factor @xmath216 is small and thus the contributions of the left - right couplings @xmath217 are suppressed , while the diagonal couplings @xmath218 and @xmath219 cancel each other to a large extent in the evaluation of the coupling @xmath220 of eq . ( [ eq : couprot ] ) . using the scheme of ref . @xcite for the mixing angle , i.e. defining the mixing angle counter terms as @xmath221 with @xmath222 or @xmath223 , the results agree with ours within less than 1% of eq . ( [ eq : sqmix ] ) develop sizeable differences to the results in our scheme for squark masses @xmath82 close to each other , where the partial decay widths @xmath224 turn out to be negative thus signalizing a basic problem with the tree - level - like mixing angle . ] . ( 100,500)(0,0 ) ( 40.0,120.0 ) ( 40.0,-135.0 ) ( 100,500)(0,0 ) ( 40.0,120.0 ) ( 40.0,-135.0 ) in order to obtain an estimate of the residual theoretical uncertainties we show the renormalization scale dependence of the partial decay widths into stop and sbottom pairs in fig . [ fg : scale_v ] . the scale dependences of the partial decay widths into stop and sbottom pairs are significantly reduced at nlo . varying the renormalization scale by a factor of 2 around the central scale @xmath225 the theoretical uncertainties can be estimated as 510% for decays into stop and sbottom pairs at nlo . [ fg : br_v ] displays the corresponding branching ratios of the dominant decay modes of the heavy scalar and the pseudoscalar higgs boson in scenario a. it is clearly visible that the decays into stop and sbottom pairs belong to the dominant decay modes for masses above about 300400 gev , i.e. where they are kinematically allowed , reaching branching ratios of up to about 50% in total . moreover , in scenario a the decay modes into @xmath226 s and neutralinos play a significant role , too . ( 100,500)(0,0 ) ( 40.0,120.0 ) ( 40.0,-135.0 ) in fig . [ fg : scen_b ] we display the final results for the scenario b. since the masses @xmath227 are close to or larger than 500 gev , the decay modes @xmath228 are kinematically forbidden for @xmath229 tev . the partial decay widths of decays into stop and sbottom pairs range at the few gev level as in scenario a once they are kinematically allowed . it can clearly be inferred from fig . [ fg : scen_b ] that the susy qcd corrections are of moderate size apart from the threshold regions where the coulomb singularities enhance the size of the corrections . it should be noted that the results with the sbottom mixing angle renormalized via the tree - level relation of eq . ( [ eq : sqmixct1 ] ) would lead to unphysical negative partial decay widths for heavy scalar higgs decays @xmath230 for higgs masses larger than 1 tev , where these decay channels open up , so that this scheme is strongly disfavoured . these negative contributions can be traced back to the uncancelled artificial singularity for @xmath231 in the finite remainders @xmath232 of eq . ( [ eq : deltath ] ) , if @xmath233 is replaced by the counter term @xmath234 of eq . ( [ eq : sqmixct1 ] ) @xcite . ( 100,500)(0,0 ) ( 40.0,120.0 ) ( 40.0,-135.0 ) in fig . [ fg : br_b ] we show the branching ratios of the heavy scalar and the pseudoscalar higgs boson in scenario b as functions of the corresponding higgs masses . as in scenario a the decay modes into stop and sbottom pairs play a significant role , once they are kinematically allowed . this starts to be the case for the heavy scalar higgs boson @xmath235 already for masses above about 400 gev , where the decay into light stop mass eigenstates opens up . the pseudoscalar higgs boson can only decay into mixed pairs of a light and heavy stop and sbottom eigenstates so that these decay modes open up for masses above 900 gev . the decays into charginos and neutralinos contribute significantly for larger higgs masses . ( 100,500)(0,0 ) ( 40.0,120.0 ) ( 40.0,-135.0 ) for smaller values of @xmath24 the decay modes @xmath236 and @xmath237 play a significant role , while the decays into sbottom pairs are usually suppressed . however , the neutral higgs boson decays into stop pairs still play a significant role and can even be the dominant heavy higgs boson decays in a large higgs mass range . qcd corrections to these decay modes are of similar size as in the scenarios with large values of @xmath24 analyzed in this work .

pr1101 neutral higgs boson decays to squark pairs reanalyzed e. accomando , g. chachamis , f. fugel , m. spira and m. walser _ university of southampton , theory group , southampton so17 1bj , united kingdom + paul scherrer institut , ch-5232 villigen psi , switzerland + institute for theoretical physics , eth zrich , ch8093 zrich , switzerland _

we analyze neutral higgs boson decays into squark pairs in the minimal supersymmetric extension of the standard model and improve previous analyses . in particular the treatment of potentially large higher - order corrections originating from the soft susy breaking parameters , the trilinear higgs coupling to sbottoms , and , the higgsino mass parameter , is investigated . the remaining theoretical uncertainties including the susy - qcd corrections are analyzed quantitatively . -1.0 cm psi pr1101 neutral higgs boson decays to squark pairs reanalyzed e. accomando , g. chachamis , f. fugel , m. spira and m. walser _ university of southampton , theory group , southampton so17 1bj , united kingdom + paul scherrer institut , ch-5232 villigen psi , switzerland + institute for theoretical physics , eth zrich , ch8093 zrich , switzerland _

0704.0032

i

the very first data of the kamland collaboration @xcite have been enough to isolate neutrino oscillations as the correct mechanism explaining the solar neutrino problem @xcite , indicating also that large mixing angle ( lma ) was the right solution . the 766.3 ton - yr kamland data sample further strengthens the validity of the lma oscillation interpretation of the data @xcite . current data imply that neutrino have mass . for an updated review of the current status of neutrino oscillations see @xcite . theories of neutrino mass @xcite typically require that neutrinos have non - standard properties such as neutrino electromagnetic transition moments @xcite or non - standard four - fermi interactions ( nsi , for short ) @xcite . the expected magnitude of the nsi effects is rather model - dependent . seesaw - type models lead to a non - trivial structure of the lepton mixing matrix characterizing the charged and neutral current weak interactions @xcite . the nsi which are induced by the charged and neutral current gauge interactions may be sizeable @xcite . alternatively , non - standard neutrino interactions may arise in models where neutrinos masses are radiatively `` calculable '' @xcite . finally , in some supersymmetric unified models , the strength of non - standard neutrino interactions may arise from renormalization and/or threshold effects @xcite . we stress that non - standard interactions strengths are highly model - dependent . in some models nsi strengths are too small to be relevant for neutrino propagation , because they are either suppressed by some large mass scale or restricted by limits on neutrino masses , or both . however , this need not be the case , and there are many theoretically attractive scenarios where moderately large nsi strengths are possible and consistent with the smallness of neutrino masses . in fact one can show that nsi may exist even in the limit of massless neutrinos @xcite . such may also occur in the context of fully unified models like @xmath3 @xcite . we argue that , in addition to the precision determination of the oscillation parameters , it is necessary to test for sub - leading non - oscillation effects that could arise from non - standard neutrino interactions . these are natural outcome of many neutrino mass models and can be of two types : flavor - changing ( fc ) and non - universal ( nu ) . these are constrained by existing experiments ( see below ) and , with neutrino experiments now entering a precision phase @xcite , an improved determination of neutrino parameters and their theoretical impact constitute an important goal in astroparticle and high energy physics @xcite . here we concentrate on the impact of non - standard neutrino interactions on supernova physics . we show how complementary information on the nsi parameters could be inferred from the detection of core - collapse supernova neutrinos . the motivation for the study is twofold . first , if a future sn event takes place in our galaxy the number of neutrino events expected in the current or planned neutrino detectors would be enormous , @xmath4 @xcite . moreover , the extreme conditions under which neutrinos have to travel since they are created in the sn core , in strongly deleptonised regions at nuclear densities , until they reach the earth , lead to strong matter effects . in particular the effect of small values of the nsi parameters can be dramatically enhanced , possibly leading to observable consequences . this paper is planned as follows . in sec . [ sec : preliminaries ] we summarize the current observational bounds on the parameters describing the nsi , including previous works on nsi in sne . in sec . [ sec : neutrino - evolution ] we describe the neutrino propagation formalism as well as the sn profiles which will be used . in sec . [ sec : two - regimes ] we analyze the effect of nsi on the @xmath5 propagation in the inner regions near the neutrinosphere and in the outer regions of the sn envelope . in sec . [ sec : observables ] we discuss the possibility of using various observables to probe the presence of nsi in the neutrino signal of a future galactic sn . finally in sec . [ sec : summary ] we present our conclusions .

we analyze the possibility of probing non - standard neutrino interactions ( nsi , for short ) through the detection of neutrinos produced in a future galactic supernova ( sn ) . this occurs for non - universal nsi strengths of a few % , and for very small flavor - changing nsi above a few .

we analyze the possibility of probing non - standard neutrino interactions ( nsi , for short ) through the detection of neutrinos produced in a future galactic supernova ( sn ) . we consider the effect of nsi on the neutrino propagation through the sn envelope within a three - neutrino framework , paying special attention to the inclusion of nsi - induced resonant conversions , which may take place in the most deleptonised inner layers . we study the possibility of detecting nsi effects in a megaton water cherenkov detector , either through modulation effects in the spectrum due to ( i ) the passage of shock waves through the sn envelope , ( ii ) the time dependence of the electron fraction and ( iii ) the earth matter effects ; or , finally , through the possible detectability of the neutronization burst . we find that the spectrum can exhibit dramatic features due to the internal nsi - induced resonant conversion . this occurs for non - universal nsi strengths of a few % , and for very small flavor - changing nsi above a few .

astro-ph0303556

i

the temporal structure of gamma - ray bursts ( grbs ) varies drastically , with no apparent pattern among bursts . of the @xmath32704 grbs detected by the batse instrument onboard the compton gamma ray observatory ( cgro ) @xcite , less than 10 @xmath2 of the detected light - curve profiles can be categorized as being similar in overall shape or morphology , in that they comprise coherent structures , or pulses of radiation . it is generally believed that these pulses represent the fundamental constituent of grb time profiles ( light curves ) , and appear as asymmetric pulses with a fast rise and a slower decay , often denoted fred `` fast rise and exponential decay '' ( see figure 1 ) . each pulse is assumed to be associated with a separate emission episode , with complex grbs being superpositions of several such episodes , of varying amplitude and intensity . although the duration and amplitude of the fred pulses vary considerably , the shape is the only recurring pattern that can be distinguished among the vast range of complex grb light curves that have been observed . the observed @xmath4-ray pulses are believed to be produced in a highly relativistic outflow , an expanding and collimated fireball , based on the large energies and the short time scales involved . there are several possible mechanisms underlying the emission , although the commonly assumed scenario is that individual pulses are created , when shocks internal to the relativistic outflow , drain the kinetic energy and accelerate leptons which radiate . in this paper we base our discussion on this standard , fireball model , in which the @xmath4-rays arise from the internal shocks at a distance of @xmath5 cm from the initial source @xcite . in the context of the fireball model , the episodic nature of the outflow causes inhomogeneities in the wind to collide and thus create the shocks . the dominant emission mechanisms are most probably non - thermal synchrotron @xcite ) and/or inverse compton emission @xcite , but there have been other suggestions , for instance , thermal , saturated comptonization @xcite . the simplest scenario here is to assume an impulsive heating of the leptons and a subsequent cooling and emission . therefore , the rise phase of the pulse is attributed to the energization of the shell and the decay phase reflects the cooling of the energized particles . as many authors have pointed out , this cooling interpretation does not work well when applied to non - thermal synchrotron and/or inverse compton emission because the radiative cooling timescales alone are typically much too short to explain the pulse durations . for example , if we interpret the average break energy of a grb spectrum ( @xmath6 ) as the characteristic energy of synchrotron self - absorption , then the resulting magnetic field must be extremely high , about @xmath7 to @xmath8 gauss . similar estimates are obtained if we assume equipartition conditions between the lepton energy and the magnetic field . in either case , such a high @xmath9 field would create a synchrotron cooling timescale of the order of @xmath10 seconds in the comoving frame @xcite . one resolution to this problem is to introduce relativistic effects . if the relativistic fireball expands with a lorentz factor of @xmath11 @xmath3 100 , then the geometry of the shell would make radiation emitted off the line of sight delayed and affected by a varying doppler boost ( see figure 2 ) . this would cause the grb spectra to evolve to lower energies and produce decay profiles much longer than the microscopic cooling timescale . these relativistic curvature effects would produce a signature decay profile that can be obtained analytically and searched for in a sample of grb pulses . thus it is of great importance to characterize the individual pulse profiles within grbs and study their parameter distributions . several investigations along the lines of pulse modelling have perviously been made . initially , the pulse profiles were modelled by `` stretched exponential '' functions , both for the rise phase and for the decay phase @xcite : @xmath12 where @xmath13 is the time of the maximum flux , @xmath14 , of the pulse , @xmath15 are the time constants for the rise and the decay phases , respectively , and @xmath16 is the peakedness parameter , equation ( [ stretch ] ) is , strictly speaking , a compressed exponential . ] . such a function is very flexible which makes it possible to describe the whole shape of most pulses , and to quantify the characteristics of the pulses for a statistical analysis , most notably their location , amplitude , width , rise phase , transition phase , and decay phase . @xcite studied a sample of bursts observed by batse and found that the decay generally lies between a pure exponential ( @xmath17 ) and a gaussian ( @xmath18 ) . @xcite studied approximately 2500 pulse structures , in individual energy channels , using the high time resolution batse tts data type . they confirmed the general behavior , namely , that pulses tend to have shorter rise times than decay times . the stretched exponential was introduced because of its very flexible nature , although recently @xcite have proposed that the decay phase would be better described by a power law , which in terms of energy flux is : @xmath19 see [ sec : decay ] for the derivation of equation ( [ fe ] ) and definition of @xmath20 . the motivation for this type of shape is entirely based on empirical relations describing the evolution of the grb spectra during the decay phase of individual pulses . @xcite have recently shown that the form expressed in equation ( [ fe ] ) can be produced through simple relativistic kinematics when applied to a spherical shell expanding at extreme relativistic velocity . the curvature of a relativistic fireball would make the photons emitted off the line of sight ( los ) delayed and affected by a varying doppler boost due to the increasing angle at which the photons were emitted with respect to the observer ( see figure 2 for an illustration ) . they show that this doppler boosting of off - axis photons can reproduce the two well known empirical correlations observed in the grb spectra , namely the hardness - intensity and hardness - fluence correlations ( hic and hfc , respectively ) , in a manner that is highly predictive of the resulting pulse profile . following @xcite , we can derive the expected emission profile from a spherical shell that radiates for an infinitesimal period of time at a peak energy @xmath21 in the comoving frame . the lorentz boosting factor for transformations from the comoving frame to the observers frame of photons emitted from different locations on the surface of a spherical shell is given by @xmath22 where the angle @xmath23 shown in figure 2 . if we define the point where the flow velocity is parallel to the line of sight ( los ) to be @xmath24 , then the difference in light travel time between photons emitted along the los and photons emitted at an angle @xmath25 is given by @xmath26 , which gives @xmath27 . substituting this into the lorentz boost factor , we find @xmath28 for extremely relativistic outflows @xmath29 , and the boost factor becomes @xmath30 the outcome of such a doppler profile is that if the emitted spectra from different parts of the shell are identical , then the observed spectra will be gradually redshifted in time by a factor of @xmath31 as photons from different parts of the shell are received by the observer . the peak energy of the spectra will be observed to evolve as @xmath32 where @xmath33 is the peak energy in the comoving frame . by similar arguments , @xcite show that the resulting bolometric energy flux should evolve as @xmath34 therefore , the decay of the resulting light curve , produced purely by relativistic effects , should exhibit a distinct profile , given by equation ( [ ft_rel ] ) . this result becomes more complicated when one considers the three primary timescales relevant for the shape of the pulse : the shell crossing time , the angular spreading time , and the cooling time . the first two timescales are comparable and dominate over the third and compete with each other to produce the observed results . the authors find that for the case of `` pure '' spherical curvature , where the curvature timescale dominates over the intrinsic light - curve profile ( the shell crossing time ) , the convolved light curves indeed reach the behavior of equation ( [ ft_rel ] ) fairly quickly . however , if the crossing timescale and the curvature timescale are comparable , then the resulting light curve will have some convolved shape and the index value of 2 will only be manifested at late times in the pulse decay . the @xcite treatment assumes that the variations in the low- and high - energy power law indices ( @xmath35 and @xmath36 ) that are commonly used to describe the grb spectra tend to be small over the length of the pulse , which may not necessarily be the case . in order to account for this , @xcite and @xcite used a photon number spectrum which they described by a single power law index equal to the average value of @xmath37 . they examined the resulting light curve and spectral evolution that would be expected if the fred profile were due primarily to relativistic effects . they conclude that the decay phase of fred profiles should be independent of intrinsic spectral variations and should scale roughly as @xmath38 . therefore , one of the primary goals of this paper is to model the fred light curves using an analytic function derived from physical first principles and relations describing the spectral evolution of grbs to obtain parameters that uniquely quantify the shape of smooth pulses and compare those values to the predicted signatures of relativistic kinematics . preliminary results of this analysis have been presented in @xcite and @xcite , where we derived analytic models and tested for a small number of pulses . this paper expands on these previous results to include a much larger sample and a more detailed analysis of the distribution of pulse attributes . in @xmath39 , we review the empirical hardness - intensity and hardness - fluence correlations which are crucial to the derivation of an analytic pulse model . in @xmath40 , we derive an analytic function based on the above - mentioned spectral correlations . in @xmath41 , we define a sample of fred pulses observed by cgro to which we fit our function to obtain a distribution of model parameters , most notably the decay power law index and pulse asymmetries . in @xmath42 , we discuss our measured parameter distributions and compare them to the values predicted by relativistic geometry . we discuss several mechanisms that can skew the distributions away from the expected values .

we analyze the time profiles of individual gamma - ray burst ( grb ) pulses , that are longer than 2 s , by modelling them with analytical functions that are based on physical first principles and well - established empirical descriptions of grb spectral evolution . we have studied a sample of 77 individual grb pulses , allowing us to examine the fluence , pulse width , asymmetry , and rise and decay power - law distributions . we find that the rise phase is best modelled with a power law of average index and that the average decay phase has an index of . although this asymmetry is largely uncorrelated to other pulse properties , a statistically significant trend is observed between the pulse asymmetry and the decay power law index , possibly hinting at the underlying physics .

we analyze the time profiles of individual gamma - ray burst ( grb ) pulses , that are longer than 2 s , by modelling them with analytical functions that are based on physical first principles and well - established empirical descriptions of grb spectral evolution . these analytical profiles are independent of the emission mechanism and can be used to model both the rise and decay profiles allowing for the study of the entire pulse light - curve . using this method , we have studied a sample of 77 individual grb pulses , allowing us to examine the fluence , pulse width , asymmetry , and rise and decay power - law distributions . we find that the rise phase is best modelled with a power law of average index and that the average decay phase has an index of . we also find that the ratio between the rise and decay times ( the pulse asymmetry ) exhibited by the grb pulse shape has an average value of 0.47 which varies little from pulse to pulse and is independent of pulse duration or intensity . although this asymmetry is largely uncorrelated to other pulse properties , a statistically significant trend is observed between the pulse asymmetry and the decay power law index , possibly hinting at the underlying physics . we compare these parameters with those predicted to occur if individual pulse shapes are created purely by relativistic curvature effects in the context of the fireball model , a process that makes specific predictions about the shape of grb pulses . the decay index distribution obtained from our sample shows that the average grb pulse fades faster than the value predicted by curvature effects , with only 39 of our sample being consistent with the curvature model . we discuss several refinements of the relativistic curvature scenario that could naturally account for these observed deviations , such as symmetry breaking and varying relative time - scales within individual pulses .

astro-ph0303556

c

the fit results presented above indicate that the analytic functions derived in 3 are very successful in describing the overall profile of individual grb pulses . these descriptions differ from those used in previous modelling surveys as they are motivated by physical first principles within the general fireball model with the requirement that the previously observed empirical relations for the spectral evolution must hold . these descriptions also build on the original @xcite analysis by including a description of the rise phase of the pulse . of the two assumed rise profiles presented in 2 , a simple , power - law rise seems to better describe the majority of the fred pulses examined . this is one of the simplest assumptions that can be made regarding the dynamic ( or shell crossing ) phase of a grb pulse and may point to the explicit time - dependance of the parameters internal to the shock such as thompson depth or the magnetic field . hence , the measured pulse parameters have the potential to be used to diagnose pulse characteristics , such as bulk lorentz factors , @xmath11 , shell radii , and thickness . the decay power - law index appears to cover a wide range of values with a median centered around 2.39 @xmath155 0.12 , which is 3.25 @xmath163 steeper than the analytically derived value of @xmath164 for pulse profiles created principally by relativistic effects due to spherical symmetric shells . overall , 30 of the 77 pulses that we analyzed had decay indices that were consistent ( within 1@xmath163 ) with the predicted @xmath164 value , constituting 39@xmath2 of our sample . we note that the distribution of hic indices , which were shown in @xmath40 to be directly related to the decay index , found by @xcite also has a broad distribution , with several cases differing substantially from @xmath165 . there are several mechanisms that can cause the decay envelope to deviate from the predicted spherical scenario , but the most obvious would be the breaking of local spherical symmetry . both prolate and oblate shell geometries as seen by the observer would create light curves with resulting power - law indices that differ from the spherical case . in @xmath39 we derived the shape that the light curve is expected to take if the pulse profile were created purely by a spherical shell . in the case of an elliptical geometry , the time delay between the arrival of off axis photons will be given by @xmath166 , where @xmath167 is the radius of the shell at @xmath24 . the radius @xmath168 of the shell is no longer independent of the angle @xmath25 , and is given by @xmath169 where e is the eccentricity of the shell , a is the semi - major axis , and @xmath170 . substituting this back into @xmath171 , we find that @xmath172 solving for @xmath173 and substituting into the doppler boost expression ( equation [ doppler ] ) gives the doppler profile ( doppler boost as a function of time ) for elliptical shells @xmath174 following from the discussion in @xmath39 , the resulting evolution of the spectral break - energy and light curve of the energy - flux should follow @xmath175 and @xmath176 , so the profile of the varying doppler boost should directly give rise to the time dependence of the @xmath59 evolution and the pulse light curve . the doppler profile , expressed in equation [ doppler2 ] , is shown for several different prolate and oblate shock fronts in figure 13 , with the corresponding shell geometry plotted as an inset . it shows that the prolate shells ( solid lines ) have steeper doppler profiles resulting in asymptotic power law slopes which are greater than the spherical case ( thick solid line ) whereas the opposite is true for the oblate geometries ( dashed lines ) . the extreme limit of the oblate scenario is such that the shell becomes a parallel slab , in which case for an unresolved source the doppler profile approaches zero and any pulse evolution is directly due to the shell s intrinsic emission profile . because of this effect , the observed range of power - law decay indices may be explained by a simple distribution of shell geometries , where the median decay index of 2.39 @xmath155 0.12 would indicate that , in the context of relativistic curvature , the majority of the analyzed pulses were produced by shells with a degree of curvature greater than that exhibited by a spherical shell . such conditions are not unreasonable in the context of the fireball model and a simple angular dependance of the bulk lorentz factor can easily produce an elliptical shock front that evolves as the shock propagates . the evolution of the shock geometry , from oblate at early times to prolate at later times , and a variation in the time at which the shell `` ignites '' during this evolution , could account for the distribution of decay indices . @xcite and @xcite provide several other arguments in support of the breaking of local spherical symmetry , the most prominent being that the pulse photon light curves appear to evolve uncoupled to the grb spectra . they find that the grb spectra also evolve faster than the predicted rate of evolution due to the simple boost factor that is expected from a spherically symmetric shell . according to the investigation performed by @xcite , this result is consistent with our findings that the average light curve profile also decays faster than predicted . in the context of their model , a range of relative sizes between the comoving and the curvature timescales defined in @xmath39 can result in a variety of pulse shapes . light curves that exhibit a substantially different shape than that predicted by spherical curvature are attributed to a scenario where the comoving timescale dominates within a burst that already has an intrinsically fast decay rate ( @xmath177 ) of the comoving light curve . this , according to their model , must also be manifested in the spectral evolution in a corresponding manner . therefore , an analysis of the spectral evolution rates and @xmath35 values of the pulses that vary the furthest from the predicted scenario of @xmath164 may test how much these values affect the resulting light curve profiles . this research is currently being pursued ( f. ryde , & d. kocevski in prep ) . the asymmetry results are rather surprising and the reason for the tight asymmetry distribution among such a variety of grb pulses is not immediately clear . it would indicate that the dynamical and angular timescales are not fully independent and that the observed rate at which the shell becomes active is dependant on the decay timescale and hence the curvature of the shell . a situation can be envisioned where a short comoving rise profile is delayed and boosted to the same degree as the shell s intrinsic cooling profile . if both of these timescales are extremely short as compared to the angular spreading timescale , then a relationship can be produced between the observed rise and decay profile . this effect could produce a narrow asymmetry distribution and would also predict a correlation between the rise timescale and decay power - law indices , which is indeed observed in our sample . @xcite have discussed extensively the effect of varying intrinsic emission profiles and angular spreading timescales on the resulting light curve that is observed . they find that the resulting pulse asymmetry relies heavily on the convolution of the intrinsic emission profile and the angular spreading timescale . therefore , future modelling of pulse timescales and shell geometries , with the constraint that they produce the observed asymmetry distribution , may yield clues to the intrinsic profile of the emission episode . we are grateful to the grossc at nasa / gsfc for providing the heasarc online service . we should also like to thank dr . vah petrosian for his valuable discussions and insights . d.k . wishes to express his gratitude to the department of physics at stanford university for hospitality and also acknowledges the nasa gsrp fellowship program for their support . f.r . acknowledges financial support from the swedish foundation for international cooperation in research and higher education ( stint ) and the ludovisi boncomagni , ne bildt , foundation . 910721 & 563 & 1.65 & 2.13 @xmath155 0.29 & 24.8 @xmath155 3.97 & 0.77 @xmath155 0.15 & 1.34 @xmath155 0.07 & 1.34 & 1.34 + 911016 & 907 & 1.47 & 3.74 @xmath155 0.34 & 19.7 @xmath155 2.56 & 0.85 @xmath155 0.11 & 1.46 @xmath155 0.05 & 1.29 & 1.29 + 911022 & 914 & 0.55 & 2.64 @xmath155 0.33 & 6.27 @xmath155 0.76 & 1.81 @xmath155 0.10 & 2.33 @xmath155 0.14 & 0.86 & 0.96 + 911031 & 973 & 2.87 & 5.71 @xmath155 0.41 & 17.9 @xmath155 0.99 & 1.23 @xmath155 0.08 & 3.07 @xmath155 0.10 & 1.34 & 1.35 + 911031 & 973 & 23.9 & 3.17 @xmath155 0.40 & 17.9 @xmath155 2.03 & 1.21 @xmath155 0.23 & 2.15 @xmath155 0.09 & 1.27 & 1.33 + 911104 & 999 & 3.94 & 12.4 @xmath155 0.65 & 1.98 @xmath155 0.20 & 2.40 @xmath155 0.33 & 2.73 @xmath155 0.07 & 1.24 & 3.05 + 911209 & 1157 & 4.83 & 12.2 @xmath155 0.55 & 8.58 @xmath155 1.07 & 1.60 @xmath155 0.58 & 1.62 @xmath155 0.10 & 1.30 & 1.58 + 920216 & 1406 & 3.14 & 2.10 @xmath155 0.27 & 25.1 @xmath155 3.18 & 0.95 @xmath155 0.07 & 2.29 @xmath155 0.11 & 1.06 & 1.07 + 920307 & 1467 & 4.32 & 2.59 @xmath155 0.27 & 18.3 @xmath155 2.05 & 2.53 @xmath155 0.08 & 2.62 @xmath155 0.08 & 1.01 & 1.06 + 920801 & 1733 & 3.30 & 3.20 @xmath155 0.32 & 17.3 @xmath155 1.73 & 1.97 @xmath155 0.08 & 2.05 @xmath155 0.06 & 1.17 & 1.29 + 920830 & 1883 & 1.26 & 5.36 @xmath155 0.37 & 8.19 @xmath155 0.51 & 1.48 @xmath155 0.04 & 2.60 @xmath155 0.08 & 1.06 & 1.07 + 920925 & 1956 & 2.81 & 2.80 @xmath155 0.28 & 10.7 @xmath155 1.04 & 1.31 @xmath155 0.38 & 3.31 @xmath155 0.22 & 1.47 & 1.50 + 921015 & 1989 & 116 & 2.96 @xmath155 0.31 & 18.3 @xmath155 1.83 & 2.00 @xmath155 0.18 & 2.40 @xmath155 0.06 & 1.35 & 1.66 + 921207 & 2083 & 8.59 & 46.6 @xmath155 0.92 & 4.00 @xmath155 0.20 & 2.12 @xmath155 0.05 & 1.85 @xmath155 0.02 & 1.25 & 1.71 + 921218 & 2102 & 1.88 & 1.79 @xmath155 0.26 & 10.9 @xmath155 1.51 & 1.90 @xmath155 1.03 & 2.94 @xmath155 0.29 & 0.89 & 0.95 + 930120 & 2138 & 1.50 & 7.08 @xmath155 0.39 & 9.73 @xmath155 1.27 & 2.00 @xmath155 0.06 & 4.00 @xmath155 0.20 & 1.28 & 1.15 + 930120 & 2138 & 48.9 & 35.6 @xmath155 0.59 & 9.73 @xmath155 1.77 & 1.46 @xmath155 0.47 & 2.23 @xmath155 0.29 & 0.96 & 1.00 + 930120 & 2138 & 86.1 & 9.81 @xmath155 0.10 & 15.0 @xmath155 1.18 & 0.42 @xmath155 0.06 & 2.10 @xmath155 0.11 & 1.29 & 1.35 + 930214 & 2193 & 10.9 & 1.78 @xmath155 0.26 & 70.3 @xmath155 10.3 & 0.80 @xmath155 0.01 & 2.50 @xmath155 0.04 & 1.04 & 1.02 + 930612 & 2387 & 6.57 & 4.11 @xmath155 0.33 & 32.8 @xmath155 2.91 & 1.20 @xmath155 0.04 & 2.87 @xmath155 0.06 & 1.07 & 1.17 + 930807 & 2484 & 1.87 & 1.75 @xmath155 0.27 & 13.5 @xmath155 1.87 & 1.26 @xmath155 0.29 & 3.26 @xmath155 0.43 & 1.10 & 1.17 + 930909 & 2519 & 63.5 & 1.68 @xmath155 0.28 & 15.0 @xmath155 3.21 & 1.69 @xmath155 0.16 & 1.43 @xmath155 0.12 & 1.13 & 1.21 + 930914 & 2530 & 114 & 2.03 @xmath155 0.27 & 25.3 @xmath155 3.28 & 1.12 @xmath155 0.05 & 2.34 @xmath155 0.12 & 1.13 & 1.14 + 931127 & 2662 & 1.10 & 1.82 @xmath155 0.29 & 14.9 @xmath155 2.94 & 1.20 @xmath155 0.05 & 1.30 @xmath155 0.03 & 1.07 & 1.04 + 931128 & 2665 & 1.34 & 2.10 @xmath155 0.31 & 12.8 @xmath155 2.25 & 1.74 @xmath155 0.43 & 1.65 @xmath155 0.10 & 1.00 & 1.16 + 931221 & 2700 & 53.8 & 4.17 @xmath155 0.35 & 13.0 @xmath155 1.13 & 0.75 @xmath155 0.09 & 3.01 @xmath155 0.18 & 1.33 & 1.52 + 940313 & 2880 & 0.4 & 3.20 @xmath155 0.29 & 4.16 @xmath155 0.54 & 1.32 @xmath155 0.27 & 2.13 @xmath155 0.15 & 1.51 & 1.61 + 940410 & 2919 & 0.30 & 6.11 @xmath155 0.39 & 10.6 @xmath155 0.80 & 1.55 @xmath155 0.14 & 1.97 @xmath155 0.04 & 1.28 & 1.55 + 940529 & 3003 & 9.56 & 3.04 @xmath155 0.32 & 28.8 @xmath155 3.13 & 1.51 @xmath155 0.04 & 2.62 @xmath155 0.08 & 1.11 & 1.21 + 940830 & 3143 & 0.63 & 2.69 @xmath155 0.29 & 5.5 @xmath155 0.76 & 1.84 @xmath155 0.68 & 2.40 @xmath155 0.14 & 1.04 & 1.16 + 940904 & 3155 & 0.66 & 1.92 @xmath155 0.26 & 3.39 @xmath155 0.46 & 1.24 @xmath155 0.21 & 3.84 @xmath155 0.60 & 0.88 & 1.01 + 941023 & 3256 & 1.25 & 1.89 @xmath155 0.22 & 14.0 @xmath155 2.68 & 0.80 @xmath155 0.02 & 1.50 @xmath155 0.04 & 1.28 & 1.16 + 941026 & 3257 & 3.27 & 3.21 @xmath155 0.27 & 36.8 @xmath155 5.49 & 0.52 @xmath155 0.04 & 1.57 @xmath155 0.07 & 1.02 & 1.08 + 941026 & 3259 & 4.65 & 2.28 @xmath155 0.23 & 25.0 @xmath155 3.28 & 1.55 @xmath155 0.17 & 2.89 @xmath155 0.16 & 0.96 & 1.15 + 941121 & 3290 & 2.91 & 10.9 @xmath155 0.36 & 1.98 @xmath155 0.47 & 1.47 @xmath155 0.25 & 2.04 @xmath155 0.09 & 0.92 & 1.52 + 950211 & 3415 & 0.25 & 10.3 @xmath155 0.40 & 6.91 @xmath155 1.77 & 2.76 @xmath155 2.14 & 1.68 @xmath155 0.15 & 0.99 & 1.22 + 950211 & 3415 & 11.5 & 2.36 @xmath155 0.11 & 3.78 @xmath155 0.34 & 1.26 @xmath155 0.14 & 2.47 @xmath155 0.17 & 1.48 & 1.36 + 950624 & 3648 & 2.65 & 5.91 @xmath155 0.31 & 22.0 @xmath155 3.97 & 0.84 @xmath155 0.44 & 2.67 @xmath155 0.60 & 0.82 & 0.82 + 950624 & 3648 & 24.1 & 36.6 @xmath155 1.22 & 17.0 @xmath155 3.51 & 1.10 @xmath155 0.04 & 2.40 @xmath155 0.14 & 1.03 & 0.97 + 950624 & 3648 & 40.9 & 1243 @xmath155 3.71 & 11.7 @xmath155 1.16 & 2.54 @xmath155 0.07 & 1.57 @xmath155 0.03 & 1.45 & 1.19 + 950818 & 3765 & 66.1 & 25.9 @xmath155 0.54 & 8.83 @xmath155 0.98 & 2.42 @xmath155 0.07 & 1.84 @xmath155 0.02 & 1.50 & 1.43 + 951016 & 3870 & 0.43 & 14.1 @xmath155 0.46 & 5.76 @xmath155 0.52 & 1.38 @xmath155 0.09 & 1.42 @xmath155 0.02 & 1.52 & 1.78 + 951019 & 3875 & 0.21 & 3.02 @xmath155 0.23 & 4.03 @xmath155 0.42 & 0.96 @xmath155 0.11 & 1.73 @xmath155 0.13 & 1.57 & 1.51 + 951030 & 3886 & 0.20 & 2.27 @xmath155 0.21 & 2.82 @xmath155 0.65 & 1.27 @xmath155 0.12 & 2.45 @xmath155 0.27 & 1.00 & 1.55 + 951102 & 3892 & 0.61 & 1.86 @xmath155 0.20 & 5.31 @xmath155 0.51 & 1.26 @xmath155 0.24 & 2.67 @xmath155 0.29 & 0.97 & 1.03 + 951213 & 3954 & 0.70 & 8.45 @xmath155 0.39 & 10.3 @xmath155 0.70 & 4.31 @xmath155 3.52 & 2.54 @xmath155 0.50 & 1.06 & 1.52 + 951228 & 4157 & 7.67 & 2.32 @xmath155 0.24 & 17.7 @xmath155 2.16 & 1.92 @xmath155 0.09 & 2.53 @xmath155 0.12 & 1.21 & 1.36 + 960113 & 4350 & 0.51 & 3.52 @xmath155 0.25 & 6.66 @xmath155 0.83 & 2.41 @xmath155 0.16 & 1.95 @xmath155 0.07 & 1.29 & 1.86 + 960113 & 4350 & 14.3 & 1.65 @xmath155 0.27 & 6.66 @xmath155 0.75 & 1.00 @xmath155 0.02 & 2.00 @xmath155 0.03 & 1.39 & 1.22 + 960113 & 4350 & 34.1 & 8.71 @xmath155 0.45 & 6.66 @xmath155 0.98 & 1.70 @xmath155 0.34 & 2.66 @xmath155 0.23 & 1.30 & 1.47 + 960114 & 4368 & 2.45 & 58.6 @xmath155 0.83 & 10.0 @xmath155 0.75 & 2.87 @xmath155 0.68 & 2.53 @xmath155 0.07 & 1.26 & 2.01 + 960530 & 5478 & 1.98 & 3.10 @xmath155 0.24 & 14.3 @xmath155 1.43 & 0.98 @xmath155 0.08 & 2.54 @xmath155 0.17 & 0.97 & 0.98 + 960530 & 5478 & 261 & 7.69 @xmath155 1.70 & 37.2 @xmath155 6.22 & 1.20 @xmath155 0.02 & 3.00 @xmath155 0.08 & 1.12 & 1.16 + 960613 & 5495 & 0.23 & 2.39 @xmath155 0.23 & 5.44 @xmath155 1.66 & 0.63 @xmath155 0.34 & 1.65 @xmath155 0.16 & 1.16 & 1.14 + 960624 & 5517 & 0.83 & 2.06 @xmath155 0.23 & 7.42 @xmath155 0.79 & 1.72 @xmath155 0.11 & 3.61 @xmath155 0.37 & 1.04 & 1.05 + 960628 & 5523 & 1.03 & 3.73 @xmath155 0.28 & 6.98 @xmath155 0.71 & 1.92 @xmath155 0.07 & 3.17 @xmath155 0.15 & 1.19 & 1.34 + 960715 & 5541 & 1.32 & 1.84 @xmath155 0.23 & 12.6 @xmath155 1.68 & 1.51 @xmath155 0.47 & 2.96 @xmath155 0.39 & 1.13 & 1.16 + 960912 & 5601 & 7.55 & 4.94 @xmath155 0.29 & 9.00 @xmath155 0.74 & 1.30 @xmath155 0.26 & 2.64 @xmath155 0.16 & 1.29 & 1.38 + 970405 & 6159 & 3.20 & 2.16 @xmath155 0.25 & 12.0 @xmath155 1.79 & 1.82 @xmath155 0.13 & 1.30 @xmath155 0.11 & 1.18 & 1.28 + 970815 & 6335 & 98.3 & 4.29 @xmath155 0.29 & 21.3 @xmath155 3.02 & 1.29 @xmath155 0.08 & 3.52 @xmath155 0.40 & 1.10 & 1.17 + 970925 & 6397 & 3.30 & 6.02 @xmath155 0.30 & 20.4 @xmath155 1.44 & 1.25 @xmath155 0.07 & 2.25 @xmath155 0.05 & 1.61 & 1.53 + 971127 & 6504 & 3.12 & 2.79 @xmath155 0.24 & 22.1 @xmath155 3.00 & 1.18 @xmath155 0.12 & 1.78 @xmath155 0.08 & 1.00 & 1.09 + 980301 & 6621 & 32.5 & 6.85 @xmath155 0.34 & 7.36 @xmath155 0.47 & 1.51 @xmath155 0.05 & 1.65 @xmath155 0.03 & 1.21 & 1.59 + 980302 & 6625 & 5.12 & 2.04 @xmath155 0.26 & 31.4 @xmath155 4.19 & 1.32 @xmath155 0.05 & 3.12 @xmath155 0.19 & 1.04 & 1.16 + 980401 & 6672 & 6.85 & 5.60 @xmath155 0.29 & 3.80 @xmath155 0.41 & 1.17 @xmath155 0.07 & 2.34 @xmath155 0.17 & 0.78 & 0.84 + 980718 & 6930 & 31.7 & 5.76 @xmath155 0.36 & 6.34 @xmath155 0.30 & 1.51 @xmath155 0.04 & 3.70 @xmath155 0.16 & 1.15 & 1.10 + 990102 & 7293 & 3.53 & 3.06 @xmath155 0.23 & 25.2 @xmath155 2.92 & 0.96 @xmath155 0.07 & 1.99 @xmath155 0.07 & 1.20 & 1.20 + 990102 & 7295 & 2.14 & 3.50 @xmath155 0.35 & 8.50 @xmath155 1.05 & 1.20 @xmath155 0.42 & 2.08 @xmath155 0.35 & 0.97 & 0.98 + 990316 & 7475 & 8.54 & 3.87 @xmath155 0.29 & 34.4 @xmath155 2.96 & 0.99 @xmath155 0.07 & 4.03 @xmath155 0.19 & 1.12 & 1.05 + 990505 & 7548 & 3.7 & 3.14 @xmath155 0.25 & 10.6 @xmath155 1.02 & 1.92 @xmath155 0.46 & 2.94 @xmath155 0.17 & 0.82 & 1.04 + 990528 & 7588 & 2.76 & 2.32 @xmath155 0.24 & 15.5 @xmath155 1.77 & 1.15 @xmath155 0.13 & 3.11 @xmath155 0.25 & 0.83 & 0.92 + 990707 & 7638 & 1.12 & 1.92 @xmath155 0.22 & 15.0 @xmath155 2.68 & 1.27 @xmath155 0.30 & 1.22 @xmath155 0.06 & 1.30 & 1.33 + 990712 & 7648 & 4.45 & 1.78 @xmath155 0.21 & 24.7 @xmath155 3.45 & 1.22 @xmath155 0.13 & 3.79 @xmath155 0.41 & 1.05 & 1.17 + 990816 & 7711 & 1.86 & 3.97 @xmath155 0.26 & 13.2 @xmath155 1.32 & 0.85 @xmath155 0.04 & 3.26 @xmath155 0.24 & 1.34 & 1.48 + 323 & 8049 & 30.5 & 1.77 @xmath155 0.19 & 36.6 @xmath155 4.23 & 1.13 @xmath155 0.04 & 4.97 @xmath155 0.42 & 1.04 & 1.24 + 519 & 8111 & 4.98 & 4.33 @xmath155 0.28 & 13.8 @xmath155 1.68 & 1.69 @xmath155 0.03 & 1.48 @xmath155 0.02 & 1.36 & 1.27 +

these analytical profiles are independent of the emission mechanism and can be used to model both the rise and decay profiles allowing for the study of the entire pulse light - curve . using this method , we also find that the ratio between the rise and decay times ( the pulse asymmetry ) exhibited by the grb pulse shape has an average value of 0.47 which varies little from pulse to pulse and is independent of pulse duration or intensity . we compare these parameters with those predicted to occur if individual pulse shapes are created purely by relativistic curvature effects in the context of the fireball model , a process that makes specific predictions about the shape of grb pulses . the decay index distribution obtained from our sample shows that the average grb pulse fades faster than the value predicted by curvature effects , with only 39 of our sample being consistent with the curvature model . we discuss several refinements of the relativistic curvature scenario that could naturally account for these observed deviations , such as symmetry breaking and varying relative time - scales within individual pulses .

we analyze the time profiles of individual gamma - ray burst ( grb ) pulses , that are longer than 2 s , by modelling them with analytical functions that are based on physical first principles and well - established empirical descriptions of grb spectral evolution . these analytical profiles are independent of the emission mechanism and can be used to model both the rise and decay profiles allowing for the study of the entire pulse light - curve . using this method , we have studied a sample of 77 individual grb pulses , allowing us to examine the fluence , pulse width , asymmetry , and rise and decay power - law distributions . we find that the rise phase is best modelled with a power law of average index and that the average decay phase has an index of . we also find that the ratio between the rise and decay times ( the pulse asymmetry ) exhibited by the grb pulse shape has an average value of 0.47 which varies little from pulse to pulse and is independent of pulse duration or intensity . although this asymmetry is largely uncorrelated to other pulse properties , a statistically significant trend is observed between the pulse asymmetry and the decay power law index , possibly hinting at the underlying physics . we compare these parameters with those predicted to occur if individual pulse shapes are created purely by relativistic curvature effects in the context of the fireball model , a process that makes specific predictions about the shape of grb pulses . the decay index distribution obtained from our sample shows that the average grb pulse fades faster than the value predicted by curvature effects , with only 39 of our sample being consistent with the curvature model . we discuss several refinements of the relativistic curvature scenario that could naturally account for these observed deviations , such as symmetry breaking and varying relative time - scales within individual pulses .

1703.06022

i

the development of short and intense laser pulses has opened the possibility to control and observe electronic and nuclear motion on the attosecond time scale @xcite . the new light sources are key to probe and manipulate the electronic structure and dynamics in many - electron atoms @xcite and molecules @xcite . for instance , few photon ionization using short pulses results in ejected electrons whose spatial distribution depends on the energy spectrum and angular momentum of the initial state as well as the ionic channels involved @xcite . likewise it has become clear that accurate modelling of time - delays in photoionization require careful consideration of electron - correlation effects ( see , e.g. , refs . @xcite and the recent review ref . accordingly , there is a range of processes that require explicit time - dependent methods capable of treating electron correlations beyond mean - field and single - active electron approximations . in the case of he , it is possible to solve numerically the time - dependent schrdinger equation ( tdse ) ( see , e.g. , refs . @xcite ) . for larger systems , and for photon energies that only affect the valence shell , one can consider two electrons immersed in the mean - field potential produced by the inner electrons @xcite . in general , however , in order to consider more than two electrons in an atom and to make the tdse tractable it is mandatory to use approximations to the wave function and hence the tdse . to this end , the time - dependent configuration - interaction ( td - ci ) method consists of expanding the many - electron wave function as @xmath0 where @xmath1 denotes the full ci hilbert space of all accessible configurations . it is the finite size of @xmath1 that introduces approximations . in eq . , @xmath2 is the time - dependent coefficient of the configuration @xmath3 , formed by a set of spin - orbitals . in this formalism , the tdse corresponds to a set of first - order differential equations for @xmath2 . the description of the continuum , however , demands a large number of orbitals and configurations , which makes the ci approach numerically intractable with increasing number of electrons . to overcome this limitation , there are several methods such as the time - dependent configuration - interaction singles ( td - cis ) @xcite , the time - dependent restricted - active - space configuration - interaction ( td - ras - ci ) @xcite and the time - dependent generalized - active - space configuration - interaction ( td - gas - ci ) method @xcite which impose restrictions on the allowed excitations and the active orbital spaces . these approximations still require many configurations in addition to a careful design of the partitions in the active space . it is also very challenging to extend those methodologies to situations with more than a single electron in the continuum , as is also the case with the @xmath4-matrix method @xcite although some progress has been reported in that direction @xcite . despite the difficulties , it is nevertheless attractive to explore a wave function approach , because of , e.g. , the unambiguous extraction of observables . the theory should ideally reduce as much as possible the number of orbitals needed for an accurate description of the configuration space . a breakthrough along those lines came with the multiconfiguration time - dependent hartree ( mctdh ) method @xcite and the mctdh - fock ( mctdhf ) method ( see , e.g. , refs . @xcite ) , where time - dependent spin - orbitals are introduced in the ansatz , making @xmath5 time - dependent @xmath6 the main advantage of this method is that the use of time - dependent spin - orbitals makes it possible to describe the wave function and , in particular , the continuum with a smaller number of orbitals and configurations than with the time - independent orbitals used in the ci approach corresponding to eq . . the mctdhf method has , e.g. , been applied to describe high - harmonic generation ( hhg ) in low dimensions @xcite , polarization of the continuum @xcite and to calculate cross sections of atomic @xcite and molecular systems @xcite . since the spatial orbitals are time - dependent , the one- and two - body operators must be updated at each time step , leading to a high numerical cost , especially in the 3d case . moreover , as in the ci picture , the use of many orbitals may still imply an intractable number of accessible configurations . there are several strategies to diminish the numerical effort without loss of accuracy , such as the time - dependent occupation - restricted multiple - active - space ( td - ormas ) @xcite , the time - dependent complete - active - space self - consistent - field ( td - casscf ) @xcite and the time - dependent restricted - active - space self - consistent - field ( td - rasscf ) @xcite methods . in particular , the td - rasscf method benefits from the ras to diminish the accessible configurations and hence allows the consideration of only a subset @xmath7 of the configurations in @xmath8 by dividing the active space into two or more parts . among these parts electron excitations take place with certain restrictions @xcite , specified at will , and most often chosen by physical insight into the problem at hand . in the present work we apply the td - rasscf method with double excitations ( td - rasscf - d ) to address the role of electron correlation in be in the ground state , in photoionization spectra induced by short xuv pulses and in time - delay studies . the td - rasscf - d method was previously shown to be accurate and computationally efficient in 1d cases @xcite , and the td - rasscf theory was recently extended with a space partitioning concept @xcite . the main advantage of the approach resides in the possibility of selecting an appropriate ras which captures the most important configurations for a given system and physical process . for a very recent discussion of these aspects in the case of cold atomic bosons see ref . @xcite . the flexibility in choosing the ras is remarkable in the imaginary time propagation ( itp ) , where we show that the active space concept facilitates the convergence . by identifying the most important active orbitals , the td - rasscf - d method can be as accurate as the mctdhf method , but with a smaller number of configurations highlighting the important role of double excitations for the ground state . the application of this method to 3d systems is , however , still computationally challenging due to the large number of non - zero matrix elements of the two - body operator . to overcome this issue , we develop and use the _ coupled basis _ method to diminish the number of operations required to evaluate the two - body operator . in addition to the itp studies for the ground state , we present studies of be subject to short linearly polarized xuv laser pulses . in general the photoelectron energy spectra ( pes ) reveal detailed properties of atomic , molecular or solid targets , including energies , structural and symmetrical properties of the states of the system . for instance , the directional distribution of the ejected electrons depends on the angular momentum of the final and initial states and the number of absorbed photons @xcite . as for the ground state studies , the present td - rasscf - d method allows the identification of the most important active orbitals for an accurate description of the photoelectron spectra . furthermore , the electronic dynamics of the remaining ion during the photoionization has an impact on the outgoing electrons , enclosed , in particular , in the apparent time of ionization @xcite . the experimental and theoretical computation of this quantity is very sensitive to the method , and constitutes a fundamental probe of the many - body dynamics @xcite . in this work we investigate the relative time - delay in ionization between the channel ( i ) be[@xmath9)@xmath10s@xmath11 @xmath12 [ be@xmath13(@xmath14 ) + @xmath15 ] @xmath10p@xmath16 , and the channel ( ii ) be[@xmath9)@xmath10s@xmath11 @xmath12 [ be@xmath13(@xmath17 ) + @xmath18 ] @xmath10p@xmath16 with @xmath19 . as is evident from dipole selection rules , process ( i ) is possible without electron - electron correlation , while in process ( ii ) ionization is accompanied by a shakeup in the ion and requires electron - electron correlation . the study shows that an accurate description of time - delays in be requires a treatment beyond the mean - field time - dependent hartree - fock theory , and identifies the ras scheme that provides an accurate value for the delay . the paper is organized as follows . in sec . [ sec : the_system_and_the_method ] we describe the hamiltonian , the td - rasscf - d method and the numerical techniques used , including the coupled basis method . in sec . [ sec : results ] we present the results for be , both concerning the ground state studies ( sec . [ sec : results].a ) , the pes ( sec . [ sec : results].b ) and the relative time - delays in ionization ( sec . [ sec : results].c ) . [ sec : conclusions_and_outlook ] summarizes the main findings and concludes . atomic units are used throughout unless indicated otherwise .

we apply a three - dimensional ( 3d ) implementation of the time - dependent restricted - active - space self - consistent - field ( td - rasscf ) method to investigate effects of electron correlation in the ground state of be as well as in its photoionization dynamics by short xuv pulses , including time - delay in photoionization . first , we obtain the ground state by propagation in imaginary time . we show that the flexibility of the td - rasscf on the choice of the active orbital space makes it possible to consider only relevant active space orbitals , facilitating the convergence to the ground state compared to the multiconfigurational time - dependent hartree - fock method , used as a benchmark to show the accuracy and efficiency of td - rasscf . we compare the spectra for different ras schemes , and in this way we identify the orbital spaces that are relevant for an accurate description of the photoelectron spectra .

we apply a three - dimensional ( 3d ) implementation of the time - dependent restricted - active - space self - consistent - field ( td - rasscf ) method to investigate effects of electron correlation in the ground state of be as well as in its photoionization dynamics by short xuv pulses , including time - delay in photoionization . first , we obtain the ground state by propagation in imaginary time . we show that the flexibility of the td - rasscf on the choice of the active orbital space makes it possible to consider only relevant active space orbitals , facilitating the convergence to the ground state compared to the multiconfigurational time - dependent hartree - fock method , used as a benchmark to show the accuracy and efficiency of td - rasscf . second , we solve the equations of motion to compute photoelectron spectra of be after interacting with a short linearly polarized xuv laser pulse . we compare the spectra for different ras schemes , and in this way we identify the orbital spaces that are relevant for an accurate description of the photoelectron spectra . finally , we investigate the effects of electron correlation on the magnitude of the relative time - delay in the photoionization process into two different ionic channels . one channel , the ground state channel in the ion , is accessible without electron correlation . the other channel is only accessible when including electron correlation . the time - delay is highly sensitivity to the choice of the active space , and hence to the account of electron - electron correlation .

1703.06022

r

in this section , we describe the impact of electron correlation on the ground state of be and the photoionization process , including time - delays , due to the interaction with a linearly polarized xuv laser pulse of short duration . we use be for these illustrative calculations because it allows for converged mctdhf reference data . in this way we can identify the most important part of the orbital space for a given physical observable . we describe the radial coordinate from @xmath157 to @xmath158 using 8 fes of length @xmath159 . from @xmath160 to the end of the box we add elements of length @xmath161 , with @xmath162 . to calculate the ground state we perform an imaginary - time propagation ( itp ) of an initial guess function in a box from @xmath163 . the dynamics due to the interaction with the laser is subsequently described performing a real - time propagation ( rtp ) , where we set the end of the box to @xmath164 by adding 43 elements of length 4 with 8 nodes in each . for the itp , the angular part of the orbitals is described with a maximum orbital angular momentum @xmath165 and magnetic quantum numbers @xmath166 for 7 or less orbitals and @xmath167 and @xmath168 otherwise . for the rtp , we use @xmath167 and @xmath168 in all the cases , and this is sufficient to obtain convergence for the xuv pulses considered in the present work . for the itp and rtp we use an adaptative runge - kutta propagator . the typical time step @xmath169 ranges from @xmath170 atomic units . .[tab : ground_state_energies ] ground state energies of be for several ras schemes . @xmath30 and @xmath33 denote the numbers of spatial orbitals in @xmath29 and @xmath32 ( fig . [ fig : fig1 ] ) , respectively . when all the orbitals are in @xmath29 ( @xmath171 and @xmath172 ) , the td - rasscf approach is equal to the mctdhf approach with @xmath173 orbitals . when , for be , @xmath174 , the td - rasscf approach is equal to the tdhf approach . the @xmath175 entry denoted by _ random _ is an example , where we use a random initial wave function . in the other cases the initial guess wave function was designed as described in the text . [ cols="^,^,^,^,^ " , ] to obtain the ground state we perform an itp for an appropriate initial guess function @xcite . the choice of the initial guess function is crucial , since there exists an infinite number of non - physical standing wave solutions which are local minima of the td variational principle @xcite . to ensure that the ground state obtained in the itp is not affected by the selection of the initial guess function we may choose to take an initial random wave function @xcite . the coefficients @xmath176 of the orbitals [ eq . ( [ eq : phip ] ) ] are chosen random , and the amplitudes @xmath177 are taken as @xmath178 , where @xmath179 is a random number @xmath180 and @xmath181 the number of configurations . this strategy , however , turns out to be problematic for many ras partitions , including the mctdhf case , due to the many local minima of the energy located in the manifold @xcite . then a more careful consideration of the design of the initial guess wave function becomes mandatory in order to reach a good approximation , ideally the global minimum , for the ground state @xcite . one of the great advantages of the td - rasscf method is that we can choose the partition in the active space which induces the most important slater determinants for a given physical process . in the 3d case this choice becomes very important , since an appropriate set of configurations can facilitate the couplings of the spherical harmonics to the @xmath182 ground state . for example , in the case of be , the main configuration for the ground state is @xmath183 , and an appropriate ras scheme would be two spatial orbitals in the @xmath29 space and the rest in @xmath32 . the orbitals in the @xmath29 space would be close to @xmath184-type orbitals , whereas the orbitals in @xmath32 would be linear combinations of a set of orbitals which together with the orbitals in @xmath29 can couple to @xmath182 . as an example we focus on the case of @xmath175 orbitals , included in table [ tab : ground_state_energies ] , where we show the ground state energy for different ras schemes . on the one hand , we use a random initial guess function for the mctdhf approach with @xmath175 orbitals and we obtain the energy @xmath185 ( the entry in table [ tab : ground_state_energies ] denoted by _ random _ ) . this value of the mctdhf energy is in agreement with the energy previously reported in ref . @xcite . on the other hand we design an initial guess function as follows : i ) we choose two orbitals as the @xmath186 and @xmath187 hydrogenic functions for @xmath188 , ii ) we set the amplitude of the slater determinant which contains them equal to @xmath189 , iii ) we choose the 3rd orbital randomly and iv ) we set the rest of the coefficients of the configurations to the same non - negative value to obtain a normalized wave function . in this case we obtain the lower @xmath175 mctdhf energy @xmath190 shown in table [ tab : ground_state_energies ] . we note that this design procedure is somewhat similar to first performing a hf calculation with @xmath184 electrons , and then adding a third orbital to perform a mcscf calculation ; a strategy often followed in quantum chemistry multi - configurational self - consistent - field calculations . in the case of td - rasscf - d , we impose the most important configurations by setting @xmath191 and @xmath192 and we obtain again @xmath193 now using a random initial guess function , obtained by choosing the coefficients and amplitudes as described in the beginning of this section . the difference between these two approximations to the ground state lies in the orbitals . for the ground state with energy @xmath185 , the angular part of all the orbitals turns out to be @xmath194 , that is , the many - electron wave function corresponds to a multiconfigurational hartree - fock ( mchf ) using @xmath195 orbitals . however , for @xmath193 and ( @xmath196 ) we obtain that the main contribution to the angular part of the two orbitals @xmath197 is spherically symmetric , while the third orbital @xmath198 is a linear combination of @xmath199 and @xmath200 , such that the expansion coefficients [ eq . ] fulfil @xmath201 . this condition ensures that the total magnetic quantum number of the ground state is vanishing , consistent with its @xmath182 term . note that the ground state energies of the ras @xmath202 and @xmath203 are the same because these two schemes are equivalent @xcite . this improvement in the ground state energy for @xmath175 orbitals manifests the importance of the mixing of the orbitals with different values of @xmath98 . if this mixing is not permitted , we would require at least 5 orbitals to improve the hf energy , i.e. , the @xmath204 orbitals , to guarantee the coupling to @xmath182 . let us remark that the ground state energy for mctdhf with 5 orbitals is lower than the energy obtained from time - independent multiconfigurational hartree fock calculations with 5 orbitals with fixed @xmath205 and @xmath98 @xcite , and that the @xmath206 and @xmath207 results , for which case comparison is possible , are in good agreement with mchf results @xcite . for a given number of orbitals @xmath24 , the ras scheme @xmath191 and @xmath208 , may be seen as an improvement to the tdhf solution by adding the possibility for double excitations . the wave function associated with this ras @xmath209 is formed by @xmath210 configurations , whereas the number of configurations of the mctdhf is @xmath211 . for example , for @xmath207 , the number of configurations required for this ras is @xmath212 , whereas it is 1296 for the mctdhf approach . the discrepancy in the energy is , however , only @xmath213 ( see table [ tab : ground_state_energies ] ) . because of the reduction in configurations , the results in table [ tab : ground_state_energies ] are obtained with the td - rasscf - d approach at a reduced computational cost in terms of cpu and memory compared to those obtained with the mctdhf approach . the number of operations scales with the sum of two major contributions : the calculation of the two - body operator and the integration of the amplitude equations @xcite . the numerical effort of the first one is discussed in detail in sec . the integration of the amplitude equations scales with the number of configurations , @xmath214 , as @xmath215 . we will come back to the reduction in computational cost in connection with the photoelectron spectra discussed below . in this section we illustrate the application of the td - rasscf - d method to photoelectron spectra ( pes ) of be after interacting with short linearly polarized xuv laser pulses . we consider pulses described by the vector potential @xmath216 , where the duration of the pulse is @xmath217 and the frequency bandwidth @xmath218 with @xmath219 the number of cycles . for the photon energies considered in this paper , the photoelectrons come from the ionization of be to one of the three low - lying states of @xmath220 : @xmath221 $ ] ( with an ionization potential of @xmath222 ev ) , @xmath223 $ ] ( @xmath224 ev ) , @xmath225 $ ] ( @xmath226 ev ) and the higher lying channel @xmath227 $ ] ( @xmath228 ev ) @xcite , see fig . [ fig : fig2 ] . energy levels of be and @xmath220 involved in the photoionization process . experimental energies @xcite are labelled by their terms and dominant configurations . as indicated by the arrows , we consider lasers with central frequencies corresponding to photon energies of 30 ev and 150 ev . the zig - zag curve above the 30 ev arrow denotes a change in scale beweeen the 30 ev and the 150 ev arrows . ] photoelectron spectra for linearly polarized laser pulses with ( a ) 6 and ( b ) 10 cycles with a central frequency corresponding to 30 ev , and an intensity of @xmath229 w/@xmath230 . the ras schemes are @xmath231 ( black , solid ) , @xmath232 ( red , solid ) , @xmath233 ( blue , long - dashed ) , @xmath234 ( orange , dotted ) , @xmath235 ( dark green , dash - dotted ) , @xmath236 ( black , long dash - double dotted ) and @xmath237 ( purple , thin - dotted ) . ] first , we consider laser pulses with a central frequency corresponding to a photon energy of @xmath238 ev and an intensity of @xmath229 w/@xmath230 . to illustrate the accuracy of the td - rasscf - d method , we show the pes after the ionization with pulses containing @xmath239 [ fig . [ fig : fig3](a ) ] and @xmath240 cycles [ fig . [ fig : fig3](b ) ] for several ras schemes . according to the ionization channels in fig . [ fig : fig2 ] , the peaks of the photoelectron spectrum should be located at @xmath241 , @xmath242 and @xmath243 ev . we first note that the result of the tdhf @xmath244 calculation overestimates the height of the pes compared with the results of the rest of the ras schemes . this behavior of the tdhf result clearly shows the inadequacy of this approach to describe the electronic structure and dynamics of be during the ionization process . we find for mctdhf with 4 orbitals and 6 cycles that the main peak is located at @xmath245 21.02 ev , and ranges from 20.3 - 20.5 ev for the rest of the schemes in fig . [ fig : fig3](a ) . the pes for the 10 cycles pulse in fig . [ fig : fig3](b ) , presents more narrow peaks in the pes , since the bandwidth of the pulse is reduced from @xmath246 ev to @xmath247 ev but the peak positions remain similar to the ones in fig . [ fig : fig3](a ) . for the schemes with more than 4 orbitals , the main peak is located at identical positions at the scale of the figure . also note that the results for mctdhf for 6 , 7 and 9 orbitals are indistinguishable over the entire energy range . in the tail at lower energies , however , the ras schemes @xmath248 and @xmath249 differ from the mctdhf results . this disagreement lies at energies corresponding to the peak of the ionization channel @xmath250\rightarrow\text{be}^+~[(1s^22p)^2\text{p}^o]$ ] , fig . [ fig : fig2 ] . this means that @xmath191 and only two electrons in @xmath32 is not sufficient to describe one electron in an excited orbital and another in the continuum , even for @xmath251 . to isolate the corresponding peak we use that single ionization changes the angular momentum of the system by @xmath252 and @xmath253 . since the ionic channels @xmath254 and @xmath255 have different symmetries , the ejected electron must be @xmath256 for the first ionic channels and @xmath257 for the second channel . the maximum in the probability of the @xmath256 continuum electron lies in the direction parallel to the polarization of the laser , whereas it vanishes in the perpendicular direction . the @xmath184 and @xmath258 photoelectrons can be detected in both directions . then , we can disentangle the contributions of the two peaks by analyzing the momentum distributions in the directions parallel and perpendicular to the laser polarizations , such differential quantities are shown in figs . [ fig : fig4 ] and [ fig : fig5 ] for 6 and 10 cycles , respectively . triply differential probabilities for @xmath259 ( parallel to the laser polarization direction ) @xmath260 ( perpendicular to the laser polarization direction ) and @xmath261 for linearly polarized laser pulses with 6 cycles , central frequency corresponding to 30 ev and an intensity of @xmath229 w/@xmath230 . the ras schemes shown are as in fig . [ fig : fig3 ] . ] in figs . [ fig : fig4](a ) and [ fig : fig4](b ) we show the triply differential probabilities [ eq . ] parallel and perpendicular to the polarization of the laser pulse . we note that the tdhf is not sufficient to obtain the peak in the perpendicular direction , because the channel be@xmath262 $ ] is inaccurately described at that level of approximation . the reason is that the one - body operator can not couple directly to that correlated channel . in fig . [ fig : fig4](a ) the peak along the polarization direction is smaller than for mctdhf with 4 orbitals . by carefully analyzing the triply differential probability we find that the angular distribution for tdhf is wider which explains the large pes . we see that the probability for ionization in the parallel direction [ fig . [ fig : fig4](a ) ] is much higher for mctdhf with 4 orbitals than with the other schemes . around 10 ev there is a small peak which contributes to the main peak , and which comes from the @xmath184 and @xmath258 electrons associated with the be@xmath262 $ ] channel . the energy and angle resolved signals for the other methods overlap and are indistinguishable on the scale of the figure . for 10 cycles there is , however , a small difference among them between approximately 10 and 17 ev , as shown in fig . [ fig : fig5](a ) . compared to the 6 cycles case , for 10 cycles , the bandwidth of the pulse is smaller , @xmath263 ev , and the influence of the @xmath184 and @xmath258 electrons is present in the pes for all the ras schemes considered . to investigate this difference further , we turn to the perpendicular direction . for both 6 and 10 cycles , the mctdhf solution for 6 , 7 and 9 orbitals overlap , [ fig . [ fig : fig4](b ) and fig . [ fig : fig5](b ) ] , whereas they are different from the ras schemes @xmath264 and @xmath265 . for a 10 cycles pulse , the peaks are located at 16.24 ev for mctdhf , 15.7 ev for ( @xmath266 ) and 15.3 ev for ( @xmath267 ) . for the 6 cycle pulse , the peaks are shifted by approximately 0.3 ev for all the active spaces . this effect may be caused by the enhancement of other ionization channels opening up due to the wider bandwidth . triply differential probabilities for @xmath268 and @xmath261 for a linearly polarized laser pulse with 10 cycles , a central frequency corresponding to 30 ev and an intensity of @xmath229 w/@xmath230 . the ras schemes shown are as in fig . [ fig : fig3 ] . ] photoelectron spectrum for linearly polarized laser pulses with ( a ) 6 and ( b ) 10 cycles , a central frequency corresponding to 30 ev , and an intensity of @xmath229 w/@xmath230 . ] to analyze only the influence on the spectra of choosing different ras schemes , we describe the pes for several partition schemes fixing the number of orbitals . in figs . [ fig : fig6 ] and [ fig : fig7 ] we show the pes and the triply differential probabilities , respectively , for several ras schemes for 7 orbitals , i.e. , @xmath269 . for 10 cycles , the peak at 20.3 ev corresponding to ionization into the ionic @xmath254 channel as well as the tail for higher energies coincide for all the schemes , whereas for 6 cycles , the peak is shifted to lower energies , probably due to the ionization into the ionic state @xmath255 . as in the previous cases , the disagreement comes at lower energies corresponding to the ionic state @xmath255 . in this range , the mctdhf and the ras @xmath270 results can not be distinguished on the scale of fig . [ fig : fig6 ] . however , for the ras @xmath271 there is an excess in the signal for energies lower than 17 ev , whereas for larger energies we find a smaller signal than for mctdhf . this effect is more pronounced for @xmath264 . this can be understood in terms of the differential energy distribution in fig . [ fig : fig7 ] . in the parallel direction , the curves for these last two ras schemes overlap , and they differ between the @xmath272 and @xmath273 schemes . in the perpendicular direction we can see differences among all the schemes . the peak of the mctdhf calculation is located at 16.25 ev with a value @xmath274 , which is slightly larger than @xmath275 for @xmath276 . for @xmath277 and @xmath278 , the peak is shifted to lower energies , both lying at 15.24 ev . the height of these peaks is very similar to the heights obtained with the mctdhf results . triply differential probabilities for @xmath279 and @xmath261 for a linearly polarized laser pulse with 10 cycles , a central frequency corresponding to 30 ev and an intensity of @xmath229 w/@xmath230 for a ras scheme with @xmath280 orbitals . ] the peak in the pes coming from the ionic state @xmath225 $ ] is not observed in the present results due to the small cross section of this transition @xcite . for the pulses of finite duration used here , this peak is buried in the tails of the other peaks . the rtp calculations also illustrate the reduction of the numerical effort of the td - rasscf - d approach compared with the mctdhf method . for the ras scheme @xmath248 , 110 cycles of propagation takes 18h in 20 cores compared to 22h for mctdhf . in the case of 9 spatial orbitals the difference is more marked , taking 34h for the ras scheme @xmath281 and 47h for mctdhf . photoelectron spectrum for a linearly polarized laser pulse with 10 cycles , a central frequency corresponding to 150 ev and an intensity of @xmath282 w/@xmath230 . the ras schemes shown are as in fig . [ fig : fig3 ] . ] we analyze the core ionization to the ionic channel @xmath283 $ ] [ fig . [ fig : fig2 ] ] using @xmath284 ev linearly polarized laser pulses for several ras schemes . the pes is shown in fig . [ fig : fig8 ] for a 10 cycles pulse with @xmath285 ev and an intensity of @xmath282 w/@xmath230 . the pes are almost overlapping for all the ras schemes used , which means that the mctdhf and td - rasscf - d methods describe with the same accuracy the ionization into this channel , even for the minimum number of configurations , that is , using the ras scheme @xmath286 . these ras schemes contain the most relevant configurations needed to describe the dynamics of the process , that is , @xmath287s@xmath288 and an electron @xmath15 in the continuum . the peak is located at @xmath245 21.37 ev , corresponding to an ionization energy of 128.63 ev , a bit higher than the experimental value 123.35 ev @xcite , which is in agreement with the @xmath161 ev shift found in ref . @xcite . in recent years there has been a large interest in time - delays in photoionization studies ( see , e.g. , the review ref . @xcite and references therein ) . here we consider the delay between the apparent times of ionization into the channels @xmath289 $ ] @xmath290 and @xmath291 $ ] @xmath292 and we exploit the flexibility of the td - rasscf method to address the role of electron correlation on photoionization time - delays . we do so in the following by considering the angle - resolved radial density after the pulse for several ras schemes . we show in figs . [ fig : fig9](a)-(b ) the density along the polarization direction and in figs . [ fig : fig9](c)-(d ) the density in the perpendicular direction at different times after the end of the laser pulse . as we have discussed in previous sections , the ionization into both channels contributes in the parallel direction , whereas in the perpendicular direction only the @xmath184 and @xmath258 photoelectrons associated with the @xmath291 $ ] channel contribute . let us remark that the results of the mctdhf calculations have also been obtained with 9 spatial orbitals , and on the scale of the figure they coincide with the results of the calculation for 7 orbitals . in the parallel direction , the height of the density decreases as it spreads during the propagation . in the perpendicular direction the outgoing wavepacket is not yet formed at @xmath293 a.u . , therefore the peak in the density increases for later times . the ras @xmath270 reproduces accurately the dynamics for ionization into the channel @xmath289 $ ] [ fig . [ fig : fig9](a ) ] , whereas there are small differences with the @xmath277 scheme , as shown in fig . [ fig : fig9](b ) . the main differences between the different levels of theory are found in the perpendicular direction shown in figs . [ fig : fig9](c ) and ( d ) . in the case of @xmath270 , we find that the heights of the density peaks are smaller than in mctdhf case , but remain on equal positions . in contrast to this case , for @xmath271 the density distributions are similar , but the ras result is shifted in the radial coordinate with respect to the mctdhf result . to analyze independently the dynamics of the ejected electrons from each ionic channels we can use that the ejected @xmath256 electron associated with the ionic channel @xmath289 $ ] only contributes in the direction parallel to the polarization axis of the laser , whereas the @xmath184 and @xmath258 electrons associated with the @xmath291 $ ] channel contribute to both the parallel and perpendicular directions . to distinguish between these two channels by the angle resolved radial density in the parallel and perpendicular directions we benefit from the fact that the influence of the @xmath184 and @xmath258 electrons in the parallel direction is negligible compared to the @xmath256 electron ejected from @xmath289 $ ] , as seen in fig . [ fig : fig9 ] . this allows us to obtain the expectation value of the position of the electron in the outer region , which fulfils ehrenfest s theorem , @xmath294 , with @xmath295 the ionization time . we now calculate the time - delays for td - rasscf and mctdhf and compare the impact of the electron correlation by varying the ras scheme . let us remark that we need to include correlation in the photoionization process of be , because we can not resolve the ionization process @xmath296\rightarrow$ ] @xmath291+e^{-}(s~\text{or}~d)$ ] using tdhf . we find for mctdhf with 7 orbitals a time - delay between the two channels of @xmath297 as , which is a bit smaller than the result for 9 orbitals , @xmath298 as . by reducing @xmath29 and adding two orbitals to @xmath32 , @xmath270 , @xmath299 is @xmath300 as , which further diminishes to @xmath301 as for @xmath271 . the ras scheme @xmath264 leads to @xmath302 as . even if we increase the number of orbitals in @xmath32 to @xmath303 we obtain @xmath304 as , far from the mctdhf value . for these two ras schemes the ionization from the channel @xmath291 $ ] is not well described , leading to a value of @xmath305 which largely differs from the mctdhf result . however , the ionization times of the @xmath184 and @xmath258 electrons are similar for all the ras used , differing less than @xmath306 . in conclusion the relative time - delay of ionization into @xmath291 $ ] and @xmath289 $ ] is around 7 - 8 as . note that this method is sensitive to an error in the calculation of @xmath307 . it can be estimated that for this process , an error of @xmath308 a.u . implies an error in the time - delay of the order of @xmath309 as . triply differential probabilities in position space for @xmath272 , @xmath264 and @xmath310 ras schemes with 7 spatial orbitals after the interaction with a linearly polarized laser pulse with a central frequency corresponding to 30 ev , 10 cycles and an intensity of @xmath229 w/@xmath230 , where ( a ) and ( b ) corresponds to the @xmath311 and ( c ) and ( d ) to @xmath312 . all the panels contain the results for mctdhf with 7 spatial orbitals at @xmath313 ( red , solid ) , @xmath314 ( blue , dashed ) and @xmath315 ( orange , dotted ) , together with @xmath276 in panels ( a ) and ( c ) ( @xmath313 : black , dash - double dotted , @xmath314 : green , dash - dotted and @xmath315 : purple , dotted ) and @xmath277 in panels ( b ) and ( d ) ( @xmath313 : blue , dash - double dotted , @xmath314 : black , dash - dotted and @xmath315 : gray , dotted ) . the instants of time in atomic units are indicated in panel ( d ) . ]

second , we solve the equations of motion to compute photoelectron spectra of be after interacting with a short linearly polarized xuv laser pulse . finally , we investigate the effects of electron correlation on the magnitude of the relative time - delay in the photoionization process into two different ionic channels . one channel , the ground state channel in the ion , is accessible without electron correlation . the other channel is only accessible when including electron correlation . the time - delay is highly sensitivity to the choice of the active space , and hence to the account of electron - electron correlation .

we apply a three - dimensional ( 3d ) implementation of the time - dependent restricted - active - space self - consistent - field ( td - rasscf ) method to investigate effects of electron correlation in the ground state of be as well as in its photoionization dynamics by short xuv pulses , including time - delay in photoionization . first , we obtain the ground state by propagation in imaginary time . we show that the flexibility of the td - rasscf on the choice of the active orbital space makes it possible to consider only relevant active space orbitals , facilitating the convergence to the ground state compared to the multiconfigurational time - dependent hartree - fock method , used as a benchmark to show the accuracy and efficiency of td - rasscf . second , we solve the equations of motion to compute photoelectron spectra of be after interacting with a short linearly polarized xuv laser pulse . we compare the spectra for different ras schemes , and in this way we identify the orbital spaces that are relevant for an accurate description of the photoelectron spectra . finally , we investigate the effects of electron correlation on the magnitude of the relative time - delay in the photoionization process into two different ionic channels . one channel , the ground state channel in the ion , is accessible without electron correlation . the other channel is only accessible when including electron correlation . the time - delay is highly sensitivity to the choice of the active space , and hence to the account of electron - electron correlation .

1604.02551

r

as explained in the previous section , the lets allow one to perform consistency checks of lattice - qcd results for nn scattering provided more than a single observable is extracted . unfortunately , most of the lattice calculations in the nn sector have so far focused on the determination of the binding energies . one exception is the work by the nplqcd collaboration at the pion mass of @xmath94 mev @xcite , which provides , in addition to the binding energies , also the values of the scattering length , effective range and even the first shape parameter . it is , furthermore , conjectured in that paper that the effective range , expressed in units of the pion mass , may be approximated by a linear function of @xmath14 . while the lets are certainly beyond their range of applicability at such heavy pion masses , this conjecture was tested using the lets in our previous work @xcite , where the resulting @xmath95-dependence of the deuteron binding energy was indeed found to be in good agreement with the general trend of lattice data @xcite . recently , new results for nn scattering in the @xmath1 and @xmath2 channels have been reported by the nplqcd collaboration at @xmath96 mev @xcite . the calculations were performed for @xmath97 flavors of light quarks at three lattice volumes of @xmath98 fm , @xmath99 fm , and @xmath100 fm using the lattice spacing of @xmath101 fm . in analogy to their previous work , the scattering phase shifts for the @xmath1 and @xmath2 partial waves were extracted for several values of the cms nn momenta using the extended lscher approach @xcite as shown by the black filled regions in fig . [ fig:3s1let ] for the case of the @xmath1 channel . channel calculated on the lattice at @xmath102 mev @xcite ( filled black regions ) in comparison with the predictions based on the lets at lo ( orange light - shaded bands ) and nlo ( blue dark - shaded and hatched blue light - shaded bands ) using the nplqcd result for the deuteron binding energy @xmath103 as input . the uncertainty at lo shown by the orange bands is entirely given by the uncertainty of @xmath103 in eq . . the nlo dark - shaded ( hatched light - shaded ) bands correspond to the uncertainty in @xmath103 and the theoretical uncertainty of the lets estimated via the variation of @xmath76 with @xmath89 ( @xmath92 ) combined in quadrature . the grey light- and dark - shaded bands in the right panel depict the fit results of the lattice points of ref . @xcite based on the effective range approximation . the energy of the bound ( virtual ) states corresponds to the intersection points of the effective - range function @xmath104 and the unitarity term @xmath105 , shown by the dotted line in the right panel , in the lower ( upper ) half - plane . the phase shift corresponds to the blatt - biedenharn parametrization of the s - matrix @xcite . [ fig:3s1let ] , title="fig:",scaledwidth=49.0% ] channel calculated on the lattice at @xmath102 mev @xcite ( filled black regions ) in comparison with the predictions based on the lets at lo ( orange light - shaded bands ) and nlo ( blue dark - shaded and hatched blue light - shaded bands ) using the nplqcd result for the deuteron binding energy @xmath103 as input . the uncertainty at lo shown by the orange bands is entirely given by the uncertainty of @xmath103 in eq . . the nlo dark - shaded ( hatched light - shaded ) bands correspond to the uncertainty in @xmath103 and the theoretical uncertainty of the lets estimated via the variation of @xmath76 with @xmath89 ( @xmath92 ) combined in quadrature . the grey light- and dark - shaded bands in the right panel depict the fit results of the lattice points of ref . @xcite based on the effective range approximation . the energy of the bound ( virtual ) states corresponds to the intersection points of the effective - range function @xmath104 and the unitarity term @xmath105 , shown by the dotted line in the right panel , in the lower ( upper ) half - plane . the phase shift corresponds to the blatt - biedenharn parametrization of the s - matrix @xcite . [ fig:3s1let ] , title="fig:",scaledwidth=49.0% ] in addition to the phase shifts , the binding energies of the deuteron and the dineutron were extracted . thus , it is interesting to test whether these results fulfill the lets introduced above . the deuteron binding energy calculated in ref . @xcite at @xmath106 mev at three lattice volumes and extrapolated to the infinite volume is @xmath107 where the errors include statistical and systematic uncertainties as well as the extrapolation uncertainty combined in quadrature . further , the first two coefficients in the effective range expansion , namely the scattering length and the effective range , were determined in ref . @xcite by fitting the effective range approximation of the effective range function , @xmath108 to the two lowest - energy scattering data points and the deuteron binding energy , see the grey bands in the right panel of fig . [ fig:3s1let ] . notice that all three lattice data correspond to nucleon momenta below the branch point @xmath109 of the left - hand cut from the opep . the resulting values for the inverse scattering length and the effective range in units of the pion mass reported in ref . @xcite are @xmath110 where the uncertainties in the first and second brackets are statistical and systematic , respectively . in fig . [ fig:3s1let ] , we confront the lattice - qcd phase shifts of ref . @xcite with the predictions of the lets at lo and nlo . we use the nplqcd result for the deuteron binding energy given in eq . as input to adjust the leading - order contact term @xmath38 . this is sufficient to predict the phase shift at lo . as explained in the previous section , there are no additional parameters at nlo . as shown in the left panel of fig . [ fig:3s1let ] , the change in the phase shifts when going from lo to nlo is reasonably small which confirms a good convergence of the lets in this channel . the expected accuracy of the nlo prediction can be roughly estimated by the width of the blue band generated by the variation of the parameter @xmath76 as described above and appears to be consistent with the shift from lo to nlo . notice that the lo ( orange ) band reflects the uncertainty in the nplqcd prediction of the binding energy and does not include the theoretical uncertainty of the lets . as required by the levinson theorem for the case of a bound deuteron , the phase shifts generated by the lets go through @xmath111 at the origin . comparing the nplqcd results for phase shifts and the effective range function in the @xmath1 channel with those based on the lets as visualized in fig . [ fig:3s1let ] , we end up with the following conclusions : * first , as shown in the right panel of fig . [ fig:3s1let ] , only _ positive _ values of the scattering length appear to be consistent with the nplqcd result for the deuteron binding energy quoted in eq . ( [ bd ] ) as opposed to the negative central value for @xmath112 reported in ref . our results for the inverse scattering length extracted from @xmath103 by means of the lets disagree with the nplqcd ones given in eq . ( [ ere3s1 ] ) as can be inferred from the right panel of fig . [ fig:3s1let ] . * while the lattice phase shifts at higher momenta are in reasonable agreement with the ones predicted by the lets , their low - momentum behavior is incompatible ( within the quoted errors ) with that predicted by the lets as demonstrated in both panels in fig . [ fig:3s1let ] . in particular , the phase shift calculated on the lattice at the lowest considered momentum of @xmath113 mev , @xmath114 degrees , is a factor of three smaller than the corresponding value of @xmath115 degrees extracted from the lets . * an extrapolation of the lattice data to zero momenta in the left panel of fig . [ fig:3s1let ] seems to indicate that the phase shift goes to zero . this would , however , contradict the existence of a bound state in this partial wave as a consequence of the levinson theorem ( or require shifting @xmath116 by @xmath117 degrees in the entire plotted energy range which would be inconsistent with the lets ) . one may raise a question whether the observed inconsistencies between the lattice - qcd results for phase shifts and the lets predictions could originate from underestimating the quark mass dependence of the nlo contact interaction by constraining the function @xmath118 as described in the previous section . to clarify this issue , we have increased the allowed variation of @xmath76 by a factor of two , i.e. we set @xmath119 instead of @xmath89 . this corresponds to the allowed variation of the strength of the short - range term at @xmath87 mev by @xmath120 as compared to its value at the physical point . the resulting predictions for the phase shifts and the effective range function are shown by the hatched blue light - shaded bands in fig . [ fig:3s1let ] . with the resulting uncertainty nearly covering the shift from our lo to nlo results , we expect such an error estimation to be too conservative . still , none of our conclusions appear to be affected by employing this very conservative uncertainty estimation . we are now in the position to employ the lets in order to extract the scattering length and the effective range from the deuteron binding energy calculated by the nplqcd collaboration . such an extraction is possible because the effective range function does not possess poles at low momenta and , therefore , can be taylor expanded around the origin mev where the phase shift crosses zero but these momenta are already beyond the region of the validity of the effective range expansion . ] . in fig . [ fig : lets_3s1 ] , we plot the deuteron binding energy and the effective range as functions of the inverse scattering length in units of the pion mass predicted by the lets at lo ( shown by the lines ) and nlo ( shown by the bands ) . , effective range @xmath16 and the binding energy in the @xmath1 partial wave induced by the one - pion exchange potential . the red solid and dashed magenta lines show the predictions of the lo lets for @xmath121 and @xmath103 . the light - shaded bands between the red solid and dashed magenta lines visualize the predictions of the nlo lets for @xmath121 and @xmath103 , respectively , and reflect the theoretical uncertainty estimated via the variation of @xmath76 with @xmath89 as described in the text . the horizontal dotted lines specify the range of values for @xmath103 consistent with the lattice - qcd results of ref . @xcite for this observable . the solid dark - red circle ( blue rectangle ) shows the lo ( nlo ) let predictions for the effective range . the open black circle gives the result for the inverse scattering length and effective range reported by the nplqcd collaboration @xcite while the grey area around it shows the estimated uncertainty from that paper . all results correspond to the blatt - biedenharn parametrization of the s - matrix @xcite . [ fig : lets_3s1 ] , scaledwidth=70.0% ] specifically , the red band between two solid lines represents the nlo let calculation for the effective range as a function of the inverse scattering length . similarly , the magenta band between two dashed lines shows the deuteron binding energy versus the inverse scattering length at nlo . further , the two horizontal dotted lines separate the region of the binding energies consistent with the nplqcd result of ref . @xcite , eq . , for the binding energy . projecting this area onto the @xmath122-axis , as shown by the vertical lines , one obtains the corresponding values of the scattering length and the effective range from the lets . in particular , we find @xmath123 which correspond to the following values in units of fm @xmath124 here , the errors in the first brackets reflect the uncertainty in the value of the deuteron binding energy in eq . ( [ bd ] ) used as input . for the nlo results , we also give in the second brackets an estimation of the theoretical uncertainty corresponding to the choice of @xmath89 . clearly , the above values are at variance with those extracted by the nplqcd collaboration and given in eq . ( [ ere3s1 ] ) . in particular , our value for the effective range is about a factor of @xmath125 smaller than the one found in ref . interestingly , the nlo let prediction for the effective range is in excellent agreement with the assumed linear in @xmath126 behavior of the quantity @xmath127 conjectured in ref . @xcite , cf . [ fig:3s1eff_rad_mpi ] and the right panel of fig . [ fig : eff_rad_mpi ] . for the sake of completeness , we also give the nlo let results based on a more conservative uncertainty estimation resulting by employing a weaker constraint on the allowed @xmath14-dependence of the subleading contact interaction corresponding to the choice of @xmath128 : @xmath129 or @xmath130 in units of fm . to understand the origin of the disagreement between our results for the scattering length and effective range with those of ref . @xcite , it is instructive to take a closer look at the procedure for their determination employed by the nplqcd collaboration . to this aim , a fit of the lattice phase - shift data at the two lowest energies and the deuteron pole was performed using the effective - range approximation ( [ eq : ere ] ) . note that the considered phase - shifts and the deuteron pole correspond to momenta below the branch point of the @xmath131-channel cut due to the opep . for non - singular potentials of a finite range , the applicability region of the effective range expansion is given by the inverse range of the interaction which determines the position of the first left - hand singularity . consequently , the effective range and shape parameters may be expected to scale with the corresponding powers of the pion mass . for example , for the physical value of the pion mass , one has @xmath132 and @xmath133 . the very large value of the effective range reported by the nplqcd collaboration , @xmath134 , either indicates that the range of the nuclear force is considerably larger than that of the opep or signals the appearance of a pole in the effective - range function in the near - threshold region .- wave channel for neutron - deuteron scattering . ] in both cases , the applicability range of the effective range expansion of @xmath135 would be significantly smaller than one may expect based on the position of the left - hand cut due to the opep . as a consequence , the solution for @xmath136 and @xmath137 reported in ref . @xcite and listed in eq . ( [ ere3s1 ] ) is not self - consistent in the sense that it is obtained by fitting the effective range approximation to the data points outside of its validity region which can be roughly estimated as @xmath138 . specifically , the deuteron binding momentum at @xmath139 mev is of the order of @xmath140 , whereas the phase - shifts data employed in the analysis correspond to @xmath141 and @xmath142 . to get further insights into this issue , consider the two roots of the quadratic equation @xmath143 which determines the pole positions of the scattering amplitude within the effective - range approximation , @xmath144 where we have expanded the square root in powers of @xmath145 and neglected terms of order @xmath146 . this is justified both for the physical value of the pion mass and for the solution given in eq . ( [ ere3s1 ] ) , since in both cases one has @xmath147 . at the physical pion mass , the second root yields the deuteron binding momentum @xmath148 mev while the first root , @xmath149 mev , lies outside of the applicability region of the effective range expansion and is an artifact of the effective range approximation . in particular , it disappears or changes the position upon including higher - order terms in the effective range expansion . on the contrary , for the solution in eq . ( [ ere3s1 ] ) at @xmath150 mev , the deuteron pole corresponds to the first root , @xmath151 mev , where the dominant contribution comes from the effective range . meanwhile , because the scattering length in eq . is negative , the second root corresponds to the momentum , @xmath152 mev , lying on the imaginary axis in the lower half plane . therefore , the results of ref . @xcite imply the existence of a shallow virtual state with the excitation energy less than @xmath153 mev in addition to the deuteron , which is not supported by our analysis based on the lets . finally , it is interesting to compare our results based on the lets with the ones obtained using an alternative approach proposed in ref . @xcite , which will be referred to as bbsvk , where the expansion of the nuclear force around the chiral limit was employed , see , however , ref . @xcite for a criticism . this approach was used in ref . @xcite to calculate the phase shifts and the mixing angle in the @xmath154 channel . a comparison of results from the two approaches is presented in fig . [ fig : comp_3s1 ] . ( color online ) neutron - proton phase shifts in the @xmath1 channel ( left panel ) and the mixing angle @xmath155 ( right panel ) at @xmath93 mev based on the lets at lo and nlo in comparison with the results obtained in ref . @xcite using the eft formulation of ref . @xcite , labelled as bbsvk , at lo ( light - shaded band between pink dotted lines ) and nlo ( light - shaded band between blue dashed lines ) . the results for the @xmath17s@xmath18 phase shift correspond to the blatt - biedenharn parametrization of the s - matrix @xcite while the mixing parameter is shown for the stapp parameterization to allow for the comparison with the results of ref . @xcite . for remaining notation see fig . [ fig:3s1let ] . , title="fig:",scaledwidth=49.0% ] ( color online ) neutron - proton phase shifts in the @xmath1 channel ( left panel ) and the mixing angle @xmath155 ( right panel ) at @xmath93 mev based on the lets at lo and nlo in comparison with the results obtained in ref . @xcite using the eft formulation of ref . @xcite , labelled as bbsvk , at lo ( light - shaded band between pink dotted lines ) and nlo ( light - shaded band between blue dashed lines ) . the results for the @xmath17s@xmath18 phase shift correspond to the blatt - biedenharn parametrization of the s - matrix @xcite while the mixing parameter is shown for the stapp parameterization to allow for the comparison with the results of ref . @xcite . for remaining notation see fig . [ fig:3s1let ] . , title="fig:",scaledwidth=49.0% ] while the @xmath1 phase shift and the mixing angle show a very similar behavior at lo , there are more sizable differences at nlo . notice that apart from the different treatment of pions , the two approaches also differ in the way the nlo short - range interaction is taken into account . in particular , in ref . @xcite , the strength of this subleading short - range term was adjusted to fit the lattice phase shifts . in contrast , in our approach , the strength of the subleading contact interaction @xmath76 is determined by the value of the effective range at the physical point while its allowed @xmath14 dependence at unphysical pion masses is used to estimate the theoretical uncertainty as explained in sec . [ general ] . this procedure ensures that both the lo and nlo let results depend on a single unknown parameter . we further emphasize that the low - energy behavior of the mixing angle found in ref . @xcite and shown in the right panel of fig . [ fig : comp_3s1 ] seems to be at variance with the expected threshold behavior for this quantity , @xmath156 ( for details see , e.g. @xcite ) . irregardless of these differences , the two approaches yield similar numerical results for the @xmath1 phase shift and the mixing angle @xmath155 in the considered range of momenta . the values of the scattering length and effective range extracted in ref . @xcite from the lattice data using the framework of ref . @xcite read @xmath157 where the uncertainties in the first and second brackets correspond to the statistical and systematic uncertainties of the lattice results . as already pointed out , the lo values are in agreement with our lo predictions given in eq . ( [ erenlofm ] ) , while the deviations at nlo and , in particular , the large value of the effective range are presumably caused by an attempt to reproduce the lattice - qcd result for the @xmath1 phase shift at @xmath158 gev within the bbsvk approach . we now turn to the spin - singlet channel . in fig . [ fig:1s0_letseb ] , we confront the phase shifts extracted based on the lets with the lattice - qcd results for the @xmath2 partial wave . here we apply the same procedure as in the @xmath1 channel and use the nplqcd result for the dineutron binding energy , @xcite @xmath159 as input to fix the short - range interaction at lo . the nlo short - range interaction is again taken into account by means of resonance saturation , see eq . ( [ satur ] ) , with the strength @xmath76 being determined by the effective range at the physical point . the allowed @xmath14-dependence of @xmath76 is specified by eq . ( [ beta_range ] ) , and the blue dark - shaded bands in fig . [ fig:1s0_letseb ] correspond to the choice @xmath160 . notice that the shift in the predictions when going from lo to nlo is now much larger than in the spin - triplet channel which is in line with the lower predictive power of the lets in the @xmath2 partial wave . consequently , we believe that a variation of the strength @xmath76 with @xmath89 does not provide a realistic estimation of the theoretical uncertainty at nlo in this channel . to have a more conservative estimation , we will allow for a larger @xmath14-dependence in this channel and set @xmath119 as visualized by the hatched blue light - shaded bands in fig . [ fig:1s0_letseb ] . as shown in fig . [ fig:1s0_letseb ] , we arrive at similar conclusions as in the case of the spin - triplet channel . while our nlo let predictions for @xmath161 mev are in very good agreement with the phase shifts calculated by the nplqcd collaboration , there is a clear discrepancy for the two lowest values of the momentum @xmath162 . in particular , for the lowest momentum of @xmath163 mev , the phase shift from the nlo lets is roughly a factor of two larger than that from the lattice - qcd analysis . similarly to the @xmath1 channel , the predictions of the lets based on the dineutron binding energy are only compatible with positive values of the scattering length , see the right panel of fig . [ fig:1s0_letseb ] . specifically , we obtain @xmath164 which correspond to the following values in units of fm @xmath165 here , the errors at lo and in the first brackets at nlo correspond to the uncertainty in the dineutron binding energy while the ones in the second brackets at nlo reflect the unknown @xmath14-dependence of @xmath76 subject to the constraint @xmath119 . these results are in conflict with the nplqcd determination based on the effective range expansion , namely @xcite : @xmath166 channel calculated on the lattice at @xmath102 mev @xcite in comparison with the predictions based on the lets at lo and nlo using the nplqcd result for the dineutron binding energy @xmath167 as input . for notation see fig . [ fig:3s1let ] . [ fig:1s0_letseb ] , title="fig:",scaledwidth=49.0% ] channel calculated on the lattice at @xmath102 mev @xcite in comparison with the predictions based on the lets at lo and nlo using the nplqcd result for the dineutron binding energy @xmath167 as input . for notation see fig . [ fig:3s1let ] . [ fig:1s0_letseb ] , title="fig:",scaledwidth=49.0% ] again , we believe that the analysis performed by the nplqcd collaboration and based on the effective range approximation is not self - consistent . all arguments given in the previous section apply to the @xmath2 channel too , even though our conclusions in this case are somewhat less stringent due to the lower accuracy of the lets . to further elaborate on this point and to provide an assessment of the robustness of our conclusions , we have re - done the calculations by using the lattice phase shifts instead of the dineutron binding energy as input . specifically , we vary the scattering length , which is now used as input for the lets at nlo , in the range consistent with the lattice - qcd phase shifts at the two lowest energies . the resulting phase shifts , corresponding to the inverse scattering length in the range of @xmath168 are shown in the left panel of fig . [ fig:1s0_letsa ] . here , we set @xmath169 , and the width of the band reflects the uncertainty of the lattice - qcd phase shifts used as input . notice that while the nplqcd value of the inverse scattering length given in eq . ( [ ere1s0nplqcd ] ) is indeed consistent with the range of values in eq . ( [ ainvphases ] ) , the obtained solutions correspond to the bound ( virtual ) state binding energy of @xmath170 mev ( @xmath171 mev ) which is in conflict with the lattice - qcd prediction . the apparent bound state corresponding to the leftmost intersection point of the gray bands with the unitarity term @xmath172 in the right panel of fig . [ fig:1s0_letseb ] is an artifact of the effective range approximation . finally , it is interesting to compare our results for the scattering length and effective range with the values obtained in ref . @xcite within the ksw approach to chiral eft @xcite , namely @xmath173 notice that the effective range vanishes at lo in the ksw approach , and the number of independent parameters fitted to lattice data is equal to one , two and three at lo , nlo and next - to - next - to - leading order ( nnlo ) , respectively . our nlo let results are in excellent agreement with the nlo ksw values and also nearly consistent with the nnlo ksw results . channel calculated on the lattice at @xmath102 mev @xcite in comparison with the predictions based on the lets at nlo ( blue shaded bands ) using the scattering length in eq . ( [ ainvphases ] ) as input . for remaining notation see fig . [ fig:3s1let ] . [ fig:1s0_letsa ] , title="fig:",scaledwidth=49.0% ] channel calculated on the lattice at @xmath102 mev @xcite in comparison with the predictions based on the lets at nlo ( blue shaded bands ) using the scattering length in eq . ( [ ainvphases ] ) as input . for remaining notation see fig . [ fig:3s1let ] . [ fig:1s0_letsa ] , title="fig:",scaledwidth=49.0% ]

using the binding energies of the deuteron and dineutron as input , we employ the low - energy theorems to predict the phase shifts and extract the scattering length and the effective range in the and channels . our results for these quantities are consistent with those obtained by the nplqcd collaboration from effective field theory analyses but are in conflict with their determination based on the effective - range approximation .

we apply the low - energy theorems to analyze the recent lattice qcd results for the two - nucleon system at a pion mass of mev obtained by the nplqcd collaboration . we find that the binding energies of the deuteron and dineutron are inconsistent with the low - energy behavior of the corresponding phase shifts within the quoted uncertainties and vice versa . using the binding energies of the deuteron and dineutron as input , we employ the low - energy theorems to predict the phase shifts and extract the scattering length and the effective range in the and channels . our results for these quantities are consistent with those obtained by the nplqcd collaboration from effective field theory analyses but are in conflict with their determination based on the effective - range approximation .

1604.02551

i

in this paper , we have employed the low - energy theorems for nn scattering , which have been generalized in ref . @xcite to the case of unphysical pion masses , to analyze the recent lattice - qcd results at @xmath9 mev reported by the nplqcd collaboration @xcite . the pertinent results of our work can be summarized as follows . * we have used the lets along with the lattice - qcd results for the deuteron and dineutron binding energies in order to extract the energy behavior of the nn phase shifts in the @xmath1 and @xmath2 partial waves and the mixing angle @xmath181 at @xmath139 mev . our lo and nlo calculations suggest a good ( fair ) convergence of our theoretical approach in the spin - triplet ( spin - singlet ) channel . in both channels , the resulting phase shifts are in good agreement with the lattice - qcd results of ref . @xcite for momenta of @xmath182 mev , but are inconsistent with the lattice - qcd predictions at lower energies . * we have used the lets to extract the values of the scattering length and effective range in the @xmath1 and @xmath2 partial waves from the bound state energies obtained on the lattice . the extracted value of @xmath183 is in excellent agreement with the linear in @xmath14 behavior of this quantity conjectured in ref . @xcite . on the other hand , our results are in strong disagreement with the values obtained by the nplqcd collaboration from fits to the lattice - qcd data based on the effective range approximation . we have argued that the very large values for the effective range found in ref . @xcite make the effective range approximation invalid in the energy region corresponding to the lattice data . * our results for phase shifts , scattering lengths and effective ranges agree reasonably well with those obtained in ref . @xcite by analyzing lattice - qcd data within the various eft approaches . given considerable evidence of a bound dineutron and a stronger bound deuteron at heavy pion masses @xcite , our findings indicate that the lattice - qcd calculations of the nn phase shifts of ref . @xcite using the extended lscher approach may possibly suffer from underestimated systematic errors at the lowest considered energies . in addition , using lattice results for the binding energies of the deuteron and dineutron at various pion masses as input @xcite , we demonstrate that the effective range expressed in units of the pion mass behaves as a linear function of @xmath126 . our work demonstrates that the lets provide a useful tool to analyze lattice qcd results for the nn system by allowing one to extract the scattering phase shifts from the calculated bound state energies and/or test consistency of lattice calculations if several observables are computed . we would like to thank jambul gegelia for sharing his insights into the topic discussed here and for a careful reading of the manuscript . we are also grateful to the organizers of the yipqs long - term and nishinomiya - yukawa memorial international workshop on `` computational advances in nuclear and hadron physics '' at yukawa institute for theoretical physics , kyoto university and to the organizers of the int-16 - 1 program `` nuclear physics from lattice qcd '' at int seattle , where a part of this work was carried out . work supported in part by the erc ( project 259218 nucleareft ) , the bmbf ( verbundprojekt 05p2015 - nustar r&d ) and the dfg ( grant gz : ba 5443/1 - 1 aobj : 616443 ) . meiner , sci . bull . * 60*(1 ) , 43 ( 2015 ) , [ arxiv:1409.2959 [ hep - th ] ] . h. oberhummer , a. csoto and h. schlattl , nucl . a * 689 * , 269 ( 2001 ) , [ nucl - th/0009046 ] . e. epelbaum _ et al . _ , phys . * 110 * , no . 11 , 112502 ( 2013 ) , [ arxiv:1212.4181 [ nucl - th ] ] . e. epelbaum , h. krebs , t. a. lhde , d. lee and u .- g . meiner , eur . j. a * 49 * , 82 ( 2013 ) , [ arxiv:1303.4856 [ nucl - th ] ] . f. bedaque , t. luu and l. platter , phys . c * 83 * , 045803 ( 2011 ) , [ arxiv:1012.3840 [ nucl - th ] ] . j. c. berengut _ et al . _ , phys . d * 87 * , no . 8 , 085018 ( 2013 ) , [ arxiv:1301.1738 [ nucl - th ] ] . s. r. beane _ et al . _ [ nplqcd collaboration ] , phys . d * 85 * , 054511 ( 2012 ) , [ arxiv:1109.2889 [ hep - lat ] ] . t. yamazaki , k. i. ishikawa , y. kuramashi and a. ukawa , phys . d * 92 * , no . 1 , 014501 ( 2015 ) , [ arxiv:1502.04182 [ hep - lat ] ] . k. orginos , a. parreno , m. j. savage , s. r. beane , e. chang and w. detmold , phys . rev . d * 92 * , no . 11 , 114512 ( 2015 ) [ arxiv:1508.07583 [ hep - lat ] ] . s. r. beane , p. f. bedaque , m. j. savage and u. van kolck , nucl . a * 700 * , 377 ( 2002 ) , [ nucl - th/0104030 ] . s. r. beane and m. j. savage , nucl . a * 713 * , 148 ( 2003 ) , [ hep - ph/0206113 ] . e. epelbaum , u .- g . meiner and w. glckle , nucl . a * 714 * , 535 ( 2003 ) , [ nucl - th/0207089 ] . s. r. beane and m. j. savage , nucl . a * 717 * , 91 ( 2003 ) , [ nucl - th/0208021 ] . e. epelbaum , u .- g . meiner and w. glckle , nucl - th/0208040 . j. w. chen , t. k. lee , c .- p . liu and y. s. liu , phys . c * 86 * , 054001 ( 2012 ) , [ arxiv:1012.0453 [ nucl - th ] ] . j. soto and j. tarrus , phys . c * 85 * , 044001 ( 2012 ) , [ arxiv:1112.4426 [ nucl - th ] ] . e. epelbaum and j. gegelia , pos cd * 12 * , 090 ( 2013 ) , [ arxiv:1301.6134 [ nucl - th ] ] . s. r. beane _ et al . _ [ nplqcd collaboration ] , phys . d * 87 * , no . 3 , 034506 ( 2013 ) , [ arxiv:1206.5219 [ hep - lat ] ] . s. r. beane _ et al . _ [ nplqcd collaboration ] , phys . rev . c * 88 * , no . 2 , 024003 ( 2013 ) , [ arxiv:1301.5790 [ hep - lat ] ] . e. berkowitz _ et al . _ , arxiv:1508.00886 [ hep - lat ] . t. yamazaki , k. i. ishikawa , y. kuramashi and a. ukawa , phys . d * 86 * , 074514 ( 2012 ) , [ arxiv:1207.4277 [ hep - lat ] ] . t. inoue _ et al . [ hal qcd collaboration ] , nucl . a * 881 * , 28 ( 2012 ) , [ arxiv:1112.5926 [ hep - lat ] ] . v. v. flambaum and r. b. wiringa , phys . c * 76 * , 054002 ( 2007 ) , [ arxiv:0709.0077 [ nucl - th ] ] . v. baru , e. epelbaum , a. a. filin and j. gegelia , phys . c * 92 * , no . 1 , 014001 ( 2015 ) , [ arxiv:1504.07852 [ nucl - th ] ] . t. d. cohen and j. m. hansen , phys . c * 59 * , 13 ( 1999 ) , [ nucl - th/9808038 ] . t. d. cohen and j. m. hansen , phys . c * 59 * , 3047 ( 1999 ) , [ nucl - th/9901065 ] . j. v. steele and r. j. furnstahl , nucl . a * 645 * , 439 ( 1999 ) , [ nucl - th/9808022 ] . e. epelbaum and j. gegelia , eur . j. a * 41 * , 341 ( 2009 ) , [ arxiv:0906.3822 [ nucl - th ] ] . e. epelbaum and j. gegelia , pos cd * 09 * , 077 ( 2009 ) . e. epelbaum , arxiv:1001.3229 [ nucl - th ] . j. j. de swart , c. p. f. terheggen and v. g. j. stoks , nucl - th/9509032 . h. van haeringen and l. p. kok , phys . * a26 * , 1218 ( 1982 ) . e. epelbaum and j. gegelia , phys . b * 716 * , 338 ( 2012 ) , [ arxiv:1207.2420 [ nucl - th ] ] . e. epelbaum , a. m. gasparyan , j. gegelia and h. krebs , eur . phys . j. a * 51 * , no . 6 , 71 ( 2015 ) , [ arxiv:1501.01191 [ nucl - th ] ] . v. g. kadyshevsky , nucl . b * 6 * , 125 ( 1968 ) . v. baru , e. epelbaum , a. a. filin , j. gegelia and a. v. nefediev , phys . d * 92 * , no . 11 , 114016 ( 2015 ) , [ arxiv:1509.01789 [ hep - ph ] ] . j. m. blatt and j. d. jackson , phys . rev . * 76 * , 18 ( 1949 ) . b. midya _ et al . _ , arxiv:1501.04011 [ quant - ph ] . m. lscher , commun . phys . * 105 * , 153 ( 1986 ) . m. lscher , nucl . b * 354 * , 531 ( 1991 ) . r. a. brice@xmath184o , z. davoudi , t. luu and m. j. savage , phys . d * 88 * , no . 11 , 114507 ( 2013 ) , [ arxiv:1309.3556 [ hep - lat ] ] . j. m. blatt and l. c. biedenharn , rev . * 24 * , 258 ( 1952 ) . d. b. kaplan , m. j. savage and m. b. wise , nucl . b * 534 * , 329 ( 1998 ) , [ nucl - th/9802075 ] . d. b. kaplan , m. j. savage and m. b. wise , phys . b * 424 * , 390 ( 1998 ) [ nucl - th/9801034 ] . m. pavon valderrama and e. ruiz arriola , phys . rev . c * 72 * , 044007 ( 2005 ) .

we apply the low - energy theorems to analyze the recent lattice qcd results for the two - nucleon system at a pion mass of mev obtained by the nplqcd collaboration . we find that the binding energies of the deuteron and dineutron are inconsistent with the low - energy behavior of the corresponding phase shifts within the quoted uncertainties and vice versa .

we apply the low - energy theorems to analyze the recent lattice qcd results for the two - nucleon system at a pion mass of mev obtained by the nplqcd collaboration . we find that the binding energies of the deuteron and dineutron are inconsistent with the low - energy behavior of the corresponding phase shifts within the quoted uncertainties and vice versa . using the binding energies of the deuteron and dineutron as input , we employ the low - energy theorems to predict the phase shifts and extract the scattering length and the effective range in the and channels . our results for these quantities are consistent with those obtained by the nplqcd collaboration from effective field theory analyses but are in conflict with their determination based on the effective - range approximation .

1206.6512

i

a conservation law ought to explain the change in some physical quantity contained inside a volume of space ( e.g. , total energy ) in terms of related fluxes passing through the bounding surface of that volume . the standard approach to constructing conservation laws is based on the identity : @xmath5 , where @xmath6 is the matter stress - energy - momentum tensor , and @xmath7 is a vector that determines the type of conservation law , viz . , energy , momentum , or angular momentum . in the context of general relativity , matter energy - momentum is locally covariantly conserved , i.e. , @xmath8 , and the identity reduces to @xmath9 . as is well known , the problem with this local conservation law is that the right hand side is , in general , not zero ( or even a covariant divergence ) , resulting in a bulk term in the integrated conservation law that spoils what a conservation law ought to be . this problem is essentially gravitational in nature . there are several ways to see this : ( 1 ) the offending bulk term disappears when the spacetime has a suitable symmetry , i.e. , admits a killing vector , @xmath7 , but dynamically interesting spacetimes ( e.g. , ones containing gravitational effects due to objects in motion ) generically do not . the idea of relying on a spacetime symmetry to construct a conservation law is a throwback to pre - general relativity days , e.g. , special relativity , where spacetime is maximally symmetric . the same goes for relying on asymptotic spacetime symmetries , where we are still in essentially a special relativistic mindset . given that gravity _ is _ nontrivial spacetime geometry , an approach relying on spacetime symmetries can not hope to properly incorporate gravitational effects in general . ( 2 ) the local conservation law above is _ homogeneous _ in @xmath6 . in any matter - free region it is vacuous , even if that region contains interesting gravitational physics , e.g. , gravitational waves . the local conservation law is essentially blind to gravitational physics . we need a conservation law that is nontrivial even when @xmath10 . ( 3 ) because of the equivalence principle , gravitational effects , e.g. , gravitational energy , are not localizable , so we have no hope of capturing gravitational physics with a conservation law based on a local stress - energy - momentum tensor . for example , there is no such thing as a local gravitational energy density ( energy per unit volume ) , that when integrated over a volume gives the total gravitational energy in that volume ( see , e.g. , 20.4 of reference @xcite ) . ( 4 ) a bulk term in a local conservation law can be a symptom of the presence of fields that are not being accounted for in the stress - energy - momentum tensor . for example , in the standard poynting theorem , the @xmath11 bulk term is present because @xmath6 excludes the charged matter field that is the source of the electromagnetic field , and represents an energy transfer mechanism between the electromagnetic field and the charged matter field . we contend that the bulk term in the local conservation law is , similarly , a result of @xmath6 not properly accounting for the physics of the gravitational field . a solution to this problem is to move from local to _ quasi_local conservation laws , which _ can _ properly account for the gravitational physics . in this paper we construct a general quasilocal conservation law based not on the local _ matter _ stress - energy - momentum tensor , but on the brown and york quasilocal _ total _ stress - energy - momentum tensor ( matter _ plus _ gravity ) @xcite . here , quasilocal " means that the differential conservation law is integrated not over the history of a volume of space , but over the history of the _ boundary _ of that volume . we focus on the case of energy conservation , and show that in the quasilocal approach , the quasilocal analogue of the offending @xmath12 bulk term becomes a _ surface flux _ term , which immediately solves the main problem mentioned in the opening paragraph above . moreover , this surface flux term has two components : ( i ) the first component is a stress times strain " term that can always be made to vanish by a suitable choice of frame , called a _ rigid quasilocal frame _ ( or rqf ) @xcite . the reader need not be familiar with rqfs to read this paper ; it is sufficient to mention that , regarding point ( 1 ) in the previous paragraph , an rqf satisfies a certain quasilocally projected " form of the timelike killing vector condition for stationary spacetimes that allows us to move just far enough away from the spacetime symmetry mindset to include generic ( i.e. , non - stationary ) spacetimes in conservation laws for energy , momentum , and angular momentum . ( ii ) the second component is an acceleration times momentum " term . this term is familiar from classical mechanics , and represents the rate at which the kinetic energy of an object increases due to one s acceleration toward it . motivated by a simple equivalence principle argument , we show that this second term is actually a _ gravitational _ energy flux involving the general relativistic effect of frame dragging . we thus show precisely how quasilocal conservation laws resolve the bulk term problem in local conservation laws by properly accounting for the physics of the gravitational field . our paper is organized as follows . in [ paradox ] we introduce a very simple example of energy conservation in the context of special relativity , for the purpose of having a concrete example with which to illustrate the development of the general ideas . we consider a variant of bell s spaceship paradox in which a box accelerates rigidly in a transverse , uniform electric field . obviously , the electromagnetic energy inside the box increases , but how would co - moving observers explain this increase ? paradoxically , only _ half _ of the increasing energy comes from a net poynting flux , and , according to the local energy conservation law , the other half comes from a bulk acceleration times momentum " term integrated over the volume of the box . in [ local ] we examine local conservation laws in general , with a particular focus on the role played by the @xmath12 bulk term in our paradox example . this provides a point of comparison for [ quasilocal ] , in which we construct a general quasilocal conservation law and argue how it properly accounts for gravitational physics . we also apply the energy form of this quasilocal conservation law to the general relativistic version of our paradox example to concretely illustrate how , what we would normally think of as a bulk acceleration times momentum " term , is actually a gravitational energy flux entering through the boundary of the box . in [ conclusions ] we present a complementary summary and conclusions , and argue that quasilocal conservation laws are necessary to understand more deeply a wide variety of phenomena , including the simple example of dropping an apple .

we argue that conservation laws based on the _ local _ matter - only stress - energy - momentum tensor ( characterized by energy and momentum per unit _ volume _ ) can not adequately explain a wide variety of even very simple physical phenomena because they fail to properly account for gravitational effects . pmcgrath@uwaterloo.ca , repp@perimeterinstitute.ca , rbmann@sciborg.uwaterloo.ca_

we argue that conservation laws based on the _ local _ matter - only stress - energy - momentum tensor ( characterized by energy and momentum per unit _ volume _ ) can not adequately explain a wide variety of even very simple physical phenomena because they fail to properly account for gravitational effects . we construct a general _ quasi_local conservation law based on the brown and york _ total _ ( matter _ plus _ gravity ) stress - energy - momentum tensor ( characterized by energy and momentum per unit _ area _ ) , and argue that it _ does _ properly account for gravitational effects . as a simple example of the explanatory power of this quasilocal approach , consider that , when we accelerate toward a freely - floating massive object , the kinetic energy of that object increases ( relative to our frame ) . but how , exactly , does the object acquire this increasing kinetic energy ? using the energy form of our quasilocal conservation law , we can see precisely the actual mechanism by which the kinetic energy increases : it is due to a bona fide gravitational energy flux that is exactly analogous to the electromagnetic poynting flux , and involves the general relativistic effect of frame dragging caused by the object s motion relative to us . * quasilocal conservation laws : why we need them * paul l. mcgrath , richard j. epp and robert b. mann _ department of physics and astronomy , university of waterloo , waterloo , ontario n2l 3g1 , canada _ _ perimeter institute for theoretical physics , waterloo , ontario n2l 2y5 , canada _ _ pmcgrath@uwaterloo.ca , repp@perimeterinstitute.ca , rbmann@sciborg.uwaterloo.ca_

1206.6512

i

using the standard , local way of constructing conservation laws see equations ( [ bulkdifferential ] ) and ( [ bulkintegrated])we analyzed conservation of energy in the context of a simple example in special relativity , viz . , a box , rigidly accelerating along the @xmath15-axis , that is immersed in a transverse , uniform electric field . according to the local energy conservation law , the electromagnetic energy inside the box increases due to two separate mechanisms : ( 1 ) half of the increasing energy is due to energy flowing in from outside the box via a poynting flux . interestingly , even though the instantaneous proper poynting vector is uniform throughout the box ( suggesting no net flux ) , there is a net proper time - integrated flux due to the acceleration - induced relative time dilation between observers at the top and bottom of the box . ( 2 ) the other half of the increasing energy is _ not _ due to energy flowing in from the outside ; rather , it is a bulk effect due to the co - moving observers accelerating relative to the existing electromagnetic momentum inside the box , i.e. , an acceleration times momentum " energy transfer mechanism familiar from classical mechanics , integrated over the volume of the box . one might wonder if these two energy transfer mechanisms adequately explain what s happening . the answer is : no . first , in special relativity we assume that spacetime is flat , even though there is an electromagnetic field present . this precludes any possible general relativistic effects such as a flux of gravitational energy associated with the curvature of the spacetime caused by the electromagnetic field . secondly , even in the context of general relativity , a _ local _ conservation law can not properly capture all of the gravitational physics ; for example , gravitational energy is not localizable there is no such thing as a gravitational energy per unit volume , so a local conservation law can not tell the whole story . another way to see this problem is to notice that the standard local conservation law is _ homogeneous _ in the matter stress - energy - momentum tensor , and so has nothing to say in a matter - free region of space , even though that region may contain dynamical curvature , e.g. , gravitational waves . to address these shortcomings in general , and in particular see what s really happening with regards to the increasing energy inside the box , we constructed a _ quasi_local conservation law based on the brown & york quasilocal ( matter plus gravitational ) stress - energy - momentum tensor defined on the history of the boundary of a spatial volume see equations ( [ quasilocaldifferential ] ) and ( [ quasilocalintegrated ] ) . using the energy form of this quasilocal conservation law , we analyzed the general relativistic analogue of the simple example described above . we found , again , that the electromagnetic energy inside the box increases due to two separate mechanisms . the first mechanism is identical in form to the poynting flux mechanism described above [ number ( 1 ) ] , but conceptually it has a completely different origin : it is actually analogous to a surface flux version of the @xmath11 bulk term in the standard poynting theorem , except instead of energy being transferred locally from the electromagnetic field to the four - current source of the field , it represents energy being transferred quasilocally from the matter fields to the system " contained inside the box . the second mechanism is , at first sight , conceptually identical to the acceleration times momentum " energy transfer mechanism described above [ number ( 2 ) ] , except the volume integral has been converted to a _ surface flux _ integral over the boundary of the box . going further , we argued that this surface flux is actually a _ gravitational _ energy flux exactly analogous to the electromagnetic poynting flux , @xmath243 , with @xmath244 replaced by the acceleration of the co - moving observers on the boundary of the box , and @xmath245 replaced by the precession rate of their gyroscopes due to the frame dragging caused by the electromagnetic momentum ( in general , matter and gravitational momentum ) flowing through the box . in _ both _ cases , now , energy is entering from outside the box via surface fluxes : half is an electromagnetic energy flux ( entering the box through its top and bottom ) and the other half is a gravitational energy flux ( entering the box through its _ sides _ ) . because an electromagnetic field is intimately intertwined with the spacetime curvature it produces , general relativity does not distinguish between electromagnetic and gravitational energy entering the box both contribute on the same footing to the increasing electromagnetic energy inside the box . we can understand the second , gravitational energy flux mechanism intuitively as follows . imagine being inside an accelerating box in empty space , which contains a freely - floating massive body that appears to be accelerating toward you . from your perspective , its kinetic energy is increasing . where does the increasing kinetic energy come from ? explain " it as simply the acceleration times momentum " energy transfer mechanism familiar from classical mechanics . alternatively , we could invoke the equivalence principle and say that our box is at rest in a uniform gravitational field , and that the kinetic energy is coming from the gravitational field outside the box via some kind of gravitational energy flux passing through the boundary of the box . an analogous mechanism exists in the context of electrodynamics that explains , in detail , how an accelerating charge acquires kinetic energy from the external electric field causing the particle s acceleration @xcite ; moreover , the gravitational version of this mechanism has been shown to exist in the context of the linearized , weak field approximation to general relativity @xcite . in this paper we have established the existence of this very basic , but subtle mechanism in the full , nonlinear general theory of relativity , with arbitrary matter and no approximations . our analysis made use of the concept of _ rigid quasilocal frames _ ( rqfs ) , discussed more fully in references @xcite , in order to properly isolate the relevant energy fluxes passing through the boundary of the box . in conclusion , we have explained the bulk acceleration times momentum " energy transfer mechanism familiar in classical mechanics _ exactly _ in terms of a simple , operationally defined , purely geometrical , general relativistic gravitational energy flux passing through the _ boundary _ of the volume in question . naively , one might argue that since there is no @xmath246 or @xmath247 in acceleration times momentum " , this can not be a general relativistic effect . but it _ is_. it is based on frame dragging ( the gravitational analogue of @xmath245 " in @xmath243 " ) , which is a general relativistic effect . we do nt notice this mechanism in our day - to - day experiences because the typical gyroscopic precession rate vector due to a nearby object in motion is very tiny ; but it is precisely this vector , multiplied by the huge number @xmath189 , that we identify as the momentum " of the object [ more precisely , the quasilocal momentum surface density , rotated by @xmath248 degrees see equation ( [ gravitationalpoynting ] ) ] . this general relativistic gravitational energy flux mechanism is what s _ really _ happening in the bulk acceleration times momentum " energy transfer mechanism in classical mechanics . this deeper understanding would not be possible in the context of local conservation laws , and is a nice example of why we need _ quasi_local conservation laws .

we construct a general _ quasi_local conservation law based on the brown and york _ total _ ( matter _ plus _ gravity ) stress - energy - momentum tensor ( characterized by energy and momentum per unit _ area _ ) , and argue that it _ does _ properly account for gravitational effects . as a simple example of the explanatory power of this quasilocal approach , consider that , when we accelerate toward a freely - floating massive object , the kinetic energy of that object increases ( relative to our frame ) . but how , exactly , does the object acquire this increasing kinetic energy ? using the energy form of our quasilocal conservation law , we can see precisely the actual mechanism by which the kinetic energy increases : it is due to a bona fide gravitational energy flux that is exactly analogous to the electromagnetic poynting flux , and involves the general relativistic effect of frame dragging caused by the object s motion relative to us . * quasilocal conservation laws : why we need them * paul l. mcgrath , richard j. epp and robert b. mann _ department of physics and astronomy , university of waterloo , waterloo , ontario n2l 3g1 , canada _ _ perimeter institute for theoretical physics , waterloo , ontario n2l 2y5 , canada _ _

we argue that conservation laws based on the _ local _ matter - only stress - energy - momentum tensor ( characterized by energy and momentum per unit _ volume _ ) can not adequately explain a wide variety of even very simple physical phenomena because they fail to properly account for gravitational effects . we construct a general _ quasi_local conservation law based on the brown and york _ total _ ( matter _ plus _ gravity ) stress - energy - momentum tensor ( characterized by energy and momentum per unit _ area _ ) , and argue that it _ does _ properly account for gravitational effects . as a simple example of the explanatory power of this quasilocal approach , consider that , when we accelerate toward a freely - floating massive object , the kinetic energy of that object increases ( relative to our frame ) . but how , exactly , does the object acquire this increasing kinetic energy ? using the energy form of our quasilocal conservation law , we can see precisely the actual mechanism by which the kinetic energy increases : it is due to a bona fide gravitational energy flux that is exactly analogous to the electromagnetic poynting flux , and involves the general relativistic effect of frame dragging caused by the object s motion relative to us . * quasilocal conservation laws : why we need them * paul l. mcgrath , richard j. epp and robert b. mann _ department of physics and astronomy , university of waterloo , waterloo , ontario n2l 3g1 , canada _ _ perimeter institute for theoretical physics , waterloo , ontario n2l 2y5 , canada _ _ pmcgrath@uwaterloo.ca , repp@perimeterinstitute.ca , rbmann@sciborg.uwaterloo.ca_

1504.03245

i

recent experimental studies of nuclei in the nobelium region provided rich spectroscopic data @xcite , which , in principle , can be used as a benchmark information for extrapolations into the region of superheavy nuclei . numerous theoretical studies are aimed at modelling of these spectroscopic data @xcite so as to make such extrapolations as reliable as possible . the estimation of theoretical uncertainties is one of the most essential aspects of extrapolating nuclear models into exotic nuclei @xcite . one , fairly easy part of it , is the evaluation of statistical uncertainties of observables that are related to the uncertainties of model parameters adjusted , in one way or another , to experimental data . another one , very difficult , pertains to those systematic uncertainties related to the definition and contents of the different terms that make up the models themselves . an obvious strategy , which , anyhow , gives us only a limited glimpse on possible systematic uncertainties , is to study a set of variants of a given model , and to analyze differences obtained for calculated observables . in the present study , we aim at such an analysis of results obtained within three fairly different energy - density - functional ( edf ) approaches . namely , we employ the covariant edfs @xcite , with one classic ( nl1 @xcite ) and one recent ( nl3 * @xcite ) parameter set , skyrme edfs @xcite , with one classic ( sly4 @xcite ) and one recent ( unedf2 @xcite ) parameter set , as well as gogny edfs @xcite , again with one classic ( d1s @xcite ) and one recent ( d1 m @xcite ) parameter set . our goal is thus to determine , present , and compare results obtained within these six models for a common set of calculated observables . we aim at performing these analyses within the most similar and/or equivalent conditions , so as to meaningfully discuss general _ qualitative _ similarities and differences . in all cases , pairing correlations are treated on the bogoliubov level . in the literature , it is customary to label such calculations as hartree - fock - bogoliubov ( hfb ) in the non - relativistic cases and as relativistic hartree - bogoliubov ( rhb ) for the specific variant of relativistic mean - field model used here , thereby emphasizing that hfb - like equations are solved instead of simpler hf+bcs equations . only in the calculations with a gogny force , however , the same effective interaction is used to determine direct , exchange , and pairing matrix elements . by contrast , in case of skyrme edf and the relativistic approach particle - hole and pairing matrix elements relate to different effective interactions , which can be used to simplify their form and phenomenological adjustment . also , in the rhb approach all exchange terms are neglected , whereas in the case of many skyrme parameterizations some are modified in order to improve the description of data @xcite . none of these formal differences is relevant for our discussion , and we will use whenever possible the generic notion of an edf method for all three approaches . indeed , in all cases the total energy can be cast into the form of a functional of normal and anomalous one - body density matrices from which the equations - of - motion are then derived by variation . we do not attribute too much of an importance to _ quantitative _ similarities and differences between the obtained results , especially when the models are compared to experimental data . indeed , a detailed agreement with the data may crucially depend on specific model - parameter adjustments , or on various corrections taken into account or disregarded . the _ phenomenological _ edf used include a limited set of parameters ( typically between seven and twenty ) and aim at a global description of a wide variety of nuclear properties and therefore a perfect agreement with experimental data is out of reach at present . certainly , in the future all edf approaches will be improved ; here we only look into generic properties obtained for selected current global parameterisations thereof . in the present analysis , we systematically calculated the ground states of even - even and odd - mass nuclei from uranium ( @xmath2 ) to rutherfordium ( @xmath3 ) and for neutron numbers between @xmath4 and 156 . the selection of this region of heaviest actinides / lightest superheavy nuclei is guided by the need for reliable experimental data on spectroscopic properties ( in particular , on the single - particle energies of deformed one - quasiparticle states ) based on which the extrapolability of a given theory / functional towards region of superheavy nuclei may be judged . in addition , we determined low - lying quasiparticle spectra of odd - mass nuclei and low - spin moments of inertia of even - even nuclei . the main thrust of the analysis was on the attempt to identify single - particle and shell - structure properties of these nuclei by looking at many - body observables such as masses , odd - even and two - particle mass staggering , and excitation energies . the paper is organised as follows . selected theoretical aspects of our calculations are presented in section [ sec2 ] , with four subsections discussing the methods related to obtaining results for the skyrme edf sly4 ( [ sec2b ] ) , skyrme edf unedf2 ( [ sec2d ] ) , gogny edfs ( [ sec2c ] ) , and covariant edfs ( [ sec2a ] ) . the results of the calculations are given in section [ sec3 ] , with subsections devoted to the nilsson diagrams ( [ sec3b ] ) , quasiparticle spectra ( [ sec3a ] and [ sec3c ] ) , odd - even and two - particle mass staggering ( [ sec3d ] ) , and moments of inertia ( [ sec3e ] ) . conclusions are presented in section [ sec4 ] .

a comparative analysis of the results obtained for quasiparticle spectra , odd - even and two - particle mass staggering , and moments of inertia allows us to identify single - particle and shell effects that are characteristic to these different models and to illustrate possible systematic uncertainties related to using the edf modelling . utf8gbsn heavy and superheavy nuclei ; nuclear masses ; quasiparticle excitations ; odd - even mass staggering ; two - particle mass staggering ; moments of inertia ; nuclear energy density functionals

we calculate properties of the ground and excited states of nuclei in the nobelium region for proton and neutron numbers of and , respectively . we use three different energy - density - functional ( edf ) approaches , based on covariant , skyrme , and gogny functionals , each with two different parameter sets . a comparative analysis of the results obtained for quasiparticle spectra , odd - even and two - particle mass staggering , and moments of inertia allows us to identify single - particle and shell effects that are characteristic to these different models and to illustrate possible systematic uncertainties related to using the edf modelling . utf8gbsn heavy and superheavy nuclei ; nuclear masses ; quasiparticle excitations ; odd - even mass staggering ; two - particle mass staggering ; moments of inertia ; nuclear energy density functionals

0807.3802

i

over the last decades , our understanding of cosmological reionization has improved considerably . observations of high - redshift quasars clearly indicate that reionization must end around @xmath5 @xcite , and the wmap 5-year - measurement finds a reionization optical depth of @xmath6 @xcite , yielding clear evidence that reionization started significantly earlier and is thus a continuous process . reionization through miniquasars would produce a soft - x - ray background that is significantly higher than the observed background , and can thus be ruled out @xcite . simulations of stellar reionization further show that the process is highly inhomogeneous and based on the growth and merging of ionized bubbles around the first stellar sources @xcite . understanding the essential physical processes , it is possible to build semi - analytic models that describe stellar reionization , which can be tested over a wide parameter space @xcite . additional constraints on the cosmic star formation rate are now available from gamma - ray burst observations @xcite . the reionization framework thus provides an increasingly reliable test for the stellar population during reionization and can be used to constrain global physical conditions in the early universe . + + regarding the stellar population , the works @xcite and @xcite suggest that the first stars were top - heavy with a peak in the imf at around @xmath7 . on the contrary , @xcite and @xcite indicate that gas especially in more massive systems can fragment because of dips in the equation of state , which may lead to the formation of a stellar cluster . it was shown that cooling in previously ionized gas is enhanced and leads to typical stellar masses of @xmath8 @xcite . it was further suggested that the presence of weak magnetic fields is sufficient to lead to a more present - day like mode of star formation , resulting in considerably lower masses @xcite . recently , a new phase of stellar evolution was suggested in which the stars would be powered by dark matter annihilation instead of nuclear fusion @xcite . various follow - up works have explored such a scenarios in more detail . studies by @xcite explored the main - sequence and pre - main - sequence phase of dark stars , and other works calculated the effect of dark matter capture by off - scattering from baryons @xcite . while many predictions are still model - dependent , it has often been suggested that such stars may have typical masses of @xmath9 , giving rise to a very bright main - sequence phase , or may have much longer lifetimes due to modifications in the stellar evolution . in the end , all these suggestions must face the constraint that the stellar population must be able to provide the correct reionization optical depth . + + complications may arise through the presence of additional physics that are often not considered in standard reionization calculations and simulations on the first stars . such possibilities include the presence of primordial magnetic fields , dark matter decay and dark matter annihilation . magnetic fields have been observed on all scales in the universe , and recently , it has been demonstrated that they were present already in high - redshift galaxies @xcite . they are found in the interstellar gas as well as in the intergalactic medium @xcite , but their origin is still unclear . there is a viable possibility that these fields have a primordial origin @xcite . so far , the most stringent constraints on the strength of these putative fields come from the measurements of the cosmic microwave background radiation ( cmbr ) and from big - bang nucleosynthesis ( bbn ) calculations . a homogeneous magnetic field would produce temperature anisotropies in the cmbr @xcite whose maximal amplitudes are limited by the cobe satellite measurements which in turn limit the field strength , as measured today , to @xmath10 @xcite . the presence of any primordial field would also alter the cmbr power spectrum by changing the characteristic velocities . with the sensitivity of the planck satellite one should be able to detect fields with present day strength of @xmath11 @xcite . so far , measurements by the wmap satellite are compatible with the absence of primordial magnetic fields . strong magnetic fields in the early universe can also change the abundance of relic @xmath12he and other light elements during the big bang nucleosynthesis @xcite . to comply with observational limits on light element abundances these primordial fields must not exceed @xmath13 at the time when the universe was @xmath14 which corresponds to a present day field @xmath15@xcite . effects of primordial magnetic fields have already been considered in @xcite , finding that density perturbations can be enhanced by the lorentz force from tangled magnetic fields . both the evolution of perturbations in the presence of magnetic fields as well as their effect on the thermodynamics via ambipolar diffusion heating and decaying mhd turbulence was considered in @xcite . recent calculations of @xcite show that the enhancement of structure due to magnetic fields is pronounced at about @xmath16 , but becomes less effective on larger mass scales and appears as a subdominant contribution on the scale of the magnetic jeans mass . consequences for @xmath17 cm observations have been explored as well @xcite . in this work , we examine the consequences for reionization in more detail and calculate the backreaction on structure formation according to the work of @xcite . the wmap 5 year data @xcite have measured the thomson scattering optical depth from reionization and allow to constrain different reionization scenarios in the early universe . the nature of dark matter is still unclear , and consequences of various particle physics like massive neutrinos or axion decay have been explored early ( e. g. * ? ? ? * ; * ? ? ? * ; * ? ? ? observational progress allowed to refine these studies and to explore such scenarios in the framework of @xmath18cdm cosmology @xcite . recently , the possibility was discussed to detect such effects using future @xmath17 cm telescopes@xcite , and it was shown that the fraction of the energy absorbed into the igm can be calculated in detail for specific models of dark matter decay and annihilation @xcite . indeed , secondary ionization through the decay / annihilation products can provide a way to ionize the igm which is independent of the stellar contribution @xcite , whereas the additional heat input increases the jeans mass and delays the formation of the first structures . in this work , we show how reionization constrains the properties of the stellar population as well as some additional heat sources like primordial magnetic fields , dark matter annihilation and decay . in [ reionization ] , we present our model for stellar reionization , which considers the igm as a two - phase - medium consisting of ionized bubbles and overall neutral gas . based on the thermal evolution , we self - consistently determine the minimal mass scale of halos which can collapse . in [ bfields ] , we explain our treatment of primordial magnetic fields and show how they modify the thermal evolution . the treatment of dark matter annihilation and decay , as well as some implications for dark stars , are discussed in [ darkness ] . the optical depth for different models is given in [ cmbfast ] . further discussion and outlook is given in [ outlook ] .

we find that stellar populations based on a scalo - type initial mass function for population ii stars can be ruled out as sole sources for reionization , unless star formation efficiencies of more than or very high photon escape fractions from the parental halo are adopted . when considering primordial magnetic fields , we find that the additional heat injection from ambipolar diffusion and decaying mhd turbulence has significant impact on the thermal evolution and the ionization history of the post - recombination universe and on structure formation .

we calculate the reionization history for different models of the stellar population and explore the effects of primordial magnetic fields , dark matter decay and dark matter annihilation on reionization . we find that stellar populations based on a scalo - type initial mass function for population ii stars can be ruled out as sole sources for reionization , unless star formation efficiencies of more than or very high photon escape fractions from the parental halo are adopted . when considering primordial magnetic fields , we find that the additional heat injection from ambipolar diffusion and decaying mhd turbulence has significant impact on the thermal evolution and the ionization history of the post - recombination universe and on structure formation . the magnetic jeans mass changes the typical mass scale of the star forming halos , and depending on the adopted stellar model we derive upper limits to the magnetic field strength between andng ( comoving ) . for dark matter annihilation , we find an upper limit to the thermally averaged mass - weighted cross section of . for dark matter decay , our calculations yield a lower limit to the lifetime of dark matter particles ofs . these limits are in agreement with constraints from recombination and provide an independent confirmation at a much later epoch .

0807.3802

c

we have calculated the reionization optical depth for different stellar models in the presence of primordial magnetic fields as well as dark matter annihilation and decay . the results indicate which star formation efficiencies are required in the presence of some additional heating mechanism for a given stellar model . considering different stellar models and primordial magnetic fields , we find the following results : 1 . independent of the model for the stellar population , we can securely exclude primordial magnetic fields larger than @xmath194 ng . 2 . for the most realistic case with a mixed stellar population ( model c ) , we even find an upper limit of @xmath1 ng , as higher magnetic fields would require star formation efficiencies larger than @xmath192 , which is unrealistic . similar results are found for model b , assuming reionization completely due to pop . iii stars . 3 . reionization only due to population ii stars ( model d ) is ruled out completely . 1 . dark matter annihilation provides noticeable contributions to the reionization optical depth only for thermally averaged mass - weighted cross sections @xmath208 . parameters @xmath209 can be ruled out by @xmath188 on the basis of wmap 5 year data . dark matter decay becomes important for the reionization optical depth for lifetimes below @xmath202 s. 4 . dark matter lifetimes below @xmath203 s are ruled out by @xmath188 . these results are in agreement with conservative constraints obtained from the gamma - ray background @xcite . we further showed that reionization can not be due to @xmath210 dark stars alone , as the corresponding optical depth would be significantly too high . one might wonder whether heating from dark matter annihilation might help to significantly delay stellar reionization , in order to reconcile this model with observations . however , as can be seen in fig . [ img : annihilation ] , this is more than compensated by the effects of secondary ionization , once that dark matter annihilation starts to have a significant influence on the igm . in case collider experiments like the lhc or other dark matter detection experiments find evidence for a self - annihilating dark matter candidate , this can be seen as evidence for a rapid transition towards a different mode of star formation , or a problem in our understanding of dark stars . to reconcile dark stars with observations , the following scenarios seem feasible : 1 . dark stars with @xmath211 may be extremely rare objects , and their actual mass scale is closer to the mass scale for typical pop . iii stars . in such a case , reionization could not distinguish between dark stars and conventional pop . iii stars . 2 . the transition to lower - mass stars occurs very rapidly , such that dark stars only contribute to the very early phase of reionization . reasons for that might be chemical , radiative as well as mechanical feedback ( see also the discussion in [ dark star ] ) . in fact , even a double - reionization scenario might be conceivable , in which very massive dark stars ionize the universe at high redshifts . due to chemical and radiative feedback , formation of such stars might be suppressed and the universe might become neutral again , until the formation of less massive stars becomes efficient enough to reionize the universe . 3 . dark stars do not reach a main - sequence phase , but are disrupted earlier by some non - linear instability . such an instability would be constrained by the fact that it neither appears in a linear stability analysis nore in 1d simulations . violent explosions of dark stars might even be considered as a source for gamma - ray bursts . while too definite conclusions on the existence of dark stars are not yet possible , it is at least indicated that the possibilities mentioned above should be explored in more detailed , and a better understanding of the properties of the dark stars . a better understanding of their evolution after the dark phase will certainly help to better understand their possible role during reionization . the constraints derived here are independent of other works that essentially rely on the physics of recombination to derive upper limits on additional physics ( e. g. * ? ? ? * ; * ? ? ? * ; * ? ? ? in particular , magnetic fields can evolve dynamically and their field strength may thus change between these epochs . it has recently been suggested that the biermann battery effect creates magnetic fields in the presence of an electron pressure gradient@xcite . we thus need to probe magnetic fields at different epochs . as we will show in a separate work @xcite , upcoming @xmath17 cm measurements will allow to probe the thermal history before and during reionization in great detail , and may allow to detect primordial magnetic fields of the order of @xmath212 ng . additional ways of probing the reionization history and the dark ages exist as well : scattering of cmb - photons in fine - structure lines of heavy elements may lead to a frequency - dependent cmb power spectrum and may allow to measure metal - abundances as a function of redshift @xcite . before reionization , molecules may form in the igm and introduce further frequency - dependent features in the cmb @xcite . such features are likely enhanced in the presence of either primordial magnetic fields or dark matter decay / annihilation , as the increased electron fraction catalyses the formation of molecules , and the additional heat input leads to a departure of the level populations from the radiation temperature . further improvements are expected from the upcoming measurement of planck , that will measure the reionization optical depth with unprecedent accuracy and thus allow to strengthen the constraints obtained here on the stellar populations and additional physics . in addition , a more accurate determination of the cosmological parameters will remove further uncertainties in the present models of reionization . we thank paul clark , andrea ferrara , katherine freese , daniele galli , simon glover , thomas greif and francesco palla for many exciting discussions on this topic . drgs thanks the heidelberg graduate school of fundamental physics ( hgsfp ) , the lgfg for financial support and the inaf - osservatorio astrofisico di arcetri for financial support . the hgsfp is funded by the excellence initiative of the german government ( grant number gsc 129/1 ) . rb is funded by the emmy - noether grant ( dfg ) ba 3607/1 . rsk thanks for support from the emmy noether grant kl 1358/1 . all authors also acknowledge subsidies from the dfg sfb 439 _ galaxies in the early universe_. we thank the anonymous referee for help improving the manuscript . becker , r. h. et al . , 2001 , @jnlaj , 122 , 2850 komatsu , e. , et al . , 2008 , @jnlapjs , submit ted nolta , m. , et al . , 2008 , @jnlapjs , submit ted dijkstra , m. , haiman , z. , loeb , a. , 2004 , , 613 , 646 salvaterra , r. , haardt , f. , ferrara , a. , 2005 , monthly notices of the royal astronomical society : lett ers , 362 , l50 gnedin , n. y. , 2005 , , 542 , 535 ciardi , b. , ferrara , a. , white , s. d. m. , 2003 , @jnlmnras , 344 , l7 kohler , k. , gnedin , n. y. , ha milton , a. j. s. , 2005 , , 657 , 15 shapiro , p. r. , giroux , m. l. , 1987 , , 321 , l107 haiman , z. , loeb , a. , 1997 , , 483 , 21 barkana , r. , loeb . , a. , 2001 , phys . , 349 , 125 loeb , a , barkana , r. , 2001 , @jnlara&a , 39 , 19 l choudhury , t. r. , ferrara , a. , 2 005 , @jnlmnras , 361 , 577 schneider , r. , salvaterra , r. , ferra ra , a. , ciardi , b. , 2006 , @jnlmnras , 369 , 825 yuksel , h. , kistler , m. d. , beacom , j. f. , 2008 , , 683l , 5 abel , t. , bryan , g. l. , norman , m. l . , 2002 , science , 295 , 93 bromm , v. , larson , r. , 2004 , @jnlara&a , 42 , 7 9 clark , p. c. , glover , s. c. o. , klessen , r. s. , 2008 , , 672 , 757 omukai , k. , schneider , r. , h aiman , z. , 2008 , submitted to yoshida , n. , oh , s. p. , kitayama , t. , h ernquist , l. , 2007 , , 663 , 687 yoshida , n. , omukai , k. , hernquist , l. , 2007 , , 667 , l117 barrow , j. d. , ferreira , p. g. , & silk , j. 1997 , physical review letters , 78 , 3610 silk , j. , langer , m. , 2006 , @jnlmnras , 371 , 44 4 spolyar , d. , freese , k. , gondolo , p. , 2008 , , 100 , 051101 iocco , f. , 2008 , , 677 , l1 freese , k. , bodenheimer , p. , spolyar , d. , iocco , f. , bressan , a. , ripamonti , e. , schneider , r. , ferrara , a. , marigo , p. , 2008 , mnras , in press yoon , s .- c . , iocco , f. , akiyama , s. , 2008 , eprint arxiv:0806.4016 taoso , m. , bertone , g. , meynet , g. , ekstrom , s. , 2008 , eprint arxiv 0806.2681 freese , k. , spolyar , d. , aguirre , a. , 2008 , eprint arxiv:0802.1724 gondolo , p. , 2008 , eprint arxiv:0806.0617 bernet , m. l. , miniati , f. , lilly , s. j. , kronberg , p. p. , dessauges - 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monteagudo , c. ; sunyaev , r. a. , 2004 , a&a , 416 , 447 schleicher , d. r. g. , galli , d. , palla , f. , camenzind , m. , klessen , r. , bartelmann , m. , glover , s. c. o. , 2008 , @jnla&a , 490 , 521

we calculate the reionization history for different models of the stellar population and explore the effects of primordial magnetic fields , dark matter decay and dark matter annihilation on reionization . these limits are in agreement with constraints from recombination and provide an independent confirmation at a much later epoch .

we calculate the reionization history for different models of the stellar population and explore the effects of primordial magnetic fields , dark matter decay and dark matter annihilation on reionization . we find that stellar populations based on a scalo - type initial mass function for population ii stars can be ruled out as sole sources for reionization , unless star formation efficiencies of more than or very high photon escape fractions from the parental halo are adopted . when considering primordial magnetic fields , we find that the additional heat injection from ambipolar diffusion and decaying mhd turbulence has significant impact on the thermal evolution and the ionization history of the post - recombination universe and on structure formation . the magnetic jeans mass changes the typical mass scale of the star forming halos , and depending on the adopted stellar model we derive upper limits to the magnetic field strength between andng ( comoving ) . for dark matter annihilation , we find an upper limit to the thermally averaged mass - weighted cross section of . for dark matter decay , our calculations yield a lower limit to the lifetime of dark matter particles ofs . these limits are in agreement with constraints from recombination and provide an independent confirmation at a much later epoch .

hep-ph0105003

i

branching ratios of @xmath3 meson two - body nonleptonic decays have been measured by cleoiii , belle and babar collaborations @xcite . cp violations in these modes may be observed in near future . cognizant of this point , we have presented some theoretical anticipations for the @xmath10 @xcite , @xmath11 @xcite , and @xmath12 @xcite decays in the perturbative qcd ( pqcd ) framework . in particular , @xmath13 cp violation is expected in the @xmath10 decays . the @xmath14 transition form factors are the integral part of two - body nonleptonic decay amplitudes . in this paper we shall convince readers that these form factors in the large recoil region of light mesons are calculable in pqcd . this is where our approach starts to differ from other approaches to exclusive @xmath3 meson decays . according to pqcd factorization theorem , a form factor is written as the convolution of a hard amplitude with initial - state and final - state hadron distribution amplitudes @xmath15 , where @xmath16 is the momentum fraction associated with one of the partons . it has been pointed out that perturbative evaluation of the pion form factor suffers nonperturbative enhancement from the end - point region with a momentum fraction @xmath17 @xcite . if this is true , the hard amplitude is characterized by a low scale , such that expansion in terms of a large coupling constant @xmath18 is not reliable . more serious end - point ( logarithmic ) singularities have been observed in the twist-2 ( leading - twist ) contribution to the @xmath19 transition form factor @xcite . the singularities even become linear at twist 3 ( next - to - leading twist ) @xcite . because of these singularities , it was claimed that the @xmath19 form factor is dominated by soft dynamics and not calculable in pqcd @xcite . we shall argue that this conclusion is false . we shall show that at the end points , where the above singularities occur , the double logarithms @xmath20 should be resummed in order to justify perturbative expansion . the result , called threshold resummation @xcite , leads to strong sudakov suppression at @xmath17 @xcite . therefore , the end - point singularities do not exist in a self - consistent pqcd analysis . in this work we shall investigate contributions to the @xmath21 and @xmath22 transition form factors from twist-2 and from two - parton twist-3 distribution amplitudes . in sec . ii we illustrate the pqcd formalism by studying the pion electromagnetic form factor . we review the reasoning why one might conclude that the form factor is not calculable , and explain why these objections are not justified in qcd . in secs . iii and iv we derive the @xmath3 meson transition form factors . it will be shown that the twist-3 contributions , which seem to be proportional to @xmath23 or @xmath24 , do not vanish in the @xmath25 limit . here @xmath26 , @xmath27 , and @xmath2 are the chiral symmetry breaking scale , @xmath28 meson mass , and @xmath3 meson mass , respectively . we record our results of the form factors at large recoil : the @xmath19 form factor @xmath29 and the @xmath22 form factor @xmath30 . meson distribution amplitudes are defined and the sudakov factor from threshold resummation is derived in the appendices .

we explain the basic principle by discussing the pion electromagnetic form factor . it is shown that the logarithmic and linear singularities occurring at small momentum fractions of light meson distribution amplitudes do not exist in a self - consistent perturbative analysis , which includes and threshold resummations .

we calculate the transition form factors in the framework of perturbative qcd to leading power of , being the meson mass . we explain the basic principle by discussing the pion electromagnetic form factor . it is shown that the logarithmic and linear singularities occurring at small momentum fractions of light meson distribution amplitudes do not exist in a self - consistent perturbative analysis , which includes and threshold resummations . epsfig.sty # 1[eq:#1 ] # 1#2#3 _ phys . rev . _ * d#1 * # 2 ( # 3 ) # 1#2#3 _ phys . rev . lett . _ * # 1 * # 2 ( # 3 ) # 1#2#3 _ phys . lett . _ * # 1 * # 2 ( # 3 ) = -10 mm = -6 mm = -6 mm = 10000 * ncku - hep-01 - 04 + dpnu-00 - 13 * 1.cm 0.8 cm * .3 cm t. kurimoto , hsiang - nan li and a.i . sanda * * _ department of physics , toyama university , toyama 930 - 8555 , japan _ * * _ department of physics , national cheng - kung university , + tainan , taiwan 701 , republic of china _ * * _ national center for theoretical sciences , hsinchu , taiwan 300 , republic of china _ * * _ department of physics , nagoya university , nagoya 464 - 8602 , japan _ * 2.0 cm * pacs index : 13.25.hw , 11.10.hi , 12.38.bx , 13.25.ft *

hep-ph0105003

c

in this paper we have presented a complete leading - power and leading - order pqcd evaluation of the @xmath19 , @xmath28 transition form factors in the large recoil region . it has been shown that under sudakov suppression arising from @xmath4 and threshold resummations , the end - point singularities ( logarithmic at twist 2 and linear at twist 3 ) do not exist . the soft contribution to the form factors , being sudakov suppressed , becomes smaller than the perturbative contribution . the physical picture for the mechanism of sudakov suppression has been discussed . we have emphasized that the twist-3 contributions are in fact not power - suppressed in the @xmath219 limit . the treatment of the parton transverse momenta @xmath4 and the light spectator momentum @xmath48 in the @xmath3 meson in the computation of the hard amplitudes has been clearly explained : the hard amplitudes should not be expanded in powers of @xmath115 as the end - point region is important . using the light meson distribution amplitudes derived from qcd sum rules , and choosing an appropriate @xmath3 meson distribution amplitude , we have derived reasonable results for the @xmath19 , @xmath28 form factors , which are in agreement with those from light - cone qcd sum rules and from lattice calculations . our study indicates that in a self - consistent perturbative analysis , the heavy - to - light form factors are calculable . the jet function from threshold resummation needs more thorough exploration . we shall investigate the relevant subjects , such as factorization theorem in moment space , threshold resummation up to next - to - leading logarithms , application to nonleptonic @xmath3 meson decays @xcite , and numerical effects elsewhere . note that if considering only @xmath220 resummation @xcite , twist-3 contributions , though infrared finite , are still too large to give reasonable heavy - to - light transition form factors , because the large double logarithms @xmath20 have not yet been organized . * acknowledgements * we thank s. brodsky and h.y . cheng for helpful discussions . the work was supported in part by grant - in aid for special project research ( physics of cp violation ) , by grant - in aid for scientific research from the ministry of education , science and culture of japan . the work of h.n.l . was supported in part by the national science council of r.o.c . under the grant no . nsc-89 - 2112-m-006 - 033 , and by theory group of slac . the work of t.k was supported in part by grant - in aid for scientific research from the ministry of education , science and culture of japan under the grant no . 11640265 .

* * _ department of physics , toyama university , toyama 930 - 8555 , japan _ * * _ department of physics , national cheng - kung university , + tainan , taiwan 701 , republic of china _ * * _ national center for theoretical sciences , hsinchu , taiwan 300 , republic of china _ * * _ department of physics , nagoya university , nagoya 464 - 8602 , japan _ * 2.0 cm * pacs index : 13.25.hw , 11.10.hi , 12.38.bx , 13.25.ft *

we calculate the transition form factors in the framework of perturbative qcd to leading power of , being the meson mass . we explain the basic principle by discussing the pion electromagnetic form factor . it is shown that the logarithmic and linear singularities occurring at small momentum fractions of light meson distribution amplitudes do not exist in a self - consistent perturbative analysis , which includes and threshold resummations . epsfig.sty # 1[eq:#1 ] # 1#2#3 _ phys . rev . _ * d#1 * # 2 ( # 3 ) # 1#2#3 _ phys . rev . lett . _ * # 1 * # 2 ( # 3 ) # 1#2#3 _ phys . lett . _ * # 1 * # 2 ( # 3 ) = -10 mm = -6 mm = -6 mm = 10000 * ncku - hep-01 - 04 + dpnu-00 - 13 * 1.cm 0.8 cm * .3 cm t. kurimoto , hsiang - nan li and a.i . sanda * * _ department of physics , toyama university , toyama 930 - 8555 , japan _ * * _ department of physics , national cheng - kung university , + tainan , taiwan 701 , republic of china _ * * _ national center for theoretical sciences , hsinchu , taiwan 300 , republic of china _ * * _ department of physics , nagoya university , nagoya 464 - 8602 , japan _ * 2.0 cm * pacs index : 13.25.hw , 11.10.hi , 12.38.bx , 13.25.ft *

1611.00392

i

in this section we briefly review the different models that , at the background level , lead to distinct future cosmological abrupt events : ( i ) big rip ( br ) , ( ii ) little rip ( lr ) and ( iii ) little sibling of the big rip ( lsbr ) . we will consider a homogeneous and isotropic universe described by the friedmann - lematre - robertson - walker ( flrw ) metric : @xmath4 \,,\end{aligned}\ ] ] where @xmath5 is the scale factor and @xmath6 for open , flat and closed spatial geometry , respectively . we will focus on the spatially flat case @xmath7 , for which the friedmann and raychaudhuri equations read @xmath8 @xmath9 here , @xmath10 is the hubble parameter , a dot represents a derivative with respect to the cosmic time , @xmath11 , @xmath12 is the cosmological constant and @xmath13 and @xmath14 are the total energy density and pressure of all the matter content of the universe . in this work , we will consider the universe to be filled by radiation , dust ( cold dark matter and baryons ) , and de . as such , we can decompose @xmath13 and @xmath14 as @xmath15 where @xmath16 , @xmath17 , and @xmath18 correspond to the energy density of radiation , matter ( cold dark matter and baryonic ) and de . similarly , @xmath19 , @xmath20 , and @xmath21 are the pressure of radiation @xmath22 , matter @xmath23 , and de @xmath24 . we will not take into account interactions between the individual matter components . consequently , each fluid @xmath25,@xmath26,@xmath27 verifies the usual conservation equation : @xmath28 for latter convenience , we define the fractional energy density of the individual mater components as @xmath29 and the individual parameters of eos @xmath30 the de parameter of eos , @xmath31 , will be fixed later for each individual model . from ( [ back1 ] ) and ( [ back2 ] ) we can obtain the total parameter of eos , @xmath32 , from the individual @xmath33 as : @xmath34 in the following subsections , we present the three models which will be studied in this work . from this point onward a @xmath35-subscript denotes the present value of a given quantity and we set @xmath36 . a br singularity @xcite can be induced by a perfect fluid whose eos is constant and smaller than @xmath37 . @xmath38 therefore , using the conservation equation ( [ conservindiv ] ) , the energy density evolves with the scale factor as @xmath39 finally , the asymptotic evolution of the scale factor is @xmath40^{\frac{2}{3\left(1+w_\textrm{d}\right ) } } \,.\end{aligned}\ ] ] in this kind of future singularity , the scale factor , the hubble parameter and its cosmic time derivatives blow up at a finite cosmic time . for the rest of the work , for the br model we fix the free parameters of the models to the best fit in accordance with the planck data for wcdm model @xcite : @xmath41 , @xmath42 and @xmath43 ( please , cf . page 687 of @xcite ) . the case of a lr @xcite can be caused by a perfect fluid whose eos fulfils @xcite @xmath44 where the constant @xmath45 is positive and has dimensions of inverse length square . applying the conservation equation ( [ conservindiv ] ) , the energy density in terms of the scale factor reads @xmath46 ^ 2 \,.\end{aligned}\ ] ] finally , the asymptotic future evolution of the scale factor can be written as @xcite @xmath47\right\}\right ) \,,\end{aligned}\ ] ] where @xmath48 . in this kind of abrupt event , the scale factor , the hubble parameter and its cosmic time derivatives blow up at an infinite cosmic time . to fix the values of the parameters of the model we choose the best fit found in @xcite , where the authors used the data of @xcite to constrain the lr model observationally from a background point of view with respect to its evolution . the results obtained in @xcite were @xmath49 , @xmath50 and @xmath51 , and these are the values that we will use in this work . the lsbr can be induced by a perfect fluid whose eos deviates from that of a cosmological constant as @xcite @xmath52 where @xmath53 is a positive constant and whose dimensions are length to the fourth power . making use of the conservation equation ( [ conservindiv ] ) , the energy density on this case reads @xmath54 where @xmath55 plays the role of a cosmological constant . finally , the future asymptotic growth of the scale factor with respect to the cosmic time can be written as @xcite @xmath56 ^ 2 - 1\right\}\right ) \,,\end{aligned}\ ] ] where we have introduced the dimensionless constant @xmath57 . in this type of abrupt event , the scale factor and the hubble parameter blow up at infinite cosmic time . however , the cosmic time derivative of the hubble parameter remains constant . for practical purposes , we will choose the numerical values taken in @xcite : @xmath58 . for @xmath59 and @xmath60 , we choose the same values used in the model ( i ) according to the planck results @xcite , i.e. @xmath42 being @xmath43 .

these three set - ups are described classically by perfect fluids with a phantom nature and represent deviations from the most widely acceptedcdm model . in addition , each of the models under study induce different future singularities or abrupt events known as ( i ) big rip , ( ii ) little rip and ( iii ) little sibling of the big rip .

we carry out an analysis of the cosmological perturbations in general relativity for three different models which are good candidates to describe the current acceleration of the universe . these three set - ups are described classically by perfect fluids with a phantom nature and represent deviations from the most widely acceptedcdm model . in addition , each of the models under study induce different future singularities or abrupt events known as ( i ) big rip , ( ii ) little rip and ( iii ) little sibling of the big rip . only the first one is regarded as a true singularity since it occurs at a finite cosmic time . for this reason , we refer to the others as abrupt events . with the aim to find possible footprints of this scenario in the universe matter distribution , we not only obtain the evolution of the cosmological scalar perturbations but also calculate the matter power spectrum for each model . finally , we constrain observationally these models using several measurements of the growth rate function , more precisely , and compare our results with the observational ones reaching the conclusion that even if these three models are very similar at present there are small differences that could allow us to distinguish them .

1611.00392

c

in this work , we analyse the cosmological perturbations within the framework of gr , taking into full account the presence of de at the perturbative level . the de component is described by three different models , where each one of them behaves almost as @xmath0cdm model at present but induces a unique doomsday scenario in the future : model ( i ) leads to a br ; model ( ii ) leads to a lr ; model ( iii ) leads to a lsbr . at late time , the parameter of eos of de for each of these models is very close to but slightly smaller than @xmath37 , thus corresponding to a phantom - like behaviour of de . despite the small variations of the parameter of the eos for the three models , the asymptotic behaviour of the universe is quite different from the one in @xmath0cdm , with the unavoidable rip of all the structure in the universe no matter the interaction that bound them . the cosmological parameters of the models are fixed as follows : the parameters for the model ( i ) are chosen according to the best fit in the planck2015 data @xcite ; for the model ( ii ) we use the results of ref . @xcite , where a fit to the cosmological parameters of the model was performed using the results of wmap7 @xcite ; finally , for the model ( iii ) we use the same parameters given by planck2015 data for the model ( i ) , while setting @xmath53 small enough ( @xmath261 ) to ensure a good approximation to @xmath0cdm until the present time @xcite . an improved analysis would incorporate in the calculations an observationally constrained value for the parameter @xmath53 , obtained by constraining the homogeneous and isotropic evolution of the model using standard candles like sneia . for each of the models studied , we analyse the evolution of the linear cosmological perturbations and , in particular , we compute numerically the evolution of the matter density contrast for the dm and de components , together with the evolution of the gravitational potential . the integrations are performed from well inside the radiation era till the far future . the outcome , which we present in fig . [ perturbationsgraphs ] , shows that in all the models there is a very similar behaviour in the evolution of the perturbations . the largest difference seems to lie in the magnitude of de perturbations , which can vary by up to two orders of magnitude . this fact can be explained by the sensibility of the adiabatic initial conditions , which are imposed during the radiation epoch , to small deviations in the value of the parameter of eos of de , @xmath262 . this difference in the initial values is then propagated along the whole evolution as a consequence of the linearity of the dynamical equations ( [ seteq1each ] ) and ( [ gtequations3n ] ) . using the results of the numerical integrations , we obtain for each model the theoretical prediction for the matter power spectrum , as observed today , and the late - time evolution of the observable combination @xmath1 . in all three models the deviations of the matter power spectrum to the results of @xmath0cdm are within the @xmath263 margin , cf . [ diflambda ] , with the model ( iii ) presenting the smallest deviation . this result can be seen as a consequence of the value selected for @xmath53 , which makes the lsbr model almost indistinguishable from @xmath0cdm at the background level at the present time . we compare the evolution of @xmath1 for low reshift ( @xmath264 ) with the latest observations and find that , for all the models , the curve of @xmath1 is within the error bars for most data points . we quantify the deviation from the observations by calculating the corresponding @xmath265 , which allows us to make a preliminary comparison of the results for the three models . we find that the model ( ii ) is the most favoured by observations . we thus conclude that although the @xmath0cdm model gives the best fit to the observations , we can not exclude other models like the ones analysed in this work . the obtained results are in agreement with the observations and a further examination is necessary to find the footprints that can further differentiate each model . however , we stress that as we did not make an observational fit of these models ( from a homogeneous and isotropic point of view and for the same set of observational data ) , all our results should be taken as a guideline for a more accurate study that we hope to carry in the future . while the classical cosmological pertubations of these models at first order are well defined , as we have shown , there are still some fundamental and intrinsic problems related to phantom dark energy models . in fact , as discussed in @xcite , when a particle - physics description of the phantom dark energy is attempted , some instabilities may rise in the theory due to higher order effects . in the particular case of the phantom scalar field it was found that an infinite decay rate of dark energy particles into gravitons would occur unless an appropriate cut - off is introduced at some energy scale below the planck scale , rendering the phantom scalar field as an effective description up to that enegy scale . in all three models presented in this work , this kind of effects can potentially become more problematic as the universe evolves into one of the cosmological events considered , as the energy density becomes increasingly high . though a thorough examination of these effects and the compatibility of the phantom dark energy models with a particle physics description is outside the scope of this paper , we will take this question into account in a future work .

for this reason , we refer to the others as abrupt events . with the aim to find possible footprints of this scenario in the universe matter distribution , finally , we constrain observationally these models using several measurements of the growth rate function , more precisely , and compare our results with the observational ones reaching the conclusion that even if these three models are very similar at present there are small differences that could allow us to distinguish them .

we carry out an analysis of the cosmological perturbations in general relativity for three different models which are good candidates to describe the current acceleration of the universe . these three set - ups are described classically by perfect fluids with a phantom nature and represent deviations from the most widely acceptedcdm model . in addition , each of the models under study induce different future singularities or abrupt events known as ( i ) big rip , ( ii ) little rip and ( iii ) little sibling of the big rip . only the first one is regarded as a true singularity since it occurs at a finite cosmic time . for this reason , we refer to the others as abrupt events . with the aim to find possible footprints of this scenario in the universe matter distribution , we not only obtain the evolution of the cosmological scalar perturbations but also calculate the matter power spectrum for each model . finally , we constrain observationally these models using several measurements of the growth rate function , more precisely , and compare our results with the observational ones reaching the conclusion that even if these three models are very similar at present there are small differences that could allow us to distinguish them .

1606.06837

i

in this article we present a lagrangian approach for studying possibly nonsymmetric diffusion operators . for instance , we consider operators of the form @xmath3 where @xmath4 is the laplace - beltrami operator of a compact smooth riemannian manifold @xmath5 and @xmath6 is a smooth @xmath1-form on @xmath7 . then the bakry - emery @xmath2-ricci tensor associated to @xmath8 is defined by @xmath9 for @xmath10 $ ] where @xmath11 denotes the symmetric derivation of @xmath12 with respect to the levi - civita connection @xmath13 of @xmath7 . note @xmath14 is also meaningful for @xmath15 but we will not consider these cases . if @xmath16 , @xmath8 is the diffusion operator of the canonical symmetric dirichlet form associated to the smooth metric measure space @xmath17 with @xmath18 , and @xmath19 is understood as the ricci curvature of @xmath17 . in celebrated articles by lott , sturm and villani @xcite - built on previous results in @xcite - a definition of lower ricci curvature bounds for general metric measure spaces in terms of convexity properties of entropy functionals on the @xmath0-wasserstein space was introduced . in smooth context these definitions are equivalent to lower bounds for the bakry - emery tensor provided @xmath6 is exact . for diffusion operators where @xmath6 is not necessarily exact such a geometric picture was missing . though the operator @xmath8 yields a bilinear form , in general this form is not symmetric and therefore can not arise as dirichlet form of a metric measure space . nevertheless , there are numerous results dealing with probabilistic , analytic and geometric properties of @xmath8 under lower bounds on @xmath14 . the results are very similar to properties that one derives for symmetric operators with lower bounded ricci curvature , e.g. @xcite . in this article we derive a geometric picture associated to the diffusion operator @xmath20 for general @xmath1-forms @xmath12 in the spirit of the work by lott , sturm and villani . we characterize lower bounds on @xmath14 in terms of convexity for line integrals along @xmath0-wasserstein geodesics . moreover , for generalized smooth metric measures spaces ( definition [ gsmms ] ) we impose the following definition . for simplicity , in this introduction we assume @xmath21 . we will say @xmath22 together with a @xmath1-form @xmath6 satisfies the curvature - dimension condition @xmath23 if and only if for every pair @xmath24 there exists an @xmath0-wasserstein geodesic @xmath25 such that @xmath26 \\ & \hspace{1 cm } -\frac{1}{2}kt(1-t)kw_2(\mu_0,\mu_1)^2,\end{aligned}\ ] ] where @xmath27 and @xmath28 denotes the line integral of @xmath6 along @xmath29 . for the case @xmath30 corresponding definitions are made in definition [ defa ] and definition [ defb ] . in particular , we emphasize that definition [ defb ] is also meaningful in the class of general metric measure spaces together with @xmath0-integrable @xmath1-forms in the sense of @xcite . however , in this article we will only study the generalized smooth case . we prove several geometric consequences : generalized bishop - gromov estimates , pre - compactness under gromov - hausdorff convergence , and a generalized bonnet - myers theorem . the latter generalizes a result of kuwada in @xcite - even for smooth ingredients . then , we show that the condition @xmath31 is stable under @xmath2-warped product constructions . this also includes so - called euclidean @xmath2-cones and @xmath2-suspensions . in the last section we introduce the notion of @xmath32-flows that arise naturally on generalized smooth metric measure spaces together with a @xmath1-form satisfying a curvature - dimension condition . more preciely , if @xmath33 is the semigroup associated to the operator @xmath3 on a smooth riemannian manifold @xmath7 such that @xmath34 satisfies @xmath23 , and if @xmath35 is the dual flow acting on probability measures , then it is an absolutely continuous curve in @xmath0-wasserstein space and for any probability measure @xmath36 , @xmath37 satisfies the following inequality @xmath38 provided standard regularity assumption for the corresponding heat kernel ( proposition [ propa ] ) . @xmath39 is any absolutely continuous probability measure , and @xmath40 is the @xmath0-wasserstein geodesic between @xmath41 and @xmath39 . this yields a contraction estimate for @xmath35 that is again equivalent to the bakry - emery conditon for @xmath33 by @xcite . therefore , we obtain the following theorem . let @xmath5 be a compact smooth riemannian manifold , and let @xmath6 be a smooth @xmath1-form . we denote with @xmath42 the corresponding metric measure space , and let @xmath33 and @xmath35 be as in the section 7 . then , the following statements are equivalent . * @xmath43 , * @xmath44 satisfies the condition @xmath23 , * for every @xmath45 @xmath37 is an @xmath46-flow curve starting in @xmath36 , * @xmath35 satisfies the contraction estimate in corollary [ contractionxxx ] , * @xmath33 satisfies the condition @xmath47 . this work was partly done while the author was in residence at the mathematical sciences research institute in berkeley , california during the spring 2016 semester , supported by the national science foundation . i want to thank the organizers of the differental geometry program and msri for providing great environment for research .

we characterize lower bounds for the bakry - emery ricci tensor of nonsymmetric diffusion operators by convexity of entropy on the-wasserstein space , and define a curvature - dimension condition for general metric measure spaces together with a square integrable-form in the sense of . this extends the lott - sturm - villani approach for lower ricci curvature bounds of metric measure spaces . in generalized smooth context , consequences are new bishop - gromov estimates , pre - compactness under measured gromov - hausdorff convergence , and a bonnet - myers theorem that generalizes previous results by kuwada . we show that-warped products together with lifted vector fields satisfy the curvature - dimension condition . for smooth riemannian manifolds we derive an evolution variational inequality and contraction estimates for the dual semigroup of nonsymmetric diffusion operators . another theorem of kuwada yields bakry - emery gradient estimates .

we characterize lower bounds for the bakry - emery ricci tensor of nonsymmetric diffusion operators by convexity of entropy on the-wasserstein space , and define a curvature - dimension condition for general metric measure spaces together with a square integrable-form in the sense of . this extends the lott - sturm - villani approach for lower ricci curvature bounds of metric measure spaces . in generalized smooth context , consequences are new bishop - gromov estimates , pre - compactness under measured gromov - hausdorff convergence , and a bonnet - myers theorem that generalizes previous results by kuwada . we show that-warped products together with lifted vector fields satisfy the curvature - dimension condition . for smooth riemannian manifolds we derive an evolution variational inequality and contraction estimates for the dual semigroup of nonsymmetric diffusion operators . another theorem of kuwada yields bakry - emery gradient estimates .

1404.1386

i

it is common knowledge that effective theories valid above some distance scale provide an excellent description of phenomena down to that scale . hydrodynamics does not require us to even know about the existence of atoms , and applies at distance scales much larger than the size of atoms . likewise , an understanding of the atoms and molecules does not require knowledge of quarks or even of nuclear physics , for that matter . the reductionist s hope is that _ the principles _ governing all phenomena stem from a fundamental underlying theory which , in turn , would enable us to derive seemingly fundamental concepts from a deeper origin . the derivation of the empirical laws governing the behaviour of ideal gases from kinetic theory provides a simple illustration of this . a different example is the derivation of the stefan - boltzmnn law for the emissive power of a blackbody ( which also enables us to write stefan s constant in terms of the more fundamental planck s constant ) . the derivation of the magnetic susceptibility and polarizability of mono - valent gases in terms of atomic properties of the corresponding atoms provides an illustration of how `` long - distance characteristics '' in this example , some bulk properties of gases can be obtained from the underlying microphysics . continuing in this vein , we may hope that in the future , some of the many disparate parameters of the standard model which has been remarkably successful in describing data up to distance scales down to ( 100 gev)@xmath4 , will be derived from an underlying ( more ) fundamental theory that includes a detailed description of new degrees of freedom with mass scales ( much ) higher than 100 gev . it is perhaps worth emphasizing that realizing such a top - down program may prove very difficult , even in principle , because the low energy theory may turn out to be sensitive to physics at all energy scales . although most of us implicitly assume that very high energy scale degrees of freedom decouple from low energy physics , it remains logically possible that this may not be the case . it could , for instance , be that the multiplicity of massive states grows so rapidly with mass , that even though the effect of any individual state is negligible , their collective effect remains at low energy . in this case , one would have to know the detailed physics at all energy scales to realize the top - down program . the other possibility is that low energy physics is insensitive to the details of high scale physics because the effects of the latter are suppressed by a power of the high scale @xmath5 . this view provides a rationale for the success that renormalizable relativisitic quantum field theories have enjoyed in the describing strong and electro - weak phenomena today , and makes a strong case that any mass scale associated with unknown degrees of freedom lies well above the highest energies accessible today , so that the effect of non - renormalizable operators is sufficiently suppressed . there is , however , an associated issue , brought to the forefront by the discovery of the first ( seemingly ) elementary spin - zero particle at the cern collider with attributes remarkably consistent with those of the higgs boson of the standard model @xcite . although , as we just said , low energy phenomena are essentially independent of @xmath5 , the _ dimensionful _ parameters of the _ renormalized _ theory are generally speaking sensitive to the high scale @xmath5 , and hence to the physics at high energy scales . for instance , in a generic quantum field theory , the radiative corrections to the squared mass of an elementary spin - zero particle take the form , m_^2 - m_0 ^ 2 = c_1 ^2 + c_2 m_low^2 ( ) + c_3 m_low^2 . [ eq : generic ] the @xmath6 term could also include `` small logarithms '' @xmath7 that we have not exhibited . we see the well - known quadratic sensitivity of scalar mass parameters to the scale @xmath5 where new massive degrees of freedom that couple to the sm reside ; _ e.g. _ @xmath8 when the sm is embedded in a grand unified framework . here is not _ a regulator _ associated with divergences that occur in loop calculations in quantum field theory . rather , it is the mass scale associated with new particles with large couplings to the higgs boson , a point also made explicitly in ref . @xcite . from this viewpoint , and tempting though it is , we would not logically be able to associate @xmath5 with @xmath9 , the scale at which the effects of gravity become important . we do not really know quantum gravitational dynamics and , in particular , do not know that there are associated new particles with significant couplings to the higgs boson . see also ref . @xcite . ] in eq . ( [ eq : generic ] ) , @xmath10 is the physical mass of the quantum of the field @xmath11 , @xmath12 is the typical coupling of the field @xmath11 , @xmath13 is the corresponding mass parameter in the lagrangian , @xmath14 is a loop factor , and @xmath15 are dimensionless coefficients that aside from spin , colour and other multiplicity factors are numbers @xmath16 . finally , @xmath17 denotes the highest mass scale in the low energy theory , while @xmath5 is the scale at which this effective theory description becomes invalid because the effects of heavy states not included in the lagrangian that provides a description of physics at low energies become important . if @xmath18 , unless @xmath12 is also tiny , the first term dominates the corrections . moreover , in order for the physical mass @xmath10 to be at its fixed value in the low energy theory , it must be that there are large cancellations between @xmath19 and the @xmath20 term in eq . ( [ eq : generic ] ) . this quadratic sensitivity of the radiative corrections to the squared mass parameter of elementary spin - zero fields leads to the _ fine - tuning problem _ in the standard model ( sm ) @xcite when the sm is embedded into a grand unified theory . we stress that this is not a logical problem in the sense it does not render the theory inconsistent , nor a practical problem that precludes the possibility of making precise predictions using the sm . it is only a problem in the sense that seemingly unrelated quantities in eq . ( [ eq : generic ] ) the mass parameter @xmath19 of the low energy lagrangian and contributions from radiative corrections from very massive degrees of freedom governed by very different physics need a cancellation of many orders of magnitude if @xmath21 . why should two quantities with very different physical origins balance out with such exquisite precision ? the remarkable ultra - violet properties of softly broken supersymmetric ( susy ) theories , with susy broken near the weak scale , ensure that the low energy theory is at most logarithmically sensitive to high scale ( hs ) physics , _ i.e. _ , that the @xmath22 term in eq . ( [ eq : generic ] ) is absent . this led to the realization @xcite that weak scale susy potentially solves the _ big gauge hierarchy problem _ endemic to the standard model ( sm ) @xcite embedded into a gut framework , and provided much impetus for its study over the last three decades . the recent discovery of a standard model ( sm)-like higgs boson with mass @xmath23 gev @xcite at the lhc seemingly provides support for the simplest susy models of particle physics @xcite which had predicted @xmath24 gev @xcite . however , no sign of supersymmetric matter has yet been found at the lhc , resulting in mass limits @xmath25 tev ( for @xmath26 ) and @xmath27 tev ( for @xmath28)@xcite . naively , this pushes up the susy scale @xmath17 to beyond the tev range . if @xmath5 is not much above the susy scale , the @xmath29 terms in eq . ( [ eq : generic ] ) each have a scale @xmath30 , which is comparable to the observed value of the higgs boson mass for @xmath31 tev , and no large cancellations are necessary . however , one of the most attractive features of supersymmetric theories is that they can be perturbatively valid up to energy scales as high as @xmath32 at which the measured values of the three sm gauge couplings appear to unify . in this case , @xmath33 gev , so that the @xmath34 term becomes two orders of magnitude larger than ( 100 gev)@xmath35 , requiring cancellations at the percent level to obtain measured value of the higgs boson mass . this need for fine - tuning is what has been termed as the _ little hierarchy problem _ , to be contrasted with the _ big hierarchy problem _ that is solved by the introduction of weak scale susy as we mentioned earlier . fine - tuning in the minimal supersymmetric standard model ( mssm ) is seemingly exacerbated because experiments at the lhc have discovered a sm - like higgs boson with a mass at 125 - 126 gev , well beyond its tree - level upper bound @xmath36 . radiative corrections can readily accommodate this , but only with top squark masses beyond the tev scale along with large mixing@xcite . since top squarks have large yukawa couplings to the higgs boson , it has been argued that naturalness considerations prefer @xmath37 gev@xcite . we will return to this issue below . we recognize the inherent subjectivity of the notion of naturalness . however , in order to decide whether one model is more natural than another , we need to introduce a measure of fine - tuning . as we discuss in the next section , this is traditionally done by checking the sensitivity of @xmath38 rather than the higgs mass as in eq . ( [ eq : generic ] ) , to the model parameters . since both gauge and higgs boson masses arise dynamically from the scalar potential , the corresponding sensitivities are not unrelated . in the next section , we compare and contrast three different sensitivity measures , @xmath0 , @xmath1 and @xmath2 that have been the subject of discussion in the literature . while much of what we say here and in the rest of this paper is a review , our perspective differs from that of other authors . we emphasize that while not a fine - tuning measure , @xmath3 ( which is essentially determined by the particle spectrum ) is nonetheless a very useful quantity because @xmath0 quantifies the minimum fine - tuning present in any theory with a specific spectrum . we also highlight the importance of incorporating correlations between various parameters in dicussions of fine - tuning , something ignored in many generic analyses . in sec . [ sec : example ] , we provide simple examples that suggest that if we can find hs theories with specific correlations amongst parameters , the value of the traditional fine - tuning measure @xmath2 would automatically be close to @xmath0 . we then set up the radiatively driven natural susy framework that we advocate for phenomenological analyses of natural models of susy , and review its phenomenological implications in sec . [ sec : phen ] . we conclude with our perspective and a brief summary in sec . [ sec : concl ] .

we compare and contrast three different sensitivity measures , , and that have been used in discussions of fine - tuning . we argue that though not a fine - tuning measure , , which is essentially determined by the particle spectrum , is important because quantifies the _ minimum _ fine - tuning present in any theory with a specified spectrum . we emphasize the critical role of incorporating correlations between various model parameters in discussions of fine - tuning . we provide toy examples to show that if we can find high scale theories with specific correlations amongst parameters , the value of the traditional fine - tuning measure ( which differs significantly from only when these correlations are important ) would be close to . we then set up the radiatively driven natural susy framework that we advocate for phenomenological analyses of natural models of supersymmetry , and review the implications of naturalness for lhc and ilc searches for susy as well as for searches for susy dark matter .

we compare and contrast three different sensitivity measures , , and that have been used in discussions of fine - tuning . we argue that though not a fine - tuning measure , , which is essentially determined by the particle spectrum , is important because quantifies the _ minimum _ fine - tuning present in any theory with a specified spectrum . we emphasize the critical role of incorporating correlations between various model parameters in discussions of fine - tuning . we provide toy examples to show that if we can find high scale theories with specific correlations amongst parameters , the value of the traditional fine - tuning measure ( which differs significantly from only when these correlations are important ) would be close to . we then set up the radiatively driven natural susy framework that we advocate for phenomenological analyses of natural models of supersymmetry , and review the implications of naturalness for lhc and ilc searches for susy as well as for searches for susy dark matter . keywords : supersymmetry , naturalness , higgsino signatures , large hadron collider , + linear collider pacs numbers : 14.80lv , 12.60jv uh-511 - 1231 - 14 * supersymmetry , naturalness , and light higgsinos * + azar mustafayev and xerxes tata _ dept . of physics and astronomy , university of hawaii , honolulu , hi 96822 , usa + _

1409.8304

i

ly@xmath2 is the most common electronic transition in the universe . most often , it is a product of the photo - ionizing photons emitted by young stars : as recombining electrons cascade through the energy levels , they are funneled into hydrogen s @xmath10 state by the high optical depth of the interstellar medium to lyman series transitions . the result is that strong ly@xmath2 is a signature of star formation , and indeed , @xcite noted that this feature may be our best probe for identifying galaxies in the act of formation . due to the resonant nature of the line , a typical ly@xmath2 photon must undergo tens or even hundreds of absorptions and re - emissions before escaping into intergalactic space . consequently , the radiative transfer of this line is quite complex , and even a small amount of dust can break the chain of interactions which is necessary for its escape . this fact is reflected in the observed redshift evolution of ly@xmath2 emitting galaxies ( laes ) : in the nearby universe , such objects are quite rare , but between @xmath11 @xcite and @xmath12 there is a strong increase in both the number density of ly@xmath2 emitters and their characteristic luminosity @xcite . three - dimensional radiative transfer models have demonstrated that the ly@xmath2 emission line can contain a great deal of information about the distribution of a galaxy s ism , its surrounding circum - galactic medium , and the physics of its on - going star formation ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? however , to extract this information , one needs accurate measurements of the fraction of ly@xmath2 photons escaping the galaxy ( ) , and the profile of the emission line . over the past decade , there have been numerous attempts to estimate in the normal ( non - agn ) galaxies of the distant ( @xmath13 ) universe , mostly by comparing ly@xmath2 to measurements of galactic emission in the rest - frame uv ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , the far - infrared @xcite , or the x - ray @xcite . the premise behind these measurements is straightforward : like ly@xmath2 , the strength of a galaxy s uv , far - ir , and x - ray emission all depend in some way on the existence of young stars and star formation . consequently , the ratio of ly@xmath2 to these quantities should yield a measure how efficiently ly@xmath2 is escaping its environment . using a compilation of such measurements , @xcite determined that , over time , the `` volumetric '' ly@xmath2 escape fraction of the universe has declined monotonically , from @xmath14 at @xmath15 to @xmath16 locally . this evolution is consistent with models in which ly@xmath2 is quenched by dust , which slowly builds up as the universe ages . there is , however , one difficulty with this analysis : all the star - formation rate tracers listed above are somewhat indirect and rely on empirical calibrations derived from galaxies in the local @xmath17 universe . for example , not only is the observed uv luminosity of a galaxy extremely sensitive to the effects of internal extinction , which may depend on such factors as star formation rate , inclination , and redshift ( e.g. , * ? ? ? * ; * ? ? ? * ) , but it also arises from a stellar population that is slightly different from that which is producing the ionizing photons . although both the uv continuum and ly@xmath2 are generated by the flux from hot , young stars , ly@xmath2 is excited by the far - uv emission of stars with @xmath18 , whereas the uv light originates in the atmospheres of @xmath19 objects ( e.g. , * ? ? ? thus , the ratio of the two quantities is subject to shifts in the initial mass function , metallicity , extinction law , and the timescale over which star formation is occurring . indeed , @xcite has examined these effects and has shown that , even if both the star - formation rate ( sfr ) and extinction are well determined , measurements of the rest - frame uv in galaxies at @xmath20 will underestimate the flux of ionizing photons by almost a factor of two . to overcome the need for empirical calibrations , one requires a more direct probe of the ionizing flux from hot , young stars . since ly@xmath2 is produced by transitions out of the @xmath10 state of hydrogen , the best possible tracer of its intrinsic strength is one which measures the preceding transitions into the @xmath10 state . to date , only one such investigation of this type has been made in the @xmath13 universe . by performing narrow - band surveys for @xmath21 galaxies in both h@xmath2 and ly@xmath2 , @xcite was able to fix the epoch s volumetric ly@xmath2 escape fraction at @xmath22% . however , the precision of this measurement was limited by the survey s small volume ( @xmath23 mpc@xmath6 ) , and the dearth of galaxies brighter than @xmath24 . to improve upon this situation , we have combined the data from four recent surveys : 3d - hst and aghast @xcite , the pilot survey for hetdex , the hobby - eberly telescope dark energy experiment ( hps ; * ? ? ? * ) , and the 3727 narrow - band observations of the chandra deep field south ( cdf - s ; * ? ? ? * ; * ? ? ? the first two of these studies unambiguously measures total h@xmath0 fluxes in the redshift range @xmath1 via wfc3 grism observations with the _ hubble space telescope ; _ the latter two provide ly@xmath2 measurements ( or upper limits ) for many of these same galaxies via integral field spectroscopy and narrow - band imaging . by comparing their data products , we can place constraints on via statistically complete samples of star - forming galaxies in the goods - n , goods - s , and cosmos fields . in section 2 , we describe the observational data and detail the procedures used for identifying and measuring h@xmath0 and ly@xmath2 in our target fields . in section 3 , we use these data to measure ( or place limits on ) the ly@xmath2/h@xmath0 ratio of 73 galaxies in the redshift range @xmath25 . by converting stellar reddenings into nebular extinctions via the empirical @xcite obscuration law , we show that the typical ly@xmath2 escape fraction of these galaxies is just a few percent . in section 4 , we consider the epoch s volumetric ly@xmath2 escape fraction by deriving the h@xmath0 and ly@xmath2 luminosity functions for a @xmath5 mpc@xmath26 volume of space . after correcting for nebular h@xmath0 extinction , we demonstrate that , at most , only @xmath7 of the ly@xmath2 photons escape their galaxies , and argue that any systematic error associated with this measurement must be less than @xmath8 . we conclude by discussing this measurement , and the implications it has for the evolution of galaxies . for this paper , we assume a @xmath27cdm cosmology , with @xmath28 , @xmath29 and @xmath30 km s@xmath31 mpc@xmath31 @xcite .

we compare the h line strengths of star - forming galaxies observed with the near - ir grism of the _ hubble space telescope _ with ground - based measurements of ly from the hetdex pilot survey and narrow - band imaging . by examining the line ratios of 73 galaxies , we show that most star - forming systems at this epoch have a ly escape fraction below . we confirm this result by using stellar reddening to estimate the effective logarithmic extinction of the h emission line ( ) and measuring both the h and ly luminosity functions in a mpc volume of space . we show that in our redshift window , the volumetric ly escape fraction is at most , with an additional systematic uncertainty associated with our estimate of extinction . finally , we demonstrate that the bulk of the epoch s star - forming galaxies have ly emission line optical depths that are significantly greater than that for the underlying uv continuum . in our predominantly [ o iii ] -selected sample of galaxies , resonant scattering must be important for the escape of ly photons .

we compare the h line strengths of star - forming galaxies observed with the near - ir grism of the _ hubble space telescope _ with ground - based measurements of ly from the hetdex pilot survey and narrow - band imaging . by examining the line ratios of 73 galaxies , we show that most star - forming systems at this epoch have a ly escape fraction below . we confirm this result by using stellar reddening to estimate the effective logarithmic extinction of the h emission line ( ) and measuring both the h and ly luminosity functions in a mpc volume of space . we show that in our redshift window , the volumetric ly escape fraction is at most , with an additional systematic uncertainty associated with our estimate of extinction . finally , we demonstrate that the bulk of the epoch s star - forming galaxies have ly emission line optical depths that are significantly greater than that for the underlying uv continuum . in our predominantly [ o iii ] -selected sample of galaxies , resonant scattering must be important for the escape of ly photons .

1604.04648

i

carbon nanotubes ( cnts ) are quasi - one - dimensional materials with a unique set of optical and electronic properties @xcite . today , there is considerable interest in semiconducting cnts as the light - absorbing material in organic solar cells , owing to their tunable band gap , excellent carrier mobility , and chemical stability@xcite . improving the efficiency of cnt - based photovoltaic devices is possible through understanding the dynamics of excitons in cnt composites . while the intratube dynamics of excitons in cnts have been studied extensively over the past decade @xcite , the intertube exciton dynamics remain relatively unexplored , owing to the difficulties in sample preparation and measurements . the fluorescence from bundled single - wall carbon nanotube ( swnt ) samples is quenched and the absorption spectra are broadened as a result of coulomb interaction between swnts with various chiralities@xcite . the exciton lifetimes in isolated and bundled swnts were measured to be on the order of @xmath4 and @xmath5 , respectively @xcite , which underscores the importance of intertube coulomb interactions in the dynamics of excitons in swnt aggregates . there have been a number of measurements of the exciton transfer ( et ) rates in cnts , but the reported rates differ widely , within two orders of magnitude @xcite . pump - probe ( pp ) spectroscopy measurements have shown a time constant of about @xmath6 for the et process from semiconducting swnts to metalic swnts @xcite . time - resolved photoluminescence ( pl ) spectroscopy found the time constants of @xmath7 and @xmath8 for et from semiconducting swnts to metallic and semiconducting swnts , respectively @xcite . in another study , time - resolved pl spectroscopy has been used to measure et between semiconducting swnts , with a time constant @xmath9 @xcite . used spatial high - resolution optical spectroscopy to estimate the time constant of et between two nonparallel semiconducting swnts as @xmath10 @xcite . using pp spectroscopy , the et time constant between bundled swnts was measured to be @xmath11 for @xmath12 excitons . @xcite the same study estimated the @xmath13 exciton transfer to be very slow due to momentum mismatch . another study showed a long - range fast component ( @xmath14 ) , followed by a short - range slow component ( @xmath15 ) for the et process in swnt films @xcite . _ used a diffusion - based model to explain their measurement of et in bundled semiconducting swnt samples @xcite . they found the time constants of @xmath16 for et between bundles of swnts and @xmath17 for et within swnt bundles . a more recent study by mehlenbacher _ et al . _ revealed ultrafast @xmath13 exciton transfer @xcite . many difficulties inherent in experiments can be avoided in a theoretical study of the transfer process . however , to date there have been only two theoretical studies of exciton transfer between semiconducting swnts @xcite . _ showed that the ideal dipole approximation ( known as the frster theory ) overestimates the exciton transfer rate by three orders of magnitude @xcite . _ showed that exciton phonon coupling could have a prominent effect on the exciton transfer process between ( 6,4 ) and ( 8,4 ) swnts @xcite . however , these studies did not account for some important parameters , such as the existence of low - lying optically dark excitonic states , chirality and diameter of donor and acceptor cnts , temperature , confinement of excitons , screening due to the surrounding medium , and the interaction between various exciton subbands , all of which have been shown , experimentally and theoretically , to play an important role in exciton dynamics in cnts @xcite . in this paper , we present a comprehensive theoretical analysis of coulomb - mediated intertube exciton dynamics in swnt composites , in which we pay attention to the complex structure of excitonic dispersions , exciton confinement , screening due to surrounding media , and temperature dependence of the et rate . we solve the bethe - salpeter equation in the gw approximation in the basis of single - particle states obtained from nearest - neighbor tight binding in order to calculate the exciton dispersions and wave functions . we calculate the intertube exciton transfer rate due to the coulomb interaction between swnts of different chiralities and orientations . for the sake of brevity , in the rest of this paper , we refer to single - wall carbon nanotubes simply as carbon nanotubes unless otherwise noted . we show that momentum conservation plays an important role in determining the et rate between parallel cnts of different chirality . while the et rate between similar - chirality bundled parallel tubes in pristine samples is @xmath0 @xcite , much higher than between misoriented or different - chirality cnts ( @xmath1 ) , exciton confinement due to disorder strongly reduces the et rate between parallel tubes of similar chirality , but has little effect on the et rate otherwise . consequently , the et rate dependence on the orientation of donor and acceptor cnt is not as prominent as predicted previously and the et rate is instead expected to be isotropic and @xmath18 in most experiments @xcite . moreover , the exciton transfer rate drops by about one order of magnitude if intratube exciton scattering between bright and dark excitonic states is allowed . our study shows that the transfer from @xmath13 to @xmath12 excitonic states happens with the same rate as the transfer process between same - subband states ( @xmath19 and @xmath20 ) . the et rate increases with increasing temperature . we also show that the screening of the coulomb interaction by the surrounding medium reduces the transfer rate by changing the exciton wave function and energy dispersion , as well as by reducing the coulomb coupling between the donor and acceptor cnts . the rest of this paper is organized as follows . in sec . [ sec : excitons_in_cnts ] , we provide a summary of the physics of excitonic states in cnts . we review the calculation of exciton wave functions by using the tight - binding states as the basis functions . in sec . [ sec : resonance_energy_transfer_rate ] , we introduce the formulation of excitonic energy transfer in cnts . section [ sec : results_and_discussion ] shows the et rate between various excitonic states of cnts and discusses the effect of the above mentioned parameters . section [ sec : summary ] provides a summary of the results . appendix [ sec : derivation_of_free_exciton_transfer_rate ] shows a detailed derivation of the exciton transfer rates between very long cnts .

we compute the exciton transfer ( et ) rate between semiconducting single - wall carbon nanotubes ( swnts ) . the swnt excitonic states are calculated by solving the bethe - salpeter equation using tight - binding basis functions . the et rates due to intertube coulomb interaction are computed via fermi s golden rule . in pristine samples , the et rate between parallel ( bundled ) swnts of similar chirality is very high ( ) while the et rate for dissimilar or nonparallel tubes is considerably lower ( ) . exciton confinement reduces the et rate between same - chirality parallel swnts by two orders of magnitude , but has little effect otherwise . consequently , the et rate in most measurements will be on the order of , regardless of the tube relative orientation or chirality .

we compute the exciton transfer ( et ) rate between semiconducting single - wall carbon nanotubes ( swnts ) . we show that the main reasons for the wide range of measured et rates reported in the literature are 1 ) exciton confinement in local quantum wells stemming from disorder in the environment and 2 ) exciton thermalization between dark and bright states due to intratube scattering . the swnt excitonic states are calculated by solving the bethe - salpeter equation using tight - binding basis functions . the et rates due to intertube coulomb interaction are computed via fermi s golden rule . in pristine samples , the et rate between parallel ( bundled ) swnts of similar chirality is very high ( ) while the et rate for dissimilar or nonparallel tubes is considerably lower ( ) . exciton confinement reduces the et rate between same - chirality parallel swnts by two orders of magnitude , but has little effect otherwise . consequently , the et rate in most measurements will be on the order of , regardless of the tube relative orientation or chirality . exciton thermalization between bright and dark states further reduces the et rate to about . the et rate also increases with increasing temperature and decreases with increasing dielectric constant of the surrounding medium .

1604.04648

c

in summary , we calculated the exciton transfer rates between semiconducting cnts of different chiralities and relative orientations . the exciton transfer rate is weakly dependent on the orientation of the tubes . this finding is in contradiction with previous theoretical studies , but in good agreement with experiments . the exciton transfer rate between bright excitonic states is about @xmath146 . the transfer rates between bright and dark states are at least two orders of magnitude smaller that the transfer rates between bright excitonic states . we also looked at the exciton transfer from @xmath13 to @xmath12 transition energies . we found that this type of exciton transfer process is as fast as transfer from @xmath12 to @xmath12 and from @xmath13 to @xmath13 states . this process is facilitated by coupling of tightly bound excitonic states in @xmath13 to the continuum level states ( equivalent of free - electron / free - hole states ) in @xmath12 . furthermore , we studied the environmental effects on the exciton transfer rates . we calculated the exciton transfer rate for excitons confined to quantum wells with various sizes . when the quantum - well size increases , we observed a decrease in the transfer rate between nonparallel tubes . this is due to the increase in the average distance between donor and acceptor systems . by introducing a more relevant quantity ( i.e. , transfer rate per donor tube length ) , we showed that the exciton transfer rate is almost independent of the exciton confinement length . however , exciton transfer between parallel tubes follows a different trend : transfer between same - chirality donor and acceptor tubes is extremely sensitive to confinement and free excitons have the highest transfer rate ( @xmath147 ) . the transfer rates between different - chirality tubes are not as sensitive to confinement and only slightly increase with decreasing confinement length . these findings are a result of momentum conservation rules . moreover , we looked at the effect of coulomb screening due to the surrounding media . the exciton transfer rate decreases with increasing screening . we also showed that the exciton transfer rate increases with increasing temperature . this behavior is the opposite of what one would expect based on the emission and absorption spectra of donor and acceptor systems . also , we showed that the exciton transfer rate drops by about one order of magnitude if excitons are thermalized between bright and dark excitonic states via extrinsic scattering sources ( e.g. , impurities and phonons ) . we conclude that the wide range of et - rate measurements , spanning two orders of magnitude , stems from variations in sample preparation and thus the degree of environmental disorder and homogeneity , as the et rates in pristine samples and in the samples in which environmental disorder results in exciton confinement differ by two orders of magnitude .

we show that the main reasons for the wide range of measured et rates reported in the literature are 1 ) exciton confinement in local quantum wells stemming from disorder in the environment and 2 ) exciton thermalization between dark and bright states due to intratube scattering . the et rate also increases with increasing temperature and decreases with increasing dielectric constant of the surrounding medium .

we compute the exciton transfer ( et ) rate between semiconducting single - wall carbon nanotubes ( swnts ) . we show that the main reasons for the wide range of measured et rates reported in the literature are 1 ) exciton confinement in local quantum wells stemming from disorder in the environment and 2 ) exciton thermalization between dark and bright states due to intratube scattering . the swnt excitonic states are calculated by solving the bethe - salpeter equation using tight - binding basis functions . the et rates due to intertube coulomb interaction are computed via fermi s golden rule . in pristine samples , the et rate between parallel ( bundled ) swnts of similar chirality is very high ( ) while the et rate for dissimilar or nonparallel tubes is considerably lower ( ) . exciton confinement reduces the et rate between same - chirality parallel swnts by two orders of magnitude , but has little effect otherwise . consequently , the et rate in most measurements will be on the order of , regardless of the tube relative orientation or chirality . exciton thermalization between bright and dark states further reduces the et rate to about . the et rate also increases with increasing temperature and decreases with increasing dielectric constant of the surrounding medium .

quant-ph0307220

i

the field of quantum algorithms has witnessed several important results ( e.g. , @xcite ) in the last decade , since the breakthrough discovery of shor s quantum algorithm for factoring and discrete logarithm in 1994 @xcite . despite these important developments , two problems in particular had little progress in terms of quantum algorithms : graph isomorphism ( gi ) , and gap versions of lattice problems such as the shortest vector in the lattice problem ( gapsvp ) and the closest vector in the lattice problem ( gapcvp ) . to understand why these problems are interesting in the context of quantum computation , let us first recall their definitions and what is known about them classically . graph isomorphism is the problem of deciding whether two given graphs can be permuted one to the other . it is known to be in @xmath6 @xcite and therefore , it is not np complete unless the polynomial hierarchy collapses . @xmath7 is the problem of deciding whether the shortest vector in a given @xmath8-dimensional lattice @xmath9 is shorter than @xmath10 or longer than @xmath11 . @xmath12 is the following problem : given a lattice and a vector @xmath13 , decide whether @xmath14 or @xmath15 where @xmath16 is the minimal distance between @xmath13 and any point in @xmath9 . both problems have important cryptographic applications @xcite . regarding their complexity , it is easy to see that they both lie in @xmath2 for any @xmath17 . the results of lagarias et al . @xcite imply that when @xmath18 , both problems are in @xmath19 . for @xmath20 these lattice problems are not known to be in @xmath19 but as shown in @xcite , they are in @xmath21 ( and in fact in the class statistical zero knowledge ) . this implies that for @xmath20 the problems are not np complete unless the polynomial hierarchy collapses . the fact that the graph isomorphism problem and the two lattice problem with the above parameters are very unlikely to be np complete , and that they possess a lot of structure , raised the hope that quantum computers might be able to solve them more efficiently than classical computers . despite many attempts , so far all that is known in terms of the quantum complexity of these problems are reductions to problems for which quantum algorithms are also not known @xcite , and negative results regarding possible approaches @xcite . progress in designing an algorithm for one of these problems is the holy grail of quantum algorithmic theory . in light of the difficulty of finding efficient algorithms for these problems , a weaker question attracted attention : can any quantum upper bound be given on these problems , which does not follow trivially from the classical upper bounds ? regarding graph isomorphism , which is known to be in coam , the natural question to ask is whether it is in coqma , the quantum analog of conp . it is more natural to speak in this context , and in the rest of the paper , about the _ complements _ of the problems we described , and so the question is whether the graph _ non_-isomorphism ( gni ) problem lies inside qma . qma can be viewed as the quantum analog of np , and was recently studied in various papers @xcite . strictly speaking , qma is actually the analog of merlin arthur , the probabilistic version of np , since in the quantum world it is more natural to consider probabilistic classes . attempts to prove that gni is in qma have so far failed . as for lattice problems , since @xmath22 , it follows from the classical result @xcite that if @xmath18 the complements of the problems we described , namely @xmath23 and @xmath24 , lie in @xmath4 . the interesting question , however , is whether these problems are still in @xmath4 for lower gaps , such as @xmath25 . notice that this does not follow from the classical results . in this paper we solve the question of containment in qma for one of the aforementioned problems . this is the first non trivial quantum upper bound for a lattice problem . [ thm : main ] the problem @xmath26 is in @xmath4 for some constant @xmath27 . one of the new ideas in the proof of theorem [ thm : main ] is the important connection between quantum estimations of inner products , or autocorrelation estimates , and properties of positive definite functions . the technique of using positive definite functions to analyze quantum protocols is likely to prove useful in other contexts , due to its generality : the property of positive definiteness applies to autocorrelation functions over any group , and not only over @xmath28 as in our case . another important issue in the proof theorem [ thm : main ] is a problem that arises commonly in the analysis of qma protocols . namely , in certain situations , we would like to repeat a test on several copies of the witness but the prover might use entanglement between the copies in order to cheat . we circumvent this problem by giving a new characterization of @xmath4 , named @xmath5 . we start by proving that indeed @xmath29 and then , using this new characterization , we prove the soundness of our protocol . hopefully , both the new characterization of qma and the new technique of verification using positive definite functions will help in proving that other important problems such as @xmath30 and @xmath31 lie in @xmath4 . in more generality , in this work we gain a better understanding of the class qma and the techniques used to analyze it . we hope that this work will lead to an even better understanding of this important class . understanding classical np led to a few of the most important results in theoretical computer science , including pcp and hardness of approximation . a few indications that qma is fundamental for quantum computation have already been given in @xcite . our results might also lead to progress in terms of quantum algorithms for lattice problems . in this context , it is interesting to consider theorem [ thm : main ] in light of a recent paper by aharonov and ta - shma @xcite . @xcite showed that if the state we use as the quantum witness in the qma protocol can be _ generated _ efficiently , it can be used to provide a @xmath32 algorithm for the lattice problem . the result we present here shows that certain properties of the state of @xcite can be _ verified _ efficiently , which might be a stepping stone towards understanding how to generate the state efficiently , thus providing an efficient algorithm for the lattice problem . finally , we mention that similar techniques to the one used in the proof of @xmath29 , might also prove useful in other contexts , for example for proving security of quantum cryptographic protocols . the paper starts with an overview of the proof . we continue with preliminaries in section [ sec : prelim ] . the proof of theorem [ thm : main ] is obtained by combining three theorems . the proof of each of the theorems is independent and is presented in a separate section . first , in section [ sec : qma+ ] we define the class qma+ and show that it is equal to qma . then , in section [ sec : cvp ] , we show that @xmath33 , a version of @xmath23 , is in qma+ . finally , in section [ sec : svptocvp ] we show that if @xmath33 is in qma then so is @xmath24 .

we consider , a gap version of the shortest vector in a lattice problem . this problem is known to be in but is not known to be in or in . we prove that it lies inside , the quantum analogue of . this is the first non - trivial upper bound on the quantum complexity of a lattice problem . first , we give a new characterization of , called . working with the formulation allows us to circumvent a problem which arises commonly in the context of : the prover might use entanglement between different copies of the same state in order to cheat . the second idea involves using estimations of autocorrelation functions for verification . we hope that these ideas will lead to further developments in the field .

we consider , a gap version of the shortest vector in a lattice problem . this problem is known to be in but is not known to be in or in . we prove that it lies inside , the quantum analogue of . this is the first non - trivial upper bound on the quantum complexity of a lattice problem . the proof relies on two novel ideas . first , we give a new characterization of , called . working with the formulation allows us to circumvent a problem which arises commonly in the context of : the prover might use entanglement between different copies of the same state in order to cheat . the second idea involves using estimations of autocorrelation functions for verification . we make the important observation that autocorrelation functions are positive definite functions and using properties of such functions we severely restrict the prover s possibility to cheat . we hope that these ideas will lead to further developments in the field .

hep-ph0407180

i

supersymmetry ( susy ) provides an elegant solution to the gauge hierarchy problem , and grand unified theories ( guts ) give us a simple understanding of the quantum numbers of the standard model ( sm ) fermions . in addition , the success of gauge coupling unification in the minimal supersymmetric standard model ( mssm ) strongly supports the possibility of the susy gut . other appealing features include that the electroweak symmetry breaking is induced by radiative corrections due to the large top quark yukawa coupling , and that tiny neutrino masses can be naturally explained by the see - saw mechanism . therefore , susy gut is one of the most promising candidates that describe the known fundamental interactions in nature except gravity . however , there are problems in the 4-dimensional susy gut : the doublet - triplet splitting problem , the proton decay problem , the fermion mass problem , and the gut gauge symmetry breaking mechanism . during the last few years , orbifold guts have been studied extensively @xcite . the main point is that the supersymmetric gut models exist in 5 or 6 dimensional space - time , and they are broken down to 4-dimensional @xmath0 supersymmetric sm like models for the zero modes through compactification on various orbifolds . this is because the orbifold parity projects out the zero modes of some components in vector multiplet and hypermultiplets . the gut gauge symmetry breaking problem , the doublet - triplet splitting problem and the fermion mass problem have been solved elegantly by orbifold projections . the proton decay problem can be solved because we can define a continuous @xmath9 symmetry . other interesting phenomenology , like flavour symmetry from the @xmath10 symmetry , gauge - fermion unification , gauge - higgs unification , and gauge - yukawa unification , have also been studied @xcite . on the other hand , deconstruction was proposed about three year ago to latticize the gauge theories in higher dimensions @xcite . the idea of deconstruction is interesting because it gives a uv completion to the higher dimensional theories . applying this idea to orbifold susy guts , we are able to construct interesting 4-dimensional susy guts where the problems in the usual 4-dimensional models can be solved , in other words , the merits of orbifold guts can be preserved @xcite . in addition , inspired by deconstruction of orbifold susy guts , we can construct new models which can not be obtained from orbifold guts while still retain the nice properties in orbifold models . deconstruction of the orbifold @xmath11 models were discussed in ref . @xcite . in these models the doublet - triplet splitting problem and the proton decay problem can be solved . deconstruction may also provide insight into fermion masses and mixings @xcite . since the number of fields in these models is finite , the corrections to gauge couplings can be reliably calculated , and there exist threshold corrections to the differential runnings of the gauge couplings @xcite . elements of deconstruction can be found in earlier papers @xcite . in this paper , we construct 4-dimensional @xmath0 supersymmetric @xmath1 models inspired by deconstruction of the 5-dimensional @xmath0 supersymmetric orbifold @xmath1 models and high dimensional non - supersymmetric @xmath1 models with wilson line gauge symmetry breaking . we study @xmath2 models with bi - fundamental link fields where the gauge symmetry can be broken down to the pati - salam ( ps ) , @xmath3 , flipped @xmath4 or the sm like gauge symmetry . however , we need to fine - tune the superpotential in the models , in order to have the doublet - triplet splitting . in addition , we propose an @xmath12 model where the gauge symmetry can be broken down to ps gauge symmetry , and an @xmath6 model with bi - spinor link fields ( @xmath13 ) and ( @xmath14 ) , in which the gauge symmetry is broken down to the flipped @xmath15 gauge symmetry . in these models , the gauge symmetry can be further broken down to the sm gauge symmetry , and the doublet - triplet splitting is naturally realized through the missing partner mechanism . the proton decay due to dimension-5 operators is thus negligible and the proton lifetime due to dimension-6 operators is well above the current experimental bound because the gut scale is at least a few times @xmath16 gev . therefore , there is no proton decay problem . we also discuss the gauge coupling unification in these two models . furthermore , we briefly comment on the interesting variation models with gauge groups @xmath7 and @xmath17 where the proton decay problem can be solved , and the @xmath6 model with bi - spinor link fields in which the gauge symmetry is broken down to the @xmath3 gauge symmetry . we first give a brief review of the orbifold susy guts and the non - susy guts with wilson line gauge symmetry breaking , and deconstruction of both types of models in section [ sec : review ] . we then discuss the models where the gauge symmetry can be broken down to the diagonal ps gauge symmetry in section [ sec : patsal ] . we comment on the models inspired by deconstructions of non - susy guts with wilson line gauge symmetry breaking in section [ sec : noncom ] . in section [ sec : bispinor ] , we consider gauge symmetry breaking with bi - spinor link fields . we summarize our results in section [ sec : conclu ] .

we discuss the models with bi - fundamental link fields where the gauge symmetry can be broken down to the pati - salam , , flipped or the standard model like gauge symmetry . we also propose an model with bi - fundamental link fields where the gauge symmetry is broken down to the pati - salam gauge symmetry , and an model with bi - spinor link fields where the gauge symmetry is broken down to the flipped gauge symmetry . in these two models , the pati - salam and flipped gauge symmetry can be further broken down to the standard model gauge symmetry , the doublet - triplet splittings can be obtained by the missing partner mechanism , and the proton decay problem can be solved . we also study the gauge coupling unification . we briefly comment on the interesting variation models with gauge groups and in which the proton decay problem can be solved .

we consider 4-dimensional supersymmetric models inspired by deconstruction of 5-dimensional supersymmetric orbifold models and high dimensional non - supersymmetric models with wilson line gauge symmetry breaking . we discuss the models with bi - fundamental link fields where the gauge symmetry can be broken down to the pati - salam , , flipped or the standard model like gauge symmetry . we also propose an model with bi - fundamental link fields where the gauge symmetry is broken down to the pati - salam gauge symmetry , and an model with bi - spinor link fields where the gauge symmetry is broken down to the flipped gauge symmetry . in these two models , the pati - salam and flipped gauge symmetry can be further broken down to the standard model gauge symmetry , the doublet - triplet splittings can be obtained by the missing partner mechanism , and the proton decay problem can be solved . we also study the gauge coupling unification . we briefly comment on the interesting variation models with gauge groups and in which the proton decay problem can be solved . anl - hep - pr-04 - 66 + hep - ph/0407180 +

1503.06994

i

the present paper investigates general relativistic flat friedmann - lematre - robertson - walker ( flrw ) models with a minimally coupled scalar field with a monomial potential , @xmath0 ( @xmath1 , @xmath2 ) , and a perfect fluid . the perfect fluid is assumed to obey a linear equation of state , @xmath3 , where @xmath4 and @xmath5 are the pressure and the energy density , respectively . the adiabatic index is assumed to satisfy @xmath6 , where @xmath7 corresponds to dust and @xmath8 to radiation . when @xmath9 the matter term @xmath10 can be reinterpreted as @xmath11 , where @xmath12 is the spatial 3-curvature of the open flrw model , i.e. , @xmath9 leads to equations that are the same as those for a scalar field in open flrw cosmology . the case @xmath13 corresponds to a matter content described by a cosmological constant , i.e. , @xmath14 , while @xmath15 describes a stiff perfect fluid ; both cases are associated with significant bifurcations , and we therefore refrain from discussing them . the einstein and matter field equations for these models are given by [ hphieq ] @xmath16 here an overdot signifies the derivative with respect to synchronous proper time , @xmath17 ; @xmath18 is the hubble variable , which is given by @xmath19 , where @xmath20 is the cosmological scale factor , and throughout we assume an expanding universe , i.e. @xmath21 , where @xmath18 is related to the expansion @xmath22 according to @xmath23 . we use ( reduced planck ) units such that @xmath24 , where @xmath25 is the speed of light and @xmath26 is the gravitational constant ( in the inflationary literature the gravitational constant @xmath26 is often replaced by the planck mass , @xmath27 ) . heuristically eq . can be viewed as an equation for an anharmonic oscillator with a friction term @xmath28 . this suggests that @xmath29 toward the future in an oscillatory manner , which is indeed correct . this qualitative picture , however , does not show how this comes about in a quantitative way , nor how the fluid affects the situation via its influence on @xmath18 . running the time backwards allows one to heuristically interpret @xmath28 as an energy input , which suggests that the scalar field oscillates with increasing amplitude toward the past , but this picture breaks down in the limit @xmath30 . even though this is beyond the planck regime , this limit is also needed in order to describe the classical behavior at early times after the planck epoch . furthermore , eq . yields that @xmath31 where @xmath32 an @xmath33 are constants , and hence @xmath34 at late times while @xmath35 at early times . note that the above qualitative considerations say nothing about how e.g. @xmath36 behaves asymptotically , i.e. , if the model is fluid or scalar field dominated , or neither , asymptotically . nor does the above say anything about the role of the so - called attractor solution in a global solution space setting . this exemplifies that there is a need for a more careful examination , which is illustrated by some previous heuristic considerations for a scalar field with a monomial potential by e.g. turner @xcite and mukhanov @xcite p. 242 , which in turn inspired the rigorous work by rendall @xcite ; in addition de la macorra and piccinelli introduced a new heuristic approach to study dynamics at late times for a scalar field with a monomial potential and a perfect fluid @xcite ; rigorous work in this context was also obtained for the special case @xmath37 by giambo and miritzis @xcite . nevertheless , this still leaves room for improvements and extensions , and , as will be shown in this paper , it is possible to shed light on interesting previously neglected physical and mathematical aspects . the main purpose of this paper in , primarily , mathematical cosmology is two - fold : firstly , to obtain a global visual picture of the solutions space , thus , e.g. , situating the so - called attractor solution in a global solution space context . secondly , to prove issues concerning asymptotical behavior at late and early times . this includes introducing averaging techniques to determine late time behavior , generalizing and simplifying earlier proofs in the literature , and using center manifold theory to rigorously derive approximations for the attractor solution at early times , as well as clarifying the physically important issue of asymptotic self - similarity . the outline of the paper is as follows . in the next section we introduce our new three - dimensional dynamical systems reformulation of the field equations on a relatively compact state space . we also present two other complementary dynamical systems formulations of the field equations , which allow us to effectively obtain approximations for the attractor solution . in section [ sec : globaldynsys ] we apply global and local dynamical systems techniques to obtain a complete and illustrative picture of the solution space and its properties , including asymptotics . in particular , we introduce averaging techniques in our global dynamical systems setting , which allows us to prove the following theorem : [ theorem ] it should be pointed out that similar conclusions have been reached heuristically with quite different arguments in e.g. @xcite . furthermore , giambo and miritzis gave a proof for @xmath37 for the cases ( i ) and ( ii ) in @xcite ( in the case of general relativity ) . however , apart from that our proof rigorously generalizes previous results , our method can , in principle , be modified to treat even more general situations . moreover , we tie our results to the global dynamical systems picture and discuss their physical implications , e.g. , situating them in the context of future manifest asymptotic self - similarity breaking . in section [ sec : attrappr ] we focus on the attractor solution , where we introduce and compare several approximation schemes , such as center manifold and slow - roll based expansions and pad approximants , in order to describe it quantitatively . finally , section [ sec : concl ] contains some general remarks , e.g. about the de sitter solution on the unphysical boundary of the state space .

we consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat flrw cosmology . we apply local and global dynamical systems techniques to a new three - dimensional dynamical systems reformulation of the field equations on a compact state space . this leads to a visual global description of the solution space and asymptotic behavior . at late times

we consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat flrw cosmology . we apply local and global dynamical systems techniques to a new three - dimensional dynamical systems reformulation of the field equations on a compact state space . this leads to a visual global description of the solution space and asymptotic behavior . at late times we employ averaging techniques to prove statements about how the relationship between the equation of state of the fluid and the monomial exponent of the scalar field affects asymptotic source dominance and asymptotic manifest self - similarity breaking . we also situate the ` attractor ' solution in the three - dimensional state space and show that it corresponds to the one - dimensional unstable center manifold of a de sitter fixed point , located on an unphysical boundary associated with the dynamics at early times . by deriving a center manifold expansion we obtain approximate expressions for the attractor solution . we subsequently improve the accuracy and range of the approximation by means of pad approximants and compare with the slow - roll approximation .

1511.05478

i

in recent years , molecular genetic data have been used extensively to learn about the evolutionary processes that gave rise to the observed genetic variation . one important example is the use of genetic data to try to infer whether or not gene flow occurred between closely related species during or after speciation ( see for example reviews by nadachowska 2010 , pinho and hey 2010 , smadja and butlin 2011 , bird et al . 2012 and a large number of references in these papers ) . such applications typically use computer programs such as _ mdiv _ ( nielsen and wakeley 2001 ) , _ i m _ ( hey and nielsen 2004 , hey 2005 ) , _ i m a _ ( hey and nielsen 2007 ) , _ mimar _ ( becquet and przeworski 2007 ) or _ ima2 _ ( hey 2010 ) , based on the isolation with migration " ( i m ) model , which assumes that a panmictic ancestral population instantaneously split into two or more descendant populations some time in the past and that migration occurred between these descendant populations at a constant rate ever since . whilst such methods have been extensively and successfully applied to study the relationships between different populations within species , the assumption of migration continuing at a constant rate until the present is unrealistic when studying relationships between species . becquet and przeworski ( 2009 ) and strasburg and rieseberg ( 2010 ) investigated by means of simulations how robust parameter estimates ( migration rates , divergence times and effective population sizes ) , obtained by methods based on the i m model , are to violations of the i m model assumptions . becquet and przeworski ( 2009 ) found that parameter estimates obtained with _ i m _ and _ mimar _ are often biased when the assumptions of the i m model are violated , and concluded that these methods are highly sensitive to the assumption of a constant migration rate since the population split . theoretical results derived by wilkinson - herbots ( 2012 ) also suggested that estimated levels of gene flow obtained by applying an i m model to species which are now completely isolated can not simply be interpreted as average levels of gene flow over time . thus , whilst computer programs based on the i m model can be used to test for departure from a complete isolation model ( which assumes that an ancestral population instantaneously split into two or more descendant populations which have been completely isolated ever since ) , the actual parameter estimates obtained may be difficult to interpret if the i m model is not an accurate description of the history of the populations or species concerned . furthermore , in some studies the programs _ i m a _ or _ ima2 _ have also been used to estimate the times when migration events occurred , and to try to distinguish between scenarios of speciation with gene flow and scenarios of introgression , and it has recently been demonstrated that such inferences about the timing of gene flow ( obtained with programs based on the i m model ) are not valid ( strasburg and rieseberg 2011 , sousa et al . becquet and przeworski ( 2009 ) , strasburg and rieseberg ( 2011 ) and sousa et al . ( 2011 ) all suggested that more realistic models of population divergence and speciation are needed . a first step in trying to make the i m model more suitable for the study of speciation is to allow gene flow to occur during a limited period of time , followed by complete isolation of the species , and such models have been studied by teshima and tajima ( 2002 ) , innan and watanabe ( 2006 ) and wilkinson - herbots ( 2012 ) . in the latter paper , a model of isolation with an initial period of migration " ( iim ) was studied where a panmictic ancestral population gave rise to two or more descendant populations which exchanged migrants symmetrically at a constant rate for a period of time , after which they became completely isolated from each other . explicit analytical expressions were derived for the probability that two dna sequences ( from the same descendant population or from different descendant populations ) differ at @xmath0 nucleotide sites , assuming the infinite sites model of neutral mutation . it was suggested that these results may be useful for maximum likelihood estimation of the parameters of the model , if one pair of dna sequences is available at each of a large number of independent loci , and that such an ml method should be very fast as it is based on an explicit expression for the likelihood rather than on computation by means of numerical approximations or mcmc simulation . however the proposed ml estimation method had not yet been implemented and its usefulness was still to be demonstrated . in this paper we present an implementation of the ml estimation method for the parameters of the isolation with an initial period of migration " model proposed in wilkinson - herbots ( 2012 ) , and we illustrate its potential by applying it to a set of dna sequence data from _ drosophila simulans _ and _ drosophila melanogaster _ previously analysed by wang and hey ( 2010 ) and lohse et al . the parameter estimates and maximized likelihood obtained for the iim model are also compared to those under an i m model and an isolation model , and it is illustrated that the method makes it possible to distinguish between more and less plausible evolutionary scenarios , by comparing aic scores or by means of likelihood ratio tests . the implementation was done in r ( r development core team 2011 ) . the r code for the mle method described is included as supplementary material and can readily be pasted into an r document . this mle algorithm is very fast indeed : for the drosophila data mentioned above ( using the number of nucleotide differences between two dna sequences at each of approximately 30,000 loci ) , we obtained estimates of the parameters of the iim model using a desktop pc ; the program returned results instantly ( i.e. in a small fraction of a second ) if all loci had been trimmed to the same estimated mutation rate ( as proposed by lohse et al . 2011 ) , or in approximately 20 seconds if the full sequences ( and hence different mutation rates at different loci ) were used . whereas most earlier methods used large samples from a small number of loci , recent advances in dna sequencing technology and the advent of whole - genome sequencing have led to an increased interest in methods which ( like that described in this paper ) can handle data from a small number of individuals at a large number of loci ( for example , takahata 1995 ; takahata et al . 1995 ; takahata and satta 1997 ; yang 1997 , 2002 ; innan and watanabe 2006 ; wilkinson - herbots 2008 ; burgess and yang 2008 ; wang and hey 2010 ; yang 2010 ; hobolth et al . 2011 ; li and durbin 2011 ; lohse et al . 2011 ; wilkinson - herbots 2012 ; zhu and yang 2012 ; andersen et al . this type of data set has two advantages . firstly , data from even a very large number of individuals at the same locus tend to contain only little information about very old divergence or speciation events because typically the individuals ancestral lineages will have coalesced to a very small number of ancestral lineages by the time the event of interest is reached , and in such contexts a data set consisting of a small number of dna sequences at each of a large number of independent loci may be more informative ( maddison and knowles 2006 ; wang and hey 2010 ; lohse et al . 2010 , 2011 ) . secondly , considering small numbers of sequences at large numbers of independent loci is mathematically much easier and computationally much faster than working with large numbers of sequences at the same locus . in particular , explicit analytical expressions for the likelihood have been obtained for pairs or triplets of sequences for a number of demographic models ( for example , takahata et al . 1995 ; wilkinson - herbots 2008 ; lohse et al . 2011 ; wilkinson - herbots 2012 ; zhu and yang 2012 ) , which substantially speeds up computation and maximization of the likelihood .

we consider a model of isolation with an initial period of migration " ( iim ) , where an ancestral population instantaneously split into two descendant populations which exchanged migrants symmetrically at a constant rate for a period of time but which are now completely isolated from each other . a method of maximum likelihood estimation of the parameters of the model is implemented , for data consisting of the number of nucleotide differences between two dna sequences at each of a large number of independent loci , using the explicit analytical expressions for the likelihood obtained in wilkinson - herbots ( 2012 ) . the method is extremely fast , returning parameter estimates in less than 1 minute for a data set consisting of the numbers of differences between pairs of sequences from 10,000s of loci , or in a small fraction of a second if all loci are trimmed to the same estimated mutation rate . it is also illustrated how the maximized likelihood can be used to quickly distinguish between competing models describing alternative evolutionary scenarios , either by comparing aic scores or by means of likelihood ratio tests .

we consider a model of isolation with an initial period of migration " ( iim ) , where an ancestral population instantaneously split into two descendant populations which exchanged migrants symmetrically at a constant rate for a period of time but which are now completely isolated from each other . a method of maximum likelihood estimation of the parameters of the model is implemented , for data consisting of the number of nucleotide differences between two dna sequences at each of a large number of independent loci , using the explicit analytical expressions for the likelihood obtained in wilkinson - herbots ( 2012 ) . the method is demonstrated on a large set of dna sequence data from two species of drosophila , as well as on simulated data . the method is extremely fast , returning parameter estimates in less than 1 minute for a data set consisting of the numbers of differences between pairs of sequences from 10,000s of loci , or in a small fraction of a second if all loci are trimmed to the same estimated mutation rate . it is also illustrated how the maximized likelihood can be used to quickly distinguish between competing models describing alternative evolutionary scenarios , either by comparing aic scores or by means of likelihood ratio tests . the present implementation is for a simple version of the model , but various extensions are possible and are briefly discussed .

1207.3757

i

let @xmath5 be a semimartingale , which is observed at discrete times @xmath6 for @xmath7 , over a finite time interval @xmath8 $ ] , with a discretization mesh @xmath9 which is small and eventually goes to @xmath10 ( high - frequency setting ) . one of the main problems encountered in practice is the estimation of the integrated ( squared ) volatility ( in finance terms ) , or equivalently of the continuous part of the quadratic variation @xmath11_t$ ] . by now , this is a well - understood problem , at least when @xmath5 is an it semimartingale . for example , in the continuous one - dimensional case , if @xmath5 takes the form @xmath12 the approximate quadratic variation @xmath13}(x_{i{\delta}_n}-x_{(i-1){\delta}_n})^2 $ ] , which of course converges to @xmath11_t=\int_0^t{\sigma}^2_s\,ds$ ] , enjoys a central limit theorem ( clt ) : the difference between these two processes , normalized by @xmath14 , converges stably in law to a limit which is conditionally on @xmath5 a continuous gaussian martingale with quadratic variation ( equivalently , with variance ) twice the so - called `` quarticity , '' that is , @xmath15 . although later we consider a much more general framework , allowing @xmath5 to be multi - dimensional and with jumps , in the we pursue the discussion in this special one - dimensional continuous case . in various statistical problems one needs to estimate not only the quarticity , but functionals of the form @xmath16 ( for relatively general test functions @xmath17 , and to derive associated clts , see @xcite ) ; notice that we plug in the `` spot '' squared volatility @xmath18 rather than @xmath19 , since in any case it is impossible to determine the sign of @xmath19 on the basis of the observation of the path @xmath20 . the case @xmath21 corresponds to the usual integrated volatility , and @xmath22 to the quarticity . toward this aim , two methods are currently at hand : the first one is available if @xmath23 for all , where the @xmath24 s are independent @xmath25 variables and @xmath26 is a continuous function on @xmath27 , of polynomial growth . then we know that @xmath28-k+1 } f \biggl(\frac{{\delta}^n_ix}{{\sqrt{{\delta}_n}}},\ldots,\frac{{\delta}^n_{i+k-1}x}{{\sqrt{{\delta}_n } } } \biggr)\nonumber\\[-8pt]\\[-8pt ] & & \eqntext{\displaystyle \mbox{where } { \delta}^n_ix = x_{i{\delta}_n}-x_{(i-1){\delta}_n},}\end{aligned}\ ] ] converges to @xmath29 in probability , and if @xmath26 is @xmath30 the rate of convergence is @xmath31 , and in the associated clt the limiting conditional variance is @xmath32 for a suitable function @xmath33 . the second one consists in using estimators for the spot volatility and approximating the integral @xmath29 by riemann sums , in which the spot volatility is replaced by its estimator ; that is , we set @xmath34-k_n+1}g\bigl(\widehat{c}{}^n_i \bigr)\qquad \mbox{where } \widehat{c}{}^n_i=\frac1{k_n { \delta}_n}\sum_{j=0}^{k_n-1}\bigl ( { \delta}^n_{i+j}x\bigr)^2\ ] ] for an arbitrary sequence of integers such that @xmath35 and @xmath36 . then one knows that @xmath37 ( when @xmath17 is continuous and of polynomial growth ) . but so far nothing is known about the rate of convergence of these estimators when @xmath38 goes to infinity ( the situation @xmath39 not depending on @xmath40 is studied in @xcite where the rate @xmath41 is obtained for power functions ) . the first method is quite powerful and gives optimal rates , but the special form of @xmath17 puts strong constraints on this function [ e.g. , it is @xmath42 on @xmath43 , and much more ] . to tell the truth , in the one - dimensional case , by far the most useful test functions @xmath17 are the powers @xmath44 ( recall that @xmath45 here ) for @xmath46 , which are associated as above with @xmath47 , where @xmath48 is the @xmath49th absolute moment of @xmath50 . nevertheless , some functions @xmath17 of interest might not be , or not in an obvious way , of this form or , more generally , linear combinations of functions of this form . in the multivariate case , however , with @xmath5 being @xmath51-dimensional and thus @xmath52 above as well , one typically finds asymptotic variances which are complicated functions of the @xmath53-dimensional spot volatility . this is , for instance , the case when studying multipower variations for integrated volatility estimation in the presence of jumps ; see , for example , @xcite . in this situation and more generally for an arbitrary ( smooth ) function @xmath17 on the set @xmath54 of all @xmath53 symmetric nonnegative matrices , it is rather a difficult task in practice to find an integer @xmath55 and a function @xmath26 on @xmath56 such that , for all @xmath57 , we have @xmath58 , where again the @xmath24 s are ( @xmath51-dimensional ) i.i.d . @xmath25 . in addition , this first method does not provide efficient estimation in general . to see that , consider the toy example @xmath59 , where @xmath60 is a constant , @xmath61 , @xmath62 and @xmath63 . we thus observe the increments @xmath64 for @xmath65 , or equivalently the @xmath40 variables @xmath66 . these variables are i.i.d . @xmath67 , so the asymptotically best estimators for @xmath68 ( efficient in all possible senses , and also the mle ) are @xmath69 , with convergence rate @xmath70 and asymptotic variance @xmath71 . if instead one wants to estimate @xmath72 for some @xmath73 in @xmath43 , one can use @xmath74 , and the ordinary central limit theorem tells us that the rate of convergence is again @xmath70 , and the asymptotic variance is @xmath75 : this is exactly what the first method above does . but this is not optimal , the asymptotically optimal estimators being @xmath76 ( the mle again ) , with rate @xmath70 and asymptotic variance @xmath77 , smaller than the previous one when @xmath73 . now , taking @xmath76 is exactly what the second method ( [ i-2 ] ) does . the aim of this paper is to develop the second method , and in particular to provide a central limit theorem , with the rate @xmath31 ( as it is usually the case in a nonparametric setting for integrated functionals estimation ; see , e.g. , @xcite ) , and with an asymptotic variance always smaller than if one uses the first method . this can be viewed as an extension , in several directions , of the `` block method '' of mykland and zhang in @xcite . about efficiency , and despite the title of the paper , we do not really examine the question in the general nonparametric or semi - parametric setting assumed below , since even for the simpler problem of estimating the integrated volatility , the concept of efficiency is not well established so far . instead , we will term as `` efficient '' a procedure which is efficient in the usual sense for the sub - model consisting in the toy model @xmath59 above , and efficient in the sense of the hajek convolution theorem , for the markov - type model recently studied by clment , delattre and gloter in @xcite and of the form @xmath78 where @xmath79 are unknown smooth enough functions and @xmath80 arbitrary processes and where the two brownian motions @xmath81 are independent . this will be done in the multivariate setting and when @xmath5 possibly has jumps ( upon suitably truncating the increments in ( [ i-2 ] ) if it is the case , in the spirit of ) , and under the additional assumptions that @xmath18 itself is an it semimartingale and that , when @xmath5 jumps , these jumps are summable , which are exactly the same assumptions under which the truncated versions of @xmath82 in ( [ i-1 ] ) converge with rate @xmath31 . the paper is organized as follows : section [ sec - set ] is devoted to presenting the assumptions . results are given in section [ sec - res ] , and all proofs are gathered in section [ sec - p ] .

we consider a multidimensional it semimartingale regularly sampled on $ ] at high frequency , with going to zero . the goal of this paper is to provide an estimator for the integral over $ ] of a given function of the volatility matrix . to approximate the integral we show that although the accuracy of the pointwise estimation is at most , this procedure reaches the parametric rate , as it is usually the case in integrated functionals estimation . after a suitable bias correction

we consider a multidimensional it semimartingale regularly sampled on $ ] at high frequency , with going to zero . the goal of this paper is to provide an estimator for the integral over $ ] of a given function of the volatility matrix . to approximate the integral , we simply use a riemann sum based on local estimators of the pointwise volatility . we show that although the accuracy of the pointwise estimation is at most , this procedure reaches the parametric rate , as it is usually the case in integrated functionals estimation . after a suitable bias correction , we obtain an unbiased central limit theorem for our estimator and show that it is asymptotically efficient within some classes of sub models .

patt-sol9609003

i

close to a pattern - forming transition , many hydrodynamic systems can be described by coupled one - dimensional ( 1d ) ginzburg - landau equations for some envelope functions ( order parameters ) @xmath0 and @xmath1 . these equations were first introduced in an explicit form ( with purely real coefficients , but also with the group - velocity terms ) by cross @xcite . in the presence of a small over - criticality parameter , and when rewritten in terms of two real amplitudes and two real phases , these equations for two complex order parameters are completely tantamount to a single fourth - order complex equation ( the `` complex swift - hohenberg '' equation ) introduced still earlier in ref . as is well known , the coefficient in front of the cross - coupling ( cc ) term is an essential parameter of these equations . for a small cc coefficient , homogenous bimodal states of the form @xmath2 occur , while for sufficiently large cc , this bimodal state is unstable , and the system evolves into a single - mode state in which either @xmath0 or @xmath1 is zero @xcite . in this work , we consider the case that the cc coefficient is a function of the spatial coordinate @xmath3 . in particular , we focus on the case that the cc coefficient is slightly above @xmath4 for @xmath5 and slightly below @xmath4 for @xmath6 . the simplest state that can occur in this case is a spatial juxtaposition of a single and a bimodal state , separated by a so - called domain - wall . we study this domain - wall in the nld , rgl , and cgl equations . we show that non - variational effects can destroy the stationary domain - wall and study the dynamical states that occur in this case . in particular we focus on the effect of the group - velocity terms in the coupled equations . this paper is organized as follows . first we introduce a simplified model for the occurrence of domain - walls . for stationary solutions of this model we derive a perturbation equation that allows us to predict the vanishing of stationary domain - walls when the group - velocity is sufficiently large . this is confirmed by numerical simulations of this model , and we describe the ensuing dynamical states . we study the relevance of this model for coupled rgl and cgl equations by performing numerical simulations . in particular for the cgl equations , a broad spectrum of dynamical behavior is observed , including spatio - temporal chaos . it is very difficult to characterize these states , and we restrict ourself to a limited exploration of the possible dynamical states . some of the essential features of the cgl equations that are important in the study of the domain - wall , i.e. , the stability of the single and bimodal states as a function of the cc can also be studied in simpler models . we will first consider two coupled nonlinear diffusion ( nld ) equations , to which we add group - velocity terms borrowed from the cgl equation that break the variational representation of the nld equations ( however , the group - velocity terms should not be added in the above - mentioned case of the rayleigh - bnard convection in the inhomogeneous large - aspect - ratio system @xcite ) . in the simplest approach , we take the amplitudes real - valued : @xmath7 these nld equations are the simplest set of equations that admit the dw s that we are interested in . these equations have no direct physical interpretation in terms of amplitude equations , but they have the advantage over more realistic models that the effect of the group - velocity terms on the domain - walls can be studied analytically . since the group - velocity terms have opposite sign for the @xmath0 and the @xmath1 equation of the coupled cgl equations ( [ cgl ] ) , we retain this property in the nld equations . without the cross - coupling , the group - velocity terms generate a counter propagation of the patterns in @xmath0 and @xmath1 . when the equations for @xmath0 and @xmath1 are coupled , the effect of the group - velocity terms can not be given in terms of a simple propagation rule . we will derive , in a certain limit , a single ordinary differential equation for the order parameter @xmath8 that describes stationary configurations . using this equation , we will be able to investigate the existence of a stationary dw analytically . in section [ varisec ] we consider the case that the group - velocity terms are absent . the equations are then variational and for the particular case that the cc coefficient , as a function of the spatial coordinate @xmath3 , is proportional to @xmath9 , an exact analytical solution for the dw can be obtained . next , we extend in section [ nldevsec ] the equation for @xmath10 to include the non - variational group - velocity terms , and when we take @xmath11 to be a step function , an analytical solution can be constructed . analyzing the latter solution , we find a transition from a regime where the dw is stationary to a regime where no stationary dw exists . this transition , which we show to have a nice geometrical interpretation , occurs when the group - velocity @xmath12 is equal to the critical value @xmath13 . we will show that this result remains valid for a broad class of inhomogeneous cc coefficients . direct simulations of the coupled nld equations , presented in section [ secfknum ] , confirm the analytical results and show that there is a value of the group - velocity , @xmath14 , where the stationary domain - wall looses its stability . this instability occurs because the position of the domain - wall diverges when @xmath12 approaches @xmath15 . the difference between @xmath15 and @xmath14 is of the order of a few percent . for a group - velocity just beyond @xmath14 , the dw is seen to perform small - amplitude chaotic oscillations around a mean position , without essentially disturbing the dw s shape . the study of the coupled cgl equations is of a more explorative nature . as a first step towards the study of the full coupled cgl equations , we allow the amplitudes @xmath0 and @xmath1 to be complex valued . these equations are reminiscent of the rgl equations , but it should be noted that in physical applications , the rgl equations have no group - velocity terms ; nevertheless we refer to this model as the coupled rgl equations . we explain that the main properties of the stationary domain - walls in this model can be described by the nld equations . simulations of coupled rgl equations , presented in section [ rglsec ] , show a transition between the stationary domain - walls and a dynamical state with the increase of the group - velocity that is similar to the nld - case . the role of wavenumbers of the initial conditions , which constitutes the main feature that is not present in the nld equations , is discussed briefly . for the coupled cgl equations , the numerical results presented in section [ cglsec ] show that the nonlinear dispersion terms may render the domain - walls unstable , even when the group - velocity terms are absent . spatio - temporal disordered states often occur . the oscillations of the dw can be understood qualitatively to arise from the large gradients of @xmath16 and @xmath17 around the domain - wall . it may be pertinent to note that both complex and real ginzburg - landau equations with the coefficients in front of the _ linear _ terms smoothly depending upon the spatial coordinate have been the subject of many studies @xcite . it was found that a parameter ramp in the real or complex gl equation can perform wavenumber selection @xcite . in the case of the full cgl equation , it can also render the single - mode traveling waves unstable , and can trap subcritical solitary pulses @xcite . however , as far as we know , there have been no studies aimed to consider effects of a spatial dependence in the coefficient in front of the nonlinear cc term . a spatially dependent cc can be realized in rayleigh - bnard convection in a rotating annulus of non - constant width @xcite . convection in rotating systems has recently been the focus of several studies @xcite , and quasi-1d traveling waves were shown to occur in these systems near the vertical side - walls of the annulus . in a rotating annulus , there are two so - called wall modes , localized , respectively , near its inner and outer side walls . note that there is only one wall - mode per side - wall ( instead of two ) ; this is due to a symmetry breaking that is induced by the rotation @xcite . the amplitude equations describing slow modulations of these modes in the co - rotating reference frame are two coupled cubic complex ginzburg - landau ( cgl ) equations @xcite . the strength of the cc between the two wall modes sensitively depends on the width of the annulus . when the annulus is not uniform but has a varying width , the corresponding cc can be made to vary across its critical value as a function of the longitudinal spatial coordinate ( which is going along the circumference of the rotating annulus ) . other coefficients of the amplitude equations describing such a system will also depend on this coordinate , but if we assume that these coefficients , in contrast to the cc coefficient , are not close to a critical value , their spatial dependence may be ignored , provided that it is smooth enough . a similar problem may be implemented in a related but different physical system , viz . , the rayleigh - bnard convection in a ( non - rotating ) large - aspect - ratio cell . in this case , the two modes are two orthogonal sets of parallel rolls . a single - mode state is stable provided that an effective cc coefficient between the orthogonal rolls is larger than a certain minimum value , while in the opposite case a square - lattice pattern ( the bimodal state obtained as a superposition of two orthogonal sets of rolls ) is stable @xcite . usually , the actual value of the cc coefficient is well above the above - mentioned minimum , so that the square lattice is unstable . however , in special cases , e.g. , for the convection between horizontal surfaces with poor heat conductivity , the cc coefficient may fall below the minimum @xcite . one may construct a suitable inhomogeneous system , for example , by means of a variable - thickness lid put on top of the convection layer , such that the local cc coefficient , being a function of the spatial coordinates , is passing through the minimum value . then one may expect a stationary dw separating the rolls and square lattice , which is impossible in the homogeneous system @xcite .

group - velocity terms are added to the nld and rgl equations , which breaks the variational structure of these models . in the simplest case of two coupled nld equations , dynamical behavior sets in , which we consider in detail . in the cgl equations , a spatially dependent coupling coefficient as considered in this paper can be realized at least in two different convection systems : a rotating narrow annulus supporting two traveling - wave wall modes , and a large - aspect - ratio system with poor heat conductivity at the lateral boundaries , where the two phases separated by the dw are rolls and square cells .

we consider domain walls ( dw s ) between single - mode and bimodal states that occur in coupled nonlinear diffusion ( nld ) , real ginzburg - landau ( rgl ) , and complex ginzburg - landau ( cgl ) equations with a spatially dependent coupling coefficient . group - velocity terms are added to the nld and rgl equations , which breaks the variational structure of these models . in the simplest case of two coupled nld equations , we reduce the description of stationary configurations to a single second - order ordinary differential equation . we demonstrate analytically that a necessary condition for existence of a stationary dw is that the group - velocity must be below a certain threshold value . above this threshold , dynamical behavior sets in , which we consider in detail . in the cgl equations , the dw may generate spatio - temporal chaos , depending on the nonlinear dispersion . a spatially dependent coupling coefficient as considered in this paper can be realized at least in two different convection systems : a rotating narrow annulus supporting two traveling - wave wall modes , and a large - aspect - ratio system with poor heat conductivity at the lateral boundaries , where the two phases separated by the dw are rolls and square cells .

patt-sol9609003

c

in this paper we have considered domain walls between single - mode and bimodal states for three types of coupled equations with a spatially dependent coupling coefficient . in the simplest case of two coupled nld equations with the group - velocity terms , we were able to reduce the description of stationary configurations to a single non - autonomous second - order ordinary differential equation , that was used to determine analytically a necessary condition for the existence of a stationary dw in terms of the group - velocity . we have found that our prediction for the destabilization of such a stationary dw is in good agreement with numerical simulations , and we have found chaotically oscillating dw s in the case when the group - velocity is beyond the corresponding threshold . for two coupled rgl equations we have found a similar scenario . finally , for the coupled cgl equations , we have found that , in most cases , the dw s are unstable , even when the group - velocity is zero , and spatio - temporal disordered states often occur in this model . in the future , it would be interesting to investigate the competition between the various states of the coupled cgl equations . in particular , not much is known about the periodic states that seem to play an important role here . possible research subjects include the development of analytical solutions , the development of counting arguments @xcite and the competition between periodic and phase - winding solutions . the effect of an inhomogeneity as studied in this chapter on the various states may be a valuable tool in probing the states that occur for constant @xmath20 . the effect of nonzero group - velocity on the domain - walls in the cgl equations is poorly understood ; it would be interesting to see whether the divergence and subsequent instability of the domain - wall , as observed for the nld equations and cgl equations , still has some relevance for the cgl equations when @xmath219 and @xmath218 are sufficiently different .

we consider domain walls ( dw s ) between single - mode and bimodal states that occur in coupled nonlinear diffusion ( nld ) , real ginzburg - landau ( rgl ) , and complex ginzburg - landau ( cgl ) equations with a spatially dependent coupling coefficient . we reduce the description of stationary configurations to a single second - order ordinary differential equation . we demonstrate analytically that a necessary condition for existence of a stationary dw is that the group - velocity must be below a certain threshold value . above this threshold ,

we consider domain walls ( dw s ) between single - mode and bimodal states that occur in coupled nonlinear diffusion ( nld ) , real ginzburg - landau ( rgl ) , and complex ginzburg - landau ( cgl ) equations with a spatially dependent coupling coefficient . group - velocity terms are added to the nld and rgl equations , which breaks the variational structure of these models . in the simplest case of two coupled nld equations , we reduce the description of stationary configurations to a single second - order ordinary differential equation . we demonstrate analytically that a necessary condition for existence of a stationary dw is that the group - velocity must be below a certain threshold value . above this threshold , dynamical behavior sets in , which we consider in detail . in the cgl equations , the dw may generate spatio - temporal chaos , depending on the nonlinear dispersion . a spatially dependent coupling coefficient as considered in this paper can be realized at least in two different convection systems : a rotating narrow annulus supporting two traveling - wave wall modes , and a large - aspect - ratio system with poor heat conductivity at the lateral boundaries , where the two phases separated by the dw are rolls and square cells .

1104.3128

i

facility location problems have been widely studied in the operations research community ( see , e.g. , @xcite ) . in its simplest version , _ uncapacitated facility location _ ( ) , we are given a set of facilities with opening costs , and a set of clients , and we want to open some facilities and assign each client to an open facility so as to minimize the sum of the facility - opening and client - assignment costs . this problem has a wide range of applications . for example , a company might want to open its warehouses at some locations so that its total cost of opening warehouses and servicing customers is minimized . we consider the _ lower - bounded facility location _ ( ) problem , which is a generalization of where each open facility is required to serve a certain _ minimum _ amount of demand . more formally , an instance @xmath0 is specified by a set @xmath1 of facilities , and a set @xmath3 of clients . opening facility @xmath6 incurs a _ facility - opening cost _ @xmath20 , and assigning a client @xmath5 to a facility @xmath6 incurs a _ connection cost _ @xmath7 . a feasible solution specifies a subset @xmath21 of facilities , and assigns each client @xmath5 to an open facility @xmath9 so that _ each open facility serves at least @xmath10 clients _ , where @xmath10 is an input parameter . the cost of such a solution is the sum of the facility - opening and connection costs , that is , @xmath11 , and the goal is to find a feasible solution of minimum cost . as is standard in the study of facility location problems , we assume throughout that @xmath7s form a metric . we use the terms connection cost and assignment cost interchangeably in the sequel . can be motivated from various perspectives . this problem was introduced independently by karger and minkoff @xcite , and guha , meyerson , and munagala ( who called the problem _ load - balanced facility location _ ) @xcite ( see also @xcite ) , both of whom arrived at as a means of solving their respective buy - at - bulk style network design problems . arises as a natural subroutine in such settings because obtaining a near - optimal solution to the buy - at - bulk problem often entails aggregating a certain minimum demand at certain hub locations , and then connecting the hubs via links of lower per - unit - demand cost ( and higher fixed cost ) . also finds direct applications in supply - chain logistics problems , where the lower - bound constraint can be used to model the fact that it is not profitable or feasible to use services unless they satisfy a certain minimum demand . for example ( as noted in @xcite ) , lim , wang , and xu @xcite , use to abstract a transportation problem faced by a company that has to determine the allocation of cargo from customers to carriers , who then ship their cargo overseas . here the lower bound arises because each carrier , if used , is required ( by regulation ) to deliver a minimum amount of cargo . also , is an interesting special case of _ universal facility location _ ( ) @xcite a generalization of where the facility cost depends on the number of clients served by it with non - increasing facility - cost functions . with arbitrary non - increasing functions is not a well - understood problem , clearly , with @xmath22 is simply , and hence , is _ np_-hard ; consequently , we are interested in designing approximation algorithms for . the first constant - factor approximation algorithm for was devised by svitkina @xcite , whose approximation ratio is @xmath12 . prior to this , the only known approximation guarantees were _ bicriteria guarantees_. @xcite and @xcite independently devised @xmath23-approximation algorithms via a reduction to : these algorithms return a solution of cost at most @xmath24 times the optimum where each open facility serves at least @xmath15 clients [ [ our - results - and - techniques . ] ] our results and techniques . + + + + + + + + + + + + + + + + + + + + + + + + + + + we devise an approximation algorithm for that achieves a substantially - improved approximation guarantee of @xmath13 ( theorem [ mainthm ] ) , thus significantly advancing the state - of - the - art for . our improvement comes from a combination of ideas in algorithm design and analysis , and yields new insights about the approximability of . in order to describe the ideas underlying our improvement , we first briefly sketch svitkina s algorithm . svitkina s algorithm begins by using the reduction in @xcite to obtain a bicriteria solution for @xmath0 , which is then used to convert @xmath0 into an instance @xmath25 with facility - set @xmath26 having the following structure : ( i ) all clients are aggregated at @xmath14 with each facility @xmath27 having @xmath28 co - located clients ; ( ii ) all facilities in @xmath14 have zero opening costs ; and ( iii ) near - optimal solutions to @xmath25 translate to near - optimal solutions to @xmath0 ( and vice versa ) . the goal now is to identify a subset of @xmath14 to close , such that transferring the clients aggregated at these closed facilities to the remaining ( open ) facilities in @xmath14 ensures that each remaining facility serves at least @xmath10 demand ( and the cost incurred is `` small '' ) . @xcite shows that one can achieve this by solving a suitable instance . essentially the idea is that a facility @xmath6 that remains open corresponds to a _ demand point _ in the instance that requires @xmath29 units of demand , and a facility @xmath6 that is closed maps to a _ supply point _ in the instance having @xmath30 units that can be supplied to demand points ( i.e. , open facilities ) . of course , one does not know beforehand which facilities will be closed and which will remain open ; so to encode this correspondence in the instance , we create at every location @xmath27 , a supply point with ( suitable opening cost and ) capacity @xmath10 , and a demand point with demand @xmath29 if @xmath31 ( so the supply point at @xmath6 has @xmath30 residual capacity after satisfying this demand ) . ( assume @xmath31 for simplicity ; facilities with @xmath32 are treated differently . ) finally , @xcite argues that a -solution ( where a supply point may end up sending _ less _ then @xmath30 supply to other demand points ) can be mapped to a solution to @xmath25 without increasing the cost incurred by much ; since admits an @xmath33-approximation algorithm , one obtains an @xmath33-approximate solution to @xmath25 , and hence to the original instance @xmath0 . our algorithm also proceeds by ( a ) obtaining an instance @xmath25 satisfying properties ( i)(iii ) mentioned above , ( b ) solving @xmath25 , and ( c ) mapping the @xmath25-solution to a solution to @xmath0 , but our implementation of steps ( a ) and ( b ) differs from that in svitkina s algorithm . these modified implementations , which are independent of each other and yield significant improvements in the overall approximation ratio even when considered in isolation , result in our much - improved approximation ratio . we detail how we perform step ( a ) later , and focus first on describing how we solve @xmath25 , which is our chief algorithmic contribution . our key insight is that one can solve the instance @xmath25 by reducing it to a new problem we introduce that we call _ capacity - discounted _ ( ) , which closely resembles and admits an algorithm ( that we devise ) with a much better approximation ratio than . a -instance has the property that every facility is either uncapacitated ( i.e. , has infinite capacity ) , or has finite capacity and _ zero _ facility cost . the instance we construct consists of the same supply and demand points as in the reduction of @xmath25 to in @xcite , except that all supply points with non - zero opening cost are now uncapacitated . ( an interesting consequence is that if all facilities in @xmath25 have @xmath31 , the instance is in fact a -instance ! ) we prove two crucial algorithmic results . it is not hard to see that the `` standard '' integrality - gap example for the natural lp - relaxation of can be cast as a instance , thus showing that the natural lp - relaxation for has a large integrality gap ( see appendix [ cduflgap ] ) ; in fact , we are not aware of any lp - relaxation for with constant integrality gap . circumventing this difficulty , we devise a local - search algorithm for based on add , swap , and delete moves that achieves the _ same performance guarantees _ as the corresponding local - search algorithm for @xcite ( see section [ cdufl - ls ] ) . the local - search algorithm yields significant dividends in the overall approximation ratio because not only is its approximation ratio for better than the state - of - the - art for , but also because it yields separate ( asymmetric ) guarantees on the facility - opening and assignment costs , which allows one to perform a tighter analysis . second , we show that any near - optimal -solution can be mapped to a near - optimal solution to @xmath25 ( see section [ i2-soln ] ) . as before , it could be that in the -solution , a supply point @xmath6 ( which corresponds to facility @xmath6 being closed down ) sends less than @xmath30 supply to other demand points , so that closing down @xmath6 entails transferring its residual clients to open facilities . but since some supply points are now uncapacitated , it could also be that @xmath6 sends more than @xmath30 supply to other demand points . we argue that this artifact can also be handled without increasing the solution cost by much , by opening the facilities in a carefully - chosen subset of @xmath34 and closing down the remaining facilities . for _ every value of @xmath19 _ ( recall that the instance @xmath25 is specified in terms of a parameter @xmath19 ) , the resulting approximation factor for @xmath25 ( theorem [ i2thm ] ) is better than the guarantee obtained for @xmath25 in svitkina s algorithm ; this in turn translates ( by choosing @xmath19 suitably ) to an improved solution to the original instance . we now discuss how we implement step ( a ) , that is , how we obtain instance @xmath25 . as in @xcite , we arrive at @xmath25 by computing a bicriteria solution to , but we obtain this bicriteria solution in a different fashion ( see section [ bicriteria ] ) . the reduction from to in @xcite proceeds by setting the opening cost of facility @xmath6 to @xmath35 , where @xmath36 is the set of @xmath10 clients closest to @xmath6 , solving the resulting instance , and postprocessing using ( single - facility ) delete moves if such a move improves the solution cost . we modify this reduction subtly by creating a instance , where facility @xmath6 s opening cost is instead set to @xmath37 , where @xmath38 is the distance between @xmath6 and the @xmath15-closest client to it . as in the case of the earlier reduction , we argue that each open facility @xmath6 in the resulting solution ( obtained by solving and postprocessing ) serves at least @xmath15 clients . the overall bound we obtain on the total cost now includes various @xmath38 terms . instead of plugging in the ( weak ) bound @xmath39 ( which would yield the same guarantee as that obtained via the earlier reduction ) , we are able to perform a tighter analysis by choosing @xmath19 from a suitable distribution and leveraging the fact that @xmath40 . ( this can easily be derandomized , since there are only @xmath10 combinatorially distinct choices for @xmath19 . ) these simple modifications ( in algorithm - design _ and _ analysis ) yield a surprising amount of improvement in the approximation factor , which is reminiscent of the mileage provided by ( random ) @xmath19-points for various scheduling problems ( see , e.g. , @xcite ) and @xcite . also , we observe that one can obtain further improvements by using the local - search algorithm of @xcite to solve the above instance : this is because the resulting solution is then already postprocessed , which allows us to exploit the asymmetric bounds on the facility - opening and assignment costs provided by the local - search algorithm via scaling , and improve the approximation ratio . finally , we remark that the study of may provide useful and interesting insights about . is a special case of that despite its special structure inherits the intractability of with respect to lp - based approximation guarantees . if one seeks to develop lp - based techniques and algorithms for ( which has been a long - standing and intriguing open question ) , then one needs to understand how one can leverage lp - based techniques for , and it is plausible that lp - based insights developed for may yield similar insights for ( and potentially lp - based approximation guarantees for ) . [ [ related - work . ] ] related work . + + + + + + + + + + + + + as mentioned earlier , was independently introduced by @xcite and @xcite , who used it as a subroutine to solve the ( _ rent - or - buy _ and hence , the ) _ maybecast _ problem , and the _ access network design _ problem respectively . their ideas , which lead to bicriteria guarantees for , play a preprocessing role both in svitkina s algorithm for @xcite and ( slightly indirectly ) in our algorithm . there is a large body of literature that deals with approximation algorithms for ( metric ) , and its variants ; see @xcite for a survey on . the first constant approximation guarantee for was obtained by shmoys , tardos , and aardal @xcite via an lp - rounding algorithm , and the current state - of - the - art is a 1.488-approximation algorithm due to li @xcite . local - search techniques have also been utilized to obtain @xmath33-approximation guarantees for @xcite . we apply some of the ideas of @xcite in our algorithm . starting with the work of korupolu , plaxton , and rajaraman @xcite , various local - search algorithms with constant approximation ratios have been devised for , with the current - best approximation ratio being @xmath41 @xcite . local - search approaches are however not known to work for ; in appendix [ app : lbfllocgap ] , we show that local search based on @xmath42 , @xmath43 , and @xmath44 moves yields poor approximation guarantees . universal facility location ( ) , where the facility cost is a non - decreasing function of the number of clients served by it , was introduced by @xcite , and @xcite gave a constant approximation algorithm for this . we are not aware of any work on with arbitrary non - increasing functions ( which generalizes ) . @xcite give a constant approximation for the case where the cost - functions do not decrease too steeply ( the constant depends on the steepness ) ; notice that does not fall

a feasible solution specifies a subset of facilities to open , and assigns each client to an open facility so that each open facility serves _ at least clients _ , where is an input parameter . the cost of such a solution is , and the goal is to find a feasible solution of minimum cost . the current best approximation ratio for is . we substantially advance the state - of - the - art for by devising an approximation algorithm for that achieves a significantly - improved approximation guarantee of . our improvement comes from a variety of ideas in algorithm design and analysis , which also yield new insights into . our chief algorithmic novelty is to present an improved method for solving a more - structured instance obtained from via a bicriteria approximation algorithm for , wherein all clients are aggregated at a subset of facilities , each having at least co - located clients ( for some $ ] ) . in contrast , the algorithm in proceeds by reducing to , whose current - best approximation ratio is worse than that of our local - search algorithm for , and this is one of the reasons behind our algorithm s improved approximation ratio . another new ingredient of our -algorithm and analysis is a subtly different method for constructing a bicriteria solution for ( and hence , ) , combined with the more significant change that we now choose a _ random _ from a suitable distribution . this leads to a surprising degree of improvement in the approximation factor , which is reminiscent of the mileage provided by random-points in scheduling problems .

we consider the _ lower - bounded facility location _ ( ) problem ( also sometimes called _ load - balanced facility location _ ) , which is a generalization of _ uncapacitated facility location _ ( ) , where each open facility is required to serve a certain _ minimum _ amount of demand . more formally , an instance of is specified by a set of facilities with facility - opening costs , a set of clients , and connection costs specifying the cost of assigning a client to a facility , where thes form a metric . a feasible solution specifies a subset of facilities to open , and assigns each client to an open facility so that each open facility serves _ at least clients _ , where is an input parameter . the cost of such a solution is , and the goal is to find a feasible solution of minimum cost . the current best approximation ratio for is . we substantially advance the state - of - the - art for by devising an approximation algorithm for that achieves a significantly - improved approximation guarantee of . our improvement comes from a variety of ideas in algorithm design and analysis , which also yield new insights into . our chief algorithmic novelty is to present an improved method for solving a more - structured instance obtained from via a bicriteria approximation algorithm for , wherein all clients are aggregated at a subset of facilities , each having at least co - located clients ( for some $ ] ) . one of our key insights is that one can reduce the resulting instance , denoted , to a problem we introduce , called _ capacity - discounted _ ( ) . is a special case of capacitated facility location ( ) where facilities are either uncapacitated , or have finite capacity and zero opening costs . circumventing the difficulty that inherits the intractability of with respect to lp - based approximation guarantees , we give a simple local - search algorithm for based on add , delete , and swap moves that achieves the same approximation ratio ( of ) as the corresponding local - search algorithm for . in contrast , the algorithm in proceeds by reducing to , whose current - best approximation ratio is worse than that of our local - search algorithm for , and this is one of the reasons behind our algorithm s improved approximation ratio . another new ingredient of our -algorithm and analysis is a subtly different method for constructing a bicriteria solution for ( and hence , ) , combined with the more significant change that we now choose a _ random _ from a suitable distribution . this leads to a surprising degree of improvement in the approximation factor , which is reminiscent of the mileage provided by random-points in scheduling problems .

1509.01128

i

one of the most fundamental dimension theoretic questions in geometric measure theory is : _ how does dimension behave under orthogonal projection _ ? this line of research began with the seminal paper of marstrand from 1954 @xcite , influenced by some earlier work of besicovitch . one version of marstrand s projection theorem states that if @xmath5 is an analytic set with hausdorff dimension @xmath6 $ ] , then the hausdorff dimension of the orthogonal projection of @xmath7 in almost every direction is @xmath8 , which is as big as it can be . here ` almost every ' refers to lebesgue measure on the interval @xmath9 , with projections parameterised in the obvious way . for the purposes of this paper , the important thing about this projection theorem is that , no matter what analytic set @xmath5 one considers , the hausdorff dimension of the projections @xmath10 is _ almost surely constant_. other important notions of dimension include the packing dimension and upper and lower box - counting dimension , see @xcite . the behaviour of these dimensions under projection is rather more subtle than for the hausdorff dimension , as first demonstrated by jrvenp @xcite . however , in the mid-1990s it became clear that each of these dimensions is at least _ almost surely constant _ under projection , in the same sense that the hausdorff dimension is . the precise value of the constant is more complicated than simply @xmath8 , but can be stated in terms of _ dimension profiles _ , see @xcite . there are also natural higher dimensional analogues of these projection results . in particular , the higher dimensional analogue of marstrand s theorem , where one considers projections of analytic sets @xmath11 to @xmath12-planes , was proved by mattila in 1975 @xcite . in this setting the almost sure value of the hausdorff dimension is given by @xmath13 and ` almost sure ' refers to the natural invariant measure on the grassmannian manifold @xmath14 , which consists of all @xmath12 dimensional subspaces of @xmath15 . for more information on the rich and fascinating topic of projections of fractal sets and measures , see the recent survey papers @xcite and the references therein . the assouad dimension is another notion of dimension , which has been very useful as a tool in several disparate areas of mathematics . in recent years it has been gaining more attention in the setting of fractal geometry and geometric measure theory . as such , it is natural to consider the fundamental geometric properties of the assouad dimension , such as its behaviour under orthogonal projections . we recall the definition here , but refer the reader to @xcite for more details . for any non - empty subset @xmath16 and @xmath17 , let @xmath18 be the smallest number of open sets with diameter less than or equal to @xmath19 required to cover @xmath20 . the _ assouad dimension _ of a non - empty set @xmath21 is then given by @xmath22 where @xmath23 denotes the open euclidean ball centred at @xmath24 with radius @xmath25 . it is well - known that the assouad dimension is always an upper bound for the hausdorff dimension . in this paper we prove that , unlike the hausdorff , packing and box dimensions discussed above , the assouad dimension of orthogonal projections of a compact set @xmath26 need _ not _ be almost surely constant as a function of the projection angle . however , in analogy with the result for hausdorff dimension , the essential infimum of the said function is at least @xmath27 ; even if @xmath7 is not compact , or even analytic . these results are discussed in section [ maingeneral ] . we establish the non - constancy result via a detailed study of the assouad dimensions of projections of planar self - similar sets . the hausdorff dimension of projections of self - similar sets has attracted a lot of attention in recent years , see section [ sssection ] , and thus it is natural to consider the analogous questions for assouad dimension . our results for self - similar sets are discussed in detail in section [ mainresults ] , and the applications concerning non - constancy and falconer s theorem ( mentioned in the abstract ) will be presented in sections [ nomarstrand ] and [ nofalconer ] respectively . on route to proving our main result for self - similar sets , we obtain new information about the assouad dimension of graph - directed self - similar sets in the line with overlaps , theorem [ gdassouad ] , which is the natural extension of ( * ? ? ? * theorem 1.3 ) to the graph - directed setting and is of independent interest . many questions remain unanswered by the results in this paper , and we pose some of them in sections [ maingeneral ] through [ selfaffinesets ] . in particular , very little is known for self - affine sets , and in higher dimensions . self - similar sets are arguably the most fundamental class of fractal set and have been studied extensively , see @xcite . let @xmath28 be a finite collection of contracting similarities mapping @xmath29^d$ ] into itself . by _ , we mean that for each @xmath30 , there exists a similarity ratio @xmath31 such that for all @xmath32^d$ ] we have @xmath33 which means that the contractions @xmath34 scale uniformly by @xmath35 in every direction . as such we may decompose each @xmath34 uniquely as @xmath36 where @xmath37 is a @xmath38 orthogonal matrix and @xmath39 is a translation . a fundamental result of hutchinson @xcite states that there is a unique attractor of the iterated function system ( ifs ) @xmath28 , that is , a unique non - empty compact set @xmath40^d$ ] satisfying @xmath41 the set @xmath7 is called self - similar and often has a rich fractal structure . a self - similar set satisfies the open set condition ( osc ) ( for a given ifs defining it ) if there exists a non - empty open set @xmath42^d$ ] such that @xmath43 with the sets @xmath44 pairwise disjoint . if @xmath7 satisfies the osc , then its hausdorff and assouad dimensions are given by @xmath45 where @xmath3 is the _ similarity dimension _ given by solving the equation @xmath46 if the osc is not satisfied , then the dimensions are more difficult to get hold of and indeed the assouad and hausdorff dimensions may be distinct @xcite . one still expects the hausdorff dimension to be given by @xmath45 , unless there is a good reason for it not to be , such as exact overlaps in the construction , see ( * ? ? ? * question 2.6 ) . recent major advances were made in this area by hochman @xcite . there has also been intense interest in the dimension theory of the projections of self - similar sets in recent years , see the survey @xcite . in particular , we have the following theorem : [ hausdorffprojection ] let @xmath47^d$ ] be a self - similar set containing at least two points , suppose that the group generated by @xmath48 is dense in @xmath49 or @xmath50 and fix @xmath51 less than @xmath52 . then @xmath53 for _ * all * _ @xmath54 . the particular interest of this result is that ` dense rotations ' guarantees that there are _ no _ exceptions to marstrand s theorem . this result is essentially due to hochman and shmerkin s breakthrough work @xcite , although they stated the result assuming some separation conditions . these conditions were explicitly removed by farkas @xcite and falconer - jin @xcite . the result in the planar case was obtained earlier by peres and shmerkin @xcite .

we consider the assouad dimensions of orthogonal projections of planar sets onto lines . our investigation covers both general and self - similar sets . for general sets , compared to the famous analogue for hausdorff dimension namely _ marstrand s projection theorem _ a striking difference is that the words ` at least ' can not be dispensed with : in fact , for many planar self - similar sets of dimension , we prove that the assouad dimension of projections can attain both values and for a set of directions of positive measure . for self - similar sets , we prove that every projection has assouad dimension equal to one , assuming that the planar set is not a singleton . as another application of our results . + + _ mathematics subject classification _ 2010 : 28a80 , 28a78 . + _ key words and phrases _ : assouad dimension , projection , self - similar set .

we consider the assouad dimensions of orthogonal projections of planar sets onto lines . our investigation covers both general and self - similar sets . for general sets , the main result is the following : if a set in the plane has assouad dimension $ ] , then the projections have assouad dimension at least almost surely . compared to the famous analogue for hausdorff dimension namely _ marstrand s projection theorem _ a striking difference is that the words ` at least ' can not be dispensed with : in fact , for many planar self - similar sets of dimension , we prove that the assouad dimension of projections can attain both values and for a set of directions of positive measure . for self - similar sets , our investigation splits naturally into two cases : when the group of rotations is discrete , and when it is dense . in the ` discrete rotations ' case we prove the following dichotomy for any given projection : either the hausdorff measure is positive in the hausdorff dimension , in which case the hausdorff and assouad dimensions coincide ; or the hausdorff measure is zero in the hausdorff dimension , in which case the assouad dimension is equal to 1 . in the ` dense rotations ' case we prove that every projection has assouad dimension equal to one , assuming that the planar set is not a singleton . as another application of our results , we show that there is no _ falconer s theorem _ for assouad dimension . more precisely , the assouad dimension of a self - similar ( or self - affine ) set is not in general almost surely constant when one randomises the translation vectors . + + _ mathematics subject classification _ 2010 : 28a80 , 28a78 . + _ key words and phrases _ : assouad dimension , projection , self - similar set .

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we parameterise orthogonal projections onto lines in @xmath55 by @xmath56 in the natural way , by letting @xmath57 be the projection onto the line @xmath58 passing through the origin and forming an angle @xmath59 with the positive @xmath24-axis . with this notation , our main result for general sets is the following : [ maintheoremforgeneralsets ] assume that @xmath26 . then , for almost all @xmath56 , @xmath60 theorem [ maintheoremforgeneralsets ] will be proved in section [ proofforgeneralsets ] . the lower bound is obviously sharp , and in section [ nomarstrand ] we demonstrate by example that the inequality can not be replaced by an equality : the function @xmath61 need not be almost surely constant , and it can attain both the values @xmath62 and @xmath4 for a set of @xmath59 s with positive measure . we do not know if other values are possible here , or if there can be three distinct values : given a set @xmath26 , how many distinct values can the assouad dimension of @xmath63 assume for a set of @xmath59 s with positive measure ? if there are only two such values , are they always @xmath62 and @xmath4 ? in this section we state our main results for self - similar sets , which are rather complete in the context of assouad dimension . in the @xmath64-dimensional setting the groups @xmath65 and @xmath66 are particularly simple : @xmath65 consists of counterclockwise rotations by angles @xmath67 and the corresponding reflections with orientation reversed and @xmath66 just consists of the rotations . as such , the group generated by @xmath48 will be dense if and only if one of the @xmath68 rotates by an irrational multiple of @xmath69 and otherwise it will be discrete ( in fact finite ) . here is the main result for self - similar sets : [ assouadprojection ] let @xmath70 be self - similar set containing at least two points , and first suppose that the group generated by @xmath48 is discrete . then , for a given @xmath56 , we have : 1 . if @xmath71 , then @xmath72 2 . if @xmath73 , then @xmath74 . secondly , suppose that the group generated by @xmath48 is dense in @xmath65 or @xmath66 . then @xmath75 for * all * @xmath56 . the discrete rotations case of theorem [ assouadprojection ] will be proved in section [ discreterotationsproof ] and the dense rotations case will be proved in section [ denserotationsproof ] . we emphasise that we assume no separation conditions for @xmath7 , in particular the osc may fail and the hausdorff dimension of @xmath7 may be strictly smaller than the similarity dimension . by marstrand s theorem , we have that , for almost all @xmath76 , @xmath77 , but farkas ( * ? ? ? * theorem 1.2 ) showed that in the discrete rotations case there is always at least one direction @xmath76 where the dimension drops , i.e. @xmath78 , provided the hausdorff dimension of @xmath7 is given by the similarity dimension and this value is less than or equal to 1 . in the dense rotations case erolu @xcite and farkas ( * theorem 1.5 ) proved that @xmath79 for all @xmath56 . so , the dichotomy seen in the ` discrete rotations ' part persists for dense rotations , but case _ 1 . _ never occurs . in the dense rotations case , the assouad dimension of @xmath63 is constant and independent of the dimension of @xmath7 . neither of these phenomena are generally manifest in the discrete case , but one can always find _ at least one _ direction @xmath59 for which the assouad dimension of @xmath63 attains the maximal value of 1 , independent of the dimensions of @xmath7 , provided @xmath7 is not contained in a line . [ assouadprojectionexamples ] let @xmath47 ^ 2 $ ] be a self - similar set , which is not contained in a line . then there exists @xmath56 such that @xmath80 we will prove theorem [ assouadprojectionexamples ] in section [ assouadprojectionexamplesproof ] . our key application of theorem [ assouadprojection ] is that , unlike the hausdorff , upper and lower box , and packing dimensions , the assouad dimensions of orthogonal projections of a ( compact ) set are not almost surely constant in general . thus , we do not have a ` marstrand s projection theorem for assouad dimension ' . [ mainex ] for any @xmath3 satisfying @xmath81 , there exists a compact set @xmath5 with hausdorff and assouad dimension equal to @xmath3 for which there are two non - empty disjoint intervals @xmath82 such that @xmath83 in particular , @xmath84 is not an almost surely constant function . the restriction to @xmath85 in theorem [ mainex ] may well be an artefact of our method , but at present we are unaware how to construct lower - dimensional examples : given any @xmath86 , in particular @xmath87 , can one construct a compact planar set with hausdorff dimension @xmath3 , for which the assouad dimension of the projections is not almost surely constant ? also , we do not know if the words ` almost all @xmath88 ' could be strengthened to ` all @xmath88 ' with a different construction : can one construct a compact planar set for which the assouad dimension of the projection takes different values on two sets with non - empty interior ? note that theorem [ mainex ] demonstrates the apparently strange property that assouad dimension can increase under projection ( a lipschitz map ) , which can not happen for the dimensions discussed in section 1 . this peculiarity of the assouad dimension was observed previously in ( * ? ? ? * section 3.1 ) . the rest of this section will be dedicated to constructing an example with the properties required by theorem [ mainex ] . the set @xmath7 will actually be very simple : it will be a self - similar modification of the sierpiski triangle , where the contraction ratios are equal to @xmath89 , see figure 1 . fix @xmath89 and let @xmath90 be the self - similar attractor of the ifs on @xmath29 ^ 2 $ ] given by @xmath91 . observe that @xmath90 satisfies the _ open set condition _ ( osc ) and so @xmath92 . it follows from theorem [ assouadprojection ] that 1 . @xmath93 if and only if @xmath94 2 . @xmath95 if and only if @xmath96 . in light of this dichotomy , and the fact that @xmath97 almost surely by marstrand s theorem , in order to complete the proof it is sufficient to show that there is a non - empty open interval of @xmath59 s for which @xmath98 , and a non - empty open interval of @xmath59 s within which @xmath99 almost surely . the first of these problems is straightforward , because one can easily find an open interval where the induced ifs defining the self - similar set @xmath63 satisfies the open set condition and it then follows from standard results that @xmath100 and @xmath98 , see ( * ? ? ? * chapter 9 ) . the existence of such an interval relies on the assumption @xmath101 . the second problem is more delicate , but fortunately has already been solved by peres , simon and solomyak @xcite . they defined the set of _ intersection parameters _ @xmath102 and proved that @xmath103 contains a non - empty interval provided @xmath89 and , moreover , for almost every @xmath104 we have @xmath105 . this can be found in ( * ? ? ? * theorem 1.2(i ) and example 2.8 ) . we could also have used the 4-corner cantor set with contraction parameter in the interval @xmath106 , which was discussed in @xcite , but chose the sierpiski triangle because it yielded the least restrictive conditions on the dimension of @xmath7 . ( with @xmath107 ) and two typical projections . there is a small interval of projections @xmath108 for which the 3 pieces of @xmath90 project into pairwise disjoint intervals , meaning that projections in these directions satisfy the open set condition . there is also an interval @xmath109 within which the projection map is not injective . , width=340 ] in 1988 falconer proved a seminal result in the dimension theory of self - affine sets , see @xcite . self - affine sets are closely related to self - similar sets , but the contractions in the defining ifs can be affine , i.e. @xmath110 can be replaced with any contracting invertible @xmath38 matrix . this means that the scaled copies of the attractor can scale by different amounts in different directions , as well as being skewed or sheared , which makes them much more difficult to study . even if the osc is satisfied , the dimensions may be hard to compute and the assouad , box and hausdorff dimensions may all be distinct . despite this , falconer proved that the hausdorff and box dimensions are ` generically ' equal to the _ affinity dimension _ ; the self - affine analogue of the similarity dimension . the affinity dimension depends only on the linear parts of the defining maps ( as with the similarity dimension ) and falconer proved that for lebesgue almost all choices of translation vectors @xmath111 , the box and hausdorff dimensions of the corresponding self - affine set are equal to the affinity dimension , provided the spectral norms of the matrices were all strictly less than 1/2 . in fact , falconer s original proof required 1/3 here , but solomyak relaxed this assumption to 1/2 and pointed out that this was optimal @xcite . also the affinity dimension is always an upper bound for the hausdorff and box dimensions , but this is not true for the assouad dimension @xcite . specialising to the case of self - similar subsets of the line ( which is a very restrictive class of self - affine sets ) , the assumption on norms is not required . in particular , we have the following result due to simon and solomyak @xcite : [ ssfalconer ] fix a set @xmath112 with each @xmath113 and let @xmath3 be the corresponding similarity ( affinity ) dimension given by @xmath114 for a given set of translations @xmath115 with @xmath116 , let @xmath117 denote the self - similar attractor of the ifs @xmath118 . then for lebesgue almost all @xmath119 , one has @xmath120 it is natural to ask if such a theorem exists for the assouad dimension , for example , is the assouad dimension of a self - affine or self - similar set almost surely constant upon randomising the translations in the above manner . we point out that the answer to this question is no , once again due to the example of peres , simon and solomyak @xcite discussed in section [ nomarstrand ] . [ mainex2 ] fix @xmath89 and let @xmath121 . for a given set of translations @xmath122 let @xmath117 denote the self - similar attractor of the ifs @xmath123 . then there exists two non - empty disjoint open sets @xmath124 such that @xmath125 in particular , @xmath126 is not an almost surely constant function . similar to section [ nomarstrand ] , the open set @xmath127 is easy to find : choose @xmath128 such that the osc is satisfied ( which can be done since @xmath129 ) . then observe that the osc is still satisfied for all @xmath130 in some open neighbourhood of @xmath131 in @xmath132 . again , the second set @xmath133 is more subtle , but dealt with by simon and solomyak @xcite after re - parameterisation . observe that for all @xmath134 , the associated self - similar set is equal to the self - similar set associated to @xmath135 for some @xmath136 $ ] , following translating and re - scaling . more precisely , consider the open subset of @xmath132 given by @xmath137 and the map @xmath138 defined by @xmath139 which is easily seen to be a continuous surjection satisfying @xmath140 where @xmath141 is @xmath142-dimensional lebesgue measure restricted to @xmath143 and @xmath144 is @xmath4-dimensional lebesgue measure restricted to @xmath145 . the attractor @xmath117 is affinely equivalent to the attractor corresponding to @xmath146 . here , the affine rescaling is translation by @xmath147 followed by rescaling by @xmath148 . moreover , the sets @xmath149 for @xmath150 are just a smooth bijective reparamerisation of the sets @xmath63 for @xmath151 where @xmath7 is the modification of the sierpiski triangle from the previous section . it follows by the example of peres , simon and solomyak @xcite that there exists a non - empty open interval @xmath152 such that for almost all @xmath153 , @xmath154 . it follows that the set @xmath155 is open and , by ( [ abscont ] ) , for lebesgue almost all @xmath156 we have @xmath157 . moreover , theorem [ ssfalconer ] implies that for lebesgue almost all @xmath156 we have @xmath158 and so by ( * ? ? ? * theorems 1.3 ) and ( * ? ? * corollary 3.2 ) , for lebesgue almost all @xmath156 , we have @xmath159 . this final implication also follows from our theorem [ gdassouad ] , stated in section [ gdsection ] . the higher dimensional variants of our results remain mostly open . in the dense rotations case , it is quite simple to show that the assouad dimension is constant , irregardless of the ambient dimension : [ assouadconstant ] let @xmath47^d$ ] be self - similar , suppose that the group generated by @xmath48 is dense in @xmath49 or @xmath50 and fix @xmath51 less than @xmath52 . then @xmath160 takes the same value for * all * @xmath54 . we will prove theorem [ assouadconstant ] in section [ assouadconstantproof ] . viewing the proof of the planar case in section [ denserotationsproof ] , it seems likely that this constant is always as large as possible : let @xmath47^d$ ] be a self - similar set containing at least two points , suppose that the group generated by @xmath48 is dense in @xmath49 or @xmath50 and fix @xmath51 less than @xmath52 . then is it true that @xmath161 for * all * @xmath54 ? the ` non - dense case ' is more complicated in higher dimensions , as ` non - dense ' no longer implies ` discrete ' . let @xmath47^d$ ] be self - similar and fix @xmath51 less than @xmath52 . then is it true that @xmath160 is almost surely equal to either @xmath12 or @xmath162 ? in the ` discrete ' case , in all ambient dimensions , the projections are still graph - directed self - similar sets , but in higher dimensions the assouad dimension of such sets is more complicated and can take values other than @xmath12 or @xmath163 for particular directions , see ( * ? ? ? * section 4.1 ) . the examples in section [ nofalconer ] show that there is no ` falconer s theorem for assouad dimension ' . in light of ( * theorem 1.3 ) we know that for self - similar sets in the line with random translations , the situation is still relatively simple . in particular , there are at most two values which @xmath164 can take for a set of @xmath130 with positive measure : the similarity dimension , or 1 . the situation in higher dimensions and for self-_affine _ sets is still unclear however . for @xmath165 and a finite set of non - singular contracting @xmath38 matrices @xmath166 , how many values can the assouad dimension of the attractor of the ifs @xmath167 take , for a set of translates @xmath168 with positive measure ?

the main result is the following : if a set in the plane has assouad dimension $ ] , then the projections have assouad dimension at least almost surely . our investigation splits naturally into two cases : when the group of rotations is discrete , and when it is dense . in the ` discrete rotations ' case we prove the following dichotomy for any given projection : either the hausdorff measure is positive in the hausdorff dimension , in which case the hausdorff and assouad dimensions coincide ; or the hausdorff measure is zero in the hausdorff dimension , in which case the assouad dimension is equal to 1 . in the ` dense rotations ' case , we show that there is no _ falconer s theorem _ for assouad dimension . more precisely , the assouad dimension of a self - similar ( or self - affine ) set is not in general almost surely constant when one randomises the translation vectors

we consider the assouad dimensions of orthogonal projections of planar sets onto lines . our investigation covers both general and self - similar sets . for general sets , the main result is the following : if a set in the plane has assouad dimension $ ] , then the projections have assouad dimension at least almost surely . compared to the famous analogue for hausdorff dimension namely _ marstrand s projection theorem _ a striking difference is that the words ` at least ' can not be dispensed with : in fact , for many planar self - similar sets of dimension , we prove that the assouad dimension of projections can attain both values and for a set of directions of positive measure . for self - similar sets , our investigation splits naturally into two cases : when the group of rotations is discrete , and when it is dense . in the ` discrete rotations ' case we prove the following dichotomy for any given projection : either the hausdorff measure is positive in the hausdorff dimension , in which case the hausdorff and assouad dimensions coincide ; or the hausdorff measure is zero in the hausdorff dimension , in which case the assouad dimension is equal to 1 . in the ` dense rotations ' case we prove that every projection has assouad dimension equal to one , assuming that the planar set is not a singleton . as another application of our results , we show that there is no _ falconer s theorem _ for assouad dimension . more precisely , the assouad dimension of a self - similar ( or self - affine ) set is not in general almost surely constant when one randomises the translation vectors . + + _ mathematics subject classification _ 2010 : 28a80 , 28a78 . + _ key words and phrases _ : assouad dimension , projection , self - similar set .

1207.3859

i

consider the estimation of a random vector @xmath0 from the measurement model illustrated in figure [ fig : model ] . the random vector @xmath2 , which is assumed to have independent and identically distributed ( i.i.d . ) components @xmath3 , is passed through a known linear transform that outputs @xmath4 . the components of @xmath1 are generated by a componentwise transfer function @xmath5 . this work addresses the cases where the distributions @xmath6 and @xmath5 have some unknown parameters , @xmath7 and @xmath8 , that must be learned in addition to the estimation of @xmath2 . such joint estimation and learning problems with linear transforms and componentwise nonlinearities arise in a range of applications , including empirical bayesian approaches to inverse problems in signal processing , linear regression and classification @xcite , and , more recently , bayesian compressed sensing for estimation of sparse vectors @xmath2 from underdetermined measurements@xcite . also , since the parameters in the output transfer function @xmath5 can model unknown nonlinearities , this problem formulation can be applied to the identification of linear - nonlinear cascade models of dynamical systems , in particular for neural spike responses @xcite . when the distributions @xmath6 and @xmath5 are known , or reasonably bounded , there are a number of methods available that can be used for the estimation of the unknown vector @xmath2 . in recent years , there has been significant interest in so - called approximate message passing ( amp ) and related methods based on gaussian approximations of loopy belief propagation ( lbp ) @xcite . these methods originate from cdma multiuser detection problems in @xcite , and have received considerable recent attention in the context of compressed sensing @xcite . see , also the survey article @xcite . the gaussian approximations used in amp are also closely related to standard expectation propagation techniques @xcite , but with additional simplifications that exploit the linear coupling between the variables @xmath2 and @xmath9 . the key benefits of amp methods are their computational simplicity , large domain of application , and , for certain large random @xmath10 , their exact asymptotic performance characterizations with testable conditions for optimality @xcite . this paper considers the so - called generalized amp ( gamp ) method of @xcite that extends the algorithm in @xcite to arbitrary output distributions @xmath5 ( many original formulations assumed additive white gaussian noise ( awgn ) measurements ) . however , although the current formulation of amp and gamp methods is attractive conceptually , in practice , one often does not know the prior and noise distributions exactly . to overcome this limitation , vila and schniter @xcite and krzakala _ et al . _ @xcite have recently proposed extension of amp and gamp based on expectation maximization ( em ) that enable joint learning of the parameters @xmath11 along with the estimation of the vector @xmath2 . while simulations indicate excellent performance , the analysis of these methods is difficult . this work provides a unifying analytic framework for such amp - based joint estimation and learning methods . the main contributions of this paper are as follows : * generalization of the gamp method of @xcite to a class of algorithms we call _ adaptive gamp _ that enables joint estimation of the parameters @xmath7 and @xmath8 along with vector @xmath2 . the methods are computationally fast and general with potentially large domain of application . in addition , the adaptive gamp methods include the em - gamp algorithms of @xcite as special cases . * exact characterization of the asymptotic behavior of adaptive gamp . we show that , similar to the analysis of the amp and gamp algorithms in @xcite , the componentwise asymptotic behavior of adaptive gamp can be described exactly by a simple scalar _ state evolution _ ( se ) equations . * demonstration of asymptotic consistency of adaptive gamp with maximum - likelihood ( ml ) parameter estimation . our main result shows that when the ml parameter estimation is computed exactly , the estimated parameters converge to the true values and the performance of adaptive gamp asymptotically coincides with the performance of the oracle gamp algorithm that knows the correct parameter values . remarkably , this result applies to essentially arbitrary parameterizations of the unknown distributions @xmath6 and @xmath5 , thus enabling provably consistent estimation on non - convex and nonlinear problems . * experimental evaluation of the algorithm for the problems of learning of sparse priors in compressed sensing and identification of linear - nonlinear cascade models in neural spiking processes . our simulations illustrate the performance gain of adaptive gamp and its asymptotic consistency . adaptive gamp thus provides a computationally - efficient method for a large class of joint estimation and learning problems with a simple , exact performance characterization and provable conditions for asymptotic consistency . as mentioned above , the adaptive gamp method proposed here can be seen as a generalization of the em methods in @xcite . in @xcite , the prior @xmath6 is described by a generic @xmath12-term gaussian mixture ( gm ) whose parameters are identified by an em procedure @xcite . the expectation " or e - step is performed by gamp , which can approximately determine the marginal posterior distributions of the components @xmath13 given the observations @xmath14 and the current parameter estimates of the gm distribution @xmath6 . a related em - gamp algorithm has also appeared in @xcite for the case of certain sparse priors and awgn outputs . simulations in @xcite show remarkably good performance and computational speed for em - gamp over a wide class of distributions , particularly in the context of compressed sensing . also , using arguments from statistical physics , @xcite presents state evolution ( se ) equations for the joint evolution of the parameters and vector estimates and confirms them numerically . as discussed in section [ sec : em - gamp ] , em - gamp is a special case of adaptive gamp with a particular choice of the adaptation functions . therefore , one contribution of this paper is to provide a rigorous theoretical justification of the em - gamp methodology . in particular , the current work provides a rigorous justification of the se analysis in @xcite along with extensions to more general input and output channels and adaptation methods . however , the methodology in @xcite in other ways is more general in that it can also study seeded " or spatially - coupled " matrices as proposed in @xcite . an interesting open question is whether the analysis methods in this paper can be extended to these scenarios as well . an alternate method for joint learning and estimation has been presented in @xcite , which assumes that the distributions on the source and output channels are themselves described by graphical models with the parameters @xmath7 and @xmath8 appearing as unknown variables . the method in @xcite , called hybrid - gamp , iteratively combines standard loopy bp with amp methods . one avenue of future work is to see if methodology in this paper can be applied to analyze the hybrid - gamp methods as well . finally , it should be pointed out that while simultaneous recovery of unknown parameters is appealing conceptually , it is not a strict requirement . an alternate solution to the problem is to assume that the signal belongs to a known class of distributions and to minimize the maximal mean - squared error ( mse ) for the class . this minimax approach @xcite was proposed for amp recovery of sparse signals in @xcite . although minimax approach results in the estimators that are uniformly good over the entire class of distributions , there may be a significant gap between the mse achieved by the minimax approach and the oracle algorithm that knows the distribution exactly . indeed , this gap was the main justification of the em - gamp methods in @xcite . due to its asymptotic consistency , adaptive gamp provably achieves the performance of the oracle algorithm . the paper is organized as follows : in section [ sec : gampreview ] , we review the non - adaptive gamp and corresponding state evolution equations . in section [ sec : gamp ] , we present adaptive gamp and describe ml parameter learning . in section [ sec : convprop ] , we provide the main theorems characterizing asymptotic performance of adaptive gamp and demonstrating its consistency . in section [ sec : numex ] , we provide numerical experiments demonstrating the applications of the method . section [ sec : concl ] concludes the paper . a conference version of this paper has appeared in @xcite . this paper contains all the proofs , more detailed descriptions and additional simulations .

the methodology can be applied to a large class of learning problems including the learning of sparse priors in compressed sensing or identification of linear - nonlinear cascade models in dynamical systems and neural spiking processes . gaussian transform matrices the asymptotic componentwise behavior of the adaptive gamp algorithm is predicted by a simple set of scalar state evolution equations . in addition , we show that when a certain maximum - likelihood estimation can be performed in each step , the adaptive gamp method can yield asymptotically consistent parameter estimates , which implies that the algorithm achieves a reconstruction quality equivalent to the oracle algorithm that knows the correct parameter values . remarkably , this result applies to essentially arbitrary parametrizations of the unknown distributions , including ones that are nonlinear and non - gaussian . the adaptive gamp methodology thus provides a systematic , general and computationally efficient method applicable to a large range of complex linear - nonlinear models with provable guarantees .

we consider the estimation of an i.i.d . ( possibly non - gaussian ) vector from measurements obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise ( possibly nonlinear ) measurement channel . a novel method , called adaptive generalized approximate message passing ( adaptive gamp ) , that enables joint learning of the statistics of the prior and measurement channel along with estimation of the unknown vector is presented . the proposed algorithm is a generalization of a recently - developed em - gamp that uses expectation - maximization ( em ) iterations where the posteriors in the e - steps are computed via approximate message passing . the methodology can be applied to a large class of learning problems including the learning of sparse priors in compressed sensing or identification of linear - nonlinear cascade models in dynamical systems and neural spiking processes . we prove that for large i.i.d . gaussian transform matrices the asymptotic componentwise behavior of the adaptive gamp algorithm is predicted by a simple set of scalar state evolution equations . in addition , we show that when a certain maximum - likelihood estimation can be performed in each step , the adaptive gamp method can yield asymptotically consistent parameter estimates , which implies that the algorithm achieves a reconstruction quality equivalent to the oracle algorithm that knows the correct parameter values . remarkably , this result applies to essentially arbitrary parametrizations of the unknown distributions , including ones that are nonlinear and non - gaussian . the adaptive gamp methodology thus provides a systematic , general and computationally efficient method applicable to a large range of complex linear - nonlinear models with provable guarantees .

1207.3859

c

we have presented an adaptive gamp method for the estimation of i.i.d . vectors @xmath2 observed through a known linear transforms followed by an arbitrary , componentwise random transform . the procedure , which is a generalization of em - gamp methodology of @xcite that estimates both the vector @xmath2 as well as parameters in the source and componentwise output transform . in the case of large i.i.d . gaussian transforms , it is shown that the adaptive gamp method is provably asymptotically consistent in that the parameter estimates converge to the true values . this convergence result holds over a large class of models with essentially arbitrarily complex parameterizations . moreover , the algorithm is computationally efficient since it reduces the vector - valued estimation problem to a sequence of scalar estimation problems in gaussian noise . we believe that this method is applicable to a large class of linear - nonlinear models with provable guarantees can have applications in a wide range of problems . we have mentioned the use of the method for learning sparse priors in compressed sensing . future work will include learning of parameters of output functions as well as possible extensions to non - gaussian matrices .

( possibly non - gaussian ) vector from measurements obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise ( possibly nonlinear ) measurement channel . the proposed algorithm is a generalization of a recently - developed em - gamp that uses expectation - maximization ( em ) iterations where the posteriors in the e - steps are computed via approximate message passing .

we consider the estimation of an i.i.d . ( possibly non - gaussian ) vector from measurements obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise ( possibly nonlinear ) measurement channel . a novel method , called adaptive generalized approximate message passing ( adaptive gamp ) , that enables joint learning of the statistics of the prior and measurement channel along with estimation of the unknown vector is presented . the proposed algorithm is a generalization of a recently - developed em - gamp that uses expectation - maximization ( em ) iterations where the posteriors in the e - steps are computed via approximate message passing . the methodology can be applied to a large class of learning problems including the learning of sparse priors in compressed sensing or identification of linear - nonlinear cascade models in dynamical systems and neural spiking processes . we prove that for large i.i.d . gaussian transform matrices the asymptotic componentwise behavior of the adaptive gamp algorithm is predicted by a simple set of scalar state evolution equations . in addition , we show that when a certain maximum - likelihood estimation can be performed in each step , the adaptive gamp method can yield asymptotically consistent parameter estimates , which implies that the algorithm achieves a reconstruction quality equivalent to the oracle algorithm that knows the correct parameter values . remarkably , this result applies to essentially arbitrary parametrizations of the unknown distributions , including ones that are nonlinear and non - gaussian . the adaptive gamp methodology thus provides a systematic , general and computationally efficient method applicable to a large range of complex linear - nonlinear models with provable guarantees .

1105.3716

i

you have left your smartphone on the table at a cafeteria . you soon realize and go back to take it . fortunately , it is still there ! you feel safe while you are not safe at all . an adversary has connected your smartphone to a laptop and dumped all of its memory , including public and secret cryptographic keys . it is a matter of seconds or , at most , minutes . you do nt revoke your certificates ( you feel safe ! ) and , a month later , you discover that your credentials have been used by someone else . if you think this can not happen people take very good care of their personal devices consider that according to a fairly recent report ( wtop , 15 nov 2006 ) 478 laptops have been lost or stolen from the irs ( the internal revenue service is the united states federal government agency that collects taxes and enforces the internal revenue laws ) between 20022006 ; 112 held sensitive taxpayer data , including ssns . portable personal devices smart - phones , laptops , and pdas are more and more used in our everyday life . we use them to make phone calls , to plan our activities , to surf the web , to manage our banking account , and probably very soon to make purchases . the system we consider is a network of personal smart - phones that connects to each other by using short - range communication technology like blue - tooth . the nodes are the devices and the links appear and disappear as people move and get in physical touch . as a consequence , the network is not a collection of randomly moving objects it has a social structure that can be exploited to deliver revolutionary applications , and , we believe , new and surprisingly effective solutions to classical networking and security problems . these networks have been called with several different names_pocket switched networks _ @xcite , _ mobile social networks _ , _ opportunistic mobile ad - hoc networks _ , among others and have drawn the attention of many researchers in the community . most of the work has focused on forwarding , that is how to route messages in such a way to deliver them as quickly as possible and as cheaply as possible to destination . here , we focus on security . the attack that we have described in the first rows of this paper is the _ clone attack_. the clone attack might as well be performed by a virus that infects our device and sends all the data , including secret keys associated with the certificates , to the adversary . so , you are not safe even though you never forget your smart - phone at the coffee shop . in this paper we are looking for a solution to this problem . of course , we do not want one that consists in typing a password every time we use our certificates . people do nt like passwords and tend to forget them , or , even worse , choose trivial ones . our idea is to use social physical contacts , securely collected by wireless personal smart - phones , as a biometric way to authenticate the owner of the device . indeed , our social physical contacts our family members , the same barman everyday at the coffee shop , our colleagues at work , our old friends when we hang out and relax after work characterize ourselves in a distinctive way . of course , each day is somewhat different and we do nt always meet the same people , but surely there is a strong regularity in the communities we live in and in circle of friends that we usually meet in person . we will see how to use this regularity , complemented with other essential mechanisms , to detect the clone attack in wireless networks of smart - phones or other personal devices and to prevent the misuse of stolen certificates . in this paper we introduce two protocols : personal marks and community certificates . personal marks is a simple cryptographic protocol that proves to be an excellent way to detect the attack when the adversary is an _ insider _ , a person that belongs to the same community of the victim . community certificate is a solution based on certificates that tells how the node is expected to behave in terms of social contacts . if the clone is an _ outsider _ , a node that behaves in a different way with respect to the victim and meets different nodes and different communities , then community certificate works very well , the certificate soon expires , and the clone can not authenticate any more to the other nodes of the network . the two protocols are meant to be used at the same time and , according to a large set of experiments made with well - known traces of human contacts computed during real life experiments , they collectively prove to protect the nodes against the clone attack in an excellent way .

this can happen quite easily , because of a virus that immediately after sending all the content of the infected device to the adversary destroys itself , or just because the owner has left his device unattended for a few minutes in a hostile environment . our idea is to use social physical contacts , securely collected by wireless personal smart - phones , as a biometric way to authenticate the legitimate owner of the device and detect the clone attack . we introduce two mechanisms : personal marks and community certificates . personal marks is a simple cryptographic protocol that works very well when the adversary is an insider , a malicious node in the network that is part , or not very far , from the social community of the original device that has been cloned . we prove our ideas and solutions with extensive simulations in a real world scenario with mobility traces collected in a real life experiment .

we consider the problem of detecting clones in wireless mobile ad - hoc networks . we assume that one of the devices of the network has been cloned . everything , including certificates and secret keys . this can happen quite easily , because of a virus that immediately after sending all the content of the infected device to the adversary destroys itself , or just because the owner has left his device unattended for a few minutes in a hostile environment . the problem is to detect this attack . we propose a solution in networks of mobile devices carried by individuals . these networks are composed by nodes that have the capability of using short - range communication technology like blue - tooth or wi - fi , where nodes are carried by mobile users , and where links appear and disappear according to the social relationships between the users . our idea is to use social physical contacts , securely collected by wireless personal smart - phones , as a biometric way to authenticate the legitimate owner of the device and detect the clone attack . we introduce two mechanisms : personal marks and community certificates . personal marks is a simple cryptographic protocol that works very well when the adversary is an insider , a malicious node in the network that is part , or not very far , from the social community of the original device that has been cloned . community certificates work very well when the adversary is an outsider , a node that has the goal of using the stolen credentials when interacting with other nodes that are far in the social network from the original device . when combined , these mechanisms provide an excellent protection against this very strong attack . we prove our ideas and solutions with extensive simulations in a real world scenario with mobility traces collected in a real life experiment . [ complexity measures , performance measures ]

1703.05788

i

optimal alignments are among the main two components used by most dna - alignment algorithms which try to find similar substrings in dna - sequences . because of its great practical importance , these problems have received a tremendous amount of attention . let us explain the key points from the dna perspective . dna sequencing is one of the most important areas of study in biology . this is still rather expensive and very complex . suppose now that in a certain animal population , a certain gene is detected . this gene is probably likely to appear in the dna of other animals too , but in a slightly different form . thus , instead of repeating the same costly experiments on other animals to find the gene , they just search for a dna - segment which looks similar to the gene in the first population . this is why often dna - strings in different animals are compared in order to find places that are related . for more details on the analysis of dna we refer the reader to @xcite and in particular the iid assumption which appears also in this paper is explained on page 14 of the @xcite . here is a more concrete example . assume @xmath4 is a hypothetical dna of an ancestor with two descendants , one with the dna string @xmath5 ( which lost the @xmath6 and the @xmath7 ) and another with the dna equal to @xmath8 ( which had an @xmath9 mutated into a @xmath6 ) . we align these strings ( with gaps ) , as follows : @xmath10 in the analysis of the dna one has access to the dna of the descendants only . in terms of the alignments , one is interested in the _ historic alignment_. in our example , we would have that the alignment @xmath11 is given by : @xmath12 and we call this the historic alignment . the letters which disappeared in one descendant are now represented by gaps . which alignment with gaps corresponds to the evolution history of the strings is not known apriori . in other words , in our example , we know the strings @xmath13 and @xmath8 , but not `` the true historic '' alignment given here by . to guess which alignment is historic , the natural attempt is to find an alignment which maximizes similarity . for this , one starts with a scoring function @xmath14 which measures similarity between letters . ( here @xmath15 is the alphabet augmented by one symbol for the gap ) . the _ total score _ of an alignment is then the sum of the scores of the aligned symbol pairs . in alignment , the alignment score @xmath16 is equal to @xmath17 where @xmath7 stands for a gap . an alignment @xmath18 , which for given strings @xmath19 and @xmath20 maximizes the alignment score @xmath21 is called _ an optimal alignment_. the score of an optimal alignment is called _ optimal alignment score _ and we will denote it by @xmath22 where the maximum above is taken over all alignments with gaps of @xmath19 and @xmath20 . which alignment is optimal depends ultimately on the scoring function used . often , the scoring function biologists work with is a log likelihood . for this , one assumes models of letters evolving independently of their neighboring letters . one takes as scoring function @xmath23 , the logarithm of the probability that an ancestor letter evolves into an @xmath9 in one descendant and into a @xmath24 in the other descendant . here @xmath9 and @xmath24 are any two letters from the alphabet under consideration , or also the gap symbol . with this choice of scoring function , the optimal alignment becomes the maximum - likelihood estimate for the historic alignment . a high optimal alignment score indicates relatedness of the two dna - strings . thus in testing for relatedness of dna - strings one usually takes as test statistics the optimal alignment score . the significance of such a test depends then on the order of magnitude of the fluctuation of the optimal alignment score . it has been a long open question whether for two independent i.i.d . strings of length @xmath2 , the fluctuation of the optimal alignment score is of order @xmath25 or @xmath26{n}$ ] . ( see @xcite and @xcite ) . in this paper , we think we can see why these two different conjectures co - exist at the same time . we show that for two independent i.i.d strings of length @xmath2 the optimal alignment score ( depending on the parameters ) can contain a normal component with fluctuation of order @xmath25 . this component is not relevant for finding the optimal alignment score , because it does not depend on the alignment . _ when testing for relatedness of dna - strings one should remove this normal component , since it is only noise . this can be done by modifying the scoring function . once we `` cut out this normal component '' , the question that remain is what is the asymptotic distribution of the remainder ? is it tracy - widom ? we ca nt prove it in full generality , however we check this for the special case where the number of gaps is a small power of the length of the strings and the gaps are allowed only into one string . _ _ we also exhibit a scoring function with an alignment score which is of the order @xmath25 but not normal , nor tracy - widom . this , should then show that any claim that the order @xmath27=o(n)$ ] automatically implies asymptotic normality is wrong ! ( here @xmath28 designates the optimal alignment score of two i.i.d . random strings of length @xmath2 . ) to prove normality , one needs a more detailed knowledge of the path structure of the optimal alignments ! _ the optimal alignment can be viewed as a special case of last passage percolation with correlations . to our knowledge , many of the proofs for models of first and last passage percolation , where the asymptotic distribution is known , go back to proving asymptotic equivalence with the following functional of brownian motions : consider @xmath29 a sequence of i.i.d . standard brownian motions . also consider when @xmath30 goes to infinity , the functional @xmath31+[b^2(t_2)-b^2(t_1)]+\ldots+[b^k(t_k)-b^k(t_{k-1}))]\ ] ] which properly rescaled becomes tracy - widom @xcite . now , in our case , we have a similar situation , where instead we have a sequence of _ dependent _ identically distributed standard brownian motions @xmath32 . however , the correlation structure is rather simple . precisely , there exists a brownian motion @xmath33 and i.i.d brownian motions @xmath29 so that @xmath34 for all @xmath35 . hence , instead of independent brownian motions we have correlated ones and the maximum given in can be written as @xmath36+[w^2(t_2)-w^2(t_1)]+\ldots+[w^k(t_k)-w^k(t_{k-1}))]=\\&= v(1)-v(0)+\max_{0\leq t_1<t_2<\ldots < t_k\leq 1 } [ b^1(t_1)-b^1(0)]+[b^2(t_2)-b^2(t_1)]+\ldots+[b^k(t_k)-b^k(t_{k-1}))].\end{aligned}\ ] ] hence , we get a normal component plus a term on a smaller scale which is indeed tracy - widom . this is the reason why we can prove in the current paper , under a very special situation ( adding gaps only into one string and keeping their number a small power of @xmath2 ) , that in the limit we obtain a normal plus tracy - widom on a smaller scale . however , the normal part is often irrelevant for the optimal alignment problem . note here that the normal component @xmath37 does not dependent on the choice of @xmath38 ( which in what follows , correspond to alignments ) . again , the normal component is in some sense irrelevant for finding the optimal alignment . we should leave it out because it is only added noise . we consider two random i.i.d . strings @xmath39 and @xmath40 . in the sequel , @xmath28 denotes the optimal alignment score of @xmath0 and @xmath1 . chvatal - sankoff proved @xcite that @xmath41/n$ ] converges to a constant @xmath42 , but @xmath42 is not known in most cases . in @xcite , @xcite we have good confidence intervals for @xmath43 . we have been able to prove the order @xmath44=o(n)\ ] ] in many situations @xcite,@xcite , @xcite , @xcite . this proves the conjecture of waterman @xcite ( for certain specific distributions of the letters and scoring functions ) , but is different from what chavatal - sankoff have conjectured . the order conjectured by chavatal - sankoff is the order which one would expect knowing that @xmath45 is also the weight of the heaviest path from @xmath46 to @xmath47 in an lpp - formulation of our problem . ( in the physics literature , @xcite , the order for the standard deviation of the heaviest path from @xmath46 to @xmath47 in a vast class of lpp - models is conjectured to be @xmath48 not @xmath49 . for more details see also @xcite ) . let us explain what lpp is and how our optimal alignment can be formulated as an lpp - problem with correlated weights . in lpp , one considers an oriented graph @xmath50 with a random weight function @xmath51 of the edges . let @xmath52 . a path from @xmath19 to @xmath20 in the graph @xmath50 is then defined as a sequence of vertices : @xmath53 where @xmath54 and @xmath55 for all @xmath56 . the total weight of the path @xmath53 is given by : @xmath57 an optimal path from @xmath19 to @xmath20 is then a path which maximizes the total weight among all paths from @xmath19 to @xmath20 . + now , our optimal alignment problem can be formulated as an lpp on the integer lattice with the optimal alignment score @xmath28 being the weight of the path of maximal weight from @xmath46 to @xmath47 . for this we take the set of vertices @xmath58 to be @xmath59 and the edges to go always one to the right , one up or diagonally up to the next vertex . the weight for horizontal and vertical edges is minus the gap penalty . for the edge @xmath60 the weight is @xmath61 . with this setting when we align a letter with a gap , this corresponds to moving one unit vertically or horizontally . aligning @xmath62 with @xmath63 corresponds to moving along the edge @xmath64 . the optimal path then defines an optimal alignment where for every edge @xmath60 contained in the optimal path , aligns @xmath62 with @xmath63 . the transversal fluctuation measures how far the optimal path from @xmath46 to @xmath47 deviates from the diagonal . + let us give an example . take the two strings @xmath65 and @xmath66 . consider the following alignment with gaps : @xmath67 we can represent this alignment as a path on the integer points in two dimension . we are always allowed to go to the left by one unit or up by one unit or diagonal to the next integer point . when we go horizontal or vertical , this means that we align a letter with a gap . when we go diagonal this means that we align two letters with each other . below , we show how we represent the alignment given in by a path on the two dimensional integer lattice : @xmath68 to visualize , the path represented by the last table above , draw short segments between the points : @xmath69 to @xmath70 , then @xmath70 to @xmath71 , .... and up to a segment from @xmath72 to @xmath73 . the path is then given by this sequence of segments . so , the first such segment from @xmath69 to @xmath70 is diagonal , and corresponds to aligning the two @xmath74 s with each other . the score - contribution for this is @xmath75 . then , the segment from @xmath70 to @xmath71 is diagonal and corresponds to aligning the @xmath76 s . its score contribution is @xmath77 . the segment from @xmath71 to @xmath78 is vertical and hence corresponds to aligning a letter with a gap . in the current case , it is the first @xmath79 in @xmath80 which gets aligned with a gap , and the score for this is the gap penalty @xmath81 . then @xmath82 is again diagonal and corresponds to aligning @xmath2 with @xmath2 , with score @xmath83 . then , the segment @xmath84 is horizontal and corresponds to aligning @xmath85 in @xmath86 with a gap , which contributes to minus a gap penalty to the total score . the final segment @xmath87 is diagonal , and corresponds to aligning the last @xmath79 of @xmath86 with the last @xmath79 of @xmath80 . score is then @xmath88 . in other words , the horizontal or vertical moves contribute minus a gap penalty each , whilst the diagonal moves contribute to the score by aligning the corresponding letters . in this example , we aligned only identical letters . this is not always the case . in dna - analysis , when letters can mutate we also align similar letters with each other , not just identical . formally we can view an alignment with gaps of the strings @xmath89 and @xmath90 as a couple consisting of two increasing integer sequences . the sequence @xmath18 @xmath91 and the sequence @xmath92 @xmath93 are non - negative integers . here @xmath94 is any integer non - negative number . the alignment with gaps defined by @xmath95 is then the alignment which aligns @xmath96 with @xmath97 for all @xmath98 and aligns all remaining letters with a gap . the alignment score is then @xmath99 where is @xmath100 represents the total gap penalty . ( the penalty for one given gap being @xmath101 ) . in our current example , we have the number of aligned letter pairs is @xmath102 . furthermore , we find : @xmath103 , whilst @xmath104 . the path representing the alignment given by @xmath105 is the path containing all the segments : @xmath106 for @xmath98 and additionally a minimum amount of vertical and horizontal unit length integer segments so as to make this a connected path . + first passage percolation ( fpp ) and lpp are part of a vast area of statistical physics @xcite which is concerned with random growth models for which physicists expect some universality properties . more specifically , one considers growth of a cluster where material is being attached randomly on the surface of a nucleus . there are many fundamental questions open for decades , such as the universality of the fluctuation exponents . many theoretical physicists , crystallographers and probabilists have worked on this and many conjectures have been formulated @xcite , as for example that the fluctuation should behave like @xmath48 and the transversal fluctuation should be or order @xmath107 ( see kpz - conjecture in @xcite ) . these are difficult conjectures and rigorous results were obtained only under some special circumstances of lpp models , like longest increasing subsequence @xcite , lpp on @xmath108 with exponential or geometric waiting times @xcite and the case of percolation in a narrow tube @xcite . to our knowledge , the best results show only a fluctuations of less than @xmath109 @xcite and above @xmath110 @xcite . we have been able to prove our results for several longest common subsequence ( lcs ) and optimal alignments ( oa ) models . + lcs are a special case of oa . for two strings @xmath89 and @xmath111 a common subsequence of @xmath19 and @xmath20 is a sequence which is a subsequence of @xmath19 and at the same time a subsequence of @xmath20 . a lcs of @xmath19 and @xmath20 is a common subsequence of @xmath19 and @xmath20 of maximum length . the length of the lcs of @xmath19 and @xmath20 can be viewed as an optimal alignment score of @xmath19 and @xmath20 . for this we take @xmath112 to be @xmath70 if @xmath113 and @xmath114 otherwise . on top the gap penalty should be taken @xmath69 . with this choice , the length of the lcs is also equal to the optimal alignment score . + our results together with the results of baik , deift and johansson @xcite , are among the few rigorous results determining the exact order of the fluctuation exponents for some non - trivial fpp or lpp related 2-d models . in their work , as in ours , the fluctuation is of order @xmath48 and the rescaled asymptotic limiting law is tracy - widom . another interesting paper is for the tasep model , by borodin , ferrari , praehofer and sasamoto @xcite . there they do not use the same approach of reducing the problem to formula and , and it is not the gue which appears in the limit , but goe . other methods used to establish the solvability of lpp models are the vertex operator and fock space formalism put foward by okounkov @xcite in the study of schur process . our paper is organized as follows . in section [ s:2 ] , we introduce the main decomposition of the scoring function and show examples where the limiting distribution of the optimal alignment score is normal alongside with other examples which are non - normal . in the next section , namely section [ s:3 ] , we restrict the number of gaps to a certain number @xmath30 which is finite and fixed and allow the gaps only in one sequence . here we give a general description of the optimal alignment in terms of multiple dependent random walks and outline an argument which supports the conjecture that under some conditions , if @xmath30 is replaced by @xmath115 with small @xmath116 , then the ( rescaled ) limiting distribution of the optimal alignment is tracy - widom . we can not prove this statement rigorously in general , but in the next section , namely section [ s:4 ] , we prove this for the key scoring function @xmath117 under the assumption that the number of gaps is @xmath118 for small @xmath116 and the second sequence of letters is distributed normally rather than @xmath119 . the main rigorous result is stated in theorem [ t:1 ] and appears in section [ s:4 ] . section [ s:5 ] is dedicated to technical results while the last one , section [ s:6 ] contains a few simulations .

we consider two independent binary i.i.d . random strings and of equal length and the optimal alignments according to a symmetric scoring functions only . we decompose the space of scoring functions into five components . is equivalent to aligning a string with its descendants in case of mutations and deletes .

we consider two independent binary i.i.d . random strings and of equal length and the optimal alignments according to a symmetric scoring functions only . we decompose the space of scoring functions into five components . two of these components add a part to the optimal score which does not depend on the alignment and which is asymptotically normal . we show that when we restrict the number of gaps sufficiently and add them only into one sequence , then the alignment score can be decomposed into a part which is normal and has order and a part which is on a smaller order and tends to a tracy - widom distribution . adding gaps only into one sequence is equivalent to aligning a string with its descendants in case of mutations and deletes . for testing relatedness of strings , the normal part is irrelevant , since it does not depend on the alignment hence it can be safely removed from the test statistic .

1504.06947

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let @xmath13 be @xmath0 open , bounded and simply connected sets in @xmath5 with lipschitz boundaries , containing the origin . we assume that their sizes and lipschitz constants are uniformly bounded . we set @xmath14 to be the small bodies characterized by the parameter @xmath15 and the locations @xmath16 , @xmath17 . assume that the lam coefficients @xmath2 and @xmath3 are constants satisfying @xmath18 and the mass density @xmath10 to be a constant that we normalize to a unity . let @xmath19 be a solution of the navier equation @xmath20 , @xmath21 . we denote by @xmath22 the elastic field scattered by the @xmath0 small bodies @xmath23 due to the incident field @xmath19 . we restrict ourselves to the scattering by rigid bodies . hence the total field @xmath24 satisfies the following exterior dirichlet problem of the elastic waves @xmath25 @xmath26 with the kupradze radiation conditions ( k.r.c ) @xmath27 where the two limits are uniform in all the directions @xmath28 . also , we denote @xmath29 to be the longitudinal ( or the pressure or p ) part of the field @xmath22 and @xmath30 to be the transversal ( or the shear or s ) part of the field @xmath22 corresponding to the helmholtz decomposition @xmath31 . the constants @xmath32 and @xmath33 are known as the longitudinal and transversal wavenumbers , @xmath34 and @xmath35 are the corresponding phase velocities , respectively and @xmath36 is the frequency . the scattering problem ( [ elaimpoenetrable]-[radiationcela ] ) is well posed in the hlder or sobolev spaces , see @xcite for instance , and the scattered field @xmath37 has the following asymptotic expansion : @xmath38 uniformly in all directions @xmath39 . the longitudinal part of the far - field , i.e. @xmath40 is normal to @xmath41 while the transversal part @xmath42 is tangential to @xmath41 . we set @xmath43 . as usual , we use plane incident waves of the form @xmath44 , where @xmath45 is any direction in @xmath41 perpendicular to the incident direction @xmath46 , @xmath47 are arbitrary constants . the functions @xmath48 and @xmath49 for @xmath50 are called the p - part and the s - part of the far - field pattern respectively . [ def1 ] we define 1 . @xmath51,$ ] 2 . @xmath52 @xmath53 . we assume that @xmath54 and @xmath55 is given . 3 . @xmath56 as the upper bound of the used frequencies , i.e. @xmath57 $ ] . 4 . @xmath4 to be a bounded domain in @xmath5 containing the small bodies @xmath58 . we assume that @xmath59 , with the same diameter @xmath60 , are non - flat lipschitz obstacles , i.e. @xmath61 s are lipschitz obstacles and there exist constants @xmath62 $ ] such that @xmath63 where @xmath64 are assumed to be uniformly bounded from below by a positive constant . in @xcite , we have shown that there exist two positive constants @xmath65 and @xmath66 depending only on the size of @xmath4 , the lipschitz character of @xmath67 , @xmath55 and @xmath56 such that if @xmath68 then we have the following asymptotic expansion for the p - part , @xmath69 , and the s - part , @xmath70 , of the far - field pattern : @xmath71+m(m-1)\left[\frac{a^3}{d^{2\alpha}}+\frac{a^4}{d^{4-\alpha}}+ \frac{a^4}{d^{5 - 2\alpha}}\right]+m(m-1)^2\frac{a^4}{d^{3\alpha}}\right ) \right ] , \label{x oustdie1 d_m farmainp - near}\\ & \hspace{-1cm}u^\infty_s(\hat{x},\theta)= & \frac{1}{4\pi\,c_s^{2}}(\rm \textbf{i}- \hat{x}\otimes\hat{x})\left[\sum_{m=1}^{m}e^{-i\frac{\omega}{c_s}\hat{x}\cdot\,z_m}q_m\right.\nonumber\\ & & \hspace{-2cm}\left.+o\left(m\left[a^2+\frac{a^3}{d^{5 - 3\alpha}}+\frac { a^4}{d^{9 - 6\alpha}}\right]+m(m-1)\left[\frac{a^3}{d^{2\alpha}}+\frac{a^4}{d^{4-\alpha}}+ \frac{a^4}{d^{5 - 2\alpha}}\right]+m(m-1)^2\frac{a^4}{d^{3\alpha}}\right ) \right ] , \label{x oustdie1 d_m farmains - near } \end{aligned}\ ] ] where @xmath72 , @xmath73 , is a parameter describing the relative distribution of the small bodies . the vector coefficients @xmath74 , @xmath75 are the solutions of the following linear algebraic system @xmath76 for @xmath77 with @xmath78 denoting the kupradze matrix of the fundamental solution to the navier equation with frequency @xmath36 , @xmath79 and @xmath80 is the solution matrix of the integral equation of the first kind @xmath81 with @xmath82 the identity matrix of order 3 . consider now the special case @xmath83 and @xmath84 with @xmath85 , @xmath86 , @xmath87 and @xmath88 are positive . then the asymptotic expansions ( [ x oustdie1 d_m farmainp - near]-[x oustdie1 d_m farmains - near ] ) can be rewritten as @xmath89,\quad \label{x oustdie1 d_m farmainp - near*}\\ u^\infty_s(\hat{x},\theta)&= & \frac{1}{4\pi\,c_s^{2}}(\rm \textbf{i}- \hat{x}\otimes\hat{x})\big[\sum_{m=1}^{m}e^{-i\frac{\omega}{c_s}\hat{x}\cdot\,z_m}q_m \nonumber \\ & & + o\left(a^{2-s}+a^{3-s-5t+3t\alpha}+a^{4-s-9t+6t\alpha}+a^{3 - 2s-2t\alpha}+a^{4 - 3s-3t\alpha}+a^{4 - 2s-5t+2t\alpha}\right ) \big].\quad \label{x oustdie1 d_m farmains - near * } \end{aligned}\ ] ] as the diameter @xmath60 tends to zero the error term tends to zero for @xmath8 and @xmath90 such that @xmath91 in @xcite , we have shown that @xmath92 , then we have the upper bound @xmath93 hence if the number of obstacles is @xmath94 and @xmath8 satisfies ( [ general - condition - s - t ] ) , @xmath95 , then from ( [ x oustdie1 d_m farmainp - near * ] , [ x oustdie1 d_m farmains - near * ] ) , we deduce that @xmath96 this means that this collection of obstacles has no effect on the homogeneous medium as @xmath9 . let us consider the case when @xmath97 . we set @xmath4 to be a bounded domain , say of unit volume , containing the obstacles @xmath98 . given a positive and continuous function @xmath99 , we divide @xmath4 into @xmath100 $ ] subdomains @xmath101 $ ] , each of volume @xmath102}{k(z_m)+1}$ ] , with @xmath103 as its center and contains @xmath104 $ ] obstacles , see fig [ distribution - obstacles ] . we set @xmath105 , hence @xmath106}_{j=1}[k(z_m)+1]\leq k_{max}[a^{-1}]=o(a^{-1})$ ] . [ distribution - obstacles ] [ equivalent - medimu ] let the small obstacles be distributed in a bounded domain @xmath4 , say of unit volume , with their number @xmath6 and their minimum distance @xmath107 , @xmath108 , as @xmath95 , as described above . 1 . if the obstacles are distributed arbitrarily in @xmath4 , i.e. with different capacitances , then there exists a potential @xmath109 with support in @xmath4 such that @xmath110 where @xmath111 is the farfield corresponding to the scattering problem + @xmath112 + @xmath113 + with the radiation conditions @xmath114 2 . if in addition @xmath115 is in @xmath116 , @xmath117 $ ] and the obstacles have the same capacitances @xmath118 , then @xmath119 where @xmath120 in @xmath4 and @xmath121 in @xmath122 . assume that the lam coefficients @xmath2 and @xmath3 are constants satisfying @xmath18 and the mass density @xmath10 to be a measurable and bounded function which is equal to a constant that we normalize to a unity outside of a bounded domain @xmath4 . we set @xmath123 to be the upper bound of @xmath10 . in this case , the total field @xmath124 satisfies the following exterior dirichlet problem of the elastic waves @xmath125 @xmath126 with the kupradze radiation conditions ( k.r.c ) @xmath127 where the two limits are uniform in all the directions @xmath28 and @xmath128 and @xmath129 are respectively the p - part and s - part of the scattered field @xmath130 the scattering problem ( [ elaimpoenetrable - rho]-[radiationcela - rho ] ) is well posed in the hlder or sobolev spaces , see @xcite for instance , and the scattered field @xmath37 has the following asymptotic expansion : @xmath131 uniformly in all directions @xmath39 . the longitudinal part of the far - field , i.e. @xmath132 is normal to @xmath41 while the transversal part @xmath42 is tangential to @xmath41 . we set @xmath133 . as in the case of constant background mass density , there exist two positive constants @xmath65 and @xmath66 depending only on the size of @xmath4 , the lipschitz character of @xmath67 , @xmath55 , @xmath56 , @xmath123 and @xmath123 such that if @xmath134 then we have the following asymptotic expansion for the p - part , @xmath135 , and the s - part , @xmath136 , of the far - field pattern : @xmath137+m(m-1)\left[\frac{a^3}{d^{2\alpha}}+\frac{a^4}{d^{4-\alpha}}+ \frac{a^4}{d^{5 - 2\alpha}}\right]+m(m-1)^2\frac{a^4}{d^{3\alpha}}\right ) \right ] , \label{x oustdie1 d_m farmainp - near - rho}\\ & \hspace{-1cm}u^\infty_{\rho , s}(\hat{x},\theta)= & v^\infty_{\rho , s}(\hat{x},\theta)\;+~ \left[\sum_{m=1}^{m}g_{\rho , s}^{\infty}(\hat{x } , z_m ) q_{\rho , m}\right.\nonumber\\ & & \hspace{-2cm}\left.+o\left(m\left[a^2+\frac{a^3}{d^{5 - 3\alpha}}+\frac { a^4}{d^{9 - 6\alpha}}\right]+m(m-1)\left[\frac{a^3}{d^{2\alpha}}+\frac{a^4}{d^{4-\alpha}}+ \frac{a^4}{d^{5 - 2\alpha}}\right]+m(m-1)^2\frac{a^4}{d^{3\alpha}}\right ) \right ] , \label{x oustdie1 d_m farmains - near - rho } \end{aligned}\ ] ] where @xmath138 and @xmath139 are the p - part and s - part of the farfields of the green s function @xmath140 , of the operator @xmath141 in the whole space @xmath5 , evaluated in the direction @xmath142 and the source point @xmath143 . the vector coefficients @xmath144 , @xmath75 are the solutions of the following linear algebraic system @xmath145 for @xmath77 with @xmath146 is the total field satisfying @xmath147 and the scattered field @xmath148 the kupradze radiation conditions ( k.r.c ) . [ equivalent - medimu - rho ] let the small obstacles be distributed in a bounded domain @xmath4 , say of unit volume , with their number @xmath6 and their minimum distance @xmath107 , @xmath108 , as @xmath95 , as described above . 1 . if the obstacles are distributed arbitrarily in @xmath4 , i.e. with different capacitances , then there exists a potential @xmath109 with support in @xmath4 such that @xmath149 where @xmath150 is the farfield corresponding to the scattering problem + @xmath151 + @xmath152 + with the radiation conditions . 2 . if in addition @xmath115 is in @xmath116 , @xmath117 $ ] and the obstacles have the same capacitances , then @xmath153 where @xmath120 in @xmath4 and @xmath121 in @xmath122 . the main contribution of this work is to have shown that by removing from a bounded region of an elastic background , modeled by constant lam coefficients @xmath2 and @xmath3 and a possibly variable density @xmath10 , a number @xmath154 small and rigid bodies of radius @xmath60 distant from each other of at least @xmath155 , @xmath156 , then the perforated medium behaves , as @xmath9 , as a new elastic medium modeled by the same lam coefficients @xmath2 and @xmath3 but with a mass density - like @xmath157 . the coefficient @xmath158 models the local distribution ( or the local number ) of the bodies while the coefficient @xmath159 , coming from the capacitance of the bodies , describes the geometry of the small bodies as well as their elastic directional diffusion properties ( i.e. the anisotropy character ) . in addition , we provide explicit error estimates between the far - fields corresponding to the perforated medium and the equivalent one . from this result we can make the following conclusions : 1 . assume that the removed bodies have spherical shapes . for these shapes the corresponding elastic capacitance @xmath118 is of the form @xmath160 ( i.e. a scalar multiplied by the identity matrix ) . in section [ structure - capacitance ] , we describe a more general set of shapes satisfying this property . hence the equivalent mass density @xmath161 is isotropic while for general shapes it might be anisotropic . to achieve anisotropic densities , a possible choice of the shapes might be an ellipse . 2 . if we choose the local number of bodies @xmath158 large enough or the shapes of the reference bodies , @xmath162 , @xmath163 , having a large capacitance ( i.e. a relative large radius ) so that @xmath164 , then we design elastic materials having negative mass densities . 3 . assume that the background medium is modeled by variable mass density @xmath165 in @xmath4 . if we remove small bodies from @xmath4 with appropriate @xmath158 and/ or capacitance @xmath159 so that @xmath166 , then the new elastic material will behave every where in @xmath5 as the background medium . hence the new material will not scatter the sent incident waves , i.e. the region @xmath4 modeled by @xmath10 will be cloaked . the equivalent behavior between a collection of , appropriately dense , small holes and an extended penetrable obstacle modeled by an additive potential was already observed by cioranescu and murat @xcite and also the references therein , where the coefficient @xmath158 is reduced to zero since locally they have only one hole . their analysis is based on the homogenization theory for which they assume that the obstacles are distributed periodically , see also @xcite and @xcite . in the results presented here , we do not need such periodicity and no homogenization is used . instead , the analysis is based on the invertibility properties of the algebraic system ( [ fracqcfracmain ] ) and the precise treatment of the summation in the dominant terms of ( [ x oustdie1 d_m farmainp - near])-([x oustdie1 d_m farmains - near ] ) . this analysis was already tested for the acoustic model in @xcite . compared to @xcite , here , in addition to the difficulties coming from the vector character of the lam system , we improved the order of the error estimate , i.e. @xmath167 instead of @xmath168 which , for @xmath169 for instance , reduce to @xmath170 and @xmath171 respectively . let us finally mention that a result similar to ( [ b - rho ] ) , for the acoustic model , is also derived by ramm in several of his papers , see for instance @xcite , but without error estimates . compared to his results , and as we said earlier in addition to the vector character of lame model , we provide the approximation by improved explicit error estimates without any other assumptions while , as shown in @xcite for instance , in addition to some formal arguments , he needs extra assumptions on the distribution of the obstacles . the rest of the paper is organized as follows . in section 2 , we give the detailed proof of theorem [ equivalent - medimu ] . in section 3 , we describe the one of corollary [ equivalent - medimu - rho ] by discussing the main changes one needs to make in the proof of theorem [ equivalent - medimu ] . finally , in section 4 , we discuss some invariant properties of the elastic capacitance to characterize the shapes that have a scalar capacitance .

we deal with the elastic scattering by a large number of rigid bodies of arbitrary shapes with maximum radius with constant lam coefficients and . this mass density is described by two coefficients : one modeling the local distribution of the small bodies and the other one by their geometries . in particular , if the distributed bodies have a uniform spherical shape then the equivalent mass density is isotropic while for general shapes it might be anisotropic . in addition , we can distribute the small bodies in such a way that the equivalent mass density is negative . finally , if the background density is variable in and in , then if we remove from appropriately distributed small bodies then the equivalent density will be equal to unity in , i.e. the obstacle characterized by is approximately cloaked . * keywords * : elastic wave scattering , small - scatterers , effective mass density .

we deal with the elastic scattering by a large number of rigid bodies of arbitrary shapes with maximum radius with constant lam coefficients and . we show that , when these rigid bodies are distributed arbitrarily ( not necessarily periodically ) in a bounded region of where their number is and the minimum distance between them is with in some appropriate range , as , the generated far - field patterns approximate the far - field patterns generated by an equivalent ( possibly variable ) mass density . this mass density is described by two coefficients : one modeling the local distribution of the small bodies and the other one by their geometries . in particular , if the distributed bodies have a uniform spherical shape then the equivalent mass density is isotropic while for general shapes it might be anisotropic . in addition , we can distribute the small bodies in such a way that the equivalent mass density is negative . finally , if the background density is variable in and in , then if we remove from appropriately distributed small bodies then the equivalent density will be equal to unity in , i.e. the obstacle characterized by is approximately cloaked . * keywords * : elastic wave scattering , small - scatterers , effective mass density .

1211.2630

i

recently , there has been increasing interest in analyzing on - line auction data and in inferring the underlying dynamics that drive the bidding process . each series of price bids for a given auction corresponds to pairs of random bidding times and corresponding bid prices generated whenever a bidder places a bid [ jank and shmueli ( @xcite , @xcite ) , @xcite , @xcite ] . related longitudinal data where similar sparsely and irregularly sampled noisy measurements are obtained are abundant in the social and life sciences ; for example , they arise in longitudinal growth studies . while more traditional approaches of functional data analysis require fully or at least densely observed trajectories [ @xcite , @xcite , @xcite ] , more recent extensions cover the case of sparsely observed and noise - contaminated longitudinal data [ @xcite , @xcite ] . a common assumption of approaches for longitudinal data grounded in functional data analysis is that such data are generated by an underlying smooth and square integrable stochastic process [ @xcite , @xcite , @xcite , @xcite , @xcite ] . the derivatives of the trajectories of such processes are central for assessing the dynamics of the underlying processes [ @xcite , @xcite ] . although this is difficult for sparsely recorded data , various approaches for estimating derivatives of individual trajectories nonparametrically by pooling data from samples of curves and using these derivatives for quantifying the underlying dynamics have been developed [ @xcite , @xcite , @xcite , @xcite ] . related work on nonparametric methods for derivative estimation can be found in @xcite , @xcite and on the role of derivatives for the functional linear model in @xcite . we expand here on some of these approaches and investigate an empirical dynamic equation . this equation is distinguished from previous models that involve differential equations in that it is empirically determined from a sample of trajectories , and does not presuppose knowledge of a specific parametric form of a differential equation which generates the data , except that we choose it to be a first order equation . this stands in contrast to current approaches of modeling dynamic systems , which are `` parametric '' in the sense that a prespecified differential equation is assumed . a typical example for such an approach has been developed by @xcite , where a prior specification of a differential equation is used to guide the modeling of the data , which is done primarily for just one observed trajectory . a problem with parametric approaches is that diagnostic tools to determine whether these equations fit the data either do not exist , or where they do , are not widely used , especially as nonparametric alternatives to derive differential equations have not been available . this applies especially to the case where one has data on many time courses available , providing strong motivation to explore nonparametric approaches to quantify dynamics . our starting point is a nonparametric approach to derivative estimation by local polynomial fitting of the derivative of the mean function and of partial derivatives of the covariance function of the process by pooling data across all subjects [ @xcite ] . we show that each trajectory satisfies a first order stochastic differential equation where the random part of the equation resides in an additive smooth drift process which drives the equation ; the size of the variance of this process determines to what extent the time evolution of a specific trajectory is determined by the nonrandom part of the equation over various time subdomains , and therefore is of tantamount interest . we quantify the size of the drift process by its variance as a function of time . whenever the variance of the drift process @xmath0 is small relative to the variance of the process @xmath1 , a deterministic version of the differential equation is particularly useful as it then explains a large fraction of the variance of the process . the empirical stochastic differential equation can be easily obtained for various types of longitudinal data . this approach thus provides a novel perspective to assess the dynamics of longitudinal data and permits insights about the underlying forces that shape the processes generating the observations , which would be hard to obtain with other methods . we illustrate these empirical dynamics by constructing the stochastic differential equations that govern online auctions with sporadic bidding patterns . we now describe a data model for longitudinally collected observations , which reflects that the data consist of sparse , irregular and noise - corrupted measurements of an underlying smooth random trajectory for each subject or experimental unit [ @xcite ] , the dynamics of which is of interest . given @xmath2 realizations @xmath3 of the underlying process @xmath1 on a domain @xmath4 and @xmath5 of an integer - valued bounded random variable @xmath6 , we assume that @xmath5 measurements @xmath7 , @xmath8 , are obtained at random times @xmath9 , according to @xmath10 where @xmath11 are zero mean i.i.d . measurement errors , with @xmath12 , independent of all other random components . the paper is organized as follows . in section [ sec2 ] , we review expansions in eigenfunctions and functional principal components , which we use directly as the basic tool for dimension reduction alternative implementations with b - splines or p - splines could also be considered [ @xcite , @xcite , @xcite ] . we also introduce the empirical stochastic differential equation and discuss the decomposition of variance it entails . asymptotic properties of estimates for the components of the differential equation , including variance function of the drift process , coefficient of determination associated with the dynamic system and auxiliary results on improved rates of convergence for eigenfunction derivatives are the theme of section [ sec3 ] . background on related perturbation results can be found in @xcite , @xcite , @xcite , @xcite . section [ sec4 ] contains the illustration of the differential equation with auction data , followed by a brief discussion of some salient features of the proposed approach in section [ sec5 ] . additional discussion of some preliminary formulas is provided in appendix [ seca1 ] , estimation procedures are described in appendix [ seca2 ] , assumptions and auxiliary results are in appendix [ seca3 ] and proofs in appendix [ seca4 ] .

this equation may be empirically obtained from longitudinal observations for a sample of subjects and does not presuppose specific knowledge of the underlying processes . for the nonparametric estimation of the components of the differential equation , it suffices to have available sparsely observed longitudinal measurements which may be noisy and are generated by underlying smooth random trajectories for each subject or experimental unit in the sample .

we demonstrate that the processes underlying on - line auction price bids and many other longitudinal data can be represented by an empirical first order stochastic ordinary differential equation with time - varying coefficients and a smooth drift process . this equation may be empirically obtained from longitudinal observations for a sample of subjects and does not presuppose specific knowledge of the underlying processes . for the nonparametric estimation of the components of the differential equation , it suffices to have available sparsely observed longitudinal measurements which may be noisy and are generated by underlying smooth random trajectories for each subject or experimental unit in the sample . the drift process that drives the equation determines how closely individual process trajectories follow a deterministic approximation of the differential equation . we provide estimates for trajectories and especially the variance function of the drift process . at each fixed time point , the proposed empirical dynamic model implies a decomposition of the derivative of the process underlying the longitudinal data into a component explained by a linear component determined by a varying coefficient function dynamic equation and an orthogonal complement that corresponds to the drift process . an enhanced perturbation result enables us to obtain improved asymptotic convergence rates for eigenfunction derivative estimation and consistency for the varying coefficient function and the components of the drift process . we illustrate the differential equation with an application to the dynamics of on - line auction data.=-1 and . .

1211.2630

c

the main motivation of using the dynamic system approach based on ( [ de ] ) is that it provides a better description of the mechanisms that drive longitudinal data but are not directly observable . the empirical dynamic equation may also suggest constraints on the form of parametric differential equations that are compatible with the data . in the auction example , the dynamic equation quantifies both the nature and extent of how expected price increases depend on auction stage and current price level . this approach is primarily phenomenological and does not directly lend itself to the task of predicting future values of individual trajectories . that expected conditional trajectory derivatives satisfy a first - order differential equation model ( which we refer to as the `` population level '' since this statement is about conditional expectations ) simply follows from gaussianity and in particular does not require additional assumptions . this suffices to infer the stochastic differential equation described in ( [ jt ] ) which we term `` empirical differential equation '' as it is determined by the data . then the function @xmath192 , quantifying the relative contribution of the drift process @xmath0 to the variance of @xmath134 , determines how closely individual trajectories follow the deterministic part of the equation . we could equally consider stochastic differential equations of other orders , but practical considerations favor the modeling with first - order equations . we find in the application example that online auctions follow a dynamic regression to the mean regime for the entire time domain , which becomes more acute near the end of the auction . this allows us to construct predictions of log price trajectory derivatives from trajectory levels at the same @xmath58 . these predictions get better toward the right endpoint of the auctions . this provides a cautionary message to bidders , since an auction that looks particularly promising since it has a current low log price trajectory is likely not to stay that way and larger than average price increases are expected down the line . conversely , an auction with a seemingly above average log price trajectory is likely found to have smaller than average price increases down the line . this suggests that bidders take a somewhat detached stance , watching auctions patiently as they evolve . in particular , discarding auctions that appear overpriced is likely not a good strategy as further price increases are going to be smaller than the average for such auctions . it also implies that bid snipers are ill advised : a seemingly good deal is not likely to stay that way , suggesting a more relaxed stance . conversely , a seller who anxiously follows the price development of an item , need not despair if the price seems too low at a time before closing , as it is likely to increase rapidly toward the end of the auction . for prediction purposes , drift processes @xmath175 for individual auctions are of great interest . in time domains where their variance is large , any log price development is possible . interestingly , the variance of drift processes is very small toward the right tail of the auctions , which means that the deterministic part of the differential equation ( [ de ] ) is relatively more important , and log price derivatives during the final period of an auction become nearly deterministic and thus predictable . other current approaches of statistical modeling of differential equations for time course data [ e.g. , @xcite ] share the idea of modeling with a first order equation . in all other regards these approaches are quite different , as they are based on the prior notion that a differential equation of a particular and known form pertains to the observed time courses and moreover usually have been developed for the modeling of single time courses . this established methodology does not take into account the covariance structure of the underlying stochastic process . in contrast , this covariance structure is a central object in our approach and is estimated nonparametrically from the entire ensemble of available data , across all subjects or experiments .

the drift process that drives the equation determines how closely individual process trajectories follow a deterministic approximation of the differential equation . we illustrate the differential equation with an application to the dynamics of on - line auction data.=-1 and . .

we demonstrate that the processes underlying on - line auction price bids and many other longitudinal data can be represented by an empirical first order stochastic ordinary differential equation with time - varying coefficients and a smooth drift process . this equation may be empirically obtained from longitudinal observations for a sample of subjects and does not presuppose specific knowledge of the underlying processes . for the nonparametric estimation of the components of the differential equation , it suffices to have available sparsely observed longitudinal measurements which may be noisy and are generated by underlying smooth random trajectories for each subject or experimental unit in the sample . the drift process that drives the equation determines how closely individual process trajectories follow a deterministic approximation of the differential equation . we provide estimates for trajectories and especially the variance function of the drift process . at each fixed time point , the proposed empirical dynamic model implies a decomposition of the derivative of the process underlying the longitudinal data into a component explained by a linear component determined by a varying coefficient function dynamic equation and an orthogonal complement that corresponds to the drift process . an enhanced perturbation result enables us to obtain improved asymptotic convergence rates for eigenfunction derivative estimation and consistency for the varying coefficient function and the components of the drift process . we illustrate the differential equation with an application to the dynamics of on - line auction data.=-1 and . .

1205.5283

c

decaying dark matter has come to the front stage recently as an explanation , alternative to annihilating dm , for the anomalies in cr cosmic rays in , and . but , more generally , decaying dm is a viable possibility that is or can naturally be embedded in many dm models . it is therefore interesting to explore its parameter space in the light of the recent observational results . we discussed the constraints which originate from the measurement of the isotropic @xmath24-ray background by and of the fornax cluster by , for a number of decaying channels and over a range of dm masses from 100 gev to 30 tev . we improved the analysis over previous work by using more recent data and updated computational tools . we found ( see fig . 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we derive new bounds on decaying dark matter from the gamma ray measurements of ( i ) the isotropic residual ( extragalactic ) background by and ( ii ) the fornax galaxy cluster by . * * marco cirelli* , * emmanuel moulin* , * paolo panci* , + * pasquale d. serpico* , * aion viana* _http://ph - dep - th.web.cern.ch / ph - dep - th/[cern theory division ] , ch-1211 genve , switzerland _ + _http://ipht.cea.fr / en / index.php[institut de physique thorique ] , cnrs , ura 2306 & cea / saclay , f-91191 gif - sur - yvette , france _ + _http://lapth.in2p3.fr/[lapth ] , univ . de savoie , cnrs , b.p.110 , annecy - le - vieux f-74941 , france _

we derive new bounds on decaying dark matter from the gamma ray measurements of ( i ) the isotropic residual ( extragalactic ) background by and ( ii ) the fornax galaxy cluster by . we find that those from ( i ) are among the most stringent constraints currently available , for a large range of dm masses and a variety of decay modes , excluding half - lives up to to few seconds . in particular , they rule out the interpretation in terms of decaying dm of the spectral features in , and , unless very conservative choices are adopted . we also discuss future prospects for bounds from fornax which , contrary to the present constraints of ( ii ) , may allow for an interesting improvement and may become better than those from the current or future extragalactic data . * * * marco cirelli* , * emmanuel moulin* , * paolo panci* , + * pasquale d. serpico* , * aion viana* _http://ph - dep - th.web.cern.ch / ph - dep - th/[cern theory division ] , ch-1211 genve , switzerland _ + _http://ipht.cea.fr / en / index.php[institut de physique thorique ] , cnrs , ura 2306 & cea / saclay , f-91191 gif - sur - yvette , france _ + _http://irfu.cea.fr / en/[irfu / dsm ] , cea saclay , f-91191 gif - sur - yvette , france _ + _http://cp3-origins.dk/[cp3-origins ] & the danish institute for advanced study dias , + university of southern denmark , campusvej 55 , dk-5230 odense m , denmark _ + _http://lapth.in2p3.fr/[lapth ] , univ . de savoie , cnrs , b.p.110 , annecy - le - vieux f-74941 , france _

0801.1232

r

figure [ f : f16 ] and figure [ f : f17 ] present the main result of our analysis , @xmath5 , an estimate of the circular velocity curve from @xmath98 kpc . this represents the first time that the circular curve for the galaxy has been estimated to such large distances at this accuracy . note that at small radii this estimate , though derived from halo stars , agrees well ( within @xmath13% ) with established determinations at the solar radius ( @xmath170 km @xmath171 ) . beyond the solar radius , the circular velocity curve appears to be gently falling to 175 @xmath172 at @xmath2 kpc . note also that the circular velocity curve is a conceptually more robust estimate than @xmath114 , which depends more sensitively than v@xmath173 on @xmath174 at radii beyond the measurements . using the functional form for @xmath5 expected for an nfw halo and the stellar component ( see below ) as a means to interpolate the individual circular velocity curve estimates , one obtains @xmath175 km @xmath30 , or m@xmath176m@xmath9 . this is the largest radius for which the data directly constrain @xmath177 or @xmath178 . yet this radius is only one - fourth of the expected virial radius of the milky way s halo . we therefore proceed with a separate step , to use these @xmath5 estimates to constrain parameterized models for the overall dark matter halo . we assume that the galactic potential is represented by three components , a spherical hernquist ( 1990 ) bulge , an exponential disk for the stellar components , and describe the halo by an nfw profile ( navarro et al . the total potential can then be simply expressed as @xmath179 with an assumed potential , presumed to be spherically symmetric , for the disk and bulge of @xmath180 @xmath181 where @xmath182 , @xmath183 kpc , @xmath184 , and @xmath185 kpc ( similar to smith et al . the radial potential for a spherical nfw density profile can be expressed as @xmath186 where @xmath47 is a concentration parameter , defined as the ratio of the virial radius to the scale radius . for standard @xmath187cdm cosmogonies we do not attempt to constrain halo flattening . the parameter @xmath188 is a characteristic density given by @xmath189 where @xmath190 is the critical density of the universe , @xmath191 is the contribution of matter to the critical density , and @xmath192 is the critical overdensity at virialization . the virial mass can then be determined from the virial radius , using @xmath193 for our analysis we adopt @xmath194 , @xmath195 , and h@xmath196 = 65@xmath197 @xmath198 . given recent discussions ( and doubts raised ) of whether the baryons modify the dark matter profile , as expected from `` adiabatic contraction '' ( dutton et al . 2007 ) , we consider both an unaltered and an adiabatically contracted nfw profile in the fit of @xmath199 . by fitting the observed @xmath5 with @xmath200 from @xmath201 shown as eqn 10 we can constrain the halo mass of the milky way . in this fit , we simply adopt an unaltered nfw profile and a present - day relation between the mean value of @xmath47 and @xmath104 , @xmath202 this relation is accurate over the range @xmath203 , and is based on the model of macci et al . ( 2007 ) with @xmath204 , @xmath205 , @xmath206 , and @xmath207 . therefore , the @xmath104 is derived as a 1-parameter fit ( fit only @xmath104 , presuming @xmath208 ) . the results are summarized in figure [ f : f16 ] . specifically , for the circular velocity estimates resulting from simulation i , we find @xmath209 with @xmath210 kpc and @xmath211 . for the circular velocity estimates based on simulation ii we find @xmath212 with @xmath213 kpc and @xmath214 . note that the error bars of @xmath104 , @xmath215 , and c are determined from 1-@xmath94 confidence intervals in a chi - square test . for the two cases above we have adopted an unaltered nfw profile and an average relation between @xmath47 and @xmath104 . if we fit an adiabatically contracted nfw profile ( using the prescription of blumenthal et al . 1986 and mo et al . 1998 ) and the same disk and bulge as in eqn 11 and eqn 12 , taking the concentration parameter ( @xmath47 ) and virial mass ( m@xmath11 ) of the nfw profile as independent parameters ( i.e. , we do not require that they follow the relationship in eqn 16 ) , the @xmath104 can be derived as a 2-parameter fit ( @xmath104 and @xmath47 ) , as shown in figure [ f : f17 ] . for the circular velocity estimates resulting from simulation i @xmath216 with @xmath217 kpc and @xmath218 . the virial mass calculated by the circular velocity estimates based on simulation ii is @xmath219 with @xmath220 kpc and @xmath221 . the error bars on @xmath104 and @xmath215 are determined for 1-@xmath94 confidence intervals in a chi - square test , fixing the best - fit value of c , while the error bars on c are determined for 1-@xmath94 confidence intervals in a chi - square test , fixing the best - fit value of @xmath104 . note that although contracted and uncontracted halo fits differ quite strongly in their ( initial ) concentration , reassuringly the m@xmath222 estimates remain relatively unaffected . the lower concentrations for the contracted halo fits are still reasonally consistent with the concentration scatter expected from cosmological simulations ( e.g. , nfw 96 ) . the results here show that the milky way s circular velocity curve must be gently falling to distances of 60 kpc from its value of @xmath223 km / s at the solar radius ; the null hypothesis @xmath224 has a constant value of @xmath225 is rejected by our fits with very high statistical significance ( at a level of 0.01 ) . a direct comparison with earlier work , at the data or @xmath166 level , is not straightforward to carry out , as each sample has distinct selection effects , such as differing radial distributions . our estimate of @xmath104 , taken to be the average of the four estimates derived in this section , @xmath226m@xmath9 , falls well within the ( considerably larger ) range of values estimated by battaglia et al . ( 2005 , 2006 ) : @xmath227 . this value is also reasonably consistent with the recent estimate by li & white ( 2008 ) , based on local group dynamics . in general , however , the new mass estimate presented here lies at the lower limit of most previous estimates . the method to estimate @xmath5 can also be used to derive the escape velocity curve @xmath228 . we have carried out an analogous procedure to that described in 3.2 , using @xmath229 , and found lower limits on m@xmath230 , which do not appear to be as stringent as the @xmath5 estimates .

this procedure results in an estimate of the milky way s circular velocity curve to kpc , which is found to be slightly falling from the adopted value of at the sun s location , and implies mm . if we assume an nfw halo profile of characteristic concentration holds , we can use the observations to estimate the virial mass of the milky way s dark matter halo , mm , which is lower than many previous estimates .

we derive new constraints on the mass of the milky way s dark matter halo , based on a set of halo stars from sdss as kinematic tracers . our sample comprises rigorously selected blue horizontal - branch ( bhb ) halo stars at kpc , and with distances from the galactic center up to kpc , with photometry and spectra drawn from sdss dr-6 . with distances accurate to , this sample enables construction of the full line - of - sight velocity distribution at different galactocentric radii . to interpret these distributions , we compare them to matched mock observations drawn from two different cosmological galaxy formation simulations designed to resemble the milky way , which we presume to have an appropriate orbital distribution of halo stars . specifically , we select simulated halo stars in the same volume as the observations , and derive the distributions of their line - of - sight velocities for different radii , normalized by the simulation s local circular velocity . we then determine which value of brings the observed distribution into agreement with the corresponding distributions from the simulations . these values are then adopted as observational estimates for , after a small jeans equation correction is made to account for slight data / simulation differences in the radial density distribution . this procedure results in an estimate of the milky way s circular velocity curve to kpc , which is found to be slightly falling from the adopted value of at the sun s location , and implies mm . the radial dependence of , derived in statistically independent bins , is found to be consistent with the expectations from an nfw dark matter halo with the established stellar mass components at its center . if we assume an nfw halo profile of characteristic concentration holds , we can use the observations to estimate the virial mass of the milky way s dark matter halo , mm , which is lower than many previous estimates . we have checked that the particulars of the cosmological simulations are unlikely to introduce systematics larger than the statistical uncertainties . this estimate implies that nearly 40% of the baryons within the virial radius of the milky way s dark matter halo reside in the stellar components of our galaxy . a value for m of onlym also ( re-)opens the question of whether all of the milky way s satellite galaxies are on bound orbits .

0801.1232

i

we have constrained the mass distribution of the milky way s dark matter halo , by analyzing the kinematics of nearly @xmath231 bhb stars drawn from sdss dr-6 , which reach to galactocentric distances of @xmath232 kpc . to obtain a `` clean sample '' of bhb stars , we have re - analyzed all candidate bhb spectra , following the prescription by sirko et al . 2004 , which should result in a contamination fraction ( mostly by bs stars ) of well below 10% . the metallicity distribution , centered on [ fe / h ] @xmath233 dex , confirms that most sample members must be halo stars . the distances to the bhb stars are known to @xmath234 . to account for the complex survey geometry and for plausible orbital distributions of our sample of bhb stars , we have compared the observed radial velocities to analogous quantities drawn from the `` star particles '' in galaxy formation simulations that resemble the milky way . in particular , we have placed a virtual `` observer '' at 8.0 kpc from the simulation centers , looking in the actual sdss directions and sampling radial velocities for stars that are more than 4 kpc above and below the disk plane . we then explored to what mass scale , or @xmath5 , the simulations need to be scaled to in order to match the observed line - of - sight velocity distribution in a set of radial bins . in this analysis , we adjusted this scaling using the jeans equation , to account for the slight difference in the radial profile of observed halo stars ( @xmath235 ) and simulated halo stars ( @xmath236 ) over this radial range . this procedure results in direct estimates of @xmath5 from @xmath13 kpc to @xmath2 kpc , the best such estimates to date over this range . the circular velocity estimate varies slightly with radius , dropping from @xmath237 at 10 kpc to @xmath238 in the most distant two bins . applying this procedure to two independent cosmological simulations ( simulation i and simulation ii , respectively ) results in consistent estimates of @xmath5 . the mass enclosed within 60 kpc , constrained quite directly by the data , is found to be @xmath239m@xmath9 . as a result of the much more extensive data set provided by sdss , the uncertainties on this estimate are substantially lower than those obtained by previous comparable work . a simple , jeans- equation based modeling approach , assuming ( an-)isotropies of either @xmath240 ( as found for the halo stars in the cosmological simulations ) yields results that are consistent with these values . although each of the @xmath5 points were estimated independently , the implied overall profile is consistent with both the mass profile in the simulations and with a parameterized mass model that combines a fixed disk and bulge model with an nfw dark matter halo , whose concentration c corresponds to the expected mean value for its virial mass . we have also explored halo fits with the concentration c as a free parameter , as well as halo profiles that have been modified by adiabatic contraction . we find that our data can not discriminate well whether adiabatic contraction occurs or not an uncontracted halo of higher than average concentration and a contracted halo of ( initially ) low concentration fit comparably well . the resulting virial masses , @xmath241m@xmath9 , are consistent for both fitting approaches . we have also checked that these results are quite robust with respect to distance errors , modest sample contamination ( @xmath242 ) , and the choice of a different , independent galaxy formation simulation . the estimate of @xmath104 , which does imply an extrapolation from r@xmath243 kpc to the virial radius of @xmath244 kpc , is consistent with a recent estimate from a much smaller sample of halo stars ( battaglia et al . 2006 ) , but it is lower than previous estimates that also rely on the kinematics of satellite galaxies ( e.g. , kochanek et al . however , recent results on the lmc ( kallivayalil et al . 2006 ; besla et al . 2007 ) indicate that not even the magellanic clouds may have been bound to the milky way for long , posing a potential conceptual problems for the use of satellite dynamics . it should be interesting to explore how our new constraint modifies the local group timing argument and its implication for m31 s halo mass ( li & white 2008 ) . the estimate of @xmath245m@xmath9 , together with an estimated total cold baryonic mass of @xmath246m@xmath9 and a global baryon mass fraction of @xmath247 , implies that nearly 40% of all baryons within the virial radius have cooled to form the milky way s stars and ( cold ) gas , consistent with recent estimates for galaxies of that mass scale , based on statistical arguments ( van den bosh et al . 2007 ; gnedin et al . 2007 ) . we note that parts of our analysis have been performed under the assumption that the stellar halo of the galaxy is considered as a single relaxed population , or one that matches the simulations . our data on the overall dynamics are consistent with that hypothesis . recent evidence from carollo et al . ( 2007 ) and miceli et al . ( 2007 ) suggest that the halo may well be more complex , and comprise two distinct populations of inner- and outer - halo stars , with ( slightly ) different net rotational velocities and spatial profiles . we defer all analysis of kinematic and spatial sub - structure in this particular sample to a future paper . the sdss and segue surveys have shown in this context that they can provide unparalleled sets of kinematic tracers for the milky way , enabling a direct `` circular velocity curve '' estimate of the milky way extending to 60 kpc . once the full set of spectroscopy from segue is available , a much larger set of stars for such an analysis should be available . the proposed extension of sdss , known as sdss - iii ( and using a more sensitive , 1000 fiber spectrograph ) , will provide the opportunity to obtain higher quality spectra for fainter , more distant bhb stars , thus extending the reach of our analysis to over 100 kpc . this work was made possible by the support of the chinese academy of sciences and the max - planck - institute for astronomy , and is supported by the national natural science foundation of china under grants nos . 10433010 and 10521001 . tcb and ysl acknowledge partial support from the us national science foundation under grants ast 06 - 0715 and ast 07 - 07776 , as well as from grant phy 02 - 15783 ; physics frontier center / joint institute for nuclear astrophysics ( jina ) . funding for the sloan digital sky survey ( 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 , and 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 ( arc ) 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 , the university of chicago , drexel university , fermilab , the institute for advanced study , the japan participation group , the 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 . although subtle , one can notice that the bs stars s balmer lines are wider at @xmath248 below the local continuum than the bhb star . these effects arise due to the higher gravity of the bs star . ] and @xmath37 , as determined from the @xmath38 line , for stars brighter than @xmath249 and passing the color cuts shown in figure [ f : f1 ] . the trail of stars with @xmath250 are too cool to be bhb stars , while the concentration of stars with @xmath251 is due to blue stragglers with higher surface gravity . the stars that lie well outside the main locus are the result of poor parameter determinations due to missing spectroscopic data at the location of the @xmath38 line . the region enclosed by the box is used as the bhb selection criterion for the @xmath38 , @xmath57 & @xmath58 method . ] , as a function of apparent magnitude , for the entire sample of halo bhb stars . ( lower panel ) the distribution of line - of - sight velocities , corrected to the gsr , for the entire sample of bhb stars . a gaussian of width @xmath254 km @xmath30 centered on the local standard of rest is shown for reference . , title="fig:",height=377 ] , as a function of apparent magnitude , for the entire sample of halo bhb stars . ( lower panel ) the distribution of line - of - sight velocities , corrected to the gsr , for the entire sample of bhb stars . a gaussian of width @xmath254 km @xmath30 centered on the local standard of rest is shown for reference . , title="fig:",height=377 ] as a function of galactocentric distance , @xmath87 , for the entire sample of halo bhb stars . ( lower panel ) the velocity dispersion , @xmath255 , as a function of galactocentric distance . a best fit exponentially falling relationship is plotted.,title="fig:",height=377 ] as a function of galactocentric distance , @xmath87 , for the entire sample of halo bhb stars . ( lower panel ) the velocity dispersion , @xmath255 , as a function of galactocentric distance . a best fit exponentially falling relationship is plotted.,title="fig:",height=377 ] between the halo star particles in the simulation i and the observations , shown here for all bins . the dashed line is @xmath256 , and the solid line is @xmath257 , after finding the best matching velocity scaling , @xmath128 , listed in table 3 ; the best match in this context is obtained from a k - s test . ] between the halo star particles in the simulation ii and the observations , shown here for all bins . the dashed line is @xmath256 , and the solid line is @xmath257 , after finding the best matching velocity scaling , @xmath128 , listed in table 3 ; the best match in this context is obtained from a k - s test . ] , for two different simulated galaxies . the filled circles are the v@xmath258 estimates for the observed halo bhb stars based on simulation i and the filled squares are the v@xmath258 estimates based on simulation ii . the two lines are the circular velocity curve estimates derived from the velocity dispersion profile ( figure [ f : f10 ] ) and the jeans equation with @xmath164 and @xmath168 . ] estimates , while the large symbols in the two plots are the v@xmath259 estimates . contributions of the adopted model components ( i.e. disk , bulge , and halo ) and the circular velocity curves based on the jeans equation are plotted in different linestyles . estimates of virial mass , m@xmath260 , virial radius , r@xmath260 and concentration parameter , @xmath47 , are labeled on the plots.,title="fig:",height=377 ] estimates , while the large symbols in the two plots are the v@xmath259 estimates . contributions of the adopted model components ( i.e. disk , bulge , and halo ) and the circular velocity curves based on the jeans equation are plotted in different linestyles . estimates of virial mass , m@xmath260 , virial radius , r@xmath260 and concentration parameter , @xmath47 , are labeled on the plots.,title="fig:",height=377 ] , but here the circular velocity curves were derived under the assumption of a contracted nfw profile . the solid line is the best - fit circular velocity curve to the v@xmath259 estimates , while the large symbols in the two plots are the v@xmath259 estimates . contributions of the adopted model components ( i.e. disk , bulge , and halo ) and the circular velocity curves based on the jeans equation are plotted in different linestyles . estimates of virial mass , m@xmath260 , virial radius , r@xmath260 and concentration parameter , @xmath47 are labeled on the plots.,title="fig:",height=377 ] , but here the circular velocity curves were derived under the assumption of a contracted nfw profile . the solid line is the best - fit circular velocity curve to the v@xmath259 estimates , while the large symbols in the two plots are the v@xmath259 estimates . contributions of the adopted model components ( i.e. disk , bulge , and halo ) and the circular velocity curves based on the jeans equation are plotted in different linestyles . estimates of virial mass , m@xmath260 , virial radius , r@xmath260 and concentration parameter , @xmath47 are labeled on the plots.,title="fig:",height=377 ] 51602 - 0266 - 225 & sdssj094218.23 - 002519.7 & 145.575943 & -0.422125 & 236.196579 & 36.896130 & 15.46 & -0.10 & 1.20 & 0.02 & 0.02 & 0.01 & -95.7 & 2.1 & -245.5 & 0.24 & 26.93 & 0.84 & 9.97 & bhb + 51602 - 0266 - 397 & sdssj094138.17 + 001821.5 & 145.409058 & 0.305967 & 235.328827 & 37.175690 & 18.48 & -0.11 & 1.22 & 0.04 & 0.02 & 0.02 & -36.0 & 12.8 & -183.8 & 0.20 & 27.78 & 1.12 & 10.57 & bhb + 51602 - 0266 - 634&sdssj094840.23 + 002818.0&147.167633&0.471673&236.434402 & 38.711887&18.01&-0.02&1.02&0.03&0.02&0.01&9.4&10.5 & -136.8&0.29 & 25.80 & 0.92&10.01&bhb + 51609 - 0292 - 102&sdssj125223.54 - 003708.2&193.098083 & -0.618937 & 303.444397&62.251862 & 14.29 & -0.24 & 1.27 & 0.02 & 0.02&0.02 & 227.3 & 1.6 & 148.7 & 0.23 & 27.00 & 1.03 & 10.16 & bhb + 51609 - 0292 - 155&sdssj125050.87 - 000806.1&192.711960 & -0.135032 & 302.609894&62.736347&17.84 & -0.00 & 1.06&0.02 & 0.02&0.02 & 190.8 & 7.2&112.8 & 0.24 & 27.46 & 0.85 & 10.27 & bhb + 51609 - 0292 - 232 & sdssj124759.81 - 000456.2&191.999207 & -0.082266 & 301.051117 & 62.776917&18.16 & -0.04&1.05 & 0.03&0.02 & 0.02 & -121.4 & 9.3 & -200.9 & 0.28 & 30.32 & 0.86 & 10.31 & bs + 51609 - 0292 - 269 & sdssj124721.11 - 002931.5 & 191.837952 & -0.492089 & 300.729431 & 62.362186 & 19.17 & -0.09&1.12 & 0.05 & 0.03 & 0.02 & 232.0 & 19.5 & 151.0 & 0.30 & 32.62 & 0.93 & 10.10 & ms + 51609 - 0292 - 329&sdssj124641.66 + 003751.2&191.673569 & 0.630884 & 300.275543&63.478165&17.15&-0.10&1.23 & 0.02 & 0.01&0.02 & -49.0 & 3.9 & -127.2 & 0.23 & 25.03 & 0.81&8.25&bhb + 51609 - 0292 - 351&sdssj124449.35 + 002157.4&191.205612 & 0.365958 & 299.263092&63.190571 & 17.64 & -0.26 & 1.13 & 0.02 & 0.01 & 0.01 & 4.2 & 5.7&-75.8 & 0.24 & 24.54 & 1.15 & 9.51 & bhb + 51609 - 0292 - 367 & sdssj124805.12 + 010113.5 & 192.021347&1.020428 & 301.028198 & 63.879784&16.38 & -0.17 & 1.22 & 0.03 & 0.02 & 0.02 & 84.8 & 2.8 & 8.6 & 0.24 & 34.34 & 0.87 & 11.53 & bs + 51602 - 0266 - 125 & sdssj094317.57 - 011021.2 & 145.823196 & -1.172550 & 237.138931 & 36.662491 & 16.48 & 1.17 & -0.22 & 0.55 & 26.60 & 0.21 & 1.02 & 10.07 & 15.3 & 20.2 & 14.7 & 10.3 & 9.2 & 178.0 & 3.5 & 26.2 & 8315 & 3.12 & -2.03 & bhb + 51602 - 0266 - 397 & sdssj094138.17 + 001821.5 & 145.409058 & 0.305967 & 235.328827 & 37.175690 & 18.48 & 1.22 & -0.11 & 0.55 & 27.78 & 0.20 & 1.12 & 10.57 & 38.5 & 42.8 & 25.5 & 25.3 & 23.3 & -36.0 & 12.8 & -183.8 & 8306 & 3.81 & -1.97 & bhb + 51602 - 0266 - 634 & sdssj094840.23 + 002818.0 & 147.167633 & 0.471673 & 236.434402 & 38.711887 & 18.01 & 1.02 & -0.02 & 0.60 & 25.80 & 0.29 & 0.92 & 10.01 & 30.3 & 34.6 & 21.1 & 19.7 & 19.0 & 9.4 & 10.5 & -136.8 & 7850 & 4.20 & -1.27 & bhb + 51609 - 0292 - 102 & sdssj125223.54 - 003708.2 & 193.098083 & -0.618937 & 303.444397 & 62.251862 & 14.29 & 1.27 & -0.24 & 0.55 & 27.00 & 0.23 & 1.03 & 10.16 & 5.6 & 8.5 & 6.6 & 2.2 & 5.0 & 227.3 & 1.6 & 148.7 & 8668 & 2.61 & -1.96 & bhb + 51609 - 0292 - 329 & sdssj124641.66 + 003751.2 & 191.673569 & 0.630884 & 300.275543 & 63.478165 & 17.15 & 1.23 & -0.10 & 0.55 & 25.03 & 0.23 & 0.81 & 8.25 & 20.9 & 20.6 & 3.3 & 8.1 & 18.7 & -49.0 & 3.9 & -127.2 & 7596 & 2.95 & -2.00 & bhb + 51609 - 0292 - 351 & sdssj124449.35 + 002157.4 & 191.205612 & 0.365958 & 299.263092 & 63.190571 & 17.64 & 1.13 & -0.26 & 0.60 & 24.54 & 0.24 & 1.15 & 9.51 & 25.6 & 25.1 & 2.4 & 10.1 & 22.8 & 4.2 & 5.7 & -75.8 & 9247 & 3.11 & -1.43 & bhb + 51609 - 0292 - 582 & sdssj125254.01 + 002903.2 & 193.225037 & 0.484220 & 303.747009 & 63.353657 & 16.22 & 1.23 & -0.13 & 0.55 & 26.21 & 0.25 & 0.85 & 9.09 & 13.6 & 14.0 & 4.6 & 5.1 & 12.2 & -42.9 & 3.2 & -118.0 & 7953 & 3.14 & -1.66 & bhb + 51609 - 0304 - 219 & sdssj141723.88 - 002220.8 & 214.349503 & -0.372432 & 343.356750 & 55.602268 & 16.64 & 1.05 & -0.31 & 0.70 & 23.05 & 0.20 & 1.19 & 9.68 & 15.4 & 13.0 & -0.3 & 2.5 & 12.7 & -25.0 & 3.8 & -50.1 & -9999 & -9.99 & -9.99 & bhb + 51613 - 0305 - 243 & sdssj142408.24 - 002930.7 & 216.034348 & -0.491848 & 345.608093 & 54.511181 & 15.71 & 1.17 & -0.02 & 0.60 & 25.01 & 0.25 & 0.87 & 8.94 & 10.5 & 8.9 & 2.1 & 1.5 & 8.6 & -78.4 & 2.4 & -99.4 & 7754 & 3.68 & -2.26 & bhb + 51613 - 0305 - 488 & sdssj142826.28 + 002915.4 & 217.109497 & 0.487611 & 348.109955 & 54.617874 & 17.54 & 1.17 & -0.26 & 0.60 & 24.71 & 0.22 & 1.12 & 9.55 & 24.4 & 21.0 & -5.8 & 2.9 & 19.9 & 74.7 & 4.2 & 59.4 & 9338 & 2.87 & -2.95 & bhb + 51614 - 0281 - 438 & sdssj112513.99 + 004207.5 & 171.308289 & 0.702082 & 261.294983 & 56.438610 & 18.51 & 1.13 & -0.23 & 0.60 & 24.60 & 0.22 & 1.16 & 9.44 & 38.2 & 39.7 & 11.2 & 20.9 & 31.8 & 252.4 & 9.6 & 134.5 & 8609 & 3.13 & -1.56 & bhb + lcc [ t : tbl3 ] 7.5 & @xmath261 & @xmath262 + 12.5 & @xmath263 & @xmath264 + 17.5 & @xmath265 & @xmath266 + 22.5 & @xmath267 & @xmath268 + 27.5 & @xmath269 & @xmath270 + 32.5 & @xmath271 & @xmath272 + 37.5 & @xmath273 & @xmath274 + 42.5 & @xmath275 & @xmath276 + 47.5 & @xmath277 & @xmath278 + 55.0 & @xmath279 & @xmath280 +

we derive new constraints on the mass of the milky way s dark matter halo , based on a set of halo stars from sdss as kinematic tracers . this sample enables construction of the full line - of - sight velocity distribution at different galactocentric radii . to interpret these distributions , we compare them to matched mock observations drawn from two different cosmological galaxy formation simulations designed to resemble the milky way , which we presume to have an appropriate orbital distribution of halo stars . specifically , we select simulated halo stars in the same volume as the observations , and derive the distributions of their line - of - sight velocities for different radii , normalized by the simulation s local circular velocity . these values are then adopted as observational estimates for , after a small jeans equation correction is made to account for slight data / simulation differences in the radial density distribution . the radial dependence of , derived in statistically independent bins , is found to be consistent with the expectations from an nfw dark matter halo with the established stellar mass components at its center . we have checked that the particulars of the cosmological simulations are unlikely to introduce systematics larger than the statistical uncertainties . this estimate implies that nearly 40% of the baryons within the virial radius of the milky way s dark matter halo reside in the stellar components of our galaxy . a value for m of onlym also ( re-)opens the question of whether all of the milky way s satellite galaxies are on bound orbits .

we derive new constraints on the mass of the milky way s dark matter halo , based on a set of halo stars from sdss as kinematic tracers . our sample comprises rigorously selected blue horizontal - branch ( bhb ) halo stars at kpc , and with distances from the galactic center up to kpc , with photometry and spectra drawn from sdss dr-6 . with distances accurate to , this sample enables construction of the full line - of - sight velocity distribution at different galactocentric radii . to interpret these distributions , we compare them to matched mock observations drawn from two different cosmological galaxy formation simulations designed to resemble the milky way , which we presume to have an appropriate orbital distribution of halo stars . specifically , we select simulated halo stars in the same volume as the observations , and derive the distributions of their line - of - sight velocities for different radii , normalized by the simulation s local circular velocity . we then determine which value of brings the observed distribution into agreement with the corresponding distributions from the simulations . these values are then adopted as observational estimates for , after a small jeans equation correction is made to account for slight data / simulation differences in the radial density distribution . this procedure results in an estimate of the milky way s circular velocity curve to kpc , which is found to be slightly falling from the adopted value of at the sun s location , and implies mm . the radial dependence of , derived in statistically independent bins , is found to be consistent with the expectations from an nfw dark matter halo with the established stellar mass components at its center . if we assume an nfw halo profile of characteristic concentration holds , we can use the observations to estimate the virial mass of the milky way s dark matter halo , mm , which is lower than many previous estimates . we have checked that the particulars of the cosmological simulations are unlikely to introduce systematics larger than the statistical uncertainties . this estimate implies that nearly 40% of the baryons within the virial radius of the milky way s dark matter halo reside in the stellar components of our galaxy . a value for m of onlym also ( re-)opens the question of whether all of the milky way s satellite galaxies are on bound orbits .

0707.3595

i

with the start of data taking at the large hadron collider ( lhc ) , particle physics will , for the first time , directly probe the tera scale , i.e. the scale of electroweak symmetry breaking according to the standard model ( sm ) , around @xmath2 . while the sm has been confirmed experimentally to be a very precise effective description of the physics below the tera scale , there are many serious contenders for the more fundamental theory beneath the sm . for quite some time , superstring theory has been a leading candidate for the fundamental theory unifying all known interactions . there are certain solutions of superstring theory with additional spatial dimensions , where the characteristic string scales are low enough to allow experimental tests at the lhc and the planned international @xmath3 linear collider ( ilc ) . one spectacular prediction @xcite of superstring theory is the emergence of a noncommutative ( nc ) structure of spacetime at a scale @xmath4 associated with nonvanishing commutators @xmath5 = { \mathrm{i}}\theta_{\mu\nu } = { \mathrm{i}}\frac{1}{\lambda_{\text{nc}}^2}c_{\mu\nu}\ ] ] of spacetime coordinates that correspond to oriented minimal resolvable areas of size @xmath6 . while a nonvanishing commutator like ( [ eq : nc - geometry ] ) had been proposed much earlier @xcite as a regulator of divergencies in quantum field theory ( qft ) and quantum gravity , the observation of @xcite caused intense renewed interest in qft on nc spacetimes ( ncqft ) . the commutator ( [ eq : nc - geometry ] ) can be conveniently realized on a _ commuting _ spacetime by replacing all products of functions by moyal - weyl @xmath7-products @xmath8 a prescription for constructing arbitrary gauge theories on a nc spacetime was presented in @xcite . these so - called seiberg - witten maps ( swm ) realize nc gauge transformations in the nc theory as ordinary commutative gauge transformations on an effective commutative gauge theory . by going to the enveloping algebra of the lie algebra of a given gauge group , this approach @xcite circumvents obstructions like charge quantization in @xmath9 gauge theories and the prohibition of @xmath10 gauge groups in the earlier attempts . in particular , this prescription allowed the construction of the so - called noncommutative standard model ( ncsm ) @xcite as an anomaly - free @xcite canonical nc extension of the sm without having to introduce additional particles gauge theory and subsequently break the extraneous symmetries , introducing additional particles that must be removed from the observable spectrum @xcite . ] . in the first order of an expansion in @xmath0 , one has only three new bounded parameters that depend on the choice of the representation of the enveloping algebra of the sm lie algebra and describe new couplings among gauge bosons @xcite . these couplings vanish in the minimal ncsm , where the enveloping algebra is realized by matrices acting in the vector space of the adjoint representation . furthermore , the bosonic sector of the minimal ncsm was shown to be renormalizable at one loop @xcite , where all counter terms can be expressed through the usual field strength and coupling constant renormalizations . also the nonminimal ncsm is renormalizable at one - loop , if a _ finite _ gauge invariant @xmath1-term is added to the action @xcite . finally , the fermionic sector can be shown to require a finite number of gauge invariant four - fermion operators as additional counter terms in one loop order @xcite . in euclidean nc space , the renormalizability of scalar and gauge models has been shown to all orders in @xmath0 @xcite . using the effective theory in the first order of the @xmath0-expansion , several phenomenological studies were performed for past , present , and future colliders @xcite . in a preceding paper @xcite , we have studied the associated production of photons and @xmath11-bosons at hadron colliders ( tevatron and lhc ) showing that at the lhc one can reach a noncommutativity scale @xmath4 slightly above @xmath2 @xcite . moreover , we have found that it is necessary to go beyond the first order in @xmath0 , because of significant contributions from partonic center of mass energies exceeding the noncommutativity scale that can actually be probed . while it is possible in simple cases to derive expressions for families of swm to all orders in @xmath0 @xcite , an explicit parameterization of the most general solution has not been given . therefore , we start in this paper by constructing the most general swm for the ncsm in the second order of the @xmath0-expansion . the importance of this systematic approach is stressed _ a posteriori _ by discovering ambiguities in the swm that have been missed in earlier @xmath12 constructions of swm @xcite . while these authors expected all ambiguities to cancel in observable quantities , we find that they do _ not_. in fact , using @xmath13 as an example , we will calculate the ambiguity in the corresponding scattering amplitude explicitly . the outline of this paper is as follows . in section [ sec : swm ] we derive the general swm up to second order in the noncommutativity @xmath0 . particular emphasis will be given to the ambiguities resulting from the homogeneous solutions of the gauge equivalence equations . furthermore , the lagrangian and the feynman rules of the neutral current sector of the ncsm are constructed in section [ sec : feynman ] . section [ sec : ambiguities ] presents our analysis of the impact of the swm ambiguities on physical observables . we will demonstrate by an explicit calculation of @xmath14 that not all ambiguities cancel in the @xmath12 contribution to the cross section . in section [ sec : summary ] we conclude with a brief summary . all expressions that are needed for the main results of this paper will be given in full , either in the main text or in the appendices . complete expressions in second order in @xmath0 that are too lengthy to be included in this paper can be found in the appendix of @xcite .

we derive the most general seiberg - witten maps for noncommutative gauge theories in second order of the noncommutative parameter . in particular , we demonstrate that some of these ambiguities enter observables like scattering cross sections and enlarge the parameter space of the noncommutative standard model beyond .

we derive the most general seiberg - witten maps for noncommutative gauge theories in second order of the noncommutative parameter . our results reveal the existence of more ambiguities than previously known . in particular , we demonstrate that some of these ambiguities enter observables like scattering cross sections and enlarge the parameter space of the noncommutative standard model beyond .

hep-ph9911516

i

the ground state ( `` vacuum '' ) of non - abelian gauge theories like qcd is known to be very rich . it includes topologically non - trivial fluctuations of the gauge fields , carrying an integer topological charge @xmath1 . the simplest building blocks of topological structure in the vacuum are @xcite _ instantons _ with @xmath2 and _ anti - instantons _ with @xmath3 . instantons represent gluon field configurations that are localized ( `` instantaneous '' ) in euclidean time and space . while they are believed to play an important role in various long - distance aspects of qcd , there are also important short - distance implications . in qcd with @xmath4 ( light ) flavours , instantons induce hard processes violating _ chirality _ in accord @xcite with the selection rule @xmath5 _ chirality _ @xmath6 , due to the general chiral anomaly . while in ordinary perturbative qcd ( @xmath7 ) these processes are forbidden , their experimental discovery would clearly be of basic significance . the deep - inelastic scattering regime is strongly favoured in this respect , since hard instanton - induced processes are both calculable @xcite within instanton - pertubation theory and have good prospects for experimental detection at hera @xcite . qcdins @xcite is a monte carlo package for simulating qcd - instanton induced scattering processes in deep - inelastic scattering ( hera ) . it is designed as an `` add - on '' hard process generator interfaced by default to the monte carlo generator herwig @xcite . it incorporates the theoretically predicted production rate for instanton - induced events as well as the essential characteristics that have been derived theoretically for the partonic final state of instanton - induced processes : notably , the flavour democratic @xcite and isotropic @xcite production of the final state partons , energy weight factors different for gluons and quarks @xcite , and a high average multiplicity @xmath8 of produced partons with a ( approximate ) poisson distribution of the gluon multiplicity @xcite . earlier versions of qcdins have been used already to establish first experimental bounds on the rate of instanton - induced events at hera @xcite and to develop instanton search strategies @xcite . in the present report a comprehensive description is given of the theoretical framework built into the program ( section [ theorie ] ) as well as of the various program components ( section [ qcdins ] ) and of their usage ( section [ usage ] ) .

we describe a monte carlo event generator for the simulation of qcd - instanton induced processes in deep - inelastic scattering ( hera ) . it incorporates the theoretically predicted production rate for instanton - induced events as well as the essential characteristics that have been derived theoretically for the partonic final state of instanton - induced processes : notably , the flavour democratic and isotropic production of the partonic final state , energy weight factors different for gluons and quarks , and a high average multiplicity of produced partons with a poisson distribution of the gluon multiplicity . used : _ 1 + _ has the code been vectorised or parallelized ? : _ no + _ no . of bytes in distributed program , being non - perturbative fluctuations of the gauge fields , they induce hard processes absent in conventional perturbation theory . deep - inelastic lepton - nucleon scattering at hera offers a unique possible discovery window for such processes induced by qcd - instantons through their characteristic final - state signature and a sizable rate , calculable within instanton - perturbation theory . an experimental discovery of such a novel , non - perturbative manifestation of non - abelian gauge theories would be of fundamental significance . however , instanton - induced events are expected to make up only a small fraction of all deep - inelastic events . therefore , a detailed knowledge of the resulting hadronic final state , along with a multi - observable analysis of experimental data by means of monte carlo techniques , is necessary . it incorporates the theoretically predicted production rate for instanton - induced events as well as the essential characteristics that have been derived theoretically for the partonic final state of instanton - induced processes : notably , the flavour democratic and isotropic production of the partonic final state , energy weight factors different for gluons and quarks , and a high average multiplicity of produced partons with a poisson distribution of the gluon multiplicity . _ restrictions on the complexity of the problem _ _ unusual features of the program _ phys . phys . * long write - up * +

we describe a monte carlo event generator for the simulation of qcd - instanton induced processes in deep - inelastic scattering ( hera ) . the qcdins package is designed as an `` add - on '' hard process generator interfaced to the general hadronic event simulation package herwig . it incorporates the theoretically predicted production rate for instanton - induced events as well as the essential characteristics that have been derived theoretically for the partonic final state of instanton - induced processes : notably , the flavour democratic and isotropic production of the partonic final state , energy weight factors different for gluons and quarks , and a high average multiplicity of produced partons with a poisson distribution of the gluon multiplicity . while the subsequent perturbative evolution of the generated partons is always handled by the herwig package , the final hadronization step may optionally be performed also by means of the general hadronic event simulation package jetset . and qcd ; instanton ; deep - inelastic scattering ; monte carlo simulation 11.15.kc ; 12.38.lg ; 13.60.hb * program summary * + _ title of program : _ qcdins 2.0 + _ catalogue identifier : _ + _ program obtainable from : _ http://www.desy.de/~t00fri/qcdins/qcdins.html + _ computer for which the program is designed and others on which it has been tested : _ any computer with a fortran 77 compiler + _ operating systems under which the program has been tested : _ linux 2.0.x ; hp - ux 10.2 + _ programming language used : _ fortran 77 + _ memory required to execute with typical data : _ size of executable program is approximately 2.6 mb . the size of the qcdins library itself is about 200 kb ; the required routines from the herwig and jetset libraries constitute the dominant portion of the needed memory . + _ no . of processors used : _ 1 + _ has the code been vectorised or parallelized ? : _ no + _ no . of bytes in distributed program , including test data , etc . : _ 1071106 + _ distribution format : _ ascii + _ cpc program library subprograms used : _ herwig [ 1 ] version 5.9 ; jetset 7.4 [ 2 ] + _ keywords : _ qcd ; instanton ; deep - inelastic scattering ; monte carlo simulation + _ nature of physical problem _ + instantons are a basic aspect of quantum chromodynamics . being non - perturbative fluctuations of the gauge fields , they induce hard processes absent in conventional perturbation theory . deep - inelastic lepton - nucleon scattering at hera offers a unique possible discovery window for such processes induced by qcd - instantons through their characteristic final - state signature and a sizable rate , calculable within instanton - perturbation theory . an experimental discovery of such a novel , non - perturbative manifestation of non - abelian gauge theories would be of fundamental significance . however , instanton - induced events are expected to make up only a small fraction of all deep - inelastic events . therefore , a detailed knowledge of the resulting hadronic final state , along with a multi - observable analysis of experimental data by means of monte carlo techniques , is necessary . _ method of solution _ + the qcdins package is designed as an `` add - on '' hard process generator interfaced to the general hadronic event simulation package herwig . it incorporates the theoretically predicted production rate for instanton - induced events as well as the essential characteristics that have been derived theoretically for the partonic final state of instanton - induced processes : notably , the flavour democratic and isotropic production of the partonic final state , energy weight factors different for gluons and quarks , and a high average multiplicity of produced partons with a poisson distribution of the gluon multiplicity . while the subsequent perturbative evolution of the generated partons is always handled by the herwig package , the final hadronization step may optionally be performed also by means of the general hadronic event simulation package jetset . _ restrictions on the complexity of the problem _ + the default values of the implemented kinematical cuts represent the state of the art limits for the reliability of the generated instanton - induced event rate and event topology . _ typical running time _ + 10 - 100 events per second for a pc with pentium cpu , depending on its clock frequency . on a hp 9000/735 ( 99 mhz ) workstation , 6 events per second are generated . _ unusual features of the program _ + none _ references _ + [ 1 ] g. marchesini et al . , comput . phys . commun . 67 ( 1992 ) 465 . + [ 2 ] t. sjstrand , comput . phys . commun . 82 ( 1994 ) 74 . * long write - up * +

astro-ph9806001

i

the issue of whether galaxy disks are significantly opaque is a lively topic of current research and debate ( e.g. , davies & burstein 1995 , and papers therein ) , and the conclusions of different workers often differ widely . statistical evidence that most large presented by valentijn ( 1990 ) based on a diameter - selected sample of galaxies from the eso survey . valentijn s result indicated that the bright galaxies are substantially opaque right out to the 25 @xmath9 mag arcsec@xmath10 isophote . this conclusion has been challenged by burstein and others , who initially questioned the selection effects inherent in the sample used by valentijn , and have maintained that very little extinction is present . more detailed studies on individual galaxies have generally concluded in favor of at least some extinction ( e.g. , studies of multicolor optical and infrared images by block et al . 1994 , and peletier et al . there is also some indication that even galaxy halos may contain dust ; zaritski ( 1994 ) compared faint galaxies in fields bordering nearby spirals ( ngc 2835 and ngc 3521 ) and in control fields further away on the sky , and found a small difference in the average colors . however , from analysis of surface photometry on a sample of 1700 galaxies , giovanelli et al . ( 1995 ) have recently concluded that less luminous galaxies are completely transparent , and that even the most luminous spirals suffer from only small amounts of extinction ( 0.1 mag ) at an isophotal radius of 23.5 mag arcsec@xmath10 in @xmath11 . tests of the opacity of spiral disks which rely on intrinsic properties of the galaxies ( surface brightness , inclination angle , isophotal profiles ) are strongly dependent on the necessary assumption of just how the dust is distributed within the galaxy ( witt , thronson , & capuano 1992 ; witt & gordon 1996 ) . for instance , layered models with a physically thin but optically thick dust layer behave like optically thin disks ( disney , davies , & phillips 1989 ) . in the case of edge - on galaxies , surface photometry can help determine the geometrical dust distribution ( kylafis & bahcall 1987 ) , but in more general cases the results are inconclusive . the use of stars or star clusters embedded in the galaxy can only tell us something about the remaining opacity between us and the star , and is clearly biased to low opacities . hii regions have also been used ; they have the same bias , but in addition those bright enough to be easily observed may alter the surrounding ism so drastically that they are poor test objects ( e.g. , allen et al . 1997 ) . a more direct approach has been proposed by white & keel ( 1992 ) , and followed up by white , keel , & conselice ( 1996 ) and berlind et al . they have looked at partially - overlapping galaxy pairs , the first two studies at optical wavelengths , the last one in both the optical and the near - infrared . assuming that the background galaxy isophotes are smooth and/or symmetric , they use the unobscured part of the background galaxy to calculate the amount of background light that is lost in crossing the foreground disk . all three studies have found higher extinction in the arms than in the interarm regions , and extinction curves flatter than galactic , consistent with a patchy dust distribution in the foreground galaxy . the use of background illuminating objects has the advantage that no assumptions need to be made about the relative distribution of dust and light in the foreground galaxy . also , the overlapping - galaxy method in particular provides results with good spatial resolution . however , it is necessary to assume that the light distribution in the background galaxy image is smooth and centrally symmetric . in addition , there is an uncertain contribution of scattered light from the background galaxy into the line of sight . but perhaps the biggest disadvantage is that there are only about two dozen galaxy pairs which offer the right geometry for the method to be applied ( white et al . 1996 ) . a potentially more general way to establish the opacity of a galaxy is to look for effects on the counts , colors , and morphologies of distant field galaxies seen through the disk of the foreground galaxy . this conceptually simple approach unfortunately suffers from an equally simple problem ; the general distribution of disk stars in the foreground galaxy reduces the contrast on background galaxy images , and foreground star clusters and hii regions add strongly to the confusion . high sensitivity is required in order to reach a surface density of background galaxies which is large enough to derive a statistically significant result . high angular resolution and color information are required to assist with the separation and identification of background galaxy images from objects in the foreground galaxy . hubble space telescope ( hst ) wide - field planetary camera 2 ( wfpc2 ) images offer a significant advantage over images from ground - based telescopes in their greatly improved resolution . this reduces the perturbation of faint galaxy images by nearby foreground objects , and facilitates the separation of stellar objects from galaxies . color information is also important ; a foreground compact hii region will be blue compared to the image of a distant galaxy , whether or not there is any amount of obscuration . once galaxies have been identified , their counts and colors can be compared with counts and colors of galaxies in reference fields not covered by a foreground galaxy . the hst wfpc2 archive contains many images of background galaxy fields and of fields covering parts of nearby galaxies . as an example of the data available for this study , and an illustration of the analysis problems which must be overcome before quantitative results can be obtained , we show in the left panel of figure 1 one wf frame ( wf3 , 13 @xmath12 13 in size ) from a typical reference field ( the hubble deep field ) , and in the right panel a similar - sized portion of a deep exposure on ngc 4536 . we shall describe both of these images in more detail in following sections of this paper . for the moment it is sufficient to note that the differences in the counts and colors of background galaxies visible in the two panels contain the information we seek on the opacity of the foreground galaxy . only a few background galaxies can be discerned visually with any certainty in the right panel . however , before we can conclude that the foreground galaxy is quite opaque , we obviously need to understand quantitatively how the data analysis methods we use to determine the counts and colors of the background galaxies are affected by structural features in the foreground galaxy . in this paper we describe a new method , the _ synthetic field method _ , which permits us to quantify and calibrate the effects of crowding and confusion and to determine the accuracy with which statements can be made about the total opacity and reddening of an average line of sight through the foreground galaxy . these synthetic fields are obtained by adding the hdf reference field images into the foreground galaxy image ; the combined image is then processed in the same way as the original foreground galaxy image alone . the procedure is repeated with different values of extinction applied to the reference field , and a plot drawn of the final number counts in each simulation versus the assumed extinction in order to ascertain the `` best '' fit to the actual counts of real background galaxies . can be estimated separately from the biases owing to confusion and crowding in the foreground galaxy field . finally , a comparison between the average colors of , respectively , the control hdf galaxies and the real background galaxies will allow an estimate of the degree of reddening . compared to the foreground galaxy fields we analyze , the hdf frames are virtually noiseless ; synthetic fields can therefore be constructed by adding suitably attenuated versions of them directly into the foreground galaxy images , without degrading the sensitivity of the data . figure [ histograms ] shows 4 cumulative histograms of galaxy counts in @xmath13 images which illustrate the steps in the _ synthetic field method _ : histogram _ a _ is for field galaxies in a version of the hdf to which noise has been added in order to approximate the shorter integration time used for the exposures of ngc 4536 , as well as the higher sky background at the position of the spiral ; _ b _ is for hdf `` control '' galaxies in an un - extincted ngc 4536 simulation ; _ c _ is for hdf galaxies in a simulation with @xmath14 0.6 mag of extinction at @xmath11 control field has been attenuated to mimic @xmath14 0.6 mag of extinction . ] ; and finally _ d _ is for real background galaxies in the ngc 4536 field . from the figure , we would conclude that there is about 1 mag of extinction at @xmath11 averaged over the wf2 and wf3 fields in this region of the foreground galaxy , and about 0.1 mag of average extinction at @xmath11 in the region of ngc 4536 covered by the wf4 field . clearly , one major limitation of our method is that the results are only statistical in nature , i.e. , the method does not give an answer for the extinction and reddening along any _ specific _ line of sight through the foreground galaxy , but only a statistical estimate of these quantities averaged over some substantial fraction of the foreground galaxy image . the accuracy of the method is limited not only by the counting statistics of background galaxies , but also by the intrinsic inhomogeneities in their spatial distribution . these uncertainties must also be quantified in order to provide a convincing result . in addition , there are several smaller selection effects which plague the analysis and which will be discussed later ; for instance , the fact that field galaxies also show a mild color magnitude dependence ( tyson 1988 ; williams et al . 1996 ) must also be taken into account . another limitation is that , while the numbers of galaxies probe the whole disk ( there is useful information in both detecting or not detecting a background galaxy ) , the conclusions from the colors of the galaxies will be biased in favor of regions of lower opacity ( because we need to detect the galaxies in order to measure there colors ) . therefore , it is possible to determine an extinction law by combining the number - count and color information only when we can safely assume that nowhere in the region of interest is the extinction so high that we can not sample it with background galaxies ( see appendix ) . in this paper we present a description of the _ synthetic field method _ through a detailed application to deep wfpc2 images of the sc spiral ngc 4536 . in order to examine the range of applicability of the method , we also analyze shallow images of the sbm magellanic dwarf irregular ngc 3664 ( ddo95 ) . we find substantial opacity in both galaxies , although the precision of the result is low for ngc 3664 , a consequence of the shorter exposure time used for the observations of this galaxy . in future papers we intend to apply the method to images of other nearby galaxies drawn from the hst archives . we begin in [ reffield ] with a discussion of the reference field and the processing necessary in order to render it useful for our present purposes . next in [ n4536 ] we describe the data on the foregound galaxy ngc 4536 which we have chosen to illustrate the method . section [ photometry ] describes the methods we use to identify and measure the magnitudes of field galaxies . section [ results ] presents the synthetic field simulations and the results on extinction through the disk of ngc 4536 . section [ n3664 ] presents an abbreviated discussion applying the method to ngc 3664 . in [ errors ] we examine the various sources of errors and biases we have been able to identify . finally , we summarize and discuss our results on the extinction and reddening through these two galaxies in [ summary ] .

we describe a new , direct method for determining the opacity of foreground galaxies which does not require any _ a priori _ assumptions about the spatial distribution or the reddening law of the obscuring material . the method is to measure the colors and counts of background galaxies which can be identified through the foreground system . the method is calibrated , and the effects of confusion and obscuration are decoupled by adding various versions of a suitable deep reference frame containing only field galaxies with known properties into the image of the foreground galaxy , and analyzing these `` synthetic field '' images in the same way as the real images . we test the method on hst wfpc2 archived images of two galaxies which are quite different : ngc 4536 is a large sc spiral , and ngc 3664 is a small magellanic irregular . 2h 3coco 3nh # 110 2 3 # 1 # 2 # 3 # 4 # 1 , # 2 , # 3 , # 4 # 1#2=.45 = .45 # 1 = 0.85 # 1#2#3#4#5#6#7 to#2 ' '' '' = 2 = 2

we describe a new , direct method for determining the opacity of foreground galaxies which does not require any _ a priori _ assumptions about the spatial distribution or the reddening law of the obscuring material . the method is to measure the colors and counts of background galaxies which can be identified through the foreground system . the method is calibrated , and the effects of confusion and obscuration are decoupled by adding various versions of a suitable deep reference frame containing only field galaxies with known properties into the image of the foreground galaxy , and analyzing these `` synthetic field '' images in the same way as the real images . we test the method on hst wfpc2 archived images of two galaxies which are quite different : ngc 4536 is a large sc spiral , and ngc 3664 is a small magellanic irregular . the reference frames are taken from the hubble deep field . from the background galaxy counts , ngc 4536 shows an extinction 1 mag in the northwestern arm region , and lower than 0.5 mag in the corresponding interarm region ( no correction for inclination has been attempted ) . however , from the galaxy colors , the same reddening of is observed in both the arm and the interarm regions . in the interarm region , the combination of extinction and reddening can be explained by a diffuse component with a galactic reddening law ( ) . in the spiral arm , however , the same diffuse , low opacity component seems to coexist with regions of much higher opacity . since the exposures are shorter the results for ngc 3664 are less clear , but also appear to be consistent with a two component distribution . 2h 3coco 3nh # 110 2 3 # 1 # 2 # 3 # 4 # 1 , # 2 , # 3 , # 4 # 1#2=.45 = .45 # 1 = 0.85 # 1#2#3#4#5#6#7 to#2 ' '' '' = 2 = 2

astro-ph9806001

r

synthetic fields were produced with varying + amounts of ( spatially uniform ) attenuation and reddening ( table 2 ) . the idea is to attenuate the hdf fields until one recovers the same number of simulated and real background galaxies . this attenuation , derived from the number - counts , should correspond to the average extinction through the disk of ngc 4536 to an uncertainty given by the poisson and clustering errors . in practice , what we measure is : @xmath39 @xmath40 is the normalization , in this case the number of hdf galaxies recovered in the synthetic fields without attenuation , and @xmath41 parametrizes the dependence of the number vs. extinction curve on object selection biases ( [ ext4536 ] ) . the reddening suffered by the background galaxies is found by comparing their average color to the average color of the hdf galaxies recovered from the synthetic fields . because galaxies have a color magnitude dependence , one must be careful to perform this comparison with simulations that have the same extinction as that measured ( from the counts ) for the real galaxies or that have the same magnitude limit as the extinction - corrected limit of the real galaxies . the selection biases of the real and synthetic samples of galaxies , and especially the color selection bias ( [ colbias ] ) , should also be the same for the comparison to be meaningful . to produce the synthetic fields , we : ( 1 ) scaled the hdf wfc frames to the exposure times of the ngc 4536 mosaics ; ( 2 ) attenuated the hdf frames to mimic different amounts of attenuation and reddening ; ( 3 ) added them in directly to the images of the spiral . to improve the statistics , at each attenuation / reddening we added the three hdf wfc frames , one at a time , to each one of the ngc 4536 wfc frames . what we call one simulation includes the results of repeating the procedure with 3 synthetic fields , one for each hdf wfc frames . as in the case of the real background galaxies , the photometry on the synthetic frames was done with sextractor , and the threshold surface brightness was fixed in the @xmath11 image . the identification of control galaxies was done , like that of real background galaxies , by visual inspection of each synthetic frame ( as opposed to , for example , through cross - correlation with a list of known hdf galaxies ) . systematics and confusion should thereby affect synthetic and real galaxies in the same way . since we did not know _ a priori _ the extinction law for the disk , we made simulations with both galactic reddening ( fitzpatrick 1986 ) and completely grey extinction ( i.e. , the hdf was attenuated equally in both the f555w and the f814w passbands ) . we hypothesize that the extinction through galaxy disks will lie somewhere in between these two limiting cases . another reason to have the two sets of simulations is that they should establish a relative scale that takes into account all possible systematic errors , against which to measure the attenuation and the reddening of the background galaxies . we also constructed synthetic field simulations with a `` mixed '' extinction law ( the hdf @xmath36 frame was more attenuated than the @xmath13 frame , but less than for galactic reddening ) , to check that the color scale established by the two limiting cases was roughly linear . we covered a large range in attenuation , from no attenuation at all up to 2.6 mag in both passbands . since ngc 4536 is inclined at @xmath42 to the line of sight ( de vaucouleurs et al . 1991 ) , we performed these highly - attenuated simulations anticipating the possibility of a face - on optical depth of @xmath43 = 1 , both with grey and with galactic reddening extinction curves . table 2 shows the input parameters of the simulations , as well as the number and average output color of the hdf galaxies recovered from the ngc 4536 frames ; a line indicating the actual ngc 4536 observations is included for comparison . to assess the effects of crowding alone , we compared the `` degraded '' hdf frames ( [ synthetic ] ) to the simulation without extinction , i.e. , a synthetic field where the hdf was added to the ngc 4536 frames without any attenuation . figures [ ihist ] and [ vhist ] compare the average numbers , of hdf galaxies only , recovered from the ngc 4536 frames in the simulation , against the average number per @xmath20 and @xmath44 bin , respectively , of galaxies in the `` degraded '' hdf . the effect of crowding on the number - counts is , indeed , dramatic . given the isophotal @xmath13 brightness limit , while the hdf galaxies in the `` degraded '' frame are complete to at least @xmath20 = 25 , when added to the ngc 4536 they are complete only to @xmath20 = 24 in the wf4 frame and , optimistically , to @xmath20 = 23 in the wf2 and wf3 frames . this is the range where galaxy clustering is most noticeable ( [ clusterr ] ) . on the other hand , we were able to detect galaxies up to an integrated ( isophotal ) magnitude of @xmath20 = 26 in all frames . the @xmath36 histogram shows that we were able to detect many more blue , faint galaxies in the wf4 ngc 4536 field . the histograms of the recovered synthetic galaxies , however , might suffer from two competing effects : the confusion of faint wings with the foreground disk , and the contamination of the photometric aperture with foreground objects . as described below ( [ bgerr ] ) , when using isophotal magnitudes galaxies are measured , on average , 0.1 mag too bright in the f814w bandpass , and up to 0.6 mag in the f555w filter , depending both on the crowding and on the faintness of the object . fortunately , our investigation does not require absolute or total measurements of the galaxy brightnesses , as long as everything is compared in the same _ relative _ scale provided by the simulations . an absolute measurement of the total magnitude limit is needed only to estimate the expected clustering error . for this purpose , we correct the @xmath20 completeness limit for the faulty background subtraction , and we also assume that total magnitudes are 0.3 brighter than isophotal . after an additional correction for the extinction ( [ ext4536 ] ) , we set our completeness limits at @xmath20 = 23.7 in the wf4 field , and at @xmath20 = 21.7 in the wf2 and wf3 frames . figures [ simreali ] , [ simrealv ] , and [ simrealcol ] compare the number of real galaxies to the number of hdf `` control '' galaxies recovered in the simulations without attenuation , per @xmath13 ( isophotal ) magnitude bin , @xmath36 ( isophotal ) magnitude bin , and color bin , respectively . the effects of extinction are readily noticeable in the wf2 and wf3 fields , both from the reduction in the number - counts and from the shift to fainter magnitudes of the real galaxies . for the wf4 field , any effects are much less apparent . the reddening , though , is harder to discern from figure [ simrealcol ] , even for the more extincted wf2 and wf3 images . the relative photometric error for the individual galaxies was estimated by comparing the three measurements we had of each one of the simulated objects in the synthetic fields without attenuation ( each hdf frame was added to each ngc 4536 frame ) . therefore , it includes the effect of differential crowding , and amounts to 0.16 mag at @xmath13 ( isophotal ) and 0.26 mag at @xmath36 ( isophotal ) . however , the error in ( @xmath45 ) for each galaxy is only 0.10 mag , given that the color has been measured using a small , fixed aperture of 05 diameter , precisely to minimize the impact of crowding ( see [ bgerr ] ) . figure [ fext4536 ] shows the comparison between the number of real galaxies ( horizontal lines ) and the average number of `` control '' galaxies recovered in the simulations at each given @xmath13 attenuation . the top panel displays the results for the wf2 and wf3 fields ; the bottom panel , those for the wf4 image . the solid triangles are for simulations with galactic reddening ; the open triangles , for synthetic fields with grey extinction . the different shapes of the curves for both types of extinction illustrate the dependence of the number - counts on the colors of the galaxies . the actual measurement of the extinction @xmath46 was performed by linearly interpolating between the simulations bracketing the real galaxies . the error bars include poisson and clustering errors ( [ clusterr ] ) . we find for the arm region of ngc 4536 ( wf2 and wf3 fields ) an absorption of @xmath47 mag in the case of grey extinction , and @xmath48 mag in the case of a galactic reddening law . without the contribution for clustering , the purely poisson error is @xmath49 mag . for the interarm and outside area ( wf4 ) , the results are , respectively , @xmath50 mag ( @xmath51 mag without clustering error ) for grey extinction , and @xmath52 0.52 mag ( @xmath53 mag without clustering error ) for galactic reddening . the @xmath54 error of 0.37 ( 0.21 ) mag is already included ; the figure shows that the difference between the attenuation inferred from the two models increases with extinction . the difference is in the sense that we expect ; it is due to our color selection bias , which favors the detection of faint galaxies ( statistically blue ) when they are reddened ( [ colbias ] ) . the difference , however , is smaller than the errors . for the background galaxies , we measure a mean color of @xmath55 in the arm , and of @xmath56 in the interarm and `` outside '' region . figure [ fred4536 ] shows the comparison of the color of the background galaxies to those of the simulations . we remind the reader that this is the appropriate comparison , rather than a confrontation between the two samples ( i.e. , wf2+wf3 and wf4 ) , given their different magnitude limits and all the systematics that come into play in the presence of severe crowding . we also point out that the purpose of this figure is to compare the color of the background galaxies to the synthetic fields closest in extinction and object selection biases ; the locus of the real galaxies in the plot does not necessarily imply an extinction law for the obscuring material in the foreground disk , unless we can safely assume that the whole region is sampled by galaxies whose colors we can measure ( [ discussion ] and appendix ) . the left panel shows the results for the wf2 and wf3 fields ; the right panel , those for wf4 . the simulations with galactic reddening ( open triangles ) do not follow exactly the theoretical extinction law ( solid line ) for large absorptions , neither do the simulations with grey extinction ( filled triangles ) follow a constant line in color . the departure of the grey simulations from the zero - reddening line is due to our selection for red galaxies [ colbias ] , and to the color magnitude relation of galaxies . as we go to larger extinctions , given our detection magnitude limit we are left with statistically brighter galaxies , which are also intrinsically redder . the deviation of the reddened simulations from the theoretical galactic reddening line is due to the systematic error in the background subtraction in crowded areas described in [ bgerr ] . in the case of wf4 , even if it is less crowded , we still see the effect because our magnitude limit is fainter , and faint galaxies are proportionally more affected by the problem . this is also the cause of the relative shift between the scales of the two panels . the wf2 and wf3 images of ngc 4536 are more crowded than the wf4 field ; statistically , _ all _ galaxies in the former fields have been measured relatively bluer , producing the downward shift of the whole color vs. extinction plot . all these systematic effects will affect the real galaxies in the same way and should not bias the estimate of the reddening , as long as the scale defined by the simulations with the two limiting extinction laws is linear . to check that this is the case we have performed simulations with a `` mixed '' extinction law light of each individual galaxy is more attenuated than the @xmath11 light , but less than in the galactic reddening case ; this type of extinction can be caused by an unresolved clumpy dust distribution ( witt & gordon 1996 ) ] . the output of the `` mixed '' simulations is shown in figure [ fmix4536 ] . when compared with their input line , the simulations with a `` mixed '' reddening law seem more affected by the selection bias that pushes the grey simulations redward than by the background subtraction that pushes the galactic reddening simulations blueward . the simulations , however , follow the input line within the errors , which shows that the color scale is , indeed , roughly linear . the background galaxies behind the northwestern arm of ngc 4536 ( wf2 and wf3 fields , figure [ fred4536 ] , left ) fall in between the lines for the completely grey extinction and the galactic reddening law in the the color vs. extinction plot . since , unfortunately , the color line of the grey simulations shows a kink precisely at the location of the real background galaxies , to find the reddening we will rather use the color obtained by interpolating between the grey simulations with @xmath46 = 0.58 mag and @xmath46 = 1.51 mag , at the extinctions ( inferred from the grey and galactic reddening models , respectively ) of the background galaxies . the interpolation yields @xmath28(@xmath57)@xmath58 at @xmath46 = 0.74 mag , and @xmath28(@xmath57)@xmath59 at @xmath46 = 1.07 mag . therefore , the background galaxies suffer a reddening of @xmath60 mag ( grey extinction model ) or @xmath61 mag ( galactic reddening law ) . the error in the reddening , already included , is 0.18 mag . the background galaxies in the interarm region ( wf4 , figure [ fred4536 ] , right ) , however , seem to follow the galactic reddening line . comparing their color to the mean color of the simulation without extinction , they exhibit a reddening of @xmath62 mag , regardless of the attenuation model used .

ngc 4536 shows an extinction 1 mag in the northwestern arm region , and lower than 0.5 mag in the corresponding interarm region ( no correction for inclination has been attempted ) . however , from the galaxy colors , the same reddening of is observed in both the arm and the interarm regions . in the interarm region , the combination of extinction and reddening can be explained by a diffuse component with a galactic reddening law ( ) . in the spiral arm , however , the same diffuse , low opacity component seems to coexist with regions of much higher opacity . since the exposures are shorter the results for ngc 3664 are less clear , but also appear to be consistent with a two component distribution .

we describe a new , direct method for determining the opacity of foreground galaxies which does not require any _ a priori _ assumptions about the spatial distribution or the reddening law of the obscuring material . the method is to measure the colors and counts of background galaxies which can be identified through the foreground system . the method is calibrated , and the effects of confusion and obscuration are decoupled by adding various versions of a suitable deep reference frame containing only field galaxies with known properties into the image of the foreground galaxy , and analyzing these `` synthetic field '' images in the same way as the real images . we test the method on hst wfpc2 archived images of two galaxies which are quite different : ngc 4536 is a large sc spiral , and ngc 3664 is a small magellanic irregular . the reference frames are taken from the hubble deep field . from the background galaxy counts , ngc 4536 shows an extinction 1 mag in the northwestern arm region , and lower than 0.5 mag in the corresponding interarm region ( no correction for inclination has been attempted ) . however , from the galaxy colors , the same reddening of is observed in both the arm and the interarm regions . in the interarm region , the combination of extinction and reddening can be explained by a diffuse component with a galactic reddening law ( ) . in the spiral arm , however , the same diffuse , low opacity component seems to coexist with regions of much higher opacity . since the exposures are shorter the results for ngc 3664 are less clear , but also appear to be consistent with a two component distribution . 2h 3coco 3nh # 110 2 3 # 1 # 2 # 3 # 4 # 1 , # 2 , # 3 , # 4 # 1#2=.45 = .45 # 1 = 0.85 # 1#2#3#4#5#6#7 to#2 ' '' '' = 2 = 2

1607.05876

i

the set of all rotations in @xmath5 forms a group denoted by @xmath1 . we may think of it as the group of @xmath6 orthogonal matrices with unit determinant . as a topological space it has the structure of a smooth @xmath7-dimensional submanifold of @xmath8 . the group structure is compatible with the smooth one in the sense that the group operations are smooth maps , so it is a lie group . the space @xmath1 when @xmath9 has a fascinating topological property there exist closed paths in it ( starting and ending at the identity ) that can not be continuously deformed to the trivial ( constant ) path , but going twice along such a path gives another path , which is deformable to the trivial one . for example , if you rotate an object in @xmath10 by @xmath11 along some axis , you get a motion that is not deformable to the trivial motion ( i.e. , no motion at all ) , but a rotation by @xmath12 is deformable to the trivial motion . further , a rotation by @xmath11 along any axis can be deformed to a rotation by @xmath11 along any other axis . we shall call a _ full rotation _ in @xmath5 any motion that corresponds to a closed path in @xmath1 , starting and ending at the identity . thus , it turns out that there are two classes of full rotations : topologically trivial , i.e. , deformable to the trivial motion , and topologically nontrivial . every nontrivial full rotation can be deformed to any other nontrivial full rotation . two consecutive nontrivial full rotations produce a trivial one . for any topological space , one can consider the set of closed paths starting and ending at some fixed point , called _ base - point_. two closed paths that can be continuously deformed to each other , keeping the base - point fixed , are called _ homotopic_. one can multiply closed paths by _ concatenation _ , i.e. , take the path obtained ( after appropriate reparametrization ) by traveling along the first and then along the second . there is also an inverse for each path the path traveled in reverse direction . these operations turn the set of homotopy classes of closed paths ( with a given base - point ) into a group and it is an important topological invariant of any topological space . it was introduced by poincar and is called the _ first homotopy group _ or the _ fundamental group _ of the space , denoted by @xmath13 . thus , the property of @xmath1 stated above is written concisely as @xmath14 . this specific topological property in the case @xmath15 plays a fundamental role in our physical world . to the two homotopy classes of closed paths in @xmath16 correspond precisely two principally different types of elementary particles : bosons , with integer spin , and fermions , with half - integer spin , having very distinct physical properties . the difference can be traced to the fact that the complex ( possibly multicomponent ) wave function determining the quantum state of a boson is left unchanged by a rotation by @xmath11 of the coordinate system while the same transformation multiplies the wave function of a fermion by @xmath17 . this is possible since only the modulus of the wave function has a direct physical meaning , so measurable quantities are left invariant under a full rotation by @xmath11 . however , as discovered by pauli and dirac , one needs to use wave functions having this ( unexpected ) transformation property for the correct description of particles with half - integer spin , such as the electron . the careful analysis showed ( @xcite ) that the wave function has to transform properly only under transformations which are in a small neighborhood of the identity . a `` large '' transformation such as a rotation by @xmath11 can be obtained as a product of small transformations , but the transformed wave function need not come back to itself there may be a complex phase multiplying it . from continuity requirements it follows that if one takes a closed path in @xmath16 which is contractible , the end - point wave function must coincide with the initial one . therefore , a rotation by @xmath12 should bring back the wave function to its initial value and so the phase factor corresponding to a @xmath11-rotation can only be @xmath17 . what we have just described is the idea of the so - called _ projective _ representations of a lie group , which we have to use in quantum physics . as we see on the example of @xmath16 , they exist because the latter is not simply - connected , i.e. , @xmath18 is not trivial . projective representations of a non - simply - connected lie group are in fact representations of its covering group . in the case of @xmath16 this is the group @xmath19 of @xmath20 unitary matrices with unit determinant . topologically , this is the three - dimensional sphere @xmath21 ; it is a double cover of @xmath16 and the two groups are locally isomorphic and have the same lie algebra . the standard proof that @xmath0 when @xmath15 uses substantially lie theory . a @xmath22 homomorphism @xmath23 is exhibited , which is a local isomorphism of lie groups . this is the double covering map in question , sending any two antipodal points of @xmath19 ( i.e. , @xmath21 ) to one point in @xmath16 . the case @xmath24 reduces to the above result by applying powerful techniques from homotopy theory . there are several more or less easy geometric methods to unveil the nontrivial topology of @xmath16 . among them , a well - known demonstration is the so - called `` dirac s belt trick '' in which one end of a belt is fastened , the other ( the buckle ) is rotated by @xmath12 . then without changing the orientation of the buckle , the belt is untwisted by passing it around the buckle ( see , e.g. , @xcite for nice java applets and explanations ) . a refinement of `` dirac s belt trick '' was proposed in @xcite where an isomorphism was constructed between homotopy classes of closed paths in @xmath16 and a certain factor group of the group @xmath25 of pure braids with three strands . this factor group turns out to be isomorphic to @xmath3 . the idea is fairly simple and is based on the following experiment : attach the ends of three strands to a ball , attach their other ends to the desk , perform an arbitrary number of full rotations of the ball to obtain a plaited braid . then try to unplait it without further rotating the ball . as expected , braids that correspond to contractible paths in @xmath16 are trivial , while those corresponding to noncontractible paths form a single nontrivial class . while the method of @xcite is simple and easy to visualize , it has the disadvantage that it does not lend itself to a generalization to higher dimensions . ( a geometric braid in @xmath5 is always trivial when @xmath24 . ) the present paper takes a different , more algebraic approach . we study a certain discrete ( in fact finite ) group of homotopy classes of paths in @xmath1 , starting at the identity and ending at points which are elements of some fixed finite subgroup of @xmath1 . it turns out that it is convenient to use the finite group of rotational symmetries of the hyperoctahedron ( the polytope in dimension @xmath4 with vertices @xmath26 ) . each homotopy class contains an element consisting of a chain of rotations by @xmath27 in different coordinate planes . these simple motions play the role of generators of our group . certain closed paths obtained in this way remain in a small neighborhood of the identity ( in an appropriate sense , explained later ) and can be shown explicitly to be contractible . thus , certain products among the generators must be set to the identity and we get a group defined by a set of generators and relations . interestingly , the number of ( independent ) generators is @xmath28 and the relations , apart from one of them , are exactly artin s relations for the braid group @xmath2 . in this way we obtain for each @xmath4 a finite group , which is the quotient of @xmath2 by the normal closure of the group generated by the additional relation . when @xmath15 the order of the group turns out to be 48 and it is the so - called _ binary octahedral group _ which is a nontrivial extension by @xmath3 of the group of rotational symmetries of the octahedron . we may think of the former as a double cover of the latter and this is a finite version of the double cover @xmath23 . the next groups in the series have orders 384 , 3840 , 46080 , etc . ; in fact the order is given by @xmath29 . note that these groups have the same orders as the coxeter groups of all symmetries ( including reflections as well as rotations ) of the respective hyperoctahedra , but they are different . this is analogous to the relationship between @xmath30 and @xmath1 on the one hand , and @xmath31 and @xmath1 on the other . it turns out that the subgroup of homotopy classes of closed paths , i.e. @xmath32 , in each case either coincides or lies in the center of the respective group and is isomorphic to @xmath3 . factoring by it , the respective rotational hyperoctahedral groups are obtained . we believe that these are new presentations of all rotational hyperoctahedral groups and their double covers .

the fundamental group of appears in our approach as the center of a certain finite group defined by generators and relations . the latter is a factor group of the braid group , obtained by imposing one additional relation and turns out to be a nontrivial central extension by of the corresponding group of rotational symmetries of the hyperoctahedron in dimension .

we describe an algebraic proof of the well - known topological fact that . the fundamental group of appears in our approach as the center of a certain finite group defined by generators and relations . the latter is a factor group of the braid group , obtained by imposing one additional relation and turns out to be a nontrivial central extension by of the corresponding group of rotational symmetries of the hyperoctahedron in dimension .

1512.05599

i

in the study of dynamical systems with complicated and possibly chaotic dynamics , average quantities are often of more interest than any particular solution trajectory . this is partly because of the difficulty of computing a trajectory precisely and partly because average quantities are more important in many applications . for instance , one might seek time - averaged drag forces in a model of an oil pipeline or ensemble - averaged temperatures in a stochastic climate model . one way to estimate averages quantitatively is to integrate the dynamical system numerically and average over the resulting particular solution . such direct numerical simulations are often straightforward , but the accuracy of the result is not guaranteed unless errors are rigorously controlled . moreover , even a perfectly accurate solution does not give information about the different trajectories that result from different initial conditions . finally , the computational cost of computing well - converged averages is often prohibitive , especially in systems that are high - dimensional or stochastic . a complementary approach , which we pursue here , is to prove bounds on average quantities directly from the governing equations . an advantage over numerical integration is that bounds can be proven without knowing any solution trajectories . furthermore , they can be proven for all possible trajectories at once , or for all trajectories within a given region of state space . on the other hand , it is generally difficult to prove bounds that are tight enough to give good estimates of the average quantities being bounded . the aim of this work is to develop methods for proving bounds that are tight , meaning that the upper and lower bounds are equal or nearly so . we assume that the quantity of interest can be described by a function @xmath0 , where @xmath1 is the state vector of a dynamical system , and we seek to bound averages of @xmath2 . in deterministic systems , we consider averages over infinite time , @xmath3 \,dt.\ ] ] if the above limit does not exist it can be replaced by limit superior or inferior for the upper and lower bound problems , respectively . the value of @xmath4 depends in general on which trajectory @xmath5 is being averaged over . in stochastic systems with a stationary probability distribution @xmath6 , we consider stationary ensemble averages , @xmath7 one obstacle to proving tight bounds is , for reasons described shortly , the need to determine whether certain complicated expressions are sign - definite . as proposed in @xcite , this can be done systematically with computer assistance for finite - dimensional systems with polynomial dynamics . the main idea , described further in [ ss : sosboundsreview ] , is to construct a polynomial whose non - negativity implies the desired bound . by the methods of sum - of - squares ( sos ) programming @xcite , a sufficient condition for this non - negativity can then be posed as a semidefinite program ( sdp ) . in deterministic systems there is a second obstacle to proving tight bounds . it is generally easiest to construct bounds that hold for all possible initial conditions . sometimes this is desired , but other times one is interested in a particular local attractor , and bounds holding globally are not generally tight for averages over a local attractor . in this sense , the local bound is spoiled by any other invariant structure in the state space , such as another attractor or an unstable fixed point . we pursue two ways of obtaining tight bounds specific to a local attractor . the first is to enforce conditions that imply the bound only on an absorbing set around the attractor , thereby omitting other invariant structures . the second is to add noise to the system and prove bounds for ensemble averages in the vanishing noise limit . if the system is stochastically stable , then under certain conditions this limit will agree with the corresponding deterministic time average @xcite . note that these ideas are applicable irrespectively of any special structure in the system ( such as hamiltonian ) , and can in principle be applied to systems of arbitrarily high but finite dimension . throughout this work , we illustrate the methods described using the van der pol oscillator @xcite , which can be written as @xmath8 where a dot denotes @xmath9 . the parameter @xmath10 sets the strength of the nonlinear damping . there is a limit cycle that attracts all trajectories except the unstable fixed point at the origin ( figure [ f : vdpphaseportrait ] ) , and the global invariant set is composed of the limit cycle and the fixed point . the system is a standard example of a nonlinear oscillator and has been studied extensively , including with stochastic forcing @xcite . here we find nearly tight bounds on averages of @xmath11 both with and without noise . the rest of this work is organized as follows . section [ ss : sosboundsreview ] reviews the framework of @xcite for bounding deterministic averages and uses it to find upper bounds on @xmath12 in the van der pol system . section [ ss : localbounds ] extends the framework to give attractor - specific bounds , which we use to find lower bounds on @xmath12 over the van der pol limit cycle . these lower bounds are larger than zero and thus do not apply to the unstable fixed point . the bounding methods for stochastic dynamical systems are described in [ ss : generalnoiseformulation ] , and they are specialized to the case of small and vanishing noise in [ ss : smallnoise][ss : vanishingnoise ] . the methods of these sections give bounds on @xmath13 in the van der pol example for a range of noise amplitudes . section [ s : furthercomments ] discusses the limitations of our methods and gives ideas for improvement , and [ s : conclusion ] offers concluding remarks .

the dynamics and the quantities to be bounded are assumed to be polynomial functions of the state variables . we describe two closely related ways past this obstacle : one that requires knowing a subset of the basin of attraction , and another that considers the zero - noise limit of the corresponding stochastic system . the bounding methods are illustrated using the van der pol oscillator . we obtain similarly tight upper and lower bounds on stochastic expectations for a range of noise amplitudes . limitations of our methods for certain types of deterministic systems are discussed , along with prospects for improvement .

we describe methods for proving upper and lower bounds on infinite - time averages in deterministic dynamical systems and on stationary expectations in stochastic systems . the dynamics and the quantities to be bounded are assumed to be polynomial functions of the state variables . the methods are computer - assisted , using sum - of - squares polynomials to formulate sufficient conditions that can be checked by semidefinite programming . in the deterministic case , we seek tight bounds that apply to particular local attractors . an obstacle to proving such bounds is that they do not hold globally ; they are generally violated by trajectories starting outside the local basin of attraction . we describe two closely related ways past this obstacle : one that requires knowing a subset of the basin of attraction , and another that considers the zero - noise limit of the corresponding stochastic system . the bounding methods are illustrated using the van der pol oscillator . we bound deterministic averages on the attracting limit cycle above and below to within 1% , which requires a lower bound that does not hold for the unstable fixed point at the origin . we obtain similarly tight upper and lower bounds on stochastic expectations for a range of noise amplitudes . limitations of our methods for certain types of deterministic systems are discussed , along with prospects for improvement .

1512.05599

c

in this work we have presented computer - assisted methods for deriving bounds on average quantities in both deterministic and stochastic dynamical systems using sum - of - squares programming . we have given particular attention to proving bounds that apply only to trajectories approaching a particular attractor . one method is to use the @xmath67-procedure to omit segments of phase space on which the bounds do not need to hold . another strategy is to remove unstable invariant structures by adding noise to the system . this idea , proposed previously in @xcite , has been extended here by analyzing the weak and vanishing noise cases when the unstable structures to be omitted are repelling fixed points . these methods give improved bounds for weak but finite noise , and also in the rigorous limit of vanishingly weak noise . our methods have worked well when applied to the van der pol oscillator . the best deterministic and stochastic bounds proven throughout are summarized in figure [ f : bestbounds_vdp ] . in the deterministic case , we obtained upper and lower bounds on the infinite - time average of @xmath221 over the limit cycle that are all within 1% of the `` true '' values found by numerical integration . in the stochastic case , bounding the stationary expectation of @xmath11 at a variety of noise strengths , we obtained upper bounds all within 1% and lower bounds all within 10% of the `` true '' values found by solving the fokker - planck equation numerically . moving to dynamical systems other than the van der pol oscillator , whether the methods we have described can yield similarly tight deterministic and stochastic bounds depends on the details of those systems . if the dimension of a system is small enough for sos optimization to be computationally feasible , we expect that tight global bounds on deterministic averages can be obtained using the methods of [ ss : sosboundsreview ] . in fact , since the first draft of this work , the bounding techniques we have presented for deterministic systems have been successfully applied to the design of control systems for fluid flows @xcite . with stochastic forcing that is not too weak , we expect that fairly tight bounds on stationary expectations also can be obtained using the methods of [ ss : generalnoiseformulation ] . as the noise strength decreases , the tendency of unstable invariant structures to spoil tight bounds can be combatted by the methods of [ ss : smallnoise ] if these structures are repelling fixed points . new methods will be needed to maintain tight bounds as noise becomes weak in systems with other unstable structures , including saddle points . lastly , the methods of [ ss : localbounds ] can be used to bound averages on trajectories within an absorbing domain and , in particular , on a single attractor . this much is true for any dynamical system , but whether these bounds can be tight depends on the nature of the attractor . for instance , bounds for a chaotic attractor must apply not just to generic chaotic trajectories but also to all trajectories embedded within the attractor , such as saddle points and unstable orbits . what can be deduced about chaotic attractors is of particular interest if the methods presented here are to be applied to complex systems of physical and engineering relevance .

we describe methods for proving upper and lower bounds on infinite - time averages in deterministic dynamical systems and on stationary expectations in stochastic systems . the methods are computer - assisted , using sum - of - squares polynomials to formulate sufficient conditions that can be checked by semidefinite programming . in the deterministic case , we seek tight bounds that apply to particular local attractors . an obstacle to proving such bounds is that they do not hold globally ; they are generally violated by trajectories starting outside the local basin of attraction .

we describe methods for proving upper and lower bounds on infinite - time averages in deterministic dynamical systems and on stationary expectations in stochastic systems . the dynamics and the quantities to be bounded are assumed to be polynomial functions of the state variables . the methods are computer - assisted , using sum - of - squares polynomials to formulate sufficient conditions that can be checked by semidefinite programming . in the deterministic case , we seek tight bounds that apply to particular local attractors . an obstacle to proving such bounds is that they do not hold globally ; they are generally violated by trajectories starting outside the local basin of attraction . we describe two closely related ways past this obstacle : one that requires knowing a subset of the basin of attraction , and another that considers the zero - noise limit of the corresponding stochastic system . the bounding methods are illustrated using the van der pol oscillator . we bound deterministic averages on the attracting limit cycle above and below to within 1% , which requires a lower bound that does not hold for the unstable fixed point at the origin . we obtain similarly tight upper and lower bounds on stochastic expectations for a range of noise amplitudes . limitations of our methods for certain types of deterministic systems are discussed , along with prospects for improvement .

astro-ph9706276

i

in a previous paper we discussed the evolution and x - ray appearance of hot interstellar gas in a family of massive , slowly rotating , isolated elliptical galaxies having different ellipticities and rotation rates ( brighenti & mathews 1996 , a.k.a . paper 1 ) . when large , non - rotating ellipticals are flattened by anisotropic stellar velocities we found that the x - ray images are rather insensitive to variations in the galactic ellipticity however , when a small rotation is introduced the x - ray images become significantly flatter than the optical image when viewed perpendicular to the axis of rotation . as the hot gas flows inward in the galactic `` cooling flow , '' it forms a large disk comparable in radius to the effective radius and spins up to the local disk - plane circular velocity which can be quite large for massive ellipticals , @xmath4 km s@xmath5 , a velocity that should be resolved with axaf . after evolving from 1 gyr , when early galactic winds are assumed to have subsided , to 15 gyrs , about ten percent of the total baryonic mass of the galaxy cooled into this large disk . the final disposition of this cooled gas is uncertain ; low - mass star formation is one possibility but a significant amount of gas may remain as low density hii gas ionized by the stellar uv . now we wish to examine the evolution and x - ray appearance of interstellar gas in a second type of elliptical galaxy having a lower luminosity and larger rotation . in recent years it has become apparent that the stellar properties of elliptical galaxies divide into two types : ellipticals of high luminosity having ( modestly ) triaxial shapes , boxy isophotes , more pronounced central cores , less rotation and ( limited ) flattening by anisotropic stellar dispersion ; by contrast , ellipticals of low luminosity generally have disky isophotes , dense central stellar cusps , rotationally induced flattening , approximately axisymmetric geometry and isotropic stellar velocities ( davies et al . 1983 ; nieto et al . 1991 ; kormendy & bender 1996 ; tremblay & merritt 1996 ; faber et al . 1997 ) the changeover in elliptical properties occurs over a range of luminosities , @xmath6 to @xmath7 where both types coexist . both high and low luminosity ellipticals coexist on the fundamental plane ( faber et al . 1997 ) . our interest in the evolution of hot interstellar gas in low luminosity ellipticals has been motivated in part by the prospect of better x - ray observations that will be provided by axaf in the near future . in low luminosity ellipticals the x - ray emission from the hot gas is likely to be masked by the collective emission from ( low - mass ) x - ray binary stars ( e.g. kim , fabbiano & trinchieri 1992 ) . however , the stellar x - ray component is expected to have the same surface brightness distribution as the optical image so it should be possible in principle to subtract the stellar contribution from high quality axaf images , leaving only the emission of the hot gas . although such a subtraction would be difficult because of the low x - ray luminosity of the gas , it would be helped by the different surface brightness distributions expected for stars and gas ( see below ) , by consistent x - ray surface brightness fluctuations anticipated from the stellar component , and by the dissimilar x - ray spectra of stars and gas . the characteristic stellar velocity dispersion ( stellar temperature ) in ellipticals decreases with total stellar mass , @xmath8 ( faber et al . 1997 ) so the temperature of thermalized interstellar gas in virial equilibrium should also decrease with galactic mass and luminosity . however , the galactic binding energy is also proportional to @xmath9 so any additional source of energy in the interstellar gas , such as supernova explosions , may cause the interstellar gas in low luminosity ellipticals to become unbound and flow out of the galaxy as a wind . little is known at present about the x - ray emission from rapidly rotating , coreless , disky , low luminosity ellipticals ; ngc 4697 may be the only such elliptical with measured x - ray fluxes ( fabbiano , kim , & trinchieri 1992 ) . while the evidence for hot gas is currently weak or nonexistent , more may be learned in the near future . the gas - dynamical history of low luminosity , disky ellipticals is also of interest because the stellar disks may result from star formation in the disk of cold gas that is a natural product of rotating cooling flows . the sense of rotation of the stellar disks is identical to that of the bulge component , supporting an internal origin for the stellar disks rather than formation in a merging event . recently de jong & davies ( 1997 ) have reported that disky ellipticals have higher h@xmath3 photometric indices , indicating the presence of youthful stars . they suggest that stars in the disk component , if sufficiently young , could account for the apparent youthful age of the entire galaxy as determined by the population studies of worthey ( 1994 ) and others . it is of some interest therefore to explore the possibility that star formation has occurred in the disks of cold gas that are expected in rapidly rotating ellipticals . finally , the large rotationally supported disks of cooled gas are exposed to ultraviolet ionizing radiation present in galactic starlight . this raises the interesting possibility that the ionized component of these disks can be ( or has been ) observed in faint optical line emission . we find that surprisingly large masses ( @xmath10 @xmath2 ) of warm ( @xmath11 k ) , low density hii gas can reside in the outer parts of these gaseous disks where is it supported by rotation at the local galactic circular velocity and in pressure equilibrium with the ambient hot interstellar gas . the density of most of this hii gas is very low and radiates line emission extremely weakly . the presence of this warm component , which has not previously been discussed , eases somewhat the mystery regarding the ultimate disposition of galactic cooling flow gas after it cools . in the following we discuss the evolution of hot interstellar gas in a family of six low luminosity , ellipticals having different ellipticities , angular momenta and supernova heating rates . as in paper 1 we consider the rotating galaxies to be isolated ; gas inflow or ram pressure effects expected in a cluster environment are not considered here . we find that the radial extent of the disks , the mass of gas entering the disks , and the current mass of hot interstellar gas throughout the galaxies are all very sensitive to the assumed type ia supernova rate , assuming that the supernova energy is shared throughout the interstellar gas . in the most favorable circumstances for disk formation in rapidly rotating galaxies , the disks are very extended .

we describe the evolution of interstellar gas in a family of low luminosity elliptical galaxies all having but with different degrees of flattening ( e0 , e2 , and e6 ) and two current supernova rates , snu = 0.01 and 0.04 . the galaxies are composed of 90 percent dark matter , are rotationally flattened and have isotropic stellar velocity dispersions . as the rotating hot interstellar gas loses energy in the galactic potential , it cools onto a large disk .

we describe the evolution of interstellar gas in a family of low luminosity elliptical galaxies all having but with different degrees of flattening ( e0 , e2 , and e6 ) and two current supernova rates , snu = 0.01 and 0.04 . the galaxies are composed of 90 percent dark matter , are rotationally flattened and have isotropic stellar velocity dispersions . the soft x - ray luminosity of the hot interstellar gas after evolving for 15 gyrs decreases dramatically with increasing galactic rotation . as the rotating hot interstellar gas loses energy in the galactic potential , it cools onto a large disk . the outer radius of the disk can be much reduced by increasing the supernova rate which drives a gentle galactic wind transporting high angular momentum gas out of the galaxy . the total mass of cooled disk gas is less sensitive to the supernova rate . although the hot interstellar gas may be difficult to observe in rotating low - luminosity ellipticals , the cooled disk gas can be observed ( i ) in optical line emission since part of the cooled disk gas is photoionized by stellar uv and ( ii ) in the optical continuum , assuming the colder disk gas forms into luminous stars . the mass of hii gas ( ) may be much greater than previously realized since rotationally supported , low density hii contributes little to the global optical line emission . we interpret the stellar disks that are common ( or ubiquitous ) in low luminosity ellipticals as stars that have formed in the cold disk gas . the total mass of cold disk gas available for star formation is similar to the masses of stellar disks observed . the high stellar h photometric index observed in disky ellipticals can be understood by combining the light of young disk stellar populations with that of the old bulge population . _ subject headings _ : galaxies : evolution galaxies : disks galaxies : interstellar gas # 1#2#3#4 # 1#2 .2 in

astro-ph9706276

c

hot interstellar gas in low - luminosity ellipticals is more vulnerable to outflow than that in brighter ellipticals because the specific gravitational binding energy decreases with galactic luminosity along the fundamental plane . low - luminosity ellipticals are also thought to be rotationally flattened which causes the x - ray luminosity of interstellar gas to decrease sharply with increasing ellipticity . in our family of galaxies all with luminosity @xmath169 @xmath170 we find that @xmath77 is also very sensitive to the assumed supernova rate . in ellipticals having a `` low '' current supernova rate , snu@xmath74 , @xmath171 varies along the sequence e0 ; e2 ; e6 in the ratios 1.0 ; 0.0091 ; 0.0027 . for a higher supernova rate , snu@xmath75 , the corresponding ratios are : 1.0 ; 0.025 ; 0.0033 . while the x - ray emission from hot interstellar gas in the e0 galaxies would be easily observed with axaf ( by subtracting the stellar component if that were possible ) , the prospects for observing the interstellar contribution to @xmath77 for more realistic rotating galaxies of this @xmath33 are less optimistic . furthermore , low luminosity e0 galaxies are rare or non existent ( tremblay & merritt 1996 ) . the influence of past and current supernova rates on @xmath77 and other important observational parameters is not entirely clear . the higher of the two current supernova rates we consider , snu@xmath75 , generates an iron abundance within the half - light radius that is 1.5 to 3 times the stellar iron abundance . of course any observation of the x - ray iron features in rotating , low - luminosity ellipticals is likely to be representative of stellar x - ray sources , not the gas . but in more massive ellipticals the iron abundance in the interstellar gas is often much _ less _ than that in the stars ( arimoto et al . 1997 ) . this could imply that the supernova iron and possibly also its energy is not distributed throughout the interstellar medium as we have assumed here ; indeed the supernova energy is concentrated in hot bubbles that may rise in the cooling flow atmosphere . because of this as yet unsolved problem , we can not be sure that we have treated the supernova energy correctly in our models , particularly for the high supernova rate solutions . if our treatment of supernova energy is correct , however , the disks of cool gas are severely truncated when snu@xmath172 due to an enhanced outflow of high angular momentum gas from the outer parts of the galaxy . the mass of the disk remaining at time @xmath45 gyr @xmath78 is reduced by @xmath173 as snu@xmath174 increases from 0.01 to 0.04 . more luminous ellipticals such as those we discussed in paper 1 require much higher snu@xmath174 to alter the cold disks . of particular interest is the possibility of observing disks of cold gas that are expected in rotating ellipticals either directly as optical line emission or indirectly in the form of a younger stellar population . the column of unionized disk gas in our disks would produce profound and observable absorption of soft x - rays , but this can be avoided since gravitational clumping is expected in this neutral or molecular gas . we have estimated the density of ionizing photons along the disk plane and computed the column density of warm hii disk gas . the presence of hii disk gas should be independent of the likelihood of star formation in the colder neutral gas . for our low value of snu@xmath174 , we find that large masses of hii gas can be rotationally supported beyond @xmath175 kpc amounting to about one tenth of all the gas ejected from galactic stars but the density of this gas is too low to contribute to the observed optical line flux . in previous estimates of the total hii mass in ellipticals a constant hii density is usually assumed ; these masses may seriously underestimate the true mass by several orders of magnitude . in the future we intend to investigate the survivability of gas in the outer disk if the galaxy is moving through an external ( inter - cluster ) medium . most of the optical line emission in the disk comes from the central parts of the disk which are less sensitive to rotation and the supernova rate . the total h@xmath3 luminosities expected from disk hii are similar to those observed in ellipticals , implying that a significant component of optical line emission from these galaxies may originate in cooling flow disks . if the disk hii emission is not masked by other sources of warm gas , the optical line - emitting gas should be ( i ) systematically flatter than the stellar image and ( ii ) rotating at the circular velocity which exceeds the local mean line of sight velocity of galactic stars . we have found considerable support for the notion that stellar disks in low luminosity ellipticals are a natural result of the evolution of the interstellar gas . the inevitability of cold disk formation in galactic cooling flows is consistent with the finding that all low luminosity ellipticals may contain stellar disks since many are hidden due to low inclinations ( rix & white 1990 ) . the stellar disk and bulge are observed to share the same sense of rotation ; this argues against random merging events and supports star formation in cold disks as we propose here . the total mass of gas that enters the cold disk in 1 - 15 gyrs , about 10 percent of the total stellar mass @xmath56 , is very similar to the typical stellar mass observed in elliptical disks . within the approximation of our galactic models ( e.g. king and isothermal density profiles ; constant satoh @xmath176 factor , etc . ) and that of current observations of stellar disks ( most of which have been studied only in very flat e5 or e6 ellipticals ) , we believe that our non - exponential disks are similar to those observed . only three of the nine stellar disks studied by scorza & bender ( 1995 ) could be modeled with exponential disks and exponential fits can always be made over a limited range in radius . finally , we have demonstrated that the range of observed h@xmath3 photometric indices observed in disky ellipticals is just spanned by our models if luminous stars form in the cold gaseous disks . we are implicitly assuming here that the type ia supernova rate may vary among ellipticals to generate a range of disk masses ; at present there is no compelling reason to believe otherwise . a similar variation of disk masses could be obtained by beginning our calculation shortly before or after 1 gyr . if our ideas about star formation in disky ellipticals are correct , these galaxies could become ideal laboratories for studying successive generations of star formation . in principle abundances in the parent population ( bulge ) stars , in the interstellar gas that they have expelled , and in subsequent stellar ( disk ) generations can all be directly observed . while luminous star formation in disks provides a satisfactory explanation for the ultimate fate of cooled gas in low luminosity ellipticals , it is at present unclear why more luminous , slowly rotating ellipticals do not also have visible stellar disks since cold disks are expected there too ( paper 1 ) . within the many uncertainties regarding the star formation process , the stellar properties of all elliptical disks can be understood if stars of lower mass are favored in high pressure environments . maximum interstellar pressures in the most massive ellipticals are about 1000 times that in the interstellar medium of our galaxy so even the most massive stars formed may not be optically luminous ; in low - luminosity ellipticals such as we consider here the pressures are lower so stars at the upper imf cutoff may be optically luminous but insufficiently massive ( @xmath177 @xmath2 ) to produce snii . alternatively , cold and dynamically fragile stellar disks may have formed in luminous ellipticals and subsequently been destroyed or altered perhaps in the same merging events responsible for the overall boxy shapes of these galaxies . finally , hot ambient ( cluster ) gas of low angular momentum may move into luminous ellipticals and greatly reduce the size of cooling flow disks . we hope to address these problems in the near future .

the soft x - ray luminosity of the hot interstellar gas after evolving for 15 gyrs decreases dramatically with increasing galactic rotation . the outer radius of the disk can be much reduced by increasing the supernova rate which drives a gentle galactic wind transporting high angular momentum gas out of the galaxy . the mass of hii gas ( ) may be much greater than previously realized since rotationally supported , low density hii contributes little to the global optical line emission . the total mass of cold disk gas available for star formation is similar to the masses of stellar disks observed .

we describe the evolution of interstellar gas in a family of low luminosity elliptical galaxies all having but with different degrees of flattening ( e0 , e2 , and e6 ) and two current supernova rates , snu = 0.01 and 0.04 . the galaxies are composed of 90 percent dark matter , are rotationally flattened and have isotropic stellar velocity dispersions . the soft x - ray luminosity of the hot interstellar gas after evolving for 15 gyrs decreases dramatically with increasing galactic rotation . as the rotating hot interstellar gas loses energy in the galactic potential , it cools onto a large disk . the outer radius of the disk can be much reduced by increasing the supernova rate which drives a gentle galactic wind transporting high angular momentum gas out of the galaxy . the total mass of cooled disk gas is less sensitive to the supernova rate . although the hot interstellar gas may be difficult to observe in rotating low - luminosity ellipticals , the cooled disk gas can be observed ( i ) in optical line emission since part of the cooled disk gas is photoionized by stellar uv and ( ii ) in the optical continuum , assuming the colder disk gas forms into luminous stars . the mass of hii gas ( ) may be much greater than previously realized since rotationally supported , low density hii contributes little to the global optical line emission . we interpret the stellar disks that are common ( or ubiquitous ) in low luminosity ellipticals as stars that have formed in the cold disk gas . the total mass of cold disk gas available for star formation is similar to the masses of stellar disks observed . the high stellar h photometric index observed in disky ellipticals can be understood by combining the light of young disk stellar populations with that of the old bulge population . _ subject headings _ : galaxies : evolution galaxies : disks galaxies : interstellar gas # 1#2#3#4 # 1#2 .2 in

1208.3351

i

the study of star formation , stellar populations and galactic structure is currently being transformed by a new generation of galactic plane surveys . these surveys have much higher resolution and sensitivity than previous surveys and are at infrared and longer wavelengths that can penetrate the high extinction of the galactic mid - plane . they also cover sufficiently wide areas of the plane to provide samples that are large enough to be representative and statistically robust for rare and short - lived phases of evolution . blind surveys that cover contiguous , wide areas also allow the study of phenomena and trends across a large range of scales . a wide wavelength coverage is required to distinguish and characterise the different populations found at both the early and later phases of stellar evolution and so it is also important to ensure that the same wide areas are covered by all the relevant wavelengths . here we describe the design and implementation of a new radio continuum survey of the galactic plane and its role in the context of the other multi - wavelength surveys . advances in various wide - field technologies have led to a new generation of galactic plane surveys . those with relevance here , and to star formation in particular , are listed in table [ surveys ] . leading the way is the glimpse i ( galactic legacy infrared mid - plane survey extraordinaire ) survey ( benjamin et al . 2003 ; churchwell et al . 2009 ) . this _ spitzer _ irac legacy programme covered the inner galaxy ( @xmath3 and @xmath4 , @xmath5 ) at 3.6 , 4.5 , 5.8 and 8.0 . glimpse is two orders of magnitude more sensitive ( limit at l - band ( 3.6)@xmath6 magnitude although usually confusion limited ) and has ten times higher spatial resolution ( @xmath7 ) than any previous mid - ir survey . it has catalogued over 49 million sources in a wavelength regime which preferentially selects sources with hot circumstellar dust emission such as young and evolved stars ( e.g. , robitaille et al . more embedded and cooler sources are the subject of the mipsgal survey with _ spitzer _ ( carey et al . 2009 ) and the pacs element of the hi - gal survey with herschel ( molinari et al . 2010 ) . @l@c@c@c@ c@ c@ l@ iphas & h@xmath8 & 1.7 & @xmath9@xmath10 & @xmath11 & nebulae & stars & drew et al . ( 2005 ) + ukidss & jhk & 0.8 & @xmath12@xmath13 & @xmath14 & stars , nebulae & lucas et al . ( 2008 ) + vvv & zyjhk & 0.8 & @xmath15@xmath16 & @xmath17 & & minniti et al . ( 2010 ) + glimpse & 4 - 8 & 2 & @xmath15@xmath18&@xmath14 & stars , hot dust & churchwell et al . ( 2009 ) + msx & 8 - 21 & 18 & all & @xmath11 & warm dust & price et al . ( 2001 ) + mipsgal & 24,70 & 6 , 20 & @xmath15@xmath18&@xmath14 & & carey et al . ( 2009 ) + akari & 50 - 200 & 30 - 50 & all sky & & cool dust & white et al . ( 2009 ) + hi - gal & 70 - 500 & 10 - 34 & all & @xmath14 & & molinari et al . ( 2010 ) + jps & 450,850 & 8 - 14 & @xmath19@xmath20&@xmath14 & & moore et al . ( 2005 ) + atlasgal & 850 & 19 & @xmath21@xmath20&@xmath22 & & schuller et al . ( 2009 ) + bolocam & 1100 & 33 & @xmath23@xmath24 & @xmath25 & & aguirre et al . ( 2010 ) + grs & @xmath26co 1 - 0 & 46 & @xmath27@xmath28&@xmath14 & molecular gas & jackson et al . ( 2006 ) + mmb & 6.7ghz & 192 & @xmath29@xmath20&@xmath17 & methanol masers & green et al . ( 2009 ) + hops & 22ghz & 132 & @xmath29@xmath20&@xmath17 & water masers & walsh et al . ( 2011 ) + oh & 1.6ghz & @xmath3010 & @xmath31@xmath32 & @xmath33 & hydroxyl masers & sevenster et al . ( 2001 ) + cornish & 6 cm & 1.5 & @xmath19@xmath18&@xmath14&compact ionized gas & this work + s / v / cgps & 21 cm & 60 & @xmath34@xmath35 & @xmath36&atomic gas & stil et al . ( 2006 ) + magpis & 20 cm & 5 & @xmath37@xmath38 & @xmath39&diffuse ionized gas & helfand et al . ( 2006 ) + mgps-2 & 35 cm & 45 & @xmath40@xmath41&@xmath42 & & murphy et al . ( 2007 ) + an even deeper probe of the general stellar population is becoming available via the deep near - ir galactic plane survey ( gps ) that is part of the uk ir deep sky surveys ( ukidss ) programme ( lucas et al . 2008 ) . this survey is about 3 magnitudes more sensitive and two to three times better resolution than the 2mass all sky near - ir survey ( skrutskie et al . 2006 ) and will detect upwards of a billion sources . the addition of near - ir data , where photospheric and scattered light contributions dominate , allows a much better separation and characterisation of the general stellar population , than from mid - ir colours alone . near - ir surveys are also being used to map the extinction due to molecular clouds ( e.g. , rowles & froebrich 2009 ) . the optical h@xmath8 survey iphas ( drew et al . 2005 ) is providing both stellar characterisation , 3d extinction maps and tracing nebular emission in less obscured regions of the northern plane with the southern vphas+ survey ( see www.vphasplus.org ) scheduled to do the same in the south . to place the stellar populations in a galactic context , commensurate studies of the various components of the ism are required . for the study of star formation in particular , the molecular component is provided in part by the bu - fcrao @xmath26co1 - 0 galactic ring survey ( jackson et al . 2006 ) , which covers over half of the northern glimpse area with extensions over much of the northern mid - plane ( mottram & brunt 2010 ) . the mostly optically thin @xmath26co1 - 0 data traces the distribution and dynamics of the cold molecular gas . the cool dust in these molecular clouds can also be mapped via its sub - millimetre continuum emission . this is currently being achieved with the atlasgal survey ( schuller et al . 2009 ) at 870 and bolocam survey at 1100 ( aguirre et al . 2010 ) , whilst the forthcoming jcmt galactic plane survey ( jps , www.jach.hawaii.edu/jcmt/surveys/ ) will map the continuum at 450 and 850 with higher sensitivity and resolution . together with the spire element of the hi - gal survey with the herschel satellite ( molinari et al . 2010 ) this will provide temperature and dust emissivity information across the glimpse region . the more widely distributed atomic hydrogen component is covered by the international galactic plane survey at about 1 resolution ( www.ras.ucalgary.ca/igps/ ) . this is made up of the vla galactic plane survey ( vgps , stil et al . 2006 ) , southern galactic plane survey ( sgps ; mcclure - griffiths et al . 2005 ) and canadian galactic plane survey ( taylor et al . 2003 ) . a sub - section of the plane is covered by the much deeper galfa survey of hi at 4 resolution using the arecibo telescope ( peek et al . the hi component traces where most of the mass of interstellar gas is located and its velocity structure . 21 cm absorption lines can also help to solve the near / far distance ambiguity in relation to the kinematic distances derived towards the embedded @xmath2 regions ( sewilo et al . 2004 ; fish et al . 2003 ) and dense , molecular clouds ( jackson et al . 2002 ; gibson et al . 2005 ; busfield et al . 2006 ; roman - duval et al . this combination of atomic and molecular kinematic data can therefore provide the 3d galactic setting of the neutral gas . the one major component missing from the multi - wavelength surveys of the galaxy is that of the ionized gas . no existing radio continuum survey has sufficient resolution , depth or coverage to provide the data that would complete the picture of the galaxy . ionized gas arises in nebulae and stellar winds around hot stars and is crucial to understanding key phases of the early and late evolution of high and intermediate mass stars . dense , photo - ionized regions around young and evolved stars are often optically thick with a turnover frequency of around a few ghz , where the radio continuum spectral index @xmath8 ( @xmath43 ) changes from the optically thick value of + 2.0 to the optically thin slope of @xmath44 . ionized stellar winds have a positive spectral index @xmath45 , and so it is also much more efficient to carry out systematic searches for these sources at high frequencies . furthermore , the resolution should be comparable to the arcsecond resolution of the ir surveys to allow ir counterparts to be uniquely identified . it was to fill this need for a high frequency , high resolution radio continuum survey covering the area of the _ spitzer _ survey that the concept of the co - ordinated radio ` n ' infrared survey for high - mass star formation ( cornish ) survey was conceived . many single - dish surveys of the galactic plane have been carried out at 5ghz with a resolution of a few arcminutes that is totally inadequate to complement the new generation of ir surveys ( e.g. , altenhoff et al . 1978 ; haynes et al . 1978 ; gregory & condon 1991 ; griffith et al . most higher resolution interferometric surveys have been carried out at the relatively low frequency of 1.4 ghz ( zoonematkermani et al . 1990 ; becker et al . 1990 ; condon et al . 1998 ; giveon et al . although the multi - configuration magpis survey ( helfand et al . 2006 ) and mgps-2 survey ( murphy et al . 2007 ) are good for tracing the optically thin thermal emission from extended , evolved @xmath2 regions and non - thermal supernova remnants , they are not appropriate for the study of dense , thermal sources due to the unfavourable spectral index and compactness . becker et al . ( 1994 ) , with infills by giveon et al . ( 2005 ) and white et al . ( 2005 ) have surveyed part of the inner galaxy ( @xmath46 , @xmath47 ) at 5ghz with the vla in c configuration giving a resolution of 4@xmath489 . however , these surveys cover only one fifth of the northern glimpse region and the spatial resolution is poorer than that of _ spitzer _ irac , which causes problems with source identification . at this resolution the vast majority of their sources are unresolved and thus we have no morphological information . in the southern hemisphere the at20 g survey at 20ghz and @xmath3030 resolution ( murphy et al . 2010 ) that was primarily designed to study the extragalactic radio source population is detecting many @xmath2 regions , but again not at sufficient depth or resolution to address the science opened up by current surveys of the galactic plane at infrared wavelengths .

we describe the motivation , design and implementation of the cornish survey , an arcsecond resolution radio continuum survey of the inner galactic plane at 5ghz using the karl g. jansky very large array ( vla ) . it is a blind survey co - ordinated with the northern _ spitzer _ glimpse i region covering 10 and at similar resolution . the cornish survey for compact ionized sources complements other galactic plane surveys that target diffuse and non - thermal sources as well as atomic and molecular phases to build up a complete picture of the ism in the galaxy .

we describe the motivation , design and implementation of the cornish survey , an arcsecond resolution radio continuum survey of the inner galactic plane at 5ghz using the karl g. jansky very large array ( vla ) . it is a blind survey co - ordinated with the northern _ spitzer _ glimpse i region covering 10 and at similar resolution . we discuss in detail the strategy that we employed to control the shape of the synthesised beam across this survey that covers a wide range of fairly low declinations . two snapshots separated by 4 hours in hour angle kept the beam elongation to less that 1.5 over 75% of the survey area and less than 2 over 98% of the survey . the prime scientific motivation is to provide an unbiased survey for ultra - compact regions to study this key phase in massive star formation . a sensitivity around 2mjy will allow the automatic distinction between radio loud and quiet mid - ir sources found in the _ spitzer _ surveys . this survey has many legacy applications beyond star formation including evolved stars , active stars and binaries , and extragalactic sources . the cornish survey for compact ionized sources complements other galactic plane surveys that target diffuse and non - thermal sources as well as atomic and molecular phases to build up a complete picture of the ism in the galaxy .

1208.3351

c

the cornish survey is a new sensitive , high spatial resolution galactic plane survey at 5ghz . it is targeted at compact thermal sources and @xmath54 regions in particular . conceived to complement the _ spitzer _ glimpse survey , it will systematically address key questions in massive star formation such as the lifetime and evolution of the @xmath54 phase as a function of exciting star parameters and environment . uniform coverage of the northern glimpse region enables the distinction between radio - loud and radio - quiet objects such as mysos/@xmath54s and ppn / pn that otherwise have very similar mid - ir colours . legacy survey science in combination with other recent and upcoming optical , near - ir , far - ir , sub - mm and longer wavelength radio surveys of the plane will be possible with applications in evolved stars , active stars and active binaries . data taking for the cornish survey has been completed and the basic goal of uniformity of coverage achieved . the data reduction , source extraction and statistical properties of the survey and sources will be discussed in the forthcoming paper by purcell et al . ( 2012 ) . at that time the catalogue and image data will be publically available at http://www.ast.leeds.ac.uk/cornish . we have also achieved the aim of controlling the beam shape across the survey such that the elongation of the synthesised beam is mostly less than 1.5 and nearly always less than 2 . this was achieved by using a strategy of two snapshots separated by 4 hours in hour angle . a more uniform and rounder beam could be achieved by more snapshots but that would increase the overheads and has diminishing returns with the vla . our simulations show that snapshots separated by 6 hours in hour angle would have produced a better beam . however , this would have complicated the scheduling of the survey into 8 hour runs and more than likely compromised the very uniform coverage that we ultimately achieved . such tradeoffs will be the case for any survey with the evla at these declinations and for future galactic plane surveys in particular . aguirre , j. e. et al . 2011 , apjs , 192 , 4 altenhoff , w. j. , downes , d. , pauls , t. , & schraml , j. 1978 , a&as , 35 , 23 anglada , g. , villuendas , e. , estalella , r. , beltrn , m. t. , rodrguez , l. f. , torrelles , j. m. , & curiel , s. 1998 , aj , 116 , 2953 arthur , s. j. , & hoare , m. g. 2006 , apjs , 165 , 283 behrend , r. , & maeder , a. 2001 , a&a , 373 , 190 becker , r. h. , white , r. l. , mclean , b. j. , helfand , d. j. , & zoonematkermani , s. 1990 , apj , 358 , 485 becker , r. h. , white , r. l. , helfand , d. j. , & zoonematkermani s. 1994 , apjs , 91 , 347 benjamin , r. a. et al . 2003 , pasp , 115 , 953 benjamin , r. a. 2009 , in the galaxy disk in cosmological context , iau symp . , 254 . j. andersen , j. bland - 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we discuss in detail the strategy that we employed to control the shape of the synthesised beam across this survey that covers a wide range of fairly low declinations . two snapshots separated by 4 hours in hour angle kept the beam elongation to less that 1.5 over 75% of the survey area and less than 2 over 98% of the survey . the prime scientific motivation is to provide an unbiased survey for ultra - compact regions to study this key phase in massive star formation . a sensitivity around 2mjy will allow the automatic distinction between radio loud and quiet mid - ir sources found in the _ spitzer _ surveys . this survey has many legacy applications beyond star formation including evolved stars , active stars and binaries , and extragalactic sources .

we describe the motivation , design and implementation of the cornish survey , an arcsecond resolution radio continuum survey of the inner galactic plane at 5ghz using the karl g. jansky very large array ( vla ) . it is a blind survey co - ordinated with the northern _ spitzer _ glimpse i region covering 10 and at similar resolution . we discuss in detail the strategy that we employed to control the shape of the synthesised beam across this survey that covers a wide range of fairly low declinations . two snapshots separated by 4 hours in hour angle kept the beam elongation to less that 1.5 over 75% of the survey area and less than 2 over 98% of the survey . the prime scientific motivation is to provide an unbiased survey for ultra - compact regions to study this key phase in massive star formation . a sensitivity around 2mjy will allow the automatic distinction between radio loud and quiet mid - ir sources found in the _ spitzer _ surveys . this survey has many legacy applications beyond star formation including evolved stars , active stars and binaries , and extragalactic sources . the cornish survey for compact ionized sources complements other galactic plane surveys that target diffuse and non - thermal sources as well as atomic and molecular phases to build up a complete picture of the ism in the galaxy .

1702.00981

i

positronium ( ps ) is a light atom that consists of an electron and its antiparticle , the positron . positron- and positronium - annihilation - lifetime spectroscopy is a widely used tool for studying materials , e.g. , for determining pore sizes and free volume . for smaller pores the radius of the ps atom itself can not be neglected . this quantity was probed in a recent experiment which measured the cavity shift of the ps @xmath3-@xmath5 line @xcite , and the data calls for proper theoretical understanding @xcite . in this paper we calculate the eigenstates of ps in a hard - wall spherical cavity and determine the effective collisional radius of ps in @xmath3 , @xmath4 , and @xmath5 states as a function of its center - of - mass momentum . the most common model for pore - size estimation is the tao - eldrup model @xcite . it considers an orthopositronium atom ( @xmath9-ps ) , i.e. , a ps atom in the triplet state , confined in the pore which is assumed to be spherical , with radius @xmath10 . the ps is modeled as a point particle with mass @xmath11 in a spherical potential well , where @xmath12 is the mass of an electron / positron . collisions of @xmath9-ps with the cavity walls allow for positron two - gamma ( @xmath13 ) annihilation with the electrons in the wall , which reduces the @xmath9-ps lifetime with respect to the vacuum @xmath14-annihilation value of 142 ns . to simplify the description of the penetration of the ps wave function into the cavity wall , the radius of the potential well is taken to be @xmath15 , where the best value of @xmath16 has been empirically determined to be 0.165 nm @xcite . the model and its extensions are still widely used for pore sizes in 1100 nm range @xcite . porous materials and ps confinement in cavities also enabled a number of fundamental studies , such as measurement of ps - ps interactions @xcite , detection of the ps@xmath17 molecule @xcite and its optical spectroscopy @xcite , and measurements of the cavity - induced shift of the ps lyman-@xmath18 ( @xmath3-@xmath5 ) transition @xcite . cavities also hold prospects of creating a bose - einstein condensate of ps atoms and an annihilation - gamma - ray laser @xcite . seen in a wider context , the old subject of confined atoms @xcite has seen renewed interest in recent years @xcite . studies in this area not only serve as interesting thought experiments but also apply to real physical situations , e.g. , atoms under high pressure @xcite or atoms trapped in fullerenes @xcite . for @xmath9-ps there is a specific question about the extent to which confinement in a cavity affects its intrinsic @xmath14 annihilation rate ( see ref . @xcite and references therein ) . for smaller cavities the effect of a finite radius of the trapped particle on its center - of - mass motion can not be ignored . in fact , the radius of a composite quantum particle depends on the way this quantity is defined and probed . for example , the proton is usually characterized by its root - mean - squared charge radius . it is measured in elastic electron - proton scattering @xcite or using spectroscopy of exotic atoms , such as muonic hydrogen @xcite ( with as yet unexplained discrepancies between these experiments ) . for a particle trapped in a cavity , any practically defined radius may depend on the nature of its interaction with the walls . in the present work we consider the simple problem of a ps atom confined in a hard - wall spherical cavity . the finite size of ps gives rise to energy shifts with respect to the energy levels of a pointlike particle in the cavity . this allows us to calculate the effective _ collisional _ radius of ps that describes its interaction with the impenetrable cavity wall . ps is a hydrogenlike atom with a total mass of 2 and reduced mass of @xmath19 ( in atomic units ) . the most probable distance between the electron and positron in a free ground - state ps atom is @xmath20 , where @xmath21 is the bohr radius , while the mean electron - positron separation is @xmath22 @xcite . for excited states ps@xmath23 ) these quantities increase as @xmath24 . the ps center of mass is halfway between the two particles , so the most probable radius of ps(@xmath3 ) is @xmath25 , its mean radius being @xmath26 . one can expect that the distance of closest approach between the ps center of mass and the wall with which it collides will be similar to these values . one can also expect that this distance will depend on the center - of - mass momentum of the ps atom , as it will be `` squashed '' when colliding with the wall at higher velocities . a proper quantum - mechanical treatment of this problem is the subject of this work . a configuration - interaction ( ci ) approach with a @xmath0-spline basis is used to construct the states of ps inside the cavity . using these we determine the dependence of the effective ps radius on the center - of - mass momentum for the @xmath3 , @xmath4 , and @xmath5 states . of course , the interaction between ps and cavity walls in real materials is different from the idealized situation considered here . it can be modeled by changing the electron - wall and positron - wall potentials . on the other hand , the hard - wall cavity can be used as a theoretical tool for studying ps interactions with atoms @xcite . an atom placed at the center of the cavity will cause a shift of the ps energy levels , whose positions can be related to the ps - atom scattering phase shifts @xmath27 for the @xmath28th partial wave @xcite , @xmath29)}{y_{l+1/2}(k [ r_c-\rho(k)])},\ ] ] where @xmath30 is the ps center - of - mass momentum , @xmath31 is the bessel function , @xmath32 is the neumann function , @xmath10 is the cavity radius , and @xmath33 is the effective collisional radius of the ps atom . the paper is organized as follows . section [ sec : theory ] describes the theory and numerical implementation of the ci calculations of the energy levels and effective radii of ps in a spherical cavity . in sec . [ sec : results ] these energies and radii are presented for a number of cavity sizes and the dependence of the radii of ps(@xmath3 ) , ps(@xmath4 ) , and ps(@xmath5 ) on the ps center - of - mass momentum is analyzed . we conclude in sec . [ sec : conclusion ] with a summary . unless otherwise stated , atomic units are used throughout .

we determine effective collisional radii of positronium ( ps ) by considering ps states in hard - wall spherical cavities . we show that for , , and states of ps , the effective radius decreases with the increasing ps center - of - mass momentum , and find a.u . in the zero - momentum limit .

we determine effective collisional radii of positronium ( ps ) by considering ps states in hard - wall spherical cavities . -spline basis sets of electron and positron states inside the cavity are used to construct the states of ps . accurate ps energy eigenvalues are obtained by extrapolation with respect to the numbers of partial waves and radial states included in the bases . comparison of the extrapolated energies with those of a pointlike particle provides values of the effective radius of ps( ) in collisions with a hard wall . we show that for , , and states of ps , the effective radius decreases with the increasing ps center - of - mass momentum , and find a.u . , a.u . , and a.u . in the zero - momentum limit .

physics0309074

i

complexes of small molecules with variable number of para - hydrogen ( @xmath3-h@xmath4 ) molecules pose a challenging and fascinating arena for the manifestation of nuclear quantum effects on structure and spectroscopy . like their better known analogous helium clusters , para - hydrogen clusters are expected to be strongly influenced by the quantum nature of the @xmath3-h@xmath4 molecules . the mass of @xmath3-h@xmath4 being one half that of @xmath5he actually suggests that larger zero point effects might be expected . however , the greater binding of @xmath3-h@xmath4 to itself and to other species means that the greater delocalization tendency of @xmath3-h@xmath4 competes with greater localizing potential energy terms . the competition between these two strong effects is what causes both calculation and analysis of para - hydrogen clusters and complexes to be considerably more difficult than that for analogous helium systems . like helium , para - hydrogen is a boson , but because of the greater binding energy , @xmath3-h@xmath4 solidifies in the bulk before cooling to a low enough temperature for macroscopic manifestation of the boson permutation exchange symmetry to occur with a superfluid phase . however , in finite clusters vestiges of superfluidity may occur , particularly when the para - hydrogen packing is expanded or otherwise constrained by the reduced dimensionality and/or the @xmath3-h@xmath4 molecules are bound to foreign species . the linear ocs molecule has played a key role in developing our understanding of the fundamental forces controlling the properties of @xmath3-h@xmath4 complexes . experimental studies with ocs complexed by variable numbers of para - hydrogen ( @xmath6 ) and embedded in helium droplets have shown a very rich spectroscopic behavior , with both vibrational shifts and rotational fine structure providing indirect information on the symmetry and distribution of the @xmath3-h@xmath4 around the ocs molecule @xcite . in helium , the rotational spectra of the para - hydrogen complexes are well fit by asymmetric tops for @xmath0=1 - 4 , while larger clusters appear adequately described by a symmetric top hamiltonian @xcite . for certain sizes , @xmath0=5 , 6 , 11 , 14 - 16 , no @xmath7-branch is seen in the spectra . for the larger sizes , @xmath0=14 - 16 , this disappearance is temperature dependent , which led to the suggestion that it might be a manifestation of superfluidity in the para - hydrogen component . path integral monte carlo calculations for a complete solvation shell ( @xmath0=17 ) have shown that a transition to an anisotropic superfluid state is indeed found at temperatures below t@xmath8 k , and that this can account for the disappearance of the @xmath7-branch for @xmath9 @xcite . however , for the smaller sizes , the spectral anomaly is independent of temperature . in the absence of detailed knowledge of the structure and rigidity of the complex , the microscopic origin of this anomaly is less clear , although the permutation symmetry can also be expected to play a role . much less is known experimentally about the complexes of ocs with para - hydrogen in the absence of a solvating helium environment . the ocs(@xmath3-h@xmath4 ) dimes has been characterized by high resolution spectroscopy @xcite , and its strcuture has been shown to be approximate with that of an asymmetric top rotor . the structure of this dimer is very similar in the gas phase and in a helium droplet @xcite . for complexes with larger numbers of para - hydrogen molecules , no spectroscopic data have been published . we expect that ocs complexed by 1 @xmath10 17 para - hydrogen molecules will show a very rich variation in structure , energetics , and spectroscopic properties , as a consequence of the strongly modulated solvating hydrogen density along the axis of the ocs molecule seen in path integral calculations for @xmath1117 @xcite . these modulations are considerably stronger than those found in the analogous complexes of ocs with helium @xcite because of the stronger ( @xmath3-h@xmath4)-ocs and ( @xmath3-h@xmath4)-(@xmath3-h@xmath4 ) interactions . consequently we can expect a considerably more complex size dependence of the spectroscopic properties for the complexes with @xmath3-h@xmath4 as the first solvation shell is filled . the small complexes of ocs with helium have recently been shown to undergo a transition from near rigid molecular complex behavior to true quantum ( or `` superfluid '' ) solvation characterized by permutation exchanges along the molecular axis , as the number of helium atoms increases from @xmath0=1 to @xmath0=20 @xcite . given the recent demonstration of anisotropic superfluidity in ocs(@xmath3-h@xmath4)@xmath12 @xcite , we expect an analogous transition for complexes with molecular hydrogen . however , the considerably greater competition between quantum ( kinetic ) delocalization and ( potential ) localization for para - hydrogen renders even qualitative prediction of the spectroscopic behavior impossible without detailed microscopic calculations . furthermore , for the intermediate sizes 1 @xmath10 17 , the properties of gas phase ocs(@xmath3-h@xmath4)@xmath12 complexes and their analogous embedded in helium droplets can be expected to show maximal differences , since this is the size regime in which subtle changes in para - hydrogen and helium density distributions can give rise to significant energy differences . in this paper we present results of ground and excited state calculations for ocs complexed with @xmath0=1 - 8 para - hydrogen molecules , as part of a larger systematic study of the complexes with up to a complete solvation shell @xcite . we employ two kinds of zero temperature quantum monte carlo methods , the diffusion monte carlo ( dmc ) and the projection operator imaginary time spectral evolution ( poitse ) approach . these microscopic calculations provide energy levels and rotational and distortion constants , in addition to energetics and ground state structures . we find a very interesting variation in structure for this series of small complexes , showing considerably more inhomogeneous behavior than the analogous series of complexes of ocs with @xmath5he . we determine the structure both along the molecular axis and around it , with analysis of para - hydrogen pair correlation functions and find that this allows us to provide a good description of the extent of localization in the ground state . the excited state energies are extracted from a maximum entropy analysis of the imaginary time correlation functions derived from the poitse approach . we find that a simple multi - exponential fit of these correlations functions provides similar results , but with larger uncertainties . analysis of the fitted spectral constants resulting from the excited state energies reveals a gradual change of symmetry of the ocs(@xmath3-h@xmath4)@xmath13 complexes as @xmath0 increases , which is accompanied by a monotonic decrease in the effective rotational constant over this size range . while overall the analysis of spectral constants indicates more rigid structures for these ocs complexes with para - hydrogen than those with helium , the fitted spectral constants nevertheless show a markedly strong appearance of floppy , non - rigid structures for both the @xmath0=3 and @xmath0=4 complexes . we discuss these structures and predicted spectroscopic constants in relation to available experimental data and in the context of the analogous ocs(@xmath5he)@xmath14 complexes @xcite .

we determine the structure and energetics of complexes of the linear ocs molecule with small numbers of para - hydrogen molecules ,=1 - 8 , using zero temperature quantum monte carlo methods . ground state calculations are carried out with importance - sampled rigid body diffusion monte carlo ( is - rbdmc ) and excited state calculations with the projection operator imaginary time spectral evolution ( poitse ) methodology . the ground states are found to be highly structured , with a gradual build up of two axial rings as increases to 8 . excited state calculations are made for a range of total cluster angular momentum values and the rotational energy levels fitted to obtain effective rotational and distortion constants of the complexed ocs molecule as a function of cluster size . detailed analysis of these spectroscopic constants indicates that the complexes of ocs with para - hydrogen have an unusually rich variation in dynamical behavior , with sizes=1 - 2 showing near rigid behavior , sizes=3 - 4 showing extremely floppy behavior , and the larger sizes=5 - 8 showing more rigid behavior again .

we determine the structure and energetics of complexes of the linear ocs molecule with small numbers of para - hydrogen molecules ,=1 - 8 , using zero temperature quantum monte carlo methods . ground state calculations are carried out with importance - sampled rigid body diffusion monte carlo ( is - rbdmc ) and excited state calculations with the projection operator imaginary time spectral evolution ( poitse ) methodology . the ground states are found to be highly structured , with a gradual build up of two axial rings as increases to 8 . analysis of the azimuthal density correlations around the ocs molecule shows that these rings are quite delocalized for small values , but become strongly localized for . excited state calculations are made for a range of total cluster angular momentum values and the rotational energy levels fitted to obtain effective rotational and distortion constants of the complexed ocs molecule as a function of cluster size . detailed analysis of these spectroscopic constants indicates that the complexes of ocs with para - hydrogen have an unusually rich variation in dynamical behavior , with sizes=1 - 2 showing near rigid behavior , sizes=3 - 4 showing extremely floppy behavior , and the larger sizes=5 - 8 showing more rigid behavior again . the large values of the distortion constant obtained for=3 - 4 are rationalized in terms of the coupling between the ocs rotations and the `` breathing '' mode of the first , partially filled ring of para - hydrogen molecules .

astro-ph0109365

c

in this paper , we compared model single stellar population spectra to the integrated spectrum of the metal - rich galactic globular cluster 47 tuc . the model spectra were computed from two sets of state - of - the - art theoretical isochrones . we tested the sensitivity of our predictions to variations in a number of key model inputs related to the spectral library employed , the theoretical isochrones , and the relations between fundamental and observed stellar parameters . our main conclusions can be summarized as follows : different sets of isochrones predict slightly different ages when compared to the cluster data on the color - magnitude diagram . in the case of the salaris set , the isochrone providing the best match to the turn - off of the cluster has an age of 11 - 12 gyrs . vazdekis et al . ( 2001 ) , using the same set of isochrones , obtained an age younger by about 1 gyr . the difference is minor and is due to the different reddenings assumed . when the isochrones of salasnich et al . ( 2000 ) are used , a slightly older age is obtained ( 12.5 - 14 gyrs ) the reason being that the latter set of isochrones does not consider diffusion of heavy elements . a final decision as to which set of isochrones is best awaits a better knowledge of the extent to which atomic diffusion is operating in main sequence stars . when compared to the observations in the luminosity function domain , both sets of theoretical isochrones adopted in this work underestimate the number of giant stars brighter than the horizontal branch . in the case of the salaris isochrones , which do not include agb stars , the mismatch amounts to 0.30.4 dex . the padova set , even though it does include agb stars , is also offset , though by a smaller amount ( @xmath2 0.20.3 dex ) . it is unclear to us what causes this discrepancy . at the level of the agb bump , roughly 2/3 of the mismatch seems to be due to the lack of agb stars in the isochrones , this fraction being probably lower in other parts of the upper giant branch . however , even after performing an approximate correction for the absence of agb stars , there appears to be a small residual discrepancy between models and observations for first - ascent giants . we conclude that theoretical predictions to the luminosity functions of both the rgb and the agb may be too low , though it is difficult to quantify by how much in each case . spectroscopic ages inferred from @xmath1 and @xmath0 when adopting isochrones without any agb stars are systematically older , by at least 3 gyrs , than the ages inferred from the fit to the cluster s cmd . moreover , metal - lines are systematically too weak and the integrated _ ( b v ) _ is too blue by 0.07 mag . empirically correcting the theoretical lfs to match the observed luminosity function reduces the spectroscopic age to 1112 gyrs in the case of the salaris isochrones , and @xmath2 13 gyrs in the case of the padova ones as determined from @xmath1 and @xmath0 ( the latter is obtained after correction for a systematic mismatch of the cluster s rgb by padova isochrones ) . such revised ages are now in excellent agreement with the ages inferred from fitting both sets of isochrones to the cmd . also _ ( b v ) _ and metal - lines studied are very well fit by the lf - corrected models . the best value found from the fit to @xmath6 is still higher by @xmath2 3 gyrs than found for the other balmer lines . this mismatch is in the same sense found in paper i , where @xmath6 computed directly from the cmd - based synthesis was relatively stronger than @xmath0 or @xmath1 . as @xmath6 is more strongly affected by c , n abundance anomalies , we suggested in paper i that the discrepancy was due to our failure to properly model and correct for cn lines within the passband and continuum windows of the index . we estimate the impact on spectroscopic ages of uncertainties in a number of model inputs , such as the @xmath4 and _ [ fe / h]_-scales of dwarfs and giants , the luminosity function of the red giant branch and the metallicity of the cluster . spectroscopic age - dating of old stellar populations is mostly influenced by uncertainties coming from the @xmath4 and _ [ fe / h]_-scale of giant stars , as well as the luminosity function of the upper red giant branch and the metallicity adopted for the cluster . using @xmath1 , a 1 gyr uncertainty is caused by an error of 75 k in the giant @xmath4-scale , a 0.1 dex error in the giant - branch luminosity function , and a 0.1 dex error in either the _ [ fe / h]_-scale of giants or the _ [ fe / h ] _ of the stellar population . because the uncertainties in the parameters of dwarf stars are lower , their impact on model predictions is generally less important . the contribution by blue stragglers to the integrated line indices is important only for @xmath6 and slightly less so for @xmath7 . when @xmath6 is corrected for the contribution of blue stragglers , we obtain an age 1 gyr older . in the case of @xmath7 , the age inferred is 0.5 gyr older . in summary , we conclude that the exceedingly high spectroscopic ages found for 47 tuc in previous works was due to : 1 ) the use of theoretical isochrones that neglect important effects such as he - diffusion and @xmath3-enhancement , as shown by vazdekis et al . ( 2001 ) , and 2 ) the underestimate of the number of giant stars above the horizontal branch , which was partly due to the omission of agb stars from the isochrones , and partly to a genuine apparent shortfall in the predicted numbers of agb stars and , most likely , first - ascent giants as well . another requirement , which is discussed in paper i , is on the iron abundance of the cluster . models provide a good match if _ [ fe / h ] _ is 0.05 dex lower than found by carretta & gratton ( 1997 ) . such a shift in _ [ fe / h ] _ is well within the errorbars of carretta & gratton s analysis and the uncertainties in the _ [ fe / h]_-scale of our stellar library . with regard to our long term goal of constructing metal - rich stellar population models for elliptical galaxies , we have made considerable progress . first , the ages from @xmath1 and @xmath7 agree , after the latter is corrected for the effect of c , n abundance variations ( see paper i ) . second , all metal lines are correctly predicted for the same ages obtained from balmer lines . third , the giant temperature scale of the salaris models looks to be generally correct . on the other hand , @xmath6 is shown to be a problematic feature , embedded as it is in a forest of cn lines . this problem is likely to be further exacerbated in elliptical galaxies , which have notoriously strong cn features . moreover , the present models do not include variations in type ia vs. type ii supernovae element ratios ( trager et al . 1998 ) , nor do they probe the high - metallicity regime needed for ellipticals . finally , we have identified an error in the upper giant branch luminosity function of current evolutionary models , which underestimate the aggregate number of luminous red giants in 47 tuc by roughly a factor of 2 . we have furthermore shown that an accurate lf for these stars is needed for accurate spectroscopic age determination . a major unknown is whether the red - giant excess of 47 tuc extends to all metal - rich old populations , and what its magnitude might be . testing the luminosity function in old metal - rich populations has emerged as an important prerequisite for stellar population studies . these and further improvements are left for future works . we would like to thank maurizio salaris for making his isochrones available . stefano covino is thanked for the red integrated spectrum of 47 tuc . we would also like to thank alexandre vazdekis , maurizio salaris , manuela zoccali , achim weiss and mike bolte for helpful discussions . the referee , brad gibson , is thanked for valuable suggestions that greatly improved this paper . r.p.s . thanks the hospitality of the physics dept . of the university of north carolina , chapel hill , where part of this work was developed . likewise , j.a.r . thanks the astronomy department at uc , santa cruz for hospitality during a visit in which part of this work was developed . this work has made extensive use of the simbad database . r.p.s . acknowledges support provided by the national science foundation through grant gf-1002 - 99 and from the association of universities for research in astronomy , inc . , under nsf cooperative agreement ast 96 - 13615 , and cnpq / brazil , for financial help ( 200510/99 - 1 ) . this research has also been supported by nsf grant ast-9900720 to the university of north carolina , and by nsf grants ast-9529098 and ast-0071198 to the university of california , santa cruz . albrow , m.d . , gilliland , r.l . , brown , t.m . , edmonds , p.d . , guhathakurta , p. & sarajedini , a. 2001 , apj , 559 , 1060 alonso , a. , arribas , s. & martnez - roger 1995 , , 297 , 197 alonso , a. , arribas , s. & martnez - roger 1996 , , 313 , 873 alonso , a. , arribas , s. & martnez - roger 1999 , , 139 , 335 basu , s. , pinsonneault , m.h . & bahcall , j.n . 2000 , apj , 529 , 1084 bergbusch , p.a . & vandenberg , d.a . 1992 , apjs , 81 , 163 bolte , m. 1994 , apj , 431 , 223 carretta , e. & gratton , r.g . 1997 , , 121 , 95 cassisi , s. , castellani , v. , deglinnocenti , s. , piotto , g & salaris , m. 2001 , a&a , 366 , 578 chaboyer , b. , fenton , w.h . , nelan , j.e . , patnaude , d.j . & simon , f.e . 2001 , apj , 562 , 521 cohen , j.g . , blakeslee , j.p . & ryzhov , a. 1998 , apj , 496 , 808 deliyannis , c.p . & demarque , p. 1991 , apj , 379 , 216 . gibson , b.k . , madgwick , d.s . , jones , l.a . , da costa , g.s . & norris , j.e . 1999 , 118 , 1268 gratton , r.g . 2001 , a&a , 369 , 87 hesser , j.e . , harris , w.e . , vandenberg , d.a . , allwright , j.w.b . , shott , p. & stetson , p.b . 1987 , , 99 , 739 howell , j.h . , guhathakurta , p. & gilliland , r.l . 2000 , , 112 , 1200 jones , l.a . 1999 , phd thesis , university of north carolina kaluzny , j. , wyzocka , a. , stanek , k.z . & krzemiski , w. 1998 , aca , 48 , 439 langer , g.e . , bolte , m. & sandquist , e. 2000 , apj , 529 , 936 lebreton , y. , perrin , m .- n . , cayrel , r. , baglin , a. & fernandes , f. 1999 , a&a , 350 , 587 maraston , c. 1998 , mnras , 300 , 872 richer , h.b . , et al . 1996 , , 463 , 602 rose , j.a . 1994 , 107 , 206 rubenstein , e.p . & bailyn , c.d . 1999 apj , 513 , l33 salaris , m. & weiss , a. 1998 , 335 , 943 salaris , m. & weiss , a. 2001 , 376 , 955 salaris , m. , cassisi , s. & weiss , a. 2002 , pasp , 114 , 375 salasnich , b. , girardi , l. , weiss , a. & chiosi , c. 2000 , a&a , 361 , 1023 sandquist , e. , bolte , m. , stetson , p.b . & hesser , j.e . 1996 , apj , 470 , 910 sandquist , e. , bolte , m. , langer , g.e . , hesser , j.e . & mendes de oliveira , c. 1999 , apj , 518 , 262 schiavon , r.p . , barbuy , b. & bruzual a. , g. 2000 , 532 , 453 schiavon , r.p . , faber , s.m . , rose , j.a . & castilho , b.v . 2002 , apj , submitted ( paper i ) soubiran , c. , katz , d. & cayrel , r. 1998 , , 133 , 221 spite , f. & spite , m. 1982 , a&a , 115 , 357 stetson , p.b . 1991 , in the formation and evolution of star clusters , ed . k. janes ( asp conf 13 ) , 88 straniero , o. , chieffi , a. & limongi , m. 1997 , apj , 490 , 425 trager , s.c . , worthey , g. , faber , s.m . burstein , d. & gonzlez , j.j . 1998 , apjs , 116 , 1 vazdekis , a. , salaris , m. , arimoto , n. & rose , j.a . , 2001 , apj , 549 , 274 weiss , a. & salaris , m. 1999 , 346 , 897 westera , p. , lejeune , t. , buser , r. , cuisinier , f. & bruzual , g. 2002 , a&a , 381 , 524 zoccali , m. & piotto , g. 2000 , a&a , 358 , 943 zoccali , m. , cassisi , s. , bono , g. , piotto , g. , rich , r.m . & djorgovski , s.g . 2000 , apj , 538 , 289 @xmath5 4 & @xmath29 11 & @xmath5 1.5 & @xmath29 4 & @xmath5 4.5 & @xmath29 6 & @xmath29 8.5 & @xmath29 3.5 & @xmath32 75 k + @xmath5 9 & @xmath29 1 & @xmath5 1.5 & @xmath29 1.5 & @xmath5 1.5 & @xmath29 1 & @xmath29 1 & @xmath29 @xmath15 1 & @xmath33 50 k + @xmath29 11 & @xmath5 2 & @xmath5 2 & @xmath5 5 & @xmath5 3 & @xmath5 3.5 & @xmath5 5.5 & @xmath5 4.5 & @xmath34_{giants } \pm$ ] 0.1 + @xmath29 2.5 & @xmath5 1 & @xmath5 1 & @xmath5 1.5 & @xmath5 @xmath15 1 & @xmath5 1 & @xmath5 1 & @xmath5 1 & @xmath34_{dwarfs } \pm$ ] 0.05 + @xmath29 7.5 & @xmath5 2.5 & @xmath5 4 & @xmath5 6 & @xmath5 5 & @xmath5 4 & @xmath5 5 & @xmath5 5 & @xmath34_{47 tuc } \pm$ ] 0.1 + 30 & + 10 & -6 & + 10 & -10 & + 5 & + 12 & + 11.5 & lf correction + 9.5 & + 1 & 2 & + 1 & 2 & @xmath15 1 & @xmath15 1 & @xmath15 1 & no bs + 7 & + 4 & 3 & + 4 & 4 & + 4 & + 2 & + 2 & 10 @xmath35 11 gyrs +

we develop a new set of models for intermediate - metallicity single stellar populations in the blue / optical region and use those models to determine the spectroscopic age of 47 tuc . after all corrections are made , the cmd and the spectroscopic ages ( from and ) are in close agreement : 1112 gyrs for salaris isochrones and 13 gyrs for padova . previously older spectroscopic ages were due to the underestimate of the number of red giants and/or the use of isochrones that neglected the effects of he - diffusion and-enhancement . uncertainties in spectroscopic age determinations of old stellar populations stem from a number of effects , the most important of which are the and _ [ fe / h]_-scales of the giant stars used in the stellar library , the lf on the upper giant branch , and the assumed metallicity of the target stellar population itself . a 1 gyr uncertainty in age results from uncertainties of 75 k in the-scale of the library giants , 0.1 dex in the level of the giant - branch lf , and 0.1 dex in the assumed _ [ fe / h ] _ of either the target stellar population or the assumed zeropoint of the metallicity scale of the stellar library . a similar underestimate in the bright giant lf ,

we develop a new set of models for intermediate - metallicity single stellar populations in the blue / optical region and use those models to determine the spectroscopic age of 47 tuc . the models are based on a moderately high - resolution ( 1.8 fwhm ) empirical spectral library , state - of - the - art theoretical isochrones from m. salaris and the most recent set from the padova group , and new semi - empirical calibrations between fundamental stellar parameters and observables . model line - strengths include all corrections for deficiencies of the stellar library that are described in paper i. we highlight the importance of correctly modeling the luminosity function ( lf ) of the cluster at the level of the giant branch , in order to achieve a good reproduction of the integrated spectrum ; agreement between the spectroscopic age and the age based on the cluster s color - magnitude diagram ( cmd ) is achieved only if the _ observed _ lf is used rather than the theoretical ones , which either do not include agb stars ( salaris ) or underpredict the total number counts of bright giants in the cluster by a factor of two ( padova ) . after all corrections are made , the cmd and the spectroscopic ages ( from and ) are in close agreement : 1112 gyrs for salaris isochrones and 13 gyrs for padova . the difference between the model ages is due to the inclusion of atomic diffusion in the salaris models . previously older spectroscopic ages were due to the underestimate of the number of red giants and/or the use of isochrones that neglected the effects of he - diffusion and-enhancement . uncertainties in spectroscopic age determinations of old stellar populations stem from a number of effects , the most important of which are the and _ [ fe / h]_-scales of the giant stars used in the stellar library , the lf on the upper giant branch , and the assumed metallicity of the target stellar population itself . a 1 gyr uncertainty in age results from uncertainties of 75 k in the-scale of the library giants , 0.1 dex in the level of the giant - branch lf , and 0.1 dex in the assumed _ [ fe / h ] _ of either the target stellar population or the assumed zeropoint of the metallicity scale of the stellar library . a similar underestimate in the bright giant lf , if it exists in current super - solar metallicity models , would cause spectroscopic ages of elliptical galaxies inferred from such models to be too high by approximately 30% .

1105.2479

i

consider the scattering of time - harmonic electromagnetic waves by a bounded obstacle @xmath1 in @xmath2 with a smooth and simply connected boundary @xmath3 filled with an homogeneous dielectric material . this problem is described by the system of maxwell s equations with piecewise constant electric permittivity and magnetic permeability , valid in the sense of distributions , which implies two transmission conditions on the boundary of the obstacle guaranteeing the continuity of the tangential components of the electric and magnetic fields across the interface . the transmission problem is completed by the silver mller radiation condition at infinity ( see @xcite and @xcite ) . boundary integral equations are an efficient method to solve such problems for low and high frequencies . the dielectric scattering problem is usually reduced to a system of two boundary integral equations for two unknown tangential vector fields on the interface ( see @xcite and @xcite ) . we refer to @xcite for methods developed by the authors to solve this problem using a single boundary integral equation . optimal shape design with a goal function involving the modulus of the far field pattern of the dielectric scattering problem has important applications , such as antenna design for telecommunication systems and radars . the analysis of shape optimization methods is based on the analysis of the dependency of the solution on the shape of the dielectric scatterer , and a local analysis involves the study of derivatives with respect to the shape . an explicit form of the shape derivatives is desirable in view of their implementation in shape optimization algorithms such as gradient methods or newton s method . in this paper , we present a complete analysis of the shape differentiability of the solution of the dielectric scattering problem and of its far field pattern , using integral representations . even if numerous works exist on the calculus of shape derivatives of various shape functionals @xcite , in the framework of boundary integral equations the scientific literature is not extensive . however , one can cite the papers @xcite , @xcite and @xcite , where r. potthast has considered the question , starting with his phd thesis @xcite , for the helmholtz equation with dirichlet or neumann boundary conditions and the perfect conductor problem , in spaces of continuous and hlder continuous functions . using the integral representation of the solution , one is lead to study the gteaux differentiability of boundary integral operators and potential operators with weakly singular and hypersingular kernels . the natural space of distributions ( energy space ) which occurs in the electromagnetic potential theory is @xmath0 , the set of tangential vector fields whose components are in the sobolev space @xmath4 and whose surface divergence is in @xmath4 . we face two main difficulties : on one hand , the solution of the scattering problem is given in terms of products of boundary integral operators and their inverses . in order to be able to construct shape derivatives of such products , it is not sufficient to find shape derivatives of the boundary integral operators , but it is imperative to prove that the derivatives are bounded operators between the same spaces as the boundary integral operators themselves . on the other hand , the very definition of shape differentiability of operators defined on the shape - dependent space @xmath0 poses non - trivial problems . our strategy consists in using the helmholtz decomposition of this hilbert space which gives a representation of a tangential vector field in terms of ( tangential derivatives of ) two scalar potentials . in this way , we split the analysis into two steps : first the gteaux differentiability analysis of scalar boundary integral operators and potential operators with strongly and weakly singular kernels , and second the study of shape derivatives of surface differential operators . this work contains results from the thesis @xcite where this analysis has been used to develop a shape optimization algorithm of dielectric lenses in order to obtain a prescribed radiation pattern . this is the second of two papers on shape derivatives of boundary integral operators , the first one @xcite being aimed at a general theory of shape derivatives of singular integral operators appearing in boundary integral equation methods . the paper is organized as follows : in section [ boundintop ] we recall some standard results about trace mappings and regularity properties of the boundary integral operators in electromagnetism . in section [ scatprob ] we define the scattering problem for time - harmonic electromagnetic waves at a dielectric interface . we then give an integral representation of the solution and of the quantity of interest , namely the far field of the dielectric scattering problem following the single source integral equation method developed in @xcite . the remaining parts of the paper are dedicated to the shape differentiability analysis of the solution of the dielectric scattering problem . we use the results of our first paper @xcite on the gteaux differentiability of boundary integral operators with pseudo - homogeneous kernels . we refer to this paper for a discussion of the notion of gteaux derivatives in frchet spaces and of some of their basic properties . in section [ helmholtzdec ] we discuss the difficulties posed by the shape dependency of the function space @xmath0 on which the integral operators are defined , and we present a strategy for dealing with this difficulty , namely using the well - known tool @xcite of helmholtz decomposition . in our approach , we map the variable spaces @xmath5 to a fixed reference space with a transformation that preserves the hodge structure . this technique involves the analysis of surface differential operators that have to be considered in suitable sobolev spaces . therefore in section we recall and extend the results on the differentiability properties of surface differential operators established in ( * ? ? ? * section 5 ) . using the rules on derivatives of composite and inverse functions , we obtain in section [ shapesol ] the shape differentiability properties of the solution of the scattering problem . more precisely , we prove that the boundary integral operators are infinitely gteaux differentiable without loss of regularity , whereas previous results allowed such a loss @xcite , and we prove that the shape derivatives of the potentials are smooth away from the boundary but they lose regularity in the neighborhood of the boundary . this implies that the far field is infinitely gteaux differentiable , whereas the shape derivatives of the solution of the scattering problem lose regularity . these new results generalize existing results : in the acoustic case , using a variational formulation , a characterization of the first gteaux derivative was given by a. kirsch @xcite for the dirichlet problem and then by hettlich @xcite for the impedance problem and the transmission problem . an alternative technique was introduced by kress and pivrinta in @xcite to investigate frchet differentiability in acoustic scattering by the use of a factorization of the difference of the far - field pattern of the scattered wave for two different obstacles . in the electromagnetic case , potthast used the integral equation method to obtain a characterization of the first shape derivative of the solution of the perfect conductor scattering problem . in @xcite , kress improved this result by using a far - field identity and in @xcite kress and haddar extended this technique to acoustic and electromagnetic impedance boundary value problems . at the end of section [ shapesol ] we obtain a characterization of the first shape derivative of the solution of the dielectric scattering problem as the solution of a new electromagnetic transmission problem . we show by deriving the integral representation of the solution that the first derivative satisfies the homogeneous maxwell equations , and by directly deriving the boundary values of the solution itself we see that the first derivative satisfies two new transmission conditions on the boundary . in the end we will have obtained two different algorithms for computing the shape derivative of the solution of the dielectric scattering problem and of the far field pattern : a first one by differentiating the integral representations and a second one by solving the new transmission problem associated with the first derivative . the characterization of the derivatives as solutions to boundary value problems has been obtained in the acoustic case by kress @xcite , kirsch @xcite , hettlich and rundell @xcite and hohage @xcite and has been used for the construction of newton - type or second degree iterative methods in acoustic inverse obstacle scattering . whereas the use of these characterizations requires high order regularity assumption for the boundary , we expect that the differentiation of the boundary integral operators does not require much regularity . although in this paper we treat the case of a smooth boundary , in the last section we give some ideas on possible extensions of the results of this paper to non - smooth domains . a final remark on the terminology of derivatives with respect to the variation of the domain : for the solutions of boundary value problems with a moving boundary , in the context of continuum mechanics one distinguishes frequently between _ material derivatives _ and _ shape derivatives_. the former correspond to the gteaux derivative with respect to the deformation , which is then interpreted as a flow associated with a velocity field , when the solution is pulled back to a fixed undeformed reference domain ( lagrangian coordinates ) . depending on the interpretation of the flow , other names are used , such as `` lagrangian derivative '' , or `` substantial derivative '' . the shape derivatives , on the other hand , correspond to the gteaux derivative of the solution in the deformed domain ( eulerian coordinates ) . one also talks about `` eulerian derivative '' . the difference between the two has the form of a convection term , which can lead to a loss of one order of regularity of the shape derivative on the support of the velocity field @xcite . in the context of this terminology , the derivatives of the boundary integral operators that we studied in part i of this paper @xcite for general pseudohomogeneous kernels and in this paper for the boundary integral operators of electromagnetism , correspond to the lagrangian point of view , because they are obtained by pull - back to a fixed reference boundary . however , the derivative of the solution of dielectric scattering problem that we construct in section [ shapesol ] with the help of the derivatives of the boundary integral operators is the eulerian shape derivative . we also observe the loss of one order of regularity of the shape derivative with respect to the solution of the transmission problem . finally , for the far field , the two notions of derivative coincide , because the deformation has compact support .

we develop the shape derivative analysis of solutions to the problem of scattering of time - harmonic electromagnetic waves by a penetrable bounded obstacle . since boundary integral equations are a classical tool to solve electromagnetic scattering problems , we study the shape differentiability properties of the standard electromagnetic boundary integral operators . the latter are typically bounded on the space of tangential vector fields of mixed regularity . we prove that the electromagnetic boundary integral operators are infinitely differentiable without loss of regularity . we also give a characterization of the first shape derivative of the solution of the dielectric scattering problem as a solution of a new electromagnetic scattering problem .

we develop the shape derivative analysis of solutions to the problem of scattering of time - harmonic electromagnetic waves by a penetrable bounded obstacle . since boundary integral equations are a classical tool to solve electromagnetic scattering problems , we study the shape differentiability properties of the standard electromagnetic boundary integral operators . the latter are typically bounded on the space of tangential vector fields of mixed regularity . using helmholtz decomposition , we can base their analysis on the study of pseudo - differential integral operators in standard sobolev spaces , but we then have to study the gteaux differentiability of surface differential operators . we prove that the electromagnetic boundary integral operators are infinitely differentiable without loss of regularity . we also give a characterization of the first shape derivative of the solution of the dielectric scattering problem as a solution of a new electromagnetic scattering problem .

1003.2557

i

core - collapse supernovae ( sne ) are extraordinary events situated at the crossroads of many fields of astrophysics . they mark the birth of compact objects , either neutron stars or stellar - mass black holes which , owing to their high compactness , are often the site of tremendous magnetic fields , as in magnetars , or the site of tremendous rotation rates , as in millisecond - period pulsars . their ejecta make a significant contribution to the chemical enrichment of galaxies , while affecting their dynamics and energetics . the connection to @xmath1-ray bursts , for a subset of these sne , may turn them into excellent probes of the early universe . our focus , however , is to characterize the sn ejecta itself and extract information that can help us understand the properties of the explosion and of the progenitor star . such inferences are based on the analysis of the sn light , using photometric , spectroscopic , or spectropolarimetric data . hence , developing accurate radiative - transfer tools capturing the key physics controlling the interaction of light and matter is of prime importance . of all sne , only core - collapse , and in particular type ii sne , have well - identified progenitors . numerous type ii - plateau ( ii - p ) sne have now been associated with the explosion of low - mass red - supergiant ( rsg ) stars @xcite , while the progenitor of the type ii - peculiar sn1987a was a blue - supergiant ( bsg ) star , named sk -69 202 ( for a review , see , e.g. , @xcite ) . the excellent quality of the observational data for sn1987a makes it ideal for detailed modeling . numerous radiative - transfer studies of the early - time spectra of sn1987a have been done , with some success @xcite . however , these studies are now twenty years old . they generally assumed local thermodynamic equilibrium ( lte ; at best treating only a fraction of the species / levels in non - lte ) and/or steady - state for the radiative transfer , and employed small model atoms . @xcite and @xcite have emphasized the effects of line blanketing in the uv . one explicit question raised by these studies was the problematic observation of hei lines in optical spectra , which required unacceptable helium enrichments . more recently , @xcite argued for significant mixing of @xmath2ni beyond 5000 in order to reproduce balmer line profiles during the first weeks after explosion . the balmer line strength problem has now been associated with the erroneous neglect of important time - dependent terms that appear in the energy and statistical - equilibrium equations ( @xcite ; @xcite ) , while reproducing the characteristics of hei lines seems to require a non - lte treatment . hence , some of these discrepancies may simply reflect the shortcomings of the radiative - transfer tools employed rather than a genuine peculiarity of the progenitor . taking a new look at this dataset therefore seems warranted . furthermore , studying sn1987a is a good exercise to gauge the level of accuracy of radiative - transfer codes and assumptions , facilitated by the considerable advances in computer technology over the last twenty years . because atomic data represent a fundamental and essential ingredient of radiative - transfer computations , the considerable improvements in that domain over that period make such calculations more accurate than calculations done when sn1987a went off . in this paper , we present a new approach for non - lte time - dependent radiative transfer modeling of sn ejecta using the code cmfgen @xcite . we discuss the conceptual aspects of the method and emphasize the key equations that are solved , delaying a more comprehensive presentation of the technical details to a forthcoming paper ( hillier & dessart 2010 , in preparation ) . we illustrate this new capability with results obtained for sn1987a , starting our time evolution from an hydrodynamical input of an exploded bsg star ( woosley , priv . comm . ; model lm18a7ad " ) . we do not present an in - depth study of sn1987a , but merely use this well - observed sn to check and confront our model results . a preliminary set of results were presented in @xcite . in the following section , we discuss the various approaches we have used in the recent years for sn spectroscopic modeling , emphasizing their merits and limitations . we then describe in [ sect_setup ] the hydrodynamical model we employ as a basis for this calculation , summarizing its various properties , before presenting our setup for the radiative - transfer calculation . in [ sect_results ] , we describe the ejecta evolution , such as temperature and ionization structure , and present checks on our numerical technique . we then discuss in [ sect_synthetic_rad ] the radiative properties of our non - lte time - dependent models , covering in turn synthetic spectra and the bolometric light curve , and detailing in particular the sources of line blanketing at various epochs . in [ sect_comp_to_obs ] , we compare our theoretical predictions to uv and optical observations of sn1987a . finally we present our conclusions in [ sect_ccl ] , and lay out the various projects ahead .

we discuss a new one - dimensional non - lte time - dependent radiative - transfer technique for the simulation of supernova ( sn ) spectra and light curves . starting from a hydrodynamical input characterizing the homologously - expanding ejecta at a chosen post - explosion time the effects of line blanketing on the radiation field are explicitly included , using complex model atoms and solving for all ion level populations appearing in the statistical - equilibrium equations . here , we present results for sn1987a , evolving the model `` lm18a7ad '' of woosley from 0.27 to 20.8d . the effects of time dependence on the ionization structure , discussed in dessart & hillier , are recovered , and thus nicely integrated in this new scheme . despite the 1d nature of our approach , its high physical consistency and accuracy will allow reliable inferences to be made on explosion properties and pre - sn star evolution .

we discuss a new one - dimensional non - lte time - dependent radiative - transfer technique for the simulation of supernova ( sn ) spectra and light curves . starting from a hydrodynamical input characterizing the homologously - expanding ejecta at a chosen post - explosion time , we model the evolution of the _ entire _ ejecta , including gas and radiation . the boundary constraints for this time- , frequency- , space- , and angle - dependent problem are the adopted initial ejecta , a zero - flux inner boundary and a free - streaming outer boundary . this relaxes the often unsuitable assumption of a diffusive inner boundary , but will also allow for a smooth transition from photospheric to nebular conditions . non - lte , which holds in all regions at and above the photosphere , is accounted for . the effects of line blanketing on the radiation field are explicitly included , using complex model atoms and solving for all ion level populations appearing in the statistical - equilibrium equations . here , we present results for sn1987a , evolving the model `` lm18a7ad '' of woosley from 0.27 to 20.8d . the fastest evolution occurs prior to day 1 , with a spectral energy distribution peaking in the range - 2000 , subject to line blanketing from highly ionized metal and cno species . after day 1 , our synthetic multi - band light curve and spectra reproduce the observations to within 10 - 20% in flux in the optical , with a greater mismatch for the faint uv flux . we do not encounter any of the former discrepancies associated with the hei and hi lines in the optical , which can be fitted well with a standard blue - supergiant - star surface composition and no contribution from radioactive decay . the effects of time dependence on the ionization structure , discussed in dessart & hillier , are recovered , and thus nicely integrated in this new scheme . despite the 1d nature of our approach , its high physical consistency and accuracy will allow reliable inferences to be made on explosion properties and pre - sn star evolution . [ firstpage ] radiative transfer stars : atmospheres stars : supernovae - stars : supernovae : individual : sn 1987a

1003.2557

c

we have presented a new approach for radiative - transfer modeling of sn ejecta , retaining the key assets of our former approaches . by treating non - lte explicitly and incorporating time - dependent terms in the statistical - equilibrium , energy , and moments of the radiative transfer equations , we improve the physical consistency of our computations . in particular , the simulations are performed on the entire ejecta , starting from a given hydrodynamical input at a given post - explosion time , making this an initial - value problem , while spatial boundaries are zero - flux at the inner edge and free - streaming at the outer edge . as diffusion at the inner boundary does not need to hold we can evolve the ejecta from its photospheric to its nebular phase . importantly , integrating our synthetic spectra over filter - transmission functions , we compute non - lte light - curves that account for the explicit role of line - blanketing , without recourse to the standard expansion opacities and the assumption of lte for the gas , as is typically used ( see , e.g. , @xcite ) . delaying a presentation of all the technical details of this new approach ( hillier & dessart 2010 , in preparation ) , we illustrate in this paper these modeling improvements with results for sn1987a , using as our starting conditions the ejecta composition and structure of the hydrodynamical input model `` lm18a7ad '' of woosley ( priv . we evolved the ejecta gas and radiation from 0.27 to 20.8d after explosion , corresponding to a spatial expansion of a factor of 77 , and considerable cooling . at the photosphere , the ejecta conditions evolve from fully - ionized to once - ionized and neutral . during the 21 day time sequence , the photosphere recedes in mass , and thus in velocity , while its radius increases steadily . after a few days , the photospheric location is primarily set by the location of the hydrogen ionization front . our computed temperature and electron - density evolution reproduces predictions for a radiation - dominated homologously - expanding gas , modulo the effect of cooling at the photosphere and heating from radioactive decay in the inner ejecta . at the last time in the simulation , the photosphere is at 4500 , and is not influenced , either directly or indirectly , by energy deposition from radioactive decay occurring below 2000 in our model . the surface conditions computed here and prior to 20d are thus not affected by unstable nuclei . since the sn1987a model ejecta we employ are homogeneous above 4500 , the changes we observe in the spectrum over this 21-day time span are conditioned by modulations in ionization rather than composition . adopting a distance of 50kpc and a reddening @xmath88 , we obtain very good agreement between synthetic and observed light curves in the optical . our @xmath92-band synthetic magnitudes are , however , too bright by a fraction of a magnitude at early times , and this discrepancy slowly grows as the flux in the blue ebbs . our synthetic spectra computed for the epoch 0.31d can not be compared to observations , which started one day after explosion . at such early times , we find an sed with a peak flux in the far - uv , where strong line blanketing occurs due to 3 - 4-times ionized metal species ( o , fe , ni ) , while the nearly - featureless optical range shows weak lines associated with hi , heii and hei . after day 1 and until the 14th of march 1987 , we compare our predictions to observations . in general , the flux agreement in the optical is at the 10% level ( in an absolute sense , i.e. , without any normalization ) , while in the uv range it is within 30 - 50% . in contrast with @xcite , we reproduce the strength and morphology of hei lines at early times , under a photospheric composition that is compatible with a bsg progenitor star . throughout the time span of our sequence , we reproduce well the multi - band light curve , the overall sed , and in particular the strength and shape of h@xmath35 . since radioactive decay does not influence the computed photospheric conditions in any way at such times , and given the relatively good fit to observations ( in particular if we focus on the bulk of the emergent luminosity , which falls at optical wavelengths ) , it does not play a pivotal role for understanding the radiative properties of sn1987a up to 20d , in contradiction with the proposition of @xcite . in contrast , our good reproduction of the balmer line profiles at all times , and in particular when there are no longer any photons in the lyman and balmer continua , gives strong support to our proper modeling of the time - dependent ionization structure of the sn1987a ejecta , an important issue emphasized by @xcite and @xcite . @xcite suggest that such time - dependent effects are much weaker , but their presentation for the recombination phase of sn1987a is unconvincing since they use models that are fully - ionized and uv bright ( in contradiction with observations ) . furthermore , despite the one - dimensionality of our approach , we achieve very competitive fits to observations . one may argue the unresolved problems we encounter are caused by those neglected multi - dimensional effects , but we surmise this departure from sphericity would also alter line profile shapes etc . , which are fairly well reproduced ( see , e.g. , h@xmath35 ) . we predict the fastest spectral evolution in sn1987a occurred prior to day 1 . from 0.3d to 1d , most of the flux was emitted in the range 300 - 3000 which could have been captured by the iue satellite . prior to 0.27d , the photosphere would have shone at shorter wavelengths , but the uv range would have revealed the long - wavelength tail of that sed , testifying for the hotter conditions at earlier post - breakout times . this suggests that obtaining multiple observations prior to day 1 , across as broad a wavelength range as possible , would have captured the phase of fastest evolution of sn1987a . while the uv shows the largest changes , multiple spectra , rather than a unique spectrum , of sn1987a during both the first and the second night of its evolution would have been valuable.m allows us to gather information on ca and cno lines in the red part of the spectrum , as well as constrain the reddening with the blue part . ] this applies to some extent to type ii - p sn as well , although their evolution is slower . in type i sne , the sed likely evolves too fast after breakout to allow us to capture it , but then , the first few days after explosion would be very useful for constraining the surface composition of the progenitor . overall , observing frequently at early times would provide important constraints that are generally missing in current observations . the work presented here is an essential benchmarking of our code since sn1987a is one of the best understood and best observed supernova . as it places numerous and tight observational constraints , it offers _ a valuable alternative , although not a replacement , _ to benchmarking against other codes . the combined approach of using non - lte , time dependence , and line blanketing seems very promising . the future from here is to systematize such investigations by evolving a wide range of ejecta for all supernova types and compare results with multi - epoch multi - wavelength observations . the aim is then to use such models and observations to make quantitative inferences on the progenitor properties , pre - sn star evolution , and the explosion mechanism . in the context of sn1987a , we now need to repeat the present exploration with a variety of progenitor stars and explosion properties , in order to delineate the systematics associated with core - collapse sn explosions of bsg stars . in parallel , it would be valuable to gather additional and high quality observational data for similar type ii - peculiar events like sn1987a .

problem are the adopted initial ejecta , a zero - flux inner boundary and a free - streaming outer boundary . the fastest evolution occurs prior to day 1 , with a spectral energy distribution peaking in the range - 2000 , subject to line blanketing from highly ionized metal and cno species . after day 1 , our synthetic multi - band light curve and spectra reproduce the observations to within 10 - 20% in flux in the optical , with a greater mismatch for the faint uv flux .

we discuss a new one - dimensional non - lte time - dependent radiative - transfer technique for the simulation of supernova ( sn ) spectra and light curves . starting from a hydrodynamical input characterizing the homologously - expanding ejecta at a chosen post - explosion time , we model the evolution of the _ entire _ ejecta , including gas and radiation . the boundary constraints for this time- , frequency- , space- , and angle - dependent problem are the adopted initial ejecta , a zero - flux inner boundary and a free - streaming outer boundary . this relaxes the often unsuitable assumption of a diffusive inner boundary , but will also allow for a smooth transition from photospheric to nebular conditions . non - lte , which holds in all regions at and above the photosphere , is accounted for . the effects of line blanketing on the radiation field are explicitly included , using complex model atoms and solving for all ion level populations appearing in the statistical - equilibrium equations . here , we present results for sn1987a , evolving the model `` lm18a7ad '' of woosley from 0.27 to 20.8d . the fastest evolution occurs prior to day 1 , with a spectral energy distribution peaking in the range - 2000 , subject to line blanketing from highly ionized metal and cno species . after day 1 , our synthetic multi - band light curve and spectra reproduce the observations to within 10 - 20% in flux in the optical , with a greater mismatch for the faint uv flux . we do not encounter any of the former discrepancies associated with the hei and hi lines in the optical , which can be fitted well with a standard blue - supergiant - star surface composition and no contribution from radioactive decay . the effects of time dependence on the ionization structure , discussed in dessart & hillier , are recovered , and thus nicely integrated in this new scheme . despite the 1d nature of our approach , its high physical consistency and accuracy will allow reliable inferences to be made on explosion properties and pre - sn star evolution . [ firstpage ] radiative transfer stars : atmospheres stars : supernovae - stars : supernovae : individual : sn 1987a

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by now there is convincing evidence for solar and atmospheric neutrino oscillations . the @xmath4 values and mixing angles are known with fair accuracy @xcite . for @xmath4 we have : @xmath5 ev@xmath6 and @xmath7 ev@xmath6 . as for the mixing angles , two are large and one is small . the atmospheric angle @xmath0 is large , actually compatible with maximal but not necessarily so : at @xmath8 : @xmath9 with central value around @xmath10 . the solar angle @xmath11 is large , @xmath12 , but certainly not maximal ( by about 5 - 6 @xmath13 now @xcite ) . the third angle @xmath14 is strongly limited , mainly by the chooz experiment , and has at present a @xmath8 upper limit given by about @xmath15 . in spite of this experimental progress there are still many alternative routes in constructing models of neutrino masses . this variety is mostly due to the considerable ambiguities that remain . first of all , it is essential to know whether the lsnd signal @xcite , which has not been confirmed by karmen @xcite and is currently being double - checked by miniboone @xcite , will be confirmed or will be excluded . if lsnd is right we probably need at least four light neutrinos ; if not we can do with only the three known ones , as we assume here in the following . as neutrino oscillations only determine mass squared differences a crucial missing input is the absolute scale of neutrino masses ( within the existing limits from terrestrial experiments and cosmology @xcite,@xcite ) . even for three neutrinos the pattern of the neutrino mass spectrum is still undetermined : it can be approximately degenerate , or of the inverse hierarchy type or normally hierarchical . given for granted that neutrinos are majorana particles , their masses can still arise either from the see - saw mechanism or from generic dimension - five non renormalizable operators . at a more direct level , we do not know how small the mixing angle @xmath14 is and how close to maximal is @xmath0 . one can make a distinction between `` normal '' and `` special '' models . for normal models @xmath0 is not too close to maximal and @xmath14 is not too small , typically a small power of the self - suggesting order parameter @xmath16 , with @xmath17 . special models are those where some symmetry or dynamical feature assures in a natural way the near vanishing of @xmath14 and/or of @xmath18 . normal models are conceptually more economical and much simpler to construct . we expect that experiment will eventually find that @xmath14 is not too small and that @xmath0 is sizably not maximal . but if , on the contrary , either @xmath14 very small or @xmath0 very close to maximal will emerge from experiment , then theory will need to cope with this fact . thus it is interesting to conceive and explore dynamical structures that could lead to special models in a natural way . we want to discuss here some particularly special models where both @xmath14 and @xmath18 exactly vanish . then the neutrino mixing matrix @xmath19 ( @xmath20,@xmath21,@xmath22 , @xmath23 ) , in the basis of diagonal charged leptons , is given by , apart from sign convention redefinitions : @xmath24 where @xmath25 and @xmath26 stand for @xmath27 and @xmath28 , respectively . it is much simpler to write natural models of this type with @xmath26 small and thus many such attempts are present in the early literature . more recently , given the experimental value of @xmath11 , the more complicated case of @xmath26 large was also attacked , using non abelian symmetries , either continuous or discrete @xcite . in many examples the invoked symmetries are particularly ad hoc and/or no sufficient attention is devoted to corrections from higher dimensional operators that can spoil the pattern arranged at tree level and to the highly non trivial vacuum alignment problems that arise if naturalness is required also at the level of vacuum expectation values ( vevs ) . an interesting special case of eq . ( [ ufi1 ] ) is obtained for @xmath29 , i.e. the so - called tri - bimaximal or harrison - perkins - scott mixing pattern ( hps ) @xcite , with the entries in the second column all equal to @xmath30 in absolute value : @xmath31 this matrix is a good approximation to present data . , to be compared with the latest experimental determination @xcite : @xmath32 . ] it would be interesting to find a natural and appealing scheme that leads to this matrix with good accuracy . in fact this is a most special model where not only @xmath14 and @xmath18 vanish but also @xmath11 assumes a particular value . clearly , in a natural realization of this model , a very constraining and predictive dynamics must be underlying . we think it is interesting to explore particular structures giving rise to this very special set of models in a natural way . in this case we have a maximum of `` order '' implying special values for all mixing angles : at the other extreme , anarchical models have been proposed @xcite , where no structure at all is assumed in the lepton sector , so that , for example , @xmath14 and @xmath0 are predicted to be in no way special , except that there must be a smallest angle ( probably near to the present bound ) and a largest angle ( expected sizably different from maximal ) . interesting ideas on how to obtain the hps mixing matrix have been discussed in refs @xcite . the most attractive models are based on the discrete symmetry @xmath3 , which appears as particularly suitable for the purpose , and were presented in ref . @xcite . in the present paper we start by discussing some general features of hps models . we then present a new version of an @xmath3 model , with ( moderate ) normal hierarchy , and discuss in detail all aspects of naturalness in this model , also considering effects beyond tree level and the problem of vacuum alignment . there are a number of substantial improvements in our version with respect to ma in ref . first , the hps matrix is exactly obtained in a first approximation when higher dimensional operators are neglected , without imposing ad hoc relations among parameters ( in ref . the equality of @xmath33 and @xmath34 is not guaranteed by the symmetry ) . the observed hierarchy of charged lepton masses is obtained by assuming a larger flavour symmetry . the crucial issue of the required vev alignment in the scalar sector is considered with special attention and we present a natural solution of this problem . we also keep the flavour scalar fields distinct from the normal higgs bosons ( a proliferation of higgs doublets is disfavoured by coupling unification ) and singlets under the standard model gauge group . last not least , we study the corrections from higher dimensionality operators allowed by the symmetries of the model and discuss the conditions on the cut - off scales and the vevs in order for these corrections to be completely under control .

we discuss a particularly symmetric model of neutrino mixings where , with good accuracy , the atmospheric mixing angle is maximal , and the solar angle satisfies ( harrison - perkins - scott ( hps ) matrix ) . we construct a model where the hps matrix is exactly obtained in a first approximation without imposing ad hoc relations among parameters . the crucial issue of the required vev alignment in the scalar sector is discussed and we present a natural solution of this problem based on a formulation with extra dimensions . we study the corrections from higher dimensionality operators allowed by the symmetries of the model and discuss the conditions on the cut - off scales and the vevs in order for these corrections to be completely under control . finally , the observed hierarchy of charged lepton masses is obtained by assuming a larger flavour symmetry .

we discuss a particularly symmetric model of neutrino mixings where , with good accuracy , the atmospheric mixing angle is maximal , and the solar angle satisfies ( harrison - perkins - scott ( hps ) matrix ) . the discrete symmetry is a suitable symmetry group for the realization of this type of model . we construct a model where the hps matrix is exactly obtained in a first approximation without imposing ad hoc relations among parameters . the crucial issue of the required vev alignment in the scalar sector is discussed and we present a natural solution of this problem based on a formulation with extra dimensions . we study the corrections from higher dimensionality operators allowed by the symmetries of the model and discuss the conditions on the cut - off scales and the vevs in order for these corrections to be completely under control . finally , the observed hierarchy of charged lepton masses is obtained by assuming a larger flavour symmetry . we also show that , under general conditions , a maximal can never arise from an exact flavour symmetry . 0.5 cm * tri - bimaximal neutrino mixing from discrete symmetry in extra dimensions * 0.2 cm 0.5 cm guido altarelli + .1 cm cern , department of physics , theory division + ch-1211 geneva 23 , switzerland + .1 cm and + dipartimento di fisica ` e. amaldi ' , universit di roma tre + infn , sezione di roma tre , i-00146 rome , italy + .2 cm ferruccio feruglio + .1 cm dipartimento di fisica ` g. galilei ' , universit di padova + infn , sezione di padova , via marzolo 8 , i-35131 padua , italy + 0.7 cm 2truecm

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there are by now several theoretical mechanisms that can qualitatively explain the observed large lepton mixing angles @xcite . they are sufficiently flexible to quantitatively accommodate the measured parameters . they are also compatible with our ideas on quarks masses and mixing angles so that they can be nicely embedded into a unified picture of fermion properties , such as , for instance , a grand unified theory . many of these mechanisms predict a generically large atmospheric mixing angle and a generically small @xmath14 angle , without favouring any specific value for these parameters . the best values of global fits are currently very close to @xmath52 and @xmath1 , but the experimental errors still allow for large deviations from these remarkable values . indeed , according to many of the above mentioned mechanisms , deviations from @xmath52 and @xmath1 are expected at the observable level . it may take a long time before such deviations can be actually observed . a sensitivity on @xmath14 around @xmath257 is foreseen in about ten years from now , with the full exploitation of high - intensity neutrino beams . a reduction by a factor of two of the present error on @xmath0 will also require special neutrino beams and a similar time scale . it might happen that after all this experimental effort , @xmath258 and @xmath14 still remain close to zero , within errors . at this point it would be legitimate to suspect that such special values are produced by a highly symmetric flavour dynamics . given the already good experimental precision on @xmath11 , the so - called harrison - perkins - scott mixing scheme , where @xmath52 , @xmath1 and @xmath259 , would fit very well the data . in this paper we have proposed a model that reproduces accurately the hps mixing pattern . we started by discussing whether such a pattern can be obtained from an exact flavour symmetry . we showed that , under general conditions , an exactly maximal atmospheric mixing angle can not arise from an exact flavour symmetry . the flavour symmetry should be necessarily broken and a maximal @xmath0 is the result of a special alignment between the breaking effects in the neutrino sector and those occurring in the charged lepton sector . if the flavour symmetry is spontaneously broken , this corresponds to a non - trivial vacuum alignment . our model gives rise to the hps mixing scheme in the context of a spontaneously broken @xmath3 flavour symmetry , @xmath3 being the discrete subgroup of so(3 ) leaving a tetrahedron invariant . at leading order , that is by neglecting symmetric operators of higher dimension , neutrino masses only depend on two complex yukawa coupling constants . due to the unknown phase difference between these two constants , we can not determine the absolute scale of neutrino masses . we expect that the neutrino spectrum is of the normal hierarchy type but not too far from degenerate . at leading order the model predicts @xmath260 . a remarkable feature of our model is that at the leading order the lepton mixing angles are completely independent from these two parameters , so that the hps mixing pattern is always obtained . the lepton mixing depends entirely on the relative alignment between the vevs giving masses to the neutrino sector and those giving masses to the lepton sector . we discuss in detail the problem of vacuum alignment . to avoid the proliferation of higgs doublets , the scalar fields breaking @xmath3 are gauge singlets in our model . we propose an unconventional solution to the vacuum alignment problem , where an extra dimension described by a spatial interval plays an important role . two scalar sectors live at the opposite ends of the interval and their respective scalar potentials are minimized by the desired field configurations , for natural values of the implied parameters . such a mechanism only works in the case of discrete symmetries , since in the continuous case the large symmetry of the total potential energy would make the relative orientations of the two scalar sectors undetermined . we have also extensively discussed how this lowest order picture is modified by the introduction of higher dimensional operators . the induced corrections are parametrically small , of second order in the expansion parameter @xmath261 , @xmath106 being the cut - off of the theory , and they can be made numerically negligible . last but not least , the hierarchy of the charged lepton masses can be reproduced by the usual froggatt - nielsen mechanism within the context of an abelian flavour symmetry , which turns out to be fully compatible with the present scheme . we believe that , from a purely technical point of view , we have fulfilled our goal to realize a completely natural construction of the hps mixing scheme . but to construct our model we had to introduce a number of special dynamical tricks ( like a peculiar set of discrete symmetries in extra dimensions ) . apparently this is the price to pay for a `` special '' model where all mixing angles are fixed to particular values . perhaps this exercise can be taken as a hint that it is more plausible to expect that , in the end , experiment will select a `` normal '' model with @xmath14 not too small and @xmath0 not too close to maximal . 0.2 cm

we also show that , under general conditions , a maximal can never arise from an exact flavour symmetry . 0.5 cm * tri - bimaximal neutrino mixing from discrete symmetry in extra dimensions * 0.2 cm 0.5 cm guido altarelli + .1 cm cern , department of physics , theory division + ch-1211 geneva 23 , switzerland + .1 cm and + dipartimento di fisica ` e. amaldi ' , universit di roma tre + infn , sezione di roma tre , i-00146 rome , italy + .2 cm ferruccio feruglio + .1 cm dipartimento di fisica ` g. galilei ' , universit di padova + infn , sezione di padova , via marzolo 8 , i-35131 padua , italy + 0.7 cm 2truecm

we discuss a particularly symmetric model of neutrino mixings where , with good accuracy , the atmospheric mixing angle is maximal , and the solar angle satisfies ( harrison - perkins - scott ( hps ) matrix ) . the discrete symmetry is a suitable symmetry group for the realization of this type of model . we construct a model where the hps matrix is exactly obtained in a first approximation without imposing ad hoc relations among parameters . the crucial issue of the required vev alignment in the scalar sector is discussed and we present a natural solution of this problem based on a formulation with extra dimensions . we study the corrections from higher dimensionality operators allowed by the symmetries of the model and discuss the conditions on the cut - off scales and the vevs in order for these corrections to be completely under control . finally , the observed hierarchy of charged lepton masses is obtained by assuming a larger flavour symmetry . we also show that , under general conditions , a maximal can never arise from an exact flavour symmetry . 0.5 cm * tri - bimaximal neutrino mixing from discrete symmetry in extra dimensions * 0.2 cm 0.5 cm guido altarelli + .1 cm cern , department of physics , theory division + ch-1211 geneva 23 , switzerland + .1 cm and + dipartimento di fisica ` e. amaldi ' , universit di roma tre + infn , sezione di roma tre , i-00146 rome , italy + .2 cm ferruccio feruglio + .1 cm dipartimento di fisica ` g. galilei ' , universit di padova + infn , sezione di padova , via marzolo 8 , i-35131 padua , italy + 0.7 cm 2truecm

1110.3915

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the measurement of a very weak force such as the detection of gravitational wave demands a very high resolution interferometer . the role of the interferometer is to transform small variation of the relative spatial separation of the mirrors between two arms into variation of the output photons . quantum noise presumably places a limitation on accuracy of the measurement @xcite . in quantum optics , the discussion related to quantum noise of radiation fields on the mirror has been mostly based on the photon - number approach . it is argued by caves @xcite that quantum noise in a laser interferometer may come from the quantum nature of the light directly via photon number fluctuations ( shot noise ) or indirectly via random motion of the mirror due to a fluctuating force ( radiation pressure fluctuations ) . minimizing the total uncertainty from two sources of noise , with an assumption of no correlation between them , may give the standard quantum limit ( sql ) , when an input power of the light is appropriately tuned . additionally , caves further suggests that injecting squeezed vacuum state into the unused port of an interferometer should lead to the sql with a lower optimum input power @xcite , as compared with the standard interferometer @xcite . this seminal work also shows the manipulated quantum fluctuations of the electromagnetic fields are responsible for both the radiation - pressure forces and the fluctuations of the photon number . then , an inquiry into the assumption of no correlation between these two noise sources arises . in particular , the presence of negative correlations may lead to the uncertainly even below the sql . to establish their correlations requires an unified scheme that has been proposed by loudon @xcite . the judicious use of the correlated squeezed state is proposed to establish the above correlations with which to possibly push the sensitivity of the interferometer beyond the sql @xcite . the redesign of an interferometer by adding some optical components to either manipulate the read - outs or modify the dynamics of the test mass , such as in the `` optical bar '' @xcite or the `` optical spring '' @xcite scheme , is also possibly to give non - zero correlations in order to beat the sql . the coupling between the mirror and the radiation field can be obtained by considering the mirror as a reflector that imposes boundary conditions of the field on the surface of the mirror . in 3 + 1 dimensions , field quantization is treated perturbatively for a slowly moving , perfectly reflecting mirror by vilenkin and ford @xcite , with the boundary conditions of the field on the surface of the mirror at all times . they then explore the backreaction dissipative effect on a moving mirror , induced by vacuum fluctuations of the field . later a corresponding langevin equation was derived by two of us @xcite with the method of influence functional , in which the accompanying noise , manifested from vacuum fluctuations is taken into account . thus , the effects of the backreaction dissipation and its accompanying noise can be related by the underlying fluctuation - dissipation relation . unruh @xcite extended the quantization scheme to the interferometer case where the field propagates toward a mirror and then acquires a time - dependent phase shift after reflecting off the mirror . because of the moving boundary , the phase shift in general depends on the mirror s motion , but can be obtained by assuming slow - motion of the mirror . similar phase shift was also introduced by kimble _ et al . _ @xcite , and it has been proposed to improve performance of the laster interferometer , particularly , in @xcite . here we adopt the field quantization scheme similar to unruh s proposal to investigate the problem of quantum noise and its associated correlation in a simpler configuration , shown in fig . [ fi : dksl ] . the basic idea is to consider a free , perfectly reflecting mirror . a coherent state of the quantum scalar field is normally shined on the mirror s surface , and exerts a pressure force on the mirror . it drives the mirror into motion , which in turn leads to variation of the reflected field . then the read - out field is measured by a standard monopole detector , which is placed somewhere between the mirror and the field source . since the radiation pressure is described by a surface integral of the stress - tensor of the scalar field , if the input quantum state is not an eigenstate of the operator associated with the response function of the detector or the stress - tensor , the resulting measurement will exhibit fluctuations . the goal of this paper is two - fold . first of all , we lay out a field - theoretic approach by which the effective distance between the detector and the mirror can be decoded from the read - out fields . in this simpler system , the sources of the uncertainty in the read - outs can be easily identified in the slow motion limit when the mirror is driven by radiation pressure of the incident field . thus reduction in uncertainty of this effective distance is of essence to improve the sensitivity of the interferometer . when the incident field is in the single - mode coherent state , it will be shown that the particle number approach , typically used in quantum optics , is equivalent to this field theoretic approach in the late - time limit with a large number of the scalar particles ( photon ) . we will elaborate the previously mentioned approximations later . in addition to shot noise and radiation pressure fluctuations , a new source of noise comes from modified field fluctuations . it is induced by the mean displacement of the mirror as a result of the radiation pressure . its effect can be systematically examined in the field theoretic approach . secondly , the emphasis is put on how correlation among all sources of quantum noise associated with the radiation field , can emerge when the interference of the incoming field and the reflected filed by the mirror are taken into account . we further examine the effects of correlation on possible reduction of uncertainty in the read - outs of the monopole detector . we show an example in which the overall uncertainty can be suppressed to beat the standard quantum limit . our presentation is organized as follows . in sec . [ sec1 ] , we introduce the quantization scheme of a massless scalar field subject to boundary conditions on a free , perfectly reflecting mirror when it undergoes slow motion . the motion of the mirror arises from radiation pressure of the scalar field . a monopole detector is introduced to measure the readout field . we then identify the sources of quantum noise from the fluctuations of the readouts in sec . [ sec2 ] with an emphasis on establishing correction between them . the effects of correlation are further studied in sec . [ sec3 ] for possibility of reducing overall quantum noise . in sec . [ sec4 ] the langevin equation of the mirror , including backreaction from the radiation field , is derived , and we show that this effect is negligible for slow motion . conclusions are drawn in sec [ sec6 ] . the lorentz - heaviside units and the convention @xmath0 will be used unless otherwise mentioned . the signature of the metric is @xmath1 .

the associated radiation pressure is described by a surface integral of the stress - tensor of the field . the read - out field is measured by a monople detector , form which the effective distance between the detector and mirror can be obtained . in the slow - motion limit of the mirror , we are able to identify various sources of quantum noise that lead to uncertainty of the read - out measurement . we also examine the validity of the particle number approach , which is often used in quantum optics , and compared its results with those given by the field theoretical approach .

we employ the field theoretic approach to study the quantum noise problem in the mirror - field system , where a perfectly reflecting mirror is illuminated by a single - mode coherent state of the massless scalar field . the associated radiation pressure is described by a surface integral of the stress - tensor of the field . the read - out field is measured by a monople detector , form which the effective distance between the detector and mirror can be obtained . in the slow - motion limit of the mirror , we are able to identify various sources of quantum noise that lead to uncertainty of the read - out measurement . since the mirror is driven by radiation pressure , the sources of noise , other than the shot nose given by the intrinsic fluctuations of the incident state , may also result from random motion of mirror due to radiation pressure fluctuations and from modified field fluctuations induced by the displacement of the mirror . correlation between different sources of noise can be established as the consequence of interference between the incident field and the reflected field out of the mirror in the read - out measurement . the overall uncertainty is found to decrease ( increase ) due to the negative ( positive ) correlation . in the case of negative correlation , the uncertainty can be lowered than the value predicted by the standard quantum limit . we also examine the validity of the particle number approach , which is often used in quantum optics , and compared its results with those given by the field theoretical approach . finally we discuss the backreaction effects , induced by the radiation pressure , that alter the dynamics of the mean displacement of the mirror , and we argue this backreaction can be ignored for a slowly moving mirror .

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the problem of quantum noise in the mirror - field system has been studied in the field theoretic approach . we consider that a single , perfectly reflecting mirror is illuminated by a single - mode coherent state of a massless scalar field , in addition to ambient vacuum fluctuations . the net field is read out by a monopole detector , placed between the mirror and the field source . the radiation pressure of the coherent state drives the mirror into motion . in the slow motion limit , we may identify different sources of quantum noise of the radiation field from readouts of the detector . in turn , the effective distance between the mirror and the detector can be obtained . the sources of quantum noise are respectively attributed to the intrinsic fluctuations of the field ( shot noise ) , induced fluctuations arising from stochastic motion of the mirror due to the radiation pressure fluctuations , and modified field fluctuations which result from the mean displacement of the mirror . their correlations can then be established resulting from interference between the incident field and the reflected field out of the mirror in the read - out measurement . the overall uncertainty can be found decreased ( increased ) due to negative ( positive ) correlation between noise sources . in particular , negative correlation may lead to the situation that overall uncertainty is even lower than that in the standard quantum limit . backreactions induced by the radiation pressure is studied by deriving the associated langevin equation from first principles . the backreaction effects are found insignificant for a slowly moving mirror . the langevin equation incorporates not only backreaction from radiation pressure on the mirror but also noise manifested by the field fluctuations . equipped with the langevin equation of the mirror - field system , it deserves further study to improve the performance of the interferometer as the work in @xcite by taking advantage of the backreaction effect .

we employ the field theoretic approach to study the quantum noise problem in the mirror - field system , where a perfectly reflecting mirror is illuminated by a single - mode coherent state of the massless scalar field . since the mirror is driven by radiation pressure , the sources of noise , other than the shot nose given by the intrinsic fluctuations of the incident state , may also result from random motion of mirror due to radiation pressure fluctuations and from modified field fluctuations induced by the displacement of the mirror . correlation between different sources of noise can be established as the consequence of interference between the incident field and the reflected field out of the mirror in the read - out measurement . the overall uncertainty is found to decrease ( increase ) due to the negative ( positive ) correlation . in the case of negative correlation

we employ the field theoretic approach to study the quantum noise problem in the mirror - field system , where a perfectly reflecting mirror is illuminated by a single - mode coherent state of the massless scalar field . the associated radiation pressure is described by a surface integral of the stress - tensor of the field . the read - out field is measured by a monople detector , form which the effective distance between the detector and mirror can be obtained . in the slow - motion limit of the mirror , we are able to identify various sources of quantum noise that lead to uncertainty of the read - out measurement . since the mirror is driven by radiation pressure , the sources of noise , other than the shot nose given by the intrinsic fluctuations of the incident state , may also result from random motion of mirror due to radiation pressure fluctuations and from modified field fluctuations induced by the displacement of the mirror . correlation between different sources of noise can be established as the consequence of interference between the incident field and the reflected field out of the mirror in the read - out measurement . the overall uncertainty is found to decrease ( increase ) due to the negative ( positive ) correlation . in the case of negative correlation , the uncertainty can be lowered than the value predicted by the standard quantum limit . we also examine the validity of the particle number approach , which is often used in quantum optics , and compared its results with those given by the field theoretical approach . finally we discuss the backreaction effects , induced by the radiation pressure , that alter the dynamics of the mean displacement of the mirror , and we argue this backreaction can be ignored for a slowly moving mirror .

1406.0437

i

since markowitz ( 1952 ) presented his seminal work about portfolio selection , this topic has become a very fast growing branch of finance . one of markowitz s ideas was the minimization of the portfolio variance subject to the budget constraint . this approach leads to the well - known and frequently used portfolio , the global minimum variance portfolio ( gmv ) . there is a great amount of papers dealing with the gmv portfolio ( see , e.g. , jagannathan and ma ( 2003 ) , ledoit and wolf ( 2003 ) , okhrin and schmid ( 2006 ) , kempf and memmel ( 2006 ) , bodnar and schmid ( 2008 ) , frahm and memmel ( 2010 ) among others ) . we remind that the gmv portfolio is the unique solution of the following optimization problem @xmath8 where @xmath9 denotes the vector of portfolio weights , @xmath10 is a suitable vector of ones , and @xmath11 stands for the covariance matrix of the asset returns . note that in our paper @xmath0 is a function of the sample size @xmath1 and thus the covariance matrix depends on @xmath1 as well . this is shown by the index @xmath1 . the solution of ( [ vmin ] ) is given by @xmath12 the gmv portfolio ( [ gmv ] ) has the smallest variance over all portfolios . it is also used in multi - period portfolio choice problems ( see , e.g. , brandt ( 2010 ) ) . although this portfolio possesses several nice theoretical properties , some problems arise when the uncertainty about the parameters of the asset return distribution is taken into account . indeed , we do not know the population covariance matrix in practice and , thus , it has to be suitably estimated . consequently , the estimation of the gmv portfolio is strongly connected with the estimation of the covariance matrix of the asset returns . the traditional estimator is a commonly used possibility for the estimation of the gmv portfolio ( [ gmv ] ) . this traditional estimator is constructed by replacing in ( [ gmv ] ) the covariance matrix @xmath11 by its sample counterpart @xmath13 . okhrin and schmid ( 2006 ) derived the distribution of the traditional estimator and studied its properties under the assumption that the asset returns follow a multivariate normal distribution , whereas kempf and memmel ( 2006 ) analyzed its conditional distributional properties . furthermore , bodnar and schmid ( 2009 ) derived the distribution of the main characteristics of the sample gmv portfolio , namely its variance and its expected return . the traditional estimator is not a bad choice if the number of assets @xmath0 is fixed and it is significantly smaller than the number of observations @xmath1 in the sample . this case is often used in statistics and it is called standard asymptotics ( see , le cam and yang ( 2000 ) ) . in that case the traditional estimator is a consistent estimator for the gmv portfolio and it is asymptotically normally distributed ( okhrin and schmid ( 2006 ) ) . as a result , for a small fixed dimension @xmath14 we can use the sample estimator but it is not fully clear what to do if the number of assets in the portfolio is extremely large , say @xmath15 , comparable to @xmath1 . here we are in the situation when both the number of assets @xmath0 and the sample size @xmath1 tend to infinity . this double asymptotics has an interpretation when @xmath0 and @xmath1 are of comparable size . more precisely , when @xmath16 tends to a concentration ratio @xmath17 . this type of asymptotics is known as high - dimensional asymptotics or `` kolmogorov '' asymptotics ( see , bai and silverstein ( 2010 ) ) . under the high - dimensional asymptotics the traditional estimator behaves very unpredictable and it is far from the optimum one . it tends to underestimate the risk ( see , el karoui ( 2010 ) , bai and shi ( 2011 ) ) . in general , the traditional estimator is worse for larger values of the concentration ratio @xmath18 . imposing the assumption of a factor structure on the asset returns this problem was resolved in an efficient way by bai ( 2003 ) , fan et al . ( 2008 ) , fan et al . ( 2012 ) , fan et al . ( 2013 ) , etc . nevertheless , if the factor structure is not present the question of high - dimensionality remains open . further estimators for the weights of the gmv portfolio have been proposed in this situation . demiguel et al . ( 2009 ) suggested to involve some additional portfolio constraints in order to avoid the curse of dimensionality . on the other hand , shrinkage estimators can be used which are biased but can significantly reduce the risk of the portfolio by minimizing its mean - square error . the general shrinkage estimator is a convex combination of the traditional estimator and a known target ( for the gmv portfolio it can be the naive equally weighted portfolio ) . they were first considered by stein ( 1956 ) . recently , various authors showed that shrinkage estimators for the portfolio weights indeed lead to better results ( see , e.g. , golosnoy and okhrin ( 2007 ) , frahm and memmel ( 2010 ) ) . in particular , golosnoy and okhrin ( 2007 ) considered a multivariate shrinkage estimator by shrinking the portfolio weights themselves but not the whole sample covariance matrix . the same idea was used by frahm and memmel ( 2010 ) who constructed a feasible shrinkage estimator for the gmv portfolio which dominates the traditional one . there are several problems with these estimators : first , the normal distribution is usually imposed ; second , dominating does not mean optimal ; and third , the large dimensional behavior ( large @xmath0 and large @xmath1 ) seems not to be acceptable . the aim of the paper is to derive a feasible and simple estimator for the gmv portfolio which is optimal , in some sense , for small and large sample sizes and which is distribution - free as well . for that purpose we construct an optimal shrinkage estimator , study its asymptotic properties and estimate unknown quantities consistently . the estimator is obtained using random matrix theory , a fast growing branch of probability theory . the main result of this theory was proved by mar@xmath19enko and pastur ( 1967 ) and further extended under very general conditions by silverstein ( 1995 ) . nowadays it is called mar@xmath19enko - pastur equation . its importance arises in many areas of science because it shows how the real covariance matrix and its sample estimate are connected with each other . knowing this information we can build suitable estimators for high - dimensional quantities . the rest of the paper is organized as follows . in section 2 we present a shrinkage estimator for the gmv portfolio which is optimal in terms of minimizing the out - of - sample variance . the asymptotic behavior of the resulting shrinkage intensity is investigated for @xmath20 in section 2.1 and in case of @xmath21 in section 2.2 where it is shown that the shrinkage intensity tends almost surely to a deterministic quantity when both the sample size and the portfolio dimension increase . this result allows us to determine an oracle estimator of the gmv portfolio , while the corresponding bona fide estimator is presented in section 2.3 . in section 3 we provide a simulation study for different values of @xmath22 and under various distributional assumptions imposed on the data generating process . here , the performance and the convergence rate of the derived shrinkage estimator are compared with existing estimators of the gmv portfolio . the results of our empirical study are given in section 4 where we apply the suggested estimator as well as the existing estimators to real data consisting of returns on assets included in the s&p 500 ( standard & poor s 500 ) index . section 5 summarizes all of the obtained results . the lengthy proofs are moved to the appendix ( section 6 ) .

its asymptotic properties are investigated assuming that the number of assets depends on the sample size such that as tends to infinity . this is also well - documented in a numerical study where the small- and large - sample behavior of the derived estimator are compared with existing estimators of the gmv portfolio . the resulting estimator shows significant improvements and it turns out to be robust to the deviations from normality .

we estimate the global minimum variance ( gmv ) portfolio in the high - dimensional case using results from random matrix theory . this approach leads to a shrinkage - type estimator which is distribution - free and it is optimal in the sense of minimizing the out - of - sample variance . its asymptotic properties are investigated assuming that the number of assets depends on the sample size such that as tends to infinity . the results are obtained under weak assumptions imposed on the distribution of the asset returns , namely it is only required the fourth moments existence . furthermore , we make no assumption on the upper bound of the spectrum of the covariance matrix . as a result , the theoretical findings are also valid if the dependencies between the asset returns are described by a factor model which appears to be very popular in financial literature nowadays . this is also well - documented in a numerical study where the small- and large - sample behavior of the derived estimator are compared with existing estimators of the gmv portfolio . the resulting estimator shows significant improvements and it turns out to be robust to the deviations from normality . * estimation of the global minimum variance portfolio in high dimensions * + taras bodnar , nestor parolya and wolfgang schmid + + _ department of empirical economics ( econometrics ) , leibniz university hannover , d-30167 hannover , germany _ + _ department of statistics , european university viadrina , po box 1786 , 15207 frankfurt ( oder ) , germany _ jel classification : g11 , c13 , c14 , c58 , c65 + _ keywords _ : global minimum variance portfolio , large - dimensional asymptotics , covariance matrix estimation , random matrix theory .

1406.0437

i

the global minimum variance portfolio plays an important role in investment theory and practice . this portfolio is widely used as an investment opportunity in both static and dynamic optimal portfolio choice problems . although an explicit analytical expression for the structure of the gmv portfolio weights is available in literature , the estimation of the gmv portfolio appears to be a very challenging problem , especially for high - dimensional data . we deal with this problem in the present paper by deriving a feasible and robust estimator for the weights of the gmv portfolio when the distribution of the asset returns is not prespecified and no market structure is imposed . we construct an optimal shrinkage estimator for the gmv portfolio which is optimal in the sense of minimizing the out - of - sample variance . an analytical expression for the shrinkage intensity is obtained which appears to be a complicated function of the data and the parameters of the asset return distribution . we deal with the later problem by determining an asymptotically equivalent quantity of the shrinkage intensity under high - dimensional asymptotics . we estimate this asymptotically equivalent function consistently by applying recent results from random matrix theory . this is achieved under very weak assumptions imposed on the distribution of the asset returns . namely , we only require the existence of the fourth moment , whereas no explicit distributional assumption is imposed . moreover , our findings are still valid in both cases @xmath20 and @xmath21 as well as if the spectrum of the population covariance matrix is bounded or unbounded . as a result , the suggested method can be applied to heavy - tailed distributed asset returns as well as to asset returns whose dynamics can be modeled by a factor model which is a very popular approach in financial and econometric literature . finally , using simulated and real data , we compare the optimal shrinkage estimator for the gmv portfolio with existing ones . the theoretical findings as well as the results of the monte carlo simulations and an empirical study show that the suggested estimator for the gmv portfolio weights dominates the existing estimators in case @xmath17 .

this approach leads to a shrinkage - type estimator which is distribution - free and it is optimal in the sense of minimizing the out - of - sample variance . the results are obtained under weak assumptions imposed on the distribution of the asset returns , namely it is only required the fourth moments existence . furthermore , we make no assumption on the upper bound of the spectrum of the covariance matrix . as a result ,

we estimate the global minimum variance ( gmv ) portfolio in the high - dimensional case using results from random matrix theory . this approach leads to a shrinkage - type estimator which is distribution - free and it is optimal in the sense of minimizing the out - of - sample variance . its asymptotic properties are investigated assuming that the number of assets depends on the sample size such that as tends to infinity . the results are obtained under weak assumptions imposed on the distribution of the asset returns , namely it is only required the fourth moments existence . furthermore , we make no assumption on the upper bound of the spectrum of the covariance matrix . as a result , the theoretical findings are also valid if the dependencies between the asset returns are described by a factor model which appears to be very popular in financial literature nowadays . this is also well - documented in a numerical study where the small- and large - sample behavior of the derived estimator are compared with existing estimators of the gmv portfolio . the resulting estimator shows significant improvements and it turns out to be robust to the deviations from normality . * estimation of the global minimum variance portfolio in high dimensions * + taras bodnar , nestor parolya and wolfgang schmid + + _ department of empirical economics ( econometrics ) , leibniz university hannover , d-30167 hannover , germany _ + _ department of statistics , european university viadrina , po box 1786 , 15207 frankfurt ( oder ) , germany _ jel classification : g11 , c13 , c14 , c58 , c65 + _ keywords _ : global minimum variance portfolio , large - dimensional asymptotics , covariance matrix estimation , random matrix theory .

astro-ph0301171

i

the study of the tidally induced migration of protoplanets embedded in protoplanetary disks has received renewed attention in the last few years following the discovery of extrasolar giant planets ( hereafter egps ) . it is in particular the best candidate to explain the short period egps ( the so - called hot jupiters ) which are likely to have begun to form further out in the disk and migrated radially inwards . when the planet mass is small ( i.e. when its hill radius is much smaller than the disk thickness ) , the migration rate can be evaluated using linear analysis , and is shown to be proportional to the planet mass , to the disk surface density , and inversely proportional to the square of the disk aspect ratio @xcite . the linear regime is often called the type i regime . it corresponds to a fast migration rate , although recent estimates @xcite show that the linear analytical estimate assuming a flat two dimensional disk has to be reduced by a factor @xmath1@xmath2 or more in a more realistic calculation which accounts for the disk vertical structure and a possible non - saturation of the corotation torque if the disk is viscous enough . migration in the type i regime is nevertheless still too fast , in the sense that the migration timescale it yields is shorter than the build - up timescale of a giant protocore ( see e. g. * ? ? ? we shall not address this issue here but rather assume that a giant planet embryo can form in the disk at a distance @xmath3 au , and with a mass @xmath4 , where @xmath5 @xmath6 is the critical mass above which rapid gas accretion begins . when this embryo mass is large enough , it enters another well studied migration regime , called type ii migration @xcite . in this regime , the protoplanet has a mass sufficient to open a gap in the disk , which is therefore split into an inner disk and an outer disk . the protoplanet then finds itself locked into the disk viscous evolution drifting inwards with it @xcite . as the protoplanet undergoes type ii migration towards the central object , it may accrete the surrounding nebula material . the accretion rate scales with the mass accretion rate onto the central object @xmath7 where @xmath8 is the disk surface density . here one assumes that the processes at work in the disk which contribute to the angular momentum exchange between neighboring rings can be adequately modeled by a phenomenological kinematic viscosity @xmath9 . on the other hand , the type ii migration timescale is of the order of the disk viscous timescale @xmath10 . the maximum mass that a giant protoplanet can accrete on its way to the central object should be therefore of the order of @xmath11 , that is of the order of the disk mass interior to the planet starting distance . noticeably this mass does not depend on the disk viscosity . if the planet does not migrate all the way to the central object before the disk is dispersed , then because more time is spent at larger radii , it is most likely to be left with a semi - major axis larger than the typical one for hot jupiters ( @xmath12@xmath13 au , see * ? ? ? this is consistent with the observed paucity of planets with masses exceeding two jovian masses at short periods @xcite . note too that planets undergoing type ii migration should tend to have higher masses at shorter periods . this is contrary to the observed trend . furthermore , as the planet mass grows , it becomes eventually larger than the surrounding disk mass , and its migration rate tends to drop , as the disk can not remove enough angular momentum from it . this has been investigated by @xcite . in this case , the amount of time necessary to bring the planet to a close orbit can be considerably larger than the disk viscous timescale , and can even exceed the disk lifetime . this migration slowing can be seen in the simulations of @xcite . it occurs _ soon _ after the planet has entered its type ii migration regime . from the above considerations , it is questionable whether the orbital characteristics of most close orbiters can be accounted for by type ii migration driven by the evolution of the disk . furthermore the vast majority of these have sub - jovian masses ( here one excepts and , which have large masses and which may have had a different origin ) . depending on the physical conditions of the protoplanetary disks in which they formed , they may not have fulfilled the gap opening criteria ( * ? ? ? * and references therein ) , with the consequence that they may have been involved in a migration regime intermediate between type i and type ii . this transitional regime has received little attention . @xcite and @xcite have worked out the feedback on the migration rate due to the nebula surface density profile perturbation under the action of the protoplanet lindblad torques . they introduced the concept of an inertial limit , that is the maximum mass of a protoplanet that can undergo steady state migration . it was suggested that masses above the inertial limit lead to a gap opening and to type ii migration . in their analysis , @xcite neglected the coorbital dynamics and the corotation torque it implies on the migrating planet . the purpose of this work is to give an evaluation of the corotation torque for a migrating planet , and to analyze its consequences on migration . we define the notation in section [ sec : notation ] , we present an appropriate expression for the corotation torque for a planet held on a fixed circular orbit in section [ sec : corotfix ] , we then derive the corotation torque for a migrating planet in section [ sec : derivation ] , and illustrate its properties using customized numerical simulations in section [ sec : numres ] . as we investigate the intermediate regime between type i and type ii migration , for which the disk response is affected by non - linear effects , the hill radius and the disk thickness have comparable orders of magnitude . the regime of interest thus involves mildly embedded protoplanets . we assume that it can be safely studied through two dimensional flat disk calculations provided a reasonable value is adopted for the gravitational potential smoothing length . in section [ sec : discussion ] we demonstrate the existence of runaway migration and relate the condition for its occurrence to the analytic discussion in section [ sec : derivation ] . finally in section [ sec : summary ] we summarize our results and we discuss their application to egps .

this leads to a positive feedback on the migrating planet . runaway migration is a good candidate to account for the orbital characteristics of close orbiting giant planets , most of which have sub - jovian masses . these are known to cluster at short periods whereas planets of greater than two jovian masses are rare at short periods indicating a different type of migration process operated for the two classes of object .

we evaluate the coorbital corotation torque on a migrating protoplanet . the coorbital torque is assumed to come from orbit crossing fluid elements which exchange angular momentum with the planet when they execute a u - turn at the end of horseshoe streamlines . when the planet migrates inward , the fluid elements of the inner disk undergo one such exchange as they pass to the outer disk . the angular momentum they gain is removed from the planet , and this corresponds to a negative contribution to the corotation torque , which scales with the drift rate . in addition , the material trapped in the coorbital region drifts radially with the planet giving a positive contribution to the corotation torque , which also scales with the drift rate . these two contributions do not cancel out if the coorbital region is depleted , in which case there is a net corotation torque which scales with the drift rate and the mass deficit in the coorbital region , and which has same sign as the drift rate . this leads to a positive feedback on the migrating planet . in particular , if the coorbital mass deficit is larger than the planet mass , the migration rate undergoes a runaway which can vary the protoplanet semi - major axis by % over a few tens of orbits . this can happen only if the planet mass is sufficient to create a dip or gap in its surrounding region , and if the surrounding disk mass is larger than the planet mass . this typically corresponds to planet masses in the sub - saturnian to jovian mass range embedded in massive protoplanetary disks . runaway migration is a good candidate to account for the orbital characteristics of close orbiting giant planets , most of which have sub - jovian masses . these are known to cluster at short periods whereas planets of greater than two jovian masses are rare at short periods indicating a different type of migration process operated for the two classes of object . further , we show that in the runaway regime , migration can be directed outwards , which makes this regime potentially rich in a variety of important effects in shaping a planetary system during the last stages of its formation .

1307.6631

i

quantum degenerate ultracold atomic sources have been used to study fundamental processes such as quantum phase transitions @xcite , quantum non - equilibrium thermodynamics @xcite and entanglement of massive particles @xcite . their ability to be highly isolated from their environment and controlled precisely by optical , magnetic and rf fields makes them an ideal platform for engineering and manipulating non - trivial quantum states . in quantum optics , the most common way to produce entangled states has been through squeezing , and it has been recognised that the intrinsic nonlinearities of atoms naturally lead to quadrature squeezing @xcite . number squeezing can be achieved with spin squeezing techniques @xcite , molecular dissociation of bose - einstein condensates ( becs ) @xcite , four - wave mixing @xcite , double - well potentials @xcite , or mixing quadrature - squeezed states using ramsey interferometry @xcite . the creation of these non - classical atomic states has relevance for fundamental tests of quantum mechanics such as the epr paradox @xcite , as well as atom interferometry @xcite . while these techniques have resulted in significant experimentally detectable number squeezing , they have been limited to small numbers of atoms , typically a few hundred @xcite . ultracold atomic interferometers are also reaching state of the art sensitivities in precision measurements @xcite . while all current atom interferometry is limited by technical noise sources , it appears that bec - based coherent sources offer the best chance of overcoming some of these issues , for the same reasons that optical lasers are typically preferred for optical interferometry . in particular , it appears that bose - condensed sources allow for higher fidelity mirrors and beamsplitters @xcite , are less sensitive to the effects of distortions in the optical wavefronts of the beamsplitters and mirrors and the coriolis effect @xcite , and are robust to the adverse effects of strong outcoupling when feedback - cooled @xcite . if these technical noise sources can be reduced and/or controlled , atom interferometers will be limited by atomic shot noise , which leads to a sensitivity that scales as the square root of the atomic flux . from that point , sensitivity will only be improved by increasing the atomic flux and brightness @xcite , and/or using non - classical quantum states such as squeezed states to go below the shot noise limit @xcite . producing squeezed states for metrological purposes is therefore only relevant when it can be achieved in a context of large numbers of atoms . this paper examines the generation of atomic squeezing using the inherent kerr - like nonlinearities of ultracold atoms , and demonstrates a trap geometry in which metrologically relevant levels of squeezing are present in trap geometries that are compatible with large atomic number . the creation , detection and application of squeezing requires precise mode - matching , and is therefore very sensitive to uncontrolled coupling between spatial modes of the atomic field . atomic squeezing experiments have typically attempted to operate in the single - mode regime , where the trap is tight enough such that all higher modes are frozen out @xcite . however , tight traps limit the total number of atoms , as the 3-body recombination rate places an effective maximum atomic density in the gas , and well before that limit , the interatomic interactions break the single - mode operation . both of these effects limit the number of atoms that can be squeezed effectively , so we will examine a broader range of trap geometries , and calculate the dynamics in the presence of multiple spatial modes . many similar previous simulations have been performed in one or two spatial dimensions , by integrating out some of the remaining dimensions @xcite . for simulations of semiclassical fields this can be a reasonable approximation , but it can ignore spontaneous scattering processes in full quantum field theory calculations , so we take care to include full 3d simulations . in section [ sectwomodeanalytic ] we examine the ideal behaviour of a nonlinear bosonic two - state system when that system possesses only a single spatial mode , extracting full analytic solutions for the number squeezing in each of the two states , as well as the number difference squeezing between the two states . these solutions of the ideal case provide a check on the multimode cases we consider later in the paper , as well as providing a bound on the best possible squeezing for the system . in section [ sec : mmdescription ] we show how multimode behaviour becomes important in physical systems , and introduce our model for simulating higher dimensional trap geometries . section [ sec:1dsim ] analyses one - dimensional models , highlighting some of the issues regarding optimising squeezing parameters and mode - matching in squeezing experiments . section [ sec : pipulse ] shows that the application of a @xmath0-pulse during the process can significantly improve mode - matching issues . section [ sec:2d3dsqueezing ] investigates measurable squeezing in 2d and 3d , and uses a bogoliubov analysis to explain the scaling with system size and dimensionality . section [ sectionconclusion ] describes the conclusion that large volume , flat - bottomed , three - dimensional traps , which are obviously compatible with large atom number , can produce extremely high degrees of squeezing .

we examine the feasibility of creating and measuring large relative number squeezing in multicomponent trapped bose - einstein condensates . in the absence of multimode effects , this squeezing can be arbitrarily large for arbitrarily large condensates , but a range of processes limit the measurable squeezing in realistic trap configurations . we examine these processes , and suggest methods to mitigate them . we conclude that high levels of squeezing with large numbers of atoms is feasible , but can realistically only be achieved in particular trap geometries . we also introduce a method of maximising the measurable squeezing by using a-pulse during the process to improve spatial mode - matching .

we examine the feasibility of creating and measuring large relative number squeezing in multicomponent trapped bose - einstein condensates . in the absence of multimode effects , this squeezing can be arbitrarily large for arbitrarily large condensates , but a range of processes limit the measurable squeezing in realistic trap configurations . we examine these processes , and suggest methods to mitigate them . we conclude that high levels of squeezing with large numbers of atoms is feasible , but can realistically only be achieved in particular trap geometries . we also introduce a method of maximising the measurable squeezing by using a-pulse during the process to improve spatial mode - matching .

1403.4900

i

the quantum dynamics of a single qubit or central spin coupled to a spin environment @xcite has been widely studied theoretically in several different areas , including quantum information sciences @xcite , quantum decoherence @xcite , and excitation energy transfer @xcite . one of the most promising candidates for quantum computation , solid - state spin systems , are inevitably coupled to their surrounding environment , usually through interactions with neighboring nuclear spins @xcite . the coupling of a qubit to a spin bath can in general lead to non - markovian behavior @xcite , causing the usual markovian quantum master equations to fail for such models . most recently , it was demonstrated for the first time that a spin bath can assist coherent transport in a two - level system @xcite . fully understanding the role played by a spin environment is an interesting and important issue . one commonly studied qubit - spin bath system is the so - called spin - star network @xcite , in which a preferred central spin is coupled homogeneously to a spin bath without intrabath interactions . a more realistic type of environment takes the form of quantum interacting spin chains @xcite , where the decay of the qubit s coherence is found to be related to the critical properties of the spin environments . most prior work making use of such an environment considered qubit - spin bath coupling of the ising form , which is spin conserving . as a result , it is much easier to analytically obtain the full dynamics of the system , in contrast to the situation where a spin - flip coupling is present . exceptions include refs . @xcite , where the authors considered the spin - flip xx - type qubit - bath coupling but with a spin bath having homogeneous self - interactions , and ref . @xcite , where the authors use @xmath0-dmrg to study the reduced dynamics of a qubit coupled locally to an xxz spin chain via the heisenberg - type qubit - bath interaction . it should be noted that , in general , both the spin - star network and the homogeneously coupled spin bath can be treated by introducing collective angular momentum operators which facilitates the analytical treatment . in this work , we will focus on a more realistic system with a ( not necessarily uniform ) spin - flip qubit - bath interaction as well as short range xx - type intrabath interactions . to our knowledge , the exact dynamics of such a model , which is one step closer to faithfully representing environmental spins interacting via fully general heisenberg - type interactions , has not been obtained before . the collapse and revival ( cr ) behavior of rabi oscillations of a qubit coupled to a single bosonic field mode , described by the jaynes - cummings ( jc ) model , is a fundamental consequence of field quantization and provides a much - studied illustration of the quantum nature of qubit - field systems @xcite . using a correspondence between the jc model and a spin - star network with a large number of spins , it is found in ref . @xcite that within a certain parameter regime , cr phenomena also appear in a qubit - big spin model . @xcite goes beyond the resonant jc model to the nonresonant dicke model , and notes that the dynamics depends on the sign of the detuning between the qubit and field frequency . in this work , we extend the model studied in ref . @xcite to the nonresonant case with a self - interacting spin bath modeled by the periodic xx spin chain . it is found that both nonzero detuning and the nearest neighbor coupling within the xx bath can have an effect on the qubit s dynamics . in particular , the interplay between nonresonance and intrabath interaction is able to reproduce cr behavior even for a spin bath with a relatively small number of sites . in addition , the dynamics of entanglement in many - body systems has recently been studied from different perspectives @xcite . as interacting quantum spin systems are believed to be paradigmatic for quantum information processing @xcite , their entanglement dynamics has attracted much attention @xcite . in prior works , the dynamical behavior of pairwise entanglement is found to be related to quantum phase transitions of the spin chains . another emerging focus is on the evolution of the entanglement of a pair of qubits exposed to noisy environments . in a seminal work , yu and eberly @xcite found that the markovian dynamics of the entanglement between two qubits coupled to individual bosonic baths can behave in sharp contrast to single qubit decoherence : the pairwise entanglement of two initially entangled two - level atoms suddenly disappears in a finite time proportional to the spontaneous lifetime of single atoms , while the single atom coherence only vanishes asymptotically . this phenomenon is called entanglement sudden death ( esd ) . more recently , it has been shown in the same setup that there exists a revival of the vanished entanglement if non - markovian effects are taken into account @xcite . as mentioned earlier , the non - markovian behavior caused by the spin environment may result in novel dynamics of the pairwise entanglement of two qubits each coupled to their own spin bath , as observed in a locally interacting qubit - spin - bath system @xcite . esd and subsequent revivals have also been observed to occur in two qubits when they are coupled to _ classical _ interacting spin baths @xcite and external fields @xcite , the latter of which has been demonstrated experimentally @xcite , and to stochastic noise sources @xcite . furthermore , understanding the relation between decoherence and disentanglement is believed to be of importance both for the foundations of quantum mechanics and practical applications in quantum information science @xcite . in this work , by taking the bath s initial state as the ground state of the xx chain , we first study the decoherence of a single qubit immersed in the xx bath . the decoherence dynamics is found to depend on the internal phases of the xx bath . the short time dynamics of the decoherence factor behaves like a gaussian , with the decay rate only depending on the filling number of the ground state of the bath . by considering two copies of our qubit - bath systems , we further study the disentanglement dynamics of the two initially entangled qubits coupled to their individual baths . we analytically show that the concurrence is bounded from above by the decoherence factor of a single qubit at all times . the initial bell state considered suffers from esd when the xx bath is in its critical phase . we also obtain the disentanglement time in the sudden death region and find that esd always occurs earlier than the onset of decoherence in a single qubit . the rest of the paper is structured as follows : in sec . ii , we introduce our model hamiltonian and describe how to obtain the exact qubit - bath time - dependent wavefunctions in the momentum space of the xx spin chain . the components of the bloch vector of the qubit are obtained by tracing out the bath degrees of freedom over these total wavefunctions . the results for the nonresonant and interacting cases are presented . in sec . iii , we study single qubit decoherence in a single qubit - bath system and disentanglement of two initially entangled qubits in two independent qubit - bath systems . conclusions are drawn in sec .

we examine the influence of environmental interactions on simple quantum systems by obtaining the exact reduced dynamics of a qubit coupled to a one - dimensional spin bath . next , we discuss the bath - induced decoherence of the qubit when the bath is initially in the ground state , and show that the decoherence properties depend on the internal phases of the spin bath . by considering two independent copies of the qubit - bath system , we finally probe the disentanglement dynamics of two noninteracting entangled qubits . we find that entanglement sudden death appears when the spin bath is in its critical phase .

we examine the influence of environmental interactions on simple quantum systems by obtaining the exact reduced dynamics of a qubit coupled to a one - dimensional spin bath . in contrast to previous studies , both the qubit - bath coupling and the nearest neighbor intrabath couplings are taken as the spin - flip xx - type . we first study the rabi oscillations of a single qubit with the spin bath prepared in a spin coherent state , finding that nonresonance and finite intrabath interactions have significant effects on the qubit dynamics . next , we discuss the bath - induced decoherence of the qubit when the bath is initially in the ground state , and show that the decoherence properties depend on the internal phases of the spin bath . by considering two independent copies of the qubit - bath system , we finally probe the disentanglement dynamics of two noninteracting entangled qubits . we find that entanglement sudden death appears when the spin bath is in its critical phase . we show that the single - qubit decoherence factor is an upper bound for the two - qubit concurrence .

0805.1066

i

astronomers around the world are making significant efforts to image planets in orbit around other stars beuzit07,nielsen07,lafreniere07,apai08 . work on suppressing the glare of potential parent stars has proceeded to the point where contrast ratios of @xmath7 can now typically be achieved on the telescope , and @xmath8 is on the horizon macintosh06,dohlen06 . since the contrast ratio for the jupiter / sun is @xmath9 [ a contrast ratio which has now been achieved in a laboratory,][]trauger07 , the majority of this detection work focuses on young stars , as giant planets should be warmest , largest , and brightest when they are young , but will cool , contract , and fade inexorably as they age graboske75,bodenheimer76,saumon96,burrows97 . given the difficulty of these low contrast ratio observations , the interpretation of observed photometry and spectra takes on great importance . in practice , when faint planetary candidates are detected , evolution models , which aim to predict the structural and atmospheric properties with age , are needed to convert observed photometry or spectra into a probable planetary mass . the formation mechanisms of brown dwarfs and giant planets are still not well understood in detail . while brown dwarfs likely form directly from molecular cloud gas in something akin to the star formation mechanism luhman07,whitworth07 , `` true planets '' form in a disk ( iau definitions aside for a discussion see chabrier et al . 2007 ) , perhaps predominantly via core accretion lissauer07 . recently , discussion has turned to how these distinct formation mechanisms , which may overlap at several jupiter masses , may leave observational signatures in terms of an object s orbit , evolution , and atmosphere . a given parent star may well harbor both classes of low mass objects . this paper addresses the atmospheres of extrasolar giant planets ( egps ) , while also describing the spectral properties of our recent work to couple core accretion formation to subsequent planetary evolution marley07 . in this introduction we will first review giant planet evolution models , then discuss our current understanding of the metal - enhanced atmospheres of jupiter and saturn . in 2 we describe our model atmosphere code , while in 3 we discuss the differences in atmospheric pressure - temperature ( _ p - t _ ) profiles , chemistry , and spectra between models at solar metallicity and those at 5@xmath10 solar . 4 focuses in particular on the near and mid infrared colors of metal - enhanced atmospheres while in 5 we discuss and tabulate the near- and mid - ir colors for our `` hot start '' and core - accretion start evolution models . 6 addresses nonequilibrium chemistry while 7 contains additional discussion , caveats , and our conclusions . over the past decade only a small number of workers have attempted the difficult task of coupling non - gray radiative - convective atmosphere models to thermal evolution models to enable an understanding of interior structure , atmospheric structure , atmospheric chemistry , and emitted spectra for giant planets and brown dwarfs [ e.g.,][]burrows97,chabrier00b , baraffe03,saumon08 . it has perhaps only recently become appreciated by the wider community that these models do not include a mechanism for the formation of the objects that they aim to understand . the starting point for these models is an arbitrarily large and hot , non - rotating , adiabatic sphere . these model objects are then allowed to cool and contract from this arbitrary state . the initial model is soon unimportant , as the cooling and contraction are initially very fast , since the kelvin - helmholtz time , @xmath11 is inversely proportional to both luminosity and radius . although it is true that the models forget their initial conditions eventually , it is not immediately obvious how long this may take . in the past , a common thought was that after `` a few million years '' the initial conditions are forgotten and that these standard `` hot start '' evolution models are reliable . although this type of model has been successfully applied to jupiter for decades [ e.g.,][]graboske75,hubbard77,guillot95,fh03 their application to planets at very young ages could potentially be suspect stevenson82b . more recently baraffe02 have investigated similar issues for brown dwarfs . in order to better understand the properties of gas giant planets at young ages , in marley07 we undertook an investigation of the early evolution of giant planets , with initial properties given by a state - of - the - art model of planet formation by core accretion hubickyj05 , rather than the traditional ( but arbitrary ) initial condition which we termed a `` hot start . '' as shown in , the post - formation properties of these planets are surprising . the model planets started their lives smaller and colder than their hot start brethren . the core accretion start models were less luminous by factors of a few to 100 , and the initial conditions were not forgotten for timescales of tens of millions to one billion years . the reason for the significant difference lies in the treatment of gas accretion [ see][]marley07 . in the hubickyj05 models the accreting gas arrives at nearly free fall velocity to a shock interface at the protoplanet the shock radiation transfer is not followed directly , but a shock jump condition from stahler80 is employed ; this accretion luminosity is entirely radiated away , leading to the prominent luminosity spike in these models during gas accretion . the gas that finally accretes onto the planet is therefore relatively cold , low entropy gas . it is therefore enticing to imagine that one could use the early luminosity , @xmath0 , and surface gravity to determine the formation mechanism of a faint planetary - mass companion . this may be possible , but we caution that the current generation of core accretion formation models hubickyj05,alibert05,ikoma00 are still only 1d representations of a 3d process . a detailed look at radiation transfer in the formation shock , as well as incorporating multi - dimensional accretion , should be undertaken before accurate luminosities of young planets can be confidently predicted . there is , however , another promising avenue for determining `` planethood . '' while a brown dwarf - like companion and its parent star would be expected to share common elemental abundances , the same may not be true of a companion that formed in a disk via core accretion . the _ galileo _ and _ cassini _ spacecrafts have unambiguously shown us that the atmospheres of jupiter and saturn , respectively , are enhanced in heavy elements relative to the sun . the _ galileo entry probe _ measured the abundances of oxygen , carbon , nitrogen , sulfur , and various noble gases in the atmosphere of jupiter . except for oxygen , an enhancement of @xmath122 - 4@xmath10 solar for each element was found atreya03 , although the oxygen abundance determination may have been hindered by meteorological effects showman98 . saturn s atmosphere is enhanced in carbon by factor of @xmath1210 , from an analysis of _ cassini _ spectra flasar05 , and in phosphorus by a factor of @xmath127 , from _ iso _ spectra degraauw97,visscher05 . if jupiter , saturn , and egps formed through a common mechanism , we can expect egp atmospheres to have high metallicities as well . how this atmospheric metallicity ( and indeed the _ ratios of specific elements _ ) may be set , as a function of planet mass , orbital distance , disk mass , disk metallicity , etc . , is still open territory . in particular , the relative importance of processes that have enriched the atmospheres of jupiter and saturn is still unclear . these potentially include planetesimal bombardment and accumulation during formation owen99,gautier01a , gautier01b , guillot00,alibert05b , erosion of the heavy element core stevenson85,guillot04 , direct accretion of metal - rich disk gas guillot06a , and chemical fractionation within the planet ss77b , lodders04 . clearly observations of extrasolar giant planet will shed light on giant planet formation . here we will undertake a first step at exploring how the spectra and colors of uniformly metal - enhanced atmospheres differ from strictly solar composition . since there is some evidence from both observations chauvin05 and theory boss01b , kroupa03,ida04 that the `` planetary '' and `` stellar '' formation modes may overlap at several jupiter masses , it will be important to be able to decipher a formation mechanism based on observable properties . some of this work has progressed on the orbital dynamics of given companions or classes of companions , such as by ribas07 , who found different eccentricity distributions for the radial velocity planets above and below 4 @xmath13 . additionally , transiting planet mass and radius determinations allow for calculations of bulk planet density , which shed light on the internal abundance of heavy elements guillot06,fortney07a , burrows07,baraffe08 . a hallmark of jupiter and saturn is that they are enriched in heavy elements compared to the sun , which is known from planet structure models podolak74,saumon04 . these heavy elements are partitioned between a dense core and an enrichment within the h / he envelope hubbard89,guillot99,saumon04 . all planets which form in disks around young stars are expected to be enriched in heavy elements due to these disks possessing both abundant gas _ and _ solids pollack96,ida04 . another rewarding pathway for differentiating planets from low mass brown dwarfs is from direct characterization of their atmospheres . one could spectroscopically measure the heavy element abundances of the h / he envelope directly , as has long been done in the solar system [ e.g.][]gautier89,encrenaz05 . if nature is able to form two kinds of objects with an overlapping mass distribution , these distinct formation modes may leave distinct observable atmospheric metallicities in the atmospheres of these objects chabrier07,marley07b . therefore , two classes of planetary mass companions may be revealed by their emitted spectra . there are then two tasks to be completed . we first will investigate the differences in spectra and infrared colors between models of solar composition ( m / h=[0.0 ] ) and those with a metallicity enhanced by a factor of five ( m / h=[0.7 ] ) . this metallicity enhancement is similar to that of jupiter and saturn , but still far removed from the 30 - 40@xmath10 solar enhancement ( at least in carbon ) that has been measured for uranus and neptune gautier89 . this investigation will be done at the low gravities and effective temperature most relevant for egps , ( log @xmath14@xmath154.3 , @xmath0@xmath151400 k ) , whereas field t - type brown dwarfs with similar @xmath0s in general have surface gravities 10 times larger . since we restrict ourselves to @xmath0@xmath161400 k , we will necessarily be targeting cloud - free ch@xmath17-rich , rather than co - rich , atmospheres . we focus on these relatively cool objects since a detection of ch@xmath17 together with an age estimate would significantly constrain a planetary candidate s mass , even taking into account the uncertainties in evolution models . later we will examine the evolution of infrared spectra and colors at 5@xmath10 solar metallicity , specifically for the marley07 evolution models for giant planets . as anticipated , the lower @xmath0 and radii for these models lead to dramatically fainter absolute magnitudes compared to hot start 1@xmath10 solar models .

we examine the spectra and infrared colors of the cool methane - dominated atmospheres at k expected for young gas giant planets . ( 2007 ) giant planet thermal evolution models that include formation by core accretion - gas capture . these relatively cool `` young jupiters '' can be 1 - 6 magnitudes fainter than predicted by standard cooling tracks that include a traditional initial condition , which may provide a diagnostic of formation . if correct , this would make true jupiter - like planets much more difficult to detect at young ages than previously thought . since jupiter and saturn are of distinctly super - solar composition , we examine emitted spectra for model planets at both solar metallicity and a metallicity of 5 times solar .

we examine the spectra and infrared colors of the cool methane - dominated atmospheres at k expected for young gas giant planets . we couple these spectral calculations to an updated version of the marley et al . ( 2007 ) giant planet thermal evolution models that include formation by core accretion - gas capture . these relatively cool `` young jupiters '' can be 1 - 6 magnitudes fainter than predicted by standard cooling tracks that include a traditional initial condition , which may provide a diagnostic of formation . if correct , this would make true jupiter - like planets much more difficult to detect at young ages than previously thought . since jupiter and saturn are of distinctly super - solar composition , we examine emitted spectra for model planets at both solar metallicity and a metallicity of 5 times solar . these metal - enhanced young jupiters have lower pressure photospheres than field brown dwarfs of the same effective temperatures arising from both lower surface gravities and enhanced atmospheric opacity . we highlight several diagnostics for enhanced metallicity . a stronger co absorption band at 4.5 m for the warmest objects is predicted . at all temperatures , enhanced flux in band is expected due to reduced collisional induced absorption by h . this leads to correspondingly redder near infrared colors , which are redder than solar metallicity models with the same surface gravity by up to 0.7 in and 1.5 in . molecular absorption band depths increase as well , most significantly for the coolest objects . we also qualitatively assess the changes to emitted spectra due to nonequilibrium chemistry .

0805.1066

c

we have shown how metal enhanced atmospheres differ from their solar composition counterparts , in atmospheric structure , chemistry , spectra , and colors . we have applied these results to an updated version of the @xcite evolution models , which give cooling tracks for egps that are initially significantly colder than traditional models . we urge caution in the application of the computed absolute magnitudes for these models provided in . recall that the @xcite models incorporate the formation models of @xcite , which employ a treatment of accretion that is surely much simpler than what occurs in nature . the potential agreement or disagreement between observations and the model cooling tracks and magnitudes should not be taken as evidence for or against the viability of the core accretion formation scenario . indeed , the @xcite prescription is just one of several models of core accretion , which all currently include simplifications of the gas and solid accretion . while we can claim with some confidence that young jupiters are fainter than those predicted from an arbitrarily hot start , how much fainter depends sensitively on the details of accretion marley07 . given the difficulty of predicting properties of egps at young ages , observations of these young objects will be of central importance . the next generation of direct imaging platforms will be the gemini planet imager ( gpi ) , likely at gemini south macintosh06 , and spectro - polarimetric high - contrast exoplanet research ( sphere ) , at the vlt dohlen06 . the gpi will target the @xmath44 bands , while sphere will focus on @xmath45 . both instruments will in particular emphasize @xmath31 band . in we show a four panel plot that illustrates changes to @xmath31-band fluxes due to @xmath0 , gravity , metallicity , and nonequilibrium chemistry . all are referenced from a standard case model with @xmath0=700 k. since gpi and sphere will likely employ custom narrow - band filters , we have overlain in gray possible narrow filters , kindly provided by j. graham . it is clear that the more limited the observations are in wavelength , the more difficult planetary _ characterization _ will be , as lower surface gravity and higher metallicity generally effect spectra in similar ways . we must also caution that although our understanding of the gaseous opacity in these atmospheres is improving sharp07,freedman08 , calculations of the contribution due to ch@xmath17 are quite uncertain . the absorption cross - section of ch@xmath17 is difficult to model under the relevant _ p - t _ conditions found here , which manifests itself in mismatches of our models to brown dwarf spectra , especially around @xmath31-band saumon06,saumon07 . 1 . young jupiter atmospheres will have lower pressure photospheres than old field brown dwarfs due to their lower surface gravity ( which has long been understood ) and higher atmospheric opacity ( if the planets have high atmospheric metallicities , like jupiter and saturn ) . higher metallicity atmospheres , while generally having more opacity at all wavelengths , have relatively less opacity in @xmath3-band relative to other bands , due to weakened cia h@xmath4 opacity . this leads to a @xmath3-band flux enhancement of @xmath120.5 to 1.0 magnitudes between @xmath0s of 500 to 1400 k. 3 . a spectral signature of high metallicity at @xmath0@xmath36 1000 k is a markedly deeper co absorption band at 4.5 @xmath2 m . a photometric feature of high metallicity at @xmath0@xmath16 1400 k is redder @xmath5 and @xmath6 colors , which may be redder by @xmath120.7 - 1.5 . we note that points 1 - 3 in particular echo the findings of chabrier07 , who had previously analyzed the spectrum of a representative metal - enhanced planet model within the parameter range we examine here . the agreement is encouraging . in closing , we note that the current best example of how well we may eventually be able to constrain the properties of a young egp comes from the cool t7.5 dwarf gliese 570d . this brown dwarf is a wide companion to the well - studied k4 v star gl 570a , and to a pair of m dwarfs , gl 570bc . as discussed by @xcite , the distance , metallicity , and age of the system effectively constrain the physical parameters of the t dwarf gl 570d . the spectrum is extremely well sampled from visible wavelengths , across the near infrared , to the mid infrared with _ spitzer _ irs . saumon06 constrain @xmath0=800 - 820 k , log @xmath14=5.09 - 5.23 , log ( @xmath46/@xmath47)=5.525 - 5.551 , and mass=38 - 47 @xmath13 . saumon07 additionally investigated two late field t dwarfs with similar spectral coverage , but without parent stars to constrain metallicities . uncertainties in @xmath0 increase @xmath1250 - 100 k , while mass estimates widen to @xmath4830 - 60 @xmath13 . since young jupiters will have unknown metallicities and early on these objects will sample gravity and metallicity ranges that only marginally overlap the more well understood brown dwarfs , it will be challenging to constrain planetary parameters with limited photometric and spectral data . we thank bruce macintosh and james graham for numerous useful comments and suggestions , as well as for their enthusiasm for the project . j. j. f. acknowledges the support of a spitzer fellowship from nasa and nsf grant ast-0607489 . m. s. m. acknowlodges the support of the nasa planetary atmospheres program . d. s. acknowledges support from nasa through a spitzer space telescope grant through a contract issued by jpl / caltech . work by k. l. is supported by nsf grant ast-0707377 and nasa grant nng06gc26 g . , t. , feuchtgruber , h. , bezard , b. , drossart , p. , encrenaz , t. , beintema , d. a. , griffin , m. , heras , a. , kessler , m. , leech , k. , lellouch , e. , morris , p. , roelfsema , p. r. , roos - serote , m. , salama , a. , vandenbussche , b. , valentijn , e. a. , davis , g. r. , & naylor , d. a. 1997 , , 321 , l13 , k. , beuzit , j .- l . , 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& 2.154e+06 & 747.5 & 1.53 & 17.28 & 18.13 & 16.09 & 15.67 & 15.14 & 13.49 & 11.58 + . & 4.642e+06 & 644.2 & 1.43 & 17.82 & 18.80 & 16.75 & 16.87 & 16.37 & 14.31 & 12.04 + . & 1.000e+07 & 554.6 & 1.35 & 18.22 & 19.35 & 17.41 & 18.27 & 17.87 & 15.19 & 12.63 + 2.0 & 1.000e+06 & 1266.7 & 1.72 & 14.36 & 15.00 & 13.18 & 12.41 & 11.72 & 10.43 & 10.45 + . & 2.154e+06 & 1048.8 & 1.57 & 15.36 & 16.05 & 14.23 & 13.50 & 13.12 & 11.69 & 10.99 + . & 4.642e+06 & 855.3 & 1.47 & 16.64 & 17.42 & 15.46 & 14.84 & 14.40 & 12.87 & 11.40 + . & 1.000e+07 & 710.3 & 1.39 & 17.53 & 18.41 & 16.36 & 16.05 & 15.61 & 13.80 & 11.83 + . & 2.154e+07 & 605.8 & 1.33 & 17.90 & 18.96 & 16.94 & 17.36 & 17.04 & 14.65 & 12.35 + . & 4.642e+07 & 512.9 & 1.27 & 18.42 & 19.59 & 17.71 & 18.94 & 18.85 & 15.63 & 13.02 + 4.0 & 1.000e+06 & 1657.0 & 1.92 & 12.66 & 13.29 & 11.48 & 10.91 & 10.19 & 9.18 & 9.43 + . & 2.154e+06 & 1432.0 & 1.71 & 13.73 & 14.35 & 12.53 & 11.84 & 11.09 & 9.92 & 10.15 + . & 4.642e+06 & 1207.6 & 1.56 & 14.79 & 15.43 & 13.62 & 12.80 & 12.28 & 10.97 & 10.74 + . & 1.000e+07 & 989.1 & 1.45 & 15.88 & 16.58 & 14.71 & 13.95 & 13.60 & 12.14 & 11.16 + . & 2.154e+07 & 805.3 & 1.38 & 17.00 & 17.80 & 15.80 & 15.20 & 14.84 & 13.16 & 11.57 + . & 4.642e+07 & 673.8 & 1.32 & 17.73 & 18.66 & 16.59 & 16.43 & 16.18 & 14.04 & 12.07 + . & 1.000e+08 & 574.6 & 1.26 & 18.04 & 19.13 & 17.09 & 17.75 & 17.80 & 14.93 & 12.66 + 6.0 & 1.000e+06 & 1984.0 & 2.10 & 11.58 & 12.19 & 10.50 & 10.01 & 9.40 & 8.58 & 8.75 + . & 2.154e+06 & 1720.9 & 1.82 & 12.63 & 13.25 & 11.46 & 10.89 & 10.22 & 9.25 & 9.45 + . & 4.642e+06 & 1464.2 & 1.63 & 13.70 & 14.31 & 12.50 & 11.81 & 11.10 & 9.97 & 10.19 + . & 1.000e+07 & 1219.6 & 1.50 & 14.83 & 15.45 & 13.65 & 12.82 & 12.32 & 11.04 & 10.79 + . & 2.154e+07 & 988.4 & 1.40 & 16.02 & 16.72 & 14.81 & 14.03 & 13.68 & 12.21 & 11.22 + . & 4.642e+07 & 803.5 & 1.33 & 17.06 & 17.86 & 15.80 & 15.25 & 14.91 & 13.19 & 11.63 + . & 1.000e+08 & 674.9 & 1.28 & 17.81 & 18.73 & 16.58 & 16.45 & 16.25 & 14.04 & 12.13 + . & 2.154e+08 & 574.9 & 1.22 & 18.12 & 19.19 & 17.07 & 17.75 & 17.89 & 14.94 & 12.73 + 8.0 & 1.000e+06 & 2184.9 & 2.28 & 10.91 & 11.48 & 9.92 & 9.44 & 8.89 & 8.17 & 8.30 + . & 2.154e+06 & 1987.6 & 1.93 & 11.74 & 12.34 & 10.66 & 10.18 & 9.60 & 8.78 & 8.97 + . & 4.642e+06 & 1656.0 & 1.69 & 12.91 & 13.52 & 11.72 & 11.14 & 10.47 & 9.48 & 9.70 + . & 1.000e+07 & 1400.7 & 1.54 & 14.08 & 14.68 & 12.87 & 12.13 & 11.44 & 10.29 & 10.43 + . & 2.154e+07 & 1163.4 & 1.42 & 15.15 & 15.78 & 13.97 & 13.14 & 12.71 & 11.38 & 10.95 + . & 4.642e+07 & 940.0 & 1.34 & 16.39 & 17.10 & 15.13 & 14.39 & 14.03 & 12.51 & 11.37 + . & 1.000e+08 & 769.1 & 1.28 & 17.35 & 18.16 & 16.04 & 15.59 & 15.29 & 13.43 & 11.81 + . & 2.154e+08 & 659.2 & 1.22 & 17.93 & 18.86 & 16.66 & 16.69 & 16.59 & 14.21 & 12.29 + . & 4.642e+08 & 543.2 & 1.17 & 18.41 & 19.49 & 17.35 & 18.23 & 18.59 & 15.28 & 13.02 + 10.0 & 1.000e+06 & 2315.7 & 2.44 & 10.47 & 11.00 & 9.54 & 9.07 & 8.55 & 7.89 & 7.98 + . & 2.154e+06 & 2168.4 & 2.04 & 11.18 & 11.75 & 10.18 & 9.71 & 9.17 & 8.45 & 8.61 + . & 4.642e+06 & 1873.0 & 1.75 & 12.26 & 12.87 & 11.14 & 10.63 & 10.03 & 9.15 & 9.34 + . & 1.000e+07 & 1553.8 & 1.57 & 13.34 & 13.94 & 12.15 & 11.52 & 10.85 & 9.80 & 10.06 + . & 2.154e+07 & 1307.0 & 1.44 & 14.58 & 15.19 & 13.38 & 12.58 & 11.98 & 10.77 & 10.72 + . & 4.642e+07 & 1072.7 & 1.35 & 15.68 & 16.33 & 14.47 & 13.66 & 13.30 & 11.89 & 11.17 + . & 1.000e+08 & 871.5 & 1.28 & 16.83 & 17.58 & 15.54 & 14.88 & 14.55 & 12.89 & 11.57 + . & 2.154e+08 & 735.9 & 1.22 & 17.60 & 18.45 & 16.29 & 15.95 & 15.76 & 13.68 & 12.02 + . & 4.642e+08 & 614.5 & 1.16 & 18.07 & 19.08 & 16.88 & 17.24 & 17.43 & 14.60 & 12.61 + . & 1.000e+09 & 498.2 & 1.12 & 18.88 & 19.97 & 17.84 & 18.82 & 19.51 & 15.67 & 13.36 + [ bigt1 ] ccccccccccccc 1.0 & 1.000e+06 & 672.5 & 1.46 & 21.70 & 16.75 & 18.03 & 16.16 & 17.07 & 16.15 & 14.63 & 12.19 & 16.23 + . & 2.154e+06 & 641.6 & 1.43 & 22.03 & 17.00 & 18.31 & 16.44 & 17.50 & 16.52 & 14.89 & 12.33 & 16.59 + . & 4.642e+06 & 592.9 & 1.38 & 22.58 & 17.43 & 18.76 & 16.91 & 18.22 & 17.12 & 15.32 & 12.58 & 17.21 + . & 1.000e+07 & 528.6 & 1.32 & 23.51 & 18.13 & 19.48 & 17.72 & 19.43 & 18.07 & 15.94 & 12.98 & 18.30 + . & 2.154e+07 & 455.8 & 1.26 & 24.76 & 19.21 & 20.56 & 18.95 & 21.05 & 19.40 & 16.81 & 13.55 & 19.78 + 2.0 & 1.000e+06 & 652.2 & 1.36 & 22.00 & 16.97 & 18.27 & 16.36 & 17.40 & 16.47 & 14.84 & 12.39 & 16.46 + . & 2.154e+06 & 641.1 & 1.35 & 22.11 & 17.06 & 18.36 & 16.45 & 17.55 & 16.60 & 14.92 & 12.43 & 16.58 + . & 4.642e+06 & 625.7 & 1.34 & 22.26 & 17.18 & 18.49 & 16.59 & 17.76 & 16.77 & 15.04 & 12.50 & 16.76 + . & 1.000e+07 & 599.6 & 1.32 & 22.52 & 17.39 & 18.71 & 16.82 & 18.11 & 17.06 & 15.25 & 12.62 & 17.05 + . & 2.154e+07 & 550.3 & 1.29 & 23.16 & 17.90 & 19.23 & 17.40 & 18.98 & 17.76 & 15.71 & 12.92 & 17.84 + . & 4.642e+07 & 483.5 & 1.25 & 24.09 & 18.69 & 20.02 & 18.30 & 20.26 & 18.81 & 16.41 & 13.36 & 18.99 + . & 1.000e+08 & 409.0 & 1.21 & 25.38 & 19.89 & 21.19 & 19.65 & 22.06 & 20.37 & 17.40 & 13.99 & 20.63 + 4.0 & 1.000e+06 & 585.3 & 1.26 & 22.71 & 17.57 & 18.87 & 16.97 & 18.32 & 17.29 & 15.36 & 12.78 & 17.19 + . & 2.154e+06 & 584.2 & 1.26 & 22.73 & 17.58 & 18.88 & 16.98 & 18.34 & 17.30 & 15.37 & 12.78 & 17.20 + . & 4.642e+06 & 580.6 & 1.26 & 22.77 & 17.62 & 18.92 & 17.02 & 18.40 & 17.35 & 15.41 & 12.81 & 17.26 + . & 1.000e+07 & 573.1 & 1.26 & 22.86 & 17.69 & 19.00 & 17.11 & 18.52 & 17.46 & 15.48 & 12.85 & 17.37 + . & 2.154e+07 & 558.8 & 1.25 & 23.03 & 17.84 & 19.14 & 17.27 & 18.76 & 17.66 & 15.61 & 12.94 & 17.58 + . & 4.642e+07 & 536.7 & 1.24 & 23.29 & 18.06 & 19.37 & 17.52 & 19.13 & 17.97 & 15.82 & 13.07 & 17.91 + . & 1.000e+08 & 492.8 & 1.22 & 23.83 & 18.54 & 19.84 & 18.05 & 19.90 & 18.63 & 16.26 & 13.35 & 18.60 + . & 2.154e+08 & 428.1 & 1.19 & 24.84 & 19.52 & 20.80 & 19.14 & 21.43 & 20.02 & 17.12 & 13.89 & 19.98 + 6.0 & 1.000e+06 & 563.5 & 1.21 & 22.98 & 17.83 & 19.12 & 17.22 & 18.64 & 17.63 & 15.58 & 12.97 & 17.44 + . & 2.154e+06 & 562.9 & 1.21 & 22.99 & 17.84 & 19.13 & 17.22 & 18.65 & 17.64 & 15.58 & 12.98 & 17.45 + . & 4.642e+06 & 561.2 & 1.21 & 23.01 & 17.85 & 19.15 & 17.24 & 18.68 & 17.66 & 15.60 & 12.99 & 17.47 + . & 1.000e+07 & 557.7 & 1.21 & 23.05 & 17.89 & 19.18 & 17.28 & 18.73 & 17.71 & 15.63 & 13.01 & 17.52 + . & 2.154e+07 & 550.9 & 1.21 & 23.12 & 17.96 & 19.25 & 17.36 & 18.84 & 17.81 & 15.69 & 13.05 & 17.62 + . & 4.642e+07 & 539.2 & 1.20 & 23.25 & 18.07 & 19.36 & 17.48 & 19.03 & 17.97 & 15.80 & 13.12 & 17.78 + . & 1.000e+08 & 517.2 & 1.19 & 23.50 & 18.29 & 19.58 & 17.73 & 19.38 & 18.28 & 16.01 & 13.25 & 18.09 + . & 2.154e+08 & 477.9 & 1.18 & 24.02 & 18.79 & 20.07 & 18.27 & 20.17 & 19.01 & 16.47 & 13.54 & 18.80 + . & 4.642e+08 & 423.3 & 1.15 & 24.83 & 19.59 & 20.85 & 19.16 & 21.45 & 20.21 & 17.21 & 14.00 & 19.95 + 8.0 & 1.000e+06 & 556.3 & 1.17 & 23.09 & 17.95 & 19.23 & 17.32 & 18.74 & 17.78 & 15.67 & 13.08 & 17.50 + . & 2.154e+06 & 556.0 & 1.17 & 23.09 & 17.95 & 19.24 & 17.32 & 18.74 & 17.78 & 15.67 & 13.08 & 17.50 + . & 4.642e+06 & 555.2 & 1.17 & 23.10 & 17.96 & 19.24 & 17.33 & 18.75 & 17.80 & 15.68 & 13.09 & 17.51 + . & 1.000e+07 & 553.2 & 1.17 & 23.12 & 17.98 & 19.26 & 17.35 & 18.79 & 17.82 & 15.70 & 13.10 & 17.54 + . & 2.154e+07 & 549.4 & 1.17 & 23.16 & 18.02 & 19.30 & 17.39 & 18.85 & 17.88 & 15.73 & 13.12 & 17.59 + . & 4.642e+07 & 541.2 & 1.17 & 23.25 & 18.10 & 19.38 & 17.48 & 18.97 & 17.99 & 15.81 & 13.17 & 17.71 + . & 1.000e+08 & 524.4 & 1.16 & 23.43 & 18.26 & 19.55 & 17.66 & 19.24 & 18.23 & 15.97 & 13.27 & 17.94 + . & 2.154e+08 & 496.5 & 1.15 & 23.74 & 18.55 & 19.83 & 17.98 & 19.70 & 18.65 & 16.24 & 13.45 & 18.35 + . & 4.642e+08 & 462.1 & 1.13 & 24.23 & 19.05 & 20.31 & 18.52 & 20.50 & 19.42 & 16.71 & 13.74 & 19.07 + 10.0 & 1.000e+06 & 561.0 & 1.14 & 23.07 & 17.96 & 19.23 & 17.29 & 18.66 & 17.76 & 15.65 & 13.12 & 17.42 + . & 2.154e+06 & 560.8 & 1.14 & 23.07 & 17.96 & 19.23 & 17.30 & 18.67 & 17.77 & 15.66 & 13.12 & 17.42 + . & 4.642e+06 & 560.4 & 1.14 & 23.08 & 17.96 & 19.24 & 17.30 & 18.67 & 17.77 & 15.66 & 13.12 & 17.42 + . & 1.000e+07 & 559.0 & 1.14 & 23.09 & 17.98 & 19.25 & 17.31 & 18.69 & 17.79 & 15.67 & 13.13 & 17.44 + . & 2.154e+07 & 556.1 & 1.14 & 23.12 & 18.01 & 19.28 & 17.34 & 18.74 & 17.83 & 15.70 & 13.15 & 17.48 + . & 4.642e+07 & 550.0 & 1.14 & 23.18 & 18.06 & 19.34 & 17.41 & 18.83 & 17.92 & 15.76 & 13.18 & 17.56 + . & 1.000e+08 & 537.8 & 1.13 & 23.31 & 18.18 & 19.46 & 17.54 & 19.02 & 18.09 & 15.87 & 13.26 & 17.73 + . & 2.154e+08 & 518.2 & 1.12 & 23.51 & 18.37 & 19.65 & 17.75 & 19.32 & 18.37 & 16.05 & 13.38 & 17.99 + . & 4.642e+08 & 489.7 & 1.11 & 23.84 & 18.69 & 19.96 & 18.10 & 19.83 & 18.86 & 16.36 & 13.57 & 18.45 + . & 1.000e+09 & 442.1 & 1.09 & 24.49 & 19.36 & 20.61 & 18.83 & 20.93 & 19.94 & 17.01 & 13.98 & 19.43 + [ bigt5 ] solar and includes the opacity of refractory cloud species . as in marley07 , times on the x - axis are years since formation , which takes no time ( by definition ) for hot start planets , and @xmath122.3 - 3.0 myr for core accretion planets . [ quad ] ] @xmath49 hz@xmath43 ) for 5@xmath10 solar ( [ m / h=0.7 ] , colors ) and 1@xmath10 solar models ( [ m / h=0.0 ] , black ) at , from top to bottom , 1400 , 1000 , 700 , and 500 k , for log @xmath14=3.67 . the inset shows the 700 k models on a linear @xmath50 scale ( from 0.65 to 5 @xmath2 m ) and linear @xmath51 scale ( @xmath52 , relative to the rest of the figure ) . [ spec1 ] ] objects at an age of @xmath1210 myr . in red is a hot start evolution model with solar metallicity at 1000 k. in light blue is this same model with 5@xmath10 solar metallicity , for comparison . in dark blue is a 600 k model that uses the core - accretion initial condition and 5@xmath10 solar metallicity . over - plotted in black are @xmath7 and @xmath8 contrast ratios relative to two blackbody stars . the two solid curves are for a sun - like 5770 k star and the dashed curves are for an m2v - like 3600 k star . [ spec2 ] ] @xmath49 hz@xmath43 ) for 5@xmath10 solar ( [ m / h=0.7 ] , colors ) and 1@xmath10 solar models ( [ m / h=0.0 ] , black ) at , from top to bottom , 1400 , 1000 , 700 , and 500 k , for log @xmath14=3.67 . thin lines are for equilibrium chemistry , as shown in . thick lines show models that utilize non - equilibrium chemistry with log @xmath37=4 . infrared filter bandpasses are shown in gray on the top panel . [ neq1 ] ] @xmath49 hz@xmath43 ) around @xmath31-band . all are referenced to a model with @xmath0=700 k , log @xmath14=3.67 , solar metallicity , and equilibrium chemistry . the @xmath0 panel shows a @xmath53100 k change in @xmath0 . the [ m / h ] panel compares the standard model to one that is 5@xmath10 solar metallicity , [ m / h=0.7 ] . the upper right panel ( log g ) shows the effects of gravity , while the lower right panel shows the effects of non - equilibrium chemistry due to vertical mixing . gray vertical lines guide the eye and illustrate possible locations of narrow band filters .

we couple these spectral calculations to an updated version of the marley et al . these metal - enhanced young jupiters have lower pressure photospheres than field brown dwarfs of the same effective temperatures arising from both lower surface gravities and enhanced atmospheric opacity . we highlight several diagnostics for enhanced metallicity . a stronger co absorption band at 4.5 m for the warmest objects is predicted . at all temperatures , enhanced flux in band we also qualitatively assess the changes to emitted spectra due to nonequilibrium chemistry .

we examine the spectra and infrared colors of the cool methane - dominated atmospheres at k expected for young gas giant planets . we couple these spectral calculations to an updated version of the marley et al . ( 2007 ) giant planet thermal evolution models that include formation by core accretion - gas capture . these relatively cool `` young jupiters '' can be 1 - 6 magnitudes fainter than predicted by standard cooling tracks that include a traditional initial condition , which may provide a diagnostic of formation . if correct , this would make true jupiter - like planets much more difficult to detect at young ages than previously thought . since jupiter and saturn are of distinctly super - solar composition , we examine emitted spectra for model planets at both solar metallicity and a metallicity of 5 times solar . these metal - enhanced young jupiters have lower pressure photospheres than field brown dwarfs of the same effective temperatures arising from both lower surface gravities and enhanced atmospheric opacity . we highlight several diagnostics for enhanced metallicity . a stronger co absorption band at 4.5 m for the warmest objects is predicted . at all temperatures , enhanced flux in band is expected due to reduced collisional induced absorption by h . this leads to correspondingly redder near infrared colors , which are redder than solar metallicity models with the same surface gravity by up to 0.7 in and 1.5 in . molecular absorption band depths increase as well , most significantly for the coolest objects . we also qualitatively assess the changes to emitted spectra due to nonequilibrium chemistry .

astro-ph0611607

i

we have elaborately investigated the relations among various internal ( e.g. color , luminosity , morphology , star formation rate , velocity dispersion , size , radial color gradient , and axis ratio ) and collective properties ( e.g. luminosity function , velocity dispersion distribution function , and axis ratio distribution function ) . we will study other collective properties such as the correlation function , power spectrum , topology , and peculiar velocity field , in separate works . 1 . to extend the absolute magnitude range , we have added the redshifts of the bright galaxies with @xmath39 to the sdss - nyu - vagc . six volume - limited samples with faint limits from @xmath243 to @xmath244 , are used for more efficient use of the flux - limited sdss sample . we have divided the samples into subsamples of early ( e / s0 ) and late ( s / irr ) morphology types by using our accurate morphology classifier , working in the three - dimensional parameter space of @xmath2 color , @xmath3 color gradient , and concentration index . the morphology classifier is able to separate the blue early types from the blue late types , and also to distinguish the spirals from the red e / s0 types because it does not depend only on color . the late type galaxies with isophotal axis ratio of less than 0.6 have been excluded because they suffer severely from dimming and reddening due to internal extinction and then may cause biases in luminosity , luminosity function , color , color gradient , and so on . this correction makes the blue sequence of the late type galaxies bluer and brighter compared to that obtained from all late type galaxies . the blue sequence also become better - defined with smaller width . we have found that absolute magnitude and morphology are the most important parameters in characterizing physical properties of galaxies . in other words , other parameters show relatively small scatter once absolute magnitude and morphology are fixed for early type galaxies , in particular . one very interesting fact we have noticed in our work is that many physical parameters of galaxies manifest different behaviors across the absolute magnitude of about @xmath245 . for example , the red sequence of early types changes the slope at @xmath246 in the color - magnitude space . also , at a magnitude fainter than @xmath247 , the number of blue star - forming early types increases significantly , and the surface brightness profile as parameterized by @xmath108 becomes less centrally concentrated . the passive spirals with vanishing @xmath248 emission seem to have magnitudes brighter than @xmath249 . at fixed morphology and luminosity , we find that bright ( @xmath4 ) early type galaxies show very small dispersions in color , color gradient , concentration , size , and velocity dispersion . these dispersions increase at fainter magnitudes , where the fraction of blue star - forming early types increases . concentration indices of early types are well - correlated with velocity dispersion , but are insensitive to luminosity and color for bright galaxies , in particular . the slope of the faber - jackson relation ( @xmath5 ) continuously changes from @xmath6 to @xmath7 when luminosity changes from @xmath8 to @xmath9 . the size of early types is well - correlated with stellar velocity dispersion , @xmath10 , when @xmath11 km s@xmath12 . late type galaxies show wider dispersions in all physical parameters compared to early types at the same luminosity . we find that passive spiral galaxies are well - separated from star - forming late type galaxies at @xmath1 equivalent width of about 4 . we note that the estimated lf shows significant fluctuations due to large scale structures when measured in different regions of the universe . on the other hand , the morphological fraction as a function of luminosity is relatively less sensitive to large scale structures and thus seems to be more universal . in paper ii , it is shown that the morphology fraction is a monotonic function of local density at a fixed luminosity . since luminosity in turn depends on local density , this result indicates that the probability for a galaxy to be born as a particular morphological type is basically determined when its luminosity or mass is given . to this extent , morphology is determined by galaxy mass . the question here is what determines the morphology of a galaxy having a particular mass while keeping the type fraction corresponding to its mass scale . further investigations are required to answer this question . the authors thank chan - gyung park for making the velocity dispersion function fits and ravi sheth for helpful comments . cbp acknowledges the support of the korea science and engineering foundation ( kosef ) through the astrophysical research center for the structure and evolution of the cosmos ( arcsec ) . msv acknowledges support from nasa grant nag-12243 and nsf grant ast-0507463 . msv thanks the department of astrophysical sciences at princeton university for its hospitality during sabbatical leave . yyc , cbp , and msv thank the aspen center for physics , at which much of this paper was written . 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 , cambridge university , 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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we morphologically classify galaxies using the three dimensional parameter space of color , color gradient , and concentration index . , we find that bright ( ) early type galaxies show very small dispersions in color , color gradient , concentration , size , and velocity dispersion . these dispersions increase at fainter magnitudes , where the fraction of blue star - forming early types increases . late types show wider dispersions in all physical parameters compared to early types at the same luminosity . concentration indices of early types are well correlated with velocity dispersion , but are insensitive to luminosity and color for bright galaxies , in particular . the slope of the faber - jackson relation ( ) continuously changes from to when luminosity changes from to . the size of early types is well - correlated with stellar velocity dispersion , , when km s . we find that passive spiral galaxies are well separated from star - forming late type galaxies at equivalent width of about 4 . an interesting finding is that many physical parameters of galaxies manifest different behaviors across the absolute magnitude of about .

we examine volume - limited samples of galaxies drawn from the sloan digital sky survey to look for relations among internal and collective physical parameters of galaxies as faint as . the internal physical properties of interest include morphology , luminosity , color , color gradient , concentration , size , velocity dispersion , equivalent width of line , and axis ratio . collective properties that we measure include the luminosity and velocity dispersion functions . we morphologically classify galaxies using the three dimensional parameter space of color , color gradient , and concentration index . all relations are inspected separately for early and late type galaxies . at fixed morphology and luminosity , we find that bright ( ) early type galaxies show very small dispersions in color , color gradient , concentration , size , and velocity dispersion . these dispersions increase at fainter magnitudes , where the fraction of blue star - forming early types increases . late types show wider dispersions in all physical parameters compared to early types at the same luminosity . concentration indices of early types are well correlated with velocity dispersion , but are insensitive to luminosity and color for bright galaxies , in particular . the slope of the faber - jackson relation ( ) continuously changes from to when luminosity changes from to . the size of early types is well - correlated with stellar velocity dispersion , , when km s . we find that passive spiral galaxies are well separated from star - forming late type galaxies at equivalent width of about 4 . an interesting finding is that many physical parameters of galaxies manifest different behaviors across the absolute magnitude of about . the morphology fraction as a function of luminosity depends less sensitively on large - scale structure than the luminosity function ( lf ) does , and thus seems to be more universal . the effects of internal extinction in late type galaxies on the completeness of volume - limited samples and on the lf and morphology fraction are found to be very important . an important improvement of our analyses over most previous works is that the extinction effects are effectively reduced by excluding the inclined late type galaxies with axis ratios of .

1103.3619

i

it is generally accepted that the vast amount of continuum emission of type 1 active galactic nuclei ( agns ) in uv and optical wavelengths originates in the accretion disk surrounding a supermassive black hole , and the uv - optical variability found at the beginning of agn studies has been considered a powerful tool for understanding the nature of the agn central engine . however , the mechanism of this variability is still under discussion . many models for variability have been proposed , including accretion disk instabilities , x - ray reprocessing ( krolik et al . 1991 ; kawaguchi in prep . ) , star collisions ( courvoisier , paltani , & walter 1996 ; torricelli - ciamponi et al . 2000 ) , and gravitational microlensing ( hawkins 1993 ) ; however , none of these successfully explained more than a few properties of uv - optical variability @xcite . the spectral variability of the uv - optical continuum emission during flux variation is a key property for understanding the central engines and their variability mechanisms in agns . for example , since the spectral energy distribution ( sed ) of a hot spot or a flare in the accretion disk caused by local enhancement of mass accretion or disk instabilities would be different from that of the entire disk , the spectral shape of continuum emission is expected to vary with the flux variation when caused by those mechanisms . on the other hand , a change of the global mass accretion rate of the disk and a certain reprocessing model @xcite would not change the temperature distribution of the accretion disk at larger radii ; thus , the absence of the spectral variation of optical continuum emission during flux variation suggests those variation mechanisms . sakata et al . ( 2010 ; hereafter paper i ) addressed the spectral variability of optical continuum emission of agns . paper i examined the long - term multi - band monitoring data of 11 nearby agns and precisely estimated the contaminated flux of the host galaxy and the narrow emission lines . then , it was found that the multi - epoch optical flux data in any two different bands obtained on the same night showed a very tight linear flux - to - flux relationship for all target agns and that the non - variable component of the host galaxy plus narrow lines was located on the fainter extension of the linear regression line of multi - epoch flux - to - flux plots . from these results , paper i concluded that the spectral shape of agn continuum emission in the optical region ( @xmath4 ) does not systematically change during flux variation and that the trend of spectral hardening in which the optical continuum emission becomes bluer as it becomes brighter , which has been reported by many studies @xcite , is caused by the contamination of the non - variable component of the host galaxy plus narrow emission lines , which is usually redder than agn continuum emission . in contrast to optical continuum emission , two opposite claims have not been resolved for the spectral variability of uv continuum emission . @xcite statistically examined the properties of flux variations of qsos from the two - epoch photometric observations of about 25,000 qsos obtained by the sloan digital sky survey ( sdss ) and found a larger amplitude of variation at shorter wavelengths in the uv region of @xmath5 , indicating spectral hardening during flux variation of qsos . @xcite obtained a composite of the differential spectrum of two - epoch spectroscopic observations for hundreds of sdss qsos and found that the composite differential spectrum was bluer than the composite spectrum of qsos , which also indicates spectral hardening of the uv continuum emission . on the other hand , applied principal component analysis ( pca ) to the multi - epoch uv spectra of 15 nearby agns obtained by the _ international ultraviolet explorer _ ( iue ) satellite and concluded that the uv flux variation of the agns consists of a variable component with a constant spectral shape and a non - variable component . based on the decomposition of the multi - epoch spectra to a variable and a non - variable components , they further concluded that the variable component has a power - law shape of fixed spectral index and that the non - variable component can be reproduced using the sum of a steep balmer continuum and a pseudo - continuum , which corresponds to the spectral feature of the small blue bump ( sbb ) . @xcite and @xcite observed ngc 4593 and fairall 9 , respectively , using the iue satellite . they found that the multi - epoch uv flux data in two different bands obtained on the same night showed a linear flux - to - flux relationship and that the contaminated flux of the sbb was located on a fainter extension of the linear regression line . these authors concluded that the uv continuum emission retains a constant spectral shape during the agns flux variation . in this paper , we examine the spectral variability of the uv continuum emission of agns , in the same way as in paper i , on the basis of the long - term multi - epoch photometric data of 10 mid - redshift luminous qsos obtained by the sdss . in section [ s_obsdata ] , we describe the selection of target qsos , their basic properties such as the central black hole mass and accretion rate , and present their light curves . in section [ s_result ] , we examine the uv color variability of the target qsos from the analysis of the flux - to - flux plots and the contaminated fluxes of the host galaxies . in section [ s_discuss ] , we compare our results with previous observational studies about the uv color variability of agns and also with an accretion disk model . in section [ s_summary ] , we summarize our results . we assume cosmological parameters of @xmath6 throughout this paper .

all target qsos showed clear flux variations during the monitoring period 1998 , and the multi - epoch flux data in two different bands obtained on the same night showed a linear flux - to - flux relationship for all target qsos . assigning the flux in the longer wavelength to the x - axis in the flux - to - flux diagram , this result strongly indicates that the spectral shape of the continuum emission of qsos in the uv region ( in rest - frame wavelength ) usually becomes bluer as it becomes brighter .

we examine whether the spectral energy distribution of uv continuum emission of active galactic nuclei ( agns ) changes during flux variation . we used multi - epoch photometric data of qsos in the stripe 82 observed by the sloan digital sky survey ( sdss ) legacy survey and selected 10 bright qsos observed with high photometric accuracies , in the redshift range of where strong broad emission lines such as ly and do not contaminate sdss filters , to examine spectral variation of the uv continuum emission with broad - band photometries . all target qsos showed clear flux variations during the monitoring period 1998 , and the multi - epoch flux data in two different bands obtained on the same night showed a linear flux - to - flux relationship for all target qsos . assigning the flux in the longer wavelength to the x - axis in the flux - to - flux diagram , the x - intercept of the best - fit linear regression line was positive for most targets , which means that their colors in the observing bands become bluer as they become brighter . then , the host galaxy flux was estimated on the basis of the correlation between the stellar mass of the bulge of the host galaxy and the central black hole mass ; the latter was estimated on the basis of the luminosity scaling relations for or emission lines and their line width . we found that the longer wavelength flux of the host galaxy was systematically smaller than that of the fainter extension of the best - fit regression line at the same shorter wavelength flux for most targets . this result strongly indicates that the spectral shape of the continuum emission of qsos in the uv region ( in rest - frame wavelength ) usually becomes bluer as it becomes brighter . the multi - epoch flux data in the flux - to - flux diagram were found to be consistent with the wavelength - dependent amplitude of variation presented in , which showed a larger amplitude of variation in shorter wavelengths . we also found that the multi - epoch flux - to - flux plots could be fitted well with the standard accretion disk model changing the mass accretion rate with a constant black hole mass for most targets . this finding strongly supports the standard accretion disk model for uv continuum emission of qsos .

1103.3619

c

@xcite examined the relationship between variability amplitude and the rest - frame wavelength of the uv - optical region from sdss two - epoch multi - band observations of about 25,000 qsos , and found a larger amplitude of variation at shorter wavelengths in the uv region of @xmath5 . in this section , the tracks of the flux - to - flux plot of the target qsos obtained from the photometric monitoring data , which show the hardening trend in the uv region , as presented in the previous sections , are compared with the hardening trend of the amplitude of variation presented in @xcite . assuming that the wavelength - dependent amplitude of variation always holds for the flux variation at all times for individual qsos , a power - law function of @xmath86 in a flux - to - flux plot is obtained , where @xmath87 is derived from the wavelength - dependent amplitude of variation @xmath88 , presented in equation 11 of @xcite . then , we fit the power - law function , @xmath89 , to the flux - to - flux plot data of the target qsos , fixing the parameter @xmath90 as @xmath91 , where @xmath92 and @xmath93 are the effective wavelengths of the observing filters in the rest frame . figures [ f_ff1 ] and [ f_ff2 ] present the fitting of the power - law function to the flux - to - flux plots , and the best - fit parameters and the reduced @xmath72 values are listed in table [ t_vanden ] . the reduced @xmath51 value of the power - law fit is comparable to that of the straight - line fit for most of the target qsos . the slope of the power - law fit seems to be slightly gentler than that of the flux - to - flux plots for j2123@xmath20050 , and in fact , the reduced @xmath72 of the power - law fit is slightly larger than that of the straight - line fit even if it is still as small as @xmath94 . when we refit the power - law function , @xmath89 , with both @xmath95 and @xmath90 freed , @xmath96 is derived from the new power - law fit with the reduced @xmath97 . the @xmath90 value is slightly different from @xmath98 but would be still consistent with @xcite within the fitting error and the diversity of qso properties , and the reduced @xmath72 becomes comparable to that of the straight - line fit . from these results , we conclude that our results of the hardening trend during the flux variation obtained from the flux - to - flux plots in the rest - frame uv wavelengths are consistent with the hardening trend of the variability amplitude in the uv region presented in @xcite . [ [ s_paltaniwalter ] ] observed the uv spectra of 15 nearby agns at different epochs using the iue satellite . applying pca to the multi - epoch spectra and the decomposition to a variable and a non - variable components , they explained the uv variation in almost all their targets as the sum of a variable component of a constant power - law spectral shape and a non - variable component of the sbb , which means that the spectral shape of the uv continuum emission is almost constant during the flux variation . this finding is not consistent with our results that the uv continuum emission becomes bluer as it becomes brighter for most of the target qsos . in fact , did not estimate the sbb fluxes of the target agns by fitting a spectral model of a power - law continuum plux the sbb to their uv spectrum in order to examine the consistency of that method with the conclusion from the decomposition to a variable and a non - variable components . moreover , as discussed in section [ s_effectsbp ] , the sbb is thought to originate in the blr and its flux was found to be variable . it is suspected that a sufficient amount of the sbb flux is constant , which explains the constant spectral shape of the uv continuum emission during flux variation . on the other hand , paltani & walter s finding that one eigenvalue dominated all the others in the pca of the uv flux variation is consistent with the linear relationship of the fluxes in the two different bands found in the flux - to - flux plots of our target qsos . the models of the accretion disk predict that the spectral shape of the uv - optical continuum emission depends on the mass accretion rate and the black hole mass ; thus , the spectral properties of flux variation would also depend on those agn properties . therefore , while it is beyond the scope of this paper , it is very interesting to re - examine the multi - epoch uv spectra of nearby agns of using the flux - to - flux plot analysis with accurate estimation of non - variable components such as the host galaxy and also to discuss the luminosity or the black hole mass dependency of the spectral variability of the uv continuum emission . we showed that the spectral shape of the optical continuum emission is almost constant during the flux variation for 11 seyfert galaxies in paper i , which suggests that the radial temperature profile of an optical emitting region of an accretion disk does not change during the flux variation . on the other hand , we here find that the uv continuum emission becomes bluer as it brightens for most of the target qsos , while the uv fluxes in the two different bands show a tight linear correlation . this suggests that the temperature structure of the uv emitting region of an accretion disk shows systematic change . when the mass accretion rate changes in a standard accretion disk model , the spectral shape of the continuum emission from the accretion disk changes in uv wavelengths while it remains almost constant in optical wavelengths for agns whose central black hole mass is larger than @xmath99 ( e.g. , kawaguchi , shimura , & mineshige 2001 ) . that is because the variation of the mass accretion rate changes the maximum temperature of the accretion disk , which affects the spectral shape of uv continuum emission , while it does not change the radial profile of outer accretion disk of @xmath100 where the optical continuum emission originates , which would result in an almost constant optical continuum spectral shape . @xcite presented that a standard accretion disk model in which the mass accretion rate changed from one epoch to the next could be successfully fitted to the composite differential spectrum of two epochs of observations for hundreds of sdss qsos , which is bluer than the composite spectrum of qsos indicating the spectral hardening of uv continuum emission @xcite . however , the composite spectrum represents the average characteristics of qsos ; moreover , the differential spectrum corresponds only to the slope of the linear relationship between fluxes in two different bands in the flux - to - flux plots . here , we fit a standard accretion disk model with a varying mass accretion rate to the flux - to - flux plots for individual target qsos , and examine whether the spectral variation of the uv continuum emission during flux variations at various epochs can be described by the standard accretion disk model with various mass accretion rates and a constant black hole mass . the inner radius of the standard accretion disk model is set as @xmath101 , where @xmath102 is the schwarzschild radius . the outer radius is set as @xmath103 , but it is not important for the uv spectrum . a face - on view is assumed to calculate the flux from the accretion disk . then , a trajectory of the accretion disk model in the flux - to - flux diagram can be traced by changing the mass accretion rate with a constant black hole mass . we fit the trajectory of the accretion disk model to the flux - to - flux plots of the individual target qsos with a free parameter of black hole mass . since the observed flux includes the contaminating fluxes of the host galaxy , the sbb and emission line in addition to the continuum emission , the sbc - type host galaxy flux estimated in section [ s_effectotagncont ] , and the sbb and contaminating flux estimated in section [ s_effectsbp ] are added to the trajectory of the accretion disk model before fitting . figures [ f_ffsim1 ] and [ f_ffsim2 ] present the best - fit accretion disk model for the flux - to - flux plots of the target qsos , and the best - fit black hole mass and the reduced @xmath72 are listed in table [ t_simstat ] . the error of the black hole mass in the table is estimated from the statistical uncertainty of @xmath51-fitting of the model . as shown in figures [ f_ffsim1 ] and [ f_ffsim2 ] , the flux - to - flux plots can be fitted well by the standard accretion disk model , changing the mass accretion rate with a constant black hole mass . indeed , the reduced @xmath51 values of the standard accretion disk model are comparable to those of the straight - line fitting for 9 of the 10 target qsos , and even for the exception , j2123@xmath20050 , the reduced @xmath72 is as small as @xmath94 . in addition , as shown in figure [ f_bhmass ] , the best - fit black hole mass of the standard accretion disk model is consistent with the black hole mass estimated from the emission - line width and the luminosity scaling relation in section [ s_targetselec ] , within 0.76 dex for @xmath53 error of the latter black hole mass estimation . we also calculate the bolometric luminosity of the best - fit standard accretion disk model whose mass accretion rate corresponds to the average flux of the light curve . the ratio of the bolometric luminosity to the specific luminosity in uv , the bolometric correction @xmath104 , is listed in table [ t_simstat ] . we find that the bolometric correction is consistent with those obtained for hundreds of type 1 qsos from @xcite , which are distributed between 4 to 9 and whose average value is 5.62 . the black hole mass and the luminosity of the best - fit standard accretion disk model fitted to the flux - to - flux plots in uv wavebands are reasonable , and it could be a new technique for estimating a black hole mass of luminous qsos although the systematic uncertainties should be examined . as presented in paper i , the optical color of the best - fit regression line in the flux - to - flux diagram can be regarded as that of the agn optical continuum , because the optical spectral shape remains almost constant during the flux variation and the colors derived from the flux - to - flux plot analysis of nearby seyfert galaxies were consistent with those of the standard accretion disk model , @xmath105 . although it has long been known that the standard accretion disk model apparently shows a contradiction with observations that the composite spectrum of qsos is redder than that of the standard accretion disk model @xcite , the detailed analyses of the spectral shape of the uv - optical continuum emission of agns using flux variation presented here and in paper i strongly support the standard accretion disk . a possible explanation for the composite spectra being redder is that host galaxy light contaminates the spectra preferentially at longer wavelengths . these results are consistent with the recent analyses of the spectral shape of the optical to near - infrared continuum emission , which comes from the accretion disk by flux variations @xcite and polarizations @xcite . however , it has a critical difficulty of considering the variation of global accretion rate of a standard accretion disk as a primary source of flux variation of qsos . the timescale of changes of the global mass accretion rate is believed to correspond to the viscous timescale ( e.g. , pringle 1981 ; frank et al . 2002 ) , which is about @xmath106 years for our target qsos and much longer than the timescale of the flux variation we observed . clearly , further study of the flux variation mechanism is desired , which can explain the observed properties of spectral variations of the uv - optical continuum emission of agns , suggesting a variation of the characteristic temperature of an accretion disk .

we examine whether the spectral energy distribution of uv continuum emission of active galactic nuclei ( agns ) changes during flux variation . the multi - epoch flux data in the flux - to - flux diagram were found to be consistent with the wavelength - dependent amplitude of variation presented in , which showed a larger amplitude of variation in shorter wavelengths . we also found that the multi - epoch flux - to - flux plots could be fitted well with the standard accretion disk model changing the mass accretion rate with a constant black hole mass for most targets . this finding strongly supports the standard accretion disk model for uv continuum emission of qsos .

we examine whether the spectral energy distribution of uv continuum emission of active galactic nuclei ( agns ) changes during flux variation . we used multi - epoch photometric data of qsos in the stripe 82 observed by the sloan digital sky survey ( sdss ) legacy survey and selected 10 bright qsos observed with high photometric accuracies , in the redshift range of where strong broad emission lines such as ly and do not contaminate sdss filters , to examine spectral variation of the uv continuum emission with broad - band photometries . all target qsos showed clear flux variations during the monitoring period 1998 , and the multi - epoch flux data in two different bands obtained on the same night showed a linear flux - to - flux relationship for all target qsos . assigning the flux in the longer wavelength to the x - axis in the flux - to - flux diagram , the x - intercept of the best - fit linear regression line was positive for most targets , which means that their colors in the observing bands become bluer as they become brighter . then , the host galaxy flux was estimated on the basis of the correlation between the stellar mass of the bulge of the host galaxy and the central black hole mass ; the latter was estimated on the basis of the luminosity scaling relations for or emission lines and their line width . we found that the longer wavelength flux of the host galaxy was systematically smaller than that of the fainter extension of the best - fit regression line at the same shorter wavelength flux for most targets . this result strongly indicates that the spectral shape of the continuum emission of qsos in the uv region ( in rest - frame wavelength ) usually becomes bluer as it becomes brighter . the multi - epoch flux data in the flux - to - flux diagram were found to be consistent with the wavelength - dependent amplitude of variation presented in , which showed a larger amplitude of variation in shorter wavelengths . we also found that the multi - epoch flux - to - flux plots could be fitted well with the standard accretion disk model changing the mass accretion rate with a constant black hole mass for most targets . this finding strongly supports the standard accretion disk model for uv continuum emission of qsos .

1405.2364

i

in this paper we have explored both classical and quantum dynamics of a model potential exhibiting a caldera : that is , a shallow potential well with two pairs of symmetry related index one saddles associated with the entrance / exit channels . classical trajectory simulations at several different energies confirm the existence of the ` dynamical matching ' phenomenon originally proposed by carpenter , where the momentum direction associated with an incoming trajectory initiated at a high energy ts determines to a considerable extent the outcome of the reaction ( passage through the opposite exit channel ) . by studying a ` stretched ' version of the caldera model , we have uncovered a generalized dynamical matching : bundles of trajectories can reflect off a hard potential wall so as to end up exiting predominantly via the ts opposite the reflection point . in this respect , the stretched caldera provides an example of a ` molecular billiard ' . the effects on the caldera reaction dynamics due to higher dimensional coupling and environmental factors were explored by introducing energy dissipation into the equations of motion of the caldera system , similar to our previous work on a model potential with a vri point @xcite . the results indicated that environmental and coupling effects may serve to divide the caldera reaction mechanism into a direct component , which occurs quickly and is highly dependent upon the caldera dynamics , and a statistical component where a population of reagents loses energy in the caldera intermediate region , and therefore a population of a long - lived caldera intermediate forms that reacts in accord with a statistical model . in addition to classical trajectory studies , we have examined the dynamics of quantum wavepackets on the caldera potential ( stretched and unstretched ) . our computations reveal a quantum mechanical analogue of the ` dynamical matching ' phenomenon , where the initial expectation value of the momentum direction for the wavepacket determines the exit channel through which most of the probability density passes to product . pc and sw acknowledge the support of the office of naval research ( grant no . n00014 - 01 - 1 - 0769 ) . pc , bkc and sw acknowledge the support of the uk engineering and physical sciences research council ( grant no . ep / k000489/1 ) . the work of zck and gse is supported by the us national science foundation under grant no . che-1223754 . , eq . . ( a ) scaling parameter @xmath18 . ( b ) scaling parameter @xmath19 . ( c ) scaling parameter @xmath20.,title="fig:",width=288 ] , eq . . ( a ) scaling parameter @xmath18 . ( b ) scaling parameter @xmath19 . ( c ) scaling parameter @xmath20.,title="fig:",width=288 ] + , eq . . ( a ) scaling parameter @xmath18 . ( b ) scaling parameter @xmath19 . ( c ) scaling parameter @xmath20.,title="fig:",width=288 ] ) at various times . here the wave packet is for a carbon particle with @xmath136 kcal mol@xmath34 on the @xmath116 pes , which is shown as grey contours in the background . the non - vanishing regions of the nip are indicated by orange shading and thick black boundary lines . points corresponding to expectation value pairs @xmath137 for a discrete set of @xmath138 values , @xmath139 $ ] are plotted as red circles and trace an approximate path of the portion of the packet in the caldera region . these results show quantum mechanical dynamical matching " where the wave packet passes directly from the upper saddle through the lower ts through the caldera region.,height=566 ] pes for a hydrogen wave packet with @xmath136 kcal mol@xmath34 . a significant portion ( @xmath140 ) of the packet is lost due to spreading of the initial wave packet outside the caldera region . the portion of the packet that enters the caldera region initially mostly directly exits through the opposing lower ts . however , a small delocalized remnant of the packet persists in the caldera region at longer times . the direct character of the reaction increases at higher energies ( not shown).,height=453 ] , but for a carbon particle on the @xmath109 pes with @xmath136 kcal mol@xmath34 . while most of the wave packet still passes directly from the upper ts to the lower ts , due to the scaling of the potential in the @xmath13 direction a significant portion of the wavepacket collides with the repulsive wall of the caldera and undergoes a more complex motion.,height=340 ] , but for a carbon particle on the @xmath109 pes with @xmath141 kcal mol@xmath34 , i.e. , a higher energy wave packet with more momentum in the reactive " direction . this higher energy wave packet can pass over the pes features that reflected the packet in figure [ fig : z_wp_2 ] , and so most of the packet passes out of the lower ts.,height=340 ] , but for a carbon particle on the @xmath133 pes with @xmath136 kcal mol@xmath34 . the elongated shape of the caldera region causes the wave packet to be reflected off the bottom of the wall in its initial motion and toward the opposing upper ts , through which a significant portion of the packet is lost . the subsequent dynamics sees the remaining portion of the wave packet spreading out in the caldera region and portions passing out through the four ts dividing surfaces.,height=453 ] h system on the complex @xmath133 pes with a energy @xmath142 kcal mol@xmath34 above of the upper transition state and a lifetime of @xmath143 fs . this eigenstate , and those with a similar structure , were a contributing component of the @xmath144 kcal mol@xmath34 wave packet.,height=226 ] , but for the hydrogen particle with @xmath141 kcal mol@xmath34 . the dynamics are quite similar to those observed for the carbon particle , save they occur on a shorted time scale and the spreading of the wave packet is much faster.,height=453 ] for the hydrogen - particle wave packets . the initial drop in the low energy wave packets ( @xmath140 at times @xmath146 fs ) is mainly attributed to the spreading of the wave packet backward in the reactive direction , and this amplitude never enters the caldera region . ,

we explore both classical and quantum dynamics of a model potential exhibiting a caldera : that is , a shallow potential well with two pairs of symmetry related index one saddles associated with entrance / exit channels . classical trajectory simulations at several different energies confirm the existence of the ` dynamical matching ' phenomenon originally proposed by carpenter , where the momentum direction associated with an incoming trajectory initiated at a high energy saddle point determines to a considerable extent the outcome of the reaction ( passage through the diametrically opposing exit channel ) . by studying a ` stretched ' version of the caldera model , we have uncovered a generalized dynamical matching : bundles of trajectories can reflect off a hard potential wall so as to end up exiting predominantly through the transition state opposite the reflection point . in addition to classical trajectory studies , we examine the dynamics of quantum wave packets on the caldera potential ( stretched and unstretched ) .

we explore both classical and quantum dynamics of a model potential exhibiting a caldera : that is , a shallow potential well with two pairs of symmetry related index one saddles associated with entrance / exit channels . classical trajectory simulations at several different energies confirm the existence of the ` dynamical matching ' phenomenon originally proposed by carpenter , where the momentum direction associated with an incoming trajectory initiated at a high energy saddle point determines to a considerable extent the outcome of the reaction ( passage through the diametrically opposing exit channel ) . by studying a ` stretched ' version of the caldera model , we have uncovered a generalized dynamical matching : bundles of trajectories can reflect off a hard potential wall so as to end up exiting predominantly through the transition state opposite the reflection point . we also investigate the effects of dissipation on the classical dynamics . in addition to classical trajectory studies , we examine the dynamics of quantum wave packets on the caldera potential ( stretched and unstretched ) . these computations reveal a quantum mechanical analogue of the ` dynamical matching ' phenomenon , where the initial expectation value of the momentum direction for the wave packet determines the exit channel through which most of the probability density passes to product .

1207.3879

i

one of the key goals in modern cosmology is to study the formation of the first stars and galaxies at the end of the cosmic dark ages , and how they shaped the subsequent evolution of the universe ( barkana & loeb 2001 ; bromm & larson 2004 ; ciardi & ferrara 2005 ; bromm et al . 2009 ; loeb 2010 ) . the first , so - called population iii ( pop iii ) stars are predicted to have formed at @xmath5 in minihalos with virial mass @xmath6 and temperatures @xmath7k ( haiman et al . 1996 ; tegmark et al . 1997 ; yoshida et al . the pop iii initial mass function ( imf ) is thought to be top - heavy ( bromm et al . 1999 , 2002 ; abel et al . 2002 ) , possibly extending to @xmath8 , but recent simulations indicate that the pop iii imf may be quite broad , also including a fraction of lower - mass stars ( stacy et al . 2010 ; clark et al . 2011b ; greif et al . 2011 , 2012 ) . the first bona - fide galaxies are expected to have formed at a later stage in hierarchical structure formation ( bromm & yoshida 2011 ) , when @xmath9 halos assembled at @xmath10 via the merging of progenitor minihalos ( wise & abel 2007 ; greif et al . these systems are often termed ` atomic cooling halos ' , because their virial temperature , @xmath11k , exceeds the threshold to enable efficient cooling via lines of atomic hydrogen ( oh & haiman 2002 ) . direct observations of the first galaxies at redshifts @xmath12 have so far been out of reach . in the coming decade , the _ james webb space telescope ( jwst ) _ promises to directly probe this critical period ( gardner et al . the detection of metal absorption lines in the afterglow spectrum of high - redshift gamma - ray bursts ( grbs ) , imprinted by enriched gas in the first galaxies , offers an unusual opportunity to study the physical conditions inside them . we may thus be able to derive constraints on the temperature , metallicity , ionization state , and kinematics in the interstellar medium ( ism ) of high - redshift galaxies , and in the surrounding intergalactic medium ( igm ) . it is encouraging that such diagnostics can already be obtained for bursts at somewhat lower redshifts . an example is grb 081008 , where high - resolution spectroscopy with the vlt has probed the ism of a host galaxy at @xmath13 ( delia et al . 2011 ) . long - duration grbs have been shown to be associated with the death of massive stars ( stanek et al . 2003 ; hjorth et al . 2003 ; woosley & bloom 2006 ) . their high luminosities make them detectable out to the edge of the visible universe ( ciardi & loeb 2000 ; lamb & reichart 2000 ; bromm & loeb 2002 , 2006 ; gou et al . 2004 ; inoue et al . 2007 ; mszros & rees 2010 ) , with the current record held by grb 090429b at @xmath14 ( cucchiara et al . 2011 ) . grbs provide ideal probes of the high - redshift universe , including the star formation rate ( totani 1997 ; wijers et al . 1998 ; porciani & madau 2001 ; chary et al . 2007 ; yksel et al . 2008 ; wang & dai 2009 , 2011 ; elliott et al . 2012 ) , reionization ( gallerani et al . 2008 ) , dark energy ( dai et al . 2004 ; wang et al . 2011 ) , and the igm metal enrichment ( barkana & loeb 2004 ; totani et al . 2006 ; toma et al . 2011 ; bromm & loeb 2012 ) . the leading contender for the central engine of long - duration grbs is the collapsar model ( woosley 1993 ; macfadyen et al . 2001 ) . because of their predicted high characteristic mass , a significant fraction of pop iii stars might end their lives as a black hole , potentially leading to a large number of high - redshift grbs . thus , pop iii stars are viable progenitors of long - duration grbs , triggered by the collapsar mechanism , as long as they can lose their outer envelope and retain sufficient angular momentum in their center ( bromm & loeb 2006 ; belczynski et al . 2007 ; komissarov & barkov 2010 ; stacy et al . 2011 ) . it might even be possible for pop iii collapsars to occur if the extended outer envelope were not lost ( suwa & ioka 2011 ) . the history of pre - galactic metal enrichment has several important consequences for structure formation ( madau et al . 2001 ; karlsson et al . 2012 ) . an early phase of metal injection may qualitatively change the character of star formation , from a predominantly high - mass ( pop iii ) mode to a normal , low - mass dominated ( pop i / ii ) one , once the enrichment has exceeded a ` critical metallicity ' of @xmath15 ( bromm et al . 2001a ; schneider 2002 , 2006 ; bromm & loeb 2003 ; mackey et al . the transition between these two modes has crucial implications , e.g. , for the expected redshift distribution of grbs ( bromm & loeb 2006 ; campisi et al . 2011 ; de souza et al . 2011 ) , for reionization ( cen 2003 ; wyithe & loeb 2003 ; furlanetto & loeb 2005 ) , and for the chemical abundance patterns of low - metallicity stars ( qian & wasserburg 2001 ; frebel et al . 2007 , 2009 ; tumlinson 2010 ) . it is therefore important to explore the topology of early metal enrichment , and to determine when particular regions in the universe become supercritical ( tornatore et al . 2007 ; maio et al . 2010 ) . absorption lines imprinted on the spectra of bright background sources , such as grbs or quasars , are one of the main sources of information about the physical and chemical properties of high - redshift systems ( oh 2002 ; furlanetto & loeb 2003 ; oppenheimer et al . these lines are due mainly to absorption by neutral hydrogen present in the low column - density ly@xmath16 forest , and by metals in low - ionization stages ( e.g. , , , , , ) which arise in the higher column - density gas associated with damped ly@xmath16 absorbers ( dlas ) . the analysis of the spectrum of distant grb 050904 ( totani et al . 2006 ) has resulted in a wealth of detailed insight into the physical conditions within the host galaxy at @xmath17 , and salvaterra et al . ( 2009 ) claimed that they identified two absorption lines ( and ) , although at poor signal - to - noise , in the spectrum of grb 090423 , the most distant spectroscopically confirmed burst at @xmath18 ( salvaterra et al . 2009 ; tanvir et al . grbs as background sources offer a number of advantages compared to traditional lighthouses such as quasars ( bromm & loeb 2012 ) . their number density drops much less precipitously than quasars at @xmath19 ( fan et al . 2006 ) , and the absence of a strong proximity effect , together with the near power - law character of their spectra , renders them ideal probes of the early igm . in this paper , we discuss the observational signatures of pop iii grbs and study pre - galactic metal enrichment utilizing absorption lines in the spectra of high-@xmath20 grbs which were imprinted by the first galaxies . recently , it has become feasible to study the formation of the first galaxies , including the metal enrichment from pop iii supernovae ( sne ) , with highly - resolved cosmological simulations ( wise & abel 2008 ; greif et al . we here place a bright grb into the simulation box of greif et al . ( 2010 ) , and derive the spectral signature as the afterglow light escapes from the first galaxy , thereby probing the partially enriched igm in its vicinity . the fluxes in the near - ir and radio bands may be detectable by the _ jwst _ and the very large array ( vla ) out to @xmath5 . the structure of this paper is as follows . in section 2 , we derive the circumburst density profile of pop iii grbs , followed by a brief description of the underlying first galaxy simulation ( section 3 ) . we discuss the properties of the grb afterglow in section 4 , and the metal absorption line diagnostics in section 5 , followed by our conclusions .

we explore high - redshift gamma - ray bursts ( grbs ) as promising tools to probe pre - galactic metal enrichment . the circumburst density is roughly proportional to with values of about a few . in more massive halos , corresponding to the first galaxies , the density may be larger , . the resulting afterglow fluxes are weakly dependent on redshift at a fixed observed time , and may be detectable with the _ james webb space telescope ( jwst ) _ and very large array ( vla ) in the near - ir and radio wavebands , respectively , out to redshift . the metal absorption line signature is expected to be detectable in the near future . grbs are ideal tools for probing the metal enrichment in the early igm , due to their high luminosities and featureless power - law spectra .

we explore high - redshift gamma - ray bursts ( grbs ) as promising tools to probe pre - galactic metal enrichment . we utilize the bright afterglow of a population iii ( pop iii ) grb exploding in a primordial dwarf galaxy as a luminous background source , and calculate the strength of metal absorption lines that are imprinted by the first heavy elements in the intergalactic medium ( igm ) . to derive the grb absorption line diagnostics , we use an existing highly - resolved simulation of the formation of a first galaxy which is characterized by the onset of atomic hydrogen cooling in a halo with virial temperaturek . we explore the unusual circumburst environment inside the systems that hosted pop iii stars , modeling the density evolution with the self - similar solution for a champagne flow . for minihalos close to the cooling threshold , the circumburst density is roughly proportional to with values of about a few . in more massive halos , corresponding to the first galaxies , the density may be larger , . the resulting afterglow fluxes are weakly dependent on redshift at a fixed observed time , and may be detectable with the _ james webb space telescope ( jwst ) _ and very large array ( vla ) in the near - ir and radio wavebands , respectively , out to redshift . we predict that the maximum of the afterglow emission shifts from near - ir to millimeter bands with peak fluxes from mjy to jy at different observed times . the metal absorption line signature is expected to be detectable in the near future . grbs are ideal tools for probing the metal enrichment in the early igm , due to their high luminosities and featureless power - law spectra . the metals in the first galaxies produced by the first supernova ( sn ) explosions are likely to reside in low - ionization stages ( , , and ) . we show that if the afterglow can be observed sufficiently early , analysis of the metal lines may distinguish whether the first heavy elements were produced in a pair - instability supernova ( pisn ) , or a core - collapse ( type ii ) sn , thus constraining the initial mass function of the first stars .

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i

in this paper , we develop a diagnostic to study pre - galactic metal enrichment in the vicinity of the first galaxies . specifically , we utilize the bright afterglow of a pop iii grb as a featureless background source , and calculate the strength of metal absorption lines that are imprinted by the first heavy elements produced by pop iii sne . to approximately derive the metal absorption line statistics , we use an existing highly - resolved simulation of the formation of a first galaxy which is characterized by the onset of atomic hydrogen cooling in a halo with virial temperature @xmath0k . the reverse shock initially dominates the afterglow flux a few hours after explosion , followed by the forward shock emission later on . the fluxes in the near - ir and radio bands may be detectable with the _ jwst _ and the vla out to @xmath225 . we predict that the afterglow emission peaks from near - ir to millimeter bands with peak fluxes from mjy to jy at different observed times . metal absorption lines in the grb afterglow spectrum , giving rise to ews of a few tens of , may allow us to distinguish whether the first heavy elements were produced in a pop iii star that died as a pisn , or a core - collapse sn . to this extent , the spectrum needs to be obtained sufficiently early , within the first few hours after the trigger . the absorption signature of the first sn events might allow us to constrain the underlying mass scale of pop iii stars . this is the key input parameter to predict their evolution , nucleosynthetic yields , and modes of death , which in turn determine how the first stars impact subsequent cosmic history . the strength of the associated stellar feedback governs the assembly process of the first galaxies , in the sense that the stronger feedback from more massive stars shifts their formation to later stages in the hierarchical build - up of structure ( e.g. , ricotti et al . 2002 ; greif et al . 2010 ; frebel & bromm 2012 ; ritter et al . 2012 ; wise et al . 2012 ) . it will , however , be very challenging to directly probe the initial epoch of cosmic star formation . the reason is that even the _ jwst _ will not be able to detect individual first stars , but instead only more massive stellar systems or clusters that form later on in more massive host systems ( e.g. , pawlik et al . pop iii grbs may thus afford us one of the few direct windows into the crucial epoch of first light , another one being the extremely energetic pair - instability sn or hypernova explosions that are predicted to end the lives of the most massive pop iii stars ( e.g. , pan et al . 2012 ; hummel et al . the promise provided by the combination of a wide field grb trigger mission , such as janus or lobster , with the next - generation of highly - sensitive near - ir telescopes , such as the _ jwst _ or the planned ground - based extremely large facilities ( the e - elt , gmt , and tmt ) , is huge . grbs are likely to play a key role in finally opening up the high - redshift frontier , all the way back to the very beginning of star and black hole formation . we are indebted to anna frebel and steve finkelstein for helpful discussions . this work is supported by the national natural science foundation of china ( grants 11103007 and 11033002 ) . v. b. acknowledges support from nsf grant ast-1009928 and nasa atfp grant nnx09aj33 g . k. s. c. is supported by the grf grants of the government of the hong kong sar under hku 7011/09p . the simulations presented here were carried out at the texas advanced computing center ( tacc ) . abel , t. , norman , m. l. , & madau , p. 1999 , apj , 523 , 66 abel , t. , bryan , g. l. , & norman , m. l. 2002 , science , 295 , 93 abel , t. , wise , j. h. , & bryan , g. l. 2007 , apj , 659 , l87 alvarez , m. a. , bromm , v. , & shapiro , p. r. 2006 , apj , 639 , 621 baraffe , i. , heger , a. , & woosley , s. e. 2001 , apj , 550 , 890 barkana , r. & loeb , a. 2001 , phys . , 349 , 125 barkana , r. & loeb , a. 2004 , apj , 601 , 64 belczynski , k. , bulik , t. , heger , a. , & fryer , c. 2007 , apj , 664 , 986 blandford r. d. , & mckee c. f. 1976 , phys . fluid , 19 , 1130 bloom , j. s. 2011 , what are gamma - ray bursts ? 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we utilize the bright afterglow of a population iii ( pop iii ) grb exploding in a primordial dwarf galaxy as a luminous background source , and calculate the strength of metal absorption lines that are imprinted by the first heavy elements in the intergalactic medium ( igm ) . to derive the grb absorption line diagnostics , we use an existing highly - resolved simulation of the formation of a first galaxy which is characterized by the onset of atomic hydrogen cooling in a halo with virial temperaturek . we explore the unusual circumburst environment inside the systems that hosted pop iii stars , modeling the density evolution with the self - similar solution for a champagne flow . for minihalos close to the cooling threshold , we predict that the maximum of the afterglow emission shifts from near - ir to millimeter bands with peak fluxes from mjy to jy at different observed times . we show that if the afterglow can be observed sufficiently early , analysis of the metal lines may distinguish whether the first heavy elements were produced in a pair - instability supernova ( pisn ) , or a core - collapse ( type ii ) sn , thus constraining the initial mass function of the first stars .

we explore high - redshift gamma - ray bursts ( grbs ) as promising tools to probe pre - galactic metal enrichment . we utilize the bright afterglow of a population iii ( pop iii ) grb exploding in a primordial dwarf galaxy as a luminous background source , and calculate the strength of metal absorption lines that are imprinted by the first heavy elements in the intergalactic medium ( igm ) . to derive the grb absorption line diagnostics , we use an existing highly - resolved simulation of the formation of a first galaxy which is characterized by the onset of atomic hydrogen cooling in a halo with virial temperaturek . we explore the unusual circumburst environment inside the systems that hosted pop iii stars , modeling the density evolution with the self - similar solution for a champagne flow . for minihalos close to the cooling threshold , the circumburst density is roughly proportional to with values of about a few . in more massive halos , corresponding to the first galaxies , the density may be larger , . the resulting afterglow fluxes are weakly dependent on redshift at a fixed observed time , and may be detectable with the _ james webb space telescope ( jwst ) _ and very large array ( vla ) in the near - ir and radio wavebands , respectively , out to redshift . we predict that the maximum of the afterglow emission shifts from near - ir to millimeter bands with peak fluxes from mjy to jy at different observed times . the metal absorption line signature is expected to be detectable in the near future . grbs are ideal tools for probing the metal enrichment in the early igm , due to their high luminosities and featureless power - law spectra . the metals in the first galaxies produced by the first supernova ( sn ) explosions are likely to reside in low - ionization stages ( , , and ) . we show that if the afterglow can be observed sufficiently early , analysis of the metal lines may distinguish whether the first heavy elements were produced in a pair - instability supernova ( pisn ) , or a core - collapse ( type ii ) sn , thus constraining the initial mass function of the first stars .

0710.5345

i

the work presented here improves and extends our previous results . first , expanded and improved data sets are considered : three supernova samples and one radio galaxy sample . the radio galaxy data set has 11 new sources , increasing its size to 30 sources , and the supernovae data sets have increased substantially in size and quality . in addition , sz cluster distances and gamma - ray burst distances are considered . the dimensionless coordinate distances ( obtained directly from the data ) , and first and second derivatives of the distance are obtained as functions of redshift using a sliding window fit . the good agreement obtained using supernovae and radio galaxies , two completely independent methods , with sources that cover similar redshift ranges , suggests that neither method is strongly affected by systematic effects , and that each method provides a reliable cosmological tool . the first and second derivatives of the distance are combined to obtain the acceleration parameter @xmath0 , allowing for non - zero space curvature . it is shown that the zero redshift value of @xmath0 , @xmath129 , is independent of space curvature , and can be obtained from the first and second derivatives of the coordinate distance . thus , @xmath8 , which indicates whether the universe is accelerating at the current epoch , can be obtained directly from the supernova and radio galaxy data ; our determinations of @xmath0 only relies upon the validity of the robertson - walker line element , and is independent of a theory of gravity , and the contents of the universe . each of the supernova samples , analyzed using a sliding window fit , indicate that the universe is accelerating today independent of space curvature , independent of whether general relativity is the correct theory of gravity , and of the contents of the universe . the effect of non - zero space curvature on @xmath0 is to shift the redshift at which the universe transitions from acceleration to deceleration , moving this to lower redshift for negative space curvature and to higher redshift for positive space . the zero redshift values of @xmath64 obtained using a sliding window fit . for the davis et al . ( 2007 ) supernova sample is @xmath65 and that obtained for the radio galaxy sample of daly et al . ( 2007 ) is @xmath130 indicating that the universe is accelerating at the current epoch . the data were also binned so that only certain subsets of the data were used to solve for @xmath26 , @xmath27 , @xmath5 , and @xmath0 . the results for @xmath26 and @xmath5 indicate that the standard lcdm model provides a good description of the data . the results for @xmath27 and @xmath0 are consistent with the standard lcdm model , but do not independently confirm the model or the acceleration of the universe . in addition to the evaluation of the standard cosmological parameters , in an even more direct approach , we compared @xmath26 and @xmath27 obtained from the fits to the data to model predictions . comparisons of @xmath26 and @xmath27 with predictions based on general relativity indicate that general relativity provides an accurate description of the data on look - back time scales of about ten billion years , thus providing a very large scale test of general relativity . another new approach is that the data were analyzed using both a sliding window fit and fits in independent redshift bins . the fits in statistically independent redshift bins are broadly consistent with the sliding window fits , but are generally noisier ( as expected ) . we also explored the effects of non - zero space curvature on determinations of @xmath127 and @xmath0 . it is shown that the zero redshift value of @xmath64 , obtained by applying equation ( 4 ) to @xmath26 and @xmath27 , is independent of space curvature . this means that our method can be used to determine @xmath8 , and thus the degree to which the universe is accelerating at the current epoch , with only one assumption , that the robertson - walker line element is valid . in addition , it is found that the effect of space curvature on the shape of @xmath127 and @xmath0 is small , relative to the uncertainties arising from the measurement errors . after determining the expansion and acceleration rates of the universe as functions of redshift independent of a theory of gravity , we solve for the pressure , energy density , equation of state , and potential and kinetic energy of the dark energy as functions of redshift assuming that general relativity is the correct theory of gravity . we also define a new function , the dark energy indicator @xmath98 , which provides a measure of deviations of the equation of state of the dark energy @xmath2 from @xmath3 , and provides a new and independent measure of @xmath4 if @xmath86 . the results obtained using a sliding window fit indicate that a cosmological constant in a spatially flat universe provides a good description of each of these quantities over the redshift range from zero to one . the zero redshift values of these quantities obtained with the davis et al . ( 2007 ) supernovae sample are @xmath131 , @xmath132 , @xmath133 , @xmath134 , @xmath135 , and @xmath111 . in the standard lambda - cold dark matter model , @xmath136 , obtained using the first and second derivatives of the coordinate distance , provides an independent measure of @xmath85 . in addition , in this model , @xmath86 , so @xmath98 provides a measure of @xmath4 , and the value obtained here using the first and second derivatives of the coordinate distance , is @xmath112 . overall , the shapes of the pressure , energy density , equation of state , and other parameters as functions are redshift are consistent with those predicted in a standard lcdm model . there is a tantalizing hint that there may be divations from the standard model at high redshift ; more observations at high redshift will be needed to investigate this further . the results obtained using fits in independent redshift bins are consistent with the standard lcdm model , but do not independently confirm the model . we would like to thank the observers for their tireless efforts in obtaining the data used for this study . we would also like to thank the referee for helpful comments and suggesitons . this work was supported in part by u. s. national science foundation grants ast-0507465 ( r.a.d . ) and ast-0407448 ( s.g.d . ) , and the ajax foundation ( s.g.d . ) . davis , t. m. , mortsell , e. , sollerman , j. , becker , a. c. , blondin , s. , challis , p. , clocchiatti , a. , filippenko , a. v. , foley , r. j. , garnavich , p. m. , and 17 coauthors , submitted to apj , ( astro - ph/0701510 ) lllll sn & sn1994s & 0.016 & 0.0160 & 0.0016 + sn & sn2001v & 0.016 & 0.0145 & 0.0015 + sn & sn1996bo & 0.016 & 0.0135 & 0.0015 + sn & sn2001cz & 0.016 & 0.0155 & 0.0017 + sn & sn2000dk & 0.016 & 0.0161 & 0.0016 + sn & sn1997y & 0.017 & 0.0174 & 0.0018 + sn & sn1998ef & 0.017 & 0.0146 & 0.0016 + sn & sn1998v & 0.017 & 0.0160 & 0.0016 + sn & sn1999ek & 0.018 & 0.0155 & 0.0016 + sn & sn1992bo & 0.018 & 0.0190 & 0.0018 + sn & sn1992bc & 0.020 & 0.0200 & 0.0017 + sn & sn2000fa & 0.022 & 0.0205 & 0.0020 + sn & sn1995ak & 0.022 & 0.0187 & 0.0018 + sn & sn2000cn & 0.023 & 0.0226 & 0.0019 + sn & sn1998eg & 0.024 & 0.0248 & 0.0023 + sn & sn1994 m & 0.024 & 0.0239 & 0.0022 + sn & sn2000ca & 0.025 & 0.0239 & 0.0019 + sn & sn1993h & 0.025 & 0.0224 & 0.0019 + sn & sn1992ag & 0.026 & 0.0228 & 0.0023 + sn & sn1999gp & 0.026 & 0.0284 & 0.0021 + sn & sn1992p & 0.026 & 0.0281 & 0.0025 + sn & sn1996c & 0.028 & 0.0329 & 0.0027 + sn & sn1998ab & 0.028 & 0.0231 & 0.0019 + sn & sn1997dg & 0.030 & 0.0361 & 0.0032 + sn & sn2001ba & 0.031 & 0.0319 & 0.0023 + sn & sn1990o & 0.031 & 0.0309 & 0.0024 + sn & sn1999cc & 0.032 & 0.0310 & 0.0024 + sn & sn1996bl & 0.035 & 0.0350 & 0.0029 + sn & sn1994 t & 0.036 & 0.0338 & 0.0026 + sn & sn2000cf & 0.037 & 0.0395 & 0.0031 + sn & sn1999aw & 0.039 & 0.0429 & 0.0026 + sn & sn1992bl & 0.043 & 0.0417 & 0.0035 + sn & sn1992bh & 0.045 & 0.0505 & 0.0044 + sn & sn1995ac & 0.049 & 0.0431 & 0.0032 + sn & sn1993ag & 0.050 & 0.0541 & 0.0045 + sn & sn1990af & 0.050 & 0.0454 & 0.0042 + sn & sn1993o & 0.052 & 0.0553 & 0.0038 + sn & sn1998dx & 0.054 & 0.0503 & 0.0035 + rg & 3c 405 & 0.056 & 0.0514 & 0.0105 + sn & sn1992bs & 0.063 & 0.0695 & 0.0064 + sn & sn1993b & 0.071 & 0.0736 & 0.0064 + sn & sn1992ae & 0.075 & 0.0713 & 0.0069 + sn & sn1992bp & 0.079 & 0.0731 & 0.0050 + sn & sn1992br & 0.088 & 0.0718 & 0.0076 + sn & sn1992aq & 0.101 & 0.1145 & 0.0079 + sn & sn1996ab & 0.124 & 0.1174 & 0.0108 + cl & abell 1413 & 0.142 & 0.2283 & 0.0454 + cl & abell 2204 & 0.152 & 0.1801 & 0.0192 + sn & e020 & 0.159 & 0.1716 & 0.0229 + cl & abell 2259 & 0.164 & 0.1731 & 0.0806 + cl & abell 586 & 0.171 & 0.1561 & 0.0405 + cl & abell 1914 & 0.171 & 0.1321 & 0.0135 + cl & abell 2218 & 0.176 & 0.1990 & 0.0377 + sn & k429 & 0.181 & 0.1764 & 0.0138 + cl & abell 665 & 0.182 & 0.2000 & 0.0288 + cl & abell 1689 & 0.183 & 0.1971 & 0.0273 + cl & abell 2163 & 0.202 & 0.1602 & 0.0139 + sn & d086 & 0.205 & 0.1887 & 0.0261 + sn & h363 & 0.213 & 0.2103 & 0.0320 + sn & n404 & 0.216 & 0.2364 & 0.0338 + cl & abell 773 & 0.217 & 0.3057 & 0.0484 + sn & g005 & 0.218 & 0.2133 & 0.0255 + cl & abell 2261 & 0.224 & 0.2290 & 0.0518 + cl & abell 2111 & 0.229 & 0.2016 & 0.0583 + cl & abell 267 & 0.230 & 0.1892 & 0.0315 + cl & rx j2129.7 + 0005 & 0.235 & 0.1456 & 0.0301 + sn & e132 & 0.239 & 0.2146 & 0.0287 + cl & abell 1835 & 0.252 & 0.3434 & 0.0160 + cl & abell 68 & 0.255 & 0.2027 & 0.0563 + sn & 04d3ez & 0.263 & 0.2462 & 0.0238 + sn & n326 & 0.268 & 0.2509 & 0.0300 + sn & k425 & 0.274 & 0.2881 & 0.0371 + cl & abell 697 & 0.282 & 0.2892 & 0.0871 + sn & p455 & 0.284 & 0.2832 & 0.0378 + sn & 03d4ag & 0.285 & 0.2678 & 0.0160 + sn & m027 & 0.286 & 0.3447 & 0.0508 + cl & abell 611 & 0.288 & 0.2575 & 0.0594 + cl & zw 3146 & 0.291 & 0.2747 & 0.0066 + sn & 03d3ba & 0.291 & 0.2196 & 0.0324 + sn & g055 & 0.302 & 0.3192 & 0.0544 + sn & d117 & 0.309 & 0.3219 & 0.0400 + sn & n278 & 0.309 & 0.2856 & 0.0276 + cl & abell 1995 & 0.322 & 0.4033 & 0.0491 + cl & ms 1358.4 + 6245 & 0.327 & 0.3844 & 0.0323 + sn & 03d1fc & 0.331 & 0.2996 & 0.0290 + sn & e029 & 0.332 & 0.3297 & 0.0425 + sn & d083 & 0.333 & 0.2279 & 0.0147 + sn & 04d3kr & 0.337 & 0.3209 & 0.0251 + sn & g097 & 0.340 & 0.3354 & 0.0479 + sn & 04d3nh & 0.340 & 0.3463 & 0.0271 + sn & m193 & 0.341 & 0.2960 & 0.0313 + sn & d149 & 0.342 & 0.3459 & 0.0334 + sn & h364 & 0.344 & 0.2994 & 0.0234 + sn & 03d1bp & 0.346 & 0.3248 & 0.0374 + sn & h359 & 0.348 & 0.3881 & 0.0483 + sn & e136 & 0.352 & 0.3417 & 0.0425 + sn & 04d2fs & 0.357 & 0.3452 & 0.0350 + sn & 04d3fk & 0.358 & 0.3089 & 0.0299 + sn & d093 & 0.363 & 0.3566 & 0.0230 + sn & n263 & 0.368 & 0.3285 & 0.0257 + sn & 03d3ay & 0.371 & 0.3662 & 0.0388 + cl & abell 370 & 0.375 & 0.3807 & 0.0687 + sn & g052 & 0.383 & 0.3250 & 0.0329 + sn & g142 & 0.399 & 0.3862 & 0.0765 + sn & d085 & 0.401 & 0.3857 & 0.0391 + sn & k448 & 0.401 & 0.4594 & 0.0846 + rg & 3c142.1 & 0.406 & 0.3325 & 0.0607 + cl & macs j2228.5 + 2036 & 0.412 & 0.4416 & 0.0851 + sn & 04d2fp & 0.415 & 0.3999 & 0.0313 + sn & k485 & 0.416 & 0.4184 & 0.0751 + sn & g133 & 0.421 & 0.4286 & 0.0651 + sn & h342 & 0.421 & 0.4208 & 0.0310 + sn & f235 & 0.422 & 0.3498 & 0.0387 + sn & b013 & 0.426 & 0.3824 & 0.0405 + sn & e148 & 0.429 & 0.4321 & 0.0398 + sn & 04d2 gb & 0.430 & 0.3526 & 0.0292 + rg & 3c 244.1 & 0.430 & 0.3631 & 0.0671 + sn & d089 & 0.436 & 0.3922 & 0.0361 + sn & d097 & 0.436 & 0.4013 & 0.0314 + sn & 03d3aw & 0.449 & 0.3923 & 0.0434 + cl & rx j1347.5 - 1145 & 0.451 & 0.3571 & 0.0260 + sn & 04d3gt & 0.451 & 0.2812 & 0.0298 + sn & hst04yow & 0.460 & 0.4114 & 0.0625 + sn & 03d3cd & 0.461 & 0.3982 & 0.0330 + sn & 03d3cc & 0.463 & 0.4222 & 0.0331 + sn & m158 & 0.463 & 0.4914 & 0.0634 + sn & e108 & 0.469 & 0.4262 & 0.0314 + sn & 04d3df & 0.470 & 0.3796 & 0.0350 + sn & sn2002dc & 0.475 & 0.4091 & 0.0396 + cl & macs j2214.9 - 1359 & 0.483 & 0.5474 & 0.0950 + cl & macs j1311.0 - 0310 & 0.490 & 0.5271 & 0.1604 + sn & g160 & 0.493 & 0.4391 & 0.0526 + sn & h319 & 0.495 & 0.4426 & 0.0428 + sn & 03d1ax & 0.496 & 0.4283 & 0.0394 + sn & e149 & 0.497 & 0.4087 & 0.0489 + sn & h283 & 0.502 & 0.4592 & 0.0782 + sn & 03d1au & 0.504 & 0.4713 & 0.0391 + sn & p524 & 0.508 & 0.4449 & 0.0451 + sn & g120 & 0.510 & 0.4185 & 0.0405 + sn & d084 & 0.519 & 0.5612 & 0.0749 + rg & 3c172 & 0.519 & 0.6635 & 0.1366 + sn & 04d2gc & 0.521 & 0.4431 & 0.0673 + sn & 04d1ak & 0.526 & 0.4520 & 0.0604 + sn & n285 & 0.528 & 0.4814 & 0.0576 + sn & d033 & 0.531 & 0.5594 & 0.0438 + sn & 03d3af & 0.532 & 0.5289 & 0.0706 + sn & f011 & 0.539 & 0.4846 & 0.0558 + sn & f244 & 0.540 & 0.4979 & 0.0596 + cl & cl 0016 + 1609 & 0.541 & 0.5451 & 0.0869 + cl & macs j1149.5 + 2223 & 0.544 & 0.3166 & 0.0693 + cl & macs j1423.8 + 2404 & 0.545 & 0.5901 & 0.0178 + rg & 3c 330 & 0.549 & 0.3424 & 0.0652 + cl & ms 0451.6 - 0305 & 0.550 & 0.5642 & 0.0973 + sn & 04d4bq & 0.550 & 0.5016 & 0.0670 + sn & 04d3hn & 0.552 & 0.4035 & 0.0762 + sn & f041 & 0.561 & 0.4912 & 0.0385 + cl & macs j2129.4 - 0741 & 0.570 & 0.5352 & 0.1308 + sn & 03d4gf & 0.581 & 0.5149 & 0.0427 + sn & 03d1aw & 0.582 & 0.5828 & 0.0564 + cl & ms 2053.7 - 0449 & 0.583 & 1.0063 & 0.1725 + cl & macs j0647.7 + 7015 & 0.584 & 0.3126 & 0.0792 + sn & 03d4gg & 0.592 & 0.5161 & 0.0594 + sn & h323 & 0.603 & 0.5467 & 0.0554 + sn & 03d4dy & 0.604 & 0.4937 & 0.0728 + sn & 04d3do & 0.610 & 0.4987 & 0.0666 + sn & e138 & 0.612 & 0.5386 & 0.0446 + sn & 04d4an & 0.613 & 0.5611 & 0.1008 + sn & f231 & 0.619 & 0.5513 & 0.0432 + sn & 04d3co & 0.620 & 0.5904 & 0.0707 + sn & 03d4dh & 0.627 & 0.5216 & 0.0552 + rg & 3c 337 & 0.630 & 0.5064 & 0.0704 + sn & e140 & 0.631 & 0.5084 & 0.0421 + sn & n256 & 0.631 & 0.5575 & 0.0385 + sn & g050 & 0.633 & 0.4805 & 0.0398 + sn & 03d4at & 0.633 & 0.6021 & 0.0693 + rg & 3c169.1 & 0.633 & 0.6222 & 0.0708 + sn & sn2003be & 0.640 & 0.5246 & 0.0628 + sn & 04d3cy & 0.643 & 0.6209 & 0.0629 + sn & e147 & 0.645 & 0.5327 & 0.0442 + rg & 3c44 & 0.660 & 0.7621 & 0.0848 + sn & sn2003bd & 0.670 & 0.5597 & 0.0644 + sn & 03d1co & 0.679 & 0.6817 & 0.0848 + cl & macs j0744.8 + 3927 & 0.686 & 0.7261 & 0.1858 + sn & g240 & 0.687 & 0.5267 & 0.0485 + sn & h300 & 0.687 & 0.5390 & 0.0422 + sn & 03d1fl & 0.688 & 0.5486 & 0.0581 + rg & 3c34 & 0.690 & 0.5920 & 0.0644 + sn & 04d2iu & 0.691 & 0.6259 & 0.1124 + sn & p454 & 0.695 & 0.6569 & 0.0514 + sn & 03d4cz & 0.695 & 0.5414 & 0.0848 + rg & 3c441 & 0.707 & 0.5340 & 0.0667 + sn & 04d3is & 0.710 & 0.7074 & 0.1108 + rg & 3c 55 & 0.720 & 0.5852 & 0.0777 + sn & 04d1aj & 0.721 & 0.6264 & 0.0664 + sn & 04d3fq & 0.730 & 0.6556 & 0.0785 + sn & sn2002kd & 0.735 & 0.5265 & 0.0485 + sn & hst04rak & 0.740 & 0.5863 & 0.0621 + sn & 04d2ja & 0.741 & 0.6544 & 0.0723 + rg & 3c 247 & 0.749 & 0.5430 & 0.0682 + sn & 04d3ks & 0.752 & 0.5877 & 0.0622 + cl & ms 1137.5 + 6625 & 0.784 & 1.3033 & 0.2629 + sn & 03d4fd & 0.791 & 0.6880 & 0.0665 + rg & 3c41 & 0.794 & 0.6315 & 0.0714 + sn & 03d1fq & 0.800 & 0.7403 & 0.0920 + rg & 3c 265 & 0.811 & 0.5901 & 0.0793 + cl & rx j1716.4 + 6708 & 0.813 & 0.4833 & 0.2184 + rg & 3c114 & 0.815 & 0.6368 & 0.0695 + sn & 04d3nc & 0.817 & 0.6688 & 0.0647 + sn & 03d4cn & 0.818 & 0.8111 & 0.1009 + sn & 04d3lu & 0.822 & 0.6795 & 0.0688 + cl & ms 1054.5 - 0321 & 0.826 & 0.6225 & 0.1264 + rg & 3c54 & 0.827 & 0.7573 & 0.0835 + sn & 04d3cp & 0.830 & 0.6342 & 0.0496 + sn & hst05spo & 0.839 & 0.5729 & 0.0554 + sn & 04d4bk & 0.840 & 0.7110 & 0.0557 + sn & sn2003eq & 0.840 & 0.6336 & 0.0642 + rg & 3c6.1 & 0.840 & 0.7402 & 0.0861 + sn & hst04man & 0.854 & 0.7187 & 0.0993 + rg & 3c 325 & 0.860 & 0.7080 & 0.1292 + sn & 03d1ew & 0.868 & 0.7233 & 0.0566 + cl & cl j1226.9 + 3332 & 0.890 & 0.5232 & 0.1696 + sn & sn2003eb & 0.900 & 0.6052 & 0.0725 + sn & 03d4di & 0.905 & 0.6742 & 0.0497 + sn & 04d3gx & 0.910 & 0.7973 & 0.0661 + sn & 04d3ki & 0.930 & 0.8732 & 0.0764 + sn & sn2003xx & 0.935 & 0.6918 & 0.0956 + sn & 03d4cx & 0.949 & 0.7996 & 0.0626 + sn & 04d3ml & 0.950 & 0.7562 & 0.0522 + sn & sn2002dd & 0.950 & 0.6897 & 0.1112 + sn & sn2003es & 0.954 & 0.7975 & 0.1028 + sn & hst04tha & 0.954 & 0.6482 & 0.0836 + rg & 3c 289 & 0.967 & 0.5950 & 0.1097 + sn & hst04pat & 0.970 & 0.9380 & 0.1598 + rg & 3c 268.1 & 0.974 & 0.7458 & 0.1432 + sn & hst04omb & 0.975 & 0.7570 & 0.0941 + rg & 3c 280 & 0.996 & 0.6477 & 0.1221 + sn & 04d3dd & 1.010 & 0.9494 & 0.0743 + sn & hst05str & 1.010 & 0.9627 & 0.0887 + sn & hst05fer & 1.020 & 0.6688 & 0.0862 + sn & hst04eag & 1.020 & 0.8537 & 0.0786 + rg & 3c 356 & 1.079 & 0.8735 & 0.1842 + sn & hst05gab & 1.120 & 0.8716 & 0.0763 + sn & sn2002ki & 1.140 & 0.8795 & 0.1215 + sn & hst04gre & 1.140 & 0.7767 & 0.1145 + rg & 3c 267 & 1.144 & 0.7136 & 0.1396 + rg & 3c 194 & 1.190 & 1.0074 & 0.2047 + rg & 3c 324 & 1.210 & 1.0208 & 0.3089 + sn & hst05koe & 1.230 & 1.0432 & 0.1153 + sn & hst05lan & 1.230 & 0.9514 & 0.0920 + sn & sn2002fw & 1.300 & 0.9615 & 0.0930 + sn & sn2002hp & 1.305 & 0.7447 & 0.1063 + rg & 3c469.1 & 1.336 & 1.1364 & 0.3255 + sn & sn2003dy & 1.340 & 0.8860 & 0.1306 + sn & hst04mcg & 1.370 & 1.0091 & 0.1208 + sn & hst04sas & 1.390 & 0.8595 & 0.0792 + rg & 3c 437 & 1.480 & 0.9299 & 0.2697 + rg & 3c 68.2 & 1.575 & 1.5748 & 0.4873 + rg & 3c 322 & 1.681 & 1.3078 & 0.3400 + sn & sn1977ff & 1.755 & 0.9174 & 0.1521 + rg & 3c 239 & 1.790 & 1.3666 & 0.3382 + [ ytable ] lllllllll 1/6&37 & 0.025 & 0.016 & 0.052 & @xmath137&@xmath138&@xmath139&@xmath140 + 2/6&37 & 0.275 & 0.054 & 0.348 & @xmath141&@xmath142&@xmath143&@xmath144 + 3/6&37 & 0.430 & 0.352 & 0.504 & @xmath145&@xmath146&@xmath147& + 4/6&37 & 0.600 & 0.508 & 0.670 & @xmath148&@xmath149&@xmath150& + 5/6&37 & 0.790 & 0.679 & 0.905 & @xmath151&@xmath152&@xmath153& + 6/6&37 & 1.100 & 0.910 & 1.790 & @xmath154&@xmath155&@xmath156&@xmath157 + + 1/4&55 & 0.035 & 0.016 & 0.268 & @xmath158&@xmath159&@xmath160&@xmath161 + 2/4&55 & 0.400 & 0.274 & 0.502 & @xmath162&@xmath163&@xmath164&@xmath165 + 3/4&55 & 0.630 & 0.504 & 0.749 & @xmath166&@xmath167&@xmath168& + 4/4&57 & 0.965 & 0.752 & 1.790 & @xmath169&@xmath170&@xmath171&@xmath172 + + 1/3&74 & 0.050 & 0.016 & 0.348 & @xmath173&@xmath174&@xmath175&@xmath176 + 2/3&74 & 0.505 & 0.352 & 0.670 & @xmath177&@xmath178&@xmath179&@xmath180 + 3/3&74 & 0.905 & 0.679 & 1.790 & @xmath181&@xmath182&@xmath183&@xmath184 + + 1/2&111 & 0.275 & 0.016 & 0.504 & @xmath185&@xmath186&@xmath187&@xmath188 + 2/2&111 & 0.790 & 0.508 & 1.790 & @xmath189&@xmath190&@xmath191&@xmath192 + [ binresults ]

the good agreement indicates that general relativity provides an accurate description of the data on look - back time scales of about ten billion years . the effect of non - zero space curvature on is explored ; for a plausible range of values of the effect is small and causes a to shift to the redshift at which the universe transitions from deceleration to acceleration . we solve for the pressure , energy density , equation of state , and potential and kinetic energy of the dark energy as functions of redshift assuming that general relativity is the correct theory of gravity . results obtained using a sliding window fit indicate that a cosmological constant in a spatially flat universe provides a good description of each of these quantities over the redshift range from zero to about one .

we extend and apply a model - independent analysis method developed earlier by daly & djorgovski to new samples of supernova standard candles , radio galaxy and cluster standard rulers , and use it to constrain physical properties of the dark energy as functions of redshift . similar results are obtained for the radio galaxy and supernova data sets , which rely upon completely independent methods , suggesting that systematic errors are relatively small for both types of distances ; distances to sz clusters show a scatter which can not be explained by the quoted measurement errors . the first and second derivatives of the distance are compared directly with predictions in a standard model based on general relativity . the good agreement indicates that general relativity provides an accurate description of the data on look - back time scales of about ten billion years . the first and second derivatives are combined to obtain the acceleration parameter , assuming only the validity of the robertson - walker metric , independent of a theory of gravity and of the physical nature of the dark energy . the data are analyzed using a sliding window fit and using fits in independent redshift bins . the acceleration of the universe at the current epoch is indicated by the sliding window fit analysis . the effect of non - zero space curvature on is explored ; for a plausible range of values of the effect is small and causes a to shift to the redshift at which the universe transitions from deceleration to acceleration . we solve for the pressure , energy density , equation of state , and potential and kinetic energy of the dark energy as functions of redshift assuming that general relativity is the correct theory of gravity . results obtained using a sliding window fit indicate that a cosmological constant in a spatially flat universe provides a good description of each of these quantities over the redshift range from zero to about one . we define a new function , the dark energy indicator , in terms of the first and second derivatives of the coordinate distance and show how this can be used to measure deviations of from and to obtain a new and independent measure of .

astro-ph9912026

i

the dynamical state and mass distribution in the central regions of elliptical galaxies provide clues to the formation and evolutionary histories of these galaxies ( see merritt 1999 for a review ) . consequently , the existence of central black holes has been the target of intense scrutiny ( see kormendy & richstone 1995 for a review ) . in this paper , we study the elliptical galaxy ngc 3379 using both _ hubble space telescope _ and ground - based photometric and kinematic data in order to understand its central dynamics . at ground - based resolution ngc 3379 is a prototypical elliptical ( e1 ) galaxy with m@xmath6 ( faber _ et al . _ 1997 ) at a distance of 10.4 mpc ( ajhar _ et al . _ lauer _ et al . _ ( 1995 ) classify it as a `` core '' galaxy a galaxy that has a break in the surface brightness profile but still maintains a rising profile into the smallest measured radius . faber _ et al . _ ( 1997 ) hypothesize that core galaxies are associated with massive black holes . however , few core galaxies have strong black hole detections : m87 ( harms _ et al . _ 1994 ) , m84 ( bower _ et al . _ 1998 ) , and n4261 ( ferrarese _ et al . _ . these detections result from gas dynamics , not stellar dynamics . stellar dynamical evidence for central black holes in core galaxies is difficult to obtain since ( 1 ) core galaxies have low surface brightnesses , making kinematic observations difficult , ( 2 ) the lack of rotation complicates the dynamical modeling since velocity anisotropies potentially govern the dynamical support , and ( 3 ) stars near the center travel out to the core radius so their contribution to the central velocity profile is de - weighted ( kormendy 1992 ) . ngc 3379 was chosen for this study because of its relatively high central surface brightness among core galaxies , and because of its otherwise normal morphological and dynamical structure . the proximity , brightness , and normalcy of ngc 3379 make it the object of many ground - based photometric ( de vaucouleurs & capaccioli 1979 , lauer 1985 , capaccioli _ et al . _ 1987 , capaccioli _ et al . _ 1991 ) and kinematic ( kormendy 1997 , kormendy 1985 , van der marel _ et al . _ 1990 , bender _ et al . _ 1994 , statler 1994 , statler & smecker - hane 1999 ) studies . however , previous models for ngc 3379 have yielded inconsistent results . assuming that the departure of the light profile from the @xmath7 law signifies the existence of a stellar disk , capaccioli _ et al . _ ( 1991 ) find that the most likely model is nearly face - on with an inclination of 31@xmath0 ( intrinsic e5 galaxy ) . their conclusion was that ngc 3379 and ngc 3115 have the same intrinsic shape but are seen from different viewing angles . in their model for ngc 3379 the central region is nearly oblate , but at about @xmath8 ( @xmath9 ) the model becomes triaxial . no dynamical information was used in this model . a major uncertainty is that slight departures from a @xmath7 law , on which their model is based , may be due to tidal effects ( kormendy 1977 ) instead of a disk . furthermore , there is no reason to expect galaxies to follow a @xmath7 law exactly . kinematic information is required to determine unambiguously the inclination of a spheroidal system . van der marel _ et al . _ ( 1990 ) , using the ground - based velocity data of davies & birkinshaw ( 1988 ) and franx _ et al . _ ( 1989 ) , conclude that the inclination of ngc 3379 is 60@xmath0 ; however the two datasets are not consistent and give slightly different velocity anisotropy parameters . van der marel _ et al . _ used 2-integral flattened models with a parametrized form for the anisotropy . no goodness - of - fit criteria were given , and thus we are not able to compare their results with those of others . statler ( 1994 ) , using bayesian statistics on the same datasets , prefers models that have inclination greater than 45@xmath0 . statler rejects capaccioli s conclusion that the galaxy is flattened and triaxial at the 98% confidence level , but his results could accommodate those of van der marel _ et al . _ statler uses only the mean velocity measured along four position angles ; the radial variation in the velocity or the dispersion are not considered . furthermore , statler uses data only outside 15 . however , statler has obtained new , high s / n data ( statler & smecker - hane 1999 ) , which he will present in a future paper . the studies above use low s / n , sparse kinematic data , or no kinematic data at all . in this paper , we report results from observations of the full line - of - sight velocity distribution ( losvd ) at various position angles from high s / n ground - based data and data from hst . the data are fit to axisymmetric , three - integral orbit - based models . richstone _ et al . _ ( 1999 ) describe the modeling technique in a companion paper . we exploit the full losvds _ directly _ in the modeling . alternatively , we could use the moments of the losvds ; however , the full shape of the losvd contains important information on the underlying dynamics , and it is desirable to incorporate the full losvd when the spectra have sufficient signal - to - noise to determine this reliably . in fact , our result for ngc 3379 critically depends on the shape of the central losvd . cretton _ et al . _ ( 1999 ) and van der marel _ et al._(1998 ) present a very similar modeling technique , where the only difference from ours is that we fit the full losvd as opposed to their moment fitting procedure . there are other programs that also use the higher moments of the losvd as constraints ( dejonghe , 1987 ; gerhard 1993 ; rix _ et al . _ 1997 ) . obtaining the full losvd at many position angles is the maximum obtainable kinematic information and has now become routine ( _ e.g. _ bender _ et al . _ 1994 , carollo _ et al . _ 1995 , gebhardt & richstone 1999 ) . in 2 , we describe the photometric and kinematic data for ngc 3379 . in 3 , we describe the models and present results in 4 . discussion is given in 5 .

we fit axisymmetric 3-integral dynamical models to ngc 3379 using the line - of - sight velocity distribution obtained from hst / fos spectra of the galaxy center and ground - based long - slit spectroscopy along four position angles , with the light distribution constrained by wfpc2 and ground - based images .

we fit axisymmetric 3-integral dynamical models to ngc 3379 using the line - of - sight velocity distribution obtained from hst / fos spectra of the galaxy center and ground - based long - slit spectroscopy along four position angles , with the light distribution constrained by wfpc2 and ground - based images . we have fitted models with inclinations from 29 ( intrinsic galaxy type e5 ) to 90 ( intrinsic e1 ) and black hole masses from 0 to . the best - fit black hole masses range from , depending on inclination . the preferred inclination is 90 ( edge - on ) ; however , the constraints on allowed inclination are not very strong due to our assumption of constant _ m / l_ . the velocity ellipsoid of the best model is not consistent with either isotropy or a two - integral distribution function . along the major axis , the velocity ellipsoid becomes tangential at the innermost bin , radial in the mid - range radii , and tangential again at the outermost bins . the rotation rises quickly at small radii due to the presence of the black hole . for the acceptable models , the radial to tangential ( ( dispersion in the mid - range radii ranges from , with the smaller black holes requiring larger radial anisotropy . compared with these 3-integral models , 2-integral isotropic models overestimate the black hole mass since they can not provide adequate radial motion . however , the models presented in this paper still contain restrictive assumptions namely assumptions of constant _ m / l_ and spheroidal symmetry requiring yet more models to study black hole properties in complete generality .

astro-ph9912026

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for each model , the 702 observables ( 13 losvd bins at the 54 positions ) determine the total @xmath31 , given by @xmath48 where the @xmath49 s are the losvd bin heights for the model and the data and @xmath50 is the uncertainty from the 68% confidence band . as an example , figure 6 plots the losvds for both the data and the best model at four positions : the center , a major - axis position near to the center , a position close to one effective radius on the major axis , and a minor - axis position near to the center . judging the goodness - of - fit from the @xmath31 values of the various models is not straightforward because the number of the degrees of freedom is not easy to determine ; the derivation of the losvds includes a smoothing parameter which correlates the values and uncertainties of the velocity bin heights ( gebhardt & richstone 1999 ) . with higher s / n data than present , we could reduce the smoothing parameter to lessen this problem . we do not attempt to estimate directly the actual degrees of freedom and therefore do not have an overall goodness - of - fit measure , but instead we calculate the change in @xmath31 as a function of the three variables black - hole mass , inclination , and _ m / l_@xmath3 . the lowest @xmath31 value thus provides the best model , with the uncertainties given by the classical estimators for the @xmath51 s . 0.2 cm -0.6 cm 0.3 cm 0.2 cm 0.3 cm the total @xmath31 s for most of the models have a value near 200 , giving a reduced @xmath31 of 0.3 , assuming one observable equals one degree of freedom . a reduced @xmath31 near unity would require either that every three losvd bins are correlated by the smoothing , therefore reducing the number of degrees of freedom by three , or that the uncertainties of the bin heights are overestimated by a factor of @xmath52 . in the former case , using @xmath51 as a discriminator for the error of the best - fitting models will not be affected since the number of degrees of freedom has no influence on the calculation of the @xmath31 differences ; @xmath53 will still correspond to 1-@xmath50 . however , in the latter case , both the @xmath31 and @xmath51 values would increase by a factor of three , creating a smaller confidence band on the variables ; @xmath54 would then correspond to 1-@xmath50 . it is likely , however , that the dominant reason for the low reduced @xmath31 is the underestimation of the degrees of freedom since we know _ a priori _ that the smoothing must have an effect . to provide a quick check on smoothing effects , we refit the losvds for a subset of positions using a much smaller smoothing length . as expected , the losvd becomes noisier . measuring the @xmath31 between this new losvd and the model that we fit using the the older losvd , we find that the increase in @xmath31 ranges from 3 - 5 . thus , we conclude that the dominant effect of the smoothing is to correlate the variables and reduce the number of degrees of freedom . in retrospect , it would have been better not to have smoothed the losvds and preserve their statistical independence . note however that our decision to accept @xmath53 as the 1-@xmath50 error is conservative and , if anything , overestimates the errors . we examined models with inclinations from 29@xmath0 to 90@xmath0(intrinsic e5 to e1 galaxy ) , black holes from zero to @xmath1 , and _ m / l_@xmath3 from 4.0 to 8.0 in solar units . the @xmath31 is a function of these three variables . for each inclination , fig . 7 plots @xmath31 as a function of black - hole mass ( zero black - hole mass is shown as @xmath55 ) , using that _ m / l_@xmath3 which provides the smallest @xmath31 at that black - hole mass . all inclinations show a minimum @xmath31 at black - hole masses in the range @xmath56 . the fits clearly prefer the edge - on models ( 90@xmath0 ) . 8 presents contours of @xmath51 as a function of black - hole mass and _ m / l_@xmath3for each inclination . the points represent locations of the modeled values . the contours use a two dimensional smoothing spline ( wahba 1980 ) to estimate the @xmath31 values at positions where no models occur . as in wahba , generalized cross - validation determines the smoothing value ; however , the modeled values are relatively smooth and little smoothing is necessary . 0.4 cm -1 cm 1.0 cm since we have such a large parameter space minimizing several thousand variables we must ensure that the modeling program is finding a true minimum . furthermore , we require that the numeric noise caused by the minimizer be smaller than the quoted uncertainties of the output parameters ( e.g. , the black hole mass ) . the two conditions that govern these checks are the sampling densities that we use in parameter space , and the tolerance used to determine convergence in the minimizer . 8 demonstrates the sampling densities for the black - hole mass and the _ m / l_@xmath3 , where each point represents one model . 7 shows the range and number of modeled inclinations . the smoothness of the @xmath31 contours in both figures demonstrate that we have found the global minimum . as a further check , we have run models with both larger and smaller _ m / l_@xmath3 than those presented , however the fits are significantly worse and we do not include them in the plots . thus , we conclude that the sampling density provides adequate coverage around the global minimum . our second concern is whether the tolerance used for the stopping criteria in the minimizer creates significant noise for the parameter estimation . we must use a stopping tolerance in the program or the time it takes for the @xmath31 to asymptote becomes impractically long . both figures 7 and 8 provide an estimate of the numeric noise . from the soothness of plots , the change in @xmath31 between two adjacent points is much smaller than the global change in @xmath31 . also , in a handful of models , we iterate till there is no change in @xmath31 relative to machine precision , and find that this asymptotic value is within @xmath57 of the stopping value . therefore , the noise in @xmath31 generated from the minimization routine is not significant . the smoothness is the solution is also seen in fig . 9 , where we plot best - fit black hole mass as a function of inclination . although , the sampling of points is not dense , the fact that there are no abrupt changes signifies we are not subject to numeric noise in the solution . 0.2 cm 0.4 cm 0.2 cm 0.3 cm as described in 3.1 , we have also run models with _ m / l_@xmath3 increasing 25% log - linearly with radius towards the galaxy center . in this case , the required _ m / l_@xmath3 is systematically lower than when using the constant _ m / l_@xmath3 assumption ; however , the results for the required black hole and inclination are unchanged . the best model has an inclination of 90@xmath0 , a black hole mass of @xmath58 , and _ m / l_@xmath3@xmath59 . the allowed mass of black holes range from @xmath2 . the internal dynamics of the best - fitting model are shown in fig . the top plot shows the internal velocity dispersions of the three components along the major axis . the model is tangentially biased ( in the @xmath60 direction ) in the smallest bin , radially biased in the mid - range radii , and tangentially biased again at the largest radii . independent of inclination , fig . 10 well characterizes the orbital distribution for each of the best - fitting models . similarly , the mean velocity in the equatorial plane ( bottom plot of fig . 10 ) has a general shape for the best models ; it shows no systematic trends from @xmath61 ( 20 - 1500 pc ) , increasing significantly in the center due to the presence of the massive black hole . beyond about 60 the model is unconstrained since there is no kinematic information , but we plot the model results there since they represent the maximum entropy configuration . for each inclination the trend with black - hole mass is as follows : increasing the black - hole mass requires an increased amount of tangential anisotropy in the central bin , a decrease of the radial bias in the mid - range radii , and the orbits at the largest radii to become more isotropic . the coupling between the black - hole mass and the amount of radial anisotropy in the mid - radii stems from the need to match the same central losvd ; a large central dispersion can be modeled with a large black - hole mass or radial orbits . therefore , as the black - hole mass increases , the need for radial orbits decreases . in the very central bin , a large black - hole mass induces large rotational velocities and also large dispersion in the @xmath60 direction . at the largest radii , the situation is more complex since we have not included a dark halo ; if the projected dispersion is larger than the dispersion obtained assuming isotropy and the stellar mass profile then one can either invoke a dark halo or include tangential anisotropy . in any event , it is not clear whether meaningful analysis at large radii can be obtained from models which do not include a dark halo . to demonstrate why the data seem to prefer an edge - on model that contains a black hole , we must look at the model fits to the data . figure 11 plots gauss - hermite polynomial estimates for the data and model losvds for all four position angles . the difference between the edge - on model and the nearly face - on model is almost entirely at large radii ; the edge - on model matches the large - radial data better , specifically for the velocity and velocity dispersion . in contrast , the difference between the no - black - hole and black - hole model is so subtle that one can barely discriminate those two models in fig . 11 . only in the central bin does the the black - hole model slightly better estimate the skewness in the profile . however , fig . 11 is not the optimal way to compare models since the fit uses the full losvd and not moments . instead of plotting all 54 losvds for various models , fig . 12 plots the difference in @xmath31 at each spatial position . this difference represents the @xmath31 measured for the losvd of a particular model minus that of the best - fit model ( edge - on , black - hole model ) . the two comparison models are the same as in fig . 11 , the best no - black - hole model ( an edge - on model ) and a nearly face - on black - hole model ( at 29@xmath0 ) . as expected , the discrimination between black - hole / no - black - hole comes mainly from the hst / fos data point . a no - black - hole model fails to match the shape of the central losvd ; however , there is a limit to size of the central black hole since very high black - hole masses models over shoot the dispersions in the central few ground - based measurements . without the hst data point , we would not have been able to determine whether a black hole exists in ngc 3379 . the discrimination for the inclination comes from the data at larger radii ; here , the edge - on model is much better able to match the projected kinematics . as we discuss later , this inclination constraint is uncertain due to our assumption of constant _ m / l_@xmath3 . 0.2 cm 0.3 cm there is an uncertainty in the absolute wavelength calibration of the hst spectrum . since we do not assume that the central hst losvd is symmetric , we must determine the velocity zeropoint of this profile relative to the rest frame of the galaxy ( @xmath62 @xmath29 , borne _ et al . _ unfortunately , our original observing strategy did not include an accurate wavelength calibration , since we were concerned mainly with the central dispersion , and thus did not obtain the necessary flanking arc - lamp spectra . we therefore tried a range of velocity zeropoints , models with velocity offsets from @xmath63 @xmath29 . as the offset increases , the lower limit on the black - hole mass grows , whereas the upper limit remains the same . we are not able to fit acceptable models with offsets greater than 15 @xmath29 . therefore , our allowed range of black hole masses is largest using the 0 @xmath29velocity offset . all of the figures contain the results using this value .

we have fitted models with inclinations from 29 ( intrinsic galaxy type e5 ) to 90 ( intrinsic e1 ) and black hole masses from 0 to . the preferred inclination is 90 ( edge - on ) ; however , the constraints on allowed inclination are not very strong due to our assumption of constant _ m / l_ . the rotation rises quickly at small radii due to the presence of the black hole . for the acceptable models , the radial to tangential ( ( dispersion in the mid - range radii ranges from , with the smaller black holes requiring larger radial anisotropy . compared with these 3-integral models , 2-integral isotropic models overestimate the black hole mass since they can not provide adequate radial motion .

we fit axisymmetric 3-integral dynamical models to ngc 3379 using the line - of - sight velocity distribution obtained from hst / fos spectra of the galaxy center and ground - based long - slit spectroscopy along four position angles , with the light distribution constrained by wfpc2 and ground - based images . we have fitted models with inclinations from 29 ( intrinsic galaxy type e5 ) to 90 ( intrinsic e1 ) and black hole masses from 0 to . the best - fit black hole masses range from , depending on inclination . the preferred inclination is 90 ( edge - on ) ; however , the constraints on allowed inclination are not very strong due to our assumption of constant _ m / l_ . the velocity ellipsoid of the best model is not consistent with either isotropy or a two - integral distribution function . along the major axis , the velocity ellipsoid becomes tangential at the innermost bin , radial in the mid - range radii , and tangential again at the outermost bins . the rotation rises quickly at small radii due to the presence of the black hole . for the acceptable models , the radial to tangential ( ( dispersion in the mid - range radii ranges from , with the smaller black holes requiring larger radial anisotropy . compared with these 3-integral models , 2-integral isotropic models overestimate the black hole mass since they can not provide adequate radial motion . however , the models presented in this paper still contain restrictive assumptions namely assumptions of constant _ m / l_ and spheroidal symmetry requiring yet more models to study black hole properties in complete generality .

astro-ph9912026

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the models in this paper depend primarily on the input black - hole mass , inclination , and m / l assumption . a difficulty is that different combinations of these variables can have similar appearances in the projected kinematics . for example , the inclination and the m / l variation both affect the fit at large radii ; one can easily see how differently inclined models of the same flattened galaxy will have markedly different projected dispersion profiles , and also the dispersion profile is obviously influenced by the inclusion and shape of a dark halo . thus , by varying the shape and amount of dark halo one may be able to mimic the effect of changing the inclination . since we have not explored a full range of halo models , we will not make strong claims as to our ability to constrain the inclination of the galaxy . however , the black hole mass is mainly driven by the data at small radii , and primarily by the hst / fos data point . fig . 9 demonstrates this independence from the inclination , as our best - fit black hole mass does not depend strongly on the inclination . an even more robust measurement is the orbital structure . as either the inclination or the black - hole mass varies , we find a similar velocity ellipsoid ; at the smallest bin the velocity ellipsoid is mainly tangential , becoming radial in mid - range radii , and tangential again at the largest radii . 13 plots the radial motion relative to the tangential motion for four models at different inclinations . determination of the inclination , black - hole mass , and orbital structure is discussed in detail below . 0.3 cm -0.7 cm 0.3 cm the inclination of ngc 3379 has been the subject of some debate . capaccioli _ et al . _ ( 1991 ) conclude that ngc 3379 is similar to ngc 3115 but nearly face - on , with some degree of triaxiality . capaccioli base this conclusion only on the surface brightness profile and use no kinematic data . in contrast , statler ( 1994 ) concludes that nearly face - on , triaxial models are inconsistent with the data at the 98% confidence limit , strongly contradicting capaccioli s result . he prefers less - inclined models . statler has obtained more recent data ( statler & smecker - hane , 1999 ) and a fuller analysis is in preparation . as seen in sect . 4 , our best models prefer an edge - on configuration . preference for edge - on models arises from two observations ; first , the dispersion profiles along different axes are slightly different , and , in an axisymmetric case , this configuration is not possible for a face - on system . the difference mainly arises from the inability to match the large radial data , however the face - on model also can not match the shoulder in the dispersion profile at 1020 ( previously noted by statler & smecker - hane , 1999 ) ; the shoulder is more pronounced in the central position angles , and the edge - one models match this configuration well ( see fig . second , major - axis rotation exists which is not allowed for a face - on configuration of an oblate axisymmetric system . thus these two restrictions are mainly a result of our axisymmetry assumption . more general models can be constructed than those presented here . we could in principle extend the modeling technique to include triaxial distributions but then the parameter space becomes too large for us to search ( each axisymmetric model takes approximately 20 hours on an ultrasparc ) . second , our assumption that the galaxy is spheroidal could be relaxed . romanowsky & kochanek ( 1997 ) present a technique which provides a range of different density distributions which similarly project . third , we have assumed that _ m / l_@xmath3 is independent of radius ( _ i.e. _ , there is no dark halo ) . ciardullo _ et al . _ ( 1993 ) , using radial velocity measurements of planetary nebulae , find no evidence for a dark halo in ngc 3379 out to 3.5 effective radii ( 120 ) ; however their uncertainties are large and could , in fact , allow for some dark halo ( tremblay _ et al . _ 1995 ) . in all of our models , the last velocity dispersion measurement ( at 64 ) along each position angle is higher than the model velocity dispersion , possibly suggesting the need for an increase in _ m / l_@xmath3 . at one effective radius ( 34 ) , there is no need for an increase in _ m / l_@xmath3 , which is consistent with previous studies of other galaxies ( kormendy & westphal 1989 , kormendy & richstone 1992 , kormendy _ et al . _ thus , assumptions of axisymmetry , spheroidal distribution , and constant _ m / l_@xmath3 all lead to uncertainties in the best - fit inclination . detailed modeling including dark halos has been carried out by rix _ et al . _ ( 1998 ) for ngc 2434 and saglia _ et al . _ ( 1999 ) for ngc 1399 , but only as spherical systems . only by allowing for axisymmetric or triaxial shapes with a dark halo can we set more realistic limits on inclination . even though we are not able to place limits on the inclination , we can measure black - hole limits . the presence of a dark halo will have no effect on the need for a central black hole , or on its mass . the need for the black hole is directly a result of the shape of the central losvd observed with hst . the large dispersion and the skewness drive the models to require a black hole . we have also run models assuming a symmetrized central losvd ( the dashed line shown in fig . the allowable range of black hole masses remains the same for the inclined models in this case . however , for the edge - on case the model with no black hole fits as well . the symmetrized losvd has a dispersion of 275 @xmath29 , compared with 289 @xmath29 for the actual losvd , and has less tail weight ( as can be seen in fig . these differences permit a no - black - hole model . the central bin most influences the model ; most of the orbits ( @xmath64% for inclined models and @xmath65% for edge - on models ) contribute light to this bin , and , furthermore , many have their pericenter there . therefore , the characteristics of the central losvd , in particular the high - velocity components , have a strong effect on orbits throughout the galaxy . in the edge - on case with the symmetrized losvd , the orbits redistribute themselves in such a way as to create a slightly larger central dispersion ( 275 @xmath29 ) without the need for a black hole , and at the same time maintain a fairly flat projected dispersion profile ; _ i.e. _ , at small radii , the orbits are mainly radial , whereas at large radii they become primarily tangential . however , the actual losvd warrants matching the skewness and the high - velocity tails . with no black hole present , the model must use stars at larger radii to create the high - velocity components , thereby limiting its ability to redistribute the orbits at large radii and match the kinematics there . with a black hole , the black hole provides much of the high - velocity tail of the losvd for orbits locally and gives the model more freedom to better match the larger - radii data . the symmetrized and skewed losvds are inconsistent with each other with greater than 95% probability , both using an estimate from the binned values and using the gauss - hermite moments . given the arguments in 2.2.1 , we must include the skewness of the central losvd and thus do not consider the symmetrized losvd models further . relaxing the other two assumptions axisymmetry and spheroidal distribution is unlikely to change the black - hole limits . the models with no black holes all are extremely poor fits to the data ; therefore , even if we allow for the variation in deprojected densities given by romanowsky & kochanek , the results are unlikely to change . of course , since the deprojection is unique for the edge - on models , our results are general in the edge - on case . triaxial models will allow even greater freedom to match the data , however it is not clear whether triaxiality is a viable configuration in the centers of galaxies ( merritt & fridman 1996 , merritt 1999 ) , and we do not consider these models . the position angle of the dust ring in fig . 5 is 45@xmath0 away from the major axis of the galaxy . a dust ring in an axisymmetric system with an offset position angle is only neutrally stable but can be stabilized by a small amount of triaxiality . if the galaxy is nearly face - on , then triaxiality is not necessary to stabilize the dust ring ; in the face - on configuration , since the dust ring is close to edge - on ( about 75@xmath0 ) , it must be in an orbit close to polar , and thus can have arbitrary azimuthal angle . velocity information along the dust ring could provide an important check on the enclosed mass derived from our models . pastoriza _ et al . _ ( 1999 ) , using ground - based gas kinematics , assume that the gas disk in ngc 3379 is nearly face - on . their mass estimate inside 1.3 is @xmath66 , strongly contradicting our result . however , their large mass is due mainly to their disk inclination assumption . if one uses the inclination as measured from the dust ring , then the enclosed mass closely equals our value of @xmath58 ; only with hst can we precisely determine the gaseous disk configuration and determine whether the gas is even in a disk at all . the hst / fos spectrum includes the [ nii ] emissiom , although since it is a single pointing , we do not have the radial information to extract a meaningful dynamical analysis from the gas . however , the width of the line does provide some information on the underlying mass . the measured @xmath50 is 200@xmath29 , in agreement with the mass deduced here ; using the mass from pastoriza _ et al . _ would imply a @xmath50 around 700@xmath29 . to further understand the gas kinematics , we must have spatial information . van der marel _ et al . _ ( 1990 ) apply 2-integral flattened models for ngc 3379 using constant anisotropy . they find an acceptable fit with an inclination of 60@xmath0 and anisotropic orbits . they suffer from the same problem as we do for the inclination estimate ; without inclusion of a dark halo it is not possible to obtain adequate inclination constraints . furthermore , since our axisymmetric models are fully general while their models specify a form for the distribution function , we can not directly compare our results to theirs . van der marel _ et al . _ conclude that there is no evidence to support the need for a third integral using data from the first and second moments of the losvd from davies & birkinshaw ( 1988 ) . results presented here , which are based on higher s / n data and are determined from the full losvd , show that the best model requires three integrals and is not consistent with a 2-integral distribution function ; the internal dispersions along the long axis in the radial and @xmath41 directions are significantly different , in direct conflict with a 2-integral distribution function . as seen in fig . 13 , the ratio of the @xmath41 to the radial dispersion in our best model have a radial variation from 0.6 to 1.2 , with an average around 0.75 . for comparison , this ratio is around 0.6 for the spheroid component of our galaxy using rr lyrae halo stars ( layden 1995 ) . in addition to the measured black - hole mass , the orbital structure appears to be a robust feature as well . the radial anisotropy profile along the major axis in fig . 13 shows that this profile is nearly independent of input inclination . for all acceptable models , the velocity ellipsoid is tangentially biased in the central bin and radially biased in the mid - range radii . these orbital properties are generally true along any position angle . this central tangential bias appears in other 3-integral models studied ( gebhardt _ et al . _ 2000 ) and may be a common feature of early - type galaxies . tangential bias in the central regions around black holes appear to be a common feature in simulations ( quinlan _ et al . _ 1995 , quinlan & hernquist 1997 , merritt & quinlan ( 1998 ) , and nakano & makino 1999 ) . the radial bias in the mid - range radii has also been seen before ; using 3-integral models , both gerhard _ et al . _ ( 1999 ) for ngc 1600 and saglia _ et al . _ ( 1999 ) for ngc 1399 find radial motion throughout the main body of the galaxy . thus , we may be beginning to measure common features of the orbital properties in ellipticals tangential motion in the central regions and radial motion at mid - range radii . at large radii , we must include dark halos since they make a significant contribution there . the next step is to determine dominant evolutionary effects from theoretical models and will require detailed comparisons with n - body simulations . magorrian _ et al . _ ( 1998 ) , using the same ground - based data , fit two - integral models to the observed second - order velocity moment profiles and require a bh of @xmath67 . our more general three - integral models would allow an even larger range of bh masses had we similarly used only the losvd s second moments . when we fit to the full losvds , however , their shape requires that our models be mildly radially anisotropic , reducing the required bh mass by a factor of at least two over magorrian _ et al . _ s result . the models presented in this paper still contain restrictive assumptions namely constant _ m / l_@xmath3 and spheroidal symmetry requiring yet more models to study black hole properties in complete generality . kormendy ( 1993 ) and kormendy & richstone ( 1995 ) find that there is a correlation between the black hole mass and the mass of the spheroid . whether this relation is a real correlation or an upper envelope that extends to smaller black - hole masses remains to be seen . as the data quality and the modeling techniques improve , we should be better able to constrain the relationship between black hole and spheroid mass , and begin to measure correlations with the orbital characteristics . we thank gary bower , richard green , luis ho , and jason pinkney for detailed discussions about the results . we thank an anonymous referee who found an error in the previous version of this paper . we are grateful to c. d. keyes , j. christensen , and j. hayes for help with the data analysis . this work was supported by hst data analysis funds through grant go02600.0187a and by nserc . 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 . rrrrr 0.023 & 14.625 & 1.302 & 0.121 & 92.3 0.046 & 14.739 & 1.314 & 0.121 & 92.3 0.091 & 14.931 & 1.340 & 0.040 & 92.3 0.136 & 14.978 & 1.311 & 0.232 & 92.3 0.182 & 15.047 & 1.322 & 0.181 & 101.8 0.227 & 15.101 & 1.307 & 0.181 & 87.6 0.273 & 15.147 & 1.311 & 0.177 & 87.6 0.318 & 15.184 & 1.313 & 0.149 & 85.8 0.364 & 15.227 & 1.311 & 0.141 & 84.4 0.409 & 15.276 & 1.325 & 0.119 & 84.1 0.455 & 15.288 & 1.311 & 0.119 & 78.8 0.500 & 15.326 & 1.318 & 0.119 & 76.4 0.546 & 15.351 & 1.313 & 0.110 & 64.9 0.566 & 15.368 & 1.326 & 0.083 & 58.1 0.665 & 15.412 & 1.297 & 0.119 & 65.7 0.783 & 15.485 & 1.300 & 0.095 & 58.7 0.921 & 15.578 & 1.299 & 0.089 & 69.6 1.084 & 15.692 & 1.300 & 0.085 & 67.5 1.275 & 15.812 & 1.305 & 0.081 & 70.8 1.500 & 15.933 & 1.299 & 0.101 & 70.9 1.764 & 16.072 & 1.297 & 0.104 & 72.1 2.076 & 16.213 & 1.293 & 0.115 & 73.3 2.442 & 16.365 & 1.295 & 0.117 & 74.0 2.873 & 16.528 & 1.291 & 0.119 & 73.5 3.380 & 16.702 & 1.286 & 0.118 & 73.8 3.977 & 16.895 & 1.284 & 0.111 & 74.0 4.678 & 17.110 & 1.278 & 0.105 & 74.1 5.504 & 17.352 & 1.275 & 0.094 & 74.0 6.475 & 17.596 & 1.272 & 0.088 & 73.8 7.618 & 17.830 & 1.267 & 0.089 & 73.2 8.962 & 18.064 & 1.262 & 0.089 & 73.2 10.544 & 18.313 & 1.257 & 0.090 & 72.1 12.405 & 18.572 & 1.246 & 0.092 & 71.1 14.594 & 18.855 & 1.237 & 0.089 & 69.3 ajhar , e. , lauer , t. , tonry , j. , blakeslee , j. , dressler , a. , holtzman , j. , & postman , m. 1997 , , 114 , 626 bender , r. , 1990 , , 229 , 441 bender , r. , saglia , r.p . , & gerhard , o.e . 1994 , , 269 , 785 borne , k.d . , balcells , m. , hoessel , j.g , & mcmaster , m. 1994 , , 435 , 79 bower , g. _ et al . _ 1998 , , 492 , 111 capaccioli , m. , held , e.v . , & nieto , j.l . 1987 , , 94 , 1519 capaccioli , m. , held , e.v . , lorenz , h. & vietri , m. 1990 , , 99 , 1813 capaccioli , m. , vietri , m. , held , e.v . , & lorenz , h. 1991 , , 371 , 535 carollo , c.m . , de zeeuw , p.t . , van der marel , r.p . , danziger , i.j . , & qian , e.e . 1995 , , 441 , l25 ciardullo , r. , jacoby , g.h . , & dejonghe , h.b . 1993 , , 414 , 454 cretton , n. , de zeeuw , p.t . , van der marel , r.p . , & rix , h .- w . , 1999 , , accepted davies , r.l . , & birkinshaw , m. 1988 , , 68 , 409 dejonghe , h.b . 1987 , , 224 , 13 de vaucouleurs , g. , & capaccioli , m. 1979 , , 40 , 699 faber , s.m . _ et al . _ 1997 , , 114 , 1771 ferrarese , l. , ford , h.c . , & jaffe , w. 1996 , , 470 , 444 franx , m. , illingworth , g.d . , & heckman , t.m . 1989 , , 344 , 613 gebhardt , k. , richstone , d. _ et al . _ 1996 , , 112 , 105 gebhardt , k. , richstone , d. 1999 , in preparation gerhard , o.e . 1993 , , 265 , 213 gonzalez , j. 1994 , phd thesis , ucsc harms , r.j . _ et al . _ 1994 , , 435 , l35 keyes , c. d. , _ et al . _ 1995 , fos instrument handbook ( baltimore : stsci ) kormendy , j. 1977 , , 218 , 333 kormendy , j. 1992 , in `` testing the agn paradigm '' , eds . holt , s.g . neff , & c.m urry ( ny : aip ) , 23 kormendy , j. 1985 , , 292 , l9 kormendy , j. 1993 , in `` the nearest active galaxies '' , eds . j. beckman , l. colina , & h. netzer ( madrid ) , 197 kormendy , j. , & westphal , j. 1989 , , 338 , 752 kormendy , j. , & richstone , d. 1992 , , 393 , 559 kormendy , j. , & richstone , d. 1995 , ara&a , 33 , 581 kormendy , j. _ et al . _ 1996 , , 459 , l57 kormendy , j. _ et al . _ 1997 , , 482 , l139 kormendy , j. , bender , r. , evans , a. , & richstone , d. 1998 , , 115 , 1823 lauer , t.r . 1985 , , 216 , 429 lauer , t.r . _ et al . _ 1995 , , 110 , 2622 layden , a.c . 1995 , , 110 , 2288 magorrian , j. _ et al . _ 1998 , , 115 , 2285 merritt , d. 1997 , , 114 , 228 merritt , d. 1999 , , 111 , 129 merritt , d. , & fridman , t. 1996 , , 460 , 136 nakano , t. , & makino , j. 1999 , , 510 , 155 pastoriza , m. , winge , c. , ferrari , f. , & macchetto , d. 1999 , , accepted peletier , r.f . , davies , r.l . , illingworth , g.d . , davis , l.e . , cawson , m. 1990 , , 100 , 1091 qian , e.e . , de zeeuw , p.t . , van der marel , r.p . , & hunter , c. 1995 , , 274 , 602 quinlan , g. , hernquist , l. , & sigurdsson , s. 1995 , , 440 , 554 quinlan , g. , & hernquist , l. 1997 , newa , 2 , 533 richstone , d. , gebhardt , k. _ et al . _ 1999 , in preparation richstone , d. , & tremaine , s. 1988 , , 327 , 82 rix , h .- w . , de zeeuw , p.t . , carollo , c.m . , cretton , n. , & van der marel , r.p . 1997 , , in press romanowsky , a. , kochanek , c. 1997 , , 287 , 35 rybicki , g.b . 1987 , in structure and dynamics of elliptical galaxies , iau symposium 127 , ed . de zeeuw , p.t . , ( reidel , dordrecht ) , p.397 ryden , b. 1996 , , 461 , 146 saha , p. , & williams , t.b . 1994 , , 107 , 129 schwarzschild , m. 1979 , , 232 , 236 statler , t.s . 1994 , , 108 , 111 statler , t.s . , & smecker - hane , t. 1999 , , feb . 1999 tremblay , b. , & merritt , d. , & williams , t.b . 1995 , , 443 , l5 van der marel , r.p . , binney , j.j . , & davies , r.l . 1990 , , 245 , 582 van der marel , r.p . 1991 , , 253 , 710 van der marel , r.p . , & franx , m. 1993 , , 407 , 525 van der marel , r.p . , cretton , n. , de zeeuw , p.t . , & rix , h .- w . 1998 , , 493 , 613 van dokkum , p.g . , & franx , m. 1995 , , 110 , 2027 wahba , g. 1980 , technical report no . 595 , univ . of wisconsin worthey , g. 1994 , , 95 , 107

the best - fit black hole masses range from , depending on inclination . the velocity ellipsoid of the best model is not consistent with either isotropy or a two - integral distribution function . along the major axis , the velocity ellipsoid becomes tangential at the innermost bin , radial in the mid - range radii , and tangential again at the outermost bins . however , the models presented in this paper still contain restrictive assumptions namely assumptions of constant _ m / l_ and spheroidal symmetry requiring yet more models to study black hole properties in complete generality .

we fit axisymmetric 3-integral dynamical models to ngc 3379 using the line - of - sight velocity distribution obtained from hst / fos spectra of the galaxy center and ground - based long - slit spectroscopy along four position angles , with the light distribution constrained by wfpc2 and ground - based images . we have fitted models with inclinations from 29 ( intrinsic galaxy type e5 ) to 90 ( intrinsic e1 ) and black hole masses from 0 to . the best - fit black hole masses range from , depending on inclination . the preferred inclination is 90 ( edge - on ) ; however , the constraints on allowed inclination are not very strong due to our assumption of constant _ m / l_ . the velocity ellipsoid of the best model is not consistent with either isotropy or a two - integral distribution function . along the major axis , the velocity ellipsoid becomes tangential at the innermost bin , radial in the mid - range radii , and tangential again at the outermost bins . the rotation rises quickly at small radii due to the presence of the black hole . for the acceptable models , the radial to tangential ( ( dispersion in the mid - range radii ranges from , with the smaller black holes requiring larger radial anisotropy . compared with these 3-integral models , 2-integral isotropic models overestimate the black hole mass since they can not provide adequate radial motion . however , the models presented in this paper still contain restrictive assumptions namely assumptions of constant _ m / l_ and spheroidal symmetry requiring yet more models to study black hole properties in complete generality .

1104.5622

i

recently , we have been interested in a family of soft , long - range pair interactions that give rise to novel physical behaviors of many - particle systems including classical disordered ground states for a range of densities , negative thermal expansion , and vanishing normal - mode frequencies.@xcite this family of soft pair interactions includes those pair potentials @xmath1 with fourier transforms @xmath2 that are positive , bounded , and vanish to zero at some finite wavenumber @xmath3 and beyond . the potential energy @xmath4 of a system of @xmath5 particles in a fundamental cell with volume @xmath6 under periodic boundary conditions can be written as @xmath7 , \end{aligned}\ ] ] where @xmath8 is the distance between particles @xmath9 and @xmath10 , @xmath11 are the fourier coefficients of the density field , and @xmath12 are the wave vectors appropriate for the system size and shape . these soft pair interactions , called `` collective - coordinate '' potentials , are bounded and possess long - range oscillations in real space.@xcite because of the finite cutoff in @xmath0-space , an analytic lower bound for the potential energy per particle @xmath13 is easily obtainable , and numerical methods allow for the construction and investigation of ground states with extremely high precision . a series of studies has examined the structural characteristics of ground states in one,@xcite two,@xcite and three dimensions.@xcite three structural ground - state regimes were found to characterize these two - dimensional systems . increasing the fraction of degrees of freedom that are constrained @xmath14 , equivalently decreasing density , spans regimes that are disordered , wavy - crystalline , and crystalline . recently , an analytical connection between the fraction of constrained degrees of freedom within the system and the disorder - order phase transition for a class of target structure factors has been provided@xcite by examining the realizability of the constrained contribution to the pair correlation function . more recently , these potentials were used to construct `` stealthy '' and `` hyperuniform '' materials in two dimensions.@xcite `` stealthy '' materials refer to point patterns that completely suppress single scattering of radiation for certain wavelength ranges . while nonstealthy materials may allow for some small amount of scattering , stealthy materials are absolutely transparent at those wavelengths . `` hyperuniform '' refers to point patterns in which infinite wavelength density fluctuations vanish.@xcite ( these terms are defined more precisely in sec . [ sec : background ] . ) the hyperuniformity notion enables the rank ordering of crystals , quasicrystals and special disorderedmany - particle systems.@xcite interestingly , disordered hyperuniform many - particle ground states , and therefore also point distributions , with substantial clustering can be constructed.@xcite constructed ground states are now the basis for novel disordered materials with tunable , photonic band gaps.@xcite using a model potential from the family of collective - coordinate potentials in two dimensions , the `` @xmath0-space overlap potential , '' described in sec.[sec : background ] , we observed negative thermal expansion and vanishing normal - mode frequencies for ground - state configurations . we attributed these phenomena to the nature of the underlying energy landscape , which we described as having ground - state `` valleys '' that weave between the higher - energy portions of the landscape.@xcite despite the discovery of the existence of such unique properties , the fundamental mechanisms allowing for disordered ground states and stealthy point patterns still need to be fully elucidated . here , we analyze the energy landscape further by examining the associated inherent structures , or local potential - energy minima , for the aforementioned @xmath0-space overlap potential in two dimensions to better understand these properties . we have two primary motivations for this work . first , through the course of our previous research , we have observed several paradoxical phenomena related to local potential - energy minima and glassy behavior . while an `` inherent structure '' is in general any local potential - energy minimum , the term `` glass '' refers to an amorphous solid that is kinetically trapped in a potential - energy well . in ref . [ 2 ] , we observed an unusual equation of state when cooling a system compared to a more familiar ( _ e.g. _ , lennard - jones ) glass - forming system as fig . [ fig : glasses ] demonstrates this schematically . in fig.[fig : normglass ] , the dark and dotted lines represent the equilibrium equation of state and nonequilibrium isobaric cooling path for a lennard - jones system . figure [ fig : ccglass ] shows the corresponding cooling paths for a system interacting with the @xmath0-space overlap potential . in the more familiar glass - forming system , there is a well - defined glass transition below the freezing point that is dependent on the rate at which the system is cooled.@xcite it is well known that the glass - forming behavior of a system is a function of the underlying energy landscape.@xcite the depths of the potential - energy wells in the energy landscape dictate the dynamics of structural rearrangements of the system.@xcite for the @xmath0-space overlap potential , we observed that at high pressure the nonequilibrium curve deviated from the equilibrium curve at a temperature above the melting temperature , as demonstrated in fig . [ fig : ccglass ] . at lower pressures where there is no well - defined melting temperature , as in the wavy - crystalline regime , the nonequilibrium curve deviates similarly from the equilibrium curve . in addition , the @xmath0-space overlap potential gives rise to negative thermal expansion , generally for nondimensional @xmath15.@xcite other paradoxical behaviors have led us toward a broad analysis of the energy landscape . we have observed that some ground - state configurations , particularly crystalline structures , had many zero - energy normal modes . these ground states are therefore not mechanically rigid . however , while using numerical minimization algorithms to construct ground - state configurations , we encountered many mechanically stable local potential - energy minima . lastly , there exists a large density range in which the energy landscape was evidently devoid of all local minima . an increment in @xmath14 just outside this range introduced local potential - energy minima to the landscape . while we have previously observed these phenomena,@xcite the fundamental mechanisms that underlie them are not fully understood . the inherent - structure analysis has proven to be a fruitful method for relating the energy landscape to low - temperature phenomena . many studies have examined inherent - structure characteristics in glass - forming liquids with strong repulsive cores such as the stillinger - weber potential,@xcite water - like pair potentials,@xcite binary lennard - jones - like systems,@xcite and general repulsive potentials.@xcite the inherent structures for lennard - jones and steeply repulsive potentials are in general not hyperuniform or stealthy due to the dominance of grain boundaries and vacancy defects . in contrast to the above list of strongly repelling potentials , the @xmath0-space overlap potential is a soft interaction . soft interactions are often useful models for soft - matter systems such as colloids , polymers , and microemulsions.@xcite in addition , these @xmath0-space overlap interactions are also qualitatively similar to friedel oscillations in molten metals.@xcite the @xmath0-space overlap potential is localized in @xmath0-space and delocalized in real space as a result of the fourier transform . certain duality relations link the ground - state energies of the @xmath0-space overlap potential to the ground - state energies of real space analog.@xcite there have been several investigations of the inherent structures of various soft interactions . the gaussian - core model in two dimensions has polycrystalline inherent structure with a large correlation length even when sampled from the liquid state.@xcite energy landscape analyses revealed that the range of the morse potential affects the relation between temperature and the potential - energy distribution of sampled inherent structures.@xcite while for the yukawa potential , inherent structures varied depending on whether they were obtained from the liquid , crystal or hexatic phase.@xcite novel , stealthy dielectric materials are currently being fabricated,@xcite and nearly stealthy ceramic materials are of interest for optical applications.@xcite because of these recent experimental applications and the unusual physical behaviors discovered,@xcite we are also motivated to understand the fundamental differences between point patterns that absolutely suppress scattering for certain wavelengths and those that nearly suppress scattering . our ground - state construction procedure @xcite automatically distinguishes stealthy and hyperuniform configurations from those that do not possess such properties . in particular , we want to understand whether the particle rearrangements required to transform nearly hyperuniform and stealthy materials to configurations that are perfectly hyperuniform and stealthy are global or local in nature . while a general method for understanding these particle rearrangements would require a new algorithm to search for collective motions that increase stealthiness , the collective - coordinate approach provides an excellent framework from which to address this question . here , we provide two methods for identifying rearrangements in particle systems to achieve stealthy and hyperuniform materials . for large @xmath14 , we use the nudged - elastic - band algorithm to connect inherent structures , which are nearly hyperuniform and nearly stealthy , to ground states along a minimum - energy path . for small @xmath14 values , we have identified that there are no inherent structures higher up in the energy landscape . therefore , we study the rearrangements from a saturated random sequential addition ( rsa ) of hard disks@xcite to ground states of the @xmath0-space overlap potential . we use saturated rsa systems as initial conditions because upon saturation they suppress scattering for small wavenumbers and are nearly hyperuniform.@xcite we also introduce a stealthiness metric and a configurational proximity metric to quantify characteristics of these transitions . in this paper , we use a collective - coordinate potential and a simulation methodology to find stealthy point patterns and local potential - energy minima above the ground state . we probe the following fundamental questions : * how are inherent structures and their thermodynamic properties in collective coordinate systems different from those found in other soft - potential systems ? * to what extent are inherent structures stealthy and/or hyperuniform ? * how are the features of inherent structures related to the pair potential function ? * what collective particle rearrangements are necessary to construct a path from an inherent structure to a ground state ? * what global and/or local particle rearrangements are necessary to convert a nearly stealthy and nearly hyperuniform system in to one that is absolutely stealthy and hyperuniform ? the remainder of this paper is organized as follows . in sec.[sec : background ] , we define the @xmath0-space overlap potential , introduce several definitions , and briefly review the ground - state structural regimes . in sec . [ sec : methods ] , we detail the methods we use to obtain and characterize inherent structures . in addition , we discuss the methods we use to find transition states between inherent structures and ground states . in sec.[sec : cooling ] , we examine the thermodynamic properties of inherent structures as a function of system size and cooling rate . the inherent structures are characterized in sec . [ sec : structure ] . paths connecting inherent structures to ground states are provided in sec . [ sec : mapping ] while the rearrangements from rsa systems to ground states are explored in sec.[sec : rsa ] . concluding remarks are provided in sec . [ sec : disc ] .

we generate inherent structures , local potential - energy minima , of the ``-space overlap potential '' in two - dimensional many - particle systems using a cooling and quenching simulation technique . the ground states associated with the-space overlap potential are stealthy ( _ i.e. , _ completely suppress single scattering of radiation for a range of wavelengths ) and hyperuniform ( _ i.e. , _ infinite wavelength density fluctuations vanish ) . however , we show via quantitative metrics that the inherent structures exhibit a range of stealthiness and hyperuniformity depending on the fraction of degrees of freedom that are constrained . the structural and thermodynamic properties of inherent structures are relatively insensitive to the temperature from which they are sampled , signifying that the energy landscape is relatively flat and devoid of deep wells . using the nudged - elastic - band algorithm , we construct paths from ground - state configurations to inherent structures and identify the transition points between them . in addition , we use point patterns generated from a random sequential addition ( rsa ) of hard disks , which are nearly stealthy , and examine the particle rearrangements necessary to make the configurations absolutely stealthy . these results lead to a more complete understanding of the unusual behaviors exhibited by the family of `` collective - coordinate '' potentials to which the-space overlap potential belongs .

we generate inherent structures , local potential - energy minima , of the ``-space overlap potential '' in two - dimensional many - particle systems using a cooling and quenching simulation technique . the ground states associated with the-space overlap potential are stealthy ( _ i.e. , _ completely suppress single scattering of radiation for a range of wavelengths ) and hyperuniform ( _ i.e. , _ infinite wavelength density fluctuations vanish ) . however , we show via quantitative metrics that the inherent structures exhibit a range of stealthiness and hyperuniformity depending on the fraction of degrees of freedom that are constrained . inherent structures in two dimensions typically contain five - particle rings , wavy grain boundaries , and vacancy - interstitial defects . the structural and thermodynamic properties of inherent structures are relatively insensitive to the temperature from which they are sampled , signifying that the energy landscape is relatively flat and devoid of deep wells . using the nudged - elastic - band algorithm , we construct paths from ground - state configurations to inherent structures and identify the transition points between them . in addition , we use point patterns generated from a random sequential addition ( rsa ) of hard disks , which are nearly stealthy , and examine the particle rearrangements necessary to make the configurations absolutely stealthy . we introduce a configurational proximity metric to show that only small local , but collective , particle rearrangements are needed to drive initial rsa configurations to stealthy disordered ground states . these results lead to a more complete understanding of the unusual behaviors exhibited by the family of `` collective - coordinate '' potentials to which the-space overlap potential belongs .

astro-ph0411621

i

we have carried a detailed abundance analysis for 21 elements in a sample of four rgb stars in the metal poor distant outer halo globular cluster ngc 7492([fe / h ] @xmath48 dex ) . the analyzed spectra , obtained with hires at the keck observatory , are of high dispersion ( r=@xmath3=35,000 ) . most elements show no sign of star - to - star variation within our limited sample . we have , however , detected an anti - correlation between o and na abundances similar to that seen in our previous analyses of inner halo gcs as well as in studies of relatively nearby gcs by other . a correlation between mg and na abundance may also be present . we have compared the abundance ratios in ngc 7492 with those we previously determined for the much closer old halo gcs m3 and m13 @xcite , hoping that since all these analyses were carried out by the same two people within a timespan of only a few months in a completely consistent manner , with the same line lists , the same atomic parameters , the same analysis codes and procedures , etc . that small differences in the abundance ratios might be detectable . we evaluate the trends of abundance ratio with metallicity for old halo stars from our data combined with published large surveys of halo field star abundances . we then apply corrections to the abundances we derived for m3 and m13 for each species , when feasible , to extrapolate them to the 0.35 dex smaller [ fe / h ] of ngc 7492 . after making such corrections , all the elements in common show identical abundance ratios for ngc 7492 and for m3 and m13 , allowing for a @xmath42 dex tolerance , and 75% of them are then within the tolerance @xmath190.10 dex . this suggests that the galactic chemical evolution of the outer halo at @xmath0 25 kpc has been identical to that of the well studied much closer inner halo gcs , at least up to the time of the formation of the old globular clusters ngc 7492 , m3 and m13 . in particular , our limited evidence , based on ba , la and eu abundance ratios , suggests the neutron capture processes , both @xmath46 and @xmath47 , appear to have had similar histories throughout the spatial extent of the halo for old gc stars as well . the presence of the o / na anti - correlation in ngc 7492 , with @xmath0 of 25 kpc , and the similarity of its chemical history to that of the well studied nearby gcs , provide new constraints on any model of gc formation in the galactic halo . the entire keck / hires user communities owes a huge debt to jerry nelson , gerry smith , steve vogt , and many other people who have worked to make the keck telescope and hires a reality and to operate and maintain the keck observatory . we are grateful to the w. m. keck foundation for the vision to fund the construction of the w. m. keck observatory . 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 , none of the observations presented herein would have been possible . this publication makes use of data from the two micron all - sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center , funded by the national aeronautics and space administration and the national science foundation . we are grateful to the national science foundation for partial support under grant ast-0205951 to jgc . barnes , s. a. , 1968 , , 73 , 579 carretta , e. , cohen , j. g. , gratton , r. g. & behr , b. b. , 2001 , , 122 , 1469 carretta , e. , gratton , r. , bragaglia , a. , bonifacio , p. & pasquini , l. , 2004 , , 416 , 925 carretta , e. , bragaglia , a. & cacciari , c. , 2004 , , in press cohen , j. g. , frogel , j. a. , persson , s. e. & elias , j. h. , 1981 , , 249 , 481 , 1981 fulbright , j. p. , 2000 , , 120 , 1841 gratton , r. g. , carretta , e. , eriksson , k. & gustafsson , b. , 1999 , , 350 , 955 gratton , r. g. & sneden , c. , 1991 , , 241 , 501 gratton . r. g. , _ et al . _ , 2001 , , 369 , 87 gustafsson , b. , bell , r.a . , eriksson , k. & nordlund , , 1975 , a&a , 42 , 407 skrutskie , m. f. , schneider , s.e . , stiening , r. , strom , s.e . , weinberg , m.d . , beichman , c. , chester , t. _ et al . _ , 1997 , in _ the impact of large scale near - ir sky surveys _ , ed . et al . _ ( dordrecht : kluwer ) , p. 187 sneden , c. , kraft , r. p. , shetrone , m. d. , smith , g. h. , langer , g. e. & prosser , c. f. , 1997 , , 114 , 1964 sneden , c. , kraft , r. p. , guhathakurta , p. , peterson , r. c. & fulbright , j. p. , 2004 , , 127 , 2162 takeda , y. , zhao , g. , takada - hidai , m. , chen , y. , saito , y. & zhang , h. w. , 2003 , chin.j.astron.astrophys . , 3 , 316 thevenin , f. , carbonnel , c. , de freitas pacheco , j. a. , idiart , t. p. , jasniewsicz , g. , de lavery , p. & plez , b. , 2001 , , 373 , 905 vogt , s. e. _ et al . _ 1994 , spie , 2198 , 362 lcrrrrrr h , 231 & 23 08 22.32 @xmath49 37 43 & 14.71 & 13.36 & 20/08/2003 & 800 & 88 & @xmath50 + t , 458 & 23 08 25.75 @xmath49 37 10 & 15.50 & 14.41 & 21/08/2003 & 3600 & 92 & @xmath51 + r & 23 08 29.46 @xmath49 36 32 & 15.51 & 14.40 & 20,21/08/2003 & 3000 & 92 & @xmath52 + k , 950 & 23 08 20.83 @xmath49 36 20 & 15.77 & 14.72 & 22/08/2003 & 3600 & 105 & @xmath15 + llrrrrrrrrrrrrrrr oi & 6300.30 & 0.00 & @xmath69.78 & 30.0 & 23.5 & 13.5 & 27.3 + oi & 6363.78 & 0.02 & @xmath610.30 & 9.0 & & 8.0 & 9.5 + nai & 5682.63 & 2.10 & @xmath60.70 & 46.0 & 32.1 & 8.0 & 16.0 + nai & 5688.19 & 2.10 & @xmath60.42 & 61.0 & 49.6 & 15.0 & 28.5 + nai & 6160.75 & 2.00 & @xmath61.23 & 18.5 & & & + mgi & 4703.00 & 4.34 & @xmath60.67 & 157.2 & 126.7 & 115.8 & 136.0 + mgi & 5528.40 & 4.34 & @xmath60.48 & 170.2 & 148.0 & 133.8 & 145.8 + mgi & 5711.09 & 4.34 & @xmath61.67 & 82.7 & 64.0 & 30.0 & 46.0 + sii & 5690.43 & 4.93 & @xmath61.87 & 27.0 & 20.0 & & 23.5 + sii & 5948.54 & 5.08 & @xmath61.23 & 42.0 & 36.0 & 33.0 & 27.0 + sii & 6155.13 & 5.62 & @xmath60.76 & 24.0 & 20.0 & 17.0 & 31.0 + sii & 6237.32 & 5.62 & @xmath61.01 & 15.0 & & & + cai & 5512.99 & 2.93 & @xmath60.27 & 56.5 & 40.0 & 23.0 & 33.7 + cai & 5581.96 & 2.52 & @xmath60.47 & 82.7 & 58.3 & 44.8 & 48.1 + cai & 5588.75 & 2.52 & 0.44 & 133.4 & 116.7 & 95.3 & 103.0 + cai & 5590.11 & 2.52 & @xmath60.71 & 80.7 & 61.1 & 46.7 & 46.9 + cai & 5601.28 & 2.52 & @xmath60.44 & 77.3 & 68.3 & 49.0 & 41.5 + cai & 6161.30 & 2.52 & @xmath61.03 & 49.2 & 24.0 & & 22.0 + cai & 6162.17 & 1.90 & @xmath60.09 & & 145.4 & 132.0 & 148.0 + cai & 6166.44 & 2.52 & @xmath61.05 & 51.3 & 31.0 & 11.0 & 25.5 + cai & 6169.04 & 2.52 & @xmath60.54 & 72.5 & 54.5 & 35.9 & 43.0 + cai & 6169.56 & 2.52 & @xmath60.27 & 93.8 & 65.6 & 46.7 & 61.2 + cai & 6471.66 & 2.52 & @xmath60.59 & 83.6 & 61.9 & 38.2 & 50.8 + cai & 6493.78 & 2.52 & 0.14 & 123.8 & 90.9 & 77.8 & 89.6 + scii & 5526.79 & 1.77 & 0.13 & 94.7 & 88.6 & 78.2 & 82.6 + scii & 5657.90 & 1.51 & @xmath60.50 & 93.4 & 76.1 & 66.6 & 72.7 + scii & 5667.15 & 1.50 & @xmath61.24 & 54.0 & 41.3 & 31.0 & 32.0 + scii & 5669.04 & 1.50 & @xmath61.12 & 60.8 & 45.0 & 34.8 & 44.8 + scii & 5684.20 & 1.51 & @xmath61.08 & 77.0 & 41.0 & 36.0 & 51.0 + scii & 6245.64 & 1.51 & @xmath61.13 & 56.9 & 35.0 & 32.2 & 34.4 + scii & 6604.60 & 1.36 & @xmath61.48 & 57.2 & 34.0 & 19.0 & 45.0 + tii & 4981.74 & 0.85 & 0.50 & 167.7 & 111.3 & 97.5 & 120.7 + tii & 4999.51 & 0.83 & 0.25 & 157.4 & 113.0 & 86.3 & 106.4 + tii & 5022.87 & 0.83 & @xmath60.43 & 107.2 & 71.0 & 41.8 & 62.3 + tii & 5039.96 & 0.02 & @xmath61.13 & 148.0 & 94.4 & 73.6 & 75.7 + tii & 5426.26 & 0.02 & @xmath63.01 & 33.7 & & & + tii & 5471.20 & 1.44 & @xmath61.39 & 15.0 & & & + tii & 5490.15 & 1.46 & @xmath60.93 & 34.7 & & & + tii & 5644.14 & 2.27 & 0.05 & 41.0 & & & + tii & 5662.16 & 2.32 & @xmath60.11 & 24.5 & & & + tii & 5937.81 & 1.07 & @xmath61.89 & 16.4 & & & + tii & 5941.75 & 1.05 & @xmath61.52 & 43.6 & 17.3 & & 14.0 + tii & 5953.16 & 1.89 & @xmath60.33 & 41.1 & & & + tii & 5978.54 & 1.87 & @xmath60.50 & 29.0 & & & + tii & 6258.10 & 1.44 & @xmath60.35 & 75.0 & 37.3 & 25.4 & 35.7 + tii & 6261.10 & 1.43 & @xmath60.48 & 72.2 & 36.5 & 18.0 & 28.7 + tii & 6303.76 & 1.44 & @xmath61.57 & 9.0 & & & + tii & 6312.22 & 1.46 & @xmath61.55 & 9.5 & & & + tii & 6743.12 & 0.90 & @xmath61.63 & 45.8 & & & + tiii & 4657.20 & 1.24 & @xmath62.32 & 84.0 & 97.0 & 59.3 & 83.9 + tiii & 4708.67 & 1.24 & @xmath62.37 & 96.8 & 81.8 & 71.1 & 87.7 + tiii & 4865.62 & 1.12 & @xmath62.81 & 75.0 & 84.0 & 52.7 & 64.1 + tiii & 5185.91 & 1.89 & @xmath61.46 & 98.0 & 85.9 & 74.8 & 81.9 + tiii & 5336.79 & 1.58 & @xmath61.63 & 121.0 & 105.0 & 93.2 & 105.4 + vi & 5670.85 & 1.08 & @xmath60.43 & 35.0 & & & + vi & 5703.57 & 1.05 & @xmath60.21 & 34.3 & & & + vi & 6081.44 & 1.05 & @xmath60.58 & 29.8 & & & + vi & 6090.22 & 1.08 & @xmath60.06 & 41.7 & & & + vi & 6199.20 & 0.29 & @xmath61.28 & 32.0 & & & + vi & 6251.82 & 0.29 & @xmath61.34 & 35.4 & & & + vi & 6274.64 & 0.27 & @xmath61.67 & 21.8 & & & + vi & 6285.14 & 0.28 & @xmath61.51 & 46.2 & & & + cri & 5345.81 & 1.00 & @xmath60.97 & 134.1 & 104.3 & 75.4 & 85.6 + cri & 5348.33 & 1.00 & @xmath61.29 & 115.8 & 74.5 & 54.7 & 63.9 + cri & 5409.80 & 1.03 & @xmath60.71 & 169.5 & 126.0 & 88.8 & 106.9 + cri & 5787.96 & 3.32 & @xmath60.08 & 12.0 & & & + mni & 4754.04 & 2.28 & @xmath60.09 & 107.2 & 74.2 & 49.8 & 62.2 + mni & 4783.42 & 2.30 & 0.04 & 121.2 & 95.0 & 69.2 & 72.9 + mni & 4823.51 & 2.32 & 0.14 & 116.5 & 75.0 & 67.5 & 78.0 + mni & 5537.74 & 2.19 & @xmath62.02 & 28.0 & & & + fei & 4788.77 & 3.24 & @xmath61.81 & 49.5 & & & + fei & 4891.50 & 2.85 & @xmath60.11 & 170.7 & 144.8 & 137.7 & 142.3 + fei & 4919.00 & 2.86 & @xmath60.34 & 168.5 & 141.0 & 117.4 & 141.4 + fei & 5083.34 & 0.96 & @xmath62.96 & 165.2 & 131.2 & 112.3 & 126.2 + fei & 5166.28 & 0.00 & @xmath64.20 & & 141.4 & 118.9 & 139.7 + fei & 5194.95 & 1.56 & @xmath62.09 & 174.6 & 130.3 & 121.0 & 129.1 + fei & 5232.95 & 2.94 & @xmath60.10 & 172.0 & 139.0 & 129.6 & 139.5 + fei & 5324.19 & 3.21 & @xmath60.10 & 160.4 & 135.8 & 117.7 & 125.8 + fei & 5393.18 & 3.24 & @xmath60.72 & 114.4 & 93.0 & 81.8 & 86.1 + fei & 5410.92 & 4.47 & 0.40 & 87.1 & 73.4 & 56.0 & 68.3 + fei & 5415.21 & 4.39 & 0.64 & 105.0 & 91.0 & 66.4 & 86.9 + fei & 5424.08 & 4.32 & 0.51 & 114.7 & 87.8 & 83.1 & 99.2 + fei & 5445.05 & 4.39 & @xmath60.03 & 79.3 & 70.0 & 47.0 & 67.2 + fei & 5473.90 & 4.15 & @xmath60.69 & 42.2 & 43.9 & 20.0 & 24.5 + fei & 5493.50 & 4.10 & @xmath61.68 & 15.9 & & & + fei & 5497.52 & 1.01 & @xmath62.83 & & 147.7 & 134.3 & 143.9 + fei & 5501.46 & 0.96 & @xmath63.05 & & 138.6 & 118.5 & 136.5 + fei & 5506.79 & 0.99 & @xmath62.79 & & 146.2 & 130.0 & 142.4 + fei & 5525.55 & 4.23 & @xmath61.08 & 21.0 & & & 13.5 + fei & 5554.88 & 4.55 & @xmath60.35 & 33.9 & 35.0 & 22.0 & 25.6 + fei & 5567.39 & 2.61 & @xmath62.67 & 64.8 & 39.0 & & 31.2 + fei & 5569.62 & 3.42 & @xmath60.49 & 123.0 & 92.0 & 81.1 & 91.2 + fei & 5572.84 & 3.40 & @xmath60.28 & 146.1 & 108.6 & 100.1 & 104.3 + fei & 5576.09 & 3.43 & @xmath60.92 & 109.1 & 83.5 & 63.7 & 72.3 + fei & 5586.76 & 3.37 & @xmath60.14 & 144.8 & 117.7 & 105.1 & 114.1 + fei & 5641.44 & 4.26 & @xmath61.08 & 30.0 & & & + fei & 5662.52 & 4.18 & @xmath60.57 & 65.0 & 48.5 & 37.2 & 39.8 + fei & 5679.02 & 4.65 & @xmath60.82 & 25.0 & & & + fei & 5701.54 & 2.56 & @xmath62.14 & 106.0 & 76.3 & 46.9 & 66.7 + fei & 5705.98 & 4.61 & @xmath60.49 & 25.5 & & & 29.0 + fei & 5752.04 & 4.55 & @xmath60.94 & 19.2 & & & + fei & 5753.12 & 4.26 & @xmath60.69 & 52.5 & 38.9 & 30.0 & 30.4 + fei & 5762.99 & 4.21 & @xmath60.41 & 70.2 & 44.9 & 36.5 & 48.0 + fei & 5775.06 & 4.22 & @xmath61.30 & 22.6 & & & + fei & 5778.46 & 2.59 & @xmath63.43 & 19.6 & & & + fei & 5806.72 & 4.61 & @xmath60.95 & 11.0 & & & + fei & 5859.60 & 4.55 & @xmath60.55 & 34.0 & 22.0 & 15.6 & 17.7 + fei & 5862.35 & 4.55 & @xmath60.33 & 52.2 & 30.0 & 21.0 & 24.2 + fei & 5883.81 & 3.96 & @xmath61.26 & 27.0 & 17.5 & & 19.0 + fei & 5930.17 & 4.65 & @xmath60.14 & 47.4 & 36.7 & 21.3 & 18.0 + fei & 5934.65 & 3.93 & @xmath61.07 & 42.0 & 42.0 & 29.5 & 21.8 + fei & 5952.72 & 3.98 & @xmath61.34 & 53.3 & 35.5 & 20.0 & 24.3 + fei & 5956.69 & 0.86 & @xmath64.50 & 110.7 & 60.7 & 34.5 & 51.2 + fei & 5976.79 & 3.94 & @xmath61.33 & 41.7 & 18.0 & 17.5 & 19.3 + fei & 5983.69 & 4.55 & @xmath60.66 & 37.5 & & 16.8 & 20.0 + fei & 6024.05 & 4.55 & 0.03 & 67.4 & 40.5 & 38.9 & 48.9 + fei & 6027.05 & 4.07 & @xmath61.09 & 38.3 & & & + fei & 6055.99 & 4.73 & @xmath60.37 & 29.2 & 28.0 & & 15.0 + fei & 6065.48 & 2.61 & @xmath61.41 & 143.9 & 111.4 & 90.6 & 97.2 + fei & 6078.50 & 4.79 & @xmath60.33 & 29.2 & 25.5 & 10.5 & 12.5 + fei & 6137.69 & 2.59 & @xmath61.35 & 144.3 & 110.6 & 99.2 & 109.8 + fei & 6151.62 & 2.18 & @xmath63.37 & 66.0 & 37.8 & 17.6 & 30.1 + fei & 6157.73 & 4.07 & @xmath61.16 & 42.5 & 26.2 & 8.0 & 20.9 + fei & 6165.36 & 4.14 & @xmath61.47 & 24.9 & & & + fei & 6173.34 & 2.22 & @xmath62.88 & 91.0 & 62.6 & 36.0 & 51.6 + fei & 6180.20 & 2.73 & @xmath62.65 & 55.0 & 29.8 & 14.0 & 27.7 + fei & 6187.99 & 3.94 & @xmath61.62 & 14.0 & & & + fei & 6191.56 & 2.43 & @xmath61.42 & 174.9 & 129.4 & 99.3 & 128.8 + fei & 6200.31 & 2.61 & @xmath62.37 & 88.5 & 59.7 & 31.5 & 47.1 + fei & 6240.65 & 2.22 & @xmath63.17 & 59.3 & 35.2 & 16.0 & 23.0 + fei & 6246.32 & 3.60 & @xmath60.88 & 91.9 & 74.3 & 48.9 & 57.7 + fei & 6252.55 & 2.40 & @xmath61.77 & 146.8 & 106.8 & 100.0 & 112.0 + fei & 6254.26 & 2.28 & @xmath62.43 & 122.1 & 95.9 & 73.0 & 79.3 + fei & 6265.13 & 2.18 & @xmath62.54 & 118.9 & 89.8 & 59.1 & 77.7 + fei & 6297.79 & 2.22 & @xmath62.64 & 108.1 & 79.9 & 44.1 & 59.4 + fei & 6301.51 & 3.65 & @xmath60.72 & 93.7 & 71.0 & 50.0 & 65.1 + fei & 6315.31 & 4.14 & @xmath61.23 & 25.0 & & & + fei & 6355.03 & 2.84 & @xmath62.29 & 69.3 & 45.1 & 19.0 & 33.0 + fei & 6380.75 & 4.19 & @xmath61.38 & 22.3 & & & + fei & 6393.60 & 2.43 & @xmath61.58 & 156.6 & 118.3 & 100.8 & 115.0 + fei & 6408.03 & 3.69 & @xmath61.02 & 86.7 & 59.3 & 40.2 & 49.6 + fei & 6411.65 & 3.65 & @xmath60.72 & 109.2 & 75.1 & 58.2 & 75.7 + fei & 6421.35 & 2.28 & @xmath62.01 & 145.9 & 101.0 & 85.7 & 101.2 + fei & 6475.63 & 2.56 & @xmath62.94 & 58.8 & 33.2 & 14.6 & 19.5 + fei & 6481.87 & 2.28 & @xmath63.01 & 86.3 & 46.5 & 30.6 & 43.2 + fei & 6498.94 & 0.96 & @xmath64.69 & 98.1 & 51.2 & 31.9 & 43.5 + fei & 6546.24 & 2.76 & @xmath61.54 & 137.2 & 99.1 & 74.1 & 92.7 + fei & 6581.21 & 1.48 & @xmath64.68 & 42.7 & & & + fei & 6592.91 & 2.73 & @xmath61.47 & 130.9 & 97.4 & 81.7 & 90.8 + fei & 6593.87 & 2.43 & @xmath62.37 & 99.2 & 67.4 & 48.0 & 64.2 + fei & 6608.02 & 2.28 & @xmath63.93 & 16.0 & & & + fei & 6609.11 & 2.56 & @xmath62.66 & 79.1 & 45.5 & 26.5 & 37.5 + fei & 6633.75 & 4.79 & @xmath60.80 & 27.0 & & & 12.0 + fei & 6648.12 & 1.01 & @xmath65.92 & 13.0 & & & + fei & 6739.52 & 1.56 & @xmath64.79 & 27.0 & & & + fei & 6750.15 & 2.42 & @xmath62.58 & 101.8 & 68.0 & 46.6 & 60.2 + fei & 6839.83 & 2.56 & @xmath63.35 & 27.9 & & & + fei & 6843.65 & 4.55 & @xmath60.83 & 25.6 & & & + fei & 6855.18 & 4.56 & @xmath60.74 & 34.6 & & & + fei & 6861.95 & 2.42 & @xmath63.85 & 20.0 & & & + fei & 6978.85 & 2.48 & @xmath62.45 & 104.8 & 72.6 & 44.6 & 66.5 + fei & 6988.52 & 2.40 & @xmath63.56 & 39.7 & & & + fei & 7022.95 & 4.19 & @xmath61.15 & 38.0 & & & + fei & 7038.22 & 4.22 & @xmath61.20 & 30.1 & & & + feii & 4923.93 & 2.88 & @xmath61.32 & 138.4 & & & + feii & 5197.58 & 3.23 & @xmath62.23 & 74.0 & 64.0 & 70.9 & 76.8 + feii & 5234.63 & 3.22 & @xmath62.22 & 75.1 & 67.6 & 74.3 & 83.6 + feii & 5414.08 & 3.22 & @xmath63.62 & 22.0 & 23.5 & 10.0 & 16.5 + feii & 5425.26 & 3.00 & @xmath63.24 & 29.0 & 27.0 & 27.0 & 37.5 + feii & 5534.85 & 3.25 & @xmath62.64 & 64.3 & 56.8 & 53.2 & 52.9 + feii & 5991.38 & 3.15 & @xmath63.57 & 30.0 & & 12.0 & 27.4 + feii & 6149.26 & 3.89 & @xmath62.69 & 18.0 & 25.2 & 16.4 & 26.9 + feii & 6247.56 & 3.89 & @xmath62.36 & 40.0 & 31.9 & 31.0 & 31.6 + feii & 6369.46 & 2.89 & @xmath64.20 & 10.0 & & & + feii & 6416.92 & 3.89 & @xmath62.69 & 19.0 & 15.9 & & 15.8 + feii & 6516.08 & 2.89 & @xmath63.45 & 64.0 & 58.3 & 47.5 & 51.8 + coi & 5530.79 & 1.71 & @xmath62.06 & 30.0 & & 9.0 & 10.0 + coi & 5647.23 & 2.28 & @xmath61.56 & 21.5 & & & + coi & 6189.00 & 1.71 & @xmath62.45 & 18.0 & & & + nii & 5578.72 & 1.68 & @xmath62.64 & 86.1 & 44.1 & 32.0 & 33.0 + nii & 5587.86 & 1.93 & @xmath62.14 & 81.4 & 36.9 & 20.5 & 39.0 + nii & 5682.20 & 4.10 & @xmath60.47 & 18.0 & & & + nii & 5748.35 & 1.68 & @xmath63.26 & 41.0 & & 7.0 & 14.0 + nii & 5846.99 & 1.68 & @xmath63.21 & 34.1 & & & + nii & 6128.97 & 1.68 & @xmath63.33 & 30.0 & 23.5 & 10.4 & 10.5 + nii & 6175.37 & 4.09 & @xmath60.54 & 22.0 & & & + nii & 6176.81 & 4.09 & @xmath60.53 & 21.8 & & & + nii & 6177.24 & 1.83 & @xmath63.51 & 15.0 & & & + nii & 6482.80 & 1.93 & @xmath62.63 & 47.8 & 21.0 & 13.3 & 19.6 + nii & 6586.31 & 1.95 & @xmath62.81 & 45.5 & 22.3 & 8.0 & 13.0 + nii & 6643.63 & 1.68 & @xmath62.30 & 126.3 & 83.0 & 56.5 & 73.9 + nii & 6767.77 & 1.83 & @xmath62.17 & 106.4 & 74.8 & 51.7 & 64.1 + cui & 5105.54 & 1.39 & @xmath61.50 & 82.0 & 46.0 & 24.0 & 28.0 + cui & 5782.12 & 1.64 & @xmath61.78 & 41.5 & & & + zni & 4722.16 & 4.03 & @xmath60.39 & 45.0 & 36.6 & 41.0 & 44.0 + zni & 4810.54 & 4.08 & @xmath60.17 & 46.0 & 54.6 & 52.4 & 48.5 + yii & 4883.69 & 1.08 & 0.07 & 85.0 & 71.3 & 74.5 & 71.8 + yii & 5087.43 & 1.08 & @xmath60.17 & 71.0 & 55.0 & 56.2 & 60.1 + yii & 5200.42 & 0.99 & @xmath60.57 & 56.0 & 42.1 & 32.7 & 44.0 + zri & 6127.44 & 0.15 & @xmath61.06 & 17.0 & & & + zri & 6134.55 & 0.00 & @xmath61.28 & 13.0 & & & + zri & 6143.20 & 0.07 & @xmath61.10 & 10.0 & & & + baii & 5853.70 & 0.60 & @xmath61.01 & 117.3 & 98.1 & 99.9 & 108.2 + baii & 6141.70 & 0.70 & @xmath60.07 & 172.8 & 134.7 & 152.3 & 155.9 + baii & 6496.90 & 0.60 & @xmath60.38 & 186.6 & 146.8 & 154.9 & 163.0 + laii & 5122.99 & 0.32 & @xmath60.85 & 27.8 & & & + laii & 6390.48 & 0.32 & @xmath61.41 & 21.5 & & & + ndii & 4947.02 & 0.56 & @xmath61.13 & 18.0 & & & + ndii & 4959.12 & 0.06 & @xmath60.80 & 66.6 & 34.0 & 23.5 & 32.0 + ndii & 5092.79 & 0.38 & @xmath60.61 & 44.0 & 28.5 & 17.4 & 16.9 + ndii & 5212.35 & 0.20 & @xmath60.96 & 48.0 & & & + ndii & 5249.58 & 0.98 & 0.20 & 49.9 & 30.5 & 33.5 & 31.5 + ndii & 5319.81 & 0.55 & @xmath60.14 & 61.9 & 33.2 & 33.8 & 27.8 + euii & 6645.11 & 1.38 & 0.12 & 25.5 & & & + lclc o & 8.85 & fe & 7.45 + na & 6.33 & ni & 6.25 + mg & 7.54 & cu & 4.21 + al & 6.47 & zn & 4.60 + si & 7.55 & ba & 2.13 + ca & 6.36 & y & 2.24 + sc & 3.10 & zr & 2.60 + ti & 4.99 & la & 1.14 + v & 4.00 & nd & 1.45 + cr & 5.67 & eu & 0.51 + mn & 5.39 & dy & 1.10 + lcrlrrcrcrcccc 231 & @xmath61.76 @xmath19 0.05 * & 90 & @xmath61.72 @xmath19 0.06 & 12 & 0.26 @xmath19 0.05 * & 2 & 0.10 @xmath19 0.05 & 3 & 0.67 @xmath19 0.16 & 3 + r & @xmath61.77@xmath19 0.05 * & 66 & @xmath61.80 @xmath19 0.08 & 9 & 0.49 @xmath19 0.10 & 1 & 0.19 @xmath19 0.05 * & 2 & 0.52 @xmath19 0.06 & 3 + 458 & @xmath61.79 @xmath19 0.05 * & 70 & @xmath61.77 @xmath19 0.05 & 10 & 0.55 @xmath19 0.05 * & 2 & @xmath60.10 @xmath19 0.05 * & 2 & 0.55 @xmath19 0.20 & 3 + 950 & @xmath61.94 @xmath19 0.05 * & 64 & @xmath61.88 @xmath19 0.05 & 9 & 0.52 @xmath19 0.15 & 2 & @xmath60.28 @xmath19 0.05 * & 2 & 0.45 @xmath19 0.20 & 3 + llrrrrrlrrrlr 231 & 0.33 @xmath19 0.09 & 4 & 0.09 @xmath19 0.05 * & 11 & 0.20 @xmath19 0.07 & 7 & 0.16 @xmath19 0.05 * & 18 & @xmath60.07 @xmath19 0.06 & 8 + r & 0.36 @xmath19 0.10 & 3 & 0.11 @xmath19 0.05 * & 12 & 0.09 @xmath19 0.05 * & 7 & 0.12 @xmath19 0.08 & 7 & & 0 + 458 & 0.45 @xmath19 0.12 & 3 & 0.05 @xmath19 0.05 * & 12 & 0.10 @xmath19 0.06 & 7 & 0.18 @xmath19 0.07 & 7 & & 0 + 950 & 0.42 @xmath19 0.11 & 2 & 0.07 @xmath19 0.05 & 11 & 0.15 @xmath19 0.05 * & 7 & 0.07 @xmath19 0.05 * & 6 & & 0 + llrlllllrrrr 231 & @xmath60.24 @xmath19 0.09 & 4 & @xmath60.24 @xmath19 0.09 & 4 & 0.11 @xmath19 0.05 * & 3 & @xmath60.06 @xmath19 0.05 * & 13 & @xmath60.63 @xmath19 0.06 & 2 + r & @xmath60.16 @xmath19 0.11 & 3 & @xmath60.48 @xmath19 0.13 & 3 & & 0 & @xmath60.07 @xmath19 0.08 & 7 & @xmath60.57 @xmath19 0.10 & 1 + 458 & @xmath60.29 @xmath19 0.06 & 3 & @xmath60.43 @xmath19 0.05 * & 3 & 0.18 @xmath19 0.10 & 1 & @xmath60.09 @xmath19 0.05 * & 8 & @xmath60.72 @xmath19 0.10 & 1 + 950 & @xmath60.29 @xmath19 0.05 * & 3 & @xmath60.39 @xmath19 0.08 & 3 & 0.32 @xmath19 0.10 & 1 & @xmath60.09 @xmath19 0.06 & 8 & @xmath60.62 @xmath19 0.10 & 1 + lrlllrrrrrrrrrr 231 & @xmath60.09 @xmath19 0.08 & 2 & @xmath60.29 @xmath19 0.05 * & 4 & 0.36 @xmath19 0.10 & 3 & 0.24 @xmath19 0.10 & 3 & 0.12 @xmath19 0.16 & 2 + r & @xmath60.09 @xmath19 0.08 & 2 & @xmath60.35 @xmath19 0.05 * & 4 & & 0 & 0.05 @xmath19 0.09 & 3 & & 0 + 458 & @xmath60.16 @xmath19 0.05 & 2 & @xmath60.31 @xmath19 0.06 & 4 & & 0 & 0.34 @xmath19 0.07 & 3 & & 0 + 950 & 0.13 @xmath19 0.05 * & 2 & @xmath60.11 @xmath19 0.08 & 4 & & 0 & 0.50 @xmath19 0.08 & 3 & & 0 + lrrcrrrrrr oi & 0.46 & 0.13 & 0.10 & 1.30 & 4 + nai & @xmath60.02 & 0.21 & 0.07 & 3.00 & 4 + mgi & 0.55 & 0.09 & 0.20 & 0.45 & 4 + sii & 0.39 & 0.06 & 0.10 & 0.60 & 4 + cai & 0.08 & 0.03 & 0.12 & 0.25 & 4 + scii & 0.14 & 0.05 & 0.21 & 0.24 & 4 + tii & 0.13 & 0.05 & 0.12 & 0.42 & 4 + tiii & 0.34 & 0.06 & 0.15 & 0.40 & 4 + vi & @xmath60.07 & & 0.23 & & 1 + cri & @xmath60.25 & 0.06 & 0.17 & 0.35 & 4 + mni & @xmath60.39 & 0.10 & 0.18 & 0.55 & 4 + fei & @xmath61.82 & 0.08 & 0.10 & 0.80 & 4 + feii & @xmath61.79 & 0.07 & 0.13 & 0.54 & 4 + coi & 0.20 & 0.11 & 0.12 & 0.92 & 3 + nii & @xmath60.08 & 0.02 & 0.10 & 0.20 & 4 + cui & @xmath60.64 & 0.06 & 0.16 & 0.38 & 4 + zni & @xmath60.03 & 0.11 & 0.13 & 0.85 & 4 + yii & @xmath60.27 & 0.11 & 0.15 & 0.73 & 4 + zri & 0.36 & & 0.16 & & 1 + baii & 0.28 & 0.19 & 0.22 & 0.86 & 4 + laii & 0.12 & & 0.18 & & 1 + ndii & 0.32 & 0.11 & 0.11 & 1.00 & 4 + euii & 0.61 & & & & 1 + lrrrr o & 0.46 & 0.15 & 0.02 & + na & @xmath60.02 & 0.21 & @xmath60.10 & 0.00 + mg & 0.55 & 0.09 & 0.12 & 0.05 + si & 0.39 & 0.06 & 0.23 & 0.08 + ca & 0.08 & 0.03 & @xmath60.09 & 0.07 + sc & 0.14 & 0.05 & 0.14 & 0.07 + ti & 0.24 & 0.06 & 0.08 & 0.07 + v & @xmath60.07 & & 0.01 & + cr & @xmath60.25 & 0.06 & @xmath60.22 & @xmath60.10 + mn & @xmath60.39 & 0.10 & @xmath60.04 & @xmath60.05 + co & 0.20 & 0.11 & 0.21 & 0.07 + ni & @xmath60.08 & 0.01 & @xmath60.01 & 0.00 + cu & @xmath60.64 & 0.06 & @xmath60.02 & + zn & @xmath53 & 0.11 & 0.02 & + y & @xmath60.27 & 0.11 & @xmath60.04 & + zr & 0.36 & & 0.40 & + ba & 0.28 & 0.019 & 0.05 & @xmath60.04 + la & 0.12 & & 0.03 & + nd & 0.32 & 0.11 & 0.10 & + eu & 0.61 & & 0.07 & 0.00 +

we have carried out a detailed abundance analysis for 21 elements in a sample of four rgb stars in the outer halo globular cluster ngc 7492 ( 25 kpc ) ; we find [ fe / h ] = dex inferred from fe i lines ( from fe ii ) using high dispersion ( r==35,000 ) spectra obtained with hires at the keck observatory . most elements show no sign of star - to - star variation within our limited sample . we have , however , detected an anti - correlation between o and na abundances similar to that seen in our previous analyses of inner halo gcs as well as in studies of relatively nearby gcs by others . we compare the abundance ratios in ngc 7492 with those we previously determined for the much closer old halo gcs m3 and m13 . after making corrections for trends of abundance ratio with metallicity characteristic of halo stars , we find that for for these three gcs for each of the elements in common we deduce identical abundance ratios with respect to fe to within the probable measurement uncertainties . this applies to the neutron capture processes as well .

we have carried out a detailed abundance analysis for 21 elements in a sample of four rgb stars in the outer halo globular cluster ngc 7492 ( 25 kpc ) ; we find [ fe / h ] = dex inferred from fe i lines ( from fe ii ) using high dispersion ( r==35,000 ) spectra obtained with hires at the keck observatory . most elements show no sign of star - to - star variation within our limited sample . we have , however , detected an anti - correlation between o and na abundances similar to that seen in our previous analyses of inner halo gcs as well as in studies of relatively nearby gcs by others . we compare the abundance ratios in ngc 7492 with those we previously determined for the much closer old halo gcs m3 and m13 . after making corrections for trends of abundance ratio with metallicity characteristic of halo stars , we find that for for these three gcs for each of the elements in common we deduce identical abundance ratios with respect to fe to within the probable measurement uncertainties . thus , the chemical history of the outer halo as exemplified by the metal - poor outer halo globular cluster ngc 7492is indistinguishable from that of the inner halo , exemplified by m3 and m13 , at least through the epoch of formation of these old globular clusters . this applies to the neutron capture processes as well .

1101.1607

i

a measurement of the complete breakup of the atomic helium target by xuv radiation was achieved over @xmath3 years ago @xcite . since then , rapid developments in strong xuv light sources and momentum imaging techniques have made it possible to record all the reaction fragments , nuclei and electrons , in double photoionization of the simplest two - electron hydrogen / deuterium molecule by one - photon absorption @xcite , and most recently also for two - photon absorption @xcite . for the double ionization of h@xmath4 by single - photon absorption , only randomly oriented molecules were investigated in earlier experiments ( e.g. @xcite ) . using fixed - in - space " molecules , more recent experimental efforts include the measurements of energy- and angle - resolved differential cross sections by weber _ et al . _ for either equal energy sharing @xcite or asymmetric energy sharing @xcite , and by gisselbrecht _ @xcite for equal energy sharing at a photon energy of @xmath5 ev . these experimental studies were at least partially stimulated by the goal of understanding the similarities and differences between the hydrogen molecule and its atomic counterpart helium . however , all recorded fully differential cross sections to date suffer from some experimental uncertainties regarding the alignment angle of the molecule with respect to the polarization vector of the laser and the emission angles of the photoelectrons . from a theoretical point of view , the hydrogen molecule exhibits a significant complexity compared to helium and , therefore , provides an enormous challenge to a fully _ ab initio _ description inherent in a multi - center , multi - electron system . the single - center convergent close - coupling method was used to model the double ionization of h@xmath4 by kheifets and bray @xcite . later mccurdy , rescigno , martn and their collaborators @xcite implemented a formulation based on time - independent exterior complex scaling ( ecs ) in spherical coordinates , with the origin of the coordinate system placed at the center of the molecule , to treat the double photoionization at a photon energy of @xmath0 ev . the radial coordinates of the two electrons are measured from the center , and the radial parts of the wave function were either expanded in @xmath6-splines or using a finite - element discrete - variable representation ( fe - dvr ) . the time - dependent close - coupling ( tdcc ) method @xcite , again in spherical coordinates , was also extended to calculate the triple - differential cross section ( tdcs ) for double photoionization of the h@xmath4 molecule . while the agreement between the published tdcss from the ecs @xcite and tdcc @xcite calculations is basically acceptable , noticeable discrepancies remained for a few particular geometries . in the parallel geometry , for instance , where the molecular axis @xmath7 is chosen along the laser polarization vector @xmath8 , the coplanar tdcs predictions from the ecs and tdcc calculations differ by up to @xmath9 percent when one of the electrons ( we will refer to it as the `` fixed electron '' below ) is observed along the direction perpendicular to the @xmath8-axis . in some other cases , there exists a noticeable wing " structure in the published tdcc predictions for equal energy sharing . additional tdcc calculations @xcite suggest that the agreement can be systematically improved , albeit the above - mentioned discrepancy still exists at a somewhat reduced level . another independent approach @xcite to this problem is the very recent time - independent ecs treatment , formulated as in the current work in prolate spheroidal coordinates . quite surprisingly , the results of that calculation differed from both the earlier ecs and also the tdcc predictions , both obtained in spherical coordinates . specifically , the ecs prolate spheroidal calculations showed differences from the earlier spherical coordinate calculation for the tdcss , at a level of about @xmath10 depending on the details of the energy sharing . as will be demonstrated below , we have gone to considerable lengths in an attempt to resolve these discrepancies . however , significant differences between the present results and those of the ecs @xcite still remain . both the ecs @xcite and the tdcc @xcite calculations made some attempt to deal with the experimental uncertainties in the scattering angles . given the experimental uncertainties and the differences in the previous calculations , however , it appeared worthwhile to investigate the computational effort required to obtain accurate before averaging over any experimental acceptance angles . consequently , the present calculation represents an independent implementation of the time - dependent fe - dvr approach in prolate spheroidal coordinates . as in the other approaches mentioned above , the internuclear separation ( @xmath11 ) was held fixed at its equilibrium distance of @xmath12 bohr . the two - center prolate system , with the foci located on the nuclei , provides a suitable description for the two - center characteristics of the h@xmath4 molecule . the formulation of the schrdinger equation in prolate spheroidal coordinates for diatomic molecules is not new . the pioneering work of bates , pik , and poots @xcite for the h@xmath13 ion , which is exactly separable in prolate spheroidal coordinates , already revealed the appealing features of the prolate system . in particular , the electron - nuclear interaction is rendered benign in this coordinate system . a partial list of recent applications of prolate spheroidal coordinates to diatomic molecules can be found in @xcite . as has been demonstrated in a number of recent publications , a grid - based approach provides a very appropriate description of laser - driven atomic and molecular physics when combined with an efficient time - propagation method such as the short iterative lanczos ( sil ) method @xcite . in the present work , we employ the fe - dvr / sil approach in prolate spheroidal coordinates to study the correlated response of a two - electron molecule in the double ionization process . the remainder of this manuscript is organized as follows . after presenting the hamiltonian of the hydrogen molecule in section [ sec.2 ] and providing some details about the discretization of the system in an fe - dvr basis in sec . [ sec.3 ] , the solution of the two - center poisson equation is presented in sec . [ sec.4 ] . this is followed by a description of the procedure for extracting the cross sections of interest in sec . [ sec.5 ] . the results are presented and discussed in sec . [ sec.6 ] , before we finish with a summary in sec . [ sec.7 ] .

the spatial coordinates and are discretized in a finite - element discrete - variable representation . the wave packet of the laser - driven two - electron system is propagated in time through an effective short iterative lanczos method to simulate the double ionization of the hydrogen molecule . for both symmetric and asymmetric energy sharing , the present results agree to a satisfactory level with most earlier predictions for the absolute magnitude and the shape of the angular distributions . a notable exception , however , concerns the predictions of the recent time - independent calculations based on the exterior complex scaling method in prolate spheroidal coordinates [ phys . extensive tests of the numerical implementation were performed , including the effect of truncating the neumann expansion for the dielectronic interaction on the description of the initial bound state and the predicted cross sections .

we have carried out calculations of the triple - differential cross section for one - photon double ionization of molecular hydrogen for a central photon energy of ev , using a fully _ ab initio _ , nonperturbative approach to solve the time - dependent schrdinger equation in prolate spheroidal coordinates . the spatial coordinates and are discretized in a finite - element discrete - variable representation . the wave packet of the laser - driven two - electron system is propagated in time through an effective short iterative lanczos method to simulate the double ionization of the hydrogen molecule . for both symmetric and asymmetric energy sharing , the present results agree to a satisfactory level with most earlier predictions for the absolute magnitude and the shape of the angular distributions . a notable exception , however , concerns the predictions of the recent time - independent calculations based on the exterior complex scaling method in prolate spheroidal coordinates [ phys . rev . a * 82 * , 023423 ( 2010 ) ] . extensive tests of the numerical implementation were performed , including the effect of truncating the neumann expansion for the dielectronic interaction on the description of the initial bound state and the predicted cross sections . we observe that the dominant escape mode of the two photoelectrons dramatically depends upon the energy sharing . in the parallel geometry , when the ejected electrons are collected along the direction of the laser polarization axis , back - to - back escape is the dominant channel for strongly asymmetric energy sharing , while it is completely forbidden if the two electrons share the excess energy equally .

1101.1607

r

for the nonsequential double - ionization process induced by one- or two - photon absorption , electronic correlation plays a dominant role , as the two photoelectrons must share the available excess energy @xmath190 . double ionization by a single photon would not occur at all if the two - electron atom or molecule were approximated by an independent - electron model . therefore , the quality of the description of electron - electron correlation in a laser - driven system is crucially important for accurate results to be obtained . the coulomb interaction between the two electrons has to be described in a consistent manner for both the initial bound state and the time - evolved wave packet . before we go any further , it is worth discussing how we prepare the initial @xmath204 state at the equilibrium distance of @xmath208 bohr . as seen from eq . ( [ eq:1/r12 ] ) , the magnetic quantum number in the neumann expansion of the matrix element of @xmath80 is uniquely determined by the angular bases . however , this is not the case for the index @xmath99 , if we choose to discretize the coordinate @xmath2 , rather then expanding that part of the wave function into spherical harmonics . in practice , the summation over @xmath99 must be truncated at a finite value of @xmath137 . in principle , the higher - order expansion terms always guarantee well - converged results . however , as mentioned earlier , we approximate the relevant @xmath2-integrals by using gauss - legendre quadrature . this is the price we have to pay for making the dielectronic coulomb potential diagonal in the dvr bases . as a consequence , we need to determine how the approximation introduced in the @xmath2-integrals for the two - electron integrals affects the results for the cross sections of interest . to answer this question , we first investigate the dependence of the energy obtained for the initial @xmath209 state on the value of @xmath137 used in the neumann expansion . figure [ fig : energy ] shows the variation of the initial - state electronic energy of the hydrogen molecule with respect to @xmath137 , obtained with a @xmath1 setup of ten elements in the region of @xmath210 , five in the region @xmath211 and another five in @xmath212 . each element , in turn , contains five dvr points to further discretize the configuration space . furthermore , we employ dvr points for @xmath2 . for a given number of @xmath2 mesh points ( @xmath213 ) and @xmath214 , we observe that the resulting energy typically exhibits a plateau - like behavior with increasing @xmath137 . for given @xmath213 , when @xmath137 is relatively small , the @xmath2-integral can be computed very accurately by using gauss quadrature . however , when @xmath137 is too large , the numerical errors introduced from the gauss quadrature cause the energy value to fluctuate . this occurs when @xmath137 approaches @xmath215 and is shown by the grey stripes in fig . [ fig : energy ] . in this region of @xmath137 an unphysically _ low _ energy can be produced . beyond that point , the calculated energy increases to the next plateau . ultimately , this is not too surprising , since any gauss quadrature is only reasonably accurate up to a limited polynomial order of the integrand . consequently , if we want to keep more terms in the neumann expansion , we have to increase @xmath213 correspondingly . this finding is further substantiated by the dependence of the energy found for @xmath216 and @xmath217 . the plateaus are indeed extended to the correspondingly larger values of @xmath215 . most importantly , the amplitude of the energy fluctuation is systematically reduced with increasing @xmath213 . the error in the energy is lowered from @xmath218 to @xmath219 and finally @xmath220 a.u . , when @xmath213 increases from @xmath221 to @xmath222 and then @xmath217 for @xmath223 . we obtained the energy at @xmath208 bohr as @xmath224 a.u . for @xmath225 , @xmath226 , and @xmath223 , resulting in a double - ionization potential of @xmath227 ev . keeping the other parameters unchanged , we obtained an energy of @xmath228 a.u . for @xmath216 . the benchmark energy in the literature is @xmath229 a.u . at the same @xmath11 @xcite , after we take out the nucleus - nucleus interaction of @xmath230 a.u . to summarize : unlike for other expansion parameters , it is important to be consistent in the size of the angular quadrature and the largest @xmath137 employed in the neumann expansion in practical calculations , if we discretize the coordinate @xmath2 . however , this provides a way to examine a potential sensitivity of the physical observables of interest ( here the differential cross sections ) to the ground - state wave functions generated by varying @xmath137 and other parameters . this will be further discussed below . before we present our results for the cross sections , let us take a closer look at the survival probability @xmath231 of the aligned h@xmath4 molecule in its ground state @xmath232 . this is shown in fig . [ fig : surv ] . for homonuclear molecules , the independent alignment angle @xmath37 between the molecular axis and the polarization vector can be confined to the region from @xmath233 to @xmath234 . in the xuv regime , we observe that the hydrogen molecule shows a larger probability of being ionized or excited ( i.e. , a lower probability of staying in the initial state ) at the end of the pulse in an aligned geometry . this indicates that the perpendicular component of the temporal electric field exerts more influence on the ionization process due to the larger dipole momentum . interestingly , at the earlier stages of the time evolution ( e.g. , @xmath235 , when the ionized wave packet is driven back by the change in direction of the electric field , the tilted molecule has a larger probability of staying in its ground state . this happens near the various minima in @xmath236 . however , once the electric field has become sufficiently strong ( @xmath237 a.u . ) , the wave packet is driven out and spread into a larger space . this leads to lower minima in @xmath236 for the tilted molecule . when the wave packet is driven back to the nuclear region and therefore has a chance to recombine with the h@xmath13 ion , a maximum in @xmath236 appears . not surprisingly , the parallel geometry always has the largest probability for this to happen . although the wave packet can also be scattered for the untilted molecule in the plane perpendicular to the molecular axis , the probability is undoubtedly larger if the laser electric field is perpendicular to the molecular axis . a similar behavior of h@xmath13 in xuv pulses was observed in ref . @xcite . for most calculations performed in this study , we expose the hydrogen molecule to a laser pulse with a peak intensity of @xmath238 w/@xmath239 . looking at fig . [ fig : surv ] we see that the depletion of the initial ground state can be safely neglected for our typical interaction times . even for @xmath240 , @xmath241 remains very close to unity . the negligible depletion of the ground state suggests that the concept of cross sections is valid and applicable . on the other hand , it also presents a numerical challenge to predict the cross sections accurately from a time - dependent treatment , due to the generally small ionization probability . at first glance , a peak intensity of @xmath238 w/@xmath239 might seem very intense for most atomic and molecular targets . here , however , we consider an xuv rather than an ir pulse . for an xuv pulse with central photon energy of @xmath0 ev , such laser fields definitely fall into the weak - field " regime . the ponderomotive energy in the xuv regime is much smaller than the photon energy of interest . .[tab : parameters ] the discretization and expansion parameters of the h@xmath4 wave function in prolate spheroidal coordinates . here @xmath242 stands for the border between the inner and outer regions in the @xmath1 coordinate , while @xmath92 is the size of the @xmath1 box . in addition , @xmath243 denotes the number of @xmath1 mesh points in each element . the numbers of @xmath1 elements in the inner and outer region are @xmath244 and @xmath245 , respectively . these @xmath1 parameters produce the total number of @xmath1 mesh points @xmath246 . the @xmath1 grid i and @xmath1 grid ii are used to examine the convergence of our results . [ cols="<,^,^,^,^,^,^",options="header " , ] in this work , we are mainly interested in the triple - differential cross section , since it reveals the fine details of possible energy sharings and preferred directions of the ejected electrons in the double - ionization process . given the discrepancies between results from various calculations found in the literature , we carried out comprehensive convergence tests for our predictions of the tdcss . these tests are essentially divided into two groups . the first group concerns the laser parameters , while the second one deals with the discretization and expansion parameters . an example of two different parameter sets for the @xmath1 grid is given in table [ tab : parameters ] and will be further discussed below . in order to obtain a good handle on the sensitivity of the results to the various parameters and the resulting level of convergence " , we try to only vary a single parameter while keeping all others fixed if possible . for the dependence on the laser parameters , we use the @xmath1 grid i combined with @xmath247 . for the tests regarding the discretizations and expansions , the peak intensity of laser was fixed at @xmath238 w/@xmath239 and a time scale of `` @xmath248 '' optical cycles ( o.c . ) was used . here `` @xmath248 '' refers to a laser pulse with a sine - squared envelope for the field amplitude , followed by a field - free propagation . + + + + + + figures [ fig : tdcs - laser ] and [ fig : tdcs - discret ] show the convergence pattern of our tdcs results for asymmetric energy sharing in the parallel geometry ( @xmath249 ) . the energy sharing between electron @xmath250 ( observed at the fixed angle @xmath251 ) and electron @xmath252 ( observed at the variable angle @xmath253 ) is @xmath254 . only the electron that takes away @xmath10 of the excess energy is recorded at fixed positions either parallel or perpendicular to the polarization axis . since the laser pulse is explicitly involved in our time - dependent treatment , we first have to be sure that the extracted cross sections are essentially independent of the laser intensity and the time scales . only then are the calculations of cross sections meaningful . this also allows us to compare the physical information extracted from our time - dependent scenario to that obtained through conventional time - independent treatments , which are effectively equivalent to the weak - field approximation and infinitely " long interaction times . rather than computing the cross sections , it would be more appropriate to consider ionization rates if the cross sections were found to be sensitive to the laser parameters . in fig . [ fig : tdcs - laser ] , we display the dependences of our tdcs results upon the laser parameters . note that the tdcss extracted from @xmath255 w/@xmath239 and @xmath256 w/@xmath239 at fixed time evolution of @xmath248 " cycles are nearly identical and agree with each other to better than the thickness of the line . when we turn to the dependence of time scales at a fixed intensity of @xmath238 w/@xmath239 , we use the same pulse , but allow the system to freely evolve for a few additional cycles to extract the tdcs . this corresponds to the time scale of @xmath257 " o.c . also , we may increase the laser - molecule interaction time , but extract the tdcss at the same cycles of field - free time evolution after the pulse died off . this gives the scenario of @xmath258 " o.c . since the total time durations are the same ( @xmath259 o.c . ) , they allow us to examine the extracted tdcss from different perspectives . the increased interaction time yields a reduced bandwidth of the photon energy , while the longer field - free propagation ensures that the double - ionization wave packet is further away from the nuclear region @xcite . the calculated tdcss indeed show a slight , though in our opinion acceptable , sensitivity to the time scales . not surprisingly , the sensitivity is most visible for the smaller cross sections , when the two ejected electrons travel nearly parallel along the same direction ( c.f . [ fig : tdcs - laser]@xmath260 ) . + + + having confidence in using the current sets of laser parameters , we now turn our attention to the scheme of spatial discretization ( @xmath243 , @xmath92 , @xmath213 ) and the convergence of the expansion ( @xmath137 , @xmath261 ) . the results are displayed in fig . [ fig : tdcs - discret ] . for the discretization parameters , we obtain well - converged tdcss by increasing @xmath262 from @xmath263 to @xmath264 , @xmath265 from @xmath221 to @xmath222 , and extending the spatial box of @xmath92 from @xmath266 to @xmath267 . most importantly , however , we consider two sets of @xmath1 mesh points : @xmath1 grid i and @xmath1 grid ii ( see table [ tab : parameters ] ) . the principal motivation was to see whether or not we can reproduce the much lower tdcs values ( by about @xmath10 compared to the one - center spherical results ) that were recently obtained in an ecs calculation in two - center elliptical coordinates by tao _ et al . _ @xcite . we emphasize that these two grids in the radial " @xmath1 coordinate are completely different regarding both the distribution of the elements and the number of grid points per element . in the @xmath1 grid i , we divide the @xmath1 space into two parts , an inner and an outer region with a border at @xmath268 . we place a narrow span of elements in the inner region , and then wider elements in the outer region . in contrast to that , @xmath1 grid ii does not distinguish between inner and outer regions , i.e. , the elements uniformly span the region from @xmath250 to @xmath92 . the mesh setup in @xmath1 grid ii is the same as that used in ref . @xcite , except for the complex rotation . the @xmath1 grid i has a much denser distribution of mesh points than @xmath1 grid ii . nevertheless , the extracted tdcss from both sets of @xmath1 grids are in excellent agreement with each other , even for the smallest cross sections . this strongly suggests that the results are well converged at least with regard to the @xmath1 grid . both @xmath1 sets are good enough to capture the physics of interest . differences at the @xmath10 level are unlikely to be caused by using different sets of @xmath1 meshes . finally , we discuss the convergence of our results with respect to the expansion parameters , @xmath261 and @xmath137 . as expected for a one - photon process , @xmath223 produced well - converged results . recall the discussion above regarding the ground state , especially how the truncated neumann expansion of @xmath80 in our present fe - dvr implementation affects the initial - state energy and therefore the quality of the wave function . for consistency , we use the same @xmath137 in the real - time propagation and in the ground - state wave function . as seen from figs . [ fig : tdcs - discret]@xmath269 and [ fig : tdcs - discret]@xmath270 , our truncated neumann expansion has little effect on the calculated tdcs values . well - converged results can be obtained even with an inappropriately large value of @xmath271 , which yields a slightly higher energy of the ground state ( c.f . [ fig : energy ] ) . overall , our detailed convergence tests only reveal a very weak sensitivity of the tdcs results to both the time scales and the values of @xmath137 . well - converged tdcs results can be obtained by using either @xmath1 grid i or @xmath1 grid ii combined with @xmath247 . in the production calculations for the tdcss shown in the next subsection , we used the @xmath1 grid i to discretize the two - electron wave packet and a @xmath248 " sine - squared laser pulse with a peak intensity of @xmath238 w/@xmath239 . figures [ fig : tdcs - equal - sharing - ele1 - 00 ] , [ fig : tdcs - equal - sharing - ele1 - 90 ] , and [ fig : tdcs - nonequal - sharing - ele1 - 90 ] display the coplanar tdcss of the aligned hydrogen molecule at equal and asymmetric ( @xmath272 ) energy sharing . the two electrons are detected in the same ( coplanar ) plane defined by the @xmath7 and @xmath8 axes . the angles @xmath251 , @xmath253 , and @xmath37 are all measured with respect to the laser linear polarization axis . we compare our tdcs predictions with those obtained in the time - independent one - center spherical ecs calculation @xcite , the time - independent two - center spheroidal ecs model @xcite , and the time - dependent one - center spherical tdcc approach @xcite . the tdcc numbers were recently recalculated with a bigger box size and differ , in some cases substantially , from those published originally @xcite . except for the recent two - center prolate spheroidal ecs results of tao _ et al . _ @xcite , the agreement between the other three sets of results is very satisfactory . once again , the largest relative differences occur when the cross sections are small ( see figs . [ fig : tdcs - equal - sharing - ele1 - 00]@xmath273 and [ fig : tdcs - equal - sharing - ele1 - 90]@xmath273 ) . using spheroidal coordinates as well , as an illustrative example of their two - center ecs approach , serov and joulakian @xcite recently presented the tdcs at the same photon energy , but only for a single geometry of and for asymmetric energy sharing of @xmath274 . although not shown here , there is again good agreement between their results , vanroose _ et al . _ s one - center spherical ecs numbers @xcite , and our time - dependent fe - dvr predictions . it is also interesting to investigate the dominant escape modes for the various scenarios . these modes are strongly dependent on how the electrons share the excess energy . in an arbitrary geometry ( @xmath275 ) , for example , the back - to - back escape mode @xmath276 is forbidden for equal energy sharing . on the other hand , it becomes the dominant mode for significantly asymmetric energy sharing , including the 20%:80% scenario discussed in the present paper ( see fig . [ fig : tdcs - laser ] ) . these results can be understood from a symmetry analysis @xcite . equal - energy sharing and back - to - back emission is equivalent to @xmath277 . when we consider the exchange and parity operations simultaneously in eq . ( [ eq : two - continuum ] ) , we have @xmath278 . here @xmath279 is the parity for the gerade and ungerade states , respectively . for the singlet double - continuum state with _ parity , we therefore must have at any configuration of @xmath280 and @xmath281 . although the magnitudes of the momenta @xmath282 and @xmath283 are not exactly conserved in the time - dependent picture , the ionization events we collect must satisfy the condition @xmath284 ( because of the @xmath285 function in eq . ( [ eq : tdcs ] ) ) for the equal - energy sharing . this is the reason behind the forbidden back - to - back ( @xmath286 ) escape mode for the equal energy sharing , as we observed in figs . [ fig : tdcs - equal - sharing - ele1 - 00 ] and [ fig : tdcs - equal - sharing - ele1 - 90 ] . since the argument does not involve the relative alignment angles , it is valid for all possible values of @xmath37 . on the other hand , this is not the case when the excess energy is not evenly distributed among the two electrons . indeed , figs . [ fig : tdcs - laser]@xmath287 and [ fig : tdcs - laser]@xmath260 show maxima in the back - to - back emission , thereby illustrating the dramatic change in the dominant escape mode . for equal - energy sharing in the parallel geometry ( @xmath249 ) , the electron - electron coulomb repulsion suggests that the tdcs should be dynamically small if the two electrons travel along the same direction . this is in agreement with the numerically small cross sections ( not exactly zero , however ) at @xmath288 or @xmath289 seen in fig . [ fig : tdcs - equal - sharing - ele1 - 00]@xmath273 . recall that the one - photon double - photoionization process in helium @xcite shares the same property . the back - to - back mode is forbidden for equal - energy sharing , and this can be explained by the above argument . it is one of the similarities between the molecular hydrogen and the atomic helium targets for double photoionization . however , figs . [ fig : tdcs - equal - sharing - ele1 - 00 ] , [ fig : tdcs - equal - sharing - ele1 - 90 ] , and [ fig : tdcs - nonequal - sharing - ele1 - 90 ] also reveal significant molecular effects in the tdcs results . these are missing for the helium atom , not only in the shape of the angular distributions , but also in the magnitudes of the cross sections . depending on the relative orientation @xmath290 , there is interference between the @xmath291 and @xmath292 symmetries in h@xmath4 . a nice example of this effect was presented by reddish _ et al . _ @xcite . even without interference ( i.e. , for @xmath249 or @xmath234 ) , the perpendicular geometry shows much larger magnitudes of the tdcs than the parallel geometry . figure [ fig : tdcs - h2-helium ] shows the three cases of angular distributions : h@xmath4 @xmath293 , h@xmath4 @xmath294 , and he at equal energy sharing . interestingly , in most cases the angular distributions of the perpendicular geometry resemble those of helium . the molecular effect can definitely not be ignored in the parallel geometry for @xmath295 ( c.f . [ fig : tdcs - h2-helium]@xmath287 ) . the _ forward _ escape mode of the second electron is dominant for the h@xmath4 parallel geometry . in contrast , the _ backward _ mode is dominant for the h@xmath4 perpendicular geometry and also for helium . in fig . [ fig : tdcs - out - plane ] , we show the tdcs for noncoplanar geometries . again , all angles are defined with respect to the polarization vector . for the perpendicular geometry , [ fig : tdcs - out - plane]@xmath287 depicts the escape modes for the configuration of @xmath296 ( the fixed electron ) and at the same time @xmath297 in the plane perpendicular to the plane formed by @xmath8 and @xmath7 . figure [ fig : tdcs - out - plane]@xmath298 shows the tdcs after exchanging the directions of @xmath299 and @xmath297 in fig . [ fig : tdcs - out - plane]@xmath287 . with the same directions of @xmath299 and @xmath297 as in fig . [ fig : tdcs - out - plane]@xmath298 , fig . [ fig : tdcs - out - plane]@xmath260 is for the case of the molecular axis orientated along the polarization vector . in the parallel case ( @xmath249 ) , we observe that any escape modes of both electrons ejected in the direction perpendicular to @xmath8 are forbidden . this can be understood by analyzing the spheroidal harmonics in eq . ( [ eq : tdcs ] ) . in this case , only the @xmath205 states can be populated . hence , only partial waves with @xmath300 and @xmath301 can contribute to the cross sections , since @xmath302 at the angles of @xmath303 vanish in spherical coordinates . once again , the agreement between our fe - dvr noncoplanar tdcss and the refined tdcc results @xcite is excellent .

we observe that the dominant escape mode of the two photoelectrons dramatically depends upon the energy sharing . in the parallel geometry , when the ejected electrons are collected along the direction of the laser polarization axis , back - to - back escape is the dominant channel for strongly asymmetric energy sharing , while it is completely forbidden if the two electrons share the excess energy equally .

we have carried out calculations of the triple - differential cross section for one - photon double ionization of molecular hydrogen for a central photon energy of ev , using a fully _ ab initio _ , nonperturbative approach to solve the time - dependent schrdinger equation in prolate spheroidal coordinates . the spatial coordinates and are discretized in a finite - element discrete - variable representation . the wave packet of the laser - driven two - electron system is propagated in time through an effective short iterative lanczos method to simulate the double ionization of the hydrogen molecule . for both symmetric and asymmetric energy sharing , the present results agree to a satisfactory level with most earlier predictions for the absolute magnitude and the shape of the angular distributions . a notable exception , however , concerns the predictions of the recent time - independent calculations based on the exterior complex scaling method in prolate spheroidal coordinates [ phys . rev . a * 82 * , 023423 ( 2010 ) ] . extensive tests of the numerical implementation were performed , including the effect of truncating the neumann expansion for the dielectronic interaction on the description of the initial bound state and the predicted cross sections . we observe that the dominant escape mode of the two photoelectrons dramatically depends upon the energy sharing . in the parallel geometry , when the ejected electrons are collected along the direction of the laser polarization axis , back - to - back escape is the dominant channel for strongly asymmetric energy sharing , while it is completely forbidden if the two electrons share the excess energy equally .

1101.1607

i

we have presented calculations for one - photon double ionization of the hydrogen molecule at a photon energy of @xmath0 ev by solving the time - dependent schrdinger equation in prolate spheroidal coordinates . the triple - differential cross sections were extracted through the projection of the time - dependent wave packet onto uncorrelated two - electron continuum states , a few cycles of field - free time evolution after the laser pulse died off . exhaustive convergence studies of the tdcs results were performed with respect to a number of discretization and expansion parameters , as well as the details of the laser field . these tests provide a strong indication that the results for the triple - differential cross sections presented here are well converged and numerically accurate . excellent agreement was obtained between the current time - dependent results in prolate spheroidal coordinates , those obtained with the ecs approach in spherical coordinates @xcite and , finally , larger tdcc calculations @xcite than those published earlier @xcite . the present calculations do not confirm the significant reduction by about @xmath10 in the tdcs results predicted in recent ecs calculations in the two - center prolate spheroidal coordinates @xcite . furthermore , our results did not show the level of sensitivity to the description of the ground state that was also reported by tao _ et al . _ @xcite . the detailed analysis reported in this study provides a high level of confidence in the present results . we hope that they will be used as benchmarks for comparison in future investigations . tables of these results are available in electronic format from the authors upon request .

we have carried out calculations of the triple - differential cross section for one - photon double ionization of molecular hydrogen for a central photon energy of ev , using a fully _ ab initio _ , nonperturbative approach to solve the time - dependent schrdinger equation in prolate spheroidal coordinates .

we have carried out calculations of the triple - differential cross section for one - photon double ionization of molecular hydrogen for a central photon energy of ev , using a fully _ ab initio _ , nonperturbative approach to solve the time - dependent schrdinger equation in prolate spheroidal coordinates . the spatial coordinates and are discretized in a finite - element discrete - variable representation . the wave packet of the laser - driven two - electron system is propagated in time through an effective short iterative lanczos method to simulate the double ionization of the hydrogen molecule . for both symmetric and asymmetric energy sharing , the present results agree to a satisfactory level with most earlier predictions for the absolute magnitude and the shape of the angular distributions . a notable exception , however , concerns the predictions of the recent time - independent calculations based on the exterior complex scaling method in prolate spheroidal coordinates [ phys . rev . a * 82 * , 023423 ( 2010 ) ] . extensive tests of the numerical implementation were performed , including the effect of truncating the neumann expansion for the dielectronic interaction on the description of the initial bound state and the predicted cross sections . we observe that the dominant escape mode of the two photoelectrons dramatically depends upon the energy sharing . in the parallel geometry , when the ejected electrons are collected along the direction of the laser polarization axis , back - to - back escape is the dominant channel for strongly asymmetric energy sharing , while it is completely forbidden if the two electrons share the excess energy equally .

0804.0880

c

several pieces of evidence for the interaction between the molecular outflow driven by fir 3 and fir 4 clump were found in our observations . the extent of the sw outflow lobe from fir 3 observed in the co ( 10 , 32 ) lines ( @xmath0 0.09 pc ) is shorter than that of the ne lobe ( @xmath0 0.19 pc ) . this suggests that the propagation of the sw outflow is hampered by the material at the head of the outflow , and in fact fir 4 clump locates at the tip of the south - western outflow . these pieces of morphological evidence suggest that the south - western outflow component is dammed by fir 4 clump . we also detected the sio and submillimeter ch@xmath10oh emission at the tip of the south - western outflow . these molecular lines are often observed toward shocked regions , caused by the interaction between outflows and dense gas @xcite . hence , the detection of the sio and submillimeter ch@xmath10oh emission in fir 4 is probably the chemical evidence for the interaction between the molecular outflow and the dense gas . in addition , the line width of the h@xmath2co@xmath3 emission at fir 4 ( dv@xmath86 @xmath0 1.1 km s@xmath20 ) is larger than the average value in other omc-2/3 cores ( dv@xmath86 @xmath0 0.8 km s@xmath20 ; * ? ? ? * ) which may suggest the larger turbulence due to the interaction with the outflow . figure [ pv]a - d show position - velocity ( p - v ) diagrams in the @xmath5co , h@xmath2co@xmath3 , sio , and the ch@xmath10oh emission . the p - v diagrams in the @xmath5co , h@xmath2co@xmath3 , sio , and the ch@xmath10oh emission show successive change of the line width along the direction from fir 3 to fir 4 . first , the @xmath5co ( 10 ) emission shows a distinct l - shaped structure in the p - v diagram , and the location of the line broadening is at the most upstream . second , the ch@xmath10oh emission also shows a similar l - shape with a less broadening , which locates slightly at the downstream from the co l - shape . the sio emission shows the most extreme blueshifted components , which locates at the peak of the blueshifted ch@xmath7oh component . finally , the dense gas component traced by the h@xmath2co@xmath3 emission locates at the most downstream of the successive emission distribution and is pinched by the l - shaped co emission distribution in the p - v diagram . these successive emission distributions and the velocity structures are likely to trace the detail of the interaction . these observational results suggest an interconnection among the molecular outflow , dense gas , and the shock traced by the sio and ch@xmath10oh emission . we consider that these pieces of evidence support the presence of the interaction between the molecular outflow and dense gas . in the last section , we suggest that there is an interaction between the outflow driven by fir 3 and dense gas of fir 4 clump . on the other hand , in @xmath39 3.4 we have demonstrated that fir 4 clump consists of eleven dusty cores . from these results , we presume that the interaction causes the fragmentation of fir 4 clump into these cores and eventually the formation of the next generation of the cluster members . hereafter we will examine this possibility from consideration of the jeans instability , time scale , and the virial analyses . first , we will examine whether the fragmentation into the dusty cores can be caused by the jeans instability , by comparing the average separation of the cores to the jeans length . the average 3-dimensional separation ( @xmath19 @xmath87 ) among these cores can be estimated by the following formula @xcite ; @xmath88 @xmath89 where @xmath90 , @xmath91 , @xmath92 , @xmath93 , and @xmath94 are the volume filling factor , the average radius of the cores , the number of cores , and the average volume of fir4 clump and a single core , respectively . v@xmath95 was estimated from the average of the projected size of the dusty cores ( table [ core ] ) , and v@xmath96 was estimated from the radius of 15@xmath1 , on the assumption of the 3-dimensional spherical symmetry ( see eq . the estimated v@xmath95 , v@xmath96 , and @xmath91 are @xmath97 @xmath98 , @xmath99 @xmath98 , and @xmath100 au , respectively . then , the average separation @xmath87 is estimated to be @xmath0 @xmath101 au . in order to estimate the jeans length ( @xmath19 @xmath102 ) , we use the following equation @xcite ; @xmath103 where @xmath65 , g , and @xmath104 are the effective sound speed , gravitational constant , and the average density of fir 4 clump , respectively . @xmath65 is the effective sound speed in fir 4 clump ( @xmath0 0.62 km s@xmath20 ) derived from equation ( 4 ) , and @xmath104 is estimated to be 9.8 @xmath15 10@xmath105 @xmath82 in @xmath39 3.4 . with these values , the jeans length @xmath106 is estimated to be @xmath0 @xmath107 au , which is on the same order of the average separation of the dusty cores . hence it is possible that the fragmentation of fir 4 clump into cores was caused by the jeans instability . the jeans instability in fir 4 clump may be triggered by the interaction with the outflow from fir 3 , and in the next section we will discuss whether the fragmentation was caused after the interaction between the outflow driven by fir 3 and fir 4 clump . we can estimate the time scale of the fragmentation on the assumption that the fragmentation time scale ( @xmath19 @xmath108 ) is the sound crossing time ; @xmath109 then @xmath108 is estimated to be @xmath0 @xmath110 yr . next , we estimate the time scale of the interaction between the outflow and dense gas , on the assumption that the interaction time scale @xmath111 is similar to the dynamical time @xmath112 of the north - eastern outflow driven by fir 3 , i.e. @xmath111 @xmath0 @xmath112 . @xcite estimated @xmath112 to be @xmath113 yr . then the interaction time scale @xmath111 is estimated to be @xmath113 yr . therefore , the fragmentation time scale ( 3.8 @xmath15 10@xmath114 yr ) is similar to the interaction time scale ( 1.4 @xmath15 10@xmath114 yr ) , and we suggest that the fragmentation was triggered by the interaction with the outflow from fir 3 . moreover , the free - fall time in this region ( @xmath0 1.3 @xmath13 yr ) , which is estimated from the average density of each core ( @xmath0 1.6 @xmath15 10@xmath81 @xmath82 ) , is also similar to the interaction time - scale , and hence it is possible that class 0/i protostars are already formed in the course of the interaction @xcite . in fact , there exists an mir source ( mir 24 ) identified as a class 0 protostar , and it is possible that mir 24 is formed in the course of the interaction . we suggest that in this particular case of fir 4 the interaction between the outflow and the dense gas most likely triggers the fragmentation into cores , while we can not exclude other possibilities such as the induced fragmentation due to the interaction with the hii region ( m43 ) @xcite as well as spontaneous fragmentation due to the gravity @xcite and turbulence @xcite . finally , in order to examine whether these dusty cores have a potential to form protostars inside , we compare the h@xmath26 mass of the cores estimated from the 3.3 mm dust - continuum flux and the virial mass . the virial mass ( @xmath19 m@xmath115 ) is estimated by the following equation ; @xmath116 where @xmath91 , @xmath65 and g are the radius of the core , the effective sound speed ( equation 4 ) and the gravitational constant , respectively . here , we assume that the h@xmath2co@xmath3 emission is associated with all the dusty cores . then we adopted the h@xmath2co@xmath3 line width ( @xmath64 ; see table [ ident ] ) at each peak of the dusty core as the line width in the dusty cores . the estimated virial masses are within the range of the expected h@xmath26 mass of these cores , that is , from m@xmath84 to m@xmath85 ( table [ ident ] ) . these results suggest that the observed dusty cores have a potential to form stars . from the above considerations , we suggest that the interaction between fir 4 clump and the outflow driven by fir 3 caused the fragmentation of fir 4 clump into cores and triggered the next generation of cluster formation . our scenario of the star formation in the fir 4 region is summarized in figure [ scenario ] as ; [ step 1 ] : fir 3 was born and drove the outflow ; [ step 2 ] : the outflow driven by fir 3 started interacting with fir 4 clump ; [ step 3 ] : the interaction caused the fragmentation of fir 4 clump into cores ; [ step 4 ] : these cores will form stars . the present stage of the star formation in the fir 4 region may be between step 3 and step 4 . we speculate that dusty cores will form protostars inside , and eventually , next generation of the stellar cluster in the fir 4 region . possible outflow - triggered star formation has also been reported observationally in ngc 1333 @xcite , l1551 ne @xcite , and ngc 2264 irs 1 @xcite . in ngc 1333 , @xcite found that one of the cores in the 850 @xmath17 m emission ( sk-1 ) locates at the tip of the shell evacuated by the outflow , and they suggest that sk-1 is a possible example of the outflow - triggered star formation . in l 1551 ne , @xcite have found an arc - shape structure of dense gas open toward south - west , or the direction of the molecular outflow driven by l1551 irs 5 , in the cs ( 32 ) emission . they interpret that the dense gas in l1551 ne is affected by the outflow from l1551 irs 5 , creating an arc - shape , and the protostellar formation of l1551 ne . in ngc 2264 irs 1 , @xcite have found that a dense - gas shell seen in the h@xmath2co@xmath3 emission locates around the outflow driven by irs 1 , and at the inner edge of the dense shell there are three compact cores . they suggest that these cores are entrained or compressed material formed by the outflow and that these cores may represent future sites of the formation of a group of the low - mass stars . our observational studies in the omc-2 fir 3/4 region have suggested that the interaction between the outflow and dense gas can cause the formation of stellar clusters . recent 3-dimensional mhd simulations by @xcite suggest that protostellar outflows can trigger cluster formation through shock compression , providing a theoretical support to our scenario .

furthermore , theco (=10 ) emission shows an l - shaped structure in the p - v diagram . these results imply presence of the shock due to the interaction between the molecular outflow driven by fir 3 and the dense gas associated with fir 4 . we suggest that the interaction between the molecular outflow from fir 3 and the dense gas at fir 4 triggered the fragmentation into these dusty cores , and hence the next generation of the cluster formation in fir 4 .

we have carried out millimeter interferometric observations of the orion molecular cloud-2 ( omc-2 ) fir 3/4 region at an angular resolution of 3 - 7 with the nobeyama millimeter array ( nma ) in the hco (=10 ) ,co (=10 ) , sio (=0 ,=21 ) , and cs (=21 ) lines and in the 3.3 mm continuum emission . submillimeter single - dish observations of the same region have also been performed with atacama submillimeter telescope experiment ( aste ) in theco (=32 ) and choh (=7 ) lines . our nma observations in the hco emission have revealed 0.07 pc - scale dense gas associated with fir 4 . theco (=32,10 ) emission shows high - velocity blue and red shifted components at the both north - east and south - west of fir 3 , suggesting a molecular outflow nearly along the plane of the sky driven by fir 3 . the sio (=0 ,=21 ) and the submillimeter choh (=7 ) emission , known as shock tracers , are detected around the interface between the outflow and the dense gas . furthermore , theco (=10 ) emission shows an l - shaped structure in the p - v diagram . these results imply presence of the shock due to the interaction between the molecular outflow driven by fir 3 and the dense gas associated with fir 4 . moreover , our high angular - resolution ( 3 ) observations of fir 4 in the 3.3 mm continuum emission with the nma have first found that fir 4 consists of eleven dusty cores with a size of 1500 - 4000 au and a mass of 0.2 - 1.4 m . the separation among these cores ( 5 au ) is on the same order of the jeans length ( 13 au ) , suggesting that the fragmentation into these cores has been caused by the gravitational instability . the time scale of the fragmentation ( 3.8 yr ) , estimated from the separation divided by the sound speed , is similar to the time scale of the interaction between the molecular outflow and the dense gas ( 1.4 yr ) . we suggest that the interaction between the molecular outflow from fir 3 and the dense gas at fir 4 triggered the fragmentation into these dusty cores , and hence the next generation of the cluster formation in fir 4 .

0804.0880

i

we have carried out high angular - resolution ( @xmath0 3@xmath1 - 7@xmath1 ) millimeter interferometric observations of omc-2 fir 3/4 with the nma in the h@xmath2co@xmath3 ( @xmath4=10 ) , @xmath5co ( @xmath4=10 ) , cs ( @xmath4=21 ) , and sio ( @xmath6=0 , @xmath4=21 ) lines as well as in the 3.3 mm continuum emission , and submillimeter single - dish observations with aste in the @xmath5co ( @xmath4=32 ) and ch@xmath7oh ( @xmath8=@xmath117@xmath118 ) lines . the main results of our new millimeter and submillimeter observations are summarized as follows : 1 . we suggest that the outflow driven by fir 3 interacts with the 0.07 pc - scale dense gas associated with fir 4 ( @xmath19 fir 4 clump ) , from morphological , kinematical , chemical and physical evidence . in the morphological evidence , we found that the length of the sw outflow lobe from fir 3 observed in the co ( 10 , 32 ) lines ( @xmath0 0.09 pc ) is shorter than that of the ne lobe ( @xmath0 0.19 pc ) , and fir 4 clump is located at the tip of the sw molecular outflow . these results suggest that the sw lobe has been dammed by the interaction with fir 4 clump . in the chemical and physical evidence , we detected the sio ( @xmath6=0 , @xmath4=2 - 1 ) emission and the submillimeter ch@xmath7oh ( @xmath8=7@xmath9 - 6@xmath9 ; k=-1,0,2 ) emission around fir 4 clump , which are known to trace shocks caused by the interaction between outflows and dense cores . in the kinematical evidence , the p - v diagrams in the @xmath5co , ch@xmath10oh , sio , and h@xmath2co@xmath3 emission show a successive change of the line width along the direction from fir 3 to fir 4 . the @xmath5co ( 10 ) emission show a distinct l - shaped structure in the p - v diagram , and the location of the broadening is at the most upstream . the ch@xmath10oh emission also shows a similar l - shape at the downstream from the co l - shape , and the sio emission shows the most blueshifted component at the peak of the blueshifted ch@xmath7oh component . the dense gas component traced by the h@xmath2co@xmath3 emission locates at the most downstream of the successive emission distribution and is pinched by the l - shaped co emission distribution in the p - v diagram . these results indicate the presence of the interaction between the outflow and dense gas in fir 4 . 2 . in the 3.3-mm continuum emission , we have first resolved fir 4 clump into eleven dusty cores with a size of 1500 - 4000 au and a mass of 0.2 - 1.4 m@xmath11 . the 3-dementinal separation among these cores , 5000 au , is on the same order of the jeans length , 13000 au . moreover , the estimated time scale of the fragmentation into the cores , 3.8 @xmath119 yr , is also similar to the time scale of the interaction between fir 4 clump and the outflow from fir 3 , that is , 1.4 @xmath13 yr . therefore , it is possible that the fragmentation of fir 4 clump into the cores has been caused by the jeans instability triggered by the interaction with the outflow driven by fir 3 . we suggest that in this particular case of fir 4 the outflow interaction most likely triggers the fragmentation into cores . we speculate that the dusty cores in fir 4 will form protostellar sources eventually , and that the fir 4 region is in the course of cluster formation . we suggest that the outflow driven by fir 3 triggered the next generation of the cluster formation in the fir 4 region , and that the fir 4 region is one of the promising samples of the outflow - triggered cluster formation . we are grateful to the staffs at the nobeyama radio observatory ( nro ) for both operating the nma and helping us with the data reduction , and to m. yamada , y. kurono , and t. tsukagoshi for their helpful comments . nro is a branch of the national astronomical observatory , national institutes of natural sciences , japan . we also acknowledge the aste staffs for both operating aste and helping us with the data reduction . we would like to thank the anonymous referee for providing helpful suggestions to improve the paper . observations with aste were ( in part ) carried out remotely from japan by using ntt s gemnet2 and its partner r&e ( research and education ) networks , which are based on accessnova collaboration of university of chile , ntt laboratories , and national astronomical observatory of japan . this work was supported by grant - in - aid for scientific research a 18204017 . aso , y. , tatematsu , k. , sekimoto , y. , nakano , t. , umemoto , t. , koyama , k. , & yamamoto , s. 2000 , , 131 , 465 avery , l. w. , & chiao , m. 1996 , , 463 , 642 bachiller , r. , prez gutirrez , m. , kumar , m. s. n. , & tafalla , m. 2001 , , 372 , 899 bergin , e. a. , neufeld , d. a. , & melnick , g. j. 1998 , , 499 , 777 chini , r. , reipurth , b. , ward - 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115 & 3.0 - 30.8 & 2.9 - 23.4 & 3.2 - 113.6 + phase reference center ( j2000 ) & + primary beam hpbw [ arcsec ] & 77@xmath1 & 62@xmath1 & 77@xmath1 & 70@xmath1 + synthesized beam hpbw [ arcsec ] & 9@xmath3654@xmath1225@xmath3615 & 6@xmath3659@xmath15 5@xmath3679 & 10@xmath3622 @xmath15 6@xmath3637 & 6@xmath3668 @xmath15 4@xmath3600 + velocity resolution [ km s@xmath20 ] & 0.108 km s@xmath20 & 0.406 km s@xmath20 & 0.539 km s@xmath20 & 48.94 km s@xmath20 + gain calibrator@xmath123 & + bandpass calibrator@xmath124 & 3c273 , 0420 - 014 , 3c84 , 0528 + 134 & 3c273 , 3c84 & 3c273 , 3c84 & 3c273 , 0420 - 014 , 3c84 , 0528 + 134 + system temperature in dsb [ k]@xmath125 & 100 - 400 k & 150 - 300 k & 100 - 350 k & 100 - 400 k + rms noise level [ jy beam @xmath20 ] & 1.2@xmath12210@xmath20 jy beam @xmath20 & 5.7@xmath12210@xmath20 jy beam @xmath20 & 2.0@xmath12210@xmath20 jy beam @xmath20 & 5.1@xmath12210@xmath127 jy beam @xmath20 + [ nmaobs ] lcc baseline [ k@xmath22 ] & 2.9 - 115 & 2.9 - 115 + weighting & natural & uniform + beamsize ( hpbw ) [ arcsec ] & 6@xmath3696@xmath122 4@xmath3603 ( p.a.=-34.59@xmath34 ) & 6@xmath3655@xmath1223@xmath3634 ( p.a.=-40.31@xmath34 ) + p.a . of the beam [ @xmath34 ] & -34.59 & -40.31 + rms noise level [ jy beam@xmath20 ] & 1.2@xmath12210@xmath127 & 1.4@xmath12210@xmath127 + [ continuumobs ] lcccccccccc fir 3 & 05@xmath129 35@xmath130 27@xmath326 & -05@xmath34 09@xmath35 34@xmath360 & 11.7@xmath153.6 & 140.46 & 3.0 & 18.7 & 3.1 & & & + fir 4a@xmath131 & 05 35 27.4 & -05 09 49.0 & 5.4@xmath153.5 & 34.05 & 0.51 & 3.2 & 1.8 & 1.1 & 0.53 & 0.47 + fir 4b@xmath131 & 05 35 26.6 & -05 09 51.0 & 6.3@xmath153.9 & 150.20 & 1.1 & 6.9 & 2.6 & 2.6 & 1.28 & 0.68 + fir 4c & 05 35 27.0 & -05 09 54.0 & 9.0@xmath154.0 & 168.88 & 0.45 & 5.9 & 0.59 & 1.6 & 0.57 & 0.48 + fir 4d & 05 35 26.2 & -05 09 55.9 & 4.7@xmath154.4 & 139.87 & 0.76 & 9.6 & 2.2 & 1.2 & 0.55 & 0.47 + fir 4e & 05 35 26.9 & -05 09 57.5 & 8.4@xmath155.7 & 4.302 & 1.0 & 14.3 & 0.93 & 3.8 & 1.31 & 0.69 + fir 4f & 05 35 26.6 & -05 09 58.9 & 6.1@xmath153.1 & 168.26 & 0.6 & 7.8 & 2.0 & 1.7 & 0.98 & 0.59 + fir 4g@xmath131 & 05 35 26.6 & -05 09 59.4 & 8.3@xmath155.0 & 179.53 & 1.2 & 7.5 & 1.3 & 2.1 & 0.81 & 0.54 + fir 4h & 05 35 27.1 & -05 10 04.5 & 7.1@xmath155.7 & 156.55 & 0.64 & 8.3 & 0.70 & 3.3 & 1.25 & 0.67 + fir 4i & 05 35 26.5 & -05 10 06.0 & 6.5@xmath154.8 & 162.23 & 0.21 & 2.7 & 0.34 & 1.7 & 0.70 & 0.50 + fir 4j@xmath131 & 05 35 27.2 & -05 10 08.0 & 5.6@xmath154.0 & 111.31 & 1.38 & 8.8 & 3.7 & 1.7 & 0.90 & 0.56 + fir 4k@xmath131 & 05 35 26.3 & -05 10 16.4 & 6.35@xmath153.91 & 165.76 & 0.67 & 4.2 & 1.5 & 2.1 & 1.07 & 0.61 + fir 4 clump & & & & & 9.4 & 58.6 & 0.098@xmath132 & & & + [ core ] [ ident ] co ( @xmath4=32 ) ( left ) and @xmath5co ( @xmath4=10 ) ( right ) emission in the omc-2/fir 4 region . panel ( a ) and ( c ) show the distribution of the blue ( -9.5 km s@xmath20 - 4.6 km s@xmath20 ) and red ( 16.4 km s@xmath20 - 29.4 km s@xmath20 ) lobe in the @xmath5co ( @xmath4=32 ) line observed with aste @xcite , while panel ( b ) and ( d ) show the distribution of the blue ( 3.7 km s@xmath20 to 6.1 km s@xmath20 ) and red ( 15.1 km s@xmath20 to 18.3 km s@xmath20 ) lobe in the @xmath5co ( @xmath4=10 ) line observed with the nma , respectively . open black circles show the field of view of the nma observations , green crosses the position of mir sources @xcite , blue circles the position of 3.6 cm free - free sources @xcite , and red squares the peak position of the 1.3 mm dust - continuum emission @xcite . filled ellipses at the bottom left corner of each panel indicate the beam size . contour levels of these maps start at @xmath133 5 @xmath27 levels with an interval of 5 @xmath27 . the rms noise levels ( 1 @xmath27 ) of the panel ( a ) , ( b ) , ( c ) and ( d ) are 1.2 k , 0.45 jy , 1.2 k , and 0.70 jy beam@xmath20 , respectively.,width=415 ] co ( @xmath4=32 ; 345.705 ghz ) spectrum at fir 4 taken with aste @xcite the rms noise level ( 1@xmath68 ) is 0.5 k in t@xmath134 at a velocity resolution of 1.1 km s@xmath20 . a dashed line shows the systemic velocity ( @xmath0 11.3 km s@xmath20 ) , obtained from the gaussian fit to the spectrum.,width=566 ] = 21 ) emission in the omc-2/fir 4 region , obtained with the nma . symbols in the figure are the same as in figure [ line_map_co ] . contour levels of this map start at @xmath133 3 @xmath27 levels with an interval of 1 @xmath27 . the rms noise level ( 1 @xmath27 ) of this map is 5.1@xmath1510@xmath127 jy beam@xmath20 . , width=566 ] co@xmath3 ( @xmath4=10 ) emission ( left ) , and maps of the blueshifted ( 10.5 - 11.2 km s@xmath20 ) the redshifted ( 11.3 - 12.4 km s@xmath20 ) h@xmath2co@xmath3 components ( right ) in the fir 4 region , obtained with nma . symbols in the figure are the same as in figure [ line_map_co ] . contour levels of these maps start at @xmath133 3 @xmath68 levels with an interval of 1 @xmath27 . the rms noise levels ( 1 @xmath27 ) in panel ( a ) , the blue and red contour in panel ( b ) are 0.81 , 0.49 and 0.49 jy beam@xmath20 , respectively . , width=566 ] oh ( @xmath8=7@xmath256@xmath25 ) and nma sio ( @xmath6=0 , @xmath4=21 ) maps in the fir 4 region . panel ( a ) and ( b ) show the distribution of the blue ( 5.7 km s@xmath20 - 9.9 km s@xmath20 ) and red ( 13.1 km s@xmath20 - 14.2 km s@xmath20 ) lobe in the ch@xmath7oh ( @xmath8=7@xmath256@xmath25 ) line , respectively . panel ( c ) shows the distribution of the blue lobe in the sio ( @xmath6=0 , @xmath4=21 ) line at a velocity range from 3.4 km s@xmath20 to 6.1 km s@xmath20 . symbols in the figure are the same as in figure [ line_map_co ] . contour levels in panel ( a ) and ( b ) start at @xmath133 5 @xmath27 levels with an interval of 5 @xmath27 . contour levels in panel ( c ) start at @xmath133 3 @xmath68 levels with an interval of 1 @xmath68 . the rms noise levels ( 1 @xmath27 ) in panel ( a ) , ( b ) and ( c ) are 0.024 , 0.015 k , and 0.11 jy beam@xmath20 , respectively.,width=566 ] oh ( @xmath8=7@xmath256@xmath25 ; 338.408 ghz ) spectrum at fir 4 taken with aste . the rms noise level ( 1@xmath27 ) is 0.17 k in t@xmath135 at a velocity resolution of 0.5 km s@xmath20 . a dashed line shows the systemic velocity ( @xmath0 11.3 km s@xmath20 ) in the fir 4 region estimated from the nma h@xmath2co@xmath3 spectrum.,width=566 ] . contour levels start at @xmath133 3 @xmath68 noise levels with an interval of 1 @xmath68 . the rms noise level ( 1 @xmath68 ) in panel ( a ) and ( b ) are 1.2@xmath1510@xmath127 and 1.4@xmath1510@xmath127 jy beam@xmath20 , respectively . , width=566 ] co ( @xmath4=10 ) ( upper left ) , h@xmath2co@xmath3 ( @xmath4=10 ) ( upper right ) , sio ( @xmath6=0 , @xmath4=21 ) ( lower left ) and ch@xmath7oh ( @xmath8=7@xmath256@xmath25 ) ( lower right ) emission in the fir 4 region . two horizontal lines in each panel show the position of fir 3 and fir 4 , while a vertical line the systemic velocity of 11.3 km s@xmath20 in fir 4 estimated from the h@xmath2co@xmath3 data . the cut line of panel ( a ) , ( b ) , and ( d ) is adopted to be along p.a . = 30@xmath34 , passing through the position of fir 3 and fir 4 . the cut line of panel ( c ) is taken to be along p.a . = 35@xmath34 , passing through the compact sio emission and fir 3 . contour levels in panel ( a ) and ( d ) start at @xmath133 5 @xmath27 levels with an interval of 5 @xmath27 . contour levels in panel ( b ) start at @xmath133 3 @xmath27 levels with an interval of 3 @xmath27 . contour levels in panel ( c ) start at @xmath133 2 @xmath27 levels with an interval of 1 @xmath27 . the rms noise level ( 1 @xmath27 ) in panel ( a)-(d ) are 0.57 jy beam@xmath20 , 0.12 jy beam@xmath20 , 0.2 jy beam@xmath20 , and 0.17k , respectively . ,

we have carried out millimeter interferometric observations of the orion molecular cloud-2 ( omc-2 ) fir 3/4 region at an angular resolution of 3 - 7 with the nobeyama millimeter array ( nma ) in the hco (=10 ) ,co (=10 ) , sio (=0 ,=21 ) , and cs (=21 ) lines and in the 3.3 mm continuum emission . our nma observations in the hco emission have revealed 0.07 pc - scale dense gas associated with fir 4 . the sio (=0 ,=21 ) and the submillimeter choh (=7 ) emission , known as shock tracers , are detected around the interface between the outflow and the dense gas . moreover , our high angular - resolution ( 3 ) observations of fir 4 in the 3.3 mm continuum emission with the nma have first found that fir 4 consists of eleven dusty cores with a size of 1500 - 4000 au and a mass of 0.2 - 1.4 m . the separation among these cores ( 5 au ) is on the same order of the jeans length ( 13 au ) , suggesting that the fragmentation into these cores has been caused by the gravitational instability . the time scale of the fragmentation ( 3.8 yr ) , estimated from the separation divided by the sound speed , is similar to the time scale of the interaction between the molecular outflow and the dense gas ( 1.4 yr ) .

we have carried out millimeter interferometric observations of the orion molecular cloud-2 ( omc-2 ) fir 3/4 region at an angular resolution of 3 - 7 with the nobeyama millimeter array ( nma ) in the hco (=10 ) ,co (=10 ) , sio (=0 ,=21 ) , and cs (=21 ) lines and in the 3.3 mm continuum emission . submillimeter single - dish observations of the same region have also been performed with atacama submillimeter telescope experiment ( aste ) in theco (=32 ) and choh (=7 ) lines . our nma observations in the hco emission have revealed 0.07 pc - scale dense gas associated with fir 4 . theco (=32,10 ) emission shows high - velocity blue and red shifted components at the both north - east and south - west of fir 3 , suggesting a molecular outflow nearly along the plane of the sky driven by fir 3 . the sio (=0 ,=21 ) and the submillimeter choh (=7 ) emission , known as shock tracers , are detected around the interface between the outflow and the dense gas . furthermore , theco (=10 ) emission shows an l - shaped structure in the p - v diagram . these results imply presence of the shock due to the interaction between the molecular outflow driven by fir 3 and the dense gas associated with fir 4 . moreover , our high angular - resolution ( 3 ) observations of fir 4 in the 3.3 mm continuum emission with the nma have first found that fir 4 consists of eleven dusty cores with a size of 1500 - 4000 au and a mass of 0.2 - 1.4 m . the separation among these cores ( 5 au ) is on the same order of the jeans length ( 13 au ) , suggesting that the fragmentation into these cores has been caused by the gravitational instability . the time scale of the fragmentation ( 3.8 yr ) , estimated from the separation divided by the sound speed , is similar to the time scale of the interaction between the molecular outflow and the dense gas ( 1.4 yr ) . we suggest that the interaction between the molecular outflow from fir 3 and the dense gas at fir 4 triggered the fragmentation into these dusty cores , and hence the next generation of the cluster formation in fir 4 .

1005.3619

i

studies of galactic chemical evolution are dependent on accurately derived abundances of stars spanning all ages , populations , kinematics , masses , and metallicities . stars with masses @xmath7 are especially important given their dominance of the initial mass function ( imf ; e.g. , * ? ? ? abundance studies utilizing high - resolution spectroscopy and local thermodynamic equilibrium ( lte ) analyses of near - solar metallicity g and k dwarfs in open clusters and in the disk field , however , have revealed that the observed abundances of at least some elements derived for these cool main sequence ( ms ) dwarfs may be spurious . in particular , studies have found evidence of over - ionization and over - excitation , i.e. , larger abundances are derived from lines of singly ionized species compared to neutral species and from high - excitation lines of neutral species compared to low - excitation lines , respectively . the first indication that some abundances derived for cool ms stars are problematic may have come from @xcite , who found the over - ionization of sc , ti , cr , and fe for a sample of 10 k dwarfs ( @xmath8 @xmath0@xmath9 k ) in the solar neighborhood . after a careful analysis of the procedures and stellar parameters used in the abundance derivations , the author was unable to account for the overabundances of the ionized species . found similar over - ionization results for sc , v , cr , fe , and y in five field k dwarfs ( @xmath10 @xmath0 @xmath11 k ) . the authors could not exclude an inaccurate temperature scale that is several hundred k too low as a possible source of the anomalous abundances , but in the end , they suggest that non - lte ( nlte ) effects are the more likely cause . open clusters have been important to the identification and continued study of the over - excitation / ionization effects , because the presumed internal chemical homogeneity of the clusters provides a baseline with which anomalous abundances can be compared . @xcite derived o abundances from the high - excitation ( @xmath12 ev ) near - ir triplet of a k dwarf in each of the the pleiades and ngc 2264 open clusters , and in both cases , the abundances were highly enhanced : [ o / h ] @xmath13 and @xmath14 , respectively . such high o abundances are not expected for clusters with nominal metallicities of [ fe / h ] @xmath15 @xcite and -0.15 @xcite , respectively . following @xcite , @xcite derived the abundances of ms dwarfs in the m34 cluster ; over - ionization of fe and over - excitation of si ( the abundances of which were derived from lines with excitation potentials in the range @xmath16 ev ) are seen in the coolest stars of the sample . oxygen abundances of the cool m34 dwarfs , as well as cool pleiades dwarfs , derived from the high - excitation triplet are also highly enhanced @xcite , confirming the earlier results of @xcite . subsequent to these early open cluster studies , the over - ionization of fe has been confirmed in the hyades @xcite and ursa major ( uma ) moving group @xcite , and of ti in the young pre - ms clusters ic2602 and ic2391 . overabundances of o derived from the triplet have been reported for the uma moving group @xcite , the hyades @xcite , and ic4665 @xcite . over - excitation effects have been reported for other elements , as well , including s in the pleiades @xcite , si , ti , ni , and cr in ic4665 @xcite , ni in the hyades @xcite , and ca , ti , and na in ic2602 and ic2391 . recent abundance analyses of cool field stars have also identified over - excitation / ionization effects , confirming the findings of earlier work . the over - excitation / ionization abundance anomalies are not thought to represent real photospheric overabundances ; rather , we believe that they are a signal that our knowledge of cool dwarf atmospheres and/or spectral line formation therein is incomplete . as of yet , the source or cause of the effects has not been identified . systematically erroneous stellar parameters , e.g. , an inaccurate @xmath0 scale , could lead to the observed abundance trends , but in general , unrealistically large parameter errors would have to be present ( e.g. , * ? ? ? * ; * ? ? ? furthermore , parameter changes made in response to the overabundances of one element often increase those of another ( e.g. , * ? ? ? nlte effects have been suggested as the cause , but in general , the over - excitation / ionization effects seen in cool dwarfs are in stark contrast to extant nlte calculations . for instance , lte analyses of the high - excitation triplet in the spectra of ms dwarfs are predicted to result in increasingly discrepant abundances with increasing @xmath0 for stars with @xmath0 @xmath17 k , requiring negative nlte corrections up to 0.4 0.5 dex at 6500 k for solar metallicity dwarfs . below 6000 k , the nlte corrections are predicted to be @xmath18 dex and essentially zero below 5500 k . chromospheric emission and photospheric activity ( spots , plages , and faculae ) have also been suggested sources for the abundance anomalies ( e.g. , * ? ? ? these inhomogeneities could produce apparent over - excitation / ionization effects within a strict lte framework . continuing our efforts to delineate and understand the observed over - excitation / ionization effects in cool ms dwarfs , we have derived and abundances of 16 pleiades dwarfs , 15 of which have had o abundances derived from the high - excitation triplet @xcite . the abundances evince a steep increase , reaching [ o / h ] @xmath19 dex near 5000 k , and star - to - star dispersion below 5500 k. we use the newly derived pleiades fe abundances to investigate if the over - excitation and over - ionization effects observed in cool ms dwarfs are related and indeed manifestations of the same phenomenon . future observational studies that could place stringent constraints on these effects and bring us closer to discovering the source of the anomalous abundances are also discussed .

oxygen abundances of our pleiades sample derived from the high - excitation triplet have been previously shown to increase with decreasing , and a comparison with the abundances suggests that the over - excitation ( larger abundances derived from high excitation lines relative to low excitation lines ) and over - ionization effects that have been observed in cool open cluster and disk field main sequence ( ms ) dwarfs share a common origin . the cool star [ /h ] abundances can not be connected directly to over - excitation effects , but similarities with the and triplet trends suggest the abundances are dubious . using the [ /h ] abundances of five stars with k , we derive a mean pleiades cluster metallicity of [ fe / h ] .

we have derived fe abundances of 16 solar - type pleiades dwarfs by means of an equivalent width analysis of and lines in high - resolution spectra obtained with the hobby - eberly telescope and high resolution spectrograph . abundances derived from lines are larger than those derived from lines ( herein referred to as over - ionization ) for stars with k , and the discrepancy ( = [ /h ] - [ /h ] ) increases dramatically with decreasing , reaching over 0.8 dex for the coolest stars of our sample . the pleiades joins the open clusters m34 , the hyades , ic2602 , and ic2391 , and the ursa major moving group , demonstrating ostensible over - ionization trends . the pleiades abundances are correlated with infrared triplet and h chromospheric emission indicators and relative differences therein . oxygen abundances of our pleiades sample derived from the high - excitation triplet have been previously shown to increase with decreasing , and a comparison with the abundances suggests that the over - excitation ( larger abundances derived from high excitation lines relative to low excitation lines ) and over - ionization effects that have been observed in cool open cluster and disk field main sequence ( ms ) dwarfs share a common origin . curiously , a correlation between the pleiades abundances and chromospheric emission indicators does not exist . star - to - star abundances have low internal scatter ( dex ) , but the abundances of stars with k are systematically higher compared to the warmer stars . the cool star [ /h ] abundances can not be connected directly to over - excitation effects , but similarities with the and triplet trends suggest the abundances are dubious . using the [ /h ] abundances of five stars with k , we derive a mean pleiades cluster metallicity of [ fe / h ] .

1005.3619

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line - by - line abundances derived for each of our pleiades stars are listed in tables 2 4 , and the stellar mean abundances can be found in table 5 . the final mean abundances are given relative to solar values ( table 2 ) derived via an ew analysis of sky spectra obtained with the het / hrs as part of our observational program . the relative abundances are determined on a line - by - line basis before the mean is taken ; this strict line - by - line abundance analysis ensures that the final relative abundances are independent of the adopted oscillator strengths . the adopted solar parameters are included in table 1 . the mean [ /h ] abundances and the differences in the mean [ /h ] and [ /h ] abundances ( @xmath29 [ /h ] - [ /h ] ) are plotted in figure 1 along with errorbars for three representative stars h ii 263 , h ii 2284 , and h ii 3179 that run the @xmath0 range of our sample . the errorbars denote the total internal uncertainties ( @xmath30 ) in the derived abundances . the @xmath30 uncertainties are the quadratic sum of the abundance uncertainties resulting from errors in the adopted stellar parameters @xcite and the uncertainty in the mean abundance ( table 5 ) . abundance sensitivities to the stellar parameters were determined by individually altering effective temperature ( @xmath31 ) , surface gravity ( @xmath32 ) , and microturbulent velocity ( @xmath33 ) and are given in table 6 . the @xmath30 uncertainties in the abundances for the three representative stars are @xmath34 , @xmath35 , and @xmath36 dex for h ii 263 , h ii 2284 , and h ii 3179 , respectively . for , the @xmath30 uncertainties are @xmath37 , @xmath38 , and @xmath39 , respectively . the errorbars for the [ /h ] - [ /h ] abundances shown in figure 1 represent the quadratically combined and individual @xmath30 uncertainties . the star - to - star [ /h ] abundances fall within a narrow range of 0.11 dex and have a standard deviation in the mean of 0.04 dex . however , as can been seen in the left panel of figure 1 , the [ /h ] abundances of stars with @xmath0 @xmath1 k are systematically higher than those of stars at higher @xmath0 . the discord is verified by the spearman rank correlation coefficient ( @xmath40 ) at the 99.97% confidence level . in the right panel of figure 1 , @xmath2 abundances evince a dramatic increase at about the same @xmath0 , 5400 k. the @xmath2 abundances result from large overabundances of among the cool dwarfs ( table 5 ) , and the @xmath2 vs. @xmath0 trend for the pleiades is similar to those seen in m34 @xcite , the hyades @xcite , and the uma moving group @xcite . the increase in @xmath2 with decreasing @xmath0 presented here resembles the trend of increasing pleiades o abundances derived from the high - excitation triplet @xcite . in particular , the increase in the triplet abundances also begins to become significant at approximately 5400 k. in figure 2 @xmath2is plotted against the triplet abundances ( [ o / h]@xmath41 ) , and it is seen that a strong correlation between these two abundance anomalies does exist . according to the linear correlation coefficient ( @xmath42 ) , @xmath2 and [ o / h]@xmath41 are correlated at a greater than 99.9% confidence level . also in figure 2 we plot the _ residuals _ in the @xmath2 and [ o / h]@xmath41 abundances . the residuals are differences between the observed abundances and @xmath0-dependent fitted values calculated by fitting low - order ( second or third ) polynomials to the abundance versus @xmath0 relations ( figure 3 ) ; the fitted values are determined at each stellar @xmath0 . this procedure effectively removes the global mass dependence of the abundances so that the residuals are a measure of star - to - star abundance scatter at a given @xmath0 @xcite . similar to the @xmath2 and [ o / h]@xmath41 abundances , their residuals are correlated , but at a slightly lower confidence level , 97% ( @xmath43 ) . the strong relationship between the @xmath2 and [ o / h]@xmath41 abundances and especially their residuals suggests the anomalous abundances share a common origin . inaccurate @xmath0 scales can give rise to @xmath0-dependent abundance trends if the scales are in error in a systematic way . @xcite have raised concern as to the accuracy of color - temperature relations , like the one used for our pleiades sample , arguing that disagreements between observed open cluster color - magnitude diagrams ( cmds ) and theoretical isochrones based on color - temperature relations likely arise from systematic errors in the latter . @xcite are able to obtain near - perfect agreement between the observed cmds of four nearby open clusters and isochrones using empirical corrections to the color - temperature relations as suggested by @xcite . inaccurate @xmath0 scales , however , do not appear to be at the root of the over - excitation / ionization effects observed among cool open cluster dwarfs . the pleiades and hyades [ o / h]@xmath41 abundances of @xcite and @xcite , respectively , were derived using color - temperature relations _ and _ empirically corrected isochrones , and in both cases , the steep trends of increasing abundances with decreasing @xmath0 are present . the @xmath0 from the empirically corrected isochrones for the majority of dwarfs in both clusters are higher than those from the color - temperature relations , with the differences reaching a maximum of about 190 k. temperature corrections of this magnitude also do not alleviate the large @xmath2 abundances of the coolest stars in our sample . according to the abundance sensitivities given in table 6 , the @xmath0 of h ii 263 ( @xmath0 @xmath44 k ) would have to be higher by approximately 750 k in order to bring its and abundances into agreement ; such errors in our adopted temperature scale are not expected @xcite . furthermore , increasing the @xmath0 of h ii 263 by 750 k would result in an 0.15 dex increase in its abundance and exacerbate the disagreement in the [ /h ] abundances of the cool and warm dwarfs . whatever the cause of the anomalous @xmath2 abundances , the phenomenon may also be affecting the [ /h ] abundances of the pleiads with @xmath0 @xmath1 k. @xcite found that the abundances of the two coolest m34 dwarfs ( @xmath45 k ) they analyzed are higher by about 0.1 dex than those of the rest of the sample ; the lines have excitation potentials of @xmath46 ev . similarly , hyades abundances derived from lines with excitation potentials of approximately 4.25 ev increase with decreasing @xmath0 for dwarfs with @xmath0 @xmath47 k @xcite . more interestingly , the abundances of a single cool hyades dwarf ( @xmath0 @xmath48 k ) derived from lines with excitation potentials of @xmath49 ev were approximately 0.15 dex higher than the abundance derived from a line with a low excitation potential ( @xmath50 ev ) . for a warmer dwarf ( @xmath0 @xmath51 k ) , consistent abundances were obtained from all of the lines ( please see figure 7 of schuler et al . ) . similar behavior is not seen here in the line - by - line abundances of individual pleiads ( figure 4 ) . however , identifying such excitation potential - related effects for a given cool pleiades star is difficult , because the standard deviation , a measure of the dispersion in the line - by - line abundances , in the mean [ /h ] abundance of each pleiad ranges from 0.04 to 0.13 dex and has an average of 0.07 dex . this is of the order of the effect seen among the cooler stars in m34 and hyades dwarfs , for which the effect is expected to be more severe . thus , a direct connection between the heightened mean [ /h ] abundances and the over - excitation phenomenon can not be made , but nonetheless , the fact that the [ /h ] abundances increase at the same @xmath0 as @xmath2 and the triplet abundances is intriguing and suggests that they all are the result of the same effect . intercluster comparisons of the cool cluster dwarf abundance anomalies can provide valuable insight into the nature of the over - excitation / ionization effects by potentially linking differences in abundance trend morphologies to differences in the physical characteristics of the clusters , such as age and metallicity . in figure 5 the pleiades @xmath2 values along with those of the hyades from @xcite are plotted versus @xmath0 . the @xmath2 abundances of these two clusters follow the same trend down to a @xmath0 of about 5200 k , below which the pleiades abundances clearly diverge . similar behavior is seen in the abundances of dwarfs in the hyades , pleiades and uma moving group @xcite . the abundances of stars in all three associations increase at similar rates down to a @xmath0 of about 5200 k , below which the pleiades trend becomes much steeper than both of those of the hyades and uma , which continue to track each other . the uma moving group has an age that is comparable to that of the hyades @xcite and a metallicity that is lower than both pleiades and hyades @xcite . the divergence of the pleiades triplet abundances from those of both the hyades and uma suggests that the abundance trends may undergo an age - related diminution ; the @xmath2 abundances of the pleiades and hyades are consistent with this conclusion . chromospheric emission and photospheric spots are two age - related phenomena that have been discussed in the literature as possible sources of the observed over - excitation / ionization effects . @xcite demonstrated using multicomponent model atmospheres that spotted photospheres can plausibly account for the triplet abundances of the cool hyades dwarfs . results from efforts investigating a possible connection between chromospheric activity and the anomalous triplet abundances of cool dwarfs , on the other hand , have been mixed . no correlation between h@xmath3 and infrared triplet emission measures and triplet abundances of pleiades dwarfs nor m34 dwarfs exists @xcite . however , found a strong correlation between x - ray activity indicators and pleiades triplet abundances taken from the literature . there is no correlation between h+k emission indicators and the hyades triplet abundances @xcite . for the young cluster ic4665 , @xcite show that the abundances of the cool dwarfs are highly correlated with both h@xmath3 and infrared triplet emission indicators . it is important to note that shen et al . is the only of these studies that derived the abundances and chromospheric emission levels from the same spectra . for the others , the measurements were made or taken from different sources , and thus the actual chromospheric emission level may have been different when the spectral lines were formed . as can be seen from these various studies , it is not clear if there is a connection between chromospheric emission and the over - excitation of . furthermore , chromospheric emission is often correlated with @xmath0 , so any correlation between chromospheric emission and abundances may be masking some other @xmath0-dependent effect @xcite . using the chromospheric emission data from @xcite , we have plotted the pleiades @xmath2 versus infrared triplet chromospheric emission indicators ( @xmath52 ) in figure 6 and find a correlation that is significant at greater than the 99.9% confidence level according to the linear correlation coefficient ( @xmath53 ) . a similar correlation is found for the h@xmath3 chromospheric emission ( @xmath54 ) . these correlations , while suggestive of a connection between chromospheric emission and the over - ionization of fe , should be viewed with caution , because @xmath54 and @xmath52 are also correlated with @xmath0 at approximately the 93% and 98% confidence levels . this degeneracy makes it unclear if the @xmath2 abundances , like those of , are affected by chromospheric emission or some other @xmath0-dependent effect . more importantly , residual @xmath2 abundances and residual chromospheric emission indicators ( calculated in the same manner as the abundance residuals , i.e. , they are the differences between observed and @xmath0-dependent fitted values ; please see figure 3 ) are correlated at the 93% and 99.9% confidence levels for h@xmath3 and infrared triplet , respectively ( figure 6 ) . these relationships are more indicative of a true correlation between chromospheric emission and the over - ionization of fe . we remind the reader , however , that the @xmath2 abundances and chromospheric emission indicators were not measured using the same spectra and are thus not cotemporal . @xcite have used the same het / hrs spectra analyzed here to examine the long - standing problem of the large li abundance dispersion observed among cool pleiades dwarfs . these authors find evidence that at least a portion of the dispersion is due to real li depletion and suggest that the differential depletion may be a consequence of stellar radius modulations induced by surface magnetic activity , i.e. , spots , during pre - ms evolution . it is also suggested that such spot - induced effects could be related to the over - excitation / ionization effects observed today . @xmath2 residuals are plotted versus li abundance residuals in figure 7 . li abundances are derived from @xmath55 line strengths and are taken from @xcite . the @xmath2 and li residuals relation has a correlation coefficient of @xmath56 , corresponding to a @xmath5791% confidence level . while only marginally significant at best , the mild correlation still means that a substantial fraction ( nearly - half ) of the variance in @xmath2 is related to that in li . the abstract picture painted by this result is consistent with the conjecture presented by @xcite : the considerable li abundance dispersion in cool pleiades dwarfs has a real pre - ms depletion component , a portion of which may be driven by the same mechanism ( the influence of spots ) but perhaps by different physics ( the influence on stellar structure versus the influence on line formation in addition to or independent of stellar structure ) that is also possibly responsible for the versus differences seen in these stars . this would explain the overlap in the variance of pleiades @xmath2 and li abundances but allow for only marginally significant present - day correlations between these observables . observational tests , using the same type of pleiades spectroscopic / photometric monitoring program proposed in the conclusions section below , of this possibility are discussed in @xcite . the mean abundance of the pleiades stars above 5400 k derived from lines is [ fe / h ] @xmath6 ( uncertainty in the mean ) compared to [ fe / h ] @xmath58 ( uncertainty in the mean ) for stars below 5400 k. while a direct connection between the high [ /h ] abundances and the over - excitation effects manifested in the [ o / h]@xmath41 abundances of cool open cluster dwarfs can not be made here , the similarities are suggestive and raise doubt as to the accuracy of the cool star [ /h ] abundances . for this reason , and because of the anomalously high abundances , we feel that the mean cluster metallicity is best estimated by the [ /h ] abundances of the warmer stars only , and adopt the value of [ fe / h ] @xmath6 for the pleiades . the pleiades is one of the most well studied galactic open clusters , and fe abundances of member f , g , and k dwarfs have been derived using high - resolution spectroscopy by a handful of groups , which are summarized in table 7 . @xcite found a mean abundance of [ fe / h ] @xmath59 from one f and three g dwarfs , though the abundances are characterized by a large dispersion ( 0.02 0.26 dex ) . the spectra of three of the stars have s / n ratios of @xmath60 . in the same year , @xcite report a cluster mean abundance of [ fe / h ] @xmath61 for 13 f stars that have standard deviations in their individual [ fe / h ] abundances @xmath62 dex ; the mean abundance of their entire 17 star sample is [ fe / h ] @xmath63 . subsequent to that , @xcite and @xcite find similar values , [ fe / h ] @xmath64 and -0.02 , respectively . @xcite derived the abundances of two cool pleiades k dwarfs and obtained a mean abundance of [ fe / h ] @xmath65 from an analysis of lines . this value is almost identical to that of the stars with @xmath0 @xmath1 k in our sample , and we suspect that the abundances of the two k dwarfs from king et al . are similarly suspect . however , @xcite also derived a mean abundance of [ fe / h ] @xmath65 but for five f dwarfs . these authors noted that their result is slightly larger than that of @xcite and suggested differences in the analyses , i.e. , spectral lines used and adopted stellar parameters , as a possible cause . finally , @xcite have recently reported a cluster abundance of [ fe / h ] @xmath66 based on 22 a , f , and g stars . excluding the results of @xcite due to poor data quality and those of @xcite due to the uncertainty in the abundances of the two cool k dwarfs studied , the mean pleiades cluster abundance of the six remaining studies , including ours , is [ fe / h ] @xmath67 with a standard deviation of @xmath68 . this is identical to the value from the five stars with @xmath0 @xmath69 k in our sample , and by our assessment , represents the best estimate of the pleiades cluster metallicity .

abundances derived from lines are larger than those derived from lines ( herein referred to as over - ionization ) for stars with k , and the discrepancy ( = [ /h ] - [ /h ] ) increases dramatically with decreasing , reaching over 0.8 dex for the coolest stars of our sample . the pleiades joins the open clusters m34 , the hyades , ic2602 , and ic2391 , and the ursa major moving group , demonstrating ostensible over - ionization trends . the pleiades abundances are correlated with infrared triplet and h chromospheric emission indicators and relative differences therein . star - to - star abundances have low internal scatter ( dex ) , but the abundances of stars with k are systematically higher compared to the warmer stars .

we have derived fe abundances of 16 solar - type pleiades dwarfs by means of an equivalent width analysis of and lines in high - resolution spectra obtained with the hobby - eberly telescope and high resolution spectrograph . abundances derived from lines are larger than those derived from lines ( herein referred to as over - ionization ) for stars with k , and the discrepancy ( = [ /h ] - [ /h ] ) increases dramatically with decreasing , reaching over 0.8 dex for the coolest stars of our sample . the pleiades joins the open clusters m34 , the hyades , ic2602 , and ic2391 , and the ursa major moving group , demonstrating ostensible over - ionization trends . the pleiades abundances are correlated with infrared triplet and h chromospheric emission indicators and relative differences therein . oxygen abundances of our pleiades sample derived from the high - excitation triplet have been previously shown to increase with decreasing , and a comparison with the abundances suggests that the over - excitation ( larger abundances derived from high excitation lines relative to low excitation lines ) and over - ionization effects that have been observed in cool open cluster and disk field main sequence ( ms ) dwarfs share a common origin . curiously , a correlation between the pleiades abundances and chromospheric emission indicators does not exist . star - to - star abundances have low internal scatter ( dex ) , but the abundances of stars with k are systematically higher compared to the warmer stars . the cool star [ /h ] abundances can not be connected directly to over - excitation effects , but similarities with the and triplet trends suggest the abundances are dubious . using the [ /h ] abundances of five stars with k , we derive a mean pleiades cluster metallicity of [ fe / h ] .