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1211.4742

i

we consider the statistical problem of functional linear regression ( flr ) . in its standard version , one observes the data @xmath0 where @xmath1 are i.i.d . random variables taking their values in @xmath2)$ ] , that is , the set consisting of all continuous functions on the interval @xmath3 $ ] , and @xmath4 with @xmath5 where @xmath6 denotes the @xmath7)$]-inner product throughout this work . the i.i.d . error variables @xmath8 are assumed to be centered and normally distributed with the variance @xmath9 . moreover , all @xmath10 are independent . the goal is to estimate the regression function @xmath11)$ ] . in general , we allow for such a structure of the function class @xmath12 which does not determine @xmath13 up to finitely many real - valued parameters . thus we consider a nonparametric estimation problem . moreover we assume that @xmath14 and @xmath15 \leq c_{x,0 } \exp(-c_{x,1 } x^{c_{x,2}})$ ] for all @xmath16 and some finite constants @xmath17 where @xmath18 , @xmath19 denotes the @xmath20)$]-norm of some element of that space . thus the tails of the design distribution are restricted . such conditions are usual in nonparametric regression problems . the flr model has obtained considerable attention in the statistical community during the last years , which is reflected in the large amount of literature on this topic . various of estimation procedures have been proposed to make the regression function @xmath13 empirically accessible ( see , e.g. , @xcite ) . the minimax convergence rates in flr are investigated , for example , in @xcite . in @xcite , adaptive estimation in flr is considered . generalizations of flr are discussed in @xcite . a central limit theorem for flr is derived in @xcite . in @xcite , practical applications of flr in the field of medical statistics are described ; the authors consider two real data sets on primary biliary cirrhosis and systolic blood pressure . for a comprehensive introduction to the field of functional data analysis in general , see @xcite . in order to compare two statistical models , it is useful to prove asymptotic equivalence between those models . for the basic concept and a detailed description of this strong asymptotic property , we refer to @xcite and @xcite . also , a review on this topic is given in the following section . as an important feature , if two models @xmath21 and @xmath22 are asymptotically equivalent , then @xmath21 adopts optimal convergence rates and sharp asymptotic constants with respect to _ any _ bounded loss function from model @xmath22 and vice versa . thus , the theory of asymptotic equivalence does not only capture special loss functions such as the mean integrated squared error ( mise ) or the pointwise mean squared error ( mse ) but includes various types of semi - metrics between the estimator and the target function @xmath13 and also addresses the estimation of characteristics of @xmath13 , such as its support or its mode . furthermore , superefficiency phenomena also coincide in both models when considering subclasses @xmath23 of the target parameter space @xmath12 . in particular , research has focussed on proofs of asymptotic equivalence of experiments where @xmath24 i.i.d . data are observed , whose distribution depends on some parameter @xmath25 , and experiments where @xmath13 occurs in the drift of an empirically accessible it process . for instance , nussbaum @xcite considers an asymptotically equivalent white noise model for density estimation , while brown and low @xcite introduce such a model for nonparametric regression . in recent related literature on regression problems , carter @xcite studies the case of unknown error variance , and reiss @xcite extends asymptotic equivalence to the multivariate setting . returning to model ( [ eq:1.1 ] ) , we suppose that the nuisance parameters @xmath26 and @xmath27 , that is , the distribution of the @xmath28 , are known . that allows us to exclude those quantities from the parameter space of the experiment and to fully concentrate on the estimation of @xmath13 . this condition is also imposed in most papers dealing with asymptotic equivalence for nonparametric regression experiments . the work of @xcite represents an exception where the corresponding white noise model becomes more difficult and , apparently , less useful to derive adoptable asymptotic properties . with respect to asymptotic equivalence , we restrict our consideration to the case of known @xmath27 . however , in section [ s : new ] , we will show that the sharp minimax asymptotics with respect to the mise are extendable to the case of unknown design distribution . the main purpose of the current work is to prove asymptotic equivalence of model ( [ eq:1.1 ] ) and a statistical inverse problem in the white noise setting . that latter model is described by the observation of an it process @xmath29 , @xmath30 $ ] , @xmath31 , driven by the stochastic differential equation @xmath32(t)\,dt + n^{-1/2 } \sigma \,dw(t ) , \ ] ] where @xmath33 denotes a standard wiener process on the interval @xmath3 $ ] , and @xmath34 denotes a linear operator mapping from the hilbert space @xmath7)$ ] to itself . these models are also widely studied in mathematical statistics ( see , e.g. , @xcite and @xcite ) . they have their applications in the field of signal deblurring and econometrics . we will concentrate on a specific version of model ( [ eq:1.1.1 ] ) where @xmath34 is equal to the unique positive symmetric square root @xmath35 of the covariance operator @xmath36 , that is , @xmath37 and @xmath38 for any @xmath39)$ ] . thus , the observation @xmath29 , @xmath30 $ ] , is defined by @xmath31 and @xmath40(t)\,dt + n^{-1/2 } \sigma \,dw(t ) .\ ] ] in @xcite , the authors remark on the similarity of models ( [ eq:1.1 ] ) and ( [ eq:1.1.2 ] ) . in the current paper , we will rigorously establish asymptotic equivalence between those models . as an interesting feature , additional observation of the data @xmath41 would be redundant in model ( [ eq:1.1.2 ] ) . all information about the design points is recorded by @xmath36 in ( [ eq:1.1.2 ] ) . therefore , all what is observed in the corresponding white noise experiment is the process @xmath29 , @xmath42 $ ] . after the general introduction to the property of asymptotic equivalence as used in the current paper in section [ s1.0 ] , we will first prove ( nonasymptotic ) equivalence of model ( [ eq:1.1 ] ) and an empirical version of model ( [ eq:1.1.2 ] ) where @xmath36 is replaced by a noisy counterpart in section [ s2 ] . in section [ s3 ] , we prove asymptotic equivalence of ( [ eq:1.1 ] ) and ( [ eq:1.1.2 ] ) under some additional technical conditions . in section [ s : new ] , we show that the sharp lower bound which follows from the results of the previous section can be attained by specific estimators in the realistic case of unknown design distribution . a discussion of the findings and their conclusions are provided in section [ s5 ] .

we consider the statistical experiment of functional linear regression ( flr ) . moreover , we show equivalence of flr and an empirical version of the white noise model for finite sample sizes . as an application , we derive sharp minimax constants in the flr model which are still valid in the case of unknown design distribution . .

we consider the statistical experiment of functional linear regression ( flr ) . furthermore , we introduce a white noise model where one observes an it process , which contains the covariance operator of the corresponding flr model in its construction . we prove asymptotic equivalence of flr and this white noise model in lecam s sense under known design distribution . moreover , we show equivalence of flr and an empirical version of the white noise model for finite sample sizes . as an application , we derive sharp minimax constants in the flr model which are still valid in the case of unknown design distribution . .

1003.1197

c

in this paper , we considered the sn shock effects , the msw effects , the collective effects , and the earth matter effects in the detection of type ii sn neutrinos . also , we considered the uncertainties in the neutrino luminosities @xmath3 , their temperatures @xmath4 , and their pinching parameters @xmath5 in the calculation of different flavors of sn neutrinos . we found that quantities suitably defined in terms of event numbers of different flavors of sn neutrinos are sensitive to the neutrino mass hierarchy , the mixing angle @xmath0 , and neutrino masses . therefore , it is possible to identify the mass hierarchy , acquire information about @xmath0 , and look into certain neutrino mass patterns of sn neutrinos . firstly , we defined the ratio @xmath189 as the event number of @xmath8(@xmath9 ) for the charged - current reaction detected after one second over that detected in the first one second , and discussed the dependence of @xmath189 on @xmath0 for different mass hierarchies . with this , we may identify the mass hierarchy and obtain information about @xmath0 . this method can be applied to several detector types relying on specific physical processes , including the inverse beta decay ( fig . 7 ) , neutrino - carbon reactions ( figs . 8(a ) and 8(b ) ) , and neutrino - deuterium reactions ( figs . 9(a ) and 9(b ) ) . from our numerical calculations , the mass hierarchy may be identified by measuring @xmath192 in the neutrino - carbon reactions and the neutrino - deuterium reactions , @xmath199 in the inverse beta decay , the neutrino - carbon reaction , and the neutrino - deuterium reactions . in addition , in the case of normal mass hierarchy , @xmath192 measured in the neutrino - carbon reactions provides the most restrictive information about @xmath0 . therefore , we can both identify the mass hierarchy and measure @xmath0 from @xmath192 in the channel of neutrino - carbon reactions at several experiments such as daya bay , kamland , minboone , borexino , and double - chooz . secondly , we defined another ratio , @xmath242 , for the neutral - current reactions , as the event number of the delayed neutrinos over the total event number , with the charge current events as a monitor of undelayed events . the significance of @xmath242 is that it offers a possibility to detect possible difference between the electron neutrino and its other flavors counterparts , in particular , any significant difference in their effective masses under the cosmic setting of extreme conditions . with the plot of @xmath242 vs @xmath231 , we can study @xmath231 vs @xmath249 . this method is applied to both neutrino - carbon and neutrino - deuterium reactions and the result is given respectively in figs . 10 and 11 . what we have presented for @xmath242 is a case study with rather restricted input . in case there is an indication of non - vanishing @xmath242 a detailed refined calculation should be made . in conclusion , if a sn explosion takes place within the cosmic distance considered here , it is possible to identify the mass hierarchy and obtain information on @xmath0 . with suitable set up of the detector , a study of some unusual properties of neutrinos under the cosmic setting is possible . a summary of the detector types and their capabilities in association with the studies presented in this article is given in table ii .

we consider the supernova shock effects , the mikheyev - smirnov - wolfenstein ( msw ) effects , the collective effects , and the earth matter effects in the detection of type ii supernova neutrinos on the earth . it is found that the event number of supernova neutrinos depends on the neutrino mass hierarchy , the neutrino mixing angle , and neutrino masses .

we consider the supernova shock effects , the mikheyev - smirnov - wolfenstein ( msw ) effects , the collective effects , and the earth matter effects in the detection of type ii supernova neutrinos on the earth . it is found that the event number of supernova neutrinos depends on the neutrino mass hierarchy , the neutrino mixing angle , and neutrino masses . therefore , we propose possible methods to identify the mass hierarchy and acquire information about and neutrino masses by detecting supernova neutrinos . we apply these methods to some current neutrino experiments .

1409.6855

i

origami manifolds appeared in differential geometry recently as a generalization of symplectic manifolds @xcite . toric origami manifolds are in turn generalizations of symplectic toric manifolds . toric origami manifolds are a special class of @xmath0-dimensional compact manifolds with an effective action of a half - dimensional compact torus @xmath1 . in this paper we consider the following question . how large is this class ? which manifolds with half - dimensional torus actions are toric origami manifolds ? since the notion of a manifold with an effective half - dimensional torus action is too general to deal with , we restrict to quasitoric manifolds . this class of manifolds is large enough to include many interesting examples , and small enough to keep statements feasible . in @xcite masuda and park proved [ thm4dim ] any simply connected compact smooth @xmath2-manifold @xmath3 with an effective smooth action of @xmath4 is equivariantly diffeomorphic to a toric origami manifold . in particular , any @xmath2-dimensional quasitoric manifold is toric origami . the same question about higher dimensions was open . in this paper we give the negative answer . [ thmqtornotorigami ] for any @xmath5 there exist @xmath0-dimensional quasitoric manifolds , which are not equivariantly homeomorphic to any toric origami manifold . we will describe an obstruction for a quasitoric @xmath6-manifold to be toric origami and present a large series of examples , where such an obstruction appears . existence of such examples in higher dimensions follows from @xmath6-dimensional case . in spite of topological nature of the task , the proof is purely discrete geometrical : it relies on metric and coloring properties of planar graphs . thus we tried to separate the discussion of established facts in toric topology which motivated this study , from the proof of the main theorem to keep things comprehensible for the broad audience . the paper is organized as follows . in section [ secttopology ] we briefly review the necessary topological objects , and describe the standard combinatorial and geometrical models which are used to classify them . the objects are : quasitoric manifolds , symplectic toric manifolds , and toric origami manifolds . the corresponding combinatorial models are : characteristic pairs , delzant polytopes , and origami templates respectively . in section [ sectweightedspheres ] we introduce the notion of a weighted simplicial cell sphere , which , in a certain sense , unifies all these combinatorial models . we define a connected sum of weighted spheres along vertices . this operation is dual to the operation of producing an origami template from delzant polytopes . it plays an important role in the proof . section [ sectproof ] contains the combinatorial statement from which follows theorem [ thmqtornotorigami ] , and the proof of this statement . the interaction of our study with the study of the brownian map allows to prove that asymptotically most simple 3-polytopes admit quasitoric manifolds which are not toric origami . we describe this interaction as well as other adjacent questions in the last section [ sectconclusion ] . authors are grateful to the anonymous referee for his comments on the previous version of the paper .

we construct quasitoric manifolds of dimension 6 and higher which are not equivariantly homeomorphic to any toric origami manifold . all necessary topological definitions and combinatorial constructions are given and the statement is reformulated in discrete geometrical terms . the problem reduces to existence of planar triangulations with certain coloring and metric properties .

we construct quasitoric manifolds of dimension 6 and higher which are not equivariantly homeomorphic to any toric origami manifold . all necessary topological definitions and combinatorial constructions are given and the statement is reformulated in discrete geometrical terms . the problem reduces to existence of planar triangulations with certain coloring and metric properties .

1105.1666

i

the equation of state ( eos ) of dense matter plays an important role in various astrophysical phenomena such as supernova explosions and the formation of neutron stars and black holes @xcite . simulations of core - collapse supernovae cover a wide range of thermodynamic conditions , and extremely high density and temperature may be achieved when black holes are formed by failed supernovae . the temperature may vary from @xmath11 to more than @xmath12 mev , the proton fraction changes from @xmath11 to around @xmath13 , and the density can vary from @xmath14 to more than @xmath15 . clearly , it is very difficult to construct a complete eos over such a wide range of parameters . the information of matter under extreme conditions is far beyond our knowledge of nuclear physics from laboratory experiments . therefore , it is necessary to perform a large extrapolation based on a theoretical model that is supported by microscopic theory and consistent with available experimental data . during the past few decades , great efforts have been made to study the eos of nuclear matter @xcite . however , most of the investigations focused on detailed aspects of nuclear matter , which were often restricted to the case of zero temperature or high density with uniform distribution of particles . this kind of eos is generally not applicable for use in supernova simulations . so far , there exist only two realistic eoss which are commonly used in simulations of core - collapse supernovae , namely the one by @xcite and the one by @xcite . the lattimer swesty eos is based on a compressible liquid - drop model with a skyrme force . the shen eos is based on a relativistic mean - field ( rmf ) model and uses the thomas fermi approximation with assumed nucleon distribution functions in a wigner seitz cell for the description of non - uniform matter . recently , a hartree mean - field calculation @xcite was performed for the wigner seitz cell instead of the thomas fermi approximation used by @xcite . the hartree calculation can incorporate nuclear shell effects , but it requires much more computational resources . in our earlier work @xcite , we constructed the relativistic eos for supernova simulations , which has been widely used in astrophysical simulations over the past decade @xcite . the eos is based on the rmf theory combined with the thomas fermi approximation . the rmf theory with nonlinear @xmath16 and @xmath17 terms is able to reproduce nuclear matter saturation properties and provide a good description for both stable and unstable nuclei @xcite . the thomas fermi approximation in combination with assumed nucleon distribution functions and a free energy minimization is adopted to describe the non - uniform matter which is modeled as a mixture of a single species of heavy nuclei , alpha particles , and free nucleons that exist outside of nuclei , while the leptons can be treated as uniform non - interacting particles separately . the rmf results are taken as input in the thomas fermi calculation , so the treatments of non - uniform matter and uniform matter in this eos are sufficient to obtain the table in a consistent manner . it would be preferable to treat the mixture of nuclei as recently done in @xcite , @xcite , and @xcite for the detailed treatment of electron captures on nuclei in supernova core . however , it is beyond the scope of the current update of the shen eos table , which has been routinely used in astrophysical simulations . toward a more efficient and effective use of the shen eos table , we are required to make improvements in the eos given in @xcite , hereafter referred to as eos1 . the main demand is to increase the number of temperature points which is crucial in the simulation of core - collapse supernovae . in some cases , the temperature may reach more than @xmath12 mev , so it is encouraged to provide results at some higher temperatures although it is probably beyond the applicability of the rmf theory . it is generally believed that at sufficiently high temperature and/or density nuclear matter undergoes a phase transition to quark gluon plasma ( qgp ) . based on experimental data from high - energy heavy ion collisions and lattice quantum chromodynamics ( qcd ) calculations , it is known that the critical temperature for the qcd phase transition is around @xmath18 mev for zero baryon density @xcite . therefore , we note that the nuclear eos at extremely high temperature and/or density is not reliable due to the qcd phase transition , although results of the rmf theory are provided for practical use in astrophysical simulations . another suggestion is to use a linear grid for the proton fraction @xmath19 , instead of the logarithmic @xmath19 grid used in eos1 , which can add more points in the important region @xmath20@xmath21 for supernova simulations and save memory space by reducing the number of @xmath19 points at @xmath22 . furthermore , a proton - rich matter may be involved in astrophysical simulations @xcite , and therefore the information at @xmath23 is needed . in eos1 , the density grid spacing is only approximately equal at high density , it is now possible to perform the calculation with equal grid spacing in the whole range of density . since it is desirable and feasible to make these improvements , we work out a new version of the eos table , hereafter referred to as eos2 , which contains the same degrees of freedom as eos1 . in recent years , there has been extensive discussion in the literature on the influence of non - nucleonic degrees of freedom in dense matter @xcite . it is generally believed that hyperons appear around twice normal nuclear matter density in cold neutron star matter @xcite . the first hyperon to appear is @xmath0 that is the lightest one with an attractive potential in nuclear matter @xcite . @xmath24 hyperons are now considered to appear at a higher density than @xmath0 , because @xmath24 hyperons feel a repulsive potential in nuclear matter according to recent developments in hypernuclear physics @xcite . in the work of @xcite , the authors examined the properties of dense matter based on an extended rmf model including the full baryon octet . they presented several sets of eos including hyperons for simulations of core - collapse supernovae , which were connected with eos1 at low density in the simple procedure described in section 2.3 of their paper . the effect of @xmath25-wave pion condensation was also examined in @xcite , where the authors considered free thermal pions assuming the pion mass could not be affected by the interaction . in @xcite , the authors examined the possibility of @xmath25-wave pion condensation in dense matter by using the phenomenological optical potentials determined from the pionic atom or pion nucleus scattering data , and they concluded that @xmath25-wave pion condensation would hardly take place in neutron stars and especially have no chance if hyperons could participate in neutron star matter . the presence of boson condensation and deconfined quarks in neutron stars has been extensively discussed in many works @xcite . it has been suggested that the quark matter may exist in the core of massive neutron stars , and the hadron quark phase transition can proceed through a mixed phase of hadronic and quark matter @xcite . if deconfined quark matter does exist inside stars , it is likely to be in a color superconducting phase , and various color superconducting phases have been intensively investigated in recent years @xcite . in the works of @xcite and @xcite , the authors constructed the eos tables for simulations of core - collapse supernovae including the hadron quark phase transition at high density , which were connected with eos1 at low density . the hadron quark phase transition proceeded through a mixed phase obtained by the gibbs conditions for phase equilibrium , where the rmf model was used for the hadronic phase and the bag model was adopted for the quark phase . generally , the introduction of non - nucleonic degrees of freedom leads to a softening of the eos and thereby a corresponding reduction in the maximum mass of neutron stars . the recent measurement of the shapiro delay in the radio pulsar psr j1614 - 2230 yielded a mass of @xmath26 @xcite . such a high neutron star mass provides an important constraint on the eos at high density and rules out many predictions of non - nucleonic components in neutron star interiors . however , it is currently difficult to rule out all possible exotica with the @xmath27 observation , some theoretical calculations including hyperons and/or quarks could be compatible with the observation of psr j1614 - 2230 @xcite . among these exotic candidates , @xmath0 hyperons are the most likely to occur in dense matter . in addition , much more experimental information is now available for @xmath0 than other hyperons @xcite . from the experimental binding energies of single-@xmath0 hypernuclei , the potential depth of @xmath0 in nuclear matter is estimated to be around @xmath28 mev @xcite . several recent observations of double-@xmath0 hypernuclei ( see table 4 of @xcite ) indicate that the effective @xmath29 interaction should be considerably weaker than that deduced from the earlier measurement @xcite . in theoretical studies of @xmath0 hypernuclei , the rmf theory with nonlinear @xmath16 and @xmath17 terms is able to provide a reasonable description of single- and double-@xmath0 hypernuclei @xcite . the influence of @xmath0 hyperons on neutron star properties has been investigated within the rmf model @xcite . we would like to examine the effect of @xmath0 hyperons on the eos for simulations of core - collapse supernovae , while other hyperons such as @xmath24 and @xmath30 are ignored due to their relatively high threshold densities and lack of available experimental data . we construct the relativistic eos with the inclusion of @xmath0 hyperons , hereafter referred to as eos3 . for the contribution of @xmath0 hyperons in eos3 , we assume that the equilibrium condition @xmath31 is valid . in a supernova explosion , the dynamical timescale is of the order of milliseconds , which is long enough to establish equilibrium with respect to weak interactions that change strangeness on the timescale of microseconds or less @xcite . in fact , @xmath0 hyperons can have a noticeable effect on the properties of matter mainly at high density . it is known that weak equilibrium could be achieved at densities above @xmath32 where neutrinos begin to be trapped in the core @xcite . therefore , it is justified to use the equilibrium condition @xmath31 to determine the @xmath0 fraction of supernova matter at high density where @xmath0 hyperons have a noticeable contribution . in the work of @xcite , the authors assumed weak equilibrium among the full baryon octet when they determined the composition of supernova matter at a fixed density , temperature , and charge fraction . they examined the appearance of hyperons during the evolution of core collapse and bounce , and found that the effect of hyperons would be small in a spherical and adiabatic collapse of a @xmath33 star by the hydrodynamics without neutrino transfer @xcite . the hyperons are expected to appear and play an important role in the thermal evolution of protoneutron stars and the black hole formation from massive stars @xcite . we have two aims in this paper . the first is to improve the eos table according to the requirements of the users . in comparison with the earlier version ( eos1 ) , the following improvements are made in eos2 and eos3 ( see table 1 for details of the comparison ) . * the number of @xmath34 points is largely increased , the upper limit of @xmath34 is extended , and equal grid spacing for @xmath34 is used . * a linear @xmath19 grid is adopted instead of the logarithmic @xmath19 grid used in eos1 and the @xmath19 upper limit is extended . * the upper limit of @xmath35 is extended and equal grid spacing is used in the whole range of @xmath35 , whereas it is only approximately equal at high density in eos1 . the finer grids are favorable for better accuracy in the numerical simulations of core - collapse supernovae . the wide coverage of the conditions is necessary for numerical simulations of astrophysical phenomena including black hole formation , neutron star mergers , and nucleosynthesis . the second aim of this paper is to provide the eos table with the inclusion of @xmath0 hyperons for the use in simulations of core - collapse supernovae . the difference between eos2 and eos3 is that the contribution from @xmath0 hyperons is included in eos3 when the @xmath0 fraction is larger than @xmath36 . this paper is arranged as follows . in section [ sec:2 ] , we briefly describe the framework to calculate the eos table . we introduce the rmf model with the inclusion of @xmath0 hyperons and explain how to determine the rmf parameters . to make this paper self - contained , we give a brief description of the thomas fermi approximation for the non - uniform matter . in section [ sec:3 ] , we discuss our results without and with the inclusion of @xmath0 hyperons . we explore the properties of dense matter by examining the phase diagram , compositions , and thermodynamic quantities . section [ sec:4 ] is devoted to a summary . in appendix a , we give the definitions of the physical quantities tabulated in the eos . eos2 and eos3 are presented in electronic tables and can also be found on several web sites . in appendix b , we describe various checks made for the eos tables .

the study is based on the relativistic mean - field ( rmf ) theory , which can provide an excellent description of nuclear matter and finite nuclei . the thomas fermi approximation in combination with assumed nucleon distribution functions and a free energy minimization is adopted to describe the non - uniform matter , which is composed of a lattice of heavy nuclei .

we construct the equation of state ( eos ) of dense matter covering a wide range of temperature , proton fraction , and density for the use of core - collapse supernova simulations . the study is based on the relativistic mean - field ( rmf ) theory , which can provide an excellent description of nuclear matter and finite nuclei . the thomas fermi approximation in combination with assumed nucleon distribution functions and a free energy minimization is adopted to describe the non - uniform matter , which is composed of a lattice of heavy nuclei . we treat the uniform matter and non - uniform matter consistently using the same rmf theory . we present two sets of eos tables , namely eos2 and eos3 . eos2 is an update of our earlier work published in 1998 ( eos1 ) , where only the nucleon degree of freedom is taken into account . eos3 includes additional contributions from hyperons . the effect of hyperons on the eos is negligible in the low - temperature and low - density region , whereas it tends to soften the eos at high density . in comparison with eos1 , eos2 and eos3 have an improved design of ranges and grids , which covers the temperature range mev with the logarithmic grid spacing})=0.04 $ ] ( 92 points including ) , the proton fraction range with the linear grid spacing ( 66 points ) , and the density range with the logarithmic grid spacing } ) = 0.1 $ ] ( 110 points ) .

1105.1666

r

in this work , we construct the eos tables covering a wide range of temperature @xmath34 , proton fraction @xmath19 , and baryon mass density @xmath35 for the use of core - collapse supernova simulations . we present two sets of eos tables , namely eos2 and eos3 . eos2 takes into account only the nucleon degree of freedom , while eos3 includes additional contributions from @xmath0 hyperons . in comparison with the earlier version ( eos1 ) described in @xcite , several improvements are made in eos2 and eos3 according to the requirements of the users . we largely increase the number of @xmath34 points , and adopt a linear @xmath19 grid in eos2 and eos3 instead of the logarithmic @xmath19 grid used in eos1 . on the other hand , the numerical methods are improved to allow the calculation with equal grid spacing for @xmath35 , while it is only approximately equal at high density in eos1 . for a detailed comparison between the eos tables discussed in this paper , one can see table 1 in section [ sec:1 ] . in principle , the matter at extremely high temperatures and densities is beyond the applicability of the rmf theory , but we still include the results in these exotic regions since they are sometimes necessary in astrophysical simulations . in eos2 , we present results of matter without the inclusion of @xmath0 hyperons . for each @xmath34 , @xmath19 , and @xmath35 , we determine the thermodynamically favorable state that has the lowest free energy in the present model . we perform the free energy minimization for both non - uniform matter and uniform matter . here the phase of heavy nuclei formed together with free nucleons and alpha - particles is referred to as non - uniform matter , while the phase of nucleons mixed with alpha - particles without heavy nuclei is referred to as uniform matter . for non - uniform matter , the minimization procedure is realized by using the thomas fermi method which includes eight independent parameters as described in section [ sec:2.2 ] . for uniform matter , we perform the minimization with respect to converting two protons and two neutrons into an alpha - particle , in which there is only one independent parameter . by comparing the free energies of non - uniform matter and uniform matter , we determine the most favorable state and estimate the phase transition between non - uniform matter and uniform matter . we first discuss the phase diagram of nuclear matter at finite temperature . it is known that the density of the phase transition between uniform matter and non - uniform matter depends on both @xmath34 and @xmath19 . the non - uniform matter phase can exist only in the low - temperature region ( @xmath157 mev ) . in figure [ fig : trho ] , we show the phase diagram in the @xmath35@xmath34 plane for @xmath158 , @xmath159 , and @xmath21 . the shaded region corresponds to the non - uniform matter phase where heavy nuclei are formed . the dashed line is the boundary where the alpha - particle fraction @xmath160 changes between @xmath161 and @xmath162 . it is shown that heavy nuclei can exist in the medium - density and low - temperature region . the phase of nuclear matter at low density is a homogeneous nucleon gas with a small fraction of alpha - particles , the heavy nuclei are formed at some medium densities where the system can lower the free energy by forming heavy nuclei , and it becomes uniform matter as the density increases beyond @xmath163 . it is seen that the starting density of the non - uniform matter phase depends on @xmath34 strongly , while the ending density is nearly independent of @xmath34 . as the temperature increases , the density range of the non - uniform matter phase becomes narrower , and it disappears completely for @xmath164 mev . in figure [ fig : yprho ] , we show the phase diagram in the @xmath35@xmath19 plane for @xmath165 , @xmath166 , and @xmath12 mev . the shaded region corresponds to the non - uniform matter phase , while the dashed line is the boundary between @xmath161 and @xmath162 . it is shown that the dependence of the boundary on @xmath19 is relatively weak except at very small values of @xmath19 . in the case of @xmath167 mev ( middle panel ) , the non - uniform matter phase disappears at lower @xmath19 because it is difficult to form heavy nuclei with smaller values of @xmath19 . the alpha - particles still exist at @xmath168 mev , and @xmath160 reaches to be more than @xmath169 at some medium densities for @xmath170 as shown in the top panel of figure [ fig : yprho ] . we note that the phase diagram of nuclear matter at zero temperature has been discussed in @xcite . in the non - uniform matter , nucleon distributions are determined by minimizing the free energy density with respect to the independent parameters in the thomas fermi approximation . the heavy nuclei are assumed to form a bcc lattice in order to minimize the coulomb lattice energy . in figure [ fig : nm_t1 ] , we show the nucleon distributions along the straight line joining the centers of the nearest nuclei in the bcc lattice for the case of @xmath165 mev and @xmath171 . it is found that the nuclei become heavier and get closer with each other as the density increases . in principle , there exist free nucleons and alpha - particles outside heavy nuclei at finite temperature , but their densities are too small to be observed in figure [ fig : nm_t1 ] . we show in figure [ fig : nm_t10 ] the same quantities as in figure [ fig : nm_t1 ] but for the case of @xmath167 mev and @xmath171 . we note that the starting density of the non - uniform matter phase in this case is @xmath172 , so the heavy nucleus does not exist at @xmath173 for @xmath167 mev which is different from the case of @xmath165 mev as shown in the bottom panel of figure [ fig : nm_t1 ] . comparing with the top and middle panels of figure [ fig : nm_t1 ] , it is seen that there are much more free nucleons and alpha - particles outside nuclei , while the nucleons inside nuclei get less . this is because the role of entropy becomes more important at higher temperature and the free energy can be lowered if the nucleons are freed from nuclei . in figure [ fig : az ] , we plot the nuclear mass number @xmath174 and charge number @xmath175 as a function of the baryon mass density @xmath35 for @xmath171 at @xmath165 mev and @xmath167 mev . it is shown that @xmath174 and @xmath175 have relatively weak dependence on @xmath35 at lower density and they increase rapidly just before the phase transition at @xmath176 . for the same @xmath35 and @xmath19 , the values of @xmath174 and @xmath175 at @xmath167 mev are much smaller than those at @xmath165 mev . this is because more nucleons are freed from nuclei at higher temperature , and it is eventually impossible to form heavy nuclei for @xmath164 mev in the present model . in figure [ fig : xirho2 ] , we show the fraction of neutrons , protons , alpha - particles , and heavy nuclei as a function of the baryon mass density @xmath35 for @xmath171 at @xmath165 , @xmath166 , and @xmath177 mev . at low density , the matter is a uniform gas of neutrons and protons with a small fraction of alpha - particles . the alpha - particle fraction @xmath160 increases with increasing @xmath35 , but the formation of heavy nuclei at low temperatures causes a rapid drop of @xmath160 , @xmath178 , and @xmath179 , which is due to the fact that heavy nuclei use up most of the nucleons in non - uniform matter . when the density increases beyond @xmath163 , the heavy nuclei dissolve and the matter becomes uniform . the alpha - particles may exist up to @xmath180 where the volume excluded by alpha - particles plays an important role that it is unfavorable to have alpha - particles in the uniform matter at such high density . for @xmath164 mev , the heavy nuclei can not be formed , but there are finite values of @xmath160 , especially at medium densities as shown in the top panel of figure [ fig : xirho2 ] . the alpha - particle fraction decreases with increasing temperature , and we find that @xmath160 at @xmath168 mev is of the order of @xmath169 at some medium densities . the alpha - particle fraction may be significantly affected if the alpha - particle binding energy @xmath181 is dependent on the density and temperature as discussed in @xcite . for simplicity , we neglect this dependence and take @xmath136 mev in the present model . since we treat the uniform matter and non - uniform matter consistently using the same rmf theory , all the resulting thermodynamic quantities are consistent and smooth in the whole range . we will discuss the thermodynamic quantities in eos2 and compare with those in eos3 in the next section . in this section , we discuss results of matter with the inclusion of @xmath0 hyperons given in eos3 . it is found that the contribution from @xmath0 hyperons is negligible in the low - temperature and low - density region . in fact , at zero temperature @xmath0 hyperons appear only at high density when the equilibrium condition @xmath31 could be satisfied . at low temperature , such as @xmath167 mev , the @xmath0 fraction @xmath92 is smaller than @xmath36 at densities below normal nuclear matter density . for simplicity , we take into account the contribution from @xmath0 hyperons only when @xmath92 is larger than @xmath36 . in the non - uniform matter phase , @xmath92 is quite small , therefore we neglect the contribution from @xmath0 hyperons in the thomas fermi calculation . in figure [ fig : xirho3 ] , we show the fraction @xmath182 ( @xmath183 , @xmath66 , @xmath142 , @xmath143 , or heavy nuclei @xmath174 ) as a function of @xmath35 for @xmath171 at @xmath165 , @xmath166 , and @xmath177 mev . for lower temperatures , such as @xmath165 mev ( bottom panel ) and @xmath167 mev ( middle panel ) , there is a significant fraction of @xmath0 hyperons only at high density . it is shown that @xmath92 increases with increasing @xmath35 , which causes a decrease of @xmath179 . we note that @xmath178 , which is equal to @xmath19 in the uniform matter at high density , has been fixed to be @xmath159 in this figure . for @xmath184 mev ( top panel ) , @xmath92 is of the order of @xmath185 at low density , and increases rapidly at high density . comparing with the top panel of figure [ fig : xirho2 ] , it is seen that the inclusion of @xmath0 hyperons does not affect @xmath160 and @xmath178 significantly . we find the contribution from @xmath0 hyperons increases with increasing temperature . at @xmath168 mev , @xmath92 is about 12% at low density for the case of @xmath171 . on the other hand , @xmath92 decreases with increasing @xmath19 at fixed @xmath35 and @xmath34 , since there are less neutrons at higher @xmath19 to realize the equilibrium condition @xmath31 . we now discuss the thermodynamic quantities in eos3 and compare with those in eos2 . here we mainly discuss their properties at high density where there are noticeable differences between the results with and without @xmath0 hyperons . as for the behavior of thermodynamic quantities at low density , one can refer to our earlier work @xcite . in figure [ fig : f ] , we show the free energy per baryon @xmath186 as a function of the baryon mass density @xmath35 with @xmath158 and @xmath21 at @xmath165 , @xmath166 , and @xmath12 mev . the results with @xmath0 hyperons given in eos3 are shown by solid lines , while those without @xmath0 hyperons given in eos2 are displayed by dashed lines . it is found that the inclusion of @xmath0 hyperons can lower the free energy and this effect increases with increasing @xmath35 . however , this effect decreases with increasing @xmath19 as shown in figure [ fig : f ] , which is due to the fact that @xmath92 decreases with increasing @xmath19 . we show in figure [ fig : p ] the pressure @xmath142 as a function of @xmath35 with @xmath158 and @xmath21 at @xmath165 , @xmath166 , and @xmath12 mev . the pressure is calculated from the derivative of the free energy as described in appendix a. therefore , the effect of @xmath0 hyperons on the pressure is similar to the one observed in figure [ fig : f ] . it is obvious that the inclusion of @xmath0 hyperons tends to soften the eos at high density . in figure [ fig : s ] , we show the entropy per baryon @xmath187 as a function of @xmath35 with @xmath158 and @xmath21 at @xmath165 , @xmath166 , and @xmath12 mev . at @xmath165 mev ( bottom panel ) it is hard to see the difference between the results with and without @xmath0 hyperons , while at @xmath167 mev ( middle panel ) there are small differences at high density . for the case of @xmath168 mev ( top panel ) , the effect of @xmath0 hyperons can be seen in the whole range of density , since @xmath92 reaches @xmath188 ( @xmath189 ) at low density for @xmath158 ( @xmath21 ) at @xmath168 mev . in general , the inclusion of @xmath0 hyperons tends to increase the entropy . in @xcite , we have discussed the effect of the formation of nuclei on the entropy , which has a strong @xmath19 dependence . the behavior of @xmath187 at @xmath190 in the middle and bottom panels of figure [ fig : s ] is due to the formation of heavy nuclei in non - uniform matter . for neutron star matter at zero temperature , the inclusion of @xmath0 hyperons leads to a softening of the eos of neutron star matter and thereby a corresponding reduction in the maximum mass of neutron stars . we use eos3 to calculate the neutron star properties and find that the maximum mass of neutron stars is about 1.75 @xmath191 , whereas the value for eos1 and eos2 is 2.18 @xmath191 . according to the recent measurement of psr j1614 - 2230 ( @xmath27 ; @xcite ) , eos3 seems to be too soft due to the inclusion of @xmath0 hyperons , while eos1 and eos2 are compatible with the observation of psr j1614 - 2230 . this is a common difficulty for eoss with the inclusion of hyperons . so far , there are large uncertainties in the properties of matter at high density , which are crucial for determining the maximum mass of neutron stars .

we construct the equation of state ( eos ) of dense matter covering a wide range of temperature , proton fraction , and density for the use of core - collapse supernova simulations . we treat the uniform matter and non - uniform matter consistently using the same rmf theory . we present two sets of eos tables , namely eos2 and eos3 . eos3 includes additional contributions from hyperons .

we construct the equation of state ( eos ) of dense matter covering a wide range of temperature , proton fraction , and density for the use of core - collapse supernova simulations . the study is based on the relativistic mean - field ( rmf ) theory , which can provide an excellent description of nuclear matter and finite nuclei . the thomas fermi approximation in combination with assumed nucleon distribution functions and a free energy minimization is adopted to describe the non - uniform matter , which is composed of a lattice of heavy nuclei . we treat the uniform matter and non - uniform matter consistently using the same rmf theory . we present two sets of eos tables , namely eos2 and eos3 . eos2 is an update of our earlier work published in 1998 ( eos1 ) , where only the nucleon degree of freedom is taken into account . eos3 includes additional contributions from hyperons . the effect of hyperons on the eos is negligible in the low - temperature and low - density region , whereas it tends to soften the eos at high density . in comparison with eos1 , eos2 and eos3 have an improved design of ranges and grids , which covers the temperature range mev with the logarithmic grid spacing})=0.04 $ ] ( 92 points including ) , the proton fraction range with the linear grid spacing ( 66 points ) , and the density range with the logarithmic grid spacing } ) = 0.1 $ ] ( 110 points ) .

1105.1666

i

in this paper , we have presented two sets of the eos tables ( eos2 and eos3 ) covering a wide range of temperature @xmath34 , proton fraction @xmath19 , and baryon mass density @xmath35 for the use of core - collapse supernova simulations . the difference between eos2 and eos3 is that only the nucleon degree of freedom is taken into account in eos2 , while eos3 includes additional contributions from @xmath0 hyperons . in comparison with the earlier version ( eos1 ) described in @xcite , several improvements have been made in eos2 and eos3 according to the requirements of the users . we have largely increased the number of @xmath34 points , and adopted a linear @xmath19 grid in eos2 and eos3 instead of the logarithmic @xmath19 grid used in eos1 . in addition , we have performed the calculation with equal grid spacing in the whole range of density , while it is only approximately equal at high density in eos1 . we have presented a detailed comparison between these eoss in table 1 . we have employed the rmf theory with nonlinear @xmath16 and @xmath17 terms , which can provide an excellent description of nuclear matter and finite nuclei including unstable ones . the thomas fermi approximation in combination with assumed nucleon distribution functions and a free energy minimization has been adopted to describe the non - uniform matter that is modeled as a mixture of a single species of heavy nuclei , alpha particles , and free nucleons outside of nuclei . the rmf results have been taken as input in the thomas fermi calculation , so the treatments of non - uniform matter and uniform matter in this eos are sufficient to obtain the table in a consistent manner . it would be preferable to treat the mixture of nuclei as recently done in @xcite , @xcite , and @xcite for the detailed treatment of electron captures on nuclei in supernova core . however , it is beyond the scope of the current update of the shen eos table , which has been routinely used in astrophysical simulations . we have included the contribution from @xmath0 hyperons in eos3 , when the @xmath0 fraction is larger than @xmath36 . it is based on the consideration that the @xmath0 hyperon is most likely to occur in dense matter among all possible non - nucleonic degrees of freedom because it is the lightest hyperon with an attractive potential in nuclear matter . the potential depth of @xmath0 in nuclear matter is estimated to be around @xmath28 mev from the experimental binding energies of single-@xmath0 hypernuclei . several recent observations of double-@xmath0 hypernuclei suggest that the effective @xmath29 interaction should be weakly attractive . the rmf theory with nonlinear @xmath16 and @xmath17 terms has been extended to include hyperons , and it can provide a reasonable description of single- and double-@xmath0 hypernuclei @xcite . we have not included contributions from other hyperons , such as @xmath24 and @xmath30 , due to their relatively high threshold densities and lack of available experimental data . in eos3 , we have performed a consistent calculation including @xmath0 hyperons for the entire table , whereas the eos tables of high density matter were connected with eos1 at low density in the simple procedure described in section 2.3 of @xcite , so eos3 is considered to be constructed in a consistent manner for the inclusion of @xmath0 hyperons . we have examined the effect of @xmath0 hyperons on the properties of dense matter . the contribution from @xmath0 hyperons is negligible in the low - temperature and low - density region , whereas it tends to soften the eos at high density . in principle , the matter at extremely high temperatures and densities is beyond the applicability of the rmf theory , but we still include the results in these exotic regions since they are sometimes necessary in astrophysical simulations . it will continue to be a challenge for nuclear physics to provide realistic eos , which should be supported by microscopic theory and available experimental data , for use in astrophysical studies . we thank c. d. ott and t. fischer for helpful suggestions and fruitful discussions . k.s . expresses his thanks to k. nakazato , a. ohnishi , h. suzuki , and s. yamada for practical discussions on the development of the eos tables for simulations . h.s . and k.s thank the organizers of the micra2011 workshop hosted by the perimeter institute . this work was partially supported by the national natural science foundation of china ( grant nos . 10675064 and 11075082 ) , the grant - in - aid for scientific research on innovative areas ( nos . 20105004 and 20105005 ) , and the grant - in - aid for the scientific research ( no . 22540296 ) from the ministry of education , culture , sports , science and technology ( mext ) of japan . this work for numerical simulations of core - collapse supernovae is partially supported by the hpci strategic program of mext in japan , which assists k.s . to use the supercomputers at yukawa institute for theoretical physics ( yitp ) in kyoto university , research center for nuclear physics ( rcnp ) in osaka university , the university of tokyo , japan atomic energy agency ( jaea ) and high energy accelerator research organization ( kek ) .

eos2 is an update of our earlier work published in 1998 ( eos1 ) , where only the nucleon degree of freedom is taken into account . the effect of hyperons on the eos is negligible in the low - temperature and low - density region , whereas it tends to soften the eos at high density . in comparison with eos1 , eos2 and eos3

we construct the equation of state ( eos ) of dense matter covering a wide range of temperature , proton fraction , and density for the use of core - collapse supernova simulations . the study is based on the relativistic mean - field ( rmf ) theory , which can provide an excellent description of nuclear matter and finite nuclei . the thomas fermi approximation in combination with assumed nucleon distribution functions and a free energy minimization is adopted to describe the non - uniform matter , which is composed of a lattice of heavy nuclei . we treat the uniform matter and non - uniform matter consistently using the same rmf theory . we present two sets of eos tables , namely eos2 and eos3 . eos2 is an update of our earlier work published in 1998 ( eos1 ) , where only the nucleon degree of freedom is taken into account . eos3 includes additional contributions from hyperons . the effect of hyperons on the eos is negligible in the low - temperature and low - density region , whereas it tends to soften the eos at high density . in comparison with eos1 , eos2 and eos3 have an improved design of ranges and grids , which covers the temperature range mev with the logarithmic grid spacing})=0.04 $ ] ( 92 points including ) , the proton fraction range with the linear grid spacing ( 66 points ) , and the density range with the logarithmic grid spacing } ) = 0.1 $ ] ( 110 points ) .

hep-ph0305152

i

0.6truecm the publication of the first results of the kamland experiment marks the beginning of a new era in the studies of neutrino mixing and oscillations - the era of high precision determination of the neutrino mixing parameters . the data obtained by the solar neutrino experiments homestake , kamiokande , sage , gallex / gno and super - kamiokande ( sk ) @xcite provided the first strong evidences for oscillations of flavour ( electron ) neutrinos . strong evidences for oscillations of the atmospheric @xmath31 ( @xmath32 ) neutrinos were obtained by the super - kamiokande ( sk ) experiment @xcite . the evidences for solar @xmath4 oscillations into active neutrinos @xmath33 , were significantly reinforced during the last two years i ) by the combined first data of the sno experiment @xcite , and the sk data @xcite , ii ) by the more recent sno neutral current data @xcite , and iii ) by the first results of the kamland @xcite experiment . the kamland data practically establishes @xcite , under the plausible assumption of cpt - invariance , the large mixing angle ( lma ) msw solution as unique solution of the solar neutrino problem . this result brings us , after more than 30 years of research , initiated by the pioneer works of b. pontecorvo @xcite and the experiment of r. davis et al . @xcite , very close to a complete understanding of the true cause of the solar neutrino problem . the interpretation of the solar and atmospheric neutrino , and of the kamland data in terms of neutrino oscillations requires the existence of 3-neutrino mixing in the weak charged lepton current ( see , e.g. , @xcite ) : @xmath34 here @xmath35 , @xmath36 , are the three left - handed flavor neutrino fields , @xmath37 is the left - handed field of the neutrino @xmath38 having a mass @xmath39 and @xmath40 is the pontecorvo - maki - nakagawa - sakata ( pmns ) neutrino mixing matrix @xcite , @xmath41 where we have used a standard parametrization of @xmath40 with the usual notations , @xmath42 , @xmath43 , and @xmath44 is the dirac cp - violation phase .. ] if we identify @xmath45 and @xmath46 with the neutrino mass squared differences which drive the solar and atmospheric neutrino oscillations , @xmath47 , @xmath48 , the data suggest that @xmath49 . in this case @xmath50 and @xmath12 , represent the neutrino mixing angles responsible for the solar and atmospheric neutrino oscillations , @xmath51 , @xmath52 , while @xmath11 is the angle limited by the data from the chooz and palo verde experiments @xcite . combined @xmath53 and @xmath54 oscillation analyses of the solar neutrino and kamland @xcite data , performed under the assumption of cpt - invariance which we will suppose to hold throughout this study , show @xcite that the data favor the lma msw solution with @xmath55 and @xmath56 . a second , statistically somewhat less favored lma solution ( lma ii ) exists at @xcite @xmath57 . the atmospheric neutrino data , as is well known , is best described @xcite in terms of dominant @xmath58 ( @xmath59 ) oscillations with @xmath60 and @xmath61 . the 90% c.l . allowed intervals of values of the two - neutrino oscillation parameters found in @xcite read @xmath62 and @xmath63 . according to the more recent combined analysis of the data from the sk and k2k experiments @xcite , one has @xmath64 . we will often use in our analysis as illustrative the values @xmath65 and @xmath66 . let us note that the atmospheric neutrino and k2k data do not allow one to determine the signs of @xmath67 , and of @xmath68 when @xmath69 . this implies that in the case of 3-neutrino mixing one can have @xmath15 or @xmath16 . the two possibilities correspond to two different types of neutrino mass spectrum : with normal hierarchy ( nh ) , @xmath70 , and with inverted hierarchy ( ih ) , @xmath71 . the fact that the sign of @xmath68 is not determined when @xmath69 implies that when , e.g. , @xmath72 , two values of @xmath10 are possible , @xmath73 . in what regards the mixing angle @xmath11 , a 3-@xmath74 oscillation analysis of the chooz data @xcite led to the conclusion that for @xmath75 , the limits on @xmath9 practically coincide with those derived in the 2-@xmath74 oscillation analysis in @xcite . a combined 3-@xmath74 oscillation analysis of the solar neutrino , chooz and the kamland data , performed under the assumption of @xmath76 ( see , e.g. , @xcite ) , showed @xcite that @xmath77 at 99.73% c.l . the authors of @xcite found the best - fit value of @xmath9 to lie in the interval @xmath78 . getting more precise information about the value of the mixing angle @xmath11 , determining the sign of @xmath67 , or the type of the neutrino mass spectrum ( with normal or inverted hierarchy ) , and measuring the value of @xmath10 with a higher precision is of fundamental importance for the progress in the studies of neutrino mixing . the mixing angle @xmath11 , or the absolute value of the element @xmath79 of the pmns matrix , @xmath80 , plays a very important role in the phenomenology of the 3-neutrino oscillations . it drives the sub - dominant @xmath81 ( @xmath82 ) oscillations of the atmospheric @xmath31 ( @xmath32 ) and @xmath4 ( @xmath5 ) @xcite . the value of @xmath11 controls also the @xmath83 , @xmath84 , @xmath85 and @xmath86 transitions in the long baseline neutrino oscillation experiments ( minos , cngs ) , and in the widely discussed very long baseline neutrino oscillation experiments at neutrino factories ( see , e.g. , @xcite ) . the magnitude of the t - violating and cp - violating probabilities in neutrino oscillations is directly proportional to @xmath87 ( see , e.g. , @xcite ) . thus , in the sub - dominant channels of interest to t- and cp - violation studies , the corresponding asymmetries become proportional to @xmath88 @xcite . the value of @xmath89 is thus of prime importance . if the neutrinos with definite mass are majorana particles ( see , e.g. , @xcite ) , the predicted value of the effective majorana mass parameter in neutrinoless double @xmath90decay depends strongly in the case of hierarchical neutrino mass spectrum on the value of @xmath9 ( see , e.g. , @xcite ) . the sign of @xmath67 determines , for instance , which of the transitions ( e.g. , of atmospheric neutrinos ) @xmath83 and @xmath85 , or @xmath84 and @xmath86 , can be enhanced by the earth matter effects @xcite . the predictions for the neutrino effective majorana mass in neutrinoless double @xmath90decay depend critically on the type of the neutrino mass spectrum ( normal or inverted hierarchical ) @xcite . the knowledge of the value of @xmath11 and of the sign of @xmath48 is crucial for the searches for the correct theory of neutrino masses and mixing as well . somewhat better limits on @xmath91 than the existing one can be obtained in the minos experiment @xcite . various options are being currently discussed ( experiments with off - axis neutrino beams , more precise reactor antineutrino and long base - line experiments , etc . , see , e.g. , @xcite ) of how to improve by at least an order of magnitude , i.e. , to values of @xmath92 or smaller , the sensitivity to @xmath9 . the sign of @xmath67 can be determined in very long base - line neutrino oscillation experiments at neutrino factories ( see , e.g. , @xcite ) , and , e.g , using combined data from long base - line oscillation experiments at the jhf facility and with off - axis neutrino beams @xcite . if the neutrinos with definite mass are majorana particles , it can be determined by measuring the effective neutrino majorana mass in neutrinoless double @xmath90decay experiments @xcite . under certain rather special conditions it might be determined also in experiments with reactor @xmath5 @xcite . in the present article we study possibilities to obtain information on the value of @xmath9 and on the sign of @xmath48 using the atmospheric neutrino data , accumulated by the sk experiment , and more generally , that can be provided by future water - erenkov detectors , like uno and hyper - kamiokande . we consider 3-neutrino oscillations of the atmospheric @xmath31 , @xmath32 , @xmath4 and @xmath5 under the condition latexmath:[${\mbox{$ \delta m^2_{\odot}$}}= \delta m^2_{21 } \ll suggested to hold by the current solar and atmospheric neutrino data . under the indicated condition , the expressions for the probabilities of @xmath83 ( @xmath85 ) and @xmath84 ( @xmath86 ) transitions contain @xmath10 as a factor , which determines their maximal values . depending on the sign of @xmath46 , the earth matter effects can resonantly enhance either the @xmath83 and @xmath85 , or the @xmath84 and @xmath94 transitions if @xmath95 . the effects of the enhancement can be substantial for @xmath96 . they are larger in the multi - gev @xmath97-like and @xmath2like samples of events and for atmospheric neutrinos with relatively large path length in the earth , crossing deeply the mantle @xcite or the mantle and the core @xcite , i.e. , for @xmath19 , where @xmath0 is the nadir angle characterizing the neutrino trajectory in the earth . the @xmath83 ( @xmath84 ) and @xmath85 ( @xmath86 ) transitions in the earth lead to the reduction of the rate of the multi - gev @xmath2like events and to the increase of the rate of the multi - gev @xmath3like events in the super - kamiokande ( or any other water - erenkov ) detector with respect to the case of absence of these transitions ( see , e.g. , @xcite ) . correspondingly , as observables which are sensitive to the earth matter effects , and thus to the value of @xmath9 and the sign of @xmath46 , as well as to @xmath10 , we consider the nadir - angle distributions of the ratios @xmath98 and @xmath99 , where @xmath100 and @xmath101 and are the multi - gev @xmath2like and @xmath97-like numbers of events ( or event rates ) in the case of 3-@xmath74 oscillations of the atmospheric @xmath4 , @xmath5 and @xmath31 , @xmath32 , and @xmath102 is the number of @xmath3like events in the case of absence of oscillations ( @xmath21 ) . the ratio of the energy and nadir angle integrated @xmath2like and @xmath3like events , @xmath1 , has been measured with a relatively high precision by the sk experiment @xcite . the systematic uncertainty , in particular , in the nadir angle dependence of the ratio @xmath1 can be smaller than those on the measured nadir angle distributions of @xmath2like and @xmath3like events , @xmath103 and @xmath104 . we obtain predictions for the nadir - angle distributions of @xmath98 and of @xmath99 both for neutrino mass spectra with normal ( @xmath15 ) and inverted ( @xmath16 ) hierarchy , @xmath105 , @xmath106 , @xmath107 and @xmath108 , and for @xmath109 . we compare the latter with the predicted nadir - angle distributions i ) of the ratio @xmath110 for the case the 3-neutrino oscillations taking place in vacuum , @xmath111 , and ii ) of the ratio @xmath112 , where @xmath113 is the predicted number of @xmath2like events in the case of 2-neutrino @xmath58 and @xmath59 oscillations of the atmospheric @xmath31 and @xmath32 . predictions for the different types of ratios indicated above of the suitably integrated nadir angle distributions of the @xmath2like and @xmath3like multi - gev events are also given . our results show , in particular , that for @xmath27 @xmath17 and @xmath15 , the effects of the earth matter enhanced @xmath83 and @xmath85 transitions of the atmospheric @xmath31 and @xmath4 , might be observable with the super - kamiokande detector . conversely , if the indicated effects are indeed observed in the super - kamiokande experiment , that would suggest in turn that @xmath17 , @xmath27 and that the neutrino mass spectrum is with normal hierarchy , @xmath15 . let us note finally that the earth matter effects have been widely investigated ( for a recent detailed study see , e.g. , ref . @xcite which contains also a rather complete list of references to earlier work on the subject ) . however , the study of the magnitude of the earth matter effects in the nadir angle distribution of the ratio of the multi - gev @xmath2like and @xmath3like events , measured in water - erenkov detectors , performed here overlaps very little with the earlier investigations .

this ratio is particularly sensitive to the earth matter effects in the atmospheric neutrino oscillations , and thus to the values of and , and being the neutrino mixing angle limited by the chooz and palo verde experiments and that responsible for the dominant atmospheric ( ) oscillations . it is also sensitive to the type of neutrino mass spectrum which can be with normal ( ) or with inverted ( ) hierarchy . the effects can be as large as for , can reach in the earth core bin , and might be observable . an observation of the earth matter effects in the nadir angle distribution of the ratio would clearly indicate that and . ref . sissa 28/03/ep ftuv-03 - 0513 ific/03 - 21 * atmospheric neutrino oscillations , and neutrino mass hierarchy * j. bernabu , sergio palomares - ruiz and s. t. petcov departamento de fsica terica and ific , universidad de valencia - csic , 46100 burjassot , valencia , spain + scuola internazionale superiore di studi avanzati and istituto nazionale di fisica nucleare , i-34014 trieste , italy

we derive predictions for the nadir angle ( ) dependence of the ratio of the rates of thelike andlike multi - gev events measured in water - erenkov detectors in the case of 3-neutrino oscillations of the atmospheric ( ) and ( ) , driven by one neutrino mass squared difference , . this ratio is particularly sensitive to the earth matter effects in the atmospheric neutrino oscillations , and thus to the values of and , and being the neutrino mixing angle limited by the chooz and palo verde experiments and that responsible for the dominant atmospheric ( ) oscillations . it is also sensitive to the type of neutrino mass spectrum which can be with normal ( ) or with inverted ( ) hierarchy . we show that for , and at , the earth matter effects modify substantially the dependence of the ratio and in a way which can not be reproduced with and a different value of . for normal hierarchy the effects can be as large as for , can reach in the earth core bin , and might be observable . they are typically by smaller in the inverted hierarchy case . an observation of the earth matter effects in the nadir angle distribution of the ratio would clearly indicate that and . ref . sissa 28/03/ep ftuv-03 - 0513 ific/03 - 21 * atmospheric neutrino oscillations , and neutrino mass hierarchy * j. bernabu , sergio palomares - ruiz and s. t. petcov departamento de fsica terica and ific , universidad de valencia - csic , 46100 burjassot , valencia , spain + scuola internazionale superiore di studi avanzati and istituto nazionale di fisica nucleare , i-34014 trieste , italy

hep-ph0305152

r

0.6truecm the results of our analysis are summarized graphically in figs . 1 - 5 . we have used in the calculations the predictions for the nadir angle and energy distributions of the atmospheric neutrino fluxes given in @xcite . in this analysis , we only consider deep inelastic scattering ( dis ) cross sections and we make use of the grv94 parton distributions given in @xcite . the dependence on @xmath289 of the ratios of the multi - gev @xmath2 and @xmath3 like events ( or event rates ) , integrated over the neutrino energy in the interval @xmath290 gev , in the cases i ) of two - neutrino @xmath58 and @xmath59 oscillations in vacuum and no @xmath4 and @xmath5 oscillations , @xmath112 ( solid lines ) , ii ) three - neutrino oscillations in vacuum of @xmath31 , @xmath32 , @xmath4 and @xmath5 , @xmath291 ( dash - dotted lines ) , iii ) three - neutrino oscillations of @xmath31 , @xmath32 @xmath4 and @xmath5 in the earth and neutrino mass spectrum with normal hierarchy @xmath105 ( dashed lines ) , or with inverted hierarchy , @xmath106 ( dotted lines ) . the results shown are for @xmath292 , @xmath293 , and @xmath294 . , height=687 ] the predicted dependences on @xmath289 of the ratios of the multi - gev @xmath2 and @xmath3 like events ( or event rates ) , integrated over the neutrino energy from the interval @xmath290 gev , in the case i ) of two - neutrino @xmath58 and @xmath59 oscillations in vacuum and no @xmath4 and @xmath5 oscillations , @xmath112 , ii ) three - neutrino oscillations in vacuum of @xmath31 , @xmath32 , @xmath4 and @xmath5 , @xmath291 , iii ) three - neutrino oscillations of @xmath31 , @xmath32 , @xmath4 and @xmath5 in the earth in the cases of neutrino mass spectrum with normal hierarchy @xmath105 , and with inverted hierarchy , @xmath106 , for @xmath109 , @xmath295 and @xmath292 are shown in fig . 1 . as @xmath289 increases from 0 to @xmath296 , the neutrino path length in the earth increases from 0 to @xmath297 km . the @xmath13 ( @xmath14 ) oscillations , which for @xmath298 proceed in the earth essentially as in vacuum , fully develop . for @xmath299 and @xmath300 gev , for example , the maximum of the @xmath13 ( @xmath14 ) oscillation probability occurs for @xmath301 , or @xmath302 km . for @xmath298 and @xmath292 , the oscillations involving the atmospheric @xmath4 ( @xmath303 , @xmath304 ) and @xmath5 ( @xmath305 , @xmath306 ) with energies in the multi - gev range , @xmath307 gev , are suppressed . if @xmath15 , for instance , the earth matter effects suppress the antineutrino oscillation probability @xmath167 , but can enhance the neutrino mixing in matter , or @xmath308 . however , since the neutrino path in the earth mantle is relatively short one has @xmath309 , and correspondingly @xmath310 . thus , for @xmath298 , all four types of ratios we consider , @xmath112 , @xmath291 , @xmath105 and @xmath106 , practically coincide and exhibit the same dependence on @xmath289 : they decrease as @xmath289 increases from 0 , reaching a minimum at @xmath301 , and begin to rise as @xmath289 increases further . this behavior is clearly seen in figs . 1 and 2 . at @xmath19 , the earth matter effects in the oscillations of the atmospheric @xmath31 , @xmath32 @xmath4 and @xmath5 , can generate noticeable differences between @xmath112 ( or @xmath291 ) and @xmath311 , as well as between @xmath105 and @xmath106 . for @xmath312 and @xmath313 ( upper left panel in fig . 1 ) , we have at @xmath314 ( neutrinos crossing only the earth mantle ) : @xmath315 . for the earth - core - crossing atmospheric neutrinos , @xmath316 , the mantle - core interference effect ( or nolr ) suppresses the ratios @xmath317 with respect to @xmath112 ( or @xmath291 ) : at @xmath318 the relative averaged difference between @xmath112 and @xmath105 is and @xmath105 is defined as @xmath319 . ] @xmath320 , while the difference between @xmath105 and @xmath106 is rather small ( upper right panel in fig . 1 ) . at @xmath27 , the differences between @xmath112 and @xmath317 become noticeable already at @xmath19 . they increase with the increasing of @xmath10 and/or @xmath119 , and are maximal for @xmath321 and @xmath318 . the dependence on @xmath10 is particularly strong . the deviations from the vacuum oscillation ratio @xmath291 increase with the increasing of @xmath19 as well ; they are maximal for the earth - core - crossing neutrinos , @xmath316 . for @xmath322 and @xmath295 , the relative difference between @xmath112 and @xmath105 in the interval @xmath323 is approximately @xmath324 ; for @xmath325 and @xmath295 , it is @xmath326 . the same differences are larger in the earth core interval @xmath327 due to the mantle - core enhancement ( nolr ) @xcite , reaching on average values of @xmath328 for @xmath322 and @xmath295 , and @xmath329 for @xmath325 and the same two values of @xmath119 . for @xmath330 , and @xmath295 , the relative difference between @xmath112 and the ratio @xmath1 in the case of ih neutrino mass spectrum , @xmath106 , in the interval @xmath331 has a mean value of approximately @xmath332 , while if @xmath325 it is approximately @xmath333 . it is larger in the earth core bin , @xmath327 , reaching approximately @xmath334 for @xmath325 and @xmath318 . the magnitude of the difference between @xmath112 and @xmath311 exhibits a relatively strong dependence on the minimal value of the neutrino energy @xmath122 from the integration interval , @xmath335 , and a rather mild dependence on the maximal @xmath122 in the interval , @xmath336 . with the increase of @xmath335 , the relative magnitude of the contributions to the energy - integrated event rates of interest , coming from the energy interval in which the matter effects are significant , also increases , leading to larger difference between @xmath112 and @xmath311 . this is illustrated in fig . 2 , where the ratios of interest are shown as functions of @xmath289 for @xmath292 , @xmath330 , @xmath337 , and i ) @xmath338 gev , @xmath339 gev ( left panel ) , and ii ) @xmath340 gev , @xmath341 gev ( right panel ) . increasing @xmath335 ( @xmath336 ) while keeping @xmath336 ( @xmath335 ) intact would lead to the decreasing ( increasing ) of the statistics in the samples of @xmath2like and @xmath3like events of interest . 2 illustrates , the relative differences between i ) @xmath112 and @xmath105 and ii ) @xmath112 and @xmath106 , increase noticeably in the interval @xmath342 with the increase of @xmath335 , being almost constant for @xmath338 gev and reaching the values of approximately @xmath343 and @xmath344 , respectively . and @xmath105 is @xmath345 . ] for @xmath327 , the differences under discussion exhibit a characteristic oscillatory pattern . these differences have a completely different behavior as functions of @xmath289 if @xmath336 is increased to 100 gev , keeping @xmath340 gev ( fig . 2 , right panel ) : they increase approximately linearly with @xmath289 , starting from 0 at @xmath346 , and having at @xmath347 the values i ) @xmath348 and ii ) @xmath349 , respectively . the same as in fig . 1 but for the ratios of the @xmath2 and @xmath3 like events ( or event rates ) , integrated respectively over the neutrino energy in the intervals @xmath350 gev ( left panel ) , and @xmath351 gev ( right panel ) , and for @xmath292 , @xmath330 and @xmath318 . , height=272 ] and @xmath3 like events ( or event rates ) , integrated over the neutrino energy in the interval @xmath290 gev and over the nadir angle in the interval corresponding to @xmath352 , as functions i ) of @xmath119 for @xmath292 ( left panels ) , and ii ) of @xmath353 for @xmath318 ( right panels ) : @xmath112 ( solid lines ) , @xmath291 ( dash - dotted lines ) , @xmath105 ( dashed lines ) and @xmath106 ( dotted lines ) . the results shown are obtained for @xmath293 . , height=687 ] in fig . 3 we show the predictions for the different ratios of @xmath2like and @xmath3like event rates we consider , integrated over the neutrino energy in the interval @xmath354 gev and over @xmath289 in the interval @xmath355 , i ) as functions of @xmath119 for @xmath292 ( left panels ) , and ii ) as functions of @xmath353 for @xmath318 ( right panel ) . in each case the results presented are for three values of @xmath356 . the differences between the ratios of the integrated @xmath2like and @xmath3like event rates of interest , i.e. , i ) between @xmath112 and @xmath105 and ii ) between @xmath112 and @xmath106 , increase rather rapidly as @xmath119 increases from 0 to @xmath357 , while the increase is slower in the interval @xmath358 . at @xmath357 , the relative differences between @xmath112 and i ) @xmath105 and ii ) @xmath106 in the case under discussion are respectively @xmath359 and @xmath360 for @xmath330 ; for @xmath361 they are considerably larger , @xmath362 and @xmath359 . if @xmath363 , the same two differences for @xmath364 read @xmath365 and @xmath366 , respectively . it follows from fig . 3 , right panel , that differences between the integrated ratios @xmath112 ( or @xmath291 ) and @xmath105 , and @xmath106 and @xmath105 , are maximal for values of @xmath353 lying in the interval @xmath367 , which are favored by the current atmospheric neutrino data . of @xmath3like multi - gev events ( or event rates ) , for @xmath4 and @xmath5 taking part in 3-neutrino oscillations in the earth ( @xmath368 ) , and @xmath4 and @xmath5 not taking part in the oscillations ( @xmath369 ) , as a function of @xmath370 for @xmath371 ( dashed lines ) , and for neutrino mass spectrum with normal hierarchy ( upper solid or dashed lines ) and with inverted hierarchy ( lower solid or dashed lines ) . the results shown are for @xmath372 ( right panel ) , and for @xmath373 . see text for details . , height=272 ] i ) on @xmath374 for @xmath373 ( left panels ) , and ii ) on @xmath375 for @xmath376 ( right panels ) , in the cases of neutrino mass spectrum with normal hierarchy ( solid lines ) and inverted hierarchy ( dashed lines ) . in this figure @xmath368 and @xmath369 are the multi - gev e - like events ( or event rates ) for @xmath4 and @xmath5 taking part in 3-neutrino oscillations in the earth and @xmath4 and @xmath5 not taking part in the oscillations , respectively , integrated over the nadir angle @xmath0 in the intervals corresponding to a ) @xmath377 - neutrinos crossing the earth core ( upper panels ) , and b ) @xmath378 ( lower panels ) . the results shown are for @xmath312 ( lower doubly thick solid or dashed lines ) ; 0.50 ( middle thin solid or dashed lines ) ; 0.64 ( upper doubly thick solid or dashed lines ) . , height=453 ] in figs . 4 and 5 we present results just for the multi - gev e - like event rate . the earth matter effects are largest in the oscillations of the atmospheric @xmath4 or @xmath5 . the dependence of the ratio @xmath99 , @xmath101 and @xmath102 being the numbers of multi - gev @xmath97-like events ( or event rates ) predicted in the cases of 3-@xmath74 oscillations of @xmath4 , @xmath5 , and of absence of oscillations ( @xmath21 ) , on @xmath289 is shown in fig . 4 for @xmath364 and for @xmath379 . the deviation of @xmath99 from 1 would signal that @xmath4 and @xmath5 take part in oscillations and that @xmath380 . we can have @xmath381 only if a substantial fraction of the atmospheric @xmath31 ( or @xmath32 ) oscillate into @xmath282 ( @xmath382 ) . as fig . 4 shows , the ratio @xmath99 increases with the increasing of @xmath289 and can be significantly greater than 1 for @xmath19 . at @xmath383 , for instance , we have for @xmath330 and @xmath295 in the case of nh neutrino mass spectrum @xmath384 , while for @xmath361 one finds @xmath385 . for ih neutrino mass spectrum the ratio of interest , @xmath386 , is smaller and the corresponding values read : @xmath387 and @xmath388 , respectively . for the earth - core - crossing neutrinos both @xmath389 and @xmath386 are larger due to the nolr effect , and for @xmath361 and @xmath337 reach the values @xmath390 and @xmath391 . for given @xmath10 and and @xmath9 , the maximum of the ratio of the multi - gev e - like event rates of interest @xmath101 and @xmath392 , integrated over @xmath0 in the intervals corresponding to a ) @xmath393 ( earth core bin ) and b ) @xmath394 , occurs again for values of @xmath395 ( fig . 5 , right panels ) , favored by the existing atmospheric neutrino data . for @xmath292 , @xmath396 and @xmath361 , the two types of @xmath20 integrated ratios can be as large as : case a ) @xmath397 , and case b ) @xmath398 ( fig . 5 , left and right panels ) .

we derive predictions for the nadir angle ( ) dependence of the ratio of the rates of thelike andlike multi - gev events measured in water - erenkov detectors in the case of 3-neutrino oscillations of the atmospheric ( ) and ( ) , driven by one neutrino mass squared difference , . we show that for , and at , the earth matter effects modify substantially the dependence of the ratio and in a way which can not be reproduced with and a different value of . for normal hierarchy

we derive predictions for the nadir angle ( ) dependence of the ratio of the rates of thelike andlike multi - gev events measured in water - erenkov detectors in the case of 3-neutrino oscillations of the atmospheric ( ) and ( ) , driven by one neutrino mass squared difference , . this ratio is particularly sensitive to the earth matter effects in the atmospheric neutrino oscillations , and thus to the values of and , and being the neutrino mixing angle limited by the chooz and palo verde experiments and that responsible for the dominant atmospheric ( ) oscillations . it is also sensitive to the type of neutrino mass spectrum which can be with normal ( ) or with inverted ( ) hierarchy . we show that for , and at , the earth matter effects modify substantially the dependence of the ratio and in a way which can not be reproduced with and a different value of . for normal hierarchy the effects can be as large as for , can reach in the earth core bin , and might be observable . they are typically by smaller in the inverted hierarchy case . an observation of the earth matter effects in the nadir angle distribution of the ratio would clearly indicate that and . ref . sissa 28/03/ep ftuv-03 - 0513 ific/03 - 21 * atmospheric neutrino oscillations , and neutrino mass hierarchy * j. bernabu , sergio palomares - ruiz and s. t. petcov departamento de fsica terica and ific , universidad de valencia - csic , 46100 burjassot , valencia , spain + scuola internazionale superiore di studi avanzati and istituto nazionale di fisica nucleare , i-34014 trieste , italy

1702.06545

c

this paper presents a physical mechanism that may enable detection of inclined water maser disks orbiting massive black holes via the lensing / deflection of in - going systemic masers . the observational signature of an inclined disk is a maser line or line complex with limited doppler extent that appears to arise at the location of the black hole , as identified by its radio continuum core . with enough angular resolution , it may be possible to measure the black hole mass if the maser emission forms a lensing arc or einstein ring , but the mass precision will be limited by one s ability to measure or estimate the size of the maser - emitting portion of the disk . we suggest that if inclined maser disks can be detected at all , then they have probably already been detected in single - dish surveys but discarded for interferometric follow - up because they did not show high - velocity lines . we present original 0.070.17 ( 4100 pc ) resolution vla observations of inclined maser disk candidates with the goal of identifying systems where the maser emission is unresolved and is coincident with the 20 ghz continuum emission . of the 16 masers observed with the vla , we obtained useful data for 13 , and among these , five were detected in both 22 ghz maser line emission and in 20 ghz continuum . of these five , one maser is most likely associated with star formation ( ngc 520b ) , and one shows a significant spatial offset between the maser emission and the continuum ( cgcg 168@xmath0018 , but it could still host an inclined maser disk this case is ambiguous ) . three objects are good inclined maser disk candidates that merit further study with vlbi : ic 485 , j0804 + 3607 , and cgcg 120@xmath0039 . five maser hosts remain ambiguous , based either on non - detected or offset continua : j0350@xmath00127 , j0912 + 2304 , j1011@xmath01926 , cgcg 168@xmath0018 , and j1939@xmath00124 . more straightforward methods for measuring black hole masses from molecular lines may be in the offing . for example , @xcite and @xcite have used carbon monoxide kinematics in thin disks that approach or are within the black hole gravitational sphere of influence to obtain black hole mass measurements . @xcite , in particular , demonstrate the ability of alma to measure black hole masses with @xmath710% uncertainty . although they lack the intrinsic brightness of masers that enables vlbi mapping , thermal molecular lines have the advantage of being observable at any disk inclination . we thank a. hamilton and m. eracleous for helpful discussion and b. butler for assistance with metadata repair of bespoke observing configurations . we also thank the anonymous referee for important feedback . this research has made use of nasa s astrophysics data system bibliographic services and the nasa / ipac extragalactic database ( ned ) , which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space 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. the signature of an inclined water maser disk would be narrow masers near the systemic velocity that appear to emit from the black hole position , as identified by the radio continuum core . to explore this possibility , we present high resolution ( 0.070.17 ) very large array line and continuum observations of 13 galaxies with narrow water maser emission and show that three are good inclined disk candidates ( five remain ambiguous ) . in the best case , for cgcg 120 , we show that the maser and continuum emission are coincident to within pc ( milliarcsec ) . subsequent very long baseline interferometric maps can confirm candidate inclined disks and have the potential to show maser rings or arcs that provide a direct measurement of black hole mass , although the mass precision will rely on knowledge of the size of the maser disk .

we describe a method to identify inclined water maser disks orbiting massive black holes and to potentially use them to measure black hole masses . due to the geometry of maser amplification pathways , the minority of water maser disks are observable : only those viewed nearly edge - on have been identified , suggesting that an order of magnitude additional maser disks exist . we suggest that inward - propagating masers will be gravitationally deflected by the central black hole , thereby scattering water maser emission out of the disk plane and enabling detection . the signature of an inclined water maser disk would be narrow masers near the systemic velocity that appear to emit from the black hole position , as identified by the radio continuum core . to explore this possibility , we present high resolution ( 0.070.17 ) very large array line and continuum observations of 13 galaxies with narrow water maser emission and show that three are good inclined disk candidates ( five remain ambiguous ) . in the best case , for cgcg 120 , we show that the maser and continuum emission are coincident to within pc ( milliarcsec ) . subsequent very long baseline interferometric maps can confirm candidate inclined disks and have the potential to show maser rings or arcs that provide a direct measurement of black hole mass , although the mass precision will rely on knowledge of the size of the maser disk .

1612.09382

i

convex algebraic geometry studies convex hulls of semialgebraic sets @xcite . the convex hull of finitely many points , a zero - dimensional variety , is a polytope @xcite . polytopes have finitely many faces , which are themselves polytopes . the boundary of the convex hull of a higher - dimensional algebraic set typically has infinitely many faces which lie in algebraic families . ranestad and sturmfels @xcite described this boundary using projective duality and secant varieties . for a general space curve , the boundary consists of finitely many two - dimensional faces supported on tritangent planes and a scroll of line segments , called the edge surface . these segments are stationary bisecants , which join two points of the curve whose tangents meet . we study convex hulls of the simplest non - trivial compact space curves , those which are the union of two circles lying in distinct planes . zero - dimensional faces of such a convex hull are extreme points on the circles . one - dimensional faces are stationary bisecants . it may have two - dimensional faces coming from the planes of the circles . it may have finitely many nonexposed faces , either points of one circle whose tangent meets the other circle , or certain tangent stationary bisecants . [ fig : firsttaste ] shows some of this diversity . in the convex hull on the left , the discs of both circles are faces , and every face is exposed . in the oloid in the middle , the discs lie in the interior , @xmath0 of each circle is extreme , and no endpoint of an arc is exposed . in the convex hull on the right , there are two nonexposed stationary bisecants lying on its two - dimensional face , which is the convex hull of one circle and the point where the other circle is tangent to the plane of the first . these objects have been studied before . paul schatz discovered and patented the oloid in 1929 @xcite , this is the convex hull of two congruent circles in orthogonal planes , each passing through the center of the other . it has found industrial uses @xcite , and is a well - known toy . a curve in @xmath1 may roll along its edge surface . when rolling , the oloid develops its entire surface and has area equal to that of the sphere @xcite with equator one of the circles of the oloid . other special cases of the convex hull of two circles have been studied from these perspectives @xcite . this paper had its origins in subsection 4.1 of @xcite , which claimed that the edge surface for a general pair of circles is composed of cylinders . our results show that this is only the case when the two circles either meet in two points or are mutually tangent in all other cases , the edge surface has higher degree and it is an irrational surface of degree eight when the circles are disjoint in @xmath2 . this is related to problem 3 on convexity in @xcite , on the convex hull of three ellipsoids in @xmath1 . an algorithm was presented in @xcite ( see the video @xcite ) , using projective duality . we sketch this in section [ s : duality ] , and also apply duality to the convex hull of two circles . in section [ s : background ] we recall some aspects of convexity and convex algebraic geometry , and show that the convex hull of two circles is the projection of a spectrahedron . we study the edge surface and the edge curve of stationary bisecants of complex conics @xmath3 in section [ s : relaxation ] . we show that the edge curve is a reduced curve of bidegree @xmath4 in @xmath5 , and if @xmath6 and neither is tangent to the plane of the other , we show that the edge surface has degree eight . we also classify which curves of bidegree @xmath4 arise as edge curves to two conics . all possibilities occur , except a rational curve with a cusp singularity and a maximally reducible curve . in section [ s : circles ] we classify the possible arrangements of two circles lying in different planes in terms that are relevant for their convex hulls . we determine the face lattice and the real edge curve of each type and show that these convex hulls are spectrahedra only when the circles lie on a quadratic cone .

we describe convex hulls of the simplest compact space curves , reducible quartics consisting of two circles . when the circles do not meet in complex projective space , their algebraic boundary contains an irrational ruled surface of degree eight whose ruling forms a genus one curve . we classify which curves arise , classify the face lattices of the convex hulls and determine which are spectrahedra .

we describe convex hulls of the simplest compact space curves , reducible quartics consisting of two circles . when the circles do not meet in complex projective space , their algebraic boundary contains an irrational ruled surface of degree eight whose ruling forms a genus one curve . we classify which curves arise , classify the face lattices of the convex hulls and determine which are spectrahedra . we also discuss an approach to these convex hulls using projective duality .

1405.4883

i

the surface code @xcite is one of the simplest and most studied quantum error correcting codes . it can be realized on a two - dimensional grid of qubits such that the codespace is defined by simple four - qubit parity check operators acting on nearest - neighbor qubits . recent years have witnessed a surge of interest in the surface code as a promising architecture for a scalable quantum computing @xcite . experimental advances in manufacturing of multi - qubit devices @xcite give us hope that a small - scale quantum memory based on the surface code may become a reality soon . given high operational costs of a quantum hardware compared with the classical one , it is crucial to put enough efforts in optimizing algorithmic , or software aspects of error correction . in the present paper we focus on optimizing the decoding algorithm that takes as input measured syndromes of the parity checks and computes a recovery operation returning a corrupted state of the memory back to the codespace . as the name suggests , the maximum likelihood decoder ( mld ) is an algorithm that finds a recovery operation maximizing the probability of a successful error correction conditioned on the observed error syndrome . by definition , mld is the optimal error correction algorithm for a fixed quantum code and a fixed noise model . the first rigorous definition of mld for the surface codes was proposed by dennis et al @xcite . an important observation made in @xcite was that the computational problem associated with mld can be reduced to computing the partition function of a classical ising - like hamiltonian on the two - dimensional lattice . this observation has generated a vast body of work exploring connections between mld and the statistical physics of disordered ising - like hamiltonians , see for instance @xcite . the insights made in @xcite have also guided the search for efficient implementations of mld . although an exact and efficient algorithm for mld remains an elusive goal , several approximate polynomial - time algorithms have been discovered , most notably the renormalization group decoder due to duclos - cianci and poulin @xcite , and the markov chain monte carlo method due to hutter , wootton , and loss @xcite . in the case of concatenated codes an efficient exact algorithm for mld based on the message passing algorithm was proposed by poulin @xcite . by comparing mld with the level - by - level decoder commonly used for concatenated codes , ref . @xcite found that mld offers a significant advantage with almost two - fold increase of the error threshold for the depolarizing noise and a significant reduction of the logical error probability . here we propose an alternative method of implementing mld in the case of the surface code for two simple noise models known as the bit - flip noise and the depolarizing noise . our method combines the ideas of dennis et al @xcite and the standard classical - to - quantum mapping from classical 2d spin systems in the thermal equilibrium to quantum 1d spin chains . it enables us to reduce the computational problem associated with mld to simulating a particular type of quantum dynamics for a chain of qubits . in the case of the bit - flip noise , mld can be reduced to simulating a quantum circuit with a special type of two - qubit nearest - neighbor gates known as matchgates . it was shown by valiant @xcite that quantum circuits composed of matchgates can be efficiently simulated by classical means . matchgate circuits and their generalizations give rise to efficient holographic algorithms for certain combinatorial problems @xcite and efficient tensor network contraction methods @xcite . matchgate - based algorithms have been used to simulate quantum dynamics in systems of fermionic modes with quadratic interactions @xcite and study statistics of dimer coverings in classical lattice models @xcite . here we demonstrate that matchgates also have applications for quantum error correction . our simulation algorithm based on fermionic gaussian states @xcite provides an exact implementation of mld with the running time @xmath0 , where @xmath1 is the number of code qubits . the same algorithm can also be applied to a noise model with independent bit - flip and phase - flip errors . we note that a similar but technically different algorithm has been used by merz and chalker in the numerical study of the random - bond 2d ising model @xcite . in the case of the depolarizing noise , mld can be reduced to simulating the dynamics generated by matrix product operators with a small bond dimension . to perform the simulation efficiently we conjecture that all intermediate states generated by this dynamics are weakly entangled . this enables us to employ a vast body of efficient classical algorithms for simulating weakly entangled quantum spin chains based on matrix product states ( mps ) , see @xcite . our approximate implementation of mld for the depolarizing noise has running time @xmath2 where @xmath3 is a parameter that controls the approximation precision ( the bond dimension of the mps ) . although we do not have any rigorous arguments in support of the weak entanglement conjecture , it reflects the physical intuition that the classical 2d spin system associated with mld has a finite correlation length for error rates below the threshold @xcite . accordingly , one should expect that the classical - to - quantum mapping can not generate highly entangled states since the latter require long - range correlations . furthermore , we have justified the conjecture numerically by applying the mps - based decoder to the bit - flip noise . we observed that the logical error probabilities of the exact mld and the mps - based decoder with a relatively small bond dimension @xmath5 are virtually indistinguishable . likewise , in the case of the depolarizing noise we observed that the logical error probability exhibits a fast convergence as a function of @xmath3 suggesting that the mps - based decoder with @xmath5 implements nearly exact mld . finally , we benchmark the exact and the approximate implementations of mld against the commonly studied minimum weight matching ( mwm ) decoder @xcite . the benchmarking was performed for a fixed code distance @xmath6 and a wide range of error rates . in the case of the bit - flip noise we observed that the mwm decoder approximates the logical error probability of mld within a factor of two . the observed difference between mld and the mwm decoder can be attributed to the fact that the latter ignores the error degeneracy @xcite . since the observed difference is relatively small , we conclude that ignoring the error degeneracy does not have a significant impact on the decoder s performance for the studied noise model . in the case of the depolarizing noise we observed that the mps - based decoder is far superior than the mwm decoder offering more than two orders of magnitude reduction of the logical error probability even for small values of @xmath3 . this can be attributed to the fact that the mwm decoder often fails to find the minimum weight error consistent with the syndrome since it ignores correlations between @xmath7 and @xmath8 errors @xcite . the rest of the paper is organized as follows . we formally define the maximum likelihood decoder , the studied noise models , and the surface code in sections [ sect : mld],[sect : noise ] , and [ sect : scodes ] respectively . our exact implementation of mld for the bit - flip noise is described in section [ sect : xnoise ] . the approximate implementation of mld based on matrix product states is presented in section [ sect : xyznoise ] . a comparison between the exact mld , the approximate mld with various bond dimensions @xmath3 , and the minimum weight matching decoder is presented in section [ sect : numerics ] that describes our numerical results .

we describe two implementations of the optimal error correction algorithm known as the maximum likelihood decoder ( mld ) for the 2d surface code with a noiseless syndrome extraction . first , we show how to implement mld exactly in time , where is the number of code qubits . this reduction however requires a special noise model with independent bit - flip and phase - flip errors . secondly , we show how to implement mld approximately for more general noise models using matrix product states ( mps ) . our implementation has running time where is a parameter that controls the approximation precision . we benchmark the mps - based decoder against the standard minimum weight matching decoder observing a significant reduction of the logical error probability for .

we describe two implementations of the optimal error correction algorithm known as the maximum likelihood decoder ( mld ) for the 2d surface code with a noiseless syndrome extraction . first , we show how to implement mld exactly in time , where is the number of code qubits . our implementation uses a reduction from mld to simulation of matchgate quantum circuits . this reduction however requires a special noise model with independent bit - flip and phase - flip errors . secondly , we show how to implement mld approximately for more general noise models using matrix product states ( mps ) . our implementation has running time where is a parameter that controls the approximation precision . the key step of our algorithm , borrowed from the dmrg method , is a subroutine for contracting a tensor network on the two - dimensional grid . the subroutine uses mps with a bond dimension to approximate the sequence of tensors arising in the course of contraction . we benchmark the mps - based decoder against the standard minimum weight matching decoder observing a significant reduction of the logical error probability for .

1307.2896

i

the processes in the interstellar medium ( ism , or gas ) that determine its distribution , structure , and the formation of stars are multiple , very complex , and operate on atomic to galactic size scales ( see e.g. * ? ? ? this makes it difficult to develop a comprehensive model for the distribution of gas and star formation in galaxies from first principles . fortunately , normal galaxies are usually in a marginally stable equilibrium state . here we use this fact as the basis of a model for the distribution of gas in galaxies , and with some additional assumptions we extend this into a model of the star formation distribution . our aim is to construct an easy to implement model for the distribution of gas and star formation in galaxies that can be used to compare to observations and to easily create realistic simulated galaxies . our approach also allows difficult to observe properties of galaxies ( e.g. the molecular ism distribution ) to be inferred from those that are relatively easy to determine or infer ( the stellar mass profile and rotation curve ) . star formation has long been believed to be related to disk ( in)stability . major studies ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) have been carried out on gravitational disk stability since the 1960s and the theory of this subject is well developed . however , as early as 1972 , @xcite claimed that the whole galactic disk should be marginally stable due to negative feedback mechanism . he used this assumption to predict the gas surface density profile ; his model roughly matches the observations in the outer regions of his sample galaxies but overestimates the densities in the inner half of the galaxies . since then , observational evidence for quirk s statement that disk galaxies are usually in a marginally stable state has mounted and been noticed in various studies ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? the gravitational stability parameter @xmath3 ( see section [ threshold ] for details ) for a single component thin disk was first derived by @xcite . @xcite used a sample of tens of galaxies to show that there is very little star formation where @xmath3 is above some critical threshold . @xcite confirmed the result using more recent data . however a single fluid @xmath3 does not accurately indicate the stability of a real disk which contains both stars and gas . @xcite derived the two - fluid ( stars and gas ) stability parameter @xmath0 for a thin disk . @xcite improved the derivation by considering the stellar component as collisionless , yielding a rigorous but elaborate form of the stability parameter , @xmath4 . @xcite proposed an approximation for the two - fluid stability parameter , @xmath1 , which is widely used because of its simple form . more recently , @xcite reexamined the @xcite approximation and gave a simple but more accurate effective two - fluid stability parameters for both an infinitesimally thin ( @xmath5 ) and finite thickness ( @xmath6 ) galactic disks . inspired by the @xcite and recent studies on disk stability theory and star formation laws , we develop and test the ` constant @xmath3 disk ' ( cq - disk ) model , which we define as : a two - fluid ( gas+stars ) axisymmetric thin disk will evolve into a marginally stable state with a constant stability parameter @xmath0 through out the galactic disk . the basic idea for this model is to use the constancy of the two - fluid stability parameter to predict the distribution of gas and then use empirical molecular - to - neutral gas ratio ( @xmath2 ) relations and the best star formation law ( sfl ) to predict the distribution of neutral and molecular gas as well as star formation rate . here we compare the observed distribution of the ism , and star formation in a small sample of galaxies to our model in order to test our assumptions and to optimise the model by trialling different recipes for its key ingredients ( @xmath0 , @xmath2 , and the sfl ) . the outline of our paper is as follows : section [ bkintro ] briefly introduces background information , e.g. the gravitational stability parameter , molecular - to - neutral gas ratio model , and star formation laws ; section [ model ] presents the detailed model we construct ; section [ data ] gives a brief description of our sample galaxies ; section [ results ] shows the results ; in section [ discussion ] we discuss the assumption and implications of our model ; and in section [ application ] we discuss further tests and possible uses of our model . through out this paper , we are only concerned with the large scale star formation in the galactic disk , hence we suppose the disk is axisymmetric and focus on the radial profiles of various physical quantities . as our research progressed it became useful to divide the galactic disk in to three regions : central ( within @xmath7 ) , intermediate ( @xmath8 ) and outer ( @xmath9 ) , where @xmath10 is the optical radius , defined by where the @xmath11 band surface brightness reaches 25 mag arcsec@xmath12 . in general , our model works best in the intermediate radii , and much of the testing of the model is limited to these radii . the profiles we create often do not match the observations in detail in the central region , although , as we will show , the match to quantities integrated over the central region is reasonable . we can not test our star formation models in the outer disk because the star formation intensity was not measured beyond @xmath10 in our data sources . in @xcite we discuss the expected ism structure in the outer disk . there we showed that a gas dominated constant @xmath3 outer disk should have a surface mass density fall - off with the same profile as the dark matter for systems with a flat rotation curve , thus explaining the close relationship between dark matter and hi @xcite . the other reason that we make these divisions is that the rcs are generally more reliable in the intermediate disk : there are less or even no data points in the central regions , while often warps and asymmetries are present in the outer regions .

our tests focus on intermediate radii ( 0.3 to 1 times the optical radius ) because there are insufficient data to test the outer disks and the fits are less accurate in detail in the centre . to optimise the model , we evaluate four recipes for the stability parameter , three recipes for apportioning the ism into molecular and neutral components , and eight versions of the sfl . we find no clear - cut best prescription for the two - fluid ( gas and stars ) stability parameter and therefore for simplicity , we use the approximation ( ) . thus in the context of our modeled ism profiles , the linear molecular sfl and the two - component sfl work better than the other prescriptions we tested . we incorporate these relations into our ` constant disk ' ( cq - disk ) model . * keywords : * galaxies : ism - kinematics and dynamics - star formation

we develop a model for the distribution of the ism and star formation in galaxies based on recent studies that indicate that galactic disks stabilise to a constant stability parameter , which we combine with prescriptions of how the phases of the ism are determined and for the star formation law ( sfl ) . the model predicts the gas surface mass density and star formation intensity of a galaxy given its rotation curve , stellar surface mass density and the gas velocity dispersion . this model is tested on radial profiles of neutral and molecular ism surface mass density and star formation intensity of 12 galaxies selected from the things sample . our tests focus on intermediate radii ( 0.3 to 1 times the optical radius ) because there are insufficient data to test the outer disks and the fits are less accurate in detail in the centre . nevertheless , the model produces reasonable agreement with ism mass and star formation rate integrated over the central region in all but one case . to optimise the model , we evaluate four recipes for the stability parameter , three recipes for apportioning the ism into molecular and neutral components , and eight versions of the sfl . we find no clear - cut best prescription for the two - fluid ( gas and stars ) stability parameter and therefore for simplicity , we use the approximation ( ) . we found that an empirical scaling between the molecular to neutral ism ratio ( ) and the stellar surface mass density proposed by works marginally better than the other two prescriptions for this ratio in predicting the ism profiles , and noticeably better in predicting star formation intensity from the ism profiles produced by our model with the sfls we tested . thus in the context of our modeled ism profiles , the linear molecular sfl and the two - component sfl work better than the other prescriptions we tested . we incorporate these relations into our ` constant disk ' ( cq - disk ) model . * keywords : * galaxies : ism - kinematics and dynamics - star formation

1307.2896

i

we have developed a simple ` constant @xmath3 disk ' ( cq - disk ) model for predicting the distribution of ism and star formation in galaxies based on the assumption that the two - fluid instability parameter ( @xmath0 ) of the galactic disk is a constant . the model predicts the gas surface mass density and star formation intensity given the rotation curve , stellar surface mass density and the gas velocity dispersion . in this paper we compared radial profiles of hi , and h@xmath53 surface mass density and star formation intensity from a sample of 12 galaxies from l08 . in order to optimise our model , we tried various prescriptions for calculating @xmath0 , the ratio @xmath174 , and the star formation law ( sfl ) . we find that * the @xmath0 profiles are fairly flat over the intermediate radii of the disk , with variations of a factor of @xmath138 about the mean , no matter which recipe of @xmath0 is employed . the @xcite formulation of @xmath0 has the strongest physical basis of the recipes we tried , and also marginally the flattest @xmath0 profiles . however it is the most difficult to implement since it requires the wavelength of the most unstable mode to be derived . the @xcite approximation , is the most practical recipe for @xmath0 in terms of its very simple form , and the one we have adopted in our model . * we tested three prescriptions of @xmath2 by comparing the observed surface mass densities of neutral and molecular gas with our model predictions . all three prescriptions produce @xmath72 and @xmath73 profiles that match the observed profiles with typical variations better than a factor of 2 about the mean . overall , the empirical scaling of @xmath2 with stellar surface mass density ( sr ) proposed by @xcite produces the best fits to both the @xmath72 and @xmath73 profiles , and therefore we favor this model . while the @xcite self - shielding prescription kr produces typically better matches to the @xmath72 profiles than the sr relation , the matches to the @xmath73 profiles are worse . although the best @xmath149 relation selected here is based on the predicted @xmath117 from our cq - disk model , it is consistent with the l08 results based on observed neutral and molecular ism profiles . * we tested eight versions of the sfl , five that depend on just the total ism content ( defined as combined neutral and molecular component ) and three that require the ism be separated in to neutral and molecular phases . the latter three were tested with all three prescriptions of @xmath2 that we trialled . the linear molecular sfl , sfr@xmath175 produces the best matches to the @xmath74 profiles when used with the sr @xmath2 relation , with the models typically agreeing with the observed profiles to within a factor of 2 . the two - component sfl sfr@xmath176 , combined with the sr relation does second best with agreement to typically a factor of 2.2 , while the orbital time sfl sfr@xmath153 , at third best in terms of @xmath177 value , is the best of the single component ism sfls with agreement to within a factor of @xmath178 over the intermediate radii disk . again , the best sfls here are selected based on our model predicted @xmath179 as well as @xmath73 , not the observed gas surface mass densities . however , the results are consistent with those from l08 and @xcite who do use observed ism profiles for their tests . this consistency also supports our cq - disk model in an indirect way . * the modelled star formation intensity profiles ( figs [ sfr_s ] , [ sfr_p ] , [ sfr_k ] ) match the observations best at intermediate radii , and show the largest deviations in the central region ( where @xmath180 ) . this suggest that a more elaborate model is needed to explain the ism and gas distribution in the centres of galaxies , especially those with bulges or a steeply rising rotation curve . however , integrating the sfr over the entire central region area we find that the models agree with the observations within a factor of 3 in all but one case . this indicates the systematic discrepancy integrated over galaxy centres generally is not severe . since we are testing a model for the distribution of star formation and gas in galaxies that we base on inferences from things team results , there is no surprise that our model works well for large portions of galaxies selected from the things sample . our future papers will test our model on galaxies selected independently . one advantage of our models is that they are easy to calculate given the rotation curve and the distribution of stellar mass . this may prove to be a useful advantage in terms of implementation compared to more detailed models like that of @xcite . however to handle the central regions , some reasonable modifications may be required , such as requiring gas and sfr to only be at @xmath181 for galaxies with @xmath182 above some fiducial value . we thank a. leroy and e. de blok for kindly providing the things data . we thank the referee very much for thoughtful comments and suggestions , which largely improved the content and clarity of our paper . we also thank anahi caldu primo and fabian walter for providing the gas velocity dispersion data . zz also thanks icrar for hospitality during his visit to perth , western australia . this work is funded in part by galex gi grant nnx09af85 g .

we develop a model for the distribution of the ism and star formation in galaxies based on recent studies that indicate that galactic disks stabilise to a constant stability parameter , which we combine with prescriptions of how the phases of the ism are determined and for the star formation law ( sfl ) . the model predicts the gas surface mass density and star formation intensity of a galaxy given its rotation curve , stellar surface mass density and the gas velocity dispersion . this model is tested on radial profiles of neutral and molecular ism surface mass density and star formation intensity of 12 galaxies selected from the things sample . nevertheless , the model produces reasonable agreement with ism mass and star formation rate integrated over the central region in all but one case .

we develop a model for the distribution of the ism and star formation in galaxies based on recent studies that indicate that galactic disks stabilise to a constant stability parameter , which we combine with prescriptions of how the phases of the ism are determined and for the star formation law ( sfl ) . the model predicts the gas surface mass density and star formation intensity of a galaxy given its rotation curve , stellar surface mass density and the gas velocity dispersion . this model is tested on radial profiles of neutral and molecular ism surface mass density and star formation intensity of 12 galaxies selected from the things sample . our tests focus on intermediate radii ( 0.3 to 1 times the optical radius ) because there are insufficient data to test the outer disks and the fits are less accurate in detail in the centre . nevertheless , the model produces reasonable agreement with ism mass and star formation rate integrated over the central region in all but one case . to optimise the model , we evaluate four recipes for the stability parameter , three recipes for apportioning the ism into molecular and neutral components , and eight versions of the sfl . we find no clear - cut best prescription for the two - fluid ( gas and stars ) stability parameter and therefore for simplicity , we use the approximation ( ) . we found that an empirical scaling between the molecular to neutral ism ratio ( ) and the stellar surface mass density proposed by works marginally better than the other two prescriptions for this ratio in predicting the ism profiles , and noticeably better in predicting star formation intensity from the ism profiles produced by our model with the sfls we tested . thus in the context of our modeled ism profiles , the linear molecular sfl and the two - component sfl work better than the other prescriptions we tested . we incorporate these relations into our ` constant disk ' ( cq - disk ) model . * keywords : * galaxies : ism - kinematics and dynamics - star formation

1208.3481

i

quantum liquids are among the most sought after states of matter . one celebrated class of such quantum liquids , the fractional quantum - hall ( fqh ) states , @xcite has been a locus of scientific attention for almost three decades . initially introduced to explain the fractional quantum - hall effect ( fqhe ) observed in semiconductor devices , @xcite they describe interacting electrons constrained in two dimensions and subject to a strong perpendicular magnetic field . fractionally filling a magnetic landau level ( ll ) then yields an incompressible fqh liquid and gives rise to a precisely quantized hall conductivity . in addition , the quasiparticles of these states obey anyonic statistics , @xcite which can be either abelian or non - abelian , the latter fulfilling an essential condition for fault - tolerant quantum computation . @xcite an alternative route to quantum hall liquids is via tightly bound electrons moving in a magnetic texture . the simplest such magnetic texture is a uniform magnetic field perpendicular to the plane of the system . for non - interacting , tightly bound electrons , this gives rise to an integer quantum - hall ( iqh ) state and leads to hofstadter s fractal energy spectrum , @xcite whereas in a fractionally filled tight - binding model of electrons interacting via a screened coulomb repulsion , the realization of a fqh state is possible . @xcite haldane noted @xcite that an external magnetic field is not the only viable path to iqh states and introduced a honeycomb - lattice model , with complex hoppings that break time - reversal invariance , and defined the first integer chern insulator ( ci ) , in which the total magnetic field through the unit cell averages to zero . in the meantime , mechanisms leading to complex hoppings with the necessary properties have been identified . one realization may be found in strongly spin - orbit coupled semiconductor materials that are ferromagnetically ordered . @xcite another possibility arises through the coupling of itinerant electrons to localized magnetic moments , @xcite for example the kondo - lattice model on the triangular lattice supports a non - trivial magnetic texture , which induces an integer - quantized hall conductivity of the itinerant electrons . @xcite a considerable body of recent research has addressed the question whether the lattice counterpart of the fqhe can be observed when topologically non - trivial bands , called chern bands , are fractionally filled and electrons are interacting . several numerical studies using exact diagonalization techniques have convincingly established the existence of laughlin - series states in an number of different models on various lattices . @xcite these systems have since been called fractional chern insulators ( fci ) . very recent work has reported fci states beyond laughlin fractions . @xcite in addition to reproducing the known fqhe on a lattice and potentially at higher temperatures , cis also offer the intriguing possibility of a chern number higher than one , a departure from the analogy with lls . recent studies have explored this direction by constructing models that have higher chern numbers and studying possible fci states . @xcite from the analytical side , the problem of fci states has been approached by a careful study of emergent translational symmetries @xcite and many - body trial wave functions . @xcite others have examined the algebraic properties of the density operators projected onto one chern band and made a comparison with the girvin - macdonald - platzman algebra that is satisfied by the lowest ll density operators in the continuum fqhe . @xcite in numerical studies of fci states , one typically starts by adding inter - site interactions to topologically nontrivial but non - interacting ci models . as potential realizations of the non - interacting and nearly flat `` parent '' bands , cold atoms , @xcite oxide heterostructures , @xcite strained graphene , @xcite and strongly correlated multi - orbital models for layered oxides @xcite have been proposed . in the present paper , we build upon this last approach and thus focus our attention on a strongly correlated model on the triangular lattice . it was shown that on the mean - field level and near half - filling , a magnetically ordered ci with a very flat single - particle band emerges . doping this nearly flat band to fractional fillings was shown to give rise to fci states within the framework of an effective single - orbital model . here , we give a detailed account of the mapping onto the effective single - orbital model and show how such topologically nontrivial and nearly flat bands emerge in kondo - lattice and hubbard models both for the limit of infinite onsite interactions and for more realistic intermediate interaction strength . we then provide extensive numerical evidence , based on both eigenvalue spectra ( e.g. , ground - state degeneracy and spectral flow ) and eigenstate properties ( e.g. , many - body berry curvature and hall conductivity ) , for the existence of fci states in this model by using exact diagonalization . we discuss the robustness of fci states against disorder originating from single - site defects in the magnetic ordering , which will always occur in realistic situations . another very relevant issue in the context of fci states is their competition with other phases , @xcite e.g. symmetry - broken states such as a charge - density wave ( cdw ) . we study this issue by using a method that does not project onto the nearly flat chern band and thus keeps the effects of dispersion . the model considered in this work allows for a careful study of the competition between finite dispersion and interactions . we map out a phase diagram for filling fractions @xmath3 and @xmath4 . in the latter case , filling permits a commensurate cdw , whereas in the former it does not . the cdw is favored by fermi - surface ( fs ) nesting , and we accordingly find the fci at @xmath4 to be far more stable when the bands are poorly nested . this paper is organized as follows : in sec . [ sec : kondo_hubb ] , we extend the discussion of flat and topologically nontrivial bands arising in @xmath0 models and derive the effective model . numerical results on the model are presented in sec . [ sec : results ] , where we first focus on information obtained from eigenenergies , namely gaps and flux insertion ( sec . [ sec : spectrum ] ) and fractional statistics of charged excitations in fci states based on a recently introduced state - counting argument ( sec . [ sec : stat ] ) . @xcite we then add information obtained from the eigenstates : the hall conductivity , which allows us to address the impact of impurities in sec . [ sec : disorder ] and the static charge - structure factor , which allows us to discuss the competition with the cdw at filling @xmath4 in sec . [ sec : phdiag ] . we conclude with some remarks summarizing the main points in sec . [ sec : conclusions ]

we analyze how very flat single - particle bands with non - trivial topological character , a chern number , arise both in the limit of infinite on - site interactions as well as in more realistic regimes . exact diagonalization is then used to investigate an effective one - orbital spinless - fermion model at fractional fillings including nearest - neighbor interaction ; it reveals signatures of fractional chern insulator ( fci ) states for several filling fractions . in addition to indications based on energies , e.g. flux insertion and fractional statistics of quasiholes , chern numbers are obtained .

we discuss the low - energy limit of three - orbital kondo - lattice and hubbard models describing orbitals on a triangular lattice near half - filling . we analyze how very flat single - particle bands with non - trivial topological character , a chern number , arise both in the limit of infinite on - site interactions as well as in more realistic regimes . exact diagonalization is then used to investigate an effective one - orbital spinless - fermion model at fractional fillings including nearest - neighbor interaction ; it reveals signatures of fractional chern insulator ( fci ) states for several filling fractions . in addition to indications based on energies , e.g. flux insertion and fractional statistics of quasiholes , chern numbers are obtained . it is shown that fci states are robust against disorder in the underlying magnetic texture that defines the topological character of the band . we also investigate competition between a fci state and a charge density wave ( cdw ) and discuss the effects of particle - hole asymmetry and fermi - surface nesting . fci states turn out to be rather robust and do not require very flat bands , but can also arise when filling or an absence of fermi - surface nesting disfavor the competing cdw . nevertheless , very flat bands allow fci states to be induced by weaker interactions than those needed for more dispersive bands .

1208.3481

r

the interacting hamiltonian can be diagonalized exactly for small systems , using the lanczos method . @xcite unless otherwise noted , the results presented here are on a @xmath138 unit - cell torus ( i.e. , @xmath139 real - space sites ) . we do not project onto the flat subband , see fig . [ fig : disp](a ) , but instead model the whole system of both subbands with @xmath72 . while this approach increases the hilbert space and thus restricts system size , it has the advantage that competition with phases mixing the two subbands is included automatically . we use several observables to detect fci states and to distinguish them from other phases ; first , we discuss conclusions to be drawn from the eigenvalues , and later also include information obtained from the eigenstates , namely the many - body chern number as a topological invariant and the charge - structure factor indicating formation of a ( conventional ) charge - density wave . even though the results of our investigation do not allow for conclusive finite - size scaling , we have verified that the findings presented here are consistent for smaller as well as somewhat larger systems . furthermore , the main features of the fci states found are consistent for all aspect ratios yielding the same system size , apart from those that reduce the system to a one - dimensional chain . before passing , we note that we have obtained similar results to the ones presented here for several other filling fractions @xmath140 , with @xmath141 . conclusive evidence for 4/5 , 5/7 , 6/7 states could not be obtained , in agreement with reported results for another model . @xcite . in all panels @xmath142 . ] fci states manifest themselves in features of the obtained eigenvalue spectra . traditional fqh ground states are @xmath143-fold quasi - degenerate on a finite torus at filling @xmath140 . @xcite the same degeneracy is expected to occur for fci states as well , at least within certain well - defined limits . @xcite quasi - degenerate fqh ground - state eigenvalues must also exhibit spectral flow , leading each of them into another upon insertion of a flux quantum . @xcite magnetic fluxes can be modelled by introducing phase factors to the hopping from site @xmath144 to site @xmath145 , thus leading to the transformation @xmath146 $ ] . in this manner , an electron hopping around the lattice in the @xmath147 direction picks up a phase @xmath148 . . in all panels @xmath149 . ] the features described above are illustrated , as a function of @xmath150 , in fig . [ fig : evflux_v ] for @xmath3 . in this case , the three quasi - degenerate ground states emerge from the continuum as the interaction strength is increased . insertion of one flux quantum indeed leads from one ground - state eigenvalue to another . it can also be seen that spectral flow is a general property of the eigenvalue spectrum , and we have found that it also occurs even at @xmath151 . the @xmath4 ground states behave in a similar fashion . it can be seen that the fci states remain gapped for a range of both @xmath132 and @xmath2 . in order to define a physically meaningful phase boundary , however , one has to make sure that the ground states remain gapped upon flux insertion , not only in their own momentum sector , but also across momentum sectors . the reason is that the presence of impurities would mix the momentum sectors and therefore close the gap if the quasi - degenerate fci - state levels cross excited - state levels . as seen in fig . [ fig : evflux_v ] , interaction mostly changes the energy differences between groups of three quasi - degenerate eigenstates , which flow into each other upon flux insertion , and has less impact on the energy splitting within each manifold . when tuning the transition via increasing the band dispersion , the situation is somewhat different , see fig . [ fig : evflux_t3 ] . for @xmath152 , the fci ground state is destroyed by increasing the split between quasi - degenerate levels , permitting a higher - energy states to mix with the fci - state manifold for some flux values . the splitting between ground states in the traditional fqhe case is due to quasiparticle - quasihole excitations propagating around the torus and therefore depends mainly on system size , becoming zero in the thermodynamic limit . @xcite in the finite tight - binding lattice systems discussed here , the splitting is affected significantly by the residual kinetic energy of the partially filled band , as can be seen in fig . [ fig : evflux_t3 ] . since the dispersion is present also in the thermodynamic limit , it is not clear whether the splitting survives to the thermodynamic limit or not in this system . despite level rearrangements or increasing spread between eigenvalues , fci states remain topologically conjugate upon varying the band flatness or the interaction strength . a factor that can split this conjugacy is disorder , as will be shown in the sec . [ sec : disorder ] . at the same time , ground - state levels that remain gapped upon flux insertion along one direction may cross excited - state levels upon flux insertion along another direction . a more careful analysis , based both on eigenenergy as well as on eigenstate properties , is necessary to uniquely determine a gapped ground state for a given parameter set . this is the purpose of sec . [ sec : chern ] . before investigating eigenstates , however , the next section is going to discuss another aspect of eigenenergies , fractional statistics . -unit cell system , the filling fraction is @xmath153 . there are seven quasi - degenerate ground states ( marked in red ) , which are slightly separated from the rest of the states in the low - energy sector and exhibit spectral flow ( shown in different colors ) . their chern number is @xmath154 within the numerical error margin . ] the concept of generalized pauli principles , @xcite according to which states with clustered anyonic quasiparticles are energetically penalized , has served as a tool to indicate fractional statistics in fqh states . @xcite as was first demonstrated heuristically @xcite and later on substantiated theoretically , @xcite the same logic holds for fci states . for the @xmath3 fci state , the number of quasihole - state levels in a well separated , low - energy fock space is equal to the number of ( 1,3)-admissible partitions of the momentum sectors on the torus . the individual states per momentum sector can also be accounted for , due to an emergent translational symmetry ( see ref . for details ) . this symmetry is a characteristic feature of all the fci states we have found in the triangular lattice model . in this section , we demonstrate that quasihole states of the triangular - lattice model obey the same state - counting arguments . quasiholes can be introduced in a fci state by either removing electrons or increasing the system size . an example of both cases is presented in fig . [ fig : fractional ] . the counting rule is verified in both cases . the counting rule can also be easily generalized to all laughlin filling fractions @xmath155 and we have verified it for @xmath156 in this model . apart from the agreement to the counting rule , one can also notice the emergence of a `` daughter '' fci state within the gapped low - energy sector , as expected in the hierarchy picture . even though in the present context this is mainly a peculiarity of the small system sizes , it can nevertheless be viewed as a simple example of the formation of a hierarchical fci state among the quasiparticle states of a `` parent '' fci state . taking this observation one step further , it can be seen that the spectrum looks qualitatively different under flux insertion in the two cases presented in fig . [ fig : fractional ] , namely , the eigenvalue spectrum in the case where the filling is @xmath157 looks more like that of the non - interacting system with levels crossing upon flux insertion , whereas at @xmath153 levels come in small groups , which remain separated under flux insertion ( compare to fig . [ fig : evflux_v ] ) . this observation can be compared to the composite fermion theory of the fqhe , @xcite according to which the state of a fqh system at filling fractions with even denominators can be effectively described by free fermions with flux tubes attached to them . this composite - fermion view of the fci hierarchy of states has also been supported by recent numerical calculations . @xcite these two different facets of the same model can serve as an example of the compatibility between the hierarchy and composite - fermion pictures of the fqhe in an unconventional fqh system . the most unambiguous characteristic of a fci state is arguably its hall conductivity . the ground - state hall conductivity of a fci at filling @xmath140 should be exactly @xmath158 . occasionally , this quantity is referred to as `` fractional chern number '' , to highlight the connection to the topological aspects of fci states . the hall conductivity @xmath50 of a gapped , degenerate state , measured in units of @xmath159 in the following , can be efficiently calculated using the kubo formula : @xcite @xmath160 where @xmath161 is the number of unit cells , @xmath162 are the @xmath143-fold degenerate many - body ground states and @xmath163 are higher - energy eigenstates . the corresponding eigenenergies are @xmath164 . the @xmath148 dependence of the hamiltonian comes from magnetic fluxes going through each of the handles of the torus , as discussed in sec . [ sec : eff_model ] . , ( d - f ) their standard deviations @xmath165 from the exact average and relative deviations of hall conductivities @xmath166 as a function of grid size for the state @xmath167 , when it is in the excited - state quasi - continuum ( top ) and in the ground - state manifold ( middle and bottom ) . the integrations in eq . have been approximated by simple riemann sums . @xmath168 is the number of @xmath148 points taken in the range @xmath169 in each direction . ] the integrand in eq . is proportional to the berry curvature @xmath170 for each of the states in the degenerate ground state . for fci states , berry curvatures are periodic functions varying with @xmath148 . in fig . [ fig : berry ] , the many - body berry curvature for a specific state , which develops into one of the fci ground states , is shown . it is seen that its smoothness varies as this state emerges from the excited state continuum . the period extends over @xmath143 flux quanta in one direction and one flux quantum in the other , remains unchanged for all values of @xmath2 and it is the same for all states in the ground - state manifold . the berry curvature of the other two ground states is the same function , but translated by one and two flux quanta in the @xmath171 direction respectively . even when the many - body berry curvature of a fci state is strongly varying , it is often centered around the value corresponding to the filling fraction and , since it is periodic , the hall conductivity obtained by integration is very close to the quantized value . this occurs even if the fci state is not a ground state . in the example presented in fig . [ fig : berry ] , the hall conductivity is in all three cases equal to @xmath3 within the numerical accuracy , which we will now discuss . ) , for each of the three quasi - degenerate fci states as a function of ( a ) the interaction strength @xmath150 and ( b ) the third - neighbor hopping @xmath130 ( right ) . not the different scales on the vertical axes . ] the hall conductivities we have calculated are very close to the expected exact values in the fci regime , despite the fact that the integrations involved are performed numerically . the relative deviation with respect to the exact value for the case of @xmath3 is presented in fig . [ fig : berry ] . this example illustrates that the error in the hall conductivity due to the finite size of the system should be smaller than 1% , at least for the kubo formula approach , even for small systems . in the case of clearly gapped fci ground states , the accuracy is even better , due to the integrand being very smooth . in all cases , we have used simple riemann summation to evaluate integrals , in order to obtain upper bounds for the numerical errors . other methods , like the simpson rule , would converge for smaller grid sizes . it should be noted that when the hall conductivity of an individual state within the degenerate ground state is evaluated , the integration should be extended over the whole period of the berry curvature . this is no longer necessary when calculating the average hall conductivity and the integration range can then be restricted to @xmath172 . the effects of interaction and band dispersion can also be traced in the behavior of the hall conductivity . this is shown in fig . [ fig : chern ] . outside the fci regime , where low - energy levels cross upon flux insertion , the hall conductivity oscillates . it converges to @xmath158 at about the value of @xmath150 for which the fci states separate from the excited - state spectrum , forming a three - fold degenerate ground state . on the other hand , the hall conductivity of these states remains close to 1/3 with deviation from the flat - band limit , and only changes smoothly with @xmath130 , converging to the expected value close to the phase boundary discussed in sec . [ sec : phdiag ] . fqh states must be robust against disorder , as long as the energy scale of the disorder is smaller than the gap . @xcite the magnetic texture in the three - orbital model presented is generated spontaneously by itinerant electrons , so an expected source of disorder are local inhomogeneities in the chiral spin pattern . a simplistic approach to simulate this effect is to vary the flux picked up by an electron hopping along one selected bond of the finite cluster . this is done by varying the phase @xmath173 in the phase factor in front of the corresponding hopping . the effect of such a variation on hall conductivities at @xmath3 is shown in fig . [ fig : disorder ] . . ( c , d ) standard deviation @xmath174 of total berry curvature @xmath175 , defined by adding up the many - body berry curvatures @xmath170 of the three lowest - energy states for each value of @xmath148 , and relative deviation @xmath176 of hall conductivity as a function of grid size . @xmath168 is the number of @xmath148 points taken in the range @xmath177 in each direction . the results shown in the right panels are for @xmath178 , but are qualitatively the same for all other values of @xmath173 . ] as long as the energy scale of the disorder is small enough , the ground states remain separated by a gap from the rest of the spectrum and their average hall conductivity remains constant . the hall conductivities of the individual quasi - degenerate ground states are not smooth functions of magnetic disorder . in particular , as soon as the impurity is switched on , the hall conductivity of each individual state jumps to an integer value . also , berry curvatures are no longer smooth functions of @xmath148 . nevertheless , the hall conductivities are still numerically well defined , as demonstrated in the right panels of fig . [ fig : disorder ] , and their average , which is the proper observable quantity in the thermodynamic limit , remains constant as the disorder is varied . this invariance of the hall conductivity directly demonstrates the topological robustness of fci states . again in analogy to fqh states,@xcite disorder introduces further splitting , apart from the one due to dispersion discussed in sec . [ sec : spectrum ] , between fci ground - state eigenvalues , which no longer exchange places under flux insertion . this splitting is expected to be a finite - size effect and should disappear in the thermodynamic limit . a conclusive proof of this statement is however beyond the scope of this work . despite the similarities , the impact of disorder in general on the energy - scale balance necessary for fci states is qualitatively different than the situation in traditional fqh states . for example , disorder may have a different effect depending on the interaction strength and range , and may lead to another , possibly topologically trivial , state , as has been shown in a recent study on the checkerboard lattice involving chemical - potential disorder . @xcite early on , it was pointed out that an important prerequisite for the emergence of a fci state is the balance between three energy scales , namely the width of the topologically non - trivial band , the gap(s ) separating it from other bands and the coulomb interaction strength . @xcite if the ratio between the first two , as expressed by the figure of merit eq . ( [ eq : merit ] ) , is large , then the interaction can become strong enough to induce fci states , but remain small compared to the band gaps , which avoids mixing in wave function of different topological character . many investigations have been focused on models in the perfectly flat band limit ( exactly as in a landau level ) , supplemented by various types of interaction . rather recently , it was reported that the band flatness alone is not in fact a reliable indicator for the stability of fci states . @xcite + + + in this section , we discuss how a finite dispersion influences the stability of fci states in a triangular - lattice model , where we focus on band filling and fs nesting . the first presents a rather obvious difference to lls , as has recently also been mentioned in ref . : while a ll is expected to be particle - hole symmetric , the nearly flat subband of a lattice model is not . we are going to discuss filling fractions @xmath179 and @xmath4 that turn out to clearly exemplify this difference . the latter case , which was also shortly discussed in ref . , corresponds to @xmath180 filling of the original triangular lattice , where nn coulomb interaction can stabilize a cdw [ with particles at second - neighbor sites , see fig . [ fig : tri_cdw ] ] , while no such cdw is possible at @xmath3 . the competition between the fci and the cdw is in turn strongly affected by fs nesting , and we are going to see that the fci is far more stable for more dispersive bands without nesting than for flatter bands with a nested fermi surface . however , we are also going to see that very flat bands allow for fci states at the lowest interaction strengths , even though they are in our case very well nested . and @xmath150 , for ( a ) @xmath3 and ( b ) @xmath4 , shown in colorcode . the dashed lines indicate the phase boundary , defined by the condition that the gap remains open for all values of inserted magnetic flux . the flatness ratio @xmath132 of the flat band of @xmath131 ( bottom scale ) is adjusted by varying @xmath130 ( top scale ) . the maximum value of the flatness ratio ( @xmath181 ) is marked by the dotted lines . ] as mentioned in sec . [ sec : eff_model ] , varying @xmath130 allows us to tune the band flatness and to moreover switch between regimes with and without fs nesting . examples are shown in fig . [ fig : fbz_fs ] , where the dispersion as well as the fermi surface corresponding to @xmath4 are shown for some values of @xmath130 . both for near - optimal @xmath182 ( @xmath183 ) and for smaller @xmath184 ( @xmath185 ) , the fs contains hexagons with almost perfectly nested segments . a difference between the two cases is on one hand the flatness ratio , but on the other hand , the flatter bands also have an additional circular fs around the @xmath186 point . for @xmath187 , only the circular fs remains ( see the example with @xmath188 and @xmath189 ) and there is thus no longer good nesting . figure [ fig : phdiag ] shows the region where fci states are stable on a 24-site ( @xmath138 unit - cell ) system , as a function of coulomb interaction strength @xmath2 and the flatness ratio @xmath132 , which is in turn controlled by third - neighbor hopping , see fig . [ fig : disp ] . the two panels are for fillings @xmath3 and @xmath4 . in both cases , the ground - state manifold in the fci state is expected to be three - fold degenerate . the colorcode indicates the gap between the three ground states and the fourth lowest eigenstate in the absence of applied magnetic flux . in order to define a physically meaningful phase boundary , however , one has to make sure that the ground states remain gapped upon flux insertion , not only in their own momentum sector , but also across momentum sectors , see sec . [ sec : spectrum ] . the solid lines in fig . [ fig : phdiag ] indicate the phase boundary determined by taking these considerations into account . we have verified that the phase diagrams obtained from a 30-site torus are qualitatively the same as the ones shown here . the stability range of the fci differs for @xmath4 and system sizes commensurate with the cdw ( @xmath190 and @xmath191 sites ) , but the corresponding phase - diagram area is still finite . and @xmath150 at filling fractions ( a , b ) @xmath3 and ( c - f ) @xmath4 . the sharp peaks indicate the formation of a charge - ordered state . in the fci regime , the static structure factor of all three quasi - degenerate ground states is identical.[fig : sf ] ] for both fillings , the system is in a metallic state at small @xmath150 , while finite values of @xmath150 can lead to fci ground states for an extended range of the band flatness . in the case of @xmath3 , the fci state can be induced for any band dispersion by making @xmath2 large enough . the fci persists even for @xmath150 considerably larger than the band gap . this has also been observed for another fci model on the checkerboard lattice , @xcite and appears to indicate that the fermions are dilute enough to occupy mostly one subband regardless of @xmath150 , so that a mixing of the topological character of the two bands does not occur . in contrast , the @xmath4 fci states survive only for moderate values of @xmath150 . larger interaction strengths lead to a different ground state , which is , as we will argue below , a cdw . to determine the type of order in each of the regions in fig . [ fig : phdiag ] , we calculate key properties of the corresponding ground states . the fci states , despite the hints from the energy spectrum , have to be identified by their topological invariant , see sec . [ sec : chern ] . to find out whether there is tendency towards charge order in the rest of the phase diagram , we calculate the static ( charge-)structure factor ( ssf ) , defined as : @xmath192 where @xmath193 is the number of sites , @xmath194 is the electron - number operator acting on the site at position @xmath195 , @xmath196 is the average electron number and @xmath197 stands for the many - body ground state . charge - density modulations are marked by sharp features in @xmath198 at certain wave vectors . liquid states , on the other hand , should be featureless in comparison to charge - modulated states . even though the accessible system sizes are not large enough to exemplify the featurelessness of liquid states , a qualitative difference between liquid and charge - modulated states can be seen . examples are shown in fig . [ fig : sf ] . at @xmath3 and within the fci regime , @xmath199 remains almost unchanged upon variation of model parameters . the same holds , although less markedly , for the metallic , fermi - liquid - like state at small interaction strengths and small ( or very large ) @xmath130 . despite the fact that the shape of @xmath198 is distinct for the two liquid states , see figs . [ fig : sf](a ) and ( b ) , the differences are subtle . in order to distinguish between the fci and metallic states , one would thus rather use the topological invariant of their ground states , see sec . [ sec : chern ] , or the criterion that the quasi - degenerate ground states remain separated from higher states for all fluxes , as used for fig . [ fig : phdiag ] , see above . however , the charge - structure factor is very valuable in distinguishing the weakly correlated fermi liquid from a cdw driven by coulomb repulsion . at @xmath4 and @xmath200 , away from the fci regime , two peaks appear in @xmath198 and increase continuously upon increasing @xmath150 , see see fig . [ fig : sf](d ) . when choosing @xmath142 near the maximal flatness [ see fig . [ fig : sf](c ) ] or @xmath201 with bad fs nesting [ see fig . [ fig : sf](f ) ] , the peaks only begin to grow for large @xmath2 , where ground - state behavior upon flux insertion changes : a full gap is only obtained for lattice sizes commensurate with the ordering pattern , like the @xmath202 and @xmath203 lattices , but not on more general lattices . this indicates that the fci state breaks down and is replaced by a cdw . the peaks observed in @xmath198 for @xmath4 grow with @xmath2 , supporting their relation to a cdw . their wave vectors correspond to a state where particles sit at nnn sites on the triangular lattice , i.e. , to the regular charge pattern compatible with a filling of @xmath204 of the triangular lattice . as can be seen in fig . [ fig : tri_cdw ] , this pattern avoids any penalty due to nn coulomb interaction @xmath2 and large enough @xmath205 will thus eventually induce such a charge distribution . the phase diagrams in fig . [ fig : phdiag ] clearly show that the band flatness parametrized by @xmath132 is itself not a reliable indicator for the stability of fci states , as has also been pointed out recently in a different case . @xcite the energy gap for @xmath3 is rather symmetric with respect to the highest figure of merit , but the phase boundary determined by requiring a full gap over all momentum sectors and for all fluxes shows that the fci states are somewhat more stable for larger @xmath130 . in the case of @xmath4 , the asymmetry is far more striking ; as one can see in fig . [ fig : phdiag](b ) , fci states require rather flat bands with @xmath206 for @xmath207 , but extend to a band with a width comparable to the gap separating it from its counterpart for @xmath208 . having rather flat bands indeed makes it easier for small @xmath150 to induce fci states both at @xmath3 and @xmath4 , even though the optimal @xmath132 is still not quite the largest , at least for our system sizes . as soon as the bands acquire some dispersion , however , features beyond band flatness , in our case fs nesting , can strongly influence the stability of fci states by favoring competing states , in our case a cdw . another key feature , which extends previous results , @xcite is that in the case of competition between fci and other phases , perfect band flatness is not necessarily the ideal condition for the stability of fci ground states . before passing , a few more comments on the phase diagram have to be made . ideally , a ground - state property would be used to determine the phase boundaries . one such property , which is sensitive to phase transitions , is the ground - state fidelity , defined as a measure of the overlap @xmath209 , where @xmath210 is the ground - state wave function and @xmath30 is a control parameter varied in small steps @xmath211 . phase transitions are then marked by a divergence in the fidelity at the transition point . having calculated the ground - state fidelity upon varying interaction strength and band flatness for the cases presented here , we find that such divergences occur only at points where ground - state level crossings also occur , so the fidelity does not provide any extra information compared to the eigenvalue spectra . furthermore , it has recently been shown that the fidelity on finite systems can fail to register topological phase transitions , e.g. , between a fqh - like state and a fermi liquid .

it is shown that fci states are robust against disorder in the underlying magnetic texture that defines the topological character of the band . we also investigate competition between a fci state and a charge density wave ( cdw ) and discuss the effects of particle - hole asymmetry and fermi - surface nesting . nevertheless , very flat bands allow fci states to be induced by weaker interactions than those needed for more dispersive bands .

we discuss the low - energy limit of three - orbital kondo - lattice and hubbard models describing orbitals on a triangular lattice near half - filling . we analyze how very flat single - particle bands with non - trivial topological character , a chern number , arise both in the limit of infinite on - site interactions as well as in more realistic regimes . exact diagonalization is then used to investigate an effective one - orbital spinless - fermion model at fractional fillings including nearest - neighbor interaction ; it reveals signatures of fractional chern insulator ( fci ) states for several filling fractions . in addition to indications based on energies , e.g. flux insertion and fractional statistics of quasiholes , chern numbers are obtained . it is shown that fci states are robust against disorder in the underlying magnetic texture that defines the topological character of the band . we also investigate competition between a fci state and a charge density wave ( cdw ) and discuss the effects of particle - hole asymmetry and fermi - surface nesting . fci states turn out to be rather robust and do not require very flat bands , but can also arise when filling or an absence of fermi - surface nesting disfavor the competing cdw . nevertheless , very flat bands allow fci states to be induced by weaker interactions than those needed for more dispersive bands .

1208.3481

i

based on an earlier investigation , @xcite we have illustrated extensively how fci states can emerge in a strongly correlated multiorbital model and have shown how an effective spinless one - orbital model with nearly flat bands and non - zero chern number @xmath1 arises as the the low - energy limit of kondo - lattice and hubbard models for @xmath0 orbitals on a triangular lattice . nn coulomb interaction @xmath2 then stabilizes states with all the characteristics of fci states : the lowest eigenvalues have a near degeneracy corresponding to the denominator of the filling fraction and show spectral flow without closing of the energy gap . we have , moreover , demonstrated that the states of the ground - state manifold of this phase have a non - zero hall conductivity , which is shown to be precisely quantized and equal to the filling fraction , in units of @xmath159 . the exact quantization of the hall conductivity holds also when fci states are not ground states , and survives when the many - body berry curvature is not a particularly flat function . deviating from the exact filling fraction @xmath3 by either removing electrons or increasing the system size , we found indications of fractional quasihole statistics in the eigenvalue spectra , by application of the state - counting rule elaborated in ref . . the eigenvalue spectra contain features that remind one of both the hierarchy and the composite fermion pictures of fqh states , therefore pushing the correspondence between fci and fqh states one step further . since in the present context the magnetic texture is generated by strongly correlated itinerant electrons , imperfections in this texture are to be expected . we therefore investigate the impact of a localized impurity that mixes states across momentum sectors . disorder causes splitting of the energy levels corresponding to the degenerate fci ground states , thus making these states inequivalent in finite systems . however , the gap between these states and the excited - state spectrum remains open and their average hall conductivity remains accurately fixed to the value of the filling fraction , even though the hall conductivities of the individual states deviate from that value . this behavior illustrates the topological protection of the fci states . finally , we address the robustness of fci states with respect to band flatness , interaction strength , filling and fs nesting . very flat bands indeed turn out to require the weakest interaction to produce an fci state , corroborating the figure of merit @xmath132 [ see eq . ( [ eq : merit ] ) ] as a good first step in assessing candidate systems . as soon as one deviates from this limit , however , additional properties of the system become crucial : in contrast to a perfectly flat ll , strong particle - hole asymmetry can arise on a lattice , because some fillings allow cdws more easily than others . in addition , a cdw is favored by fs nesting and this in turn reduces the stability range of the fci states . nevertheless , it turns out that fci states can be obtained if either of the following conditions is met : ( i ) very flat bands , even near nesting and at a filling favorable to a cdw , and ( ii ) even rather dispersive bands , if the filling fraction or the absence of fs nesting are unfavorable to a cdw . this flexibility makes fci states appear more realistic . this work was supported by the deutsche forschungsgemeinschaft under the emmy - noether program ( s.k . and m.d . ) and the interphase program of the dutch science foundation nwo / fom ( jv ) . we thank j. van den brink for helpful discussions and b. a. bernevig for insightful comments . 58ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty link:\doibase 10.1103/physrevb.27.3383 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.51.605 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.52.1583 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.48.1559 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.49.957 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.67.937 [ * * , ( ) ] link:\doibase 10.1103/revmodphys.80.1083 [ * * , ( ) ] link:\doibase 10.1103/physrevb.14.2239 [ * * , ( ) ] link:\doibase 10.1088/0953 - 8984/3/23/012 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.61.2015 [ * * , ( ) ] link:\doibase 10.1103/physrevb.74.085308 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.101.146802 [ * * , ( ) ] link:\doibase 10.1103/physrevb.62.6065 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.101.156402 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.106.236802 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.106.236803 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.106.236804 [ * * , ( ) ] link:\doibase 10.1038/ncomms1380 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.107.146803 [ * * , ( ) ] link:\doibase 10.1103/physrevx.1.021014 [ * * , ( ) ] link:\doibase 10.1103/physrevb.85.075116 [ * * , ( ) ] http://link.aps.org/doi/10.1103/physrevlett.108.126405 [ * * , ( ) ] @noop @noop @noop @noop http://link.aps.org/doi/10.1103/physrevb.86.201101 [ * * , ( ) ] arxiv:1204.1697v1 ( 2012 ) http://link.aps.org/doi/10.1103/physrevlett.109.186805 [ * * , ( ) ] @noop http://link.aps.org/doi/10.1103/physrevb.86.205125 [ * * , ( ) ] link:\doibase 10.1103/physrevb.85.075128 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.107.126803 [ * * , ( ) ] http://link.aps.org/doi/10.1103/physrevb.86.085129 [ * * , ( ) ] @noop @noop @noop link:\doibase 10.1103/physrevb.85.241308 [ * * , ( ) ] link:\doibase 10.1140/epjb / e2011 - 20857 - 6 [ * * , ( ) ] link:\doibase 10.1038/ncomms1602 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.108.266801 [ * * , ( ) ] http://arxiv.org/abs/1106.4439 [ * * , ( ) ] \doibase info : doi/10.1143/jpsj.79.083711 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.105.216405 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.105.266405 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.78.1323 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.91.257003 [ * * , ( ) ] @noop _ _ ( , , ) link:\doibase 10.1103/physrev.94.1498 [ * * , ( ) ] @noop _ _ ( , ) @noop * * , ( ) @noop * * , ( ) link:\doibase 10.1103/physrevb.41.9377 [ * * , ( ) ] link:\doibase 10.1103/physrevb.30.1097 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.68.3460 [ * * , ( ) ] link:\doibase 10.1103/physrevb.49.2947 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.63.199 [ * * , ( ) ] link:\doibase 10.1103/physrevb.31.3372 [ * * , ( ) ] link:\doibase 10.1103/revmodphys.82.1959 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.90.256802 [ * * , ( ) ] http://link.aps.org/doi/10.1103/physrevb.85.205124 [ * * , ( ) ]

we discuss the low - energy limit of three - orbital kondo - lattice and hubbard models describing orbitals on a triangular lattice near half - filling . fci states turn out to be rather robust and do not require very flat bands , but can also arise when filling or an absence of fermi - surface nesting disfavor the competing cdw .

we discuss the low - energy limit of three - orbital kondo - lattice and hubbard models describing orbitals on a triangular lattice near half - filling . we analyze how very flat single - particle bands with non - trivial topological character , a chern number , arise both in the limit of infinite on - site interactions as well as in more realistic regimes . exact diagonalization is then used to investigate an effective one - orbital spinless - fermion model at fractional fillings including nearest - neighbor interaction ; it reveals signatures of fractional chern insulator ( fci ) states for several filling fractions . in addition to indications based on energies , e.g. flux insertion and fractional statistics of quasiholes , chern numbers are obtained . it is shown that fci states are robust against disorder in the underlying magnetic texture that defines the topological character of the band . we also investigate competition between a fci state and a charge density wave ( cdw ) and discuss the effects of particle - hole asymmetry and fermi - surface nesting . fci states turn out to be rather robust and do not require very flat bands , but can also arise when filling or an absence of fermi - surface nesting disfavor the competing cdw . nevertheless , very flat bands allow fci states to be induced by weaker interactions than those needed for more dispersive bands .

1212.3503

i

in a @xmath0-dimensional hilbert space @xmath3 , the description of any quantum state @xmath4 generated by a source can be obtained by quantum tomography . for any density matrix @xmath4 , which is hermitian and has trace @xmath5 , @xmath6 independent measurements are sufficient and necessary to uniquely specify @xmath4 . when @xmath7 is a pure state , one may not need as many measurements to uniquely determine @xmath8 . as we will see later , however , exactly what is meant by `` uniquely '' in this context needs to be specified . consider a set of @xmath9 linearly independent observables @xmath10 where each @xmath11 is hermitian . measurements on state @xmath4 with respect to these observables give the following average values @xmath12 we denote the set of these @xmath13 for all states @xmath4 as @xmath14 for a pure state @xmath8 , these values are given by @xmath15 and we denote the set of these values for all pure states @xmath8 as the joint numerical range @xmath16 in this work we consider two different kinds of `` unique determinedness '' for @xmath8 : 1 . we say @xmath8 is _ uniquely determined among pure states ( udp ) by measuring @xmath17 _ if there does not exist any other pure state which has the same measurement results as those of @xmath8 when measuring @xmath17 . we say @xmath8 is _ uniquely determined among all states ( uda ) by measuring @xmath17 _ if there does not exist any other state , pure or mixed , which has the same measurement results as those of @xmath8 when measuring @xmath17 . it is known that there exists a family of @xmath1 observables such that any pure state is udp , in contrast to the @xmath6 observables in the general case of quantum tomography @xcite . the physical meaning for this case is clear : it is useful for the purpose of quantum tomography to have the prior knowledge that the state to be reconstructed is pure or nearly pure . many other techniques for pure state tomography have been developed , and experiments have been performed to demonstrate the reduction of the number of measurements needed @xcite . when the state is udp , to make the tomography meaningful , one needs to make sure that the state is indeed pure . this is not in general practical , but one can readily generalize the above mentioned udp results to low rank states , where the physical constraints ( e.g. , low temperature , locality of interaction ) may ensure that the actual physical state ( which ideally supposed to be pure ) is indeed low rank . if the state is uda , however , in terms of tomography one do not need to bother with these physical assumptions , because in the event there is only a unique state compatible with the measurement results , which turns out to be pure ( or low rank ) . there is also another clear physical meaning for the states that are uda by measuring @xmath17 . consider a hamiltonian of the form @xmath18 then any unique ground state @xmath8 of @xmath19 is uda by measuring @xmath17 . this is easy to verify : if there is any other state @xmath4 that gives the same measurement results , then @xmath4 has the same energy as that of @xmath8 , which is the ground state energy . therefore , any pure state in the range of @xmath4 must also be a ground state , which contradicts the fact that @xmath8 is the unique ground state . in other words , uda is a necessary condition for @xmath8 to be a unique ground state of @xmath19 . it is in general not sufficient , but the exceptions are likely rare @xcite . the uniqueness properties for pure states , for both udp and uda , have also been studied extensively in the case of multipartite quantum systems , where the observables correspond to reduced density matrices ( rdms ) . that is , the observables are chosen to act nontrivially on only some subsystems . for an @xmath20-particle system and a constant @xmath21 , there are a total of @xmath22 @xmath23-rdms , and the corresponding measurements @xmath17 are those @xmath24-body operators . for example , for a three - qubit system and @xmath25 , one can choose @xmath17 as all the one and two - particle pauli operators . of course , one can also choose to look at some of the @xmath26-rdms , rather than all of them . for instance , for a three - particle system , one can look at @xmath27-rdms of particle pairs @xmath28 and @xmath29 . it is known that almost all three - qubit pure states are uda by their @xmath27-rdms @xcite . these authors also show that udp implies uda for three - qubit pure states , for @xmath27-rdms . this result can be further improved to @xmath27-rdms of particle pairs @xmath28 and @xmath29 @xcite . more generally one can consider a three - particle system of particles @xmath30 with hilbert spaces whose dimensions are @xmath31 , respectively . if @xmath32 , then almost all pure states are uda by their @xmath27-rdms of particle pairs @xmath28 and @xmath29 . in contrast , if @xmath33 , then almost all pure states are udp by their @xmath27-rdms of particle pairs @xmath28 and @xmath29 , as shown by diosi @xcite . for @xmath20-particle quantum systems with equal dimensional subsystems , almost all pure states are uda by their @xmath23-rdms of just over half of the parties ( i.e. , @xmath34 ) . furthermore , @xmath35 properly chosen rdms among all the @xmath26 @xmath23-rdms suffice @xcite . w - type states are uda by their @xmath27-rdms , and @xmath36 of those @xmath27-rdms are enough @xcite . general symmetric dicke states are uda by their @xmath27-rdms @xcite . it has been shown that the only @xmath20-particle pure states which can not be udp by their @xmath37-rdms are those ghz - type states , and the result is further improved to the case of uda @xcite . their results also show that udp implies uda for @xmath20-qubit pure states , for @xmath37-rdms . despite these many results , there is no systematic study of these two different types of uniqueness for pure states . this will be the focus of this paper , where we are interested in knowing for given measurements @xmath17 , whether udp and uda are the same , or are different . we will give a general argument that there is a gap between the number of observables needed for the two different cases . however , in many interesting circumstances , they can coincide . our discussions extend naturally to the case of low rank quantum states instead of just pure states . here one can also look at two kinds of uniqueness when measuring given observables @xmath17 : one is uniqueness among all low rank states , the other is among all states of any rank . we organize the paper as follows . in sec . ii , we first show that there is a set of @xmath2 observables that insures every pure state is uda ; which should be compared to the udp result @xmath1 . thus in general there is a gap between the optimal results for the udp and uda cases , and we illustrate this with some examples . sec . iii discusses the case of observables corresponding to rdms of a multipartite quantum state , where for the three particle case , we show that if @xmath38 , then almost all pure states are uda by their @xmath27-rdms of particle pairs @xmath28 and @xmath29 , improving the bounds given in @xcite . however this still leaves a gap with the diosi result for the case of udp in @xcite . we further discuss circumstances where udp can imply uda for all pure states . in sec . iv , we show that when there are only two independent measurements performed , then udp always implies uda , by making use of convexity of the numerical range of operators . in a more general case , if there is a compact group of symmetries of the state space which has the span of the operators measured as its set of fixed points , then udp implies uda for all pure states . we analyze the possible dimensions for those fixed point sets . a summary and some discussions are included in sec .

we consider two different types of uniqueness : ( 1 ) no other pure state is compatible with the same measurement results and ( 2 ) no other state , pure or mixed , is compatible with the same measurement results . for case ( 1 ) , it was known that for a-dimensional hilbert space , there exists a set of observables that uniquely determines any pure state . thus there is a gap between the results for ( 1 ) and ( 2 ) , and we give some examples to illustrate this . we further discuss circumstances where ( 1 ) can imply ( 2 ) . we use convexity of the numerical range of operators to show that when only two observables are measured , ( 1 ) always implies ( 2 ) . more generally , if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points , then ( 1 ) implies ( 2 ) . we analyze the possible dimensions for the span of such observables . our results extend naturally to the case of low rank quantum states .

we discuss the uniqueness of quantum states compatible with given measurement results for a set of observables . for a given pure state , we consider two different types of uniqueness : ( 1 ) no other pure state is compatible with the same measurement results and ( 2 ) no other state , pure or mixed , is compatible with the same measurement results . for case ( 1 ) , it was known that for a-dimensional hilbert space , there exists a set of observables that uniquely determines any pure state . we show that for case ( 2 ) , observables suffice to uniquely determine any pure state . thus there is a gap between the results for ( 1 ) and ( 2 ) , and we give some examples to illustrate this . unique determination of a pure state by its reduced density matrices ( rdms ) , a special case of determination by observables , is also discussed . we improve the best known bound on local dimensions in which almost all pure states are uniquely determined by their rdms for case ( 2 ) . we further discuss circumstances where ( 1 ) can imply ( 2 ) . we use convexity of the numerical range of operators to show that when only two observables are measured , ( 1 ) always implies ( 2 ) . more generally , if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points , then ( 1 ) implies ( 2 ) . we analyze the possible dimensions for the span of such observables . our results extend naturally to the case of low rank quantum states .

1212.3503

i

in this section we discuss the case where the hilbert space @xmath3 is a multipartite quantum system , where the observables correspond to the reduced density matrices ( rdms ) . that is , the observables are chosen to be acting nontrivially only on some subsystems . for instance , for a three - qubit system , the observables corresponding to the @xmath27-rdms of particle pairs @xmath28 can be chosen as @xmath108 where @xmath109 are pauli @xmath110 operators acting on the @xmath111th qubit . for simplicity in this section we consider only @xmath102-particle systems , labeled by @xmath30 , and each with hilbert space dimension @xmath112 , respectively . that is , @xmath113 and @xmath114 . nevertheless , our method naturally extends to systems of more than @xmath102-particles . recall that for a three particle system , it is known that almost all three - qubit pure states are uda by their @xmath27-rdms @xcite . this result can be further improved to @xmath27-rdms of particle pairs @xmath28 and @xmath29 @xcite . more generally , if @xmath32 , then almost all pure states are uda by their @xmath27-rdms of particle pairs @xmath28 and @xmath29 @xcite . in contrast , if @xmath115 , then almost every pure state is udp by its @xmath27-rdms of particle pairs @xmath28 and @xmath29 @xcite . we notice that different from the discussion in sec . ii , one no longer considers uniqueness for all pure states , but ` almost all ' of them . this means there exists a measure zero set of pure states which are not uniquely determined . for instance , for the three qubit case , any state which is local unitarily equivalent to the ghz type state @xmath116 can not be udp , as any state of the form @xmath117 has the same @xmath27-rdms as those of @xmath118 . this means that , for a three qubit pure state @xmath8 , it is either uda , or not udp . in other words , if any three qubit pure state @xmath8 is udp , then it is uda by its @xmath27-rdms of particle pairs @xmath28 and @xmath29 . in this sense , we say in this case udp implies uda for all pure states . however , for the general case of a three particle system , there is a gap between known results of uda and udp . our following result improves the bound for the uda case . [ th : rdm1 ] if @xmath119 , then almost every tripartite quantum state @xmath120 is uda by its @xmath27-rdms of particle pairs @xmath28 and @xmath29 , to see why this is the case , an arbitrary pure state @xmath121 of this system can be written as @xmath122 if there is another state @xmath4 which agrees with @xmath121 in its subsystems @xmath28 and @xmath29 , then we can find a pure state @xmath123 which agrees with @xmath4 on the subsystem @xmath124 and also agrees with @xmath125 in subsystems @xmath28 and @xmath29 . since the rank of the @xmath27-rdm of the subsystem @xmath28 is at most @xmath126 , the pure state @xmath127 can be written as a superposition of @xmath128 as follows . @xmath129 where @xmath130 for any @xmath131 . here @xmath132 will be vectors ( perhaps unnormalized ) in @xmath133 . the states @xmath132 can be chosen to be orthonormal vectors in the subsystem @xmath133 , and then for almost all states @xmath121 , the set of @xmath134 will be linearly independent . let us write @xmath135 . for any @xmath131 , we will have @xmath136 now let s consider the subsystem @xmath29 . since @xmath125 and @xmath127 have the same rdms for particles @xmath29 , this gives @xmath137 substituting eqs . and into eq . , and comparing each matrix element , results in the following equalities ( for all @xmath138 ) : @xmath139 now let us define @xmath140 . then eq . is a linear equation system with variables @xmath141 . it is not hard to verify that @xmath142 is a solution to the equation system , which corresponds to the state @xmath125 . now we need to show that when @xmath143 , eq . has only one solution which is given by eq . . it turns out that this is indeed the case which then proves theorem [ th : rdm1 ] . in fact , the linear equations above are generically linearly independent . to see this , let s fix @xmath144 and @xmath145 , the right - hand side of eq . is @xmath146 where @xmath147 . then the coefficient matrix can be written as the following : @xmath148 the @xmath149 entry in the above matrix is @xmath150 . if there are more than @xmath5 solutions , then the determinant of the above matrix should be zero . note that the determinant can be written as a polynomial of @xmath151 s and @xmath152 s . since @xmath153 appears only once in the polynomial , the determinant of the top @xmath154 by @xmath154 submatrix must be non - zero generically . therefore , @xmath155 linear equations are sufficient to determine @xmath156 variables . however , we do not know whether the sufficient condition given by theorem [ th : rdm1 ] for almost all three - particle pure state to be uda by its @xmath27-rdms of particle pairs @xmath28 and @xmath29 is also necessary . this still leaves a gap between the result of theorem [ th : rdm1 ] for uda , and the result for udp in @xcite . they both only coincide when @xmath157 , i.e. , the three qubit case . it remains open for other cases , whether udp can imply uda . following a similar discussion as in sec . ii , our result in this section also extends to uniqueness of low rank quantum states . in particular , we have the following theorem . [ th : rdm2 ] almost every tripartite density operator @xmath4 acting on the hilbert space @xmath158 with rank no more than @xmath159 can be uniquely determined among all states by its @xmath27-rdms of particle pairs @xmath28 and @xmath29 . this result is to our knowledge , the first one for uniqueness of mixed states with respect to rdms . the proof is a direct extension of that for theorem [ th : rdm1 ] , but with more lengthy details that we will include in appendix b. let us look at some consequences of theorem [ th : rdm2 ] . consider a four qubit system with qubits @xmath160 , and look at the qubits @xmath161 as a single systems @xmath162 . then theorem [ th : rdm2 ] says also that almost all four qubit states of rank @xmath27 are uda by their rdms of particles @xmath28 and @xmath163 , or one can say that almost all four qubit states of rank @xmath27 are uda by their @xmath102-rdms . this is indeed consistent with the multipartite result in @xcite which states that almost all four - qubit pure states are uda by their @xmath102-rdms , and our result is indeed stronger . this demonstrates that our analysis naturally extends to systems of more than @xmath102-particles . we also remark that the rank of a state @xmath4 which could be uda by its @xmath23-rdms needs to be relatively low , otherwise one can always find another state @xmath164 with lower rank which has the same @xmath23-rdms as those of @xmath4 @xcite .

unique determination of a pure state by its reduced density matrices ( rdms ) , a special case of determination by observables , is also discussed . we improve the best known bound on local dimensions in which almost all pure states are uniquely determined by their rdms for case ( 2 ) .

we discuss the uniqueness of quantum states compatible with given measurement results for a set of observables . for a given pure state , we consider two different types of uniqueness : ( 1 ) no other pure state is compatible with the same measurement results and ( 2 ) no other state , pure or mixed , is compatible with the same measurement results . for case ( 1 ) , it was known that for a-dimensional hilbert space , there exists a set of observables that uniquely determines any pure state . we show that for case ( 2 ) , observables suffice to uniquely determine any pure state . thus there is a gap between the results for ( 1 ) and ( 2 ) , and we give some examples to illustrate this . unique determination of a pure state by its reduced density matrices ( rdms ) , a special case of determination by observables , is also discussed . we improve the best known bound on local dimensions in which almost all pure states are uniquely determined by their rdms for case ( 2 ) . we further discuss circumstances where ( 1 ) can imply ( 2 ) . we use convexity of the numerical range of operators to show that when only two observables are measured , ( 1 ) always implies ( 2 ) . more generally , if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points , then ( 1 ) implies ( 2 ) . we analyze the possible dimensions for the span of such observables . our results extend naturally to the case of low rank quantum states .

astro-ph0609079

c

as a starting point for this discussion , we summarize the two main findings thus far , both of which concern dependencies of the measured color - magnitude slope on external factors : ( 1 ) the slope for the blue gcs decreases gradually towards fainter host galaxy luminosities , whereas there is no significant color - magnitude relation for the red gcs ; and ( 2 ) the slope is steeper for gcs which lie closer to the centers of their host galaxies . we now discuss a number of scenarios that that might help explain the observed trend : ( 1 ) contamination by super star clusters , stripped nuclei , or ucds ; ( 2 ) accretion of gcs from low - mass galaxies ; ( 3 ) stochastic effects ; ( 4 ) capture of field stars by individual gcs ; and ( 5 ) gc self enrichment . in [ metallicity ] , we briefly discuss how the observed color - magnitude trends appear after transforming into the metallicity - mass plane . [ discussion ] one idea that may explain the slope difference between inner and outer gcs is the presence of overluminous star clusters of intermediate color that may lie close to the galaxy centers . such a putative population would populate the region between the two color sequences at high luminosities . merged super star clusters ( e.g. , fellhauer & kroupa 2002 , 2005 ; kissler - patig 2006 ) could , in principle , be those objects . they are expected to be more extended than their monolithic counterparts of equal mass ( e.g. , bekki 2004 ; fellhauer & kroupa 2002 ; bastian 2005 ) . however , in the size vs. color plot shown in figure [ sizecolor ] it is the _ outer _ gcs that are slightly larger . more importantly , there is no offset in the size distribution for the inner gcs with intermediate colors ( i.e. , @xmath64 mag ) . this makes the presence of a large number of merged star clusters unlikely . another possibility is the presence of naked " or tidally stripped de , n nuclei , as suggested by harris @xcite ( see also bassino _ et al . _ 1994 ) . the de , n nuclei of virgo cluster galaxies do exhibit a color - magnitude trend and have colors comparable to those of the blue gcs ( see , e.g. , lotz 2004 ; ct 2006 ; figure [ cmdallobjects ] ) . ct @xcite find a median half - light radius of @xmath65 pc for nuclei with @xmath59 mag . this is comparable to the sizes of gcs in this same luminosity range ( figure [ sizecolor ] ) . stripped nuclei might therefore be confused with normal " blue gcs at the highest luminosities . however , as pointed out in [ comparison ] , the overall distribution of gcs with the cmd shows a _ lack _ of bright , blue objects . very generally , this dearth is not explained by the addition of an extra " population of contaminators , but rather requires an underlying trend for most of the objects . stripped nuclei would have to dominate the population of blue gcs . this seems unlikely to us for several reasons . first , the nuclei luminosity function peaks @xmath58 24 mag brighter than that of gcs ( see lotz 2004 ; , ct 2006 , see also figure [ cmdallobjects ] ) . more seriously , though , is the shear number of nuclei that would be required in this scenario . observationally , there is an upper limit on the number of naked nuclei brighter than @xmath66 mag from jones _ et al . _ these authors found nine compact objects ucds in their notation with @xmath67 mag in a survey that is almost complete within the central degree of the virgo cluster ( excluding the 1 - 2 surrounding m87 ) . their nine compact objects are distributed over an area that is @xmath68 100@xmath69 the acs field of view , in qualitative agreement with the predictions by bekki _ et al . _ @xcite for the spatial distribution of tidally stripped de , n nuclei . therefore , a presence of dozens , or possibly hundreds , of naked nuclei in our acs fields for the most luminous galaxies seems unlikely . a final note regarding the possibility of ucds as contaminators : the two most discussed formation channels for these compact stellar systems are stripped de , n nuclei and merged stellar super - clusters ( e.g. minniti _ et al . 1998 , hilker 1999a , drinkwater _ et al . _ 2003 , haegan 2005 , kissler - patig 2006 , mieske 2006 ) . since these two formation channels correspond to the two kinds of contaminators discussed in this section , we conclude that also ucds are unlikely to account for the observed trends . a population of gcs accreted from galaxies with a range of masses ( e.g. ct 1998 or hilker 1999b ) will exhibit a color - magnitude relation if : ( 1 ) the mean gc color of a single galaxy scales with galaxy mass ; and ( 2 ) more massive gcs preferentially form in more massive galaxies . indeed , both conditions are satisfied in actual early - type galaxies ( see , e.g. , peng 2005 ; kundu & whitmore 2001 ; jordn _ et al . _ 2006 in prep . and references therein ) . moreover , this simple scenario may offer , at least in principal , a way to qualitatively understand the slope differences for individual galaxies ( e.g. , the non - existence of a correlation for m49 ) as a consequence of different accretion / merger histories . in order to quantify the tilt in the cmd created by the accretion of gcs from low - mass galaxies that do not themselves have color - magnitude relations , we consider the combined gc sample of groups 24 ( see figure [ cmdall ] ) . we first calculate the mean host galaxy magnitude for each bin , and then calculate the color in each gc bin according to the relation between host galaxy magnitude and mean color of the blue and red gc subpopulations ( table 3 of peng 2006 ) . the outcome of this exercise is shown in figure [ cmdall ] . as expected , there is a ( weak ) trend between mean color with luminosity for the gc subpopulations . this trend is compared to the fits for group 1 . there is a substantial offset in the sense that the fainter luminosity groups have bluer gc colors than group 1 . in addition , the simulated slope is substantially smaller than measured for the ensemble of galaxies in group 1 . all in all , we conclude that the observed color - magnitude relations are unlikely to have been created by accretion of gcs from low - mass galaxies , although we can not rule out the possibility that accretion has contributed to the observed trend . the light of old gcs is in the red optical to near - infrared pass - bands dominated by red giant stars . generally , the number of red giants is only a small fraction of the total number of stars in a given stellar population . it is therefore worth discussing to which extent stochastic effects due to small numbers of red giants can skew the probability distribution of the integrated gc luminosity . this may cause a trend of gc color with integrated luminosity , because any stochastic effect is weaker for higher gc luminosity ( larger total number of stars ) and for bluer bands ( lower average stellar luminosity ) . in the works by cervio ( 2002 ) , and cervio & luridiana ( 2004 ; 2006 ) , the effect of discrete isochrone sampling on integrated photometric properties is discussed in detail . in cervio & luridiana ( 2006 ) , the width , skewness and kurtosis for the probability distribution of integrated luminosity of a stellar population are calculated as a function of star number and age . the faint magnitude limit of our gcs ( @xmath70 mag ) corresponds to about 10@xmath71 , and hence about @xmath72 stars . in the @xmath73-band taken to represent the @xmath12 band due to lack of estimates for the latter band , the photometric uncertainty arising from sampling effects amounts to about 0.06 mag for such a population ( cervio & luridiana ( 2006 ) ; and cervio , private communications ) . the skewness of the distribution in integrated luminosity is about 0.25 . the product of these two numbers about 0.015 mag is a measure of the difference between mode and mean of the probability distribution in integrated luminosity . given that the colour - magnitude trend in our data requires an almost ten times larger color shift , stochastic effects do probably not have a significant contribution to the observed trend . there is also a phenomenological counterargument against the importance of stochastic effects : the color - magnitude trend is shaped more by brighter gcs ( see figure [ colorhist ] ) , while stochastic effects are stronger for fainter gcs . furthermore , the environmental dependencies of the trend can not be explained by purely intrinsic stochastic effects . given that the strength of the color - magnitude trend depends on local environment , it is reasonable to examine the extent to which capture of field stars may help to explain the observed slopes . the capture of field stars has previously been considered by bica @xcite for the case of a 10@xmath74m@xmath75 star cluster orbiting within the galactic bulge at a distance of 1 kpc . they found that such a cluster could absorb a substantial fraction of its total mass during its lifetime . similarly , kroupa @xcite has shown that stellar super - clusters created in disks like that of the milky way can capture several tens of percent of their total mass in form of disk stars . field stars of the brightest early - type galaxies are significantly redder than their blue gc population , typically by about 0.5 to 0.6 mag ( peng 2006 ) . therefore , there will be a color shift towards the red by about 0.10 - 0.15 for a blue gc by the time that @xmath58 20 - 25% of the gc light originates from field stars . this effect will be notable mainly for the blue gc population , since the color of red gcs is much closer to that of field stars . as will become clear from the subsequent discussion , the capture rate per unit gc mass is higher for more massive gcs , which will lead to a slope in color - magnitude space . this qualitatively explains finding ( 1 ) from above . in addition , the effect will be stronger in the inner part of the host galaxy because of the higher field star density in such regions , consistent with finding ( 2 ) . thus , field star capture seems qualitatively consistent with the observed trend . we now quantify this scenario by considering a gc with a mass of 10@xmath76 , a mass that roughly corresponds to the brightest clusters in groups 1 and 2 in figure [ cmdclasses ] . for an assumed m / l=2.5 , this corresponds to a total of 4@xmath77 solar luminosities . we assume the gc to be on a circular orbit around m87 . this is certainly an extreme assumption , given that ct @xcite rule out such tangentially biased orbits for the gc system _ as a whole_. we nevertheless use it for the sake of this simple estimate . we adopt a radius of 3 kpc , representative for the sample within 5 kpc projected galactocentric distance . we may estimate the number of captured stars by multiplying the total number of stars within the volume of influence of the gc with the fraction of stars having relative velocities below the gc escape velocity . as the volume of influence , we define a torus around the orbit of the gc with an inner radius of the gc s tidal radius with respect to its host galaxy m87 . for calculating the tidal radius , we use the mass profile of m87 derived by romanowsky & kochanek @xcite . they quote the integrated mass at a distance of 3 kpc to be 1.1@xmath6910@xmath78 @xmath79 , which is comparable to the value found by ct @xcite . together with the 10@xmath76 mass of the gc , this gives a tidal radius of 9 pc . the total volume of the torus then is 4.8@xmath80 pc@xmath81 . we use the same paper by romanowsky & kochanek to get the 3-dimensional stellar density of m87 at 3 kpc , which is about 0.06 l@xmath82 pc@xmath83 . that is , along one orbit there will be a total of 2.9 @xmath77 solar luminosities within the volume of influence of our test gc . however , only a small fraction of those will be captured : the average escape velocity @xmath84 of the gc within its tidal radius of 9pc is about 37 km s@xmath10 , while the stellar velocity dispersion in m87 is about 275 km s@xmath10 ( romanowsky & kochanek 2001 ) . the gc population in m87 has a velocity dispersion of @xmath68 400 km s@xmath10 . the probability distribution for the relative velocity between the field stars and a gc is given by the convolution of both distributions , which is a gaussian of width @xmath36 = 485 km s@xmath10 . the fraction of stars ( in solar luminosities ) that can be captured in the 1d case is given by the area below the gaussian between + /- @xmath85 , which is 0.035 . for the full 3d case , this is @xmath86 , or one out of 2.3 @xmath87 stars . given that in total 2.9 @xmath77 stars are in the volume of influence in each orbit , this implies a capture rate of one dozen stars per orbit - body simulations , which is beyond the scope of this paper . ] . for a keplerian orbit at 3 kpc , one revolution lasts about 2.5@xmath88 years . in a hubble time , one can therefore capture about 6000 stars . this is 1.5% of the total assumed gc luminosity , not sufficient to fully explain the observed effects . only when considering a more extreme orbital distance of 1 kpc does the total number of captured stars increase to about 4@xmath87 , i.e. @xmath8910% of all stars . we now briefly examine the opposite effect of field star capture : namely cluster star evaporation . as is well known , mass segregation in gcs ( gunn & griffin 1979 ; jordn 2004 ) will result in evaporation affecting mainly the lowest mass stars . lamers et al . @xcite find for clusters of solar metallicity that evaporation will cause the overall gc color to become bluer with time ( over most of their lifetime ) due to the preferential loss of red , low - mass stars . could such a color change help to explain our observations ? two effects are important : ( 1 ) the _ maximum _ blueward shift due to evaporation is larger for more massive clusters ( lamers et al . @xcite ) , reaching up to @xmath90 0.10 mag ; and ( 2 ) the dissolution time , @xmath91 , is longer for more massive clusters . to qualitatively explain our observations one would require the massive gcs to be in an early stage of evolution , so that evaporation has not yet had a significant effect the fainter gcs would mainly define the color magnitude trend . however , figure [ colorhist ] shows that the slope changes between inner and outer gcs are mainly driven by the _ brightest _ gcs . that is , evaporation is unlikely to account fully for the observed color - magnitude trend . even more serious , evaporation can not naturally explain the simultaneous presence of a trend for the blue gcs and its absence for the red . generally speaking , self enrichment will occur in any stellar system , gcs included , if the system is able to retain a fraction of the gas expelled by the first generation of supernovae and subsequently form a new generation of stars . to create a metallicity - mass ( or , equivalently , a color - magnitude ) trend via self - enrichment , one would therefore require that more massive gcs are more efficiently self - enriched . the extent to which gcs in the milky way may have self - enriched , however , is a controversial subject : e.g. , frank & gisler @xcite , smith @xcite , gnedin @xcite , parmentier & gilmore @xcite , dopita & smith @xcite , morgan & lake @xcite , thoul @xcite . in this context , it is interesting to note that the most massive gc in the galaxy , @xmath92 cen , is known to have a metallicity distribution function that shows a long tail towards high metallicities ( e.g. , norris , freeman & mighell 1996 ; stanford _ various studies have found this high - metallicity population to be either coeval , or perhaps 24 gyr younger , than the cluster s primary ( metal - poor ) population ( e.g. , ferraro 2004 ; sollima et al . 2005 ; hughes & wallenstein 2000 ; hilker & richtler 2000 ; rey 2004 , stanford 2006 ) . this is consistent with @xmath92 cen having been at least partially self - enriched . note , however , that because of its peculiar star formation history , numerous investigators have suggested that the cluster may be the stripped nucleus of a now - dissolved dwarf galaxy ( e.g. , freeman 1993 ; hilker & richtler 2000 ; bekki & freeman 2003 ) . if true , then it may be incorrect to consider @xmath92 cen to be a typical example of a self enriched gc . this caveat aside , if self enrichment is common to the formation of the most massive gcs , then it may indeed help to explain our observations . most significantly , the lack of a correlation among the red gc subpopulation is naturally explained in this scenario : i.e. , the redder gcs are already metal - enriched , and a fixed amount _ d_z of supernovae ejecta will cause a relatively weaker metallicity increase , _ d_[fe / h ] , for metal - rich gcs . for instance , for a system with [ fe / h ] = @xmath932 ( z = 0.0002 ) , adding a fixed amount of metals _ d_z = 0.0002 will result in _ d_[fe / h]=@xmath940.3 dex . according to peng @xcite this corresponds to a shift in @xmath2 of about 0.06 mag and is about the observed amount of the color magnitude trend . however , for a system with [ fe / h ] = @xmath930.5 and the same _ d_z , we only have _ d_[fe / h]=@xmath940.013 dex , with a corresponding color change in @xmath2 well below 0.01 mag . a possible shortcoming of this self - enrichment scenario is that is does not explicitly account for environmental effects such as a dependence on galactocentric radius . on the other hand , feedback induced by pressure - confinement from the surrounding medium may be able to help reconcile this scenario with observations . to conclude this discussion , we show in figure [ met ] a metallicity - luminosity plot for the co - added sample of gcs in group 1 . to estimate gc metallicities , we have applied a quartic color - metallicity transformation based on the empirical calibration data from peng @xcite . note that the resulting metallicity distribution is _ not _ bimodal , but rather shows a single pronounced peak at [ fe / h]@xmath89 @xmath930.4 dex and a long , extended tail towards lower metallicities . this confirms recent warnings ( e.g. , richtler 2005 ; yoon , yi & lee 2006 ) that bimodality in color does not necessarily imply bimodality in metallicity . using the data in figure [ met ] , we can compare the metallicity distributions of gcs brighter and fainter than @xmath95 mag . for the metal - poor population , ( [ fe / h]@xmath96 - 0.6 ) , the fainter gcs have a significantly broader tail towards lower metallicities than do the bright ones . a ks - test gives a 0.1% probability for a common underlying distribution between both samples . in the metal - rich part of the diagram , the agreement is very good , with a ks probability of 91% . in other words , the empirical finding of a color - magnitude trend for the blue gcs can hence be re - phrased in terms of metallicity : the gc systems appear to have a skewed , but unimodal , metallicity distribution function whose metal - poor tail becomes increasingly extended at lower luminosities / masses .

there is no correlation between and for gcs belonging to the red subpopulation . we identify two environmental dependencies which influence the derived color - magnitude relation : ( 1 ) the slope of the color - magnitude relation decreases in significance with decreasing galaxy luminosity , although it remains detectable over the full luminosity range of our sample ; and ( 2 ) the slope is stronger for gc populations located at smaller galactocentric distances . these characteristics suggest that the observed trend is , at least partially , shaped by external agents .

we examine the correlation between globular cluster ( gc ) color and magnitude using hst / acs imaging for a sample of 79 early - type galaxies ( mag ) with accurate surface - brightness fluctuation distances from the acs virgo cluster survey . using the mixture modeling algorithm , we find a highly significant correlation , , between color and magnitude for the subpopulation of blue gcs in the co - added gc color - magnitude diagram of the three brightest virgo cluster galaxies ( m49 , m87 and m60 ) . the sense of the correlation is such that brighter gcs are redder than their fainter counterparts . for the single gc systems of m87 and m60 , we find similar correlations ; m49 does not appear to show a significant trend . there is no correlation between and for gcs belonging to the red subpopulation . the correlation for the blue subpopulation is much weaker than . using monte carlo simulations , we attribute this finding to the fact that the blue subpopulation in extends to higher luminosities than does the red subpopulation , which biases the fit results . the highly significant correlation between color and , however , is a real effect : this conclusion is supported by biweight fits to the same color distributions . we identify two environmental dependencies which influence the derived color - magnitude relation : ( 1 ) the slope of the color - magnitude relation decreases in significance with decreasing galaxy luminosity , although it remains detectable over the full luminosity range of our sample ; and ( 2 ) the slope is stronger for gc populations located at smaller galactocentric distances . these characteristics suggest that the observed trend is , at least partially , shaped by external agents . we examine several physical mechanisms that might give rise to the observed color - magnitude relation including : ( 1 ) presence of contaminants like super - clusters , stripped galactic nuclei , or ultra - compact dwarfs ; ( 2 ) accretion of gcs from low - mass galaxies ; ( 3 ) stochastic effects ; ( 4 ) the capture of field stars by individual gcs ; and ( 5 ) gc self - enrichment . although none of these scenarios offers a fully satisfactory explanation of the observations , we conclude that self - enrichment and field - star capture , or a combination of these processes , offer the most promising means of explaining our observations .

astro-ph0609079

i

in this paper we have analysed the color - magnitude relation for the gc subpopulations in early - type galaxies belonging to the virgo cluster . our sample consists of 79 galaxies , spanning the range @xmath0 mag , drawn from the acs virgo cluster survey ( ct 2004 ) . our principal findings can be summarized as follows : 1 . based on fits , we find a highly significant correlation @xmath1 for the blue gcs in the co - added cmd of the three brightest virgo cluster galaxies ( m49 , m87 , m60 ) . the sense of the correlation is such that brightest gcs in this subpopulation are redder than their faint counterparts . for m87 and m60 alone , we find comparable correlations ; by contrast , the blue gcs in m49 do not appear to follow such a trend . in no galaxy do we find a significant correlation between @xmath2 and @xmath3 for the gcs associated with the red subpopulation . 2 . based on fits , we find the slope @xmath97 within the blue subpopulation to be much weaker than @xmath5 . in turn , we find a mild _ positive _ correlation @xmath45 for the red subpopulation , in the opposite sense to what is found for the blue subpopulation . 3 . we test on artificial cmds with , and without , implemented slopes for the blue subpopulation , and no slope for the red population . correctly reproduces the implemented slopes when using the cmd @xmath2 vs. @xmath3 . for @xmath2 vs. @xmath6 , gives a biased estimate for the color of the blue population and yields a positive slope for the red subpopulation , although no slope had been implemented . we trace this bias to the fact that in @xmath6 unlike in @xmath3 the luminosity function of blue gcs is populated to significantly brighter luminosities than for the red gcs . we conclude that for the real data , the strong slope @xmath5 is _ not _ an artifact of the fitting method , while the weaker slope @xmath45 is an artificial feature of the fit . we derive correlations independent of by using a biweight estimator for gcs divided on the basis of a luminosity independent color . the results confirm the significant slope found by in @xmath3 and reveal no significant discrepancies between the slope measured using @xmath3 and @xmath6 . 5 . the slope measured from the blue subpopulation decreases with host galaxy luminosity . however , even among the faintest galaxies ( @xmath30 mag ) the slope is nonzero . the color - magnitude relation exhibited by the blue gcs is stronger for clusters with smaller projected galactocentric distances . this difference is driven mainly by gcs with @xmath61 mag . we examine a number of physical mechanisms that might give rise to a color - magnitude relation with these characteristics : ( 1 ) contamination by super - star - clusters , stripped galactic nuclei , or ultra - compact dwarf galaxies ; ( 2 ) accretion of gcs from low - mass galaxies ; ( 3 ) stochastic effects ; ( 4 ) capture of galactic field stars by gcs ; and ( 5 ) self - enrichment of individual gcs . neither contaminants nor accretion of low - mass galaxies appear likely to fully explain our observations . self - enrichment in more massive gcs may be able to account for the observed color - magnitude relation , although more work is needed to determine if the dependence on galactocentric radius can be explained within the context of the self - enrichment scenario . although the capture of field stars _ does _ lead to a dependence on galactocentric radius that is at least qualitatively in agreement with our observations , this mechanism does not appear efficient enough to explain the overall size of the observed trend . while none of these scenarios can fully account for the full set of observations in a straightforward manner , self - enrichment and capture of field stars seem the most promising approaches . there is , of course , no _ a priori _ reason that a single mechanism is responsible for the observed color - magnitude relation , and conceptually , the combined effects of self - enrichment and field star capture may be able to explain the observations : i.e. , field star capture could act as a second order effect , producing environmental variations of a global mass - metallicity relation induced by self - enrichment . this would alleviate the discrepancy between real and required field star capture rate estimated in this work . dedicated n - body simulations going beyond these simple estimates will be required to accurately address the efficiency of field star capture in different environments . [ conclusions ] we would like to thank pavel kroupa , mike fellhauer , holger baumgardt , h.j.g.l.m . lamers and miguel cervio for fruitful discussions . we thank the anonymous referee for her / his comments . support for program go-9401 was provided through a grant from the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , under nasa contract nas5 - 26555 . p.c . acknowledges support provided by nasa ltsa grant nag5 - 11714 . m.j.w . acknowledges support through nsf grant ast-0205960 . s.m . acknowledges additional support from nasa grant nag5 - 7697 to the acs team . d.m . acknowledges support provided by nsf grants ast-0071099 , ast-0206031 , ast-0420920 and ast-0437519 , by nasa grant nng04gj48 g , and by grant hst - ar-09519.01-a from stsci . this research has made use of the nasa / ipac extragalactic database ( ned ) which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . ashman , k. m. , zepf , s. e. 1992 , apj , 384 , 50 ashman , k. m. , bird , c. m. , zepf , s. e. 1994 , aj , 108 , 2348 bastian , n. , emsellem , e. , kissler - patig , m. , maraston , c. 2006 , a&a , 445 , 471 bassino , l. p. , muzzio , j. c. , & rabolli , m. 1994 , , 431 , 634 beasley , m. a. _ et al . _ 2002 , mnras , 333 , 383 beers , t. c. , flynn , k. , gebhardt , k. 1990 , aj , 100 , 32 bekki , k. , couch , w.j . , drinkwater , m.j . , shioya , y. , 2003a , mnras , 344 , 399 bekki , k. , & freeman , k. c. 2003 , mnras , 346 , l11 bekki , k. , couch , w.j . , drinkwater , m.j . , shioya , y. , 2004 , apjl , 610 , 13 bica , e. _ et al . _ 1997 , apj , 482 , 49 bower , r.g . , lucey , j.r . , ellis , r.s . 1992 , mnras , 254 , 589 bruzual , g. , charlot , s. 2003 , mnras , 344 , 1000 burgarella , d. , kissler - patig , m. , buat , v. 2001 , aj , 121 , 2647 cervio , m. , valls - gabaud , d. , luridiana , v. , & mas - hesse , j. m. 2002 , a&a , 381 , 51 cervio , m. , luridiana , v. 2004 , a&a , 413 , 145 cervio , m. , luridiana , v. 2006 , a&a , 451 , 475 chabrier , g. , 2003 , pasp , 115 , 763 ct , p. , marzke , r. o. , west , m. j. 1998 , apj , 501 , 554 ct , p. _ et al . _ 2001 , apj , 559 , 828 ct , p. , mclaughlin , d. e. , cohen , j. g. , & blakeslee , j. p. 2003 , apj , 591 , 850 ct , p. _ et al . _ 2004 , apjs , 153 , 223 ( paper i ) ct , p. _ et al . _ 2006 , apjs , accepted , astro - ph/0603252 ( paper viii ) dirsch , b. _ et al . _ 2003 , aj , 125 , 1908 dopita , m. a. , smith , g. h. 1986 , apj , 304 , 283 drinkwater , m.j . , gregg , m.d . , hilker , m. et al . , 2003 , nature , 423 , 519 fellhauer , m. , kroupa , p. , 2002 , mnras , 330 , 642 fellhauer , m. ; 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we examine the correlation between globular cluster ( gc ) color and magnitude using hst / acs imaging for a sample of 79 early - type galaxies ( mag ) with accurate surface - brightness fluctuation distances from the acs virgo cluster survey . using the mixture modeling algorithm , we find a highly significant correlation , , between color and magnitude for the subpopulation of blue gcs in the co - added gc color - magnitude diagram of the three brightest virgo cluster galaxies ( m49 , m87 and m60 ) . the sense of the correlation is such that brighter gcs are redder than their fainter counterparts . for the single gc systems of m87 and m60 , we find similar correlations ; m49 does not appear to show a significant trend . the correlation for the blue subpopulation is much weaker than . using monte carlo simulations , we attribute this finding to the fact that the blue subpopulation in extends to higher luminosities than does the red subpopulation , which biases the fit results . we examine several physical mechanisms that might give rise to the observed color - magnitude relation including : ( 1 ) presence of contaminants like super - clusters , stripped galactic nuclei , or ultra - compact dwarfs ; ( 2 ) accretion of gcs from low - mass galaxies ; ( 3 ) stochastic effects ; ( 4 ) the capture of field stars by individual gcs ; and ( 5 ) gc self - enrichment . although none of these scenarios offers a fully satisfactory explanation of the observations , we conclude that self - enrichment and field - star capture , or a combination of these processes , offer the most promising means of explaining our observations .

we examine the correlation between globular cluster ( gc ) color and magnitude using hst / acs imaging for a sample of 79 early - type galaxies ( mag ) with accurate surface - brightness fluctuation distances from the acs virgo cluster survey . using the mixture modeling algorithm , we find a highly significant correlation , , between color and magnitude for the subpopulation of blue gcs in the co - added gc color - magnitude diagram of the three brightest virgo cluster galaxies ( m49 , m87 and m60 ) . the sense of the correlation is such that brighter gcs are redder than their fainter counterparts . for the single gc systems of m87 and m60 , we find similar correlations ; m49 does not appear to show a significant trend . there is no correlation between and for gcs belonging to the red subpopulation . the correlation for the blue subpopulation is much weaker than . using monte carlo simulations , we attribute this finding to the fact that the blue subpopulation in extends to higher luminosities than does the red subpopulation , which biases the fit results . the highly significant correlation between color and , however , is a real effect : this conclusion is supported by biweight fits to the same color distributions . we identify two environmental dependencies which influence the derived color - magnitude relation : ( 1 ) the slope of the color - magnitude relation decreases in significance with decreasing galaxy luminosity , although it remains detectable over the full luminosity range of our sample ; and ( 2 ) the slope is stronger for gc populations located at smaller galactocentric distances . these characteristics suggest that the observed trend is , at least partially , shaped by external agents . we examine several physical mechanisms that might give rise to the observed color - magnitude relation including : ( 1 ) presence of contaminants like super - clusters , stripped galactic nuclei , or ultra - compact dwarfs ; ( 2 ) accretion of gcs from low - mass galaxies ; ( 3 ) stochastic effects ; ( 4 ) the capture of field stars by individual gcs ; and ( 5 ) gc self - enrichment . although none of these scenarios offers a fully satisfactory explanation of the observations , we conclude that self - enrichment and field - star capture , or a combination of these processes , offer the most promising means of explaining our observations .

1309.5716

i

thermodynamics and quantum optics have been intertwined since the inception of field quantization @xcite . over the years their interconnection has been repeatedly revealed , e.g. , in the derivation of the maser efficiency from thermodynamics @xcite and its extension to the micromaser @xcite , in suggestions to boost carnot - cycle efficiency through bath preparation in nonthermal ( population - inverted @xcite or `` squeezed '' @xcite ) states , and in the proposed efficiency enhancement of cavity - based amplifiers @xcite and solar cells @xcite through quantum coherence ( interference ) effects . here we wish to further expand the fruitful rapport between these two disciplines by exploring the thermodynamic capacity for work extraction and cooling of quantum states . to achieve this we study the dependence of the performance bounds of heat machines ( engines and refrigerators ) on the _ initial quantum state _ and subsequent evolution of their drive , alias piston , modeled by a quantized harmonic oscillator.the piston may be a mechanical vibrational mode as in optomechanical setups @xcite , or an electromagnetic field mode , as in masers or lasers @xcite . our goal is to provide a fully quantized treatment of _ self - contained ( autonomous ) _ heat machines , as opposed to their prevailing semiclassical description : `` working - fluid '' system , intermittently coupled to heat baths , that is _ parametrically _ driven by a classical time - dependent piston or field @xcite . the fully quantized treatment we put forward allows us to investigate work extraction and refrigeration by the tools of quantum - optical amplifier and dissipation theory @xcite , particularly , by the analysis of amplified or dissipated phase - plane quasiprobability distributions @xcite . explicit results are obtained here for a minimal design : it consists of a `` working - fluid '' realized by a single two - level system ( tls ) that is permanently coupled to two thermal baths with _ distinct spectra _ and temperatures and is driven by a quantum mechanical harmonic oscillator acting as a piston . we stress that both the tls and the piston - oscillator are _ essential _ if the design is to be self - contained , i.e. , autonomous : the tls allows heat flow to or from the baths , i.e. , it mediates between the two baths , and the piston extracts the work in an engine or provides the energy input in a refrigerator . namely , the `` working - fluid '' system can not _ directly _ extract work or refrigeration from the bath : a piston must be coupled to the system to this end . in order to analyze work extraction or refrigeration in such a _ self - contained _ quantized setup , we have to forego the standard division of energy - exchange between heat , q , and work , w , that is known to apply under _ classical ( parametric ) _ driving of the reduced state of the working - fluid system , @xmath0 , via a cyclic hamiltonian @xmath1 . this division is expressed by @xcite @xmath2 work is maximized when the evolution @xmath0 is purely unitary ( app . a ) these standard formulae _ do not apply _ in the present scenario , since @xmath3 is now time - independent , thus necessitating an alternative analysis . our analysis is based on the notion of _ non - passivity _ of @xmath4 , which defines its capacity to deliver work , i.e. , the maximal amount of work it can yield @xcite ( sec . iib ) by contrast , refrigeration does not involve non - passivity ( sec . iic ) . in sec . iii the evolving bounds on work and refrigeration efficiencies are analyzed for the minimal design discussed above , revealing their crucial dependence on the initial quantum state of the piston . although eq . does not hold for the fully quantized scenarios considered below , we discuss the correspondence of these two approaches , i.e. , the retrieval of the semiclassical eq . and the corresponding results for masers @xcite ( sec . possible implementations and their characteristics are discussed in sec .

we explore the dependence of the performance bounds of heat engines and refrigerators on the _ initial quantum state _ and the subsequent evolution of their piston , modeled by a quantized harmonic oscillator . our goal is to provide a fully quantized treatment of _ self - contained ( autonomous ) _ heat machines , as opposed to their prevailing semiclassical description that consists of a quantum system alternately coupled to a hot or a cold heat bath , and _ parametrically _ driven by a classical time - dependent piston or field . here the fully quantized treatment we put forward allows us to investigate work extraction and refrigeration by the tools of quantum - optical amplifier and dissipation theory , particularly , by the analysis of amplified or dissipated phase - plane quasiprobability distributions . the piston may be realized by a vibrational mode , as in nanomechanical setups , or an electromagnetic field mode , as in cavity - based scenarios .

we explore the dependence of the performance bounds of heat engines and refrigerators on the _ initial quantum state _ and the subsequent evolution of their piston , modeled by a quantized harmonic oscillator . our goal is to provide a fully quantized treatment of _ self - contained ( autonomous ) _ heat machines , as opposed to their prevailing semiclassical description that consists of a quantum system alternately coupled to a hot or a cold heat bath , and _ parametrically _ driven by a classical time - dependent piston or field . here by contrast , there is no external time - dependent driving . instead , the evolution is caused by the stationary simultaneous interaction of two heat baths ( having distinct spectra and temperatures ) with a single two - level system that is in turn coupled to the quantum piston . the fully quantized treatment we put forward allows us to investigate work extraction and refrigeration by the tools of quantum - optical amplifier and dissipation theory , particularly , by the analysis of amplified or dissipated phase - plane quasiprobability distributions . our main insight is that quantum states may be thermodynamic resources and can provide a powerful handle , or control , on the efficiency of the heat machine . in particular , a piston initialized in a coherent state can cause the engine to produce work at an efficiency above the carnot bound in the linear amplification regime . in the refrigeration regime , the coefficient of performance can transgress the carnot bound if the piston is initialized in a fock state . the piston may be realized by a vibrational mode , as in nanomechanical setups , or an electromagnetic field mode , as in cavity - based scenarios .

1309.5716

r

the fully quantum autonomous heat engine whose work extraction is determined by nonpassivity should be able to reproduce in the semiclassical limit the power extraction of an externally ( _ parametrically _ ) modulated heat engine ( proposed in @xcite ) that obeys the cyclic work definition [ 14 ] ( eq.(1 ) ) , and is governed , instead of @xmath195 in and by the hamiltoninan @xmath196 while the coupling to the baths is still given by the two descriptions coincide when the initial state of the quantum piston is a large - amplitude coherent state @xmath197 . the extracted power by a piston in an initially coherent state piston is ( eq . ( 35 ) ) @xmath198 . for an externally modulated engine , ( governed by ) , it is @xmath199 @xcite . thus , a parametric modulation amplitude @xmath200 provides the same power extraction as the nonpassive coherent state @xmath201 . it is instructive to compare our analysis to that of the maser , which has long been treated as a heat machine @xcite : its thermodynamic efficiency is given by the ratio of the output ( signal ) and pump frequencies , which is the same as the carnot bound . in our scenario there is no population inversion in the system , and instead the gain is provided by the hot bath , but the analogy is complete . we may recover the maser - gain result for quasiclassical coherent - state preparation of the piston , which is the counterpart of the maser - output ( signal ) mode , upon substituting the hot bath for the maser - pump mode . yet there is currently no analysis of the maser efficiency dependence on its initial state , let alone any indication that it may lead to above - carnot efficiency , since such analysis should rely on the use of nonpassivity for work capacity , as detailed above . for an initial coherent state with large @xmath202 ( semiclassical limit ) and spectrally separated baths , such that only @xmath203 and @xmath204 are non - zero , we find for @xmath205 , @xmath206 where @xmath207 the corresponding efficiency bound becomes @xmath208 which is the same as in the maser model @xcite . ) for different initial piston states : coherent ( continuous ) , fock ( dot - dashed ) and thermal ( dashed ) . the carnot cop bound ( dotted , thin ) is slightly below the coherent - state cop . both thermal - state and fock - state cop asymptotically coincide to the the absorption bound at @xmath209 . while at short times the fock state has the largest cop , the coherent state outperforms it at long times , with a cop above the carnot efficiency . ( b ) entropy ( in units of @xmath210 ) of the same states as a function of time . the initially rapid entropy increase of the fock state explains its high cop at short times , while for the coherent state the entropy increase is slow but steady , resulting in the highest cop at large times . ( c ) phase - plane plots of the distribution evolution illustrate that the high resilience of a coherent state against thermalization , as opposed to the low resilience ( fragility ) of fock and schroedinger - cat states , explains the cop evolution . the spectral separation conditions are as in fig . [ fig : work]b , but the piston frequency is chosen to ensure cooling , ( @xmath111 ) . the initial mean energy complies with eq .

by contrast , there is no external time - dependent driving . instead , the evolution is caused by the stationary simultaneous interaction of two heat baths ( having distinct spectra and temperatures ) with a single two - level system that is in turn coupled to the quantum piston .

we explore the dependence of the performance bounds of heat engines and refrigerators on the _ initial quantum state _ and the subsequent evolution of their piston , modeled by a quantized harmonic oscillator . our goal is to provide a fully quantized treatment of _ self - contained ( autonomous ) _ heat machines , as opposed to their prevailing semiclassical description that consists of a quantum system alternately coupled to a hot or a cold heat bath , and _ parametrically _ driven by a classical time - dependent piston or field . here by contrast , there is no external time - dependent driving . instead , the evolution is caused by the stationary simultaneous interaction of two heat baths ( having distinct spectra and temperatures ) with a single two - level system that is in turn coupled to the quantum piston . the fully quantized treatment we put forward allows us to investigate work extraction and refrigeration by the tools of quantum - optical amplifier and dissipation theory , particularly , by the analysis of amplified or dissipated phase - plane quasiprobability distributions . our main insight is that quantum states may be thermodynamic resources and can provide a powerful handle , or control , on the efficiency of the heat machine . in particular , a piston initialized in a coherent state can cause the engine to produce work at an efficiency above the carnot bound in the linear amplification regime . in the refrigeration regime , the coefficient of performance can transgress the carnot bound if the piston is initialized in a fock state . the piston may be realized by a vibrational mode , as in nanomechanical setups , or an electromagnetic field mode , as in cavity - based scenarios .

1211.6506

c

the recent neutrino oscillation experimental highlights : ( i ) rather large value of reactor mixing angle @xmath22 and ( ii ) indication of significant deviation of the atmospheric neutrino mixing angle @xmath7 from maximality may change our theoretical approach for constructing neutrino mass models . in this paper , we study the wolfenstein - like mixing schemes : @xmath1 mixing in which @xmath2 , @xmath3 , @xmath4 , and @xmath5 mixing , in which @xmath2 , @xmath3 , @xmath236 . the largish @xmath22 can be naturally accommodated in both of them , the two mixing patterns differ in the order of magnitude of @xmath93 , the @xmath1 texture is favored for @xmath7 in the first octant , while @xmath5 is preferred for the second octant @xmath7 . in order to produce the @xmath1 mixing without invoking unnatural cancellation , the abelian flavor symmetry should be @xmath9 with the parity of @xmath10 and @xmath11 being opposite . a concrete model based on @xmath12 family symmetry is constructed , where the light neutrino mass hierarchy @xmath171 is realized due to the discrete nature of @xmath176 . the ratio @xmath237 is expected to be of order @xmath147 in this model , which is in good agreement with experimental data in contrast with conventional @xmath42 or @xmath238 flavor symmetry constructions . furthermore , the model is embedded into the @xmath14 grand unified theory to describe the quark masses and mixing simultaneously . as for the @xmath5 mixing , it can be reproduced within the framework of pure @xmath42 flavor symmetry . however , the light neutrino mass spectrum is expected to be quasi - degenerate , hence fine - tuning of the neutrino mass parameters is needed in order to achieve the observed mass - squared differences . to improve upon this situation , the family symmetry is enlarged to @xmath13 , which gives rise to both large atmospheric neutrino mixing @xmath98 and hierarchical neutrino masses . the model is extended to @xmath14 grand unified theory as well . we show that both models can give a successful description of the observed quark and lepton masses and mixing angles , and the numerical results are nicely in agreement with the theoretical estimates and the qualitative discussions . the light neutrinos are normal mass hierarchy in both models , quasi - degenerate spectrum is strongly disfavored . if the next generation high precision neutrino oscillation experiments determine that the neutrino mass spectrum is inverted hierarchy , both our constructions will be ruled out . the present framework can not predict the cp violating phases @xmath239 , @xmath233 and @xmath234 . the @xmath240-decay effective mass @xmath241 is predicted to be rather small in both constructions , substantial part of the data are below the sensitivity of future experiments except for a region of the @xmath5 model indicated in fig . [ fig : onu2b_bl2 ] . therefore future @xmath240-decay experiments such as cuore , majorana and gerda iii will provide another important test of the present models .

the first pattern is proposed by two of us and is favored if the atmospheric mixing angle lies in the first octant , while the second one is preferred for the second octant of . in order to reproduce the second texture , we find that the flavor symmetry should be , while for the first pattern the flavor symmetry should be extended to with and of different parity .

we explore two bilarge neutrino mixing anztze within the context of abelian flavor symmetry theories : ( ) , , , and ( ) , , . the first pattern is proposed by two of us and is favored if the atmospheric mixing angle lies in the first octant , while the second one is preferred for the second octant of . in order to reproduce the second texture , we find that the flavor symmetry should be , while for the first pattern the flavor symmetry should be extended to with and of different parity . explicit models for both mixing patterns are constructed based on the flavor symmetries and . the models are extended to the quark sector within the framework of grand unified theory in order to give a successful description of quark and lepton masses and mixing simultaneously . phenomenological implications are discussed . 2.5 cm * bilarge neutrino mixing and abelian flavor symmetry * 0.2 cm 0.5 cm gui - jun ding , s. morisi , and j. w. f. valle + .2 cm_department of modern physics , _ + _ university of science and technology of china , hefei , anhui 230026 , china _ .3 cm _ ahep group , instituto de fsica corpuscular c.s.i.c./universitat de valncia + edificio de institutos de paterna , apartado 22085 , e46071 valncia , spain _ .3 cm .3 cm _ institut fr theoretische physik und astrophysik , + universitt wrzburg , 97074 wrzburg , germany _ 0.7 cm 2truecm

1409.6487

i

eccentric discs , in which the dominant motion consists of elliptical keplerian orbits , occur in a wide variety of astrophysical situations . for example , an eccentric gaseous disc is formed directly when a star ( or a giant planet ) evolves , through scattering or secular interaction , on to an orbit that closely approaches the galactic centre ( or the host star ) , and is tidally disrupted ( e.g. * ? ? ? * ; * ? ? ? * ) ; such a process might be responsible for the gas cloud g2 near sgr a@xmath1 in the galactic centre @xcite . in an eccentric binary star , a circumstellar or circumbinary disc acquires a forced eccentricity from the binary orbit via secular gravitational interaction . the importance of this for planet formation in binary stars has been recognized @xcite . even if the binary orbit is circular , certain mean - motion resonances can allow a free eccentricity of the disc to grow , initially exponentially @xcite . these effects can of course occur in non - stellar binaries such as binary black holes with accretion discs @xcite , planet satellite systems with planetary rings @xcite and protoplanetary systems . whether planet disc interactions lead to eccentricity excitation @xcite depends on the dynamics of eccentric discs , because of the strong coupling between the planet and the disc . even in the absence of an orbiting companion , a disc may become eccentric through an instability of the circular state , such as viscous overstability @xcite . in contrast to the naive expectation that viscosity tends to circularize a disc , viscous overstability may explain the eccentricity of decretion discs formed around rapidly rotating be stars ( e.g. * ? ? ? * ) . in eccentric binaries the forced eccentricity of the disc is locked to that of the binary and may not be easily detectable . however , discs with a free eccentricity precess as a result of their pressure and any gravitational influences that cause a departure from keplerian motion . this is the generally accepted explanation of the superhump phenomenon in the su uma class of dwarf novae ( e.g. * ? ? ? * ) , in which the accretion disc expands sufficiently during superoutbursts to encounter the 3:1 resonance with the binary orbit and becomes eccentric . ( some other systems exhibit steady accretion and permanent superhumps . ) the elliptical outer rim of the disc in oy car was measured by @xcite through the variation of eclipses of the hot spot . [ for a critical analysis of observational evidence for eccentric discs in su uma stars from a particular standpoint , see @xcite . ] recently , _ kepler _ has been used to observe superoutbursts and superhumps with much greater accuracy @xcite . in dwarf novae the optical emission is modulated at the frequency at which the disc precesses in the frame that rotates with the binary orbit , owing to the interaction between the eccentric mode and the tidal deformation . related phenomena are also reported in low - mass x - ray binaries , although the radiative mechanisms are different @xcite . several theoretical and computational approaches have been taken to the study of eccentric discs . one is to try to generalize the classical theory of viscous accretion discs to allow for orbits of arbitrary eccentricity @xcite . these analyses , of which the last is by far the most general , aim to derive evolutionary equations for the shape and mass distribution of eccentric discs due to viscous and other internal stresses . earlier , equations governing the evolution of narrow and slightly eccentric planetary rings were formulated by @xcite . a separate body of theoretical work relates to eccentric collisionless stellar discs in galactic nuclei , notably m31 @xcite . small eccentricities are governed by linear equations which can be derived through a perturbation analysis of a circular disc . this approach has been taken by , e.g. , @xcite , @xcite , @xcite , , @xcite and @xcite . the broad conclusion of this work is that eccentricity can propagate through a disc by means of pressure and self - gravity , as a slow one - armed density wave , while viscosity causes it to diffuse ( except in cases where it is excited by viscous overstability ) . differential apsidal precession due to the rapid rotation of the central object , relativistic effects , self - gravity of the disc or the presence of orbiting companions can be important , as can three - dimensional effects due to the vertical structure and oscillation of the disc . numerical simulations of eccentric discs have mainly been carried out using smoothed particle hydrodynamics ( sph ) , which readily produces eccentric discs in circular binary stars with mass ratios typical of su uma stars @xcite . more recently , grid - based simulations have also found the development of eccentric discs in the presence of a planetary or stellar companion . found that eccentric discs are hydrodynamically unstable in the absence of viscosity . the instability is three - dimensional and takes the form of a parametric resonance of inertial waves , as also occurs in tidally distorted discs @xcite and in the classic elliptical instability of flows with non - circular streamlines @xcite . a related phenomenon occurs in warped discs @xcite . carried out numerical simulations of the instability of eccentric discs in the absence of vertical gravity and found that it led to subsonic turbulence . this paper is organized as follows . in section [ s : large ] we describe the geometry of an eccentric disc and recall the properties of the orbital coordinates defined by @xcite . we formulate the hydrodynamic equations in this coordinate system and obtain the evolutionary equations for an eccentric disc in terms of orbital averages of force and stress components . in section [ s : local ] we derive a local model of an eccentric disc , which will be useful for analytical and computational studies of instabilities and turbulence in eccentric discs . in section [ s : laminar ] we consider the simplest hydrodynamic solutions of this local model , which are non - hydrostatic and necessarily involve a vertical oscillation of the disc ; we also discuss the evolution of eccentric discs under this laminar dynamics . in a companion paper @xcite we use the local model to analyse the linear hydrodynamic stability of an eccentric disc .

we formulate a local dynamical model of an eccentric disc in which the dominant motion consists of elliptical keplerian orbits . the simplest solutions of the local model are laminar flows consisting of a ( generally nonlinear ) vertical oscillation of the disc . we also derive the linear evolutionary equations for an eccentric disc that follow from the laminar flows in the absence of a shear viscosity . in a companion paper we show that these solutions are linearly unstable and we determine the associated growth rates and unstable modes . [ firstpage ] accretion , accretion discs hydrodynamics celestial mechanics

we formulate a local dynamical model of an eccentric disc in which the dominant motion consists of elliptical keplerian orbits . the model is a generalization of the well known shearing sheet , and is suitable for both analytical and computational studies of the local dynamics of eccentric discs . it is spatially homogeneous in the horizontal dimensions but has a time - dependent geometry that oscillates at the orbital frequency . we show how certain averages of the stress tensor in the local model determine the large - scale evolution of the shape and mass distribution of the disc . the simplest solutions of the local model are laminar flows consisting of a ( generally nonlinear ) vertical oscillation of the disc . eccentric discs lack vertical hydrostatic equilibrium because of the variation of the vertical gravitational acceleration around the eccentric orbit , and in some cases because of the divergence of the orbital velocity field associated with an eccentricity gradient . we discuss the properties of the laminar solutions , showing that they can exhibit extreme compressional behaviour for eccentricities greater than about , especially in discs that behave isothermally . we also derive the linear evolutionary equations for an eccentric disc that follow from the laminar flows in the absence of a shear viscosity . in a companion paper we show that these solutions are linearly unstable and we determine the associated growth rates and unstable modes . [ firstpage ] accretion , accretion discs hydrodynamics celestial mechanics

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although keplerian discs are usually assumed to be circular , the general keplerian disc is elliptical , in accordance with kepler s first law . as found by @xcite and other authors , viscosity ( and other dissipative effects ) do not necessarily lead to the circularization of a disc , even though circular orbits have the least energy for a given angular momentum ; this is because dissipative forces can tap the reservoir of orbital energy by causing mass redistribution . eccentricity may result from the initial conditions of the disc ( as in the case of a disc formed through tidal disruption of a body on an elliptical orbit ) , from secular forcing by a companion with an elliptical orbit , from resonant forcing by a companion with a circular or elliptical orbit , or from instability of a circular disc . in this paper we have revisited the theory of eccentric discs developed by @xcite . in particular , we have formulated a local model , which is a generalization of the well known shearing sheet ( or box ) to the geometry of an eccentric disc . we have discussed the simplest hydrodynamic solutions in the local model , which are necessarily non - hydrostatic and involve a vertical oscillation at the orbital period . these oscillations can become highly nonlinear and exhibit extreme behaviour at eccentricities significantly less than unity , especially if the disc behaves isothermally . it would be valuable to determine , using numerical simulations , whether these extreme solutions are realized in practice . we have also computed the stresses associated with the laminar flows in a linear regime and derived the associated global evolutionary equation for the eccentricity , which differs significantly from a two - dimensional theory that neglects the vertical structure and oscillation of the disc . a question not addressed in this paper is a possible vertical dependence of the eccentricity . in the absence of viscosity , turbulence and magnetic fields , layers of the disc at different heights are relatively weakly coupled by pressure gradients and can undergo independent epicyclic oscillations to some extent . as discussed by @xcite , this allows the eccentricity to propagate radially with a non - trivial vertical profile . there may therefore be a transition in behaviour when the viscous , turbulent or magnetic stresses are very small . in the companion paper @xcite we use the local model to analyse the linear hydrodynamic stability of an eccentric disc . in the absence of viscosity and magnetic fields , eccentric discs are susceptible to a hydrodynamic instability that excites internal ( inertial ) waves and may induce hydrodynamic turbulence . this is likely to be important for the evolution of the eccentricity , but also potentially for transport processes and mixing .

the model is a generalization of the well known shearing sheet , and is suitable for both analytical and computational studies of the local dynamics of eccentric discs . we discuss the properties of the laminar solutions , showing that they can exhibit extreme compressional behaviour for eccentricities greater than about , especially in discs that behave isothermally .

we formulate a local dynamical model of an eccentric disc in which the dominant motion consists of elliptical keplerian orbits . the model is a generalization of the well known shearing sheet , and is suitable for both analytical and computational studies of the local dynamics of eccentric discs . it is spatially homogeneous in the horizontal dimensions but has a time - dependent geometry that oscillates at the orbital frequency . we show how certain averages of the stress tensor in the local model determine the large - scale evolution of the shape and mass distribution of the disc . the simplest solutions of the local model are laminar flows consisting of a ( generally nonlinear ) vertical oscillation of the disc . eccentric discs lack vertical hydrostatic equilibrium because of the variation of the vertical gravitational acceleration around the eccentric orbit , and in some cases because of the divergence of the orbital velocity field associated with an eccentricity gradient . we discuss the properties of the laminar solutions , showing that they can exhibit extreme compressional behaviour for eccentricities greater than about , especially in discs that behave isothermally . we also derive the linear evolutionary equations for an eccentric disc that follow from the laminar flows in the absence of a shear viscosity . in a companion paper we show that these solutions are linearly unstable and we determine the associated growth rates and unstable modes . [ firstpage ] accretion , accretion discs hydrodynamics celestial mechanics

0910.3456

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in this paper , we give a definition of _ coherent tangent bundles _ , which is an intrinsic formulation of wave fronts . the advantage of this formulation is that the first fundamental forms and the third fundamental forms satisfy exactly the same conditions for wave fronts in space forms , and they can reverse roles with each other . then the two gauss - bonnet formulas induce two more gauss - bonnet formulas by exchanging the first and third fundamental forms . these turn out to be different from those for the first fundamental form , and using these four formulas , we get new results on fronts . in section [ sec : coherent ] , we generalize the definitions of _ coherent tangent bundles _ and _ singular curvature _ , which were given for @xmath0-dimensional coherent tangent bundles ( or fronts ) in @xcite and @xcite , to fronts of general dimension . a coherent tangent bundle on an @xmath1-manifold @xmath2 induces a positive semi - definite metric on @xmath2 ( called the first fundamental form ) , and can be regarded as a generalization of riemannian manifolds . using the concept of coherent tangent bundles , we can give a unified treatment of hypersurfaces and @xmath3-maps between the same dimensional manifolds . the points where the metric degenerates are called _ singular points_. we define a notion of @xmath4 ( singular ) points , which is a generalization of that of fronts and of @xmath3-morin maps at the same time . we define _ singular principal curvatures _ for each @xmath5-point of a given coherent tangent bundle , which are @xmath6-tuples of real numbers . one of them diverges to @xmath7 at @xmath8-points as shown in theorem [ thm : infty ] . this is a generalization of the result in @xcite for @xmath0-dimensional fronts . moreover , as shown in section [ sec : gauss - bonnet ] , our intrinsic setting enables us to introduce the singular curvature on @xmath5-morin singular points . when @xmath9 , as an application of the two intrinsic gauss - bonnet formulas , we give a new proof of quine s formula ( cf . proposition [ prop : quine ] ) , and also get a new formula ( cf . proposition [ prop : id ] ) for the total singular curvature of generic smooth maps between @xmath0-manifolds . furthermore , in section [ sec : gauss - bonnet ] , we also give several results on compact @xmath0-dimensional fronts , as an application of our new gauss - bonnet formulas for the third fundamental form . in particular , we show that the total negative gaussian curvature @xmath10 of a closed immersed surface @xmath11 in @xmath12 is equal to the signed sum of total geodesic curvature on each connected component of the singular set of its gauss map , see theorem [ thm : c ] . the deepest applications are given for surfaces of bounded gaussian curvature . for example , the euler characteristic of a closed wave front with gaussian curvature @xmath13 ( @xmath14 ) in a @xmath15-dimensional flat torus vanishes ( cf . theorem [ thm : g ] ) .

are considered as induced metrics of certain homomorphisms between vector bundles . they satisfy the completely same conditions , and so can reverse roles with each other . for a given wave front of a-manifold , there are two gauss - bonnet formulas . by exchanging the roles of the fundamental forms , we get two new additional gauss - bonnet formulas for the third fundamental form . surprisingly , these are different from those for the first fundamental form , and using these four formulas , we get several new results on the topology and geometry of wave fronts .

we give a definition of ` coherent tangent bundles ' , which is an intrinsic formulation of wave fronts . in our application of coherent tangent bundles for wave fronts , the first fundamental forms and the third fundamental forms are considered as induced metrics of certain homomorphisms between vector bundles . they satisfy the completely same conditions , and so can reverse roles with each other . for a given wave front of a-manifold , there are two gauss - bonnet formulas . by exchanging the roles of the fundamental forms , we get two new additional gauss - bonnet formulas for the third fundamental form . surprisingly , these are different from those for the first fundamental form , and using these four formulas , we get several new results on the topology and geometry of wave fronts .

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the aim of this paper is not necessarily to ` drive a wedge ' between the ` canonical ' black hole sxts and this sub - class of low / hard state x - ray transients ( lhxt ; we note that the term ` hard x - ray transient ' has been applied previously to the be + neutron star binary systems ) . while we can see that the sources studied here are not classical fred sources , neither are a large number of sxts , on account of both lightcurve morphology ( chen et al . 1997 ) and x - ray spectral state ( e.g. brocksopp et al . 2002 ) ; thus it is becoming timely for a re - definition of the ` canonical ' x - ray transient which incorporates the now numerous radio jet and spectral ( x - ray and broad - band ) observations . models for sxt outbursts have been largely based on the disc instability model ( dim ) , initially developed for the outbursts of dwarf novae but later adapted for sxts ( e.g. lasota 2001 and references therein ) . the model s success has been due to its ability to produce fred - shaped lightcurves , thus having the potential to describe observations of x - ray transient outbursts ( e.g. king & ritter 1998 ; dubus et al . the original model has been adapted to include additional physical mechanisms of relevance in x - ray binaries ; by invoking disc irradiation and truncation of the inner disc , the basic rise , decay and recurrence times can be reproduced ( lasota 2001 ) . there are a number of problems with the dim , particularly as a large number ( @xmath11 ; chen et al . 1997 ) of sxt outbursts do not display ` canonical ' fred behaviour . these problems are well - known ( e.g. chen et al . 1997 ) and it is thought that they may be rectified with the inclusion of accretion disc coronae and/or warps ( lasota 2001 ) . additionally there are difficulties in describing the quiescent and low / hard states without the inclusion of an adaf or coronal outflow ( e.g. esin et al . 1997 , merloni & fabian 2002 ) . however it is also of vital importance that the broad - band , and particularly the x - ray spectra are taken into account , especially if a truncated inner disc is required in order to model the lightcurves . in particular the dim assumes that the x - ray outburst takes place in the disc and that the optical emission is produced via reprocessing of these soft x - ray photons ( e.g. lasota 2001 ) but in the case of the outbursts which remained in the low / hard state all x - ray photons were produced in the corona ; the dim does not consider the production of this power - law x - ray emission . more recently the outburst of xte j1118 + 108 was modelled in terms of a diffusion model instead of the dim ( wood et al . 2001 ) . rather than assuming that an outburst is caused by a build - up of mass in the disc during quiescence which then becomes unstable ( as in the dim ) , this diffusion model is based on the assumption that sporadic / variable mass transfer from the companion takes place . while a fred morphology for the first of the two x - ray peaks of xte j1118 + 108 was generated by this model , as well as the non - fred second peak , it should also be noted that this model does not yet include a trigger and as such is currently incomplete . the most desirable model ( or perhaps combination of models ) would not only explain all sxt and lhxt outbursts , but would also be consistent with models for the state changes of persistent x - ray binaries such as cyg x-1 and lmc x-3 ( including the ` failed state changes ' of cyg x-1 during which the source remains in the low / hard state brocksopp et al . 1999 ) . these are all supposedly the result of variable mass transfer and/or accretion ; could they all be produced by the same mechanism as x - ray transient outbursts ? in particular , wilms et al . ( 2001 ) showed that the long modulation of lmc x-3 was produced , not by the assumed precession of the accretion disc , but by quasi - periodic changes in the mass transfer rate . likewise fender et al . ( 1999 ) suggest variable mass transfer for outbursts in cyg x-3 . we note also that , in the be + neutron star binary systems , outbursts occur at periastron of an eccentric orbit ( e.g. van paradijs & mcclintock 1995 and references therein ) again suggestive of some outbursts being the result of variable mass transfer rather than instabilities within the disc . it has also been suggested that the ` superoutbursts ' seen in the su uma class of cataclysmic variable stars are the result of a ` normal ' disc instability outburst triggering additional mass transfer from the companion , perhaps due to increased irradiation ; the dim alone can not provide sufficient power for an outburst of such magnitude and duration ( frank , king , raine 1992 ) . a similar mechanism has been suggested for xte j1118 + 480 ( kuulkers 2001 ) . however this does not explain the outburst of gro j1719@xmath124 in this case the ` superoutburst ' _ preceded _ the ` normal ' outburst . if irradiation is not the sole cause of the increased mass transfer then an alternative mechanism may be necessary ; models of an accretion disc wind instability limit cycle or a variable roche lobe filling factor have been suggested for lmc x-3 ( wilms et al . 2001 , wu et al . 2001 ) and should be considered as potential mechanisms in other sources . the suggestion that variable mass transfer from the companion might be important for x - ray transient outbursts is not new ; e.g. hameury et al . ( 1986 ) considered the possibility of unstable mass transfer caused by illumination of the stellar companion . this was later discounted in favour of the dim ( e.g. mineshige & wheeler 1989 , gontikakis & hameury 1993 ) , the main problem being that the mass transfer instability is insufficient to produce the high levels of variability observed . this problem may be avoided if the broad - band spectrum is considered . if , as appears to be the case in the low / hard state of ( at least ) xte j1118 + 480 and gx 339@xmath14 ( markoff et al . 2001 , 2003 ; corbel & fender 2002 ) , a significant proportion of the x - ray luminosity is produced via the synchrotron mechanism then acceleration within the jet is likely to be its source , thus reducing the magnitude of the required mass transfer variability . while this is particularly important in the case of the low / hard state sources , the power in the jet ejections also has significant implications on determination of the mass accretion rate in soft events . furthermore sxt outbursts of xte j1859 + 226 , xte j1550@xmath1564 and many others have been observed to pass through the low / hard state prior to softening ; they have _ not _ made a direct transition from quiescence to the high / soft ( or very high ) state . all recent black hole sxt outbursts have shown this behaviour and those less recent sources which have not appeared to exhibit this behaviour have not actually been observed in sufficient detail to be certain either way ( brocksopp et al . 2002 ) . there has been no attempt to fit the dim to any source with the inclusion of this initial hard state and it is important that the power requirements of the initial hard state ( and its associated jet ) are incorporated into models . with the low / hard state shown to be such a ubiquitous behaviour of black hole x - ray binaries it is extremely important that these lhxt ` mini - outbursts ' and the initial hard state prior to a black hole sxt outburst are not forgotten about . does the same mechanism produce both the off lhs and lhs vhs transitions ( i.e. lhs = low / hard state and vhs = very high state ) ? can we assume that the off lhs transition is produced by the same mechanism regardless of whether the outburst is a black hole sxt or lhxt ? ( we note that it is not yet certain whether or not the ` off ' and ` low / hard ' states are actually two distinct spectral states . ) what conditions are present to cause a source to then make the lhs vhs transition as well ? these questions are particularly interesting for a source such as gs 1354@xmath164 which has displayed both types of outburst . in summary , while we do not intend this paper to necessarily favour one model over others , the low / hard state outbursts studied in this paper do not appear to be explained in terms of the dim as it stands currently ; either the dim needs significant modification to include the properties of the jet and broad - band spectrum , or some new model is required , in which case a sporadic mass transfer model ( such as the diffusion model of wood et al . 2001 ) may be a viable alternative , subject to further testing and inclusion of the jet and outburst trigger . furthermore , given the ubiquity of low / hard state behaviour in black hole x - ray binaries , it is possible that some form of variable mass transfer model could apply to black hole sxt outbusts as well , at least in providing the off lhs transition at the onset of the outburst . if this is the case then we need to determine the conditions and mechanism ( disc instability ? ) by which a black hole sxt then proceeds to the very high state . the points raised in the previous sections can be well - illustrated by using xte j1550@xmath1564 as a case - study . it is particularly useful since its observing coverage has been excellent at all frequencies and all behaviours studied in this paper have been observed in this single source . xte j1550@xmath1564 was discovered when it entered a sxt outburst in 1998 , passing through all of the known x - ray spectral states over the course of this outburst , including an initial low / hard state phase ( e.g. homan et al . 2000 ) . the outburst has been studied at x - ray radio wavelengths and a mass transfer instability invoked as the trigger of the extremely hard `` spike '' , which took place at the onset of the outburst ( wu et al . 2002 ) . radio observations revealed a jet with apparent superluminal motion , as well as the ubiquitous synchrotron spectrum ( hannikainen et al . 2001 ) . more recent observations have shown that more than two years after the event the ejecta were still resolvable at radio _ and at x - ray _ wavelengths and with a broad - band synchrotron spectrum ( corbel et al . 2002 ) . furthermore there were additional outbursts in 2000 , 2001 and 2002 ; an initial low / hard state was observed in 2000 before the source softened and the two more recent outbursts remained in the low / hard state throughout ( belloni et al . radio observations in 2002 confirmed the presence of a typical low / hard state jet spectrum ( corbel et al . 2002 ) . the qpo behaviour during the 2000 outburst was particularly well - observed ; both rise and fall of qpo frequency were seen during the lhs phases of the outburst . the frequency reached a plateau briefly during the lhs vhs transition before disappearing for most of the vhs and reappearing again during the transition back to the lhs ( reilly et al 2001 ) . thus study of this one source suggests ( confirms ? ) that ( i ) there are problems in explaining the power - law x - ray emission with conventional outburst models , ( ii ) the proposed broad - band jet spectrum can be imaged and ( iii ) a single source can enter outbursts of different spectral properties .

comparison of the lightcurve morphologies , spectral behaviour , properties of the quasi - periodic oscillations and the radio jet provides the first study of such objects as a sub - class of x - ray transients . however rather than assuming that these hard state x - ray transients are different from the ` canonical ' soft x - ray transient , we prefer to consider the possibility that new analysis of both soft and hard state x - ray transients in a spectral context will provide a model capable of explaining the outburst mechanisms of ( almost ) all black hole x - ray binaries .

we have accumulated multiwavelength ( x - ray , optical , radio ) lightcurves for the eight black hole x - ray binaries which have been observed to enter a supposed ` soft x - ray transient ' outburst , but remained in the low / hard state throughout the outburst . comparison of the lightcurve morphologies , spectral behaviour , properties of the quasi - periodic oscillations and the radio jet provides the first study of such objects as a sub - class of x - ray transients . however rather than assuming that these hard state x - ray transients are different from the ` canonical ' soft x - ray transient , we prefer to consider the possibility that new analysis of both soft and hard state x - ray transients in a spectral context will provide a model capable of explaining the outburst mechanisms of ( almost ) all black hole x - ray binaries .

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we have accumulated multiwavelength datasets for the eight black hole x - ray binaries which have been observed to enter an outburst but remained in the low / hard state throughout . we show that , despite very similar x - ray spectral properties , the lightcurve morphologies of these sources are very different , as are the relationships between the x - ray , optical and radio lightcurves . however , the qpo and jet properties are comparable in each system . this comparison of the low / hard state transients suggests that some mechanism to explain the outbursts in the context of their spectral properties is necessary ; the disc instability model currently lacks the flexibility to do this and needs modification in order to allow for the the observed jet . we also suggest that in light of the more recent observations of both low / hard state and soft x - ray transients ( e.g. xte j1550@xmath1564 ) , the various models of sporadic mass transfer should not be ruled out , at least during the low / hard state phase of the outburst testing of these suggestions is work in progress .

we have accumulated multiwavelength ( x - ray , optical , radio ) lightcurves for the eight black hole x - ray binaries which have been observed to enter a supposed ` soft x - ray transient ' outburst , but remained in the low / hard state throughout the outburst .

we have accumulated multiwavelength ( x - ray , optical , radio ) lightcurves for the eight black hole x - ray binaries which have been observed to enter a supposed ` soft x - ray transient ' outburst , but remained in the low / hard state throughout the outburst . comparison of the lightcurve morphologies , spectral behaviour , properties of the quasi - periodic oscillations and the radio jet provides the first study of such objects as a sub - class of x - ray transients . however rather than assuming that these hard state x - ray transients are different from the ` canonical ' soft x - ray transient , we prefer to consider the possibility that new analysis of both soft and hard state x - ray transients in a spectral context will provide a model capable of explaining the outburst mechanisms of ( almost ) all black hole x - ray binaries .

1212.1226

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comets are understood to be frozen remnants from the formation of our solar system . as such , their chemical composition is of great significance to understanding the origin of the planets and the distribution of important molecules , including water , throughout the solar system . this was and is a major goal of the deep impact and epoxi missions , among others , as well as ground - based observations of comets . recent observations , in particular those of the deep impact and epoxi missions ( see e.g. feaga , et al . 2007 or ahearn , et al . 2011 ) , have provided better spectra of a cometary coma than were , in general , previously available . these observations include spectra with high spatial resolution very near to the nucleus . no previous observations had as much spatially well - resolved spectral data , and thus there was little observationally driven need to pay special or close attention to the densest part of the coma . ground - based observations could only see optically thick regions of comae for the brightest and/or most active of comets . ( e.g. hale bopp ; see disanti et al . 2001 . ) therefore many earlier studies that modeled spectra of comae , in keeping with the available observations of the time , did not attempt to calculate optical depth effects on spectra . optically thin comae were assumed , since the field of view in those observations being modeled would be dominated by the majority of the coma far from the nucleus , which is optically thin ( see e.g. chin & weaver 1984 ; crovisier & le bourlot 1983 ) . however , with the proliferation of space missions to comets , as well as much better instruments for ground - based observations ( see , e.g. disanti et al . 1999 ) , this is no longer a truly tenable approach . our goal is to better understand the abundances , distributions and creation mechanisms of various gases observed in comae , in particular of comet 9p / tempel 1 , the target of the deep impact mission , and 103p / hartley 2 , the subject of the epoxi mission . in order to do so , we have built a computer model of the spectrum of the comet s coma which includes the difficult and often ignored problem of accurately including radiative transfer to account for the potentially optically thick coma ( or regions of the coma ) near the nucleus . this model will facilitate analyzing the actual spectral data from the deep impact and epoxi missions to better determine abundances of key species , including co , co@xmath0 , and h@xmath0o , as well as remote sensing data on active comets . we begin our modeling of ir ro - vibrational spectra of a coma by initially following the method used by chin & weaver 1984 , crovisier 1987 , and others with some minor improvements . as in those models , we assume a constant expansion velocity , thus linearly relating any radial distance to a specific time since a `` parcel '' of gas was released from the surface of the nucleus . therefore we numerically integrate over time the linear differential equations defined by the einstein coefficients and collisional rate coefficients to get fractional molecular enegry level populations for each distance from the nucleus , from which we calculate emission spectra . @xmath1 here @xmath2 and @xmath3 indicate energy levels of a molecule with the @xmath4 s with those indices being the corresponding level populations . the einstein coefficients between levels x and y are @xmath5 and @xmath6 , and c is a similar collisional coefficient . we use @xmath7 for the mean intensity of radiation at the frequency corresponding to the transition between x and y , @xmath8 is the energy difference between levels x and y , and @xmath9 and t have their usual meanings . the summations are over all levels i , l or j which have a transition into or out of level k. for collisional coefficients @xmath10 where @xmath11 is the number density of h@xmath0o ( assumed to be the dominant collisional partner ) @xmath12 is the collisional cross section for a given transition and @xmath13 is the mean ( thermal ) molecular speed . this allows us to include a time variable production rate . we use such a coma integration as the initial basis for our coma model before including potential optical depth effects . our primary improvement is the inclusion of radiative transfer calculations using our spherical adaptation of the coupled escape probability method ( hereafter , `` cep '' ; see elitzur & asensio ramos 2006 , hereafter , `` cep06 '' ) to more correctly model optically thick ( or potentially thick ) regions of cometary comae . this is described in detail below , and is the main part of this paper . we use the coma integration results to provide the `` initial guess '' values for populations used in the subsequent radiative transfer calculations using cep . for the purposes of the initial coma model , we treat the comet as spherically symmetric , and as having a uniform and constant gas production rate over its entire surface . the outward speed of the gas is also assumed to be constant , as per chin & weaver 1984 . while this is not strictly physically accurate ( see e.g. combi 1996 ) the variation over the majority of the coma is relatively small . we use a temperature profile that varies with radial distance from the nucleus , having closely followed combi s 1989 model ( see fig . [ combi200 ] . ) these approximations make integration over time equivalent to calculating these values over increasing distances from the comet nucleus for a `` shell '' of gas expanding outwards from the nucleus . we ignore the photodestruction of co in our coma model , due to its long lifetime ( see crovisier 1994 . ) the lifetime is @xmath14 s , and we are integrating out to @xmath15 km with an expansion velocity of 0.8 km s@xmath16 . ( note that others , e.g. morgenthaler , et al . 2011 , find a shorter lifetime , but still @xmath17 s , which is still large enough that it can be neglected in our modeling out to 10@xmath18 km . ) the model can include coma morphology features as well , each modeled with its own coma integration using separate conditions . such features , as seen in the deep impact and epoxi encounters , are a main motivation for creating this model to better understand possible optical depth effects in the near nucleus regions of the coma . ( see e.g. feaga , et al . 2007 or ahearn , et al . 2011 ) after describing our method in section 2 , we present ( in section 3 ) some results demonstrating its use in better understanding possible optically thick spectra for the carbon monoxide 1 - 0 ( x@xmath19 ) band in spherically symmetric comae . these may be useful for ground - based observers ( or space telescope observations of comets ) to better fathom the depths of cometary spectra . forthcoming model results for co@xmath0 , h@xmath0o and near - nucleus morphological features will follow ( in other papers ) .

we have adapted coupled escape probability , a new exact method of solving radiative transfer problems , for use in asymmetrical spherical situations . our model is intended specifically for use in modeling optically thick cometary comae , although not limited to such use . this method enables the accurate modeling of comets spectra even in the potentially optically thick regions nearest the nucleus , such as those seen in deep impact observations of 9p / tempel 1 and epoxi observations of 103p / hartley 2 .

we have adapted coupled escape probability , a new exact method of solving radiative transfer problems , for use in asymmetrical spherical situations . our model is intended specifically for use in modeling optically thick cometary comae , although not limited to such use . this method enables the accurate modeling of comets spectra even in the potentially optically thick regions nearest the nucleus , such as those seen in deep impact observations of 9p / tempel 1 and epoxi observations of 103p / hartley 2 .

astro-ph0607616

i

following on the discovery of the anomalous absorption of the cosmic microwave background ( cmb ) at 4.83 ghz by gas - phase ortho - formaldehyde ( h@xmath0co ) molecules in a few nearby galactic dark nebula @xcite , several surveys were carried out in hopes of establishing the general galactic distribution of distant dusty molecular clouds containing gaseous h@xmath0co . @xcite used the nrao 140-foot telescope ( beam fwhm @xmath9 , system temperature t@xmath10 k ) to survey 30 positions spread out along the galactic plane near @xmath11 in the range @xmath12 and chosen to be free of radio continuum emission . with the exception of the one position near to the galactic center ( which did indeed appear to have continuum emission in the general area ) , no detections of cmb absorption could be registered , with a typical peak limits ( 5@xmath13 ) of 0.07 k in a velocity channel of width 1.6 km s@xmath14 . gordon & roberts concluded either that the excitation temperature of the general galactic distribution of h@xmath0comust be close to the brightness temperature of the cmb ( now known to be 2.73 k ) , or that the dust clouds harboring the h@xmath0co must be much smaller than the telescope beam . this disappointing result was corroborated with additional observations by @xcite using the 25-m radio telescope of the onsala space observatory ( oso ) in sweden ( fwhm @xmath15 , t@xmath16 k ) in order to map three @xmath17 fields in the galactic plane at @xmath18 , and @xmath19 . spectra were obtained in each of these fields on a grid with separation @xmath3 . no emission or absorption was found , with a typical peak limit of 0.15 k in a 0.62 km s@xmath14 channel . the first large - scale survey for h@xmath0co along the galactic plane was carried out by @xcite using the jodrell bank mark ii radio telescope ( fwhm @xmath20 , t@xmath21 k ) . observations were made at @xmath11 every @xmath22 of galactic longitude in the range @xmath23 and every @xmath24 in the range @xmath25 . these observations were successful in recording h@xmath0coabsorption in the inner galaxy , and some approximate information on the spatial distribution was obtained . however , the signal dropped to undetectable levels beyond @xmath26 , and no observations were attempted in the outer galaxy . in fact , at no position did the absorption - line profile depth exceed the observed continuum temperature . one can therefore safely conclude that what was being measured was not the anomalous cmb absorption ( which was still apparently too weak ) , but rather absorption of the galactic background radio radiation , which is strongest in the inner galaxy . although gaseous h@xmath0co may be nearly absent in parts of the ism because it is dissociated or frozen out on grains , these early surveys provided an indication that the physical conditions under which detectable anomalous h@xmath0co absorption occurs may not be common in the galaxy . observers turned their attention to other , more easily detected molecules , notably co , and we now have extensive surveys of the co(1 - 0 ) line over large sections of the galactic plane @xcite . these surveys , along with many detailed studies of specific molecular clouds in a wide range of molecular tracers , have all contributed to a much more complete ( and much more complicated ) view of physical conditions in the cool molecular ism . an explanation for the anomalous cmb absorption by h@xmath0co was first suggested by @xcite using a classical calculation for collisional excitation . subsequent work , especially by evans and his collaborators @xcite , confirmed this result using quantum mechanical calculations and observations . the collisional pumping mechanism is more effective at high collision rates , so in general the absorption is strongest at higher densities and temperatures . however , the calculations by @xcite showed that the mechanism would still be effective at rather low temperatures , below about 10k . more precise quantum mechanical calculations reported by @xcite suggested a smaller effect at very low kinetic temperatures , but both methods involved approximations . this leaves open the possibility that high - density , cold clumps of molecular gas in the ism may be detectable in h@xmath0co absorption , and has provided part of the motivation for our observing program . our approach is to carry out long integrations at a set of blindly - selected positions in the general direction of the galactic anticenter . for these observations we have again used the 25-m oso radio telescope at onsala , the same telescope used by gordon & hglund more than 33 years ago in their failed attempt to detect the general h@xmath0co cmb absorption . our present success is due entirely to the availability of more sensitive receivers and to generous allocations of observing time on this telescope . our survey has two main features : first , it is a `` blind '' survey ; we purposely avoided using maps of any other ism tracer to construct the observing program . second , we chose to observe in the galactic anticenter region , i.e. in the general direction of the outer galaxy . the galactic nonthermal background at 6 cm is exceedingly faint in this direction , so we can be fairly confident that any absorption we might detect is indeed anomalous cmb absorption . we will return to this point later . also , the velocity gradient owing to galactic rotation is small in the anticenter direction , so we might hope for some degree of `` bunching '' of absorption features , enhancing the probability of detection .

we have carried out a blind search in the general direction of the galactic anticenter for absorption of the cosmic microwave background ( cmb ) radiation near 4.83 ghz by molecular clouds containing gaseous ortho - formaldehyde ( hco ) . the observations were done using the 25-m radio telescope at onsala in sweden , and covered strips in galactic latitude at several longitudes in the region . spectra were obtained in these strips with a grid spacing corresponding to the telescope resolution of . however , the scatter in this correlation is significantly larger than the measurement errors , indicating differences of detail at and below the linear resolution of our observations ( pc ) .

we have carried out a blind search in the general direction of the galactic anticenter for absorption of the cosmic microwave background ( cmb ) radiation near 4.83 ghz by molecular clouds containing gaseous ortho - formaldehyde ( hco ) . the observations were done using the 25-m radio telescope at onsala in sweden , and covered strips in galactic latitude at several longitudes in the region . spectra were obtained in these strips with a grid spacing corresponding to the telescope resolution of . we have detected hco cmb absorption at of the survey pointings . this detection rate is likely to increase with further improvements in sensitivity , and may become comparable to the detection rate expected from a blind co survey with a corresponding sensitivity limit . we have mapped some of these detections in more detail and compared the hco absorption to existing maps of co(1 - 0 ) emission in the same regions . there appears to be a rough correlation between the velocity - integrated line strength of the co(1 - 0 ) emission and that of the hco absorption . however , the scatter in this correlation is significantly larger than the measurement errors , indicating differences of detail at and below the linear resolution of our observations ( pc ) . although these two tracers are expected to have similar excitation requirements on the microscopic level characteristic of warm , tk , dense , condensations in molecular clouds , the co(1 - 0 ) line is expected to be optically thick , whereas the hco line is not . this latter difference is likely to be responsible for a significant part of the scatter in the correlation we have found .

astro-ph0607616

c

* we have successfully detected anomalous cmb absorption by h@xmath0co - bearing dust clouds at @xmath4 of our blind survey positions in the direction of the outer galaxy . no emission profiles were found . * our success is likely due to the large improvement in sensitivity of our observations over that of earlier surveys . this strongly indicates that the detection statistics will improve further if even higher - sensitivity searches are carried out . since the absorption signal strength from more distant clouds will suffer from increasing beam dilution , future searches ought to be done with larger radio telescopes . * h@xmath62co absorption and co emission lines are spatially co - existing . all observed h@xmath0co absorption features were associated with know co emission . * we have found a rough correspondence between the h@xmath0co and the @xmath51co(1 - 0 ) line fluxes in detailed maps of two regions in our survey area . we have argued that both lines generally trace warm , dense gas in the ism , with the situation for co(1 - 0 ) being somewhat simpler owing to the fact that this line is usually optically thick . we thank prof . roy booth , director ( ret . ) of the radio observatory at onsala , for generous allocations of telescope time and for his warm hospitality during our several visits to the observatory . we are also grateful to the observatory technical and administrative staff for their capable assistance with our observing program . t. dame kindly provided a digital copy of relevant parts of the cfa co(1 - 0 ) survey of the galaxy . we acknowledge the financial support of dgapa , unam and conacyt , in mxico , and the _ director s discretionary research fund _ at the space telescope science institute . rrrrrc 30 , -70 & & & 6.0 @xmath64 1.7 & -9.6 @xmath64 2.8 + 20 , -70 & @xmath65 -9.3 & & 7.2 @xmath64 1.7 & -10.6 @xmath64 2.7 + 10 , -70 & @xmath65 -14.0 & & 6.4 @xmath64 0.8 & -11.9 @xmath64 1.8 + & & & 6.7 @xmath64 1.3 & -4.5 @xmath64 1.0 + 0 , -70 & @xmath65 -14.0 & & 4.5 @xmath64 0.8 & -11.9 @xmath64 2.6 + & & & @xmath65 3.9 & + -10 , -70 & & & @xmath66 5.7 & + -20 , -70 & & & @xmath65 6.0 & + 30 , -60 & @xmath65 -5.7 & & @xmath67 & + 20 , -60 & @xmath65 -6.9 & & 10.0 @xmath64 1.6 & -9.3 @xmath64 1.6 + 10 , -60 & -6.7 @xmath64 1.9 & -5.7 @xmath64 3.2 & 7.3 @xmath64 1.3 & -4.2 @xmath64 0.8 & y + & -4.5 @xmath64 1.2 & -10.3 @xmath64 3.3 & 12.2 @xmath64 0.9 & -10.7 @xmath64 0.9 & y + 0 , -60 & @xmath65 -3.0 & & @xmath65 3.0 & + & & & 6.7 @xmath64 0.9 & -10.7 @xmath64 1.8 + -10 , -60 & @xmath65 -6.3 & & @xmath65 6.0 & + -20 , -60 & @xmath65 -6.9 & & @xmath65 6.0 & + 30 , -50 & @xmath65 -6.6 & & 6.9 @xmath64 1.7 & -9.1 @xmath64 2.3 + 20 , -50 & @xmath65 -6.6 & & 10.0 @xmath64 1.7 & -9.4 @xmath64 1.7 + 10 , -50 & -7.8 @xmath64 2.1 & -3.2 @xmath64 2.4 & 15.0 @xmath64 1.0 & -10.2 @xmath64 0.8 & y + & & & @xmath65 3.9 & + & & & @xmath65 3.3 & + 0 , -50 & -5.0 @xmath64 1.0 & -9.7 @xmath64 2.3 & 11.3 @xmath64 1.6 & -8.9 @xmath64 1.3 & y + -10 , -50 & @xmath65 -6.0 & & 5.2 @xmath64 1.2 & -10.6 @xmath64 2.7 + & & & @xmath65 4.5 & + -20 , -50 & @xmath65 -6.0 & & @xmath65 6.9 & + 30 , -40 & @xmath65 -6.3 & & @xmath65 6.0 & + 20 , -40 & @xmath65 -7.2 & & 8.0 @xmath64 1.8 & -8.6 @xmath64 2.1 + 10 , -40 & @xmath65 -4.2 & & 17.1 @xmath64 1.2 & -10.5 @xmath64 0.8 + & & & @xmath65 3.0 & + & & & @xmath65 2.5 & + 0 , -40 & @xmath65 -3.9 & & 13.6 @xmath64 1.2 & -10.2 @xmath64 1.1 + & & & @xmath65 3.0 & + & & & @xmath65 2.5 & + -10 , -40 & @xmath65 -4.5 & & 7.6 @xmath64 1.5 & -10.5 @xmath64 2.3 + & & & @xmath65 5.1 & + -20 , -40 & @xmath65 -7.5 & & @xmath65 6.3 & + 30 , -30 & @xmath65 -8.4 & & 8.3 @xmath64 1.8 & -8.3 @xmath64 1.9 + 20 , -30 & @xmath65 -6.3 & & 12.6 @xmath64 2.0 & -8.7 @xmath64 1.4 + 10 , -30 & -8.7 @xmath64 2.5 & -8.8 @xmath64 2.6 & 18.8 @xmath64 1.0 & -10.6 @xmath64 0.7 & y + & & & @xmath65 3.9 & + 0 , -30 & -8.6 @xmath64 1.3 & -9.7 @xmath64 1.3 & 14.3 @xmath64 1.1 & -10.3 @xmath64 0.9 & y + & & & @xmath65 4.2 & + -10 , -30 & @xmath65 -9.0 & & 5.8 @xmath64 0.8 & -10.1 @xmath64 1.7 + & & & @xmath65 3.6 & + -20 , -30 & -7.3 @xmath64 2.3 & 0.7 @xmath64 2.7 & @xmath65 5.7 & + 30 , -20 & @xmath65 -7.5 & & @xmath65 6.3 & + 20 , -20 & -10.3 @xmath64 1.9 & -9.4 @xmath64 1.9 & 11.8 @xmath64 1.8 & -8.6 @xmath64 1.4 & y + 10 , -20 & -15.8 @xmath64 1.8 & -9.7 @xmath64 0.9 & 19.1 @xmath64 1.0 & -9.8 @xmath64 0.6 & y + & & & @xmath65 3.3 & + 0 , -20 & -9.1 @xmath64 1.3 & -9.7 @xmath64 1.2 & 13.4 @xmath64 1.1 & -10.4 @xmath64 1.0 & y + & & & 4.6 @xmath64 1.3 & 3.6 @xmath64 1.2 + -10 , -20 & @xmath65 -7.5 & & 4.6 @xmath64 1.2 & -10.1 @xmath64 3.1 + & & & 5.2 @xmath64 1.5 & 3.3 @xmath64 1.1 + -20 , -20 & @xmath65 -7.5 & & @xmath65 3.6 & + & & & @xmath65 4.5 & + 30 , -10 & @xmath65 -7.5 & & @xmath65 5.7 & + 20 , -10 & @xmath65 -4.8 & & @xmath65 6.0 & + 10 , -10 & -5.7 @xmath64 1.3 & -9.6 @xmath64 0.8 & 10.0 @xmath64 1.0 & -9.9 @xmath64 1.1 & y + & & & 4.0 @xmath64 1.1 & 3.8 @xmath64 1.2 + 0 , -10 & -11.3 @xmath64 1.5 & -9.7 @xmath64 0.8 & 9.4 @xmath64 1.0 & -10.2 @xmath64 1.2 & y + & & & 6.3 @xmath64 1.2 & 2.8 @xmath64 1.3 + -10 , -10 & @xmath65 -6.0 & & @xmath65 3.6 & + & & & @xmath65 4.8 & + -20 , -10 & @xmath65 -6.9 & & @xmath65 4.5 & + & & & @xmath65 3.1 & + 30 , 0 & @xmath65 -6.0 & & @xmath65 3.6 & + & & & @xmath65 3.0 & + 20 , 0 & @xmath65 -6.6 & & @xmath65 3.3 & + & & & @xmath65 2.7 & + 10 , 0 & @xmath65 -6.3 & & 9.0 @xmath64 1.1 & -10.4 @xmath64 1.4 + & & & @xmath65 4.2 & + 0 , 0 & @xmath65 -4.8 & & 8.1 @xmath64 1.0 & -10.4 @xmath64 1.5 + & & & @xmath65 3.9 & + -10 , 0 & @xmath65 -5.7 & & @xmath65 3.9 & + & & & @xmath65 3.8 & + -20 , 0 & @xmath65 -7.2 & & @xmath65 3.6 & + & & & @xmath65 2.4 & + 30 , 10 & @xmath65 -7.5 & & 7.0 @xmath64 1.2 & 0.8 @xmath64 1.3 + & & & @xmath65 3.0 & + 20 , 10 & @xmath65 -5.7 & & 7.0 @xmath64 1.4 & 1.4 @xmath64 1.3 + & & & @xmath65 5.1 & + 10 , 10 & -8.3 @xmath64 2.3 & 2.2 @xmath64 0.8 & 7.3 @xmath64 1.3 & 2.0 @xmath64 1.3 & y + & & & 8.5 @xmath64 1.0 & -10.5 @xmath64 1.5 + 0 , 10 & @xmath65 -4.5 & & 7.2 @xmath64 1.1 & 1.8 @xmath64 1.3 + & & & 8.5 @xmath64 1.0 & -9.7 @xmath64 1.3 + -10 , 10 & @xmath65 -6.6 & & 6.7 @xmath64 1.2 & 2.6 @xmath64 1.3 + & & & 6.3 @xmath64 0.9 & -9.9 @xmath64 1.7 + -20 , 10 & @xmath65 -8.1 & & @xmath65 4.2 & + & & & @xmath65 3.0 & + 30 , 20 & @xmath65 -8.2 & & @xmath65 3.9 & + & & & 3.7 @xmath64 1.0 & -9.7 @xmath64 3.2 + 20 , 20 & @xmath65 -6.6 & & 6.9 @xmath64 1.4 & 1.2 @xmath64 1.3 + & & & @xmath65 3.0 & + 10 , 20 & @xmath65 -6.0 & & 7.4 @xmath64 1.2 & 1.9 @xmath64 1.3 + & & & 4.3 @xmath64 1.2 & -9.1 @xmath64 2.8 + 0 , 20 & -7.3 @xmath64 1.6 & 1.5 @xmath64 0.5 & 10.3 @xmath64 1.2 & 2.3 @xmath64 1.3 & y + & & & 6.7 @xmath64 1.2 & -8.7 @xmath64 1.7 + -10 , 20 & -7.1 @xmath64 1.0 & 2.1 @xmath64 0.4 & 10.1 @xmath64 1.2 & 2.5 @xmath64 1.3 & y + & @xmath65 -4.5 & & 7.7 @xmath64 1.2 & -8.8 @xmath64 1.6 + -20 , 20 & @xmath65 -5.7 & & @xmath65 4.5 & + & & & 3.6 @xmath64 1.1 & -8.9 @xmath64 3.2 + 30 , 30 & @xmath65 -6.9 & & @xmath65 3.9 & + & & & 3.7 @xmath64 1.0 & -9.4 @xmath64 3.0 + 20 , 30 & @xmath65 -9.0 & & @xmath65 3.0 & + & & & @xmath65 3.6 & + 10 , 30 & @xmath65 -9.9 & & @xmath65 4.5 & + & & & @xmath65 3.3 & + 0 , 30 & @xmath65 -3.9 & & 4.5 @xmath64 1.0 & -8.6 @xmath64 2.1 + & & & @xmath65 3.7 & + -10 , 30 & @xmath65 -7.2 & & @xmath65 3.9 & + & & & 5.4 @xmath64 1.0 & -8.7 @xmath64 1.9 + -20 , 30 & @xmath65 -5.7 & & @xmath65 3.3 & + & & & @xmath65 3.0 & + rrrrrc 50 -30 & & & 5.8 @xmath64 0.9 & 6.6 @xmath645.6 + 40 -30 & @xmath65 -6.0 & & 6.2 @xmath64 0.7 & 8.5 @xmath64 6.2 + & & & 6.3 @xmath64 0.5 & 0.2 @xmath64 6.0 + 30 -30 & @xmath65 -8.1 & & 7.1 @xmath64 0.9 & 9.0 @xmath64 6.0 + & & & @xmath65 3.3 & + 20 -30 & @xmath65 -5.4 & & 7.1 @xmath64 0.7 & 11.6 @xmath64 5.0 + & & & 9.1 @xmath64 0.7 & 5.4 @xmath64 3.4 + & & & @xmath65 1.5 & + 10 -30 & @xmath65 -5.1 & & 7.4 @xmath64 0.9 & 6.7 @xmath64 5.2 + 0 -30 & @xmath65 -3.6 & & 5.8 @xmath64 0.8 & 5.1 @xmath64 4.6 + -10 -30 & @xmath65 -5.7 & & 6.0 @xmath64 1.0 & 6.3 @xmath64 6.3 + -20 -30 & @xmath65 -5.4 & & @xmath65 2.3 & + & & & 9.5 @xmath64 0.5 & 4.8 @xmath64 2.2 + & & & @xmath65 2.3 & + -30 -30 & @xmath65 -5.1 & & 7.7 @xmath64 1.1 & 7.4 @xmath64 6.3 + -40 -30 & @xmath65 -6.9 & & @xmath65 2.9 & + -50 -30 & & & @xmath65 3.0 & + 50 -20 & & & @xmath65 2.4 & + & & & @xmath65 3.0 & + 40 -20 & @xmath65 -5.7 & & 6.0 @xmath64 0.8 & 7.0 @xmath64 6.3 + & & & 5.3 @xmath64 0.5 & -0.5 @xmath64 5.0 + 30 -20 & @xmath65 -5.7 & & 10.1 @xmath64 0.7 & 9.4 @xmath64 3.9 + & & & @xmath65 3.9 & + 20 -20 & @xmath65 -5.4 & & 8.6 @xmath64 0.7 & 11.2 @xmath64 4.0 + & & & 7.9 @xmath64 0.7 & 5.4 @xmath64 3.7 + & & & @xmath65 1.5 & + 10 -20 & @xmath65 -5.7 & & 12.1 @xmath64 1.0 & 9.1 @xmath64 4.2 + 0 -20 & @xmath65 -3.3 & & 10.2 @xmath64 1.0 & 6.7 @xmath64 3.7 + -10 -20 & @xmath65 -6.0 & & 5.9 @xmath64 0.9 & 5.6 @xmath64 5.2 + -20 -20 & @xmath65 -5.4 & & 9.8 @xmath64 1.0 & 6.7 @xmath64 4.0 + -30 -20 & @xmath65 -7.2 & & 10.3 @xmath64 0.8 & 7.1 @xmath64 3.1 + -40 -20 & @xmath65 -4.8 & & 7.2 @xmath64 1.0 & 9.8 @xmath64 6.0 + & & & @xmath65 3.2 & + -50 -20 & & & @xmath65 4.0 & + 50 -10 & & & 10.0 @xmath64 0.9 & 9.3 @xmath64 5.2 + 40 -10 & @xmath65 -5.4 & & @xmath65 3.3 & + 30 -10 & @xmath65 -5.7 & & 9.5 @xmath64 0.8 & 7.9 @xmath64 4.1 + 20 -10 & @xmath65 -5.1 & & 16.5 @xmath64 0.9 & 6.5 @xmath64 2.3 + 10 -10 & @xmath65 -7.8 & & 20.3 @xmath64 1.0 & 8.7 @xmath64 2.7 + 0 -10 & @xmath65 -3.0 & & 19.2 @xmath64 0.9 & 8.1 @xmath64 2.4 + -10 -10 & @xmath65 -6.6 & & 10.9 @xmath64 1.4 & 7.0 @xmath64 5.4 + -20 -10 & -10.7 @xmath64 2.9 & 6.7 @xmath64 6.7 & 16.9 @xmath64 1.0 & 7.7 @xmath64 2.8 & y + -30 -10 & @xmath65 -5.4 & & 10.5 @xmath64 0.7 & 8.4 @xmath64 3.8 + & & & @xmath65 3.3 & + -40 -10 & @xmath65 -6.9 & & 11.2 @xmath64 0.9 & 9.2 @xmath64 4.4 + & & & @xmath65 4.2 & + -50 -10 & & & 6.4 @xmath64 1.0 & 8.7 @xmath64 7.6 + 50 0 & & & 8.7 @xmath64 1.1 & 7.8 @xmath64 5.9 + 40 0 & @xmath65 -6.0 & & 6.1 @xmath64 0.8 & 6.6 @xmath64 5.1 + 30 0 & @xmath65 -5.4 & & 5.3 @xmath64 1.1 & 7.0 @xmath64 8.9 + 20 0 & @xmath65 -5.1 & & 9.9 @xmath64 1.2 & 6.8 @xmath64 4.8 + 10 0 & @xmath65 -6.6 & & 17.8 @xmath64 0.8 & 8.1 @xmath64 2.3 + 0 0 & -8.2 @xmath64 1.3 & 7.9 @xmath64 4.8 & 20.9 @xmath64 1.0 & 8.2 @xmath64 2.4 & y + -10 0 & -5.8 @xmath64 1.6 & 7.8 @xmath64 8.8 & 21.2 @xmath64 0.9 & 7.6 @xmath64 2.0 & y + -20 0 & -14.8 @xmath64 2.4 & 8.5 @xmath64 5.4 & 28.2 @xmath64 1.0 & 7.6 @xmath64 1.8 & y + -30 0 & @xmath65 -5.4 & & 9.1 @xmath64 0.7 & 1.2 @xmath64 3.1 + & & & 15.4 @xmath64 0.9 & 8.7 @xmath64 3.1 + -40 0 & @xmath65 -6.6 & & 9.1 @xmath64 0.6 & 1.2 @xmath64 1.7 + & & & 12.0 @xmath64 0.8 & 8.9 @xmath64 3.9 + -50 0 & & & @xmath65 4.5 & + & & & @xmath65 2.6 & + 50 10 & & & 5.4 @xmath64 1.1 & 6.2 @xmath64 7.6 + 40 10 & @xmath65 -6.9 & & @xmath65 3.6 & + 30 10 & @xmath65 -6.0 & & 7.7 @xmath64 1.1 & 5.5 @xmath64 4.8 + 20 10 & @xmath65 -4.8 & & 9.7 @xmath64 1.1 & 6.2 @xmath64 4.3 + 10 10 & -14.8 @xmath64 2.3 & 6.3 @xmath64 4.7 & 25.7 @xmath64 0.9 & 7.7 @xmath64 1.7 & y + 0 10 & -11.0 @xmath64 1.7 & 7.0 @xmath64 5.0 & 31.3 @xmath64 1.4 & 7.9 @xmath64 2.1 & y + -10 10 & -16.5 @xmath64 2.2 & 8.3 @xmath64 5.2 & 40.5 @xmath64 0.8 & 7.5 @xmath64 1.2 & y + -20 10 & -22.2 @xmath64 1.9 & 7.9 @xmath64 3.2 & 38.9 @xmath64 0.8 & 7.4 @xmath64 1.1 & y + -30 10 & @xmath65 -6.6 & & 18.2 @xmath64 0.6 & 8.5 @xmath64 2.0 + & & & 9.6 @xmath64 0.5 & 0.7 @xmath64 1.5 + -40 10 & @xmath65 -5.7 & & 14.1 @xmath64 0.6 & 7.8 @xmath64 2.5 + & & & 9.1 @xmath64 0.5 & 1.4 @xmath64 1.7 + -50 10 & & & 5.7 @xmath64 1.1 & 4.1 @xmath64 5.3 + 50 20 & & & 15.4 @xmath64 1.0 & 6.3 @xmath64 2.5 + 40 20 & @xmath65 -6.0 & & 9.9 @xmath64 1.0 & 6.1 @xmath64 3.4 + 30 20 & @xmath65 -5.1 & & 7.7 @xmath64 0.9 & 5.7 @xmath64 3.8 + 20 20 & @xmath65 -6.9 & & 7.0 @xmath64 0.9 & 7.0 @xmath64 5.4 + 10 20 & @xmath65 -6.6 & & 15.0 @xmath64 0.8 & 7.6 @xmath64 2.6 + 0 20 & -17.3 @xmath64 1.7 & 8.2 @xmath64 3.8 & 29.4 @xmath64 0.9 & 7.6 @xmath64 1.5 & y + -10 20 & -29.4 @xmath64 2.0 & 8.3 @xmath64 2.7 & 50.2 @xmath64 0.6 & 7.9 @xmath64 0.9 & y + -20 20 & -19.8 @xmath64 2.0 & 8.0 @xmath64 3.8 & 19.7 @xmath64 0.5 & 8.3 @xmath64 1.4 & y + -30 20 & @xmath65 -7.5 & & 17.7 @xmath64 0.7 & 8.7 @xmath64 2.0 + -40 20 & @xmath65 -6.9 & & 10.5 @xmath64 0.6 & 9.6 @xmath64 3.5 + & & & @xmath65 4.8 & + -50 20 & & & 5.2 @xmath64 0.9 & 4.2 @xmath64 4.9 + 50 30 & @xmath65 -11.4 & & 14.6 @xmath64 1.2 & 7.1 @xmath64 3.7 + 40 30 & @xmath65 -5.7 & & 17.6 @xmath64 1.3 & 6.2 @xmath64 2.3 + 30 30 & -9.3 @xmath64 1.8 & 7.2 @xmath64 6.4 & 11.4 @xmath64 1.0 & 6.7 @xmath64 3.5 & y + 20 30 & @xmath65 -4.2 & & 7.0 @xmath64 0.8 & 6.5 @xmath64 4.2 + 10 30 & @xmath65 -5.7 & & 24.6 @xmath64 1.1 & 8.0 @xmath64 2.3 + 0 30 & -10.5 @xmath64 1.3 & 6.4 @xmath64 6.3 & 22.9 @xmath64 0.9 & 8.1 @xmath64 1.9 & y + -10 30 & -9.6 @xmath64 2.2 & 4.7 @xmath64 5.4 & 30.5 @xmath64 0.7 & 7.2 @xmath64 1.1 & y + -20 30 & @xmath65 -5.4 & & 12.9 @xmath64 0.6 & 7.3 @xmath64 1.9 + -30 30 & @xmath65 -4.5 & & @xmath65 4.9 & + & & & 6.8 @xmath64 0.5 & 9.4 @xmath64 4.1 + -40 30 & @xmath65 -6.6 & & 6.9 @xmath64 0.5 & 2.8 @xmath64 4.8 + & & & 8.1 @xmath64 0.5 & 9.9 @xmath64 4.0 + -50 30 & & & 9.4 @xmath64 0.9 & 4.5 @xmath64 2.8 + 50 40 & @xmath65 -12.0 & & 18.9 @xmath64 0.8 & 6.7 @xmath64 1.9 + 40 40 & @xmath65 -6.3 & & 22.4 @xmath64 1.0 & 7.3 @xmath64 2.0 + 30 40 & @xmath65 -6.6 & & 13.5 @xmath64 0.9 & 6.7 @xmath64 2.8 + 20 40 & @xmath65 -6.6 & & 8.1 @xmath64 1.0 & 6.7 @xmath64 4.8 + 10 40 & @xmath65 -6.3 & & 28.4 @xmath64 1.0 & 7.6 @xmath64 1.7 + 0 40 & -12.8 @xmath64 1.4 & 7.2 @xmath64 3.6 & 22.9 @xmath64 1.0 & 7.8 @xmath64 2.0 & y + -10 40 & -11.0 @xmath64 2.2 & 7.4 @xmath64 5.7 & 22.3 @xmath64 0.8 & 6.9 @xmath64 1.7 & y + -20 40 & @xmath65 -7.5 & & 12.5 @xmath64 0.8 & 6.4 @xmath64 2.4 + -30 40 & @xmath65 -7.8 & & 15.5 @xmath64 0.8 & 5.7 @xmath64 1.7 + -40 40 & @xmath65 -6.0 & & 10.2 @xmath64 0.4 & 3.8 @xmath64 1.4 + & & & @xmath65 3.8 & + -50 40 & & & 21.8 @xmath64 1.0 & 4.0 @xmath64 1.4 + 50 50 & @xmath65 -8.4 & & 6.0 @xmath64 1.1 & 5.6 @xmath64 6.0 + 40 50 & @xmath65 -8.1 & & 14.7 @xmath64 1.2 & 6.0 @xmath64 2.8 + 30 50 & @xmath65 -6.6 & & 16.9 @xmath64 0.9 & 6.6 @xmath64 2.3 + 20 50 & @xmath65 -7.5 & & 12.9 @xmath64 1.1 & 7.2 @xmath64 3.8 + 10 50 & @xmath65 -7.8 & & 7.4 @xmath64 1.1 & 8.1 @xmath64 6.9 + 0 50 & @xmath65 -3.6 & & @xmath65 4.0 & + -10 50 & @xmath65 -6.0 & & @xmath65 4.5 & + -20 50 & @xmath65 -5.7 & & 11.1 @xmath64 0.8 & 5.4 @xmath64 2.4 + -30 50 & @xmath65 -6.6 & & 15.2 @xmath64 1.2 & 4.4 @xmath64 2.2 + -40 50 & -13.6 @xmath64 1.4 & 6.7 @xmath64 4.4 & 17.2 @xmath64 1.0 & 4.6 @xmath64 1.8 & y + -50 50 & -13.1 @xmath64 2.4 & 7.0 @xmath64 4.3 & 31.2 @xmath64 0.8 & 6.0 @xmath64 1.1 & y + 50 60 & & & 5.7 @xmath64 1.0 & 4.8 @xmath64 4.9 + 40 60 & @xmath65 -4.2 & & 8.3 @xmath64 1.2 & 4.4 @xmath64 3.8 + 30 60 & @xmath65 -5.7 & & 14.5 @xmath64 0.9 & 5.9 @xmath64 2.2 + 20 60 & -11.9 @xmath64 1.8 & 7.9 @xmath64 5.1 & 8.7 @xmath64 1.0 & 7.9 @xmath64 3.8 & y + & & & @xmath65 2.2 & + 10 60 & @xmath65 -6.9 & & @xmath65 1.5 & + & & & @xmath65 4.2 & + & & & @xmath65 2.5 & + 0 60 & @xmath65 -4.2 & & @xmath65 3.6 & + -10 60 & @xmath65 -5.4 & & @xmath65 4.5 & + -20 60 & @xmath65 -8.4 & & 7.3 @xmath64 0.9 & 4.3 @xmath64 3.2 + -30 60 & @xmath65 -6.0 & & 7.1 @xmath64 0.7 & 5.2 @xmath64 3.3 + -40 60 & @xmath65 -7.8 & & 11.7 @xmath64 1.0 & 5.0 @xmath64 2.6 + -50 60 & -23.2 @xmath64 2.7 & 5.8 @xmath64 3.3 & 37.6 @xmath64 0.9 & 6.2 @xmath64 1.0 & y + 50 70 & & & @xmath65 4.6 & + 40 70 & & & @xmath65 3.0 & + 30 70 & & & 8.3 @xmath64 1.1 & 7.2 @xmath64 5.7 + 20 70 & & & 7.5 @xmath64 0.9 & 9.8 @xmath64 5.0 + & & & @xmath65 2.4 & + 10 70 & & & @xmath65 5.1 & + 0 70 & @xmath65 -6.0 & & @xmath65 3.9 & + -10 70 & @xmath65 -7.8 & & @xmath65 4.6 & + -20 70 & @xmath65 -6.9 & & @xmath65 4.6 & + -30 70 & @xmath65 -7.5 & & @xmath65 2.6 & + & & & @xmath65 4.8 & + -40 70 & @xmath65 -6.6 & & 7.4 @xmath64 0.7 & 2.1 @xmath64 5.7 + & & & 7.1 @xmath64 0.7 & 8.9 @xmath64 5.8 + -50 70 & -18.5 @xmath64 2.7 & 4.6 @xmath64 3.5 & 34.7 @xmath64 0.9 & 4.6 @xmath64 1.0 & y + dummytext avedisova , v.s . , 2002 , , 79 , 216 blitz , l. , fich , m. , & stark , a.a . 1982 , , 49 , 183 carpenter , j.m . , snell , & r.l . , schloerb , f.p . 1995 , , 445 , 246 cohen , r.j . , matthews , n. , few , r.w . , & booth , r.s . 1983 , , 203 , 1123 combes , f. 1991 , , 29 , 195 dame , t.m . , ungerechts , h. , cohen , r.s . , de geus , e.j . , grenier , i.a . , may , j. , murphy , d.c . , nyman , l.a . , & thaddeus , p. 1987 , , 322 , 706 dame , t.m . , hartmann , d. , thaddeus , p. 2001 , , 547 , 792 evans , n.j . ii , , 201 , 112 evans , n.j . ii , zuckerman , b. , morris , g. , & sato , t. 1975 , , 196 , 433 few , r.w . 1979 , , 187 , 161 garrison , b.j . , lester , w.a . jr . , miller , w.h . , & green , s. 1975 , , 200 , l175 gordon , m.a . , & roberts , m.s . 1971 , , 170 , 277 gordon , m.a . , & hglund , b. 1973 , , 182 , 41 guilloteau s. , & forveille t. 1989 , _ grenoble image and line data analysis system ( gildas ) _ , iram , http://www.iram.fr/iramfr/gildas hartmann , d. , burton , w.b . 1997 , atlas of galactic neutral hydrogen helfer , t.t . , & blitz , l. 1997 , , 478 , 233 humphreys , r.m . 1978 , , 38 , 309 , 116 , 1899 moffat , a.f.j . , jackson , p.d . , & fitzgerald , m.p . 1979 , , 38 , 197 mundy , l.g . , evans , n.j . , snell , r.l . , & goldsmith , p.f . 1987 , , 318 , 392 palmer , p. , zuckerman , b. , buhl , d. , & snyder , l.e . 1969 , , 156 , l147 reich , p. , reich , w. , & furst , e. , 1997 , a&as 126 , 413 rodriguez , m.i . et . 2006 , in preparation snell , r.l . , huang , y .- l . , dickman , r.l . , & claussen , m.j . 1988 , , 325 , 853 snell , r.l . , dickman , r.l . , huang , y .- l . 1990 , , 352 , 139 townes , c.h . , & cheung , a.c . 1969 , , 157 , l103 wouterloot , j.g.a . , & brand , j. 1989 , , 80 , 149 young , k.e . , lee , j .- e . , evans , n.j . , goldsmith , p.f . , & doty , s.d . 2004 , , 614 , 252

we have detected hco cmb absorption at of the survey pointings . although these two tracers are expected to have similar excitation requirements on the microscopic level characteristic of warm , tk , dense , condensations in molecular clouds , the co(1 - 0 ) line is expected to be optically thick , whereas the hco line is not .

we have carried out a blind search in the general direction of the galactic anticenter for absorption of the cosmic microwave background ( cmb ) radiation near 4.83 ghz by molecular clouds containing gaseous ortho - formaldehyde ( hco ) . the observations were done using the 25-m radio telescope at onsala in sweden , and covered strips in galactic latitude at several longitudes in the region . spectra were obtained in these strips with a grid spacing corresponding to the telescope resolution of . we have detected hco cmb absorption at of the survey pointings . this detection rate is likely to increase with further improvements in sensitivity , and may become comparable to the detection rate expected from a blind co survey with a corresponding sensitivity limit . we have mapped some of these detections in more detail and compared the hco absorption to existing maps of co(1 - 0 ) emission in the same regions . there appears to be a rough correlation between the velocity - integrated line strength of the co(1 - 0 ) emission and that of the hco absorption . however , the scatter in this correlation is significantly larger than the measurement errors , indicating differences of detail at and below the linear resolution of our observations ( pc ) . although these two tracers are expected to have similar excitation requirements on the microscopic level characteristic of warm , tk , dense , condensations in molecular clouds , the co(1 - 0 ) line is expected to be optically thick , whereas the hco line is not . this latter difference is likely to be responsible for a significant part of the scatter in the correlation we have found .

astro-ph0601315

i

high galactic latitude molecular clouds ( hereafter hlcs ) are typically located at @xmath17b@xmath17 @xmath18 20@xmath430@xmath4 . since the gaussiun scale height of co is estimated to be @xmath3 100 pc in the inner galactic disk ( e.g. , magnani et al . 2000 ) , hlcs are likely located very close to the sun , within a few hundred pc or less . their proximity to the sun and the low possibility of overlapping with other objects along the line of sight enable us to study them with a high spatial resolution and to compare co data unambiguously with the data at other wavelengths . hlcs have lower molecular densities compared with dark clouds where the optical obscuration is significant . therefore , hlcs are often called as translucent clouds ( e.g. , van dishoeck & black 1988 ) and most of the known hlcs are not the sites of active star formation , although a few of them are known to be associated with t tauri stars ( e.g. , magnani et al . 1995 ; pound 1996 ; hearty et al . 1999 ) . given the very small distances of hlcs , it is a challenging task for observers to make a complete survey for hlcs over a significant portion of the whole sky . @xmath6co ( @xmath7 = 10 ) emission has been used to search for hlcs because the line emission in the mm band is strongest among the thermally or sub - thermally excited spectral lines of interstellar molecular species . it is however difficult to cover an area as large as tens of square degrees subtended by some of the hlcs because of the general weakness of the @xmath6co emission , typically @xmath3 a few k ( e.g. , magnani et al . 1996 ) , with existing mm - wave telescopes in a reasonable time scale . hlcs have been therefore searched for by employing various large - scale datasets at other wavelengths including the optical obscuration ( magnani et al . 1985 ; keto & myers 1986 ) , the infrared radiation ( reach et al . 1994 ) , and the far - infrared excess over hi ( = fir excess)(blitz et al . 1990 ; onishi et al . 2001 ) . on the other hand , unbiased surveys in co at high galactic latitudes have been performed at very coarse grid separations of 1@xmath4 resulting in a small sampling factor of a few % ( hartmann et al . 1998 ; magnani et al . most recently , onishi et al . ( 2001 ) discovered 32 hlcs or hlc complexes . this search was made based on the fir excess , demonstrating the correlation among fir excess clouds with co clouds is a useful indicator of co hlcs . previous co observations of individual hlcs at higher angular resolutions show that hlcs exhibit often loop - like or shell - like distributions having filamentary features with widths of several arc min or less ( hartmann et al . 1998 ; magnani et al . 2000 ; bhatt 2000 ) , and in addition that hlcs often compose a group , whose angular extent is @xmath3 10 degrees or larger . in order to better understand the structure of hlcs and to pursue the evolution of hlc complexes , co observations covering tens of square degrees at a high angular resolution are therefore crucial . the past observations of such complexes of hlcs are limited to a few regions including polaris flare ( heithausen & thaddeus 1990 ) , ursa major ( pound & goodman 1997 ) and the hlc complex toward mbm 53 , 54 , and 55 ( yamamoto et al . pound & goodman ( 1997 ) showed an arc - like structure of the molecular cloud system and suggested that the origin of such structures could be some explosive events . most recently , yamamoto et al . ( 2003 ) carried out extensive observations of the molecular cloud complex including mbm 53 , 54 , and 55 and suggest that the hlcs may be significantly affected by past explosive events based on the arc - like morphologies of molecular hydrogen ( see also gir et al . 1994 ) . the region of mbm 53 , 54 , and 55 is of particular interest among the three , because it is associated with a large hi cloud of @xmath3 590 @xmath10 at a latitude of @xmath535 degrees and because there is a newly discovered hlc of 330@xmath10 , hlcg92@xmath535 , which is significantly hi rich with a mass ratio @xmath15(h@xmath11)/@xmath15(hi ) of @xmath3 1 , among the known hlcs ( yamamoto et al . this cloud was in fact missed in the previous surveys based on optical extinction ( magnani et al . subsequent to these observations we became aware of that the region is also very rich in interstellar matter as shown by the 100@xmath19 m dust features ( kiss et al . there is a loop - like structure shown at 100 @xmath19 m around ( @xmath1 , @xmath2 ) @xmath3 ( 109@xmath4 , @xmath545@xmath4 ) . toward the center of the loop , an early type star hd886(b2iv ) is located and may play a role in creating the loop . its proper motion is large at a velocity of a few km s@xmath20 , suggesting that the stellar winds of the star might have continued to interact with the surrounding neutral matter over a few tens of pc in @xmath3 a few myr . magnani et al . ( 1985 ) and onishi et al . ( 2001 ) yet observed only a small part of this region . in order to reveal the large scale co distribution of the region , we have carried out observations toward ( @xmath1 , @xmath2 ) @xmath3 ( 109@xmath4 , @xmath545@xmath4 ) by @xmath6co ( @xmath7 = 10 ) and @xmath9co ( @xmath7 = 10 ) with nanten 4-meter millimeter / sub - mm telescope of nagoya university at las campanas , chile . we shall adopt the distance of 100 pc from the sun to the loop - like structure which is equal to the distance of the b2 star in the center of the loop , and is also a typical value for the hlcs .

we have carried out large scale co observations with a mm / sub - mm telescope nanten toward a far infrared loop - like structure whose angular extent is about 20 degrees around ( , ) ( 109 , ) in pegasus . its diameter corresponds to 25 pc at a distance of 100 pc , adopted from that of a star hd886 ( b2iv ) near the center of the loop . we covered the loop - like structure in theco ( = 10 ) emission at 4 grid spacing and in theco ( = 10 ) emission at 2 grid spacing for theco emitting regions .

we have carried out large scale co observations with a mm / sub - mm telescope nanten toward a far infrared loop - like structure whose angular extent is about 20 degrees around ( , ) ( 109 , ) in pegasus . its diameter corresponds to 25 pc at a distance of 100 pc , adopted from that of a star hd886 ( b2iv ) near the center of the loop . we covered the loop - like structure in theco ( = 10 ) emission at 4 grid spacing and in theco ( = 10 ) emission at 2 grid spacing for theco emitting regions . theco distribution is found to consist of 78 small clumpy clouds whose masses range from 0.04 to 11 , and 83% of theco clouds have very small masses less than 1.0 . co observations revealed that 18 of the 78co clouds show significantco emission . co emission was detected in the region where the column density of h derived fromco is greater than 5 , corresponding tov of 1 mag , which takes into account that of hi . we find no indication of star formation in these clouds in iras point source catalog and 2mass point source catalog . the very low mass clouds , 1 , identified are unusual in the sense that they have very weakco peak temperature of 0.5 k2.7 k and that they aggregate in a region of a few pc with no main massive clouds ; contrarily to this , similar low mass clouds less than 1 in other regions previously observed including those at high galactic latitude are all associated with more massive main clouds of 100 . a comparison with a theoretical work on molecular cloud formation ( koyama & inutsuka 2002 ) suggests that the very low - mass clouds may have been formed in the shocked layer through the thermal instability . the star hd886 ( b2iv ) may be the source of the mechanical luminosity via stellar winds to create shocks , forming the loop - like structure where the very low - mass clouds are embedded .

astro-ph0601315

r

figure 1 shows the distribution of the velocity - integrated intensity map of @xmath6co emission . we defined a @xmath6co cloud as a collection of more than two contiguous observed positions whose integrated intensity exceeds 0.77 k km s@xmath20 ( 5@xmath30 ) . based on the definition , we identified 78 molecular clouds in this region . molecular clouds are concentrated from ( @xmath1 , @xmath2 ) @xmath3 ( 107@xmath4 , @xmath537@xmath4 ) to ( 116@xmath4 , @xmath545@xmath4 ) and around ( @xmath1 , @xmath2 ) @xmath3 ( 114@xmath4 , @xmath552@xmath4 ) . most of the molecular clouds are very small , having size of @xmath31 1@xmath4 . figure 2 shows the distribution of the co superposed on the sfd 100 @xmath19 m ( schlegel et al . 1998 ) , which was derived from a composite of the cobe / dirbe and iras / issa maps , with the foreground zodiacal light and confirmed point sources removed . co clouds are distributed along the infrared loop whose diameter is @xmath3 25 pc . we detected little co emission within the loop - like structure , while toward some of the local peaks of sfd 100 @xmath19 m there is no co emission . figure 3 shows the peak radial velocity distribution derived from the present @xmath6co data set . the velocity in figure 3 is derived by a single gaussiun fitting from all co spectra . the velocity range of the molecular clouds is from @xmath518.3 km s@xmath20 to 0.3 km s@xmath20 and there is no systematic large scale velocity gradients . some of the molecular clouds have already been known by previous observations . molecular clouds toward ( @xmath1 , @xmath2 ) @xmath3 ( 110@xmath3218 , @xmath541@xmath3223 ) and ( 117@xmath3236 , @xmath552@xmath3228 ) are identified by magnani et al . ( 1985 ) and named as mbm 1 and mbm 2 , respectively . dir117@xmath544 and dir105@xmath538 identified by reach et al . ( 1998 ) are also identified in co toward ( @xmath1 , @xmath2 ) @xmath3 ( 116@xmath325 , @xmath544@xmath320 ) and ( 105@xmath320 , @xmath538@xmath320 ) by onishi et al . magnani et al . ( 1986 ) detected co emission at ( @xmath1 , @xmath2 ) @xmath3 ( 112@xmath4 , @xmath540@xmath4 ) . magnani et al . ( 2000 ) also covered this region even though they made observations on a locally cartesian grid with 1@xmath4(true angle ) spacing in longitude and latitude for a beam size of 8@xmath218 , they detected co emission at eight positions of ( @xmath1 , @xmath2 ) @xmath3 ( 103@xmath322 , @xmath538@xmath320 ) , ( 103@xmath322 , @xmath539@xmath320 ) , ( 104@xmath324 , @xmath539@xmath320 ) , ( 106@xmath328 , @xmath537@xmath320 ) , ( 108@xmath320 , @xmath552@xmath320 ) , ( 109@xmath325 , @xmath551@xmath320 ) , ( 110@xmath324 , @xmath541@xmath320 ) , and ( 111@xmath320 , @xmath550@xmath320 ) in the present region while they missed the present small molecular clouds whose sizes are less than several arc min in figure 1 due to the coarse grid spacing . seventy - eight @xmath6co molecular clouds are identified in the present region . for each molecular cloud , @xmath33 derived from single gaussian fitting was from 0.5 to 3.7 km s@xmath20 , and the radial velocity , @xmath34 , ranges from @xmath515.7 to @xmath50.1 km s@xmath20 . the maximum brightness temperature , @xmath23(@xmath6co ) ranges from 0.5 to 5.7 k. the radius of a cloud , @xmath35 , which is defined as the radius of an equivalent circle having the same area , i.e. , and @xmath35(pc)@xmath36 where a is the total cloud surface area within the 5@xmath30contour level , ranges from 0.07 to 0.79 pc . the peak column density of molecular hydrogen , @xmath37(h@xmath11 ) , in each cloud derived by assuming a conversion factor of 1.0@xmath010@xmath12 @xmath13/(k km s@xmath20 ) ( magnani et al . 2000 ) ranges from 8.0@xmath010@xmath38 to 1.7@xmath010@xmath39 @xmath13 with the present detection limit , 7.7@xmath010@xmath38 @xmath13 , corresponding to mass detection limit of 0.014 @xmath10 . we estimate the molecular mass , @xmath15(@xmath6co ) , by using the following formula @xmath40,\ ] ] where @xmath19 is the mean molecular weight , assumed to be 2.8 by taking into account a relative helium abundance of 25% in mass , @xmath41 is the mass of the atomic hydrogen , @xmath42 is the distance from the sun to the molecular clouds , and @xmath43 is the solid angle subtended by a unit grid spacing of ( 4@xmath8)@xmath0(4@xmath8@xmath0cos(@xmath2 ) ) . @xmath15(@xmath6co ) ranges from @xmath3 0.04 to @xmath3 11 @xmath10 and the total mass of molecular clouds is @xmath3 64 @xmath10 . these physical properties are listed in table 1 and the histograms of @xmath23(@xmath6co ) , @xmath33 , log(@xmath35 ) , and log(@xmath37(h@xmath11 ) ) of these clouds are shown in figure 4 . histograms in figure 4 are divided into three different categories , _ usual cloud _ ( hereafter uc ) whose mass is greater than 1 @xmath10 , _ small cloud _ ( hereafter sc ) whose mass is between 0.1 and 1 @xmath10 , and _ very small cloud _ ( hereafter vsc ) whose mass is less than 0.1 @xmath10 . it is remarkable that there are a number of molecular clouds having mass less than 1 @xmath10 and that the fractions of sc and vsc are 43/78 @xmath3 55% and 22/78 @xmath3 28% in the present region , respectively . in addition , the sizes of sc and vsc are equal to or less than 0.1 pc . we also note that the peak temperatures of sc and vsc are typically in a range from 0.5 k to 2.7 k , well below that of uc in the same region . figure 5 shows the distribution of the velocity - integrated intensity map of the @xmath9co emission superposed on the @xmath6co distribution . the total area of the @xmath9co observations is @xmath3 29 square degrees toward 38 of the 78 @xmath6co clouds . we observed all of 13 ucs , 24 of 43 scs , and 3 of 22 vscs . we detected @xmath9co emission at 11 of the 13 ucs , 8 of the 24 scs , and none of the 3 vscs , indicating a trend that the @xmath9co intensity increases with @xmath6co cloud mass . a @xmath9co cloud is defined in the same way as for a @xmath6co cloud except for the lowest integrated intensity level , 0.3 k km s@xmath20 ( 3@xmath30 ) . based on the definition , we identified 33 @xmath9co clouds . for the 33 @xmath9co molecular clouds , @xmath44@xmath45 derived from single gaussian fitting is @xmath3 1.5 km s@xmath20 and @xmath34 of them ranges from @xmath513.1 to @xmath51.9 km s@xmath20 . other physical properties , the maximum brightness temperature , @xmath23(@xmath9co ) , and @xmath35 range from 0.3 to 2.3 k and from 0.04 to 0.21 pc , respectively . the physical parameters including the molecular column density and mass ( hereafter @xmath46 ) are derived on the assumption of local thermodynamic equilibrium ( lte ) . to derive the column density of molecular hydrogen , the optical depth of @xmath9co is estimated by using the following equations , @xmath47,\ ] ] where @xmath48 is the excitation temperature of the @xmath7 = 10 transition of co in k and was derived from @xmath49\right\}}.\ ] ] @xmath48 was estimated to be 9.4 k from our @xmath6co data . the @xmath9co column density , @xmath37(@xmath9co ) , is estimated by @xmath50 } ( { \rm cm^{-2}}).\ ] ] the ratio of @xmath37(h@xmath11)/@xmath37(@xmath9co ) was assumed to be 7@xmath010@xmath51 ( dickman 1978 ) . the @xmath46 of a cloud from @xmath37(h@xmath11 ) is derived by the same way as @xmath6co ( see equation ( 1 ) ) . the column density and @xmath46 range from 2.3@xmath010@xmath12 to 1.7@xmath010@xmath39 @xmath13 and 0.03 to 1.41 @xmath10 , respectively , where the detection limit in the column density is 2.0@xmath010@xmath12 @xmath13 , coressponding to mass limit of 0.009 @xmath10 , smaller than that of @xmath6co because the observations of @xmath9co were made by higher grid sampling and lower rms noise fluctuations than those of @xmath6co , respectively . figure 6 shows the histograms of each physical property . the virial mass , @xmath52 , of a cloud was derived by using the following equation , assuming isothermal , spherical , and uniform density distribution with no external magnetic pressure : @xmath53 where @xmath35 and @xmath54 are the radius ( pc ) and line width ( km s@xmath20 ) of the composite profile obtained by averaging all the spectra within a cloud , respectively ( for details of the line width of composite profiles , see yonekura et al . 1997 ; kawamura et al . 1998 ) . from this equation , @xmath52 is estimated to be in a range from 4.7 to 197 @xmath10 . these physical properties are also listed in table 2 .

theco distribution is found to consist of 78 small clumpy clouds whose masses range from 0.04 to 11 , and 83% of theco clouds have very small masses less than 1.0 . co emission was detected in the region where the column density of h derived fromco is greater than 5 , corresponding tov of 1 mag , which takes into account that of hi . the very low mass clouds , 1 , identified are unusual in the sense that they have very weakco peak temperature of 0.5 k2.7 k and that they aggregate in a region of a few pc with no main massive clouds ; contrarily to this , similar low mass clouds less than 1 in other regions previously observed including those at high galactic latitude are all associated with more massive main clouds of 100 . a comparison with a theoretical work on molecular cloud formation ( koyama & inutsuka 2002 ) suggests that the very low - mass clouds may have been formed in the shocked layer through the thermal instability .

we have carried out large scale co observations with a mm / sub - mm telescope nanten toward a far infrared loop - like structure whose angular extent is about 20 degrees around ( , ) ( 109 , ) in pegasus . its diameter corresponds to 25 pc at a distance of 100 pc , adopted from that of a star hd886 ( b2iv ) near the center of the loop . we covered the loop - like structure in theco ( = 10 ) emission at 4 grid spacing and in theco ( = 10 ) emission at 2 grid spacing for theco emitting regions . theco distribution is found to consist of 78 small clumpy clouds whose masses range from 0.04 to 11 , and 83% of theco clouds have very small masses less than 1.0 . co observations revealed that 18 of the 78co clouds show significantco emission . co emission was detected in the region where the column density of h derived fromco is greater than 5 , corresponding tov of 1 mag , which takes into account that of hi . we find no indication of star formation in these clouds in iras point source catalog and 2mass point source catalog . the very low mass clouds , 1 , identified are unusual in the sense that they have very weakco peak temperature of 0.5 k2.7 k and that they aggregate in a region of a few pc with no main massive clouds ; contrarily to this , similar low mass clouds less than 1 in other regions previously observed including those at high galactic latitude are all associated with more massive main clouds of 100 . a comparison with a theoretical work on molecular cloud formation ( koyama & inutsuka 2002 ) suggests that the very low - mass clouds may have been formed in the shocked layer through the thermal instability . the star hd886 ( b2iv ) may be the source of the mechanical luminosity via stellar winds to create shocks , forming the loop - like structure where the very low - mass clouds are embedded .

astro-ph0601315

c

we have made a large - scale survey of high galactic latitude molecular clouds in the @xmath7 = 10 lines of @xmath6co and @xmath9co toward a large scale structure located around ( @xmath1 , @xmath2 ) @xmath3 ( 109@xmath4 , @xmath545@xmath4 ) with nanten . this survey spatially resolved the distribution of molecular gas associated with the large scale structure . the main conclusions of the present study are summarized as follows : 1 . the @xmath6co observation covered the entire large loop - like structure . the loop - like structure consits of very small clumpy clouds . the @xmath6co clouds are concentrated on the north to north - west of the loop - like structure and toward the south of that . we identified 78 @xmath6co clouds in the observed region . the total mass is estimated to be @xmath3 64 @xmath10 if we assume the conversion factor from co intensity to @xmath37(h@xmath88 ) as 1.0@xmath010@xmath12 @xmath13/(k km s@xmath20 ) . we performed @xmath9co observations in and around the whole area where the peak temperature of @xmath6co is more than 2.0 k. we identified 33 @xmath9co clouds and derived physical properties under the assumption of lte . the mass spectra are well fitted by a power law , @xmath55 @xmath56 @xmath57 for the @xmath6co clouds and @xmath55 @xmath56 @xmath58 for the @xmath9co clouds . these spectral indices are similar to those derived in the other regions . the size and the line width relation of @xmath9co clouds is fitted by a least - squares method , log(@xmath33 ) = ( 0.22@xmath590.43 ) @xmath0 log(@xmath35 ) + ( 0.37@xmath590.52 ) ( c.c.=0.23 ) , but the correlation is not good . present @xmath9co clouds are far from the virial equilibrium , indicating that @xmath9co clouds are not gravitationally bound . @xmath52 and @xmath46 relation can be fitted by a least - squares method as log(@xmath52 ) = ( 0.91@xmath590.30 ) @xmath0 log(@xmath46 ) + ( 2.23@xmath590.29 ) ( c.c.=0.66 ) . this index is slightly different from the indices in the other regions although the tendency that molecular clouds are more vilialized as the mass increases is consistent with the other regions . there is no sign of star formation from the comparison of iras point sources and point source catalog of two - micron all - sky survey in the present region . this suggests that molecular clouds in this region are not the site of present star formation or the remnants of past star formation . . there may be two expanding shells in the present region as inferred from hi although we can not identify them from co. the total mechanical luminosity of hd886 during the last few @xmath0 10@xmath79 yr is comparable to the expanding energy of the northern expanding hi shell . this indicates that some additional source of energy other than hd886 is needed to explain the expanding energy . @xmath9co emission is significantly detected in the @xmath6co clouds having molecular column density greater than 5@xmath010@xmath12 @xmath13 . this may be explained as that the @xmath9co emitting regions become significant when @xmath14v becomes larger than @xmath3 1 mag , marginally enough to shield the ultraviolet radiation to protect @xmath9co molecules . there is a possibility that very small clouds have been formed in the shoked layer through the thermal instability . the stellar wind of hd886 may be the source to creat shocks , forming the loop - like structure where the very small clouds are embedded . we greatly appreciate the hospitality of all staff members of the las campanas observatory of the carnegie institution of washington . the nanten telescope is operated based on a mutual agreement between nagoya university and the carnegie institution of washington . we also acknowledge that the operation of nanten can be realized by contributions from many japanese public donators and companies . three of the authors ( n.m . , t.o . , and y.f . ) acknowledge financial support from the scientist exchange program under bilateral agreement between jsps ( japan society for the promotion of science ) and conicyt ( the chilean national commission for scientific and technological research ) . this research has made use of the simbad astronomical database operated by cds , strasbourg , france . this publication makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation . this research has made use of the iras point sources from the nasa / ipac infrared science archive , which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . bhatt , h. c. 2000 , , 362 , 715 blitz , l. , bazell , d. , & desert , f. x. 1990 , , 352 , 13 bohlin , r. c. , savage , b. d. , & drake , j. f. 1978 , , 224 , 132 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d. p. , & davis , m. 1998 , , 500 , 525 snow , t. p. jr 1982 , , 253 , l39 van dishoeck , e. f. , & black , j. h. , 1988 , , 334 , 771 warin , s. , benayounm , j. j. , & viala , y. p. 1996 , , 308 , 535 yamamoto , h. , onishi , t. , mizuno , a. , & fukui , y. 2003 , , 592 , 217 yonekura , y. , dobashi , k. , mizuno , a. , ogawa , h. , & fukui , y. , 1997 , , 110 , 21 ccccccccc @1 & @95.52 & @xmath550.00 & 3.2 & 1.3 & @xmath510.7 & 0.31 & @4.7 & @1.07 + @2 & @96.11 & @xmath553.13 & 1.1 & 1.3 & @@xmath59.4 & 0.09 & @0.8 & @0.07 + @3 & 101.43 & @xmath541.53 & 1.5 & 1.5 & @@xmath59.5 & 0.17 & @1.9 & @0.27 + @4 & 101.91 & @xmath541.20 & 0.7 & 0.5 & @@xmath59.5 & 0.08 & @0.9 & @0.04 + @5 & 102.09 & @xmath541.20 & 1.9 & 1.4 & @@xmath58.9 & 0.10 & @3.4 & @0.12 + @6 & 102.19 & @xmath541.07 & 0.9 & 1.1 & @@xmath58.9 & 0.08 & @1.0 & @0.04 + @7 & 102.80 & @xmath540.27 & 2.5 & 1.6 & @@xmath58.4 & 0.16 & @4.5 & @0.30 + @8 & 103.32 & @xmath540.33 & 1.1 & 1.3 & @@xmath58.3 & 0.11 & @1.6 & @0.11 + @9 & 103.47 & @xmath540.60 & 1.0 & 1.2 & @@xmath57.3 & 0.08 & @1.0 & @0.04 + 10 & 103.74 & @xmath539.33 & 5.2 & 2.9 & @xmath510.1 & 0.59 & 12.3 & @7.02 + 11 & 104.20 & @xmath538.93 & 0.8 & 1.0 & @xmath515.7 & 0.10 & @2.0 & @0.09 + 12 & 104.48 & @xmath538.53 & 1.4 & 3.5 & @@xmath58.6 & 0.16 & @4.5 & @0.44 + 13 & 104.81 & @xmath538.80 & 1.4 & 1.2 & @@xmath55.0 & 0.10 & @1.5 & @0.08 + 14 & 105.07 & @xmath538.80 & 1.1 & 1.4 & @@xmath55.7 & 0.08 & @1.8 & @0.06 + 15 & 105.08 & @xmath552.27 & 1.0 & 1.2 & @@xmath50.1 & 0.07 & @1.2 & @0.04 + 16 & 105.10 & @xmath538.07 & 2.5 & 2.4 & @xmath512.7 & 0.26 & @5.7 & @1.19 + 17 & 105.22 & @xmath553.20 & 1.2 & 1.3 & @@xmath53.7 & 0.09 & @1.1 & @0.05 + 18 & 105.40 & @xmath548.13 & 1.6 & 1.8 & @@xmath59.0 & 0.12 & @3.0 & @0.20 + 19 & 105.77 & @xmath538.40 & 5.6 & 1.9 & @@xmath55.0 & 0.47 & 10.5 & @5.60 + 20 & 105.80 & @xmath539.60 & 1.7 & 1.8 & @@xmath59.8 & 0.24 & @3.1 & @0.70 + 21 & 105.82 & @xmath554.00 & 1.1 & 1.4 & @@xmath54.8 & 0.07 & @1.3 & @0.04 + 22 & 106.76 & @xmath536.53 & 2.7 & 3.0 & @@xmath59.8 & 0.53 & @8.3 & @4.29 + 23 & 106.97 & @xmath537.87 & 1.7 & 1.7 & @@xmath51.2 & 0.12 & @3.4 & @0.17 + 24 & 107.32 & @xmath537.60 & 1.2 & 1.5 & @@xmath52.3 & 0.12 & @1.6 & @0.11 + 25 & 107.38 & @xmath552.00 & 1.0 & 2.6 & @@xmath57.5 & 0.12 & @2.1 & @0.13 + 26 & 107.87 & @xmath553.93 & 0.8 & 1.6 & @@xmath54.9 & 0.11 & @1.8 & @0.11 + 27 & 108.21 & @xmath553.73 & 2.2 & 1.4 & @@xmath55.1 & 0.16 & @2.9 & @0.25 + 28 & 108.33 & @xmath553.13 & 2.2 & 1.2 & @@xmath50.2 & 0.07 & @3.5 & @0.08 + 29 & 108.78 & @xmath552.60 & 5.7 & 2.4 & @@xmath56.6 & 0.79 & 16.6 & 11.13 + 30 & 109.00 & @xmath552.13 & 3.3 & 1.9 & @@xmath51.5 & 0.31 & @5.1 & @1.43 + 31 & 109.00 & @xmath550.07 & 2.5 & 1.6 & @@xmath54.7 & 0.13 & @5.1 & @0.26 + 32 & 109.11 & @xmath550.60 & 0.9 & 2.2 & @@xmath55.9 & 0.09 & @1.6 & @0.06 + 33 & 109.17 & @xmath537.60 & 4.0 & 1.5 & @@xmath54.4 & 0.36 & @5.6 & @1.83 + 34 & 109.55 & @xmath552.87 & 1.3 & 2.0 & @@xmath57.1 & 0.14 & @2.5 & @0.16 + 35 & 109.68 & @xmath538.27 & 4.6 & 1.4 & @@xmath58.1 & 0.17 & @5.4 & @0.52 + 36 & 109.76 & @xmath538.00 & 2.7 & 2.0 & @@xmath54.9 & 0.21 & @4.7 & @0.63 + 37 & 109.78 & @xmath553.33 & 2.8 & 1.5 & @@xmath56.4 & 0.18 & @2.6 & @0.30 + 38 & 109.84 & @xmath550.73 & 4.0 & 2.6 & @@xmath57.8 & 0.18 & @5.0 & @0.40 + 39 & 109.85 & @xmath538.60 & 0.8 & 1.8 & @@xmath58.1 & 0.12 & @2.1 & @0.13 + 40 & 110.05 & @xmath550.40 & 2.1 & 3.1 & @@xmath57.4 & 0.10 & @3.6 & @0.14 + 41 & 110.06 & @xmath541.27 & 4.4 & 2.9 & @@xmath56.1 & 0.47 & 10.2 & @4.21 + 42 & 110.32 & @xmath548.93 & 2.9 & 0.9 & @@xmath54.2 & 0.12 & @2.6 & @0.17 + 43 & 110.94 & @xmath541.00 & 1.3 & 3.4 & @@xmath56.3 & 0.17 & @5.7 & @0.67 + 44 & 110.98 & @xmath539.13 & 1.2 & 2.2 & @@xmath59.6 & 0.12 & @2.9 & @0.20 + 45 & 111.08 & @xmath550.13 & 1.6 & 1.0 & @@xmath57.2 & 0.13 & @1.7 & @0.11 + 46 & 112.04 & @xmath539.87 & 3.4 & 2.3 & @@xmath55.4 & 0.26 & @6.4 & @1.11 + 47 & 112.40 & @xmath540.07 & 1.3 & 2.6 & @@xmath57.2 & 0.10 & @3.6 & @0.19 + 48 & 112.55 & @xmath539.60 & 1.2 & 1.9 & @@xmath53.6 & 0.16 & @3.0 & @0.29 + 49 & 112.64 & @xmath550.07 & 0.7 & 1.5 & @@xmath56.5 & 0.14 & @1.7 & @0.14 + 50 & 112.72 & @xmath541.13 & 1.2 & 1.9 & @@xmath56.2 & 0.11 & @2.4 & @0.13 + 51 & 112.72 & @xmath541.13 & 1.2 & 1.9 & @@xmath56.2 & 0.11 & @2.4 & @0.13 + 52 & 112.72 & @xmath539.67 & 1.2 & 2.6 & @@xmath55.3 & 0.10 & @1.9 & @0.09 + 53 & 112.84 & @xmath540.27 & 1.3 & 1.7 & @@xmath55.1 & 0.08 & @2.9 & @0.11 + 54 & 113.15 & @xmath539.47 & 1.5 & 1.2 & @@xmath54.7 & 0.16 & @2.5 & @0.23 + 55 & 113.23 & @xmath552.07 & 4.4 & 1.3 & @@xmath57.3 & 0.30 & @5.7 & @1.32 + 56 & 113.42 & @xmath542.33 & 3.4 & 2.4 & @xmath510.5 & 0.23 & @5.9 & @0.89 + 57 & 113.47 & @xmath539.20 & 0.5 & 1.9 & @@xmath55.7 & 0.10 & @1.4 & @0.08 + 58 & 113.56 & @xmath549.93 & 1.3 & 0.9 & @@xmath57.5 & 0.12 & @1.1 & @0.09 + 59 & 113.94 & @xmath551.67 & 1.4 & 1.6 & @@xmath59.7 & 0.07 & @3.2 & @0.07 + 60 & 114.38 & @xmath551.73 & 3.9 & 1.6 & @@xmath59.7 & 0.17 & @6.7 & @0.55 + 61 & 114.49 & @xmath550.80 & 1.5 & 1.8 & @@xmath57.8 & 0.09 & @3.2 & @0.12 + 62 & 114.52 & @xmath541.53 & 2.2 & 1.1 & @@xmath57.8 & 0.15 & @2.1 & @0.20 + 63 & 114.83 & @xmath551.07 & 0.8 & 1.8 & @@xmath58.1 & 0.10 & @1.4 & @0.07 + 64 & 114.90 & @xmath541.73 & 1.5 & 1.2 & @@xmath58.3 & 0.08 & @1.1 & @0.04 + 65 & 115.10 & @xmath543.80 & 1.6 & 1.0 & @@xmath52.1 & 0.11 & @1.5 & @0.09 + 66 & 115.16 & @xmath545.33 & 1.2 & 1.6 & @@xmath58.4 & 0.17 & @1.6 & @0.25 + 67 & 115.24 & @xmath543.40 & 1.8 & 2.0 & @@xmath53.5 & 0.23 & @2.7 & @0.57 + 68 & 115.63 & @xmath543.60 & 0.8 & 1.0 & @@xmath53.3 & 0.08 & @1.6 & @0.06 + 69 & 115.74 & @xmath546.20 & 1.5 & 1.0 & @@xmath56.8 & 0.13 & @2.3 & @0.18 + 70 & 116.20 & @xmath543.73 & 3.2 & 1.5 & @@xmath52.6 & 0.16 & @3.6 & @0.31 + 71 & 116.33 & @xmath544.80 & 4.2 & 2.3 & @@xmath53.9 & 0.59 & 10.0 & @7.13 + 72 & 116.45 & @xmath550.53 & 2.3 & 1.1 & @@xmath57.3 & 0.17 & @3.5 & @0.35 + 73 & 116.64 & @xmath552.33 & 0.9 & 1.5 & @@xmath57.6 & 0.07 & @2.1 & @0.05 + 74 & 116.86 & @xmath543.87 & 0.8 & 3.7 & @@xmath54.7 & 0.18 & @2.9 & @0.41 + 75 & 117.01 & @xmath550.73 & 2.7 & 0.8 & @@xmath57.5 & 0.10 & @2.0 & @0.10 + 76 & 117.11 & @xmath544.33 & 2.3 & 1.1 & @@xmath52.6 & 0.14 & @5.1 & @0.25 + 77 & 118.12 & @xmath552.13 & 1.1 & 1.1 & @@xmath56.7 & 0.12 & @1.8 & @0.12 + 78 & 118.23 & @xmath552.67 & 4.2 & 2.0 & @@xmath57.8 & 0.43 & @8.8 & @3.12 + ccccccccccc 16a & 105.11 & @xmath538.03 & 0.7 & 1.7 & @xmath511.4 & 0.06 & 0.11 & @4.0 & 0.08 & @34.6 + 16b & 105.12 & @xmath537.80 & 0.7 & 1.0 & @xmath513.1 & 0.07 & 0.12 & @3.6 & 0.09 & @13.5 + 19a & 105.54 & @xmath538.63 & 0.8 & 1.1 & @@xmath55.5 & 0.09 & 0.14 & @2.5 & 0.17 & @23.2 + 19b & 105.77 & @xmath538.37 & 2.3 & 1.7 & @@xmath54.0 & 0.21 & 0.46 & 16.6 & 1.41 & 129.8 + 20@ & 103.70 & @xmath539.33 & 1.2 & 1.5 & @@xmath59.7 & 0.13 & 0.22 & 10.0 & 0.56 & @57.9 + 22@ & 106.93 & @xmath536.40 & 0.7 & 2.1 & @@xmath59.4 & 0.05 & 0.13 & @3.7 & 0.06 & @45.2 + 26@ & 107.87 & @xmath553.93 & 0.3 & 1.8 & @@xmath57.7 & 0.07 & 0.13 & @2.3 & 0.09 & @46.4 + 27@ & 108.10 & @xmath553.77 & 0.8 & 3.1 & @@xmath56.2 & 0.09 & 0.13 & @3.7 & 0.21 & 176.1 + 29a & 107.82 & @xmath551.70 & 1.2 & 1.6 & @@xmath55.0 & 0.08 & 0.21 & @7.0 & 0.21 & @40.7 + 29b & 108.78 & @xmath552.63 & 1.4 & 2.0 & @@xmath54.6 & 0.14 & 0.26 & 11.1 & 0.87 & 120.6 + 29c & 108.84 & @xmath552.03 & 1.2 & 0.7 & @@xmath56.2 & 0.11 & 0.21 & @5.9 & 0.29 & @10.6 + 29d & 108.89 & @xmath552.17 & 1.3 & 1.1 & @@xmath56.9 & 0.08 & 0.23 & @3.8 & 0.13 & @18.4 + 29e & 109.00 & @xmath552.40 & 1.1 & 2.1 & @@xmath57.8 & 0.12 & 0.20 & @6.0 & 0.41 & 110.6 + 29f & 109.00 & @xmath552.13 & 0.9 & 1.6 & @@xmath51.9 & 0.04 & 0.15 & @5.8 & 0.05 & @22.5 + 29 g & 109.16 & @xmath551.87 & 1.0 & 1.7 & @@xmath55.8 & 0.10 & 0.17 & @2.3 & 0.25 & @57.6 + 29h & 109.53 & @xmath551.17 & 0.8 & 0.9 & @@xmath56.5 & 0.05 & 0.15 & @2.9 & 0.04 & @@8.7 + 29i & 109.64 & @xmath551.57 & 0.3 & 2.4 & @@xmath57.0 & 0.05 & 0.12 & @3.2 & 0.04 & @59.7 + 29j & 109.80 & @xmath551.37 & 0.4 & 1.5 & @@xmath56.7 & 0.05 & 0.14 & @2.5 & 0.04 & @22.3 + 33a & 109.17 & @xmath537.60 & 0.8 & 1.0 & @@xmath54.4 & 0.05 & 0.13 & @2.4 & 0.05 & @10.7 + 33b & 109.21 & @xmath537.80 & 0.9 & 0.9 & @@xmath54.1 & 0.06 & 0.16 & @4.7 & 0.08 & @10.6 + 33c & 109.34 & @xmath537.80 & 0.7 & 0.7 & @@xmath54.5 & 0.05 & 0.13 & @3.2 & 0.05 & @@4.7 + 35@ & 109.72 & @xmath538.27 & 0.9 & 0.7 & @@xmath58.1 & 0.05 & 0.16 & @3.2 & 0.05 & @@5.1 + 38@ & 109.90 & @xmath550.73 & 1.1 & 1.8 & @@xmath57.7 & 0.11 & 0.19 & 10.5 & 0.48 & @75.3 + 41a & 110.11 & @xmath541.27 & 1.0 & 2.9 & @@xmath55.6 & 0.11 & 0.23 & 10.1 & 0.41 & 197.4 + 41b & 110.19 & @xmath541.07 & 0.6 & 2.0 & @@xmath57.6 & 0.04 & 0.10 & @2.3 & 0.03 & @33.1 + 43@ & 111.12 & @xmath541.00 & 0.7 & 1.1 & @@xmath55.6 & 0.04 & 0.12 & @4.3 & 0.03 & @@9.4 + 46@ & 112.08 & @xmath539.87 & 0.8 & 0.9 & @@xmath55.1 & 0.06 & 0.14 & @3.7 & 0.07 & @@9.3 + 55@ & 113.17 & @xmath552.03 & 1.2 & 0.7 & @@xmath57.2 & 0.11 & 0.22 & @4.3 & 0.24 & @10.6 + 56@ & 113.17 & @xmath542.60 & 0.8 & 0.9 & @xmath510.9 & 0.04 & 0.14 & @3.7 & 0.04 & @@6.5 + 60@ & 114.32 & @xmath551.70 & 0.8 & 1.2 & @@xmath59.7 & 0.08 & 0.15 & @4.8 & 0.19 & @24.9 + 71a & 115.49 & @xmath544.40 & 0.9 & 1.0 & @@xmath53.5 & 0.10 & 0.16 & @3.7 & 0.20 & @22.2 + 71b & 116.21 & @xmath544.97 & 1.2 & 1.6 & @@xmath53.9 & 0.18 & 0.22 & @9.1 & 1.04 & @93.9 + 78@ & 118.19 & @xmath552.70 & 1.5 & 1.2 & @@xmath58.1 & 0.12 & 0.28 & @9.6 & 0.53 & @36.7 + note col . ( 1 ) : cloud number of @xmath9co taken from that of @xmath6co cloud with which the @xmath9co cloud is associated . if plural @xmath9co clouds are associated with one @xmath6co cloud , a sequential alphabet is added , col . ( 2)(3 ) : cloud peak ( @xmath1 , @xmath2 ) position in degree , col . ( 4 ) : peak temperature in k , col . ( 5 ) : line width of the composite spectrum in km s@xmath20 , col . ( 6 ) : peak velocity of the composite spectrum in km s@xmath20 , col . ( 7 ) : radius of the molecular cloud in pc , col . ( 8) : optical depth of @xmath9co , col . ( 9 ) : column density of peak position in 10@xmath12 @xmath13 , col . ( 10 ) : mass of the molecular cloud assuming the lte in @xmath10 , col . ( 11 ) : virial mass of the molecular cloud in @xmath10 . ( 4 ) to ( 6 ) are derived by using a single gaussiun fitting .

we find no indication of star formation in these clouds in iras point source catalog and 2mass point source catalog . the star hd886 ( b2iv ) may be the source of the mechanical luminosity via stellar winds to create shocks , forming the loop - like structure where the very low - mass clouds are embedded .

we have carried out large scale co observations with a mm / sub - mm telescope nanten toward a far infrared loop - like structure whose angular extent is about 20 degrees around ( , ) ( 109 , ) in pegasus . its diameter corresponds to 25 pc at a distance of 100 pc , adopted from that of a star hd886 ( b2iv ) near the center of the loop . we covered the loop - like structure in theco ( = 10 ) emission at 4 grid spacing and in theco ( = 10 ) emission at 2 grid spacing for theco emitting regions . theco distribution is found to consist of 78 small clumpy clouds whose masses range from 0.04 to 11 , and 83% of theco clouds have very small masses less than 1.0 . co observations revealed that 18 of the 78co clouds show significantco emission . co emission was detected in the region where the column density of h derived fromco is greater than 5 , corresponding tov of 1 mag , which takes into account that of hi . we find no indication of star formation in these clouds in iras point source catalog and 2mass point source catalog . the very low mass clouds , 1 , identified are unusual in the sense that they have very weakco peak temperature of 0.5 k2.7 k and that they aggregate in a region of a few pc with no main massive clouds ; contrarily to this , similar low mass clouds less than 1 in other regions previously observed including those at high galactic latitude are all associated with more massive main clouds of 100 . a comparison with a theoretical work on molecular cloud formation ( koyama & inutsuka 2002 ) suggests that the very low - mass clouds may have been formed in the shocked layer through the thermal instability . the star hd886 ( b2iv ) may be the source of the mechanical luminosity via stellar winds to create shocks , forming the loop - like structure where the very low - mass clouds are embedded .

0912.1646

i

type ia supernovae ( sneia ) are currently the best cosmological tool to investigate the dark energy driving the accelerated expansion of the universe @xcite . though generally accepted as thermonuclear explosions of carbon - oxygen white dwarfs which have accreted sufficient mass from their companion , two competitive models exist for the companion scenario : the single - degenerate ( main sequence or red giant companion ) and double - degenerate ( another white dwarf ) . since the time delay between star formation and sneia explosion is scenario - dependent , rates in hosts of varying star formation rate ( sfr ) help constrain this . in fact , snia rates are known to be correlated with host morphology , b - k color , and by inference also with star formation @xcite . as such , a galaxy s snia rate is commonly expressed as the sum of a `` delayed '' component from old stellar populations and a `` prompt '' component from young stellar populations . these components are parametrized as `` a '' and `` b '' , proportional to a galaxy s mass and sfr respectively @xcite . this `` a+b '' two - component model can be matched with progenitor populations that have distributions of delay times as described by mannucci et al . ( 2006 ) , and pritchet et al . ( 2008 ) . the c99 catalog matched with very large array ( vla ) 1.4ghz radio data revealed the specific snia rate may be enhanced by 27 times in radio - loud ( @xmath3 ) over radio - quiet ( @xmath4 ) early - type galaxies ( della valle et al . 2005 , hereafter dv05 ) . although winds from active galactic nuclei ( agn ) could increase accretion rates of the interstellar medium ( ism ) onto white dwarfs , a process thought to trigger classical nova eruptions @xcite , dv05 reject this explanation for the enhanced specific snia rate in radio - loud galaxies . they find galaxy interactions are most likely to cause the radio emission and supply the necessary snia progenitors via stellar capture during dwarf accretion or star formation induced by major mergers @xcite . the existence of bright infrared counterparts for radio galaxies has been well documented and often attributed to dust obscured star formation coeval with the agn @xcite . by matching a hypothetical galaxy interaction and agn activity timeline with a recurring star formation model of ten @xmath5 year long episodes each separated by @xmath6 years , mannucci et al . ( 2006 ) find the enhanced specific snia rate in radio - loud early - type galaxies is best fit by a bimodal delay - time distribution ( dtd ) in which the `` prompt '' ( b ) delay time is constrained to just @xmath7 years . they suggest this implies two physical populations of snia progenitors , but note a broad single - population dtd could not be ruled out . as this controversial implication relies on a rate enhancement found with 21 photometrically identified sneia from dv05 , we look to confirm this in the large database of spectroscopically typed sneia from the canada - france hawaii telescope ( cfht ) supernova legacy survey ( snls ) . we use photometric redshift galaxy catalogs @xcite and 1.4 ghz radio catalogs to calculate the snia rate in radio - loud early - type galaxies , and also infrared source catalogs to look for obscured star formation in the radio - loud snia host galaxies . dust extinction in starbursts hinders sn detection : only one snia has been detected , and the snia rate remains unconstrained in starburst galaxies @xcite . we use the infrared catalogs to calculate the snia rate in bright and luminous infrared galaxies , which are known to experience bursts of star formation up to @xmath8 . we also statistically compare the snia rates in radio and infrared galaxies to predictions of the two - component `` a+b '' model , and perform an identical analysis with the low redshift c99 catalog . in [ s2obs ] we describe the snls and c99 snia databases and galaxy catalogs , the overlapping radio and infrared source catalogs , and present the radio and infrared properties of snls and c99 snia early - type host galaxies . we derive the snia rate in radio and infrared galaxies in [ srates ] , compare to expectations of the two - component `` a+b '' model in [ sabp ] , and reanalyze with relaxed data constraints in [ srelax ] . in [ ssnprop ] we juxtapose the properties of the sneia in radio and infrared host galaxies with known correlations between snia properties and stellar populations . finally , in [ sdisc ] we discuss the implications of our results regarding current snia science and future surveys , and conclude in [ sconc ] .

we have combined the large snia database of the canada - france - hawaii telescope supernova legacy survey and catalogs of galaxies with photometric redshifts , vla 1.4 ghz radio sources , and spitzer infrared sources . we also show the properties of sneia in radio and infrared galaxies suggest the hosts contain dust and support a continuum of delay time distributions for sneia , although other delay time distributions can not be ruled out based on our data .

we have combined the large snia database of the canada - france - hawaii telescope supernova legacy survey and catalogs of galaxies with photometric redshifts , vla 1.4 ghz radio sources , and spitzer infrared sources . we present eight sneia in early - type host galaxies which have counterparts in the radio and infrared source catalogs . we find the snia rate in subsets of radio and infrared early - type galaxies is times the rate in all early - type galaxies , and that any enhancement is always . rates in these subsets are consistent with predictions of the two component `` a+b '' snia rate model . since infrared properties of radio snia hosts indicate dust obscured star formation , we incorporate infrared star formation rates into the `` a+b '' model . we also show the properties of sneia in radio and infrared galaxies suggest the hosts contain dust and support a continuum of delay time distributions for sneia , although other delay time distributions can not be ruled out based on our data .

astro-ph9909514

i

the properties of galaxy clusters play an important role in constraining cosmological parameters and models of large - scale structure formation . because clusters are the most massive collapsed aggregates in the universe , the cluster mass function and its evolution with redshift constrains the spectrum of density fluctuations ( e.g. eke , cole & frenk 1996 , bahcall & cen 1992 ) . accurate cluster masses can also constrain the ratio of baryonic to total mass , and thus @xmath4 ( white et al . 1993 ) . there are several standard ways of computing cluster masses . optical redshift surveys yield a mass estimate through the application of the virial theorem , on the assumption that the galaxies trace the overall cluster mass distribution ; this method was first applied to coma by zwicky ( 1933 ) . more sophisticated variants of this method include a surface term to account for the unsampled portion of the cluster ( the & white 1986 ) , and use the jeans equation to account for the effects of orbital anisotropy ( e.g. binney & tremaine 1987 ) . for clusters with many hundreds of redshifts , the distribution of infalling galaxies in redshift space measures the gravitational potential of the dark matter halo ( diaferio & geller 1997 ) ; this method has only been successfully applied to coma so far ( geller , diaferio & kurtz 1999 ) . observations of hot intracluster gas in the x - ray provide information about the gravitational potential ; the added assumption of hydrostatic equilibrium yields a mass ( bahcall & sarazin 1977 ) . gravitational lensing of background galaxies can also be used to estimate cluster masses ( webster 1985 , bartelmann et al . 1996 and references therein ) . comparing cluster masses derived by these independent methods can provide insight into the internal structure of clusters ( loeb & mao 1994 ) and provides a consistency check on the mass derived by any one method . while the distribution of total cluster masses constrains global cosmological parameters , knowledge of the density ( or equivalently , mass ) profiles of individual clusters constrains models of cluster formation . @xmath5-body simulations of hierarchical clustering by navarro , frenk & white ( 1995,1996,1997 , hereafter nfw ) suggest that a universal two - parameter density model can adequately describe clusters over a broad range of masses . until recently , few clusters had enough measured redshifts to constrain the mass profile ; the advent of multi - fiber spectrographs has now made it possible to measure several hundred redshifts in a cluster within a reasonable time . our goal is to measure the mass profile of the cluster awm 7 , selected by albert et al . ( 1977 ) on the basis of the cd galaxy at its center . our sample consists of 179 cluster galaxies with measured redshifts ; this work expands the sample of koranyi et al . ( 1998 ) by 70% , extending the surveyed region to a projected radius of 1.7 @xmath1 mpc , and reaching fainter magnitudes in the core . we confirm the cold core seen in koranyi et al . ( 1998 ) , and fit a nfw mass profile from the projected distribution of radii for comparison with the virial mass profile ; we consider also the effect of orbital anisotropies ( still assuming the nfw profile ) on the mass estimates . the two profiles agree remarkably well within our restricted context ; the assumption of the nfw model produces self - consistent mass estimates using these two methods . relaxing the assumption that the galaxies trace an underlying nfw dark matter distribution would result in a larger range of admissible masses ( cf . the & white 1986 ) . in 2 and 3 , we describe the observations and data reduction . in 4 we describe the data , and in 5 we justify the choice of the nfw model , compute the resultant mass profiles , and comment on the reliability of the surface term correction . we defer discussion of some details until 6 , and conclude in 7 . we use @xmath6 km s@xmath7 mpc@xmath7 throughout .

we have measured 492 redshifts ( 311 new ) in the direction of the poor cluster awm 7 and have identified 179 cluster members ( 73 new ) . we use two independent methods to derive a self - consistent mass profile , under the assumptions that the absorption - line galaxies are virialized and that they trace an underlying navarro , frenk & white ( 1997 ) dark matter profile : ( 1 ) we fit such an nfw profile to the radial distribution of galaxy positions and to the velocity dispersion profile ; ( 2 ) we apply the virial mass estimator to the cluster . with these assumptions ,

we have measured 492 redshifts ( 311 new ) in the direction of the poor cluster awm 7 and have identified 179 cluster members ( 73 new ) . we use two independent methods to derive a self - consistent mass profile , under the assumptions that the absorption - line galaxies are virialized and that they trace an underlying navarro , frenk & white ( 1997 ) dark matter profile : ( 1 ) we fit such an nfw profile to the radial distribution of galaxy positions and to the velocity dispersion profile ; ( 2 ) we apply the virial mass estimator to the cluster . with these assumptions , the two independent mass estimates agree to% within 1.7 mpc , the radial extent of our data ; we find an enclosed massm . the largest potential source of systematic error is the inclusion of young emission - line galaxies in the mass estimate . we investigate the behavior of the surface term correction to the virial mass estimator under several assumptions about the velocity anisotropy profile , still within the context of the nfw model , and remark on the sensitivity of derived mass profiles to outliers . we find that one must have data out to a large radius in order to determine the mass robustly , and that the surface term correction is unreliable at small radii .

cond-mat9510150

i

the properties of strongly correlated electrons confined to a ladder ( or double chain ) and described by @xmath0-@xmath1 or hubbard models have been the subject of intensive investigation recently . the reason lies in the unusual spin liquid nature of the undoped parent system . another reason for especial interest is weakly coupled ladders compounds like @xmath7 and @xmath8.@xcite recent measurements of the magnetic susceptibility and the nuclear spin relaxation rate in these materials show the existence of a finite spin gap . the key question in the current study is the evolution of the finite gap in the spin excitation spectrum upon doping . the spin gap remains in other spin liquids systems and is a sign of strong superconducting fluctuations.@xcite a recent analysis of the @xmath0-@xmath1 ladder using a mean - field theory with gutzwiller renormalization of the matrix elements to account for the strong correlations , gave a continuous evolution of the spin gap with doping.@xcite the short range resonance valence bond ( rvb ) state evolves into a superconductor with modified @xmath4-wave symmetry within this mean - field approximation . a tendency towards modified @xmath4-wave superconductivity was also found in a bosonization approach@xcite and in a recent numerical study of the hubbard ladder.@xcite we have investigated @xmath0-@xmath1 ladders up to a size of @xmath9 sites using a lanczos diagonalization method . first results have been published in ref . . here we report in more detail our results for larger lattices including a detailed investigation of the excitation spectrum , a discussion of phase separation and the calculation of the superconducting order parameter and of the form factor of the cooper pairs . we find clear evidence of hole pairing and a modified @xmath4-wave rvb state in lightly doped systems in agreement with the mean - field theory . an interesting difference however is the discontinuous evolution of the excitation spectrum upon doping . quasiparticle " excitations appear carrying both charge and spin . these excitations are in addition to a band of magnons which evolve continuously away from the undoped spin liquid . this separation of the excitation spectrum into bound holon - spinon quasiparticles and collective magnon excitation contrasts with the full spin - charge separation found in a luttinger liquid . the @xmath0-@xmath1 ladder hamiltonian is @xmath10 where @xmath11 runs over @xmath12 rungs , and @xmath13 @xmath14 and @xmath15 @xmath16 are spin and leg indices . the @xmath0-@xmath1 ladder is sketched in fig . [ fig : geometry ] . the first two terms are the kinetic energies and the @xmath1 @xmath17 are exchange couplings along the ladder ( rungs ) . unless noted otherwise we set @xmath18 . the projection operator @xmath19 prohibits double occupancy of a site . periodic or antiperiodic boundary conditions ( pbc , apbc ) are used along the ladder . the wave vector @xmath20 is consequently well defined , @xmath21 and @xmath22 being the momenta along the ladder and rungs . the transverse momentum @xmath22 takes only the values @xmath23 and @xmath24 , corresponding to bonding and antibonding states . at half filling the @xmath0-@xmath1 ladder is equivalent to the heisenberg ladder , which was investigated in earlier publications . the ground state of the heisenberg ladder is a short range rvb state with a spin gap of @xmath25 at isotropic coupling , @xmath26 . the strong coupling limit @xmath27 is a good starting point to describe the system as there a simple description of the spectrum is available.@xcite in that limit , each eigenfunction of the total system can be written as a direct product of one - rung states , which are either spin singlets or one of the triplets , and the ground state is that with all singlets . the first excited multiplet consists of the states with one triplet rung . a small but finite value of @xmath1 lifts the degeneracy of these states . the one - magnon excitations then form a three - fold spin degenerate band with dispersion @xmath28 up to second order in @xmath1 . it has a minimum gap @xmath29 at @xmath30.@xcite the momentum perpendicular to the chains is @xmath31 . the higher excited states form a continuum of excited states and its minimum is at @xmath32 with energies slightly larger than twice the gap @xmath33 . with increasing @xmath1 the collective excitation branch crosses into the continuum , but the qualitative description is still valid . in this paper we study the effects of doping holes into such a ladder . although the isotropic case , @xmath34 , is of most interest , we also study the limit @xmath35 , which can be easily understood . in this limit the problem reduces to a system of weakly coupled rungs . the properties can be continuously followed down to the isotropic point @xmath36 . this paper is organized as follows . in sec . [ sec : ferro ] we briefly discuss the occurrence of ferromagnetism in the ladder doped with one or two holes at @xmath2 and discuss the relationship with the occurrence of ferromagnetism in two dimensions . next in sec . [ sec : pair ] we discuss the pairing of holes doped into the ladder and the occurrence of phase separation . to understand the excitation spectra we start from the single hole case in sec . [ sec : onehole ] and go on to the two - hole case in sec . [ sec : twohole ] . section [ sec : paircorr ] discusses long range correlations , in particular the interesting question of the symmetry of the pairs and the mapping to a luther - emery liquid . the single - particle excitations are discussed in sec . [ sec : chargexc ] . over all we find a remarkable similarity between the ladder and 2d clusters .

we have numerically investigated the doped- ladder using exact diagonalization . there is a simple picture of the excitation spectrum that can be continued to explain the behavior at isotropic coupling . at the ladder is phase separated into holes and a heisenberg ladder . at intermediate coupling the ground state shows hole pairing with a modified-wave symmetry . the latter evolves continuously into the magnon band of the spin liquid . at low doping the quasiparticles form a dilute fermi gas with a strong attraction but simultaneously the fermi wave vector , as would be measured in photoemission , is large .

we have numerically investigated the doped- ladder using exact diagonalization . we have studied both the limit of strong inter - chain coupling and isotropic coupling . the ladder scales to the luther - emery liquid regime in the strong inter - chain coupling limit . in this strong coupling limit there is a simple picture of the excitation spectrum that can be continued to explain the behavior at isotropic coupling . at we have indications of a ferromagnetic ground state . at a large the ladder is phase separated into holes and a heisenberg ladder . at intermediate coupling the ground state shows hole pairing with a modified-wave symmetry . the excitation spectrum separates into a limited number of quasiparticles which carry charge and spin and a triplet magnon mode . at half - filling the former vanish but the latter evolves continuously into the magnon band of the spin liquid . at low doping the quasiparticles form a dilute fermi gas with a strong attraction but simultaneously the fermi wave vector , as would be measured in photoemission , is large . the dynamical structure factors are calculated and are found to be very similar to calculations on 2d clusters .

0908.0638

r

irac has proved to be a very sensitive instrument , revealing previously unseen structures in the outer shells of expanded pne @xcite . since the nebulae in our sample are typically very compact and ir - bright , which is normal for their evolutionary status , their core emission dominates the inner few arcsec near the central source . this unfortunately usually prevents us from detecting any weak extended emission near the core , but , by psf subtraction , does not prevent us from measuring the fluxes of our sources . given the size of the psf , an upper limit of @xmath105@xmath13 to the sizes of the nebulae can be estimated ( marengo , private communication ) . in table [ tab : iracflux ] we list the photometric results obtained . for a comparison of our results to previous observations in the literature ( i.e. , @xcite ) , we show in figure [ fig : irac_distr ] four color - color diagrams based on irac data . as already shown in @xcite , pne do not seem to follow any specific track on the irac @xmath14-[4.5]$ ] versus @xmath15-[8.0]$ ] diagram . we find our targets to be generally located in an area ranging from 0 to 3 in @xmath15-[8.0]$ ] and from 0 to 1 in @xmath14-[4.5]$ ] . this region is included in the area where pne are found in the two works mentioned above . a comparison of the @xmath14-[4.5]$ ] versus @xmath16-[8.0]$ ] diagram to the analogous one in @xcite shows that the stars in our sample have on average lower values of @xmath14-[4.5]$ ] , which may be explained if pah emission features are present ( see [ spectra ] ) ; the spread in @xmath16-[8.0]$ ] indicates that different dust temperatures can be found in these objects , with the radio - detected ones ( i.e. , hotter central stars ) being redder in @xmath16-[8.0]$ ] . lccccc 01005 + 7910 & 175.6 @xmath17 9.1 & 189.2 @xmath17 9.8 & 460.0 @xmath17 24.0 & 2004.1 @xmath17 104.4 & 18.1 @xmath17 0.9 + 06556 + 1623 & 759.2 @xmath17 39.5 & 898.5 @xmath17 46.8 & 1045.5 @xmath17 54.5 & 1210.0 @xmath17 63.0 & 2.8@xmath17 0.2 + 09470 - 4617 & 70.2 @xmath17 3.7 & 89.9 @xmath17 4.7 & 191.7 @xmath17 10.0 & 1233.3 @xmath17 64.3 & 3.5 @xmath17 0.2 + 17074 - 1845 & 17.6 @xmath17 0.9 & 12.0 @xmath17 0.6 & 10.5 @xmath17 0.5 & 47.5 @xmath17 2.5 & 10.7 @xmath17 0.6 + 17203 - 1534 & 18.7 @xmath17 1.0 & 12.8 @xmath17 0.7 & 11.5 @xmath17 0.6 & 24.7 @xmath17 1.3 & 8.9 @xmath17 0.5 + 17364 - 1238 & 10.8 @xmath17 0.6 & 8.2 @xmath17 0.4 & 7.7 @xmath17 0.4 & 9.9 @xmath17 0.5 & 1.1 @xmath17 0.1 + 17381 - 1616 & 4.3 @xmath17 0.2 & 3.6 @xmath17 0.2 & 2.9 @xmath17 0.1 & 33.1 @xmath17 1.7 & 4.4 @xmath17 0.3 + 17423 - 1755 & 3425.6 @xmath17 178.4 & 4492.5 @xmath17 233.8 & 5227.3 @xmath17 272.5 & 5344.2 @xmath17 278.5 & 24.2 @xmath17 1.2 + 17542 - 0603 & 936.3 @xmath17 48.8 & 1057.1 @xmath17 55.0 & 1045.5 @xmath17 54.5 & 1105.7 @xmath17 57.6 & 5.3 @xmath17 0.3 + 18040 - 1457 & 312.1 @xmath17 16.3 & 211.4 @xmath17 11.0 & 209.1 @xmath17 10.9 & 142.5 @xmath17 7.4 & 0.11@xmath170.11 + 18062 + 2410 & 7.4 @xmath17 0.4 & 9.0 @xmath17 0.5 & 13.5 @xmath17 0.7 & 557.7 @xmath17 29.1 & 16.3 @xmath17 0.9 + 18070 - 2346 & 187.3 @xmath17 9.8 & 119.8 @xmath17 6.2 & 82.1 @xmath17 4.3 & 55.8 @xmath17 2.9 & 1.0 @xmath17 0.1 + 18367 - 1233 & 6532.6 @xmath17 340.3 & 5990.0 @xmath17 311.8 & 5750.0 @xmath17 299.8 & 7125.6 @xmath17 371.3 & + 18371 - 3159 & 7.0 @xmath17 0.4 & 6.0 @xmath17 0.3 & 7.7 @xmath17 0.4 & 22.1 @xmath17 1.2 & 5.9 @xmath17 0.3 + 18379 - 1707 & 41.3 @xmath17 2.2 & 38.2 @xmath17 2.0 & 82.1 @xmath17 4.3 & 320.7 @xmath17 16.7 & 29.9 @xmath17 1.0 + 18442 - 1144 & 16.5 @xmath17 0.9 & 18.0 @xmath17 0.9 & 71.9 @xmath17 3.7 & 320.7 @xmath17 16.7 & 12.1 @xmath17 0.6 + 19200 + 3457 & 18.7 @xmath17 1.0 & 13.8 @xmath17 0.7 & 38.3 @xmath17 2.0 & 142.5 @xmath17 7.4 & 1.6 @xmath17 0.1 + 19306 + 1407 & 40.1 @xmath17 2.1 & 30.0 @xmath17 1.6 & 88.5 @xmath17 4.6 & 583.0 @xmath17 30.4 & 47.5@xmath17 2.9 + 19336 - 0400 & 9.4 @xmath17 0.5 & 9.0 @xmath17 0.5 & 10.5 @xmath17 0.5 & 53.4 @xmath17 2.8 & 6.7 @xmath17 0.4 + 19399 + 2312 & 280.9 @xmath17 14.6 & 179.7 @xmath17 9.4 & 164.3 @xmath17 8.6 & 142.5 @xmath17 7.4 & 0.12@xmath170.11 + 19590 - 1249 & 14.0 @xmath17 0.7 & 11.2 @xmath17 0.6 & 11.5 @xmath17 0.6 & 25.7 @xmath17 1.3 & 7.9 @xmath17 0.4 + 20462 + 3416 & 24.4 @xmath17 1.3 & 16.3 @xmath17 0.9 & 17.7 @xmath17 0.9 & 27.9 @xmath17 1.5 & 11.1 @xmath17 0.6 + 20572 + 4919 & 936.3 @xmath17 48.8 & 898.5 @xmath17 46.8 & 884.6 @xmath17 46.1 & 1733.2 @xmath17 90.3 & 8.5 @xmath17 0.4 + 21289 + 5815 & 61.1 @xmath17 3.2 & 64.2 @xmath17 3.3 & 92.0 @xmath17 4.8 & 246.7 @xmath17 12.9 & 1.1 @xmath17 0.1 + 22023 + 5249 & 18.7 @xmath17 1.0 & 16.3 @xmath17 0.9 & 37.7 @xmath17 2.0 & 229.0 @xmath17 11.9 & 19.0 @xmath17 1.1 + 22495 + 5134 & 10.4 @xmath17 0.5 & 9.5 @xmath17 0.5 & 12.1 @xmath17 0.6 & 80.2 @xmath17 4.2 & 9.7 @xmath17 0.5 + we also plotted our targets on a h - k versus k-@xmath14 $ ] diagram , which can be compared to the jhk diagram in figure [ fig:2mass_distr ] . a similar trend can be found in both plots . as shown in @xcite , the jhk diagram allows us to distinguish different types of sources . many of our targets are concentrated in the _ hot star _ and _ nebula @xmath18 star _ regions , as expected for their b spectral type classification . other targets fall within regions of objects with a hot star and strong dust emission . the presence of a large amount of dust around the central stars is also evident in the @xmath14-[8.0]$ ] versus @xmath19-[24]$ ] diagram . since we do not have mips observations of our targets but we have 538 @xmath1 m irs spectra , we calculated the expected 24 @xmath1 m mips measurement by convolving our irs spectra with the mips spectral response function and then integrating over the bandpass . performing this calculation on literature targets with both irs and mips data has produced results compatible , within errors , with the observations , therefore we are confident that our expected mips values are reasonable approximations to the actual values . interestingly , among the radio detected objects in this diagram we can distinguish a group of stars clustered around ( 4,2 ) , namely iras 06556 + 1623 and 17423 - 1755 , while the others seem to be found in a stripe roughly going from ( 5,6 ) to ( 9,1 ) . after noticing these possible different distributions , we checked the positions of the central targets in the other diagrams , thus finding that although the overall distributions of our targets match those observed in @xcite , iras 06556 + 1623 and 17423 - 1755 seem not to follow the trend of the other radio detected objects . in @xmath14-[4.5]$ ] versus @xmath15-[8.0]$ ] and @xmath14-[4.5]$ ] versus @xmath16-[8.0]$ ] , these stars are found respectively around ( 0.7,0.7 ) and ( 1.3,0.7 ) , while in h - k versus k-@xmath14 $ ] they are the two top - right radio detected objects ( highest h - k and k-@xmath14 $ ] ) . , the sources are represented as squares if detected at radio wavelengths , as diamonds if not . radio detected targets tend to concentrate in what has been identified as the _ hot star _ region in @xcite.,width=302 ] the reduced irs spectra of the objects in our sample are shown in figures [ fig : spectra_crich][fig : spectra_mixed2 ] . they are split into three groups : c - rich , o - rich , and mixed chemistry . pne are usually classified as c - rich or o - rich . this classification is linked to the evolution of the central star , because it depends on the possibility for the star to go through a third dredge - up . it is this event that alters the chemistry in the envelope turning it from o - rich into c - rich during the agb phase @xcite . because of the stability of the co molecule , if c is less abundant than o , all c is trapped in co and then the envelope shows features of molecules containing oxygen ( besides co ) and vice versa if o is less abundant than c. it is known however that a minority of stars shows mixed chemistry , with c - bearing and o - bearing molecules . more than @xmath2 of the stars in our sample show both polycyclic aromatic hydrocarbons ( pah ) and silicate features , while a smaller percentage ( @xmath1010% ) is expected . among these mixed - chemistry objects about 70% are radio detected . we distinguished o - rich and c - rich envelopes on the presence of amorphous silicate ( 10-@xmath1 m bump ) or pah features ( mainly 6.2 and 7.7 @xmath1 m ) . objects with both a 10-@xmath1 m silicate feature and pah transitions were classified as mixed chemistry . it must be noticed that the sl and ll irs modules overlap around 1415 @xmath1 m , therefore this region of the spectra is subject to higher noise . shifts between the flux levels are also possible . in a few cases , we have scaled the sl spectra to the ll flux level . all the targets classified as c - rich show 6.2 , 7.7 , 8.5 , and 11.2 @xmath1 m features , commonly attributed to pah . the shape and strength of the features depend on the excitation status and size of the molecules . we address the properties of these features in the next section . we do not detect the so - called 21 @xmath1 m feature in any of our targets . this feature has in fact been found in 15 post - agb stars with f - g spectral types and in two pne @xcite . therefore , besides being a rare feature , the chances for its detection are even lower in b stars as those in our sample , because of the harder radiation field from the central star . the sources iras 01005 + 7910 and 19200 + 3457 show a strong broad feature around 30 @xmath1 m that has been previously observed in other post - agb stars and pne and is attributed to mgs . the peak position and width of this feature change as the temperature of the underlying continuum changes , corresponding to the evolution from post - agb to pn . the peak is found in the 2635 @xmath1 m range @xcite . it is likely that such emission is present in iras 18442 - 1144 around 34 @xmath1 m , although weaker and with a smaller width . this target and iras 06556 + 1623 show an excess of emission peaking around 17.7 @xmath1 m ( figure [ fig:17micron_crich ] ) that can be explained as due to vibrationally excited c - h bonds @xcite . this emission is also detected in 01005 + 7910 and 19200 + 3457 as a very broad feature . iras 06556 + 1623 also shows a weak broad emission underlying the 6.2 , 7.7 and 11.2 @xmath1 m features , which is due to pah molecules as well . in o - rich targets , as we can see in figures [ fig : spectra_orich1 ] and [ fig : spectra_orich2 ] , the 10 @xmath1 m broad feature from amorphous silicates is clearly seen , although it often appears to be structured . in iras 17074 - 1845 , 17203 - 1534 , and 20572 + 4919 we clearly distinguish the presence of single features contributing to the overall bump . the shift in shape from the smooth ism - like feature ( clearly peaked at 9.8 @xmath1 m ) to the structured plateau - like feature of the material in the solar system ( peaked at 11.3 @xmath1 m ) has been explained as due to grain processing , i.e. coagulation of small ( @xmath100.1 @xmath1 m ) grains into large ( 12 @xmath1 m ) grains and annealing of amorphous silicates into crystalline magnesium silicates and silica @xcite . a correlation of the shape and strength of the 10-@xmath1 m silicate emission feature has been observed in herbig aebe and t tauri stars and it has been interpreted as evidence of grain processing in the circumstellar disks of those stars @xcite . the shape of the feature can be estimated by comparing the continuum - subtracted flux ratio at 11.3 and 9.8 @xmath1 m to the peak - to - continuum ratio . we have performed this comparison for our o - rich targets . mixed - chemistry sources were not included because of the pah 11.2 @xmath1 m feature , which would affect the flux estimates . iras 18435 - 0052 was not included either , because it shows the 9.8 @xmath1 m feature in absorption , which would clearly make it an outlier . the plot obtained is shown in figure [ fig : silicate_plot ] . the data points are sparse in the diagram : though a similar trend as in young stars might be present , we can not conclude that this is the case . the absence of linear correlation may be explained as due to non - linear effects in highly processed dust ( 11.3/9.8 flux ratio @xmath20 ) , as pointed out by @xcite . our results match with those found by @xcite , who inspected disks around post - agb stars . the similarity of the results leads us to the conclusion that in spite of the absence of correlation , the dust in our targets shows a high degree of processing , which points to the presence of a stable structure where the grains can have time to grow and anneal . this is a hint for the presence of circumstellar / circumbinary disks in our sources . m ) as a function of the 10-@xmath1 m silicate emission feature strength ( peak flux over continuum flux).,width=302 ] as noticed above , iras 18435 - 0052 is the only target in which the silicate bump shows an absorption feature on top of the emission . since silicates are seen in absorption early after the agb , the presence of both absorption and emission features may be interpreted as an earlier evolutionary stage for this source . although this target has been classified as a bii star @xcite , its irs spectrum indicates major differences to the rest of the sample . almost all of these targets also show an emission feature around 18 @xmath1 m that can be attributed to amorphous silicates . in figure [ fig:17micron_orich ] we show two examples of this feature . in such targets as 17381 - 1616 , 17460 - 3114 , 19157 - 0247 , 18371 - 3159 , 19336 - 0400 , 19590 - 1249 , 20462 + 3416 , and 22495 + 5134 crystalline silicate features around 23.7 , 27.6 and 33.6 @xmath1 m are visible . the presence of crystalline silicates in post - agb stars has been previously reported although different hypotheses exist about the production mechanism of these crystals @xcite . in figures [ fig : spectra_mixed1 ] and [ fig : spectra_mixed2 ] the spectra of those sources with both silicate and pah features are shown . the 10 @xmath1 m silicate bump is typically much stronger than the 6.2 and 7.7 @xmath1 m pah features . the 11.2 @xmath1 m feature is blended with the silicate emission and detected on top of it . six of these stars also show the [ ] 12.8 @xmath1 m line , which proves their ionized status . four of them also have the [ ] 7 @xmath1 m emission line . the presence of pah features in post - agb envelopes is well - known , although it is not yet clear how these molecules are produced @xcite . as a first step in the analysis of these features , we have classified our targets according to the scheme developed in @xcite , with the exception of iras 06556 + 1623 and 17542 - 0603 because of their s / n ratio in the 511 @xmath1 m range . almost all of our sources have their peak of the 6.2 @xmath1 m emission feature beyond 6.235 @xmath1 m , which puts them in class _ b_. if we also consider the 7.7 @xmath1 m and 8.5 @xmath1 m features , the stars in our sample show a more complicated picture . while the three _ a _ class sources are also classified as _ a@xmath21 _ and _ a@xmath22 _ , class _ b _ sources spread into a group of intermediate subclasses . tables [ tab : pah_summary1 ] and [ tab : pah_summary2 ] report the classification for every target . the wavelengths calculated do not correspond to the peaks of the features , but to their central ( median - flux ) wavelengths , which better accounts for the different components within each complex . the 7.7 @xmath1 m features have been classified as a@xmath21 or b@xmath21 if their central wavelength was respectively smaller or larger than 7.7 @xmath1 m , since the complex appears to be mainly due to two features peaking around 7.6 and 7.8 @xmath1 m . lccccc 01005 + 7910 & 6.231 @xmath17 0.005 & 7.58 @xmath17 0.08 & 8.59 @xmath17 0.03 & 11.21 @xmath17 0.07 & aa@xmath21a@xmath22 + 09470 - 4617 & 6.227 @xmath17 0.005 & 7.66 @xmath17 0.03 & 8.60 @xmath17 0.06 & 11.29 @xmath17 0.01 & aa@xmath21a@xmath22 + 18442 - 1144 & 6.238 @xmath17 0.001 & 7.64 @xmath17 0.01 & 8.60 @xmath17 0.07 & 11.205 @xmath17 0.004 & ba@xmath21a@xmath22 + 19200 + 3457 & 6.24 @xmath17 0.04 & 7.61 @xmath17 0.07 & 8.58 @xmath17 0.02 & 11.250 @xmath17 0.006 & ba@xmath21a@xmath22 + 18371 - 3159 & 6.28 @xmath17 0.01 & 7.68 @xmath17 0.09 & 8.61 @xmath17 0.09 & 11.2 @xmath17 0.1 & ba@xmath21a@xmath22 + 18379 - 1707 & 6.266 @xmath17 0.004 & 7.62 @xmath17 0.04 & 8.57 @xmath17 0.06 & 11.03 @xmath17 0.06 & ba@xmath21a@xmath22 + 19306 + 1407 & 6.240 @xmath17 0.003 & 7.74 @xmath17 0.04 & 8.6 @xmath17 0.1 & 11.30 @xmath17 0.07 & bb@xmath21b@xmath22 + 19336 - 0400 & 6.25 @xmath17 0.01 & 7.61 @xmath17 0.02 & 8.70 @xmath17 0.02 & 11.30 @xmath17 0.03 & ba@xmath21b@xmath22 + 19590 - 1249 & 6.22 @xmath17 0.06 & 7.58 @xmath17 0.02 & 8.62 @xmath17 0.03 & 11.21 @xmath17 0.03 & aa@xmath21a@xmath22 + 20462 + 3416 & 6.25 @xmath17 0.01 & 7.66 @xmath17 0.06 & 8.58 @xmath17 0.04 & 11.26 @xmath17 0.03 & ba@xmath21a@xmath22 + 21289 + 5815 & 6.251 @xmath17 0.001 & 7.74 @xmath17 0.03 & 8.64 @xmath17 0.08 & 11.25 @xmath17 0.07 & bb@xmath21b@xmath22 + 22023 + 5249 & 6.23 @xmath17 0.01 & 7.69 @xmath17 0.03 & 8.55 @xmath17 0.09 & 11.23 @xmath17 0.07 & ba@xmath21a@xmath22 + 22495 + 5134 & 6.25 @xmath17 0.01 & 7.58 @xmath17 0.02 & 8.5 @xmath17 0.1 & 11.45 @xmath17 0.05 & ba@xmath21a@xmath22 + lcccc 01005 + 7910 & 24 @xmath17 1 & 38 @xmath17 2 & 9 @xmath17 1 & 29 @xmath17 3 + 09470 - 4617 & 11.5 @xmath17 0.6 & 19 @xmath17 1 & 2.6 @xmath17 0.5 & 14 @xmath17 1 + 18442 - 1144 & 4.34 @xmath17 0.05 & 8.2 @xmath17 0.3 & 2.2 @xmath17 0.2 & 2.41 @xmath17 0.04 + 19200 + 3457 & 1.77 @xmath17 0.05 & 3.3 @xmath17 0.1 & 0.64 @xmath17 0.06 & 1.10 @xmath17 0.03 + 18371 - 3159 & 0.12 @xmath17 0.02 & 0.25 @xmath17 0.05 & 0.04 @xmath17 0.01 & 0.13 @xmath17 0.05 + 18379 - 1707 & 4.0 @xmath17 0.2 & 5.6 @xmath17 0.4 & 0.5 @xmath17 0.1 & 1.1 @xmath17 0.3 + 19306 + 1407 & 3.98 @xmath17 0.03 & 8.6 @xmath17 0.4 & 0.2 @xmath17 0.1 & 4.9 @xmath17 0.8 + 19336 - 0400 & 0.17 @xmath17 0.03 & 0.74 @xmath17 0.05 & 0.06 @xmath17 0.01 & 0.33 @xmath17 0.04 + 19590 - 1249 & 0.17 @xmath17 0.05 & 0.37 @xmath17 0.05 & 0.03 @xmath17 0.01 & 0.18 @xmath17 0.06 + 20462 + 3416 & 0.49 @xmath17 0.02 & 1.5 @xmath17 0.1 & 0.14 @xmath17 0.03 & 0.28 @xmath17 0.07 + 21289 + 5815 & 1.20 @xmath17 0.02 & 2.2 @xmath17 0.2 & 0.18 @xmath17 0.05 & 0.35 @xmath17 0.07 + 22023 + 5249 & 2.4 @xmath17 0.1 & 4.7 @xmath17 0.2 & 0.6 @xmath17 0.1 & 1.0 @xmath17 0.2 + 22495 + 5134 & 0.31 @xmath17 0.04 & 0.52 @xmath17 0.04 & 0.13 @xmath17 0.03 & 0.6 @xmath17 0.06 + @xcite propose that objects in class _ b _ contain fresh pah molecules , since the post - agb stars and pne they observed fall in this class . class _ a _ objects , which include pdrs and reflection nebulae ( ism - like pahs ) , are sources with more processed pahs . in the attempt to characterize the pah population in our targets , we have followed @xcite in their inspection of pah features in herbig aebe stars . we fit a spline to the continuum in the 514 @xmath1 m region of the spectra , including in the spline the 10 @xmath1 m bump from amorphous silicates , when present . the continuum - subtracted spectra are shown in figure [ fig : pah_spectra ] . we notice that despite the spline subtraction , which should remove the 10 @xmath1 m silicate feature , residual emission in the 911 @xmath1 m range remains . as noted above , these features may be due to hot crystalline silicates . after calculating the central wavelengths as in their study , we compare our results to @xcite , who found a correlation between the effective temperature of the central star and the central wavelength of both the 11.2 and the 7.7 @xmath1 m features . although the astrophysical targets are quite different ( young and post - agb stars ) , the properties of the pahs can be compared to determine how these molecules behave in different environments . in figure [ fig:7_11 ] , we show the correlation between the central wavelengths of the features at 6.2 , 7.7 , and 11.2 @xmath1 m . a trend with increasing temperature from red to blue wavelengths is clear . with the exception of two outliers ( 22495 + 5134 in the top and 18379 - 1707 in the bottom of the 7.7 vs 11.2 @xmath1 m plot ) , our data follow the trend in @xcite , being located at the high - temperature limit , as expected for stars with an ionized envelope ( t@xmath23 20000 k ) . although the plots show a clear correlation , the position occupied by the hot pn ngc 7027 ( t@xmath24 k ) - shown as a dark green dot just as an example of hot pn - points out that other factors play an important role . this complicated dependence is evident when inspecting the pah ionization fraction . since the intensity of the features in the 69 @xmath1 m range relative to that of the 11.2 @xmath1 m one is an order of magnitude higher for ionized than for neutral pahs @xcite , in figure [ fig : ion_frac ] we plot i@xmath25i@xmath26 vs i@xmath27i@xmath26 ratios . while @xcite could not conclude that a correlation was present in this diagram , the inclusion of our sample allows us to find a remarkable correlation , but no clear link between the ionization fraction and t@xmath28 . our sample of post - agb stars contains hotter stars than the haebe stars in @xcite ( figure [ fig:7_11 ] and the presence of radio continuum ) but it has a somewhat lower fraction of ionized pahs . this trend for a decrease of ionization fraction in the post - agb has been reported in @xcite for 3 objects . we find this as a general trend within our sample . since the ionization fraction does not seem to correlate with the temperature of the central star , we tried to link it to the local physical conditions experienced by the pahs , by plotting the i@xmath25i@xmath26 ratio versus the ionization factor g@xmath29n@xmath30t@xmath31 , where g@xmath29 is the radiation field in habing units , n@xmath30 the electron density in @xmath32 , and t the gas temperature in 10@xmath33 k. we have calculated this parameter by applying the empirical formula in @xcite that links it to i@xmath27i@xmath26 in its lorentzian formulation , since it extends to lower values of i@xmath27i@xmath26 . in figure [ fig : ion_frac ] , we show the result for @xmath34g@xmath29n@xmath30t@xmath35 ( limits of reliability of the formula ) . although the data are spread in the plot , a weak correlation can be identified , indicating that the ionization fraction increases with the ionization factor . once again , no clear correlation with t@xmath28 is observed , indicating that the local conditions in the envelope play a major role . the results of our analysis of the pah features are somewhat conflicting . on one side we see that the central wavelengths of the features are shifted toward the blue , as expected in photo - processed molecules ; on the other side , we find a low ionization fraction , which implies low processing . we conclude that a higher effective temperature implies a harder field and stronger processing in terms of shift of the central wavelength toward the blue , but not necessarily a higher ionization fraction , this being dependent on the available amount of ionizing photons , thefore on the distance to the central star . our plots indicate that the pah molecules in our stars are located in the outflows , where they are subject to a more diluted field . although the probability of interaction between photons and molecules far from the star is smaller , the hard photons from the central star - when interacting - determine a major damage to the molecules , resulting in the shift in central wavelength . in this scenario , the closer molecules must have been previously destroyed by the radiation field . since pah features with red central wavelengths are found in post - agb stars ( rafgl 2688 is one of the two class _ c _ objects in @xcite ) , this disruption should occur during the few 10@xmath33 yr between the early post - agb and the development of an ionized shell . high - angular resolution observations in the pah emission ranges are necessary to support such an interpretation , which confirms the idea of c - bearing molecules being located in the outflows of mixed - chemistry nebulae . finally , it must be noticed that the wavelength shifts observed can be determined not only by photo - processing : nitrogenation can in fact be another explanation @xcite . as shown in @xcite , the mass that goes into pahs can be linked to the ratio of the flux emitted in the pah features to the continuum flux in the far infrared range ( fir ) , nominally between 40 and 500 @xmath1 m . we have therefore taken advantage of our sed models ( see [ seds ] ) to calculate the fir flux by integrating our curves in the mentioned interval . the fraction of carbon trapped in pahs can be estimated as @xcite @xmath36 where @xmath37 is the average uv absorption cross section of pahs per c atom and @xmath38 is the pah to continuum flux ratio . we assume @xmath39 @xmath40 as a typical value for @xmath37 @xcite . the fraction of c in pahs can then be estimated as : @xmath41 table [ tab : abundances ] lists the results of the calculation , along with the estimates of the number abundance of pah molecules to h nuclei , assuming that the average pah molecule has 50 c atoms . the errors in the table have been calculated by standard error propagation , including a 15% uncertainty in the model estimation of the underlying continuum . lcccc _ c - rich _ + 01005 + 7910 & 6 & 2 & 51 & 19 + 09470 - 4617 & 43 & 37 & 336 & 293 + 18442 - 1144 & 1.0 & 0.3 & 8 & 2 + 19200 + 3457 & 2.7 & 0.9 & 21 & 7 + _ mixed _ + 18371 - 3159 & 0.07 & 0.02 & 0.55 & 0.18 + 18379 - 1707 & 1.1 & 0.4 & 8.7 & 2.8 + 19306 + 1407 & 0.48 & 0.15 & 3.7 & 1.1 + 19336 - 0400 & 0.12 & 0.04 & 0.9 & 0.3 + 19590 - 1249 & 0.10 & 0.03 & 0.7 & 0.2 + 20462 + 3416 & 0.12 & 0.03 & 0.9 & 0.3 + 21289 + 5815 & 5.2 & 1.9 & 41 & 15 + 22023 + 5249 & 0.5 & 0.1 & 3.8 & 1.2 + 22495 + 5134 & 0.12 & 0.04 & 1.0 & 0.3 + the results show a trend for larger values of @xmath42 and pah abundance in c - rich stars . in these sources , the values of c fraction range from 1% to 43% ( 3% is a typical value in the ism ) , while those of the pah abundance are between 7@xmath43 and 336@xmath43 . with the remarkable exception of iras 21289 + 5815 , stars with both pah and silicate features show lower values : 0.11% for @xmath42 and 0.58@xmath43 for the pah abundance . we notice here that since in our modeling we lack observations in the sub - mm and mm ranges , our estimation of the fir flux and the values derived from it should be taken with caution .

we have observed a small sample of hot post - agb stars with the infrared array camera ( irac ) and the infrared spectrograph ( irs ) on - board the spitzer space telescope . we obtained irs spectra to identify the chemistry of the envelopes and found that more than of the sources in our sample have mixed chemistry , showing both mid - ir bands attributed to polycyclic aromatic hydrocarbons ( pah ) and silicate features .

we have observed a small sample of hot post - agb stars with the infrared array camera ( irac ) and the infrared spectrograph ( irs ) on - board the spitzer space telescope . the stars were selected from the literature on the basis of their far - infrared excess ( i.e. , post - agb candidates ) and b spectral type ( i.e. , close to the ionization of the envelope ) . the combination of our irac observations with 2mass and iras catalog data , along with previous radio observations in the cm range ( where available ) allowed us to model the seds of our targets and find that in almost all of them at least two shells of dust at different temperatures must be present , the hot dust component ranging up to k. in several targets grains larger than 1 m are needed to match the far - ir data points . in particular , in iras 17423 - 1755 grains up to 100 m must be introduced to match the emission in the mm range . we obtained irs spectra to identify the chemistry of the envelopes and found that more than of the sources in our sample have mixed chemistry , showing both mid - ir bands attributed to polycyclic aromatic hydrocarbons ( pah ) and silicate features . the analysis of the pah features indicates that these molecules are located in the outflows , far away from the central stars . we consider the larger than expected percentage of mixed - chemistry targets as a selection bias towards stars with a disk or torus around them . our results strengthen the current picture of mixed chemistry being due to the spatial segregation of different dust populations in the envelopes .

0908.0638

c

the number density of post - agb / proto - pn is estimated to be around 0.4 kpc@xmath68 . as a comparison , the density of agb stars is 15 kpc@xmath68 and of main sequence stars is @xmath102@xmath69 kpc@xmath68 @xcite . knowledge about this phase is mostly derived from a handful of objects , such as the c - rich source rafgl 618 and the o - rich object oh231.8 + 4.2 . because of the paucity of known to , the identification and study of new to is very important for testing models of stellar evolution . among to candidates , we have selected hot targets ( b spectral type ) , therefore searching for recently - ionized or close - to - ionize envelopes . 2mass and iras data were combined with our irac and radio observations to construct the seds of the sample stars . dusty modeling shows the presence of more than one emitting component in the dust envelopes and indicates that dust temperatures range from @xmath101000 k to @xmath10100 k. the modeling also gives hints about the presence of large ( @xmath70 1 @xmath1 m ) grains , although sub - mm and mm observations are necessary to constrain the seds in these ranges , where such grains would give a major contribution . as an example , in iras 17423 - 1755 it is necessary , to account for its mm emission , to have three dust components ( at 1150 , 132 , and 80 k ) with grain size up to 100 @xmath1 m ( see fig [ fig:17423 ] ) . the irs spectra we obtained allow us to classify the to candidates as c - rich , o - rich , or mixed - chemistry . we have classified as mixed - chemistry objects those stars with both a 10 @xmath1 m silicate bump and pah features in the 611 @xmath1 m range . a possible explanation for the mixed chemistry involves the presence of a circumbinary disk / torus , where o - bearing molecules would be preserved from the third dredge up , while elsewhere in the outflow features from c - bearing molecules would arise . this picture appears to be confirmed by our analysis of the pah features , which indicates that pah molecules in our targets are not located close to the central star . since these objects are typically compact ( @xmath102@xmath13 ) , sub - arcsec imaging may evidence if different dust species have different spatial distributions . in most of our targets with o - rich dust , the 10 @xmath1 m silicate emission feature often appears with a structured shape and/or a peak shift to larger wavelengths . our analysis of the shape and strength of this feature indicates a high degree of dust processing . such processing , which typically consists in dust growth and crystallization , indicates again the presence of large dust grains and/or of crystalline silicates and more interestingly is a further hint for the presence of a circumstellar / circumbinary disk : a stable structure where the grains can have the time to grow and crystallize . whereas the expected fraction of mixed - chemistry envelopes is less than 10% , we find that about 40% of the stars in our sample show both pah and silicate features . our sample has been selected on the basis of b optical spectral type and far - ir excess . these two conditions are indeed typical of hot post - agb stars . nevertheless , selections based on infrared thermal emission ( iras fluxes , for instance ) introduce a bias towards far - ir bright objects . among post - agb stars , objects hosting a disk or torus are stronger ir emitters . these circumstellar ( or circumbinary ) structures are highly stable and store the dust around the central star / s on a much longer time - scale than in stellar envelopes without a disk / torus @xcite . as these envelopes are brighter and live longer , selections based on far - ir emission are biased towards stars surrounded by a disk or torus . the higher percentage of mixed - chemistry envelopes in our sample can therefore be connected to a higher percentage of disks ( or tori ) . this confirms the general picture of a disk / torus as a reservoir preserving o - bearing molecules from the third dredge up . if we refer to the red rectangle as an example , mixed chemistry and large grains are linked together by the presence of a disk , where the particles can survive enough orbits to grow by coagulation to sizes as large as 1 mm @xcite . with only a few examples of this phenomenon , several hints for it found in this project provide us with candidate targets to test the current understanding of dust processing in pn envelopes . l. cerrigone acknowledges funding from the smithsonian astrophysical observatory through the sao predoctoral program . this work is based in part on observations made with the spitzer space telescope , which is operated by the jet propulsion laboratory , california institute of technology under a contract with nasa . support for this work was provided by nasa through an award issued by jpl / caltech . we would like to thank an anonymous referee for his criticism , which led to a substantial improvement of the paper . + _ facilities : _

the combination of our irac observations with 2mass and iras catalog data , along with previous radio observations in the cm range ( where available ) allowed us to model the seds of our targets and find that in almost all of them at least two shells of dust at different temperatures must be present , the hot dust component ranging up to k. in several targets grains larger than 1 m are needed to match the far - ir data points . in particular , in iras 17423 - 1755 grains up to 100 m must be introduced to match the emission in the mm range . the analysis of the pah features indicates that these molecules are located in the outflows , far away from the central stars . we consider the larger than expected percentage of mixed - chemistry targets as a selection bias towards stars with a disk or torus around them .

we have observed a small sample of hot post - agb stars with the infrared array camera ( irac ) and the infrared spectrograph ( irs ) on - board the spitzer space telescope . the stars were selected from the literature on the basis of their far - infrared excess ( i.e. , post - agb candidates ) and b spectral type ( i.e. , close to the ionization of the envelope ) . the combination of our irac observations with 2mass and iras catalog data , along with previous radio observations in the cm range ( where available ) allowed us to model the seds of our targets and find that in almost all of them at least two shells of dust at different temperatures must be present , the hot dust component ranging up to k. in several targets grains larger than 1 m are needed to match the far - ir data points . in particular , in iras 17423 - 1755 grains up to 100 m must be introduced to match the emission in the mm range . we obtained irs spectra to identify the chemistry of the envelopes and found that more than of the sources in our sample have mixed chemistry , showing both mid - ir bands attributed to polycyclic aromatic hydrocarbons ( pah ) and silicate features . the analysis of the pah features indicates that these molecules are located in the outflows , far away from the central stars . we consider the larger than expected percentage of mixed - chemistry targets as a selection bias towards stars with a disk or torus around them . our results strengthen the current picture of mixed chemistry being due to the spatial segregation of different dust populations in the envelopes .

1204.1334

c

our spectroscopic studies have revealed intrinsic variability and amazing structure in the h@xmath5 line profiles caused by high velocity gas flows in the vicinity of the stars within the kh 15d system . the profiles observed during ingress and egress are distinctly different , changing from an inverse p - cygni profile during ingress to an enhanced double - peaked profile with broad extended wings during egress . the differences in these profiles can be understood in terms of models of accretion flows within an eccentric binary ( artymowicz & lubow 1996 ; gnther & kley 2002 ; and de val - borro et al . measurements of the flux and ew of the blue - shifted emission located in the wings of h@xmath5 ( velocity ranging from 280 km s@xmath7 to 85 km s@xmath7 ) give us an indication that the h@xmath5 emitting region is compact and variable in brightness on the time scale of the orbital period . there is potentially a great deal more information locked in these spectra than we have been able to extract . the present study will hopefully serve as an incentive and guide to more detailed modeling . the dynamics of the binary system are very well understood ( w06 ) and it should be quite possible to model with definiteness the expected gas flows and accretion dynamics using codes that have already been applied to similar systems . these data could potentially serve as a critical test of such models . some subtleties of the profile variations have undoubtedly escaped us and comparison with models of this particular system may reveal them . we would like to thank the anonymous referee for the suggested improvements to this paper . we also thank dr . frederic v. hessman for graciously allowing us to use the data he collected with the het . c.m.h would like to thank dr . eric mamajek and dr . david james for helpful advice and discussions regarding the creation of figure 1 . c.m.h . acknowledges partial support by the american association of university women through an american fellowship . .- k . acknowledges partial support by the nasa origins of solar systems program through the following grants to rice university : nnx08ah86 g and nnx10ai53 g . w.h . acknowledges partial support by the nasa origins of solar systems program . some of the data presented herein were obtained at the w. m. keck observatory , which is operated as a scientific partnership among the california institute of technology , the university of california , and the national aeronautics and space administration . the observatory was made possible by the generous financial support of the w.m . keck foundation . the authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of mauna kea has always had within the indigenous hawaiian community . we are most fortunate to have the opportunity to conduct observations from this mountain . the hobby - eberly telescope ( het ) is a joint project of the university of texas at austin , the pennsylvania state university , stanford university , ludwig - maximilians - universitt mnchen , and georg - august - universitt gttingen . the het is named in honor of its principal benefactors , william p. hobby and robert e. eberly . this paper is based in part on observations collected at the european southern observatory ( program 074.c- 0604a ) . c.m.h . would also like to thank darla and steve mckee , as well as the masci family , for graciously supporting her and her daughter throughout the beginning , and final production , of this work , respectively . this paper is dedicated to robert masci . hinkle , k. , wallace , l. , valenti , j. , & harmer , d. 2000 , visible and near infrared atlas of the arcturus spectrum 3727 - 9300 ed . k. hinkle , l. wallace , j. valenti , & d. harmer . ( san francisco : asp ) isbn : 1 - 58381 - 037 - 4 2001 nov 29 & vlt / uves & 4800 - 6800 & 44,000 + 2001 dec 14 & vlt / uves & 4800 - 6800 & 44,000 + 2001 dec 20 & vlt / uves & 4800 - 6800 & 44,000 + 2002 dec 06 & het / hrs & 6380 - 7330 & 15,000 + 2002 dec 10 & het / hrs & 6380 - 7330 & 15,000 + 2002 dec 13 & het / hrs & 6380 - 7330 & 15,000 + 2003 jan 23 & het / hrs & 6380 - 7330 & 15,000 + 2003 jan 26 & het / hrs & 6380 - 7330 & 15,000 + 2003 feb 02 & het / hrs & 6380 - 7330 & 15,000 + 2003 feb 05 & het / hrs & 6380 - 7330 & 15,000 + 2003 feb 08 & keck / hires & 4200 - 6600 & 70,000 + 2003 feb 09 & keck / hires & 4200 - 6600 & 70,000 + 2003 feb 10 & keck / hires & 4200 - 6600 & 70,000 + 2003 mar 06 & het / hrs & 6380 - 7330 & 15,000 + 2003 mar 23 & het / hrs & 6380 - 7330 & 15,000 + 2003 dec 16 & keck / hires & 4400 - 6800 & 40,000 + 2003 dec 18 & keck / hires & 4400 - 6800 & 40,000 + 2004 jan 04 & mcd / ce & 5600 - 6900 & 30,000 + 2004 jan 05 & mcd / ce & 5600 - 6900 & 30,000 + 2004 jan 10 & mcd / ce & 5600 - 6900 & 30,000 + 2004 feb 05 & keck / hires & 4400 - 6800 & 39,000 + 2004 mar 10 & keck / hires & 4700 - 7100 & 40,000 + 2004 mar 12 & keck / hires & 4800 - 7100 & 40,000 + 2004 dec 10 & mcd / ce & 5600 - 6900 & 30,000 + 2004 dec 13 & vlt / uves & 5800 - 7300 & 44,000 + 2004 dec 14 & vlt / uves & 5900 - 7300 & 44,000 + 2004 dec 15 & vlt / uves & 5800 - 7300 & 44,000 + 2004 dec 16 & vlt / uves & 5800 - 7300 & 55,000 + 2004 dec 17 & vlt / uves & 5800 - 7300 & 55,000 + 2004 dec 18 & vlt / uves & 5800 - 7300 & 55,000 + 2005 feb 27 & keck / hires & 4800 - 7100 & 42,000 + 2005 feb 28 & keck / hires & 4800 - 7100 & 42,000 + 2005 mar 01 & keck / hires & 4800 - 7100 & 42,000 + 2005 dec 12 & mag / mike & 5800 - 6800 & 25,000 + 2005 dec 13 & mag / mike & 5800 - 6800 & 25,000 + 2005 dec 14 & mag / mike & 5800 - 6800 & 25,000 + 2005 dec 15 & mag / mike & 5800 - 6800 & 25,000 + 2005 dec 20 & het / hrs & 5880 - 6770 & 30,000 + 2005 dec 21 & het / hrs & 5880 - 6770 & 30,000 + 2005 dec 22 & het / hrs & 5880 - 6770 & 30,000 + 2005 dec 23 & het / hrs & 5880 - 6770 & 30,000 + 2005 dec 24 & het / hrs & 5880 - 6770 & 30,000 + 2006 feb 07 & het / hrs & 5880 - 6770 & 30,000 + 2006 feb 09 & het / hrs & 5880 - 6770 & 30,000 + 2006 feb 10 & het / hrs & 5880 - 6770 & 30,000 + 2006 feb 12 & het / hrs & 5880 - 6770 & 30,000 + 2006 feb 13 & het / hrs & 5880 - 6770 & 30,000 + 2006 feb 14 & het / hrs & 5880 - 6770 & 30,000 + 2452242.7446 & vlt / uves & -0.26 & -1.46 & -9.95 & 4.52 & 15.28 & 14.49 & 0.990 & 16.23 + 2452257.8271 & vlt / uves & 0.05 & 8.74 & 59.86 & -27.21 & 18.86 & 18.18 & 0.036 & 9.10 + 2452263.7026 & vlt / uves & 0.17 & 1.95 & -2.19 & 0.99 & 18.31 & 17.61 & 0.060 & 6.35 + 2452614.9333 & het / hrs & 0.44 & -3.90 & -18.89 & 8.58 & 15.25 & 14.48 & 1.020 & 12.80 + 2452618.9292 & het / hrs & -0.48 & -4.02 & -18.43 & 8.61 & 15.27 & 14.50 & 1.000 & 10.89 + 2452621.7431 & het / hrs & -0.43 & -3.65 & -17.34 & 7.88 & 15.26 & 14.49 & 1.010 & 9.90 + 2452662.6451 & het / hrs & 0.42 & -3.68 & -18.83 & 8.55 & 15.25 & 14.48 & 1.020 & -10.68 + 2452665.8014 & het / hrs & 0.49 & -3.95 & -18.76 & 8.52 & 15.25 & 14.48 & 1.020 & -12.51 + 2452672.6090 & het / hrs & -0.37 & -2.91 & -15.82 & 7.18 & 15.29 & 14.52 & 0.980 & -15.23 + 2452675.7688 & het / hrs & -0.31 & -1.71 & -12.99 & 5.90 & 15.29 & 14.52 & 0.980 & -16.92 + 2452678.8193 & keck / hires & -0.26 & -0.12 & -8.94 & 4.06 & 15.57 & 14.80 & 0.760 & -18.29 + 2452679.8276 & keck / hires & -0.24 & 0.50 & -7.20 & 3.27 & 16.20 & 15.46 & 0.420 & -18.71 + 2452680.8356 & keck / hires & -0.22 & 1.17 & -5.15 & 2.42 & 18.09 & 17.39 & 0.070 & -19.13 + 2452704.6771 & het / hrs & 0.29 & -1.39 & -15.35 & 6.97 & 15.33 & 14.56 & 0.950 & -26.23 + 2452721.6361 & het / hrs & -0.36 & -2.59 & -15.33 & 6.96 & 15.28 & 14.46 & 0.990 & -28.70 + 2452990.0431 & keck / hires & 0.18 & 2.72 & -4.83 & 2.19 & 18.29@xmath28 & 17.62 & 0.060 & 7.84 + 2452992.0413 & keck / hires & 0.22 & 1.09 & -10.63 & 4.83 & 18.11@xmath28 & 17.42 & 0.070 & 6.84 + 2453008.7960 & mcd / ce & -0.42 & -2.71 & -17.33 & 7.87 & 15.25 & 14.47 & 1.020 & -1.33 + 2453009.8729 & mcd / ce & -0.40 & -2.48 & -16.74 & 7.60 & 15.22 & 14.44 & 1.050 & -2.06 + 2453014.7920 & mcd / ce & -0.30 & -0.77 & -12.58 & 5.71 & 15.34 & 14.57 & 0.940 & -4.42 + 2453040.8025 & keck / hires & 0.22 & 0.92 & -11.45 & 5.20 & 18.24 & 17.56 & 0.060 & -16.88 + 2453074.7882 & keck / hires & -0.07 & 7.61 & 23.23 & -10.56 & 18.85@xmath28 & 18.25 & 0.040 & -27.41 + 2453076.8125 & keck / hires & -0.03 & 9.36 & 42.73 & -19.43 & 18.51@xmath28 & 17.81 & 0.050 & -27.79 + 2453349.8684 & mcd / ce & -0.38 & -1.31 & -15.86 & 7.20 & 15.28 & 14.51 & 0.990 & 10.85 + 2453352.7976 & vlt / uves & -0.31 & -0.28 & -13.29 & 6.03 & 15.35 & 14.59 & 0.930 & 9.56 + 2453353.6774 & vlt / uves & -0.29 & 0.11 & -12.31 & 5.59 & 15.51 & 14.74 & 0.800 & 9.28 + 2453354.7199 & vlt / uves & -0.27 & 0.60 & -11.01 & 5.00 & 16.35 & 15.60 & 0.370 & 8.73 + 2453355.6510 & vlt / uves & -0.25 & 1.09 & -9.69 & 4.40 & 17.55 & 16.85 & 0.120 & 8.32 + 2453356.6724 & vlt / uves & -0.23 & 1.66 & -8.04 & 3.65 & 17.89 & 17.20 & 0.090 & 7.80 + 2453357.6852 & vlt / uves & -0.21 & 2.28 & -6.16 & 2.79 & 18.20 & 17.50 & 0.067 & 7.28 + 2453428.8268 & keck / hires & 0.26 & 1.09 & -13.25 & 6.02 & 17.31 & 16.60 & 0.150 & -24.91 + 2453429.8250 & keck / hires & 0.28 & 0.52 & -14.70 & 6.67 & 15.86 & 15.10 & 0.580 & -25.18 + 2453430.8201 & keck / hires & 0.30 & 0.02 & -15.84 & 7.19 & 15.47 & 14.70 & 0.830 & -25.45 + 2453716.7708 & mag / mike & 0.21 & 3.31 & -8.20 & 3.72 & 18.80 & 18.13 & 0.040 & 9.98 + 2453717.7708 & mag / mike & 0.23 & 2.58 & -10.71 & 4.86 & 18.27 & 17.59 & 0.060 & 9.49 + 2453718.7708 & mag / mike & 0.25 & 1.93 & -12.69 & 5.76 & 18.14 & 17.45 & 0.070 & 9.00 + 2453719.7708 & mag / mike & 0.27 & 1.35 & -14.25 & 6.47 & 17.60 & 16.90 & 0.120 & 8.51 + 2453724.7264 & het / hrs & 0.38 & -0.63 & -18.26 & 8.30 & 15.38 & 14.61 & 0.900 & 6.35 + 2453725.7340 & het / hrs & 0.40 & -0.87 & -18.59 & 8.44 & 15.31 & 14.52 & 0.960 & 5.83 + 2453726.7222 & het / hrs & 0.42 & -1.05 & -18.79 & 8.53 & 15.28 & 14.51 & 0.990 & 5.35 + 2453727.7181 & het / hrs & 0.44 & -1.19 & -18.89 & 8.58 & 15.27 & 14.50 & 1.000 & 4.84 + 2453728.7090 & het / hrs & 0.46 & -1.28 & -18.90 & 8.58 & 15.22 & 14.45 & 1.050 & 4.35 + 2453773.7556 & het / hrs & 0.39 & -0.67 & -18.49 & 8.40 & 15.49 & 14.73 & 0.820 & -17.81 + 2453775.7458 & het / hrs & 0.43 & -1.03 & -18.86 & 8.57 & 15.34 & 14.57 & 0.940 & -18.59 + 2453776.5862 & het / hrs & 0.45 & -1.12 & -18.91 & 8.59 & 15.28 & 14.50 & 0.990 & -18.59 + 2453778.7409 & het / hrs & 0.50 & -1.21 & -18.72 & 8.51 & 15.23 & 14.46 & 1.040 & -19.74 + 2453779.5889 & het / hrs & -0.49 & -1.19 & -18.55 & 8.43 & 15.25 & 14.48 & 1.020 & -19.74 + 2453780.7305 & het / hrs & -0.47 & -1.12 & -18.22 & 8.28 & 15.26 & 14.49 & 1.010 & -20.45 + @xmath11x = -4 to -2 & 2002 dec 10 & -4.02 & het / hrs + ( ingress ) & 2002 dec 13 & -3.65 & het / hrs + & 2003 feb 02 & -2.91 & het / hrs + & 2004 jan 04 & -2.71 & mcd / ce + & 2003 mar 23 & -2.59 & het / hrs + & 2004 jan 05 & -2.48 & mcd / ce + @xmath11x = 2 to 1 & 2001 dec 20 & 1.95 & vlt / uves + ( egress ) & 2005 dec 14 & 1.93 & magellan / mike + & 2005 dec 15 & 1.35 & magellan / mike + & 2005 feb 27 & 1.10 & keck / hires + & 2003 dec 18 & 1.09 & keck / hires + @xmath11x = -1 to -2 & 2006 feb 09 & -1.03 & het / hrs + ( egress ) & 2005 dec 22 & -1.05 & het / hrs + & 2006 feb 10 & -1.12 & het / hrs + & 2005 dec 23 & -1.19 & het / hrs + & 2006 feb 12 & -1.21 & het / hrs + & 2005 dec 24 & -1.28 & het / hrs + & 2003 mar 06 & -1.39 & het / hrs +

we have obtained 48 high resolution echelle spectra of the pre - main sequence eclipsing binary system kh 15d ( v582 mon , p = 48.37 d , 0.6 , m = 0.6 m , m = 0.7 m ) . other observed variations depend on the orbital phase : the h emission line profile changes from an inverse p cygni type profile during ingress to an enhanced double - peaked profile , with both a blue and red emission component , during egress . we find that the complex data set can be largely understood in the context of accretion onto the stars from a circumbinary disk with gas flows as predicted by the models of eccentric t tauri binaries put forward by artymowicz & lubow , gnther & kley , and de val - borro et al .

we have obtained 48 high resolution echelle spectra of the pre - main sequence eclipsing binary system kh 15d ( v582 mon , p = 48.37 d , 0.6 , m = 0.6 m , m = 0.7 m ) . the eclipses are caused by a circumbinary disk seen nearly edge on , which at the epoch of these observations completely obscured the orbit of star b and a large portion of the orbit of star a. the spectra were obtained over five contiguous observing seasons from 2001/2002 to 2005/2006 while star a was fully visible , fully occulted , and during several ingress and egress events . the h line profile shows dramatic changes in these time series data over timescales ranging from days to years . a fraction of the variations are due to edge effects " and depend only on the height of star a above or below the razor sharp edge of the occulting disk . other observed variations depend on the orbital phase : the h emission line profile changes from an inverse p cygni type profile during ingress to an enhanced double - peaked profile , with both a blue and red emission component , during egress . each of these interpreted variations are complicated by the fact that there is also a chaotic , irregular component present in these profiles . we find that the complex data set can be largely understood in the context of accretion onto the stars from a circumbinary disk with gas flows as predicted by the models of eccentric t tauri binaries put forward by artymowicz & lubow , gnther & kley , and de val - borro et al . in particular , our data provide strong support for the pulsed accretion phenomenon , in which enhanced accretion occurs during and after perihelion passage . draft version :

cond-mat9612133

i

for a wide variety of substrates , adsorbed films of @xmath0he thicker than approximately two atomic layers are superfluid at zero temperature . as the temperature is increased , a transition occurs to a non - superfluid phase at a critical temperature @xmath1 . although the details of this transition depend on the topology of the substrate,@xcite the phase diagrams for films adsorbed on substrates such as mylar , porous glasses , or packed powders are similar . in each case , there is a line of transition temperatures in the density temperature plane separating non - superfluid from superfluid films . at @xmath2 , this line terminates at a _ critical coverage _ @xmath3 , below which superfluidity does not occur . only cesium substrates , which are not wetted by @xmath0he,@xcite and the atomically ordered substrates graphite and molecular h@xmath4,@xcite lead to exceptions to this general picture . although the existence of a non - zero critical coverage @xmath3 has been known since the earliest experiments on unsaturated @xmath0he films , the onset of superfluidity as a function of coverage at @xmath2 has received much less experimental attention than the superfluid transition at @xmath5 . this has followed in part from the difficulty in making thermodynamic measurements on extremely thin @xmath0he films , but also from a conviction that the non - superfluid film of coverage @xmath3 forms an essentially inert pseudo - substrate for the overlying superfluid film . most aspects of thin - film superfluidity can indeed be understood without any consideration of the critical coverage @xmath3 , and the @xmath0he coverage is often renormalized by taking the effective density of the film to be @xmath6 . for example , the superfluid density of films with transition temperatures above 200 mk is observed to be proportional to @xmath6 for many substrates.@xcite in contrast to the inert - layer model used for the interpretation of most experiments , there has been considerable theoretical work suggesting that the onset of superfluidity at @xmath2 in @xmath0he films is analagous to a metal - insulator transition in fermi systems . this approach follows from a suggestion of hertz , fleishman , and anderson@xcite and has been pursued in depth by fisher _ et al._,@xcite who exploited the existence of a natural order parameter in bose systems to develop a scaling theory for the onset of superfluidity in strongly disordered systems . the spirit of this approach is that the onset transition is driven by the competition between exchange , which favors superfluidity , and the _ combined _ effects of disorder and the repulsive he he interactions , which favor localization . the localized phase in the case of a @xmath0he film adsorbed on a strongly disordered substrate is presumed to be a `` bose glass , '' with a gapless excitation spectrum and a correspondingly nonzero compressibility . this paper presents superfluid density measurements of @xmath0he films adsorbed in aerogel glass and heat capacity measurements of @xmath0he films adsorbed in vycor for coverages close to the critical coverage @xmath3 and temperatures down to 10 mk . our measurements demonstrate that the picture of a superfluid - insulator transition developed by fisher _ et al . _ and others@xcite is qualitatively appropriate . the heat capacity measurements , for example , indicate that a non - superfluid film is far from inert . in fact , the density of states of the non - superfluid film has a characteristic energy which vanishes as the onset transition is approached from _ below _ in coverage . we do not , however , find good quantitative agreement with the scaling predictions of fisher _ et al . _ for the temperature dependence of the heat capacity and the coverage dependence of the superfluid density and the superfluid transition temperature . we find that the non - superfluid film is best characterized as an insulator with a gap as opposed to a bose glass . the scaling behavior of thin superfluid films is complicated by both the large energy scale characteristic of physical adsorption and the existence of the thermodynamic superfluid transition at non - zero temperatures . the thermodynamic transition appears to be the dominant critical point , at least over the temperature and coverage range of our study .

torsional oscillator measurements of thehe - aerogel system were used to determine the superfluid density of films with transition temperatures as low as 20 mk . heat capacity measurements of thehe - vycor system probed the excitation spectrum of both non - superfluid and superfluid films for temperatures down to 10 mk . the heat capacity measurements show that the non - superfluid phase is better characterized as an insulator with a gap .

we have studiedhe films adsorbed in two porous glasses , aerogel and vycor , using high precision torsional oscillator and dc calorimetry techniques . our investigation focused on the onset of superfluidity at low temperatures as thehe coverage is increased . torsional oscillator measurements of thehe - aerogel system were used to determine the superfluid density of films with transition temperatures as low as 20 mk . heat capacity measurements of thehe - vycor system probed the excitation spectrum of both non - superfluid and superfluid films for temperatures down to 10 mk . both sets of measurements suggest that the critical coverage for the onset of superfluidity corresponds to a mobility edge in the chemical potential , so that the onset transition is the bosonic analog of a superconductor - insulator transition . the superfluid density measurements , however , are not in agreement with the scaling theory of an onset transition from a gapless , bose glass phase to a superfluid . the heat capacity measurements show that the non - superfluid phase is better characterized as an insulator with a gap .

0810.1140

i

the luminous ( @xmath11 ) orion bn / kl infrared nebula is the nearest ( @xmath12 pc : @xcite ) and probably most studied high - mass star forming region ( hmsfr ) in the galaxy . more than 20 spectral line surveys have been carried out in the mm and submm bands over the last 25 years ( 72 - 91 ghz : @xcite ; 70 - 115 ghz : @xcite ; 138 - 151 ghz : @xcite ; 150 - 160 ghz : @xcite ; 160 - 165 ghz : @xcite ; 215 - 247 ghz : @xcite ; 218 - 243 ghz : @xcite ; 247 - 263 ghz : @xcite ; 257 - 273 ghz : @xcite ; 330 - 360 ghz : @xcite ; 325 - 360 ghz : @xcite ; 342 - 359 ghz : @xcite ; 334 - 343 ghz : @xcite ; 455 - 507 ghz : @xcite ; 486 - 492 and 541 - 577 ghz : @xcite ; 607 - 725 ghz : @xcite ; 795 - 903 ghz : @xcite ) . imaging line surveys of orion - bn / kl have also been conducted using the submillimeter array interferometer ( sma ) in the submm ranges 337.2 - 339.2 ghz and 347.2 - 349.2 ghz @xcite , and 679.78 - 681.75 ghz and 689.78 - 691.75 ghz @xcite . we report here the first high spectral resolution survey at 7 mm between frequencies of 42.3 and 43.6 ghz . the main target of our survey was sio which is a well - known tracer of shocks in hmsfrs , and so it is particularly suitable for tracing high - velocity outflowing molecular gas . in this context , sio observations provide observational constraints on the acceleration mechanisms of high - mass protostellar outflows , and thus also test different theories of massive star formation . for example , if massive stars form from massive cores in a qualitatively similar but scaled - up fashion to low - mass stars @xcite then similar disk and outflow properties are expected , such as magneto - centrifugally launched x - winds @xcite and/or disk - winds @xcite that are aligned and collimated orthogonally to the plane of the accretion disk . alternatively , if massive stars form via more chaotic accretion processes , such as competitive accretion @xcite or stellar mergers @xcite , then more disordered disks and outflows might be expected . a generic prediction of x - wind and disk - wind models is that the outflow is initially accelerated to about the local escape speed of the launching region . relatively large ( @xmath1310 - 30% ) fractions of the accretion flow are predicted to be launched from the inner disk , within a few stellar radii , where the escape speeds can approach @xmath131000 km s@xmath7(the escape speed from the surface of a 20 m@xmath14 protostar that has contracted to the zero age main sequence , for example ) . however , such high - speed winds have never been observed close to high mass protostars . orion bn / kl is a good target for observations at 7 mm . first , strong sio maser emission from three vibrational states are excited at 7 mm by a high - mass protostar in the region , source i @xcite , and their exceptionally high brightness temperature might facilitate detection of ( weak ) high - velocity components in the protostellar wind compared to thermal emission @xcite . second , though orion is a rich source of line emission at millimeter wavelengths @xcite , one may reasonably anticipate a lower density of lines in the relatively long wavelength 7 mm band . third , source i is the only known origin of sio emission in orion bn / kl @xcite , diminishing the risk of confusion . on the theoretical side , @xcite presented models for magneto - centrifugally launched outflows from a massive protostar , such as the source that may be powering the orion - bn / kl region , source i. @xcite pointed out that close passage of the bn object , which is a runaway b star , may have tidally perturbed the accretion disk within the last 1000 yr , perhaps leading to enhanced accretion and outflow activity that may help to explain the explosive " appearance of the outflow on larger scales @xcite . alternatively , @xcite have argued that the explosive , poorly - collimated nature of the outflow may have been caused by a protostellar merger . observations of fast ( and inner ) portions of the outflow , and their relation to any protostellar accretion disk , are essential to distinguish these various scenarios . thus , in this paper we searched for high velocity outflows by using single - dish observations of sio transitions . although the beam ( @xmath15 ) of our observations is not sufficient to identify the driving source of the outflow in the region , previous high - angular resolution observations showed unequivocally that the sio maser emission probes circumstellar gas at distances 10 - 1000 au from source i ( e.g. , @xcite ) . while we found evidence for flows up to @xmath16 km s@xmath7 , we did not find any conclusive indication of higher - speed winds , although several unidentified emission lines are candidates . as an additional byproduct of this search , we have detected for the first time in orion bn / kl the @xmath6 transition of two sio isotopologues , @xmath4sio and @xmath5sio , and we have identified a number of other chemical species in the region . in this paper , we present the spectral profiles for the @xmath3sio @xmath17 and @xmath4sio and @xmath5sio @xmath18 lines as well as all the molecular identifications in the surveyed range of frequencies . this work is structured as follows : 2 describes the observations and data reduction , the results of the line identification are illustrated in 3 , and an analysis on individual species is presented in 4 . a summary is presented in 5 .

we have surveyed molecular line emission from orion bn / kl from 42.3 to 43.6 ghz with the green bank telescope . we report here for the first time the spectra of thesio andsio emission in orion bn / kl , and we show that they have double - peaked profiles with velocity extents similar to the main isotopologue . the main motivation for the survey was the search of high - velocity ( 100 - 1000 km s ) outflows in the bn / kl region as traced by sio doppler components

we have surveyed molecular line emission from orion bn / kl from 42.3 to 43.6 ghz with the green bank telescope . sixty - seven lines were identified and ascribed to 13 different molecular species . the spectrum at 7 mm is dominated by sio , so , choch , and chcn . five transitions have been detected from the sio isotopologuessio ,sio , andsio . we report here for the first time the spectra of thesio andsio emission in orion bn / kl , and we show that they have double - peaked profiles with velocity extents similar to the main isotopologue . the main motivation for the survey was the search of high - velocity ( 100 - 1000 km s ) outflows in the bn / kl region as traced by sio doppler components . some of the unidentified lines in principle could be high - velocity sio features , but without imaging data their location can not be established . wings of emission are present in thesio ,sio andsio profiles , and we suggest that the emission from the three isotopologues might trace a moderately high - velocity ( km s ) component of the flows around the high - mass protostar sourcei in the orion bn / kl region . we also confirm the 7 mm detection of a complex oxygen - bearing species , acetone ( chcoch ) , which has been recently observed towards the hot core at 3 mm , and we have found further indications of the presence of long cyanopolyynes ( hcn and hcn ) in the quiescent cold gas of the extended ridge .

0810.1140

i

in this line survey of the orion bn / kl region we find 67 spectral features , attributed to 13 species . the spectrum is dominated by sio , so@xmath0 , c@xmath0h@xmath2cn , ch@xmath1och@xmath1 , and ch@xmath1coch@xmath1 . we confirm the detection of acetone towards the hot core at 7 mm , and we find further indications of the association of long c - chain molecules with the extended ridge : hc@xmath2n , hc@xmath10n , and possibly the cation hc@xmath1nh@xmath41 . the detections of these c - chain molecules are based only on single transitions , so follow - up observations are necessary to obtain confirmation . five transitions from sio isotopologues have been detected . the profiles of the strong @xmath3sio @xmath127 maser transitions extend in the velocity range from @xmath236 to @xmath237 km s@xmath7 . some of the unidentified lines in principle could be high - velocity ( 100 - 1000 km s@xmath7 ) doppler components of sio , but without imaging data the location of the presumed high - velocity features can not be established . future observations with the nrao evla interferometer , providing broad instantaneous bandwidth , tuning flexibility , and high sensitivity , will be crucial to establish the origins of the candidate high - velocity emission . we report for the first time spectral profiles of the line @xmath120 from @xmath4sio and @xmath5sio , which overlap well with the velocity range of the @xmath8 @xmath3sio emission . in particular , the profiles of the @xmath8 emission from all the @xmath3sio , @xmath4sio and @xmath5sio isotopologues show a redshifted wing of emission extending up to 50 km s@xmath7(and a less prominent blueshifted wing up to 40 km s@xmath7 ) . we speculate that the wing emission may trace a moderately high - velocity wind component from source i , but with only single - dish spectra no firm conclusion can be drawn about the origin of the emission . imaging at high - angular resolution the @xmath8 emission from all the sio isotopologues will be uniquely important in the mapping of the local gas dynamics . that would also be essential to establish without ambiguity the nature ( thermal vs maser ) of the @xmath8 emission from @xmath4sio and @xmath5sio . indeed , with the aim of establishing the origin and the nature of the @xmath4sio and @xmath5sio @xmath120 emission , we conducted follow - up observations of orion - bn / kl in the three isotopologues with the nrao vla interferometer ; the results will be discussed in a forthcoming paper . the presence of two vibrationally excited transitions and three isotopologues from sio , makes orion - bn / kl the only laboratory for studying excitation mechanisms of isotopic sio masers in sfrs ( and possibly in late - type stellar envelopes ) . we wish to thank r. maddalena , d. balser , and t. minter for helpful discussions on gbt calibration parameters . we thank m. stennes and t. minter for analyses that explained the spectral artifacts reported here . we are also very grateful to the amp spectroscopy group at the cfa , in particular s. brunken and m. mccarthy , for very helpful discussions about some identifications reported in the present survey . the data presented here were obtained under the gbt program 07a-102 . this material is based upon work supported by the national science foundation under grant no . nsf ast 0507478 . allen , d. a. , & burton , m. g. 1993 , , 363 , 54 bally , j. , & zinnecker , h. 2005 , , 129 , 2281 baudry , a. , herpin , f. , & lucas , r. 1998 , , 335 , 654 bell , m. b. , feldman , p. a. , travers , m. j. , mccarthy , m. c. , gottlieb , c. a. , & thaddeus , p. 1997 , , 483 , l61 belloche , a. , menten , k. m. , comito , c. , mller , h. s. p. , schilke , p. , ott , j. , thorwirth , s. , & hieret , c. 2008 , , 482 , 179 beuther , h. , et al . 2005 , , 632 , 355 beuther , h. , et al . 2006 , , 636 , 323 blake , g. a. , masson , c. r. , phillips , t. g. , & sutton , e. c. 1986 , , 60 , 357 blake , g. a. , mundy , l. g. , carlstrom , j. e. , padin , s. , scott , s. l. , scoville , n. z. , & woody , d. p. 1996 , , 472 , l49 bonnell , i. a. , bate , m. r. , & zinnecker , h. 1998 , , 298 , 93 bonnell , i. a. , & bate , m. r. 2006 , , 370 , 488 buhl , d. , snyder , l. e. , lovas , f. j. , & johnson , d. r. 1974 , , 192 , l97 chandler , c. j. , & de pree , c. g. 1995 , , 455 , l67 charnley , s. b. 2004 , advances in space research , 33 , 23 cho , s .- h . , chung , h .- s . , kim , h .- , oh , b .- y . , lee , c .- h . , & han , s .- 1998 , , 115 , 277 cho , s .- h . , & ukita , n. 1998 , , 116 , 2495 cho , s .- h . , chung , h .- s . , kim , h .- , & roh , d .- g . 1999 , , 117 , 1485 comito , c. , schilke , p. , phillips , t. g. , lis , d. c. , motte , f. , & mehringer , d. 2005 , , 156 , 127 friedel , d. n. , et al . 2005 , , 630 , 623 genzel , r. , reid , m. j. , moran , j. m. , & downes , d. 1981 , , 244 , 884 genzel , r. , & stutzki , j. 1989 , , 27 , 41 greaves , j. s. , & white , g. j. 1991 , , 91 , 237 greenhill , l. j. , reid , m. j. , chandler , c. j. , diamond , p. j. , & elitzur , m. 2004 , star formation at high angular resolution , 221 , 155 groner , p. , albert , s. , herbst , e. , & de lucia , f. c. 1998 , , 500 , 1059 groner , p. , albert , s. , herbst , e. , de lucia , f. c. , lovas , f. j. , drouin , b. j. , & pearson , j. c. 2002 , , 142 , 145 ikeda , m. , ohishi , m. , nummelin , a. , dickens , j. e. , bergman , p. , hjalmarson , . , & irvine , w. m. 2001 , , 560 , 792 jewell , p. r. , hollis , j. m. , lovas , f. j. , & snyder , l. e. 1989 , , 70 , 833 johansson , l. e. b. , et al . 1984 , , 130 , 227 kawaguchi , k. , kasai , y. , ishikawa , s .- i . , ohishi , m. , kaifu , n. , & amano , t. 1994 , , 420 , l95 keto , e. r. , welch , w. j. , reid , m. j. , & ho , p. t. p. 1995 , , 444 , 765 konigl , a. , & pudritz , r. e. 2000 , protostars and planets iv , 759 lee , c. w. , cho , s .- h . , & lee , s .- m . 2001 , , 551 , 333 lee , c. w. , & cho , s .- h . 2002 , journal of korean astronomical society , 35 , 187 lockett , p. , & elitzur , m. 1992 , , 399 , 704 lovas , f. j. , johnson , d. r. , buhl , d. , & snyder , l. e. 1976 , , 209 , 770 lovas , f. j. 2004 , journal of physical and chemical reference data , 33 , 177 mckee , c. f. , & tan , j. c. 2003 , , 585 , 850 menten , k. m. , reid , m. j. , forbrich , j. , & brunthaler , a. 2007 , , 474 , 515 minter , a. h. 2007 , gbt memo no . 247 minter , a. h. & stennes , m. j. 2007 , gbt memo no . 257 nikolic , b. , prestage , r. m. , balser , d. s. , chandler , c. j. , & hills , r. e. 2007 , , 465 , 685 ohishi , m. , ishikawa , s .- i . , yamamoto , s. , saito , s. , & amano , t. 1995 , , 446 , l43 olofsson , h. , hjalmarson , a. , & rydbeck , o. e. h. 1981 , , 100 , l30 olofsson , a. o. h. , et al . 2007 , , 476 , 791 pickett , h. m. , poynter , i. r. l. , cohen , e. a. , delitsky , m. l. , pearson , j. c. , & muller , h. s. p. 1998 , journal of quantitative spectroscopy and radiative transfer , 60 , 883 remijan , a. j. , hollis , j. m. , snyder , l. e. , jewell , p. r. , & lovas , f. j. 2006 , , 643 , l37 schilke , p. , groesbeck , t. d. , blake , g. a. , & phillips , t. g. 1997 , , 108 , 301 schilke , p. , benford , d. j. , hunter , t. r. , lis , d. c. , & phillips , t. g. 2001 , , 132 , 281 shu , f. h. , najita , j. r. , shang , h. , & li , z .- y . 2000 , protostars and planets iv , 789 snyder , l. e. , lovas , f. j. , mehringer , d. m. , miao , n. y. , kuan , y .- j . , hollis , j. m. , & jewell , p. r. 2002 , , 578 , 245 snyder , l. e. , et al . 2005 , , 619 , 914 sutton , e. c. , blake , g. a. , masson , c. r. , & phillips , t. g. 1985 , , 58 , 341 sutton , e. c. , peng , r. , danchi , w. c. , jaminet , p. a. , sandell , g. , & russell , a. p. g. 1995 , , 97 , 455 tan , j. c. , & mckee , c. f. 2003 , arxiv astrophysics e - prints , arxiv : astro - ph/0309139 tan , j. c. 2004 , , 607 , l47 taylor , k. , dyson , j. e. , axon , d. j. , & hughes , s. 1986 , , 221 , 155 thaddeus , p. , mather , j. , davis , j. h. , & blair , g. n. 1974 , , 192 , l33 turner , b. e. 1989 , , 70 , 539 turner , b. e. 1991 , , 76 , 617 white , g. j. , griffin , m. j. , rainey , r. , monteiro , t. s. , & richardson , k. j. 1986 , , 162 , 253 white , g. j. , araki , m. , greaves , j. s. , ohishi , m. , & higginbottom , n. s. 2003 , , 407 , 589 wolff , r. s. 1980 , , 242 , 1005 wright , m. c. h. , plambeck , r. l. , mundy , l. g. , & looney , l. w. 1995 , , 455 , l185 ziurys , l. m. , & mcgonagle , d. 1993 , , 89 , 155

the spectrum at 7 mm is dominated by sio , so , choch , and chcn . . some of the unidentified lines in principle could be high - velocity sio features , but without imaging data their location can not be established . we also confirm the 7 mm detection of a complex oxygen - bearing species , acetone ( chcoch ) , which has been recently observed towards the hot core at 3 mm , and we have found further indications of the presence of long cyanopolyynes ( hcn and hcn ) in the quiescent cold gas of the extended ridge .

we have surveyed molecular line emission from orion bn / kl from 42.3 to 43.6 ghz with the green bank telescope . sixty - seven lines were identified and ascribed to 13 different molecular species . the spectrum at 7 mm is dominated by sio , so , choch , and chcn . five transitions have been detected from the sio isotopologuessio ,sio , andsio . we report here for the first time the spectra of thesio andsio emission in orion bn / kl , and we show that they have double - peaked profiles with velocity extents similar to the main isotopologue . the main motivation for the survey was the search of high - velocity ( 100 - 1000 km s ) outflows in the bn / kl region as traced by sio doppler components . some of the unidentified lines in principle could be high - velocity sio features , but without imaging data their location can not be established . wings of emission are present in thesio ,sio andsio profiles , and we suggest that the emission from the three isotopologues might trace a moderately high - velocity ( km s ) component of the flows around the high - mass protostar sourcei in the orion bn / kl region . we also confirm the 7 mm detection of a complex oxygen - bearing species , acetone ( chcoch ) , which has been recently observed towards the hot core at 3 mm , and we have found further indications of the presence of long cyanopolyynes ( hcn and hcn ) in the quiescent cold gas of the extended ridge .

1201.3874

i

ground - based remote sensing of the ionosphere is a rich field of study that has developed over several decades and now includes a host of different instruments including , but not limited to , gps , certo @xcite , and other radio beacon receivers , ionosondes , and radar / hf arrays . a powerful yet relatively underused resource for remote sensing are radio - frequency arrays , particularly those that operate in the vhf regime . designed as radio synthesis telescopes , they are chiefly used to observe cosmic sources . while such observations require detailed calibration schemes to remove the effects of the ionosphere , this calibration data is seldom used to actually study the ionosphere . these interferometers basically measure the time - averaged correlation of complex voltages from pairs of antennas which can be combined with fourier methods to make relatively high angular resolution images of cosmic sources ( for a detailed discussion of the methods involved , see * ? ? ? the correlated signals , or `` visibilities '' have an extra phase term added to them by the ionosphere proportional to the difference in the total electron content ( tec ) between the two antennas lines of sight . because of the relatively large collecting area of the individual elements ( usually dishes , dozens of meters across ) , and the brightness of many cosmic sources , these additional phase terms can typically be converted to differential tec ( @xmath7 ) measurements with a precision of @xmath8 tecu or better . in addition , the range of scales that can be probed with such interferometers ( dozens of meters to hundreds of kilometers ) and the virtual ubiquity of target sources available on the sky make them valuable assets for the exploration of ionospheric dynamics from very fine to medium size scales . consequently , radio arrays have been used , to a somewhat limited degree , for ionospheric studies . because of the relative stability of its electronics , quiet radio frequency interference ( rfi ) environment , and available vhf system ( bands at 74 and 330 mhz ) , the very large array ( vla ) has been used almost exclusively in these efforts . seminal experiments were performed by @xcite using 330 mhz vla observations of several sources to explore the environment of ionospheric waves above the vla . among other results , they discovered a new class of magnetic eastward directed waves that were later shown to actually be located within the plasmasphere @xcite . subsequent larger - scale investigations using data from the vla low - frequency sky survey ( vlss ; * ? ? ? * ) , a survey of the northern sky at 74 mhz , have shown that the median behavior of ionospheric fluctuations observed by the vla over several years is essentially consistent with turbulence @xcite . joint observations made with an all - sky optical camera and the vla at 74 and 330 mhz by @xcite demonstrated the vla s ability to aid in the exploration of the interaction between gravity waves generated lower in the atmosphere and relatively small - scale phenomena such as sporadic-@xmath4 . recently , from a campaign using the vla and the cosmic satellite , @xcite were able to detect a relatively rare instance of a southeastward - propagating traveling ionospheric disturbance ( tid ) . in a companion paper @xcite , we described in detail the methods for extracting ionspheric information from the calibration of vla vhf system data . we demonstrated that when observing a bright cosmic source , the vla vhf system was capable of achieving a typical @xmath7 precision of @xmath9 tecu . since arrays such as the vla are essentially only sensitive to the tec gradient , we also detailed techniques for measuring time series of the tec gradient to a precision of about @xmath1 tecu km@xmath2 . here , we seek to develop this effort further by presenting new spectral analysis techniques for these tec gradient measurements . we will demonstrate that these techniques are capable of detecting and characterizing several phenomena from medium ( @xmath10 km ) to small ( @xmath11 km ) scales while also providing a broader statistical description of the spectrum of tec fluctuations observable with the vla .

, we showed that the vla can detect fluctuations in total electron content ( tec ) with amplitudes of tecu and can measure tec gradients with a precision of about tecu km . we detail two complementary techniques for producing spectral analysis of these tec gradient measurements . * ; * ? ? ? * ) .

we have used a relatively long , contiguous vhf observation of a bright cosmic radio source ( cygnus a ) with the very large array ( vla ) through the nighttime , midlatitude ionosphere to demonstrate the phenomena observable with this instrument . in a companion paper , we showed that the vla can detect fluctuations in total electron content ( tec ) with amplitudes of tecu and can measure tec gradients with a precision of about tecu km . we detail two complementary techniques for producing spectral analysis of these tec gradient measurements . the first is able to track individual waves with wavelengths of about half the size of the array ( km ) or more . this technique was successful in detecting and characterizing many medium - scale traveling ionospheric disturbances ( mstids ) seen intermittently throughout the night and has been partially validated using concurrent gps measurements . smaller waves are also seen with this technique at nearly all times , many of which move in similar directions as the detected mstids . the second technique allows for the detection and statistical description of the properties of groups of waves moving in similar directions with wavelengths as small as 5 km . combining the results of both spectral techniques , we found a class of intermediate and small scale waves which are likely the quasi - periodic ( qp ) echoes that have been observed to occur within sporadic- ( ) layers . we find two distinct populations of these waves . the members of one population are coincident in time with mstids and are consistent with being generated within layers by the coupling instability . the other population seems more influenced by the neutral wind , similar to the predominant types of qp echoes found by the sporadic- experiments over kyushu ( seek * ? ? ? * ; * ? ? ? * ) . we have also found that the spectra of background ( i.e. , isotropic ) fluctuations can be interpreted as the sum of two turbulent components with maximum scales of about 300 km and 10 km .

1201.3874

c

our exploration of a long , vhf observation of cyg a with the vla has successfully demonstrated the power of this instrument to characterize a variety of transient ionospheric phenomena . for this observation , the typical @xmath109 uncertainty in the @xmath7 measurements was @xmath9 tecu , yielding more than an order of magnitude better sensitivity to tec fluctuations than can be achieved with gps - based relative tec measurements ( see , e.g. , * ? ? ? * ) . through our new spectral - based analysis , we have demonstrated the ability of the vla to detect and characterize individual instances of mstids as well as smaller - scale structures likely associated with @xmath5 layers . we note that since disturbances within the plasmasphere have been observed and in fact discovered with the vla , it stands to reason that some of the phenomena we have detected may be located within the plasmasphere as well . however , the phenomena discovered by @xcite have azimuth angles clustered around @xmath110 ( i.e. , near magnetic east for the vla ) , and few if any of the wave - like structures we have detected meet this criterion . therefore , the vast majority ( if not all ) of the phenomena we have observed were likely within the ionosphere . among these phenomena are mstids , small - scale wave - like phenomena consistent with @xmath5 layer disturbances , and turbulent fluctuations . both the mstids and the small - scale fluctuations were present intermittently throughout the night , and turbulent fluctuations were seen at all times , which is common within vhf observations with the vla @xcite . the mstids appear to change direction after local midnight from being directed generally westward to being directed toward the northeast ( see below ) . there is also a noticeable change in the turbulent activity near midnight , namely the spectral power of these fluctuations on small ( @xmath41 km ) scales peaks near midnight and gradually decreases toward dawn . before midnight local time , we observed instances of westward / northwestward moving mstids ( see fig . [ waveprop ] ) with an additional group moving westward observed briefly near @xmath111 ( see fig . [ armspecpa ] ) . while atypical for what is observed for most of north america ( see * ? ? ? * ) , the directions of these waves are similar to what is typically observed near the west coast in california during summer nighttime ( see * ? ? ? * ) , especially those directed closer to due west . small - scale waves were detected coincident with nearly all of these mstids moving toward either the northeast or southwest . given the difference in directions , it is unlikely that these are simply the signatures of wavefront distortions within the mstids themselves . as discussed above , the amplitudes and orientations of these small - scale waves are consistent with them being generated within @xmath5 layers via the @xmath5li . coupling between the @xmath5li and the perkins instability in the f region ( see * ? ? ? * ; * ? ? ? * ) may be what has influenced the mstids observed near dawn to move closer to northward as they were detected concurrently with northeastward - directed small - scale waves . in contrast , those waves seen near @xmath111 were moving closer to due west and were accompanied by small - scale waves moving toward the southwest . unusual , northeastward - directed mstids were observed near @xmath50 to @xmath60 and @xmath57 to @xmath58 . as discussed above , @xcite observed similar phenomena over japan at midlatitudes during the night when the height of the f region was seen to drop significantly . similarly , we have found evidence within data from relatively nearby ionosondes that suggests that the f region may have experienced a similar drop in height during the instances of northeastward - directed mstids observed with the vla . small - scale waves were also observed at the same times as these unusual mstids . they were also mostly directed toward the northeast , suggesting that they may represent small - scale structures within the mstids themselves . however , we note that ( 1 ) fig . [ armspeckv ] shows that they were moving significantly more slowly than the mstids , ( 2 ) the distribution of azimuth angles seen in fig . [ padist ] to peak near the azimuth angle of the vla s southwestern arm indicates a bias that only affects groups of waves that span an area smaller than the array , and ( 3 ) toward the end of the night , the small - scale waves change direction toward the southwest while the mstids remained northeastward directed . these factors seem to indicate that the small - scale waves are separate phenomena , similar to the other observed small - scale waves that are consistent with qp echoes generated within @xmath5 layers . it could be that coupling between these disturbances and the larger waves in the f region plays some role in the unusual direction of the observed mstids . in any case , a more thorough , statistical examination of these phenomena seems warranted . there are two distinct groups of small - scale waves which were detected with no coincident mstids . they were predominantly directed toward the southeast ( from @xmath62 to @xmath50 ) with a shorter period of activity of waves moving toward the southwest ( between @xmath112 and @xmath113 ) . the southeastward - directed waves in particular seem to be somewhat different from the other observed small - scale waves . given their orientations , they can not have been generated via the @xmath5li . they appear to be moving somewhat faster with typical speeds of about 150 m s@xmath2 while most of the other small - scale waves have speeds between 30 and 100 m s@xmath2 ( see fig . [ armspeckv ] ) . they also seem to be largely unaffected by the arm - based bias discussed in 4.3 , indicating that as a group , the likely span an area larger than that of the array . despite these differences , the southeastward - directed small - scale waves are generally consistent with qp echoes generated in @xmath5 layers , both in amplitude and wavelength . they are more specifically consistent with the qp echoes observed by the sporadic-@xmath4 experiments over kyushu ( seek * ? ? ? * ; * ? ? ? * ) , which were heavily influenced by the direction of the neutral wind at the height of the @xmath5 layer(s ) . the shift in direction at around @xmath61 from southwestward to southeastward may then be an indication of a change in @xmath5 layer height from above the wind sheer altitude to below it . this may imply the formation / dissipation of @xmath5 layers near this time . in addition , these waves occurred during the peak in small - scale turbulent activity as evidenced by the results shown in fig . [ armspecfit ] . this suggests that the same mechanism that generated these qp echoes also caused a significant turbulent disturbance in the lower ionosphere / thermosphere . since the rocky mountains lie largely to the north and northwest of the vla , this mechanism is likely gravity waves associated with wind flow over the rocky mountains . the authors would like to thank the referees for useful comments and suggestions . basic research in astronomy at the naval research laboratory is supported by 6.1 base funding . the vla was operated by the national radio astronomy observatory which is a facility of the national science foundation operated under cooperative agreement by associated universities , inc . part of this research was carried out at the jet propulsion laboratory , california institute of technology , under a contract with the national aeronautics and space administration . coker , c. , s. e. thonnard , k. f. dymond , t. j. w. lazio , j. j. makela , and p. j. loughmiller ( 2009 ) , simultaneous radio interferometer and optical observations of ionospheric structure at the very large array _ rad . , 44 _ , rs0a11 cosgrove , r. b. , r. t. tsunoda , s. fukao , and m. yamamoto ( 2004 ) , coupling of the perkins instability and the sporadic _ e _ layer instability derived from physical arguments , _ j. of geophys . res . , 109 _ , a06301 dymond , k. f. , c. watts , c. coker , s. a. budzien , p. a. bernhardt , n. kassim , t. j. lazio , k. weiler , p. c. crane , p. s. ray , a. cohen , t. clarke , l. j. rickard , g. b. taylor , f. schinzel , y. pihlstrom , m. kuniyoshi , s. close , p. colestock , s. myers , and a. datta ( 2011 ) , a medium - scale traveling ionospheric disturbance observed from the ground and from space , _ rad . , 46 _ , rs5010 larsen , m. f. , d. l. hysell , q. h. zhou , s. m. smith , j. friedman , and r. l. bishop ( 2007 ) , imaging coherent scatter radar , incoherent scatter radar , and optical observations of quasiperiodic structures associated with sporadic @xmath4 layers , _ j. of geophys . , 112 _ , a06321 shiokawa , k. , y. otsuka , n. nishitani , t. ogawa , t. tsugawa , t. maruyama , s. e. smirnov , v. v. bychkov , and b. m. shevtsov ( 2008 ) , northeastward motion of nighttime medium - scale traveling ionospheric disturbances at middle latitudes observed by an airglow imager _ j. of geophys . res . , 113 _ , a12312 tolman , b. , r. b. harris , t. gaussiran , d. munton , j. little , r. mach , s. nelsen , and b. renfro ( 2004 ) , the gps toolkit : open source gps software , paper presented at 16th international technical meeting of the satellite division of the institute of navigation , long beach , calif . tsugawa , t. y. , y. otsuka , a. j. coster , and a. saito ( 2007 ) , medium - scale traveling ionospheric disturbances detected with dense and wide tec maps over north america , _ geophys . lett . , 34 _ , l22101 yokoyama , t. , d. l. hysell , y. otsuka , and m. yamamoto ( 2009 ) , three - dimensional simulation of the coupled perkins and @xmath5-layer instabilities in the nighttime midlatitude ionosphere _ j. of geophys . res . , 114 _ , a03308 yokoyama , t. and d. l. hysell ( 2010 ) , a new midlatitude ionosphere electrodynamics coupling model ( mieco ) : latitudinal dependence and propagation of medium - scale traveling ionospheric disturbances _ geophys . lett . , 37 _ , l08105 wang , w. , t. l. killeen , a. g. burns , and r. g. roble ( 1999 ) , a high - resolution , three - dimensional , time dependent , nested grid model of the coupled thermosphere - ionosphere , _ phys , 61 _ , 385397 , as a function of local time ( abscissa ) and temporal frequency ( ordinate ) of fourier modes within the @xmath7 data . middle : the azimuth angle of the wavenumber vector of each fourier mode with power significantly larger than background levels ( see 3.2 ) . lower : the velocity of each fourier mode , using the same masking as in the middle panel . in all panels , the white contours are of spectral power.,width=576 ] , for each of the vla arms . the noise - equivalent spectrum ( see 4.1 ) is also plotted in each panel as a grey curve . the vertical dotted grey lines denote values of @xmath115 which corresponds to the approximate nyquist sampling limit for the average antenna separation of 2.5 km along the vla arms ( in a configuration).,width=576 ] and @xmath78 detections ( see 4.2 ) for each of the three wavenumber classes . time ranges where mstids were detected from the data displayed in the upper panel of fig . [ waveprop ] are shaded in grey.,width=576 ] azimuth angles for @xmath100 detections of small - scale moving structures displayed in fig . [ armspecpa ] ( shaded grey histograms ) . the same distribution for those detections that were coincident with mstid detections ( see fig . [ armspecpa ] ) are displayed in red . the growth rate for the @xmath116 layer instability is plotted as a black curve ( see right ordinate for scale ) , allowing for a range in meridional wind components ( see 4.3 and * ? ? ? * ) .,width=576 ] azimuth angles for the @xmath100 detections of small - scale moving structures . the light - grey shaded regions indicate the typical range in altitudes for @xmath5 layers , 100110 km . each dark - gray horizontal line indicates the altitude where the wind direction changes from eastward at lower altitudes to westward at higher altitudes , i.e. , where the wind shear necessary for creating an @xmath5 layer exists.,width=576 ] , the power at the maximum wavelength ( upper ) and the maximum wavelength ( lower ) for each component as functions of local time [ see 4.4 and equation ( 4 ) ] . here , turbulent component 1 ( green curves in fig . [ armspecbin ] ) refers to the smaller - scale turbulent component and turbulent component 2 ( blue curves in fig . [ armspecbin ] ) refers to the larger - scale component.,width=576 ]

we have used a relatively long , contiguous vhf observation of a bright cosmic radio source ( cygnus a ) with the very large array ( vla ) through the nighttime , midlatitude ionosphere to demonstrate the phenomena observable with this instrument . in a companion paper this technique was successful in detecting and characterizing many medium - scale traveling ionospheric disturbances ( mstids ) seen intermittently throughout the night and has been partially validated using concurrent gps measurements . the members of one population are coincident in time with mstids and are consistent with being generated within layers by the coupling instability . the other population seems more influenced by the neutral wind , similar to the predominant types of qp echoes found by the sporadic- experiments over kyushu ( seek * ? ? ?

we have used a relatively long , contiguous vhf observation of a bright cosmic radio source ( cygnus a ) with the very large array ( vla ) through the nighttime , midlatitude ionosphere to demonstrate the phenomena observable with this instrument . in a companion paper , we showed that the vla can detect fluctuations in total electron content ( tec ) with amplitudes of tecu and can measure tec gradients with a precision of about tecu km . we detail two complementary techniques for producing spectral analysis of these tec gradient measurements . the first is able to track individual waves with wavelengths of about half the size of the array ( km ) or more . this technique was successful in detecting and characterizing many medium - scale traveling ionospheric disturbances ( mstids ) seen intermittently throughout the night and has been partially validated using concurrent gps measurements . smaller waves are also seen with this technique at nearly all times , many of which move in similar directions as the detected mstids . the second technique allows for the detection and statistical description of the properties of groups of waves moving in similar directions with wavelengths as small as 5 km . combining the results of both spectral techniques , we found a class of intermediate and small scale waves which are likely the quasi - periodic ( qp ) echoes that have been observed to occur within sporadic- ( ) layers . we find two distinct populations of these waves . the members of one population are coincident in time with mstids and are consistent with being generated within layers by the coupling instability . the other population seems more influenced by the neutral wind , similar to the predominant types of qp echoes found by the sporadic- experiments over kyushu ( seek * ? ? ? * ; * ? ? ? * ) . we have also found that the spectra of background ( i.e. , isotropic ) fluctuations can be interpreted as the sum of two turbulent components with maximum scales of about 300 km and 10 km .

1208.5518

i

the redshift @xmath82 - 3 epoch stands out as a unique era for studying galaxy formation and evolution . at this epoch , the cosmic star formation rate reaches its peak ( heavens et al . 2004 ; hopkins & beacom 2006 ; reddy et al . 2008 ) , and ultra - luminous infrared galaxies ( ulirgs , @xmath9 , sanders & mirabel 1996 ) contribute a significant fraction to the infrared luminosity density ( elbaz et al . 2002 , chapman et al . 2005 , caputi et al . 2007 , reddy et al . 2008 , magnelli et al . 2009 ) . the cosmic quasar density also peaks around @xmath82 ( hopkins et al . 2007 , assef et al . 2011 ) . a framework of galaxy evolution through major mergers has been gradually built up by theorists ( barnes & hernquist 1992 , schweizer 1998 , jogee 2006 , hopkins et al . 2006 , 2008 ) . in one of the most popular scenarios ( e.g. hopkins et al . 2008 ) , the tidal torques generated by major mergers funnel gas into the center of galaxies , leading to a central starburst and rapid growth of a supermassive black hole ( smbh ) . black hole and supernova feedback terminate further star formation , evacuating the residual gas and dust , leaving a visible quasar and remnant spheroid . this picture establishes the evolutionary connections between ulirgs , quasars , and massive elliptical galaxies . submillimeter galaxies ( smgs ) are thought to be the analogues of local ulirgs at high redshift ( blain et al . 2002 , tacconi et al . smgs are selected by their strong cold dust emission at 850 @xmath2 m ( @xmath105 mjy ) . they are characterized by very high star formation rates ( 100 - 1000 m@xmath11yr@xmath12 ) and infrared luminosity ( @xmath13 , chapman et al . 2005 , magnelli et al 2012 ) . although most smgs host growing black holes ( e.g. , alexander et al . 2005 , 2008 ) , their luminosities are normally dominated by star formation ( swinbank et al . 2004 ; menndez - delmestre et al . 2007 , younger et al . 2008 , hainline et al . the redshift distribution of smgs strongly peaks at @xmath1=2 - 3 ( chapman et al . 2005 ) , and the surface density of smgs is several hundred per square degree . an 850@xmath2 m selected sample ( smgs ) may be biased toward ulirgs with large amounts of dust , but miss a substantial population of ulirgs with a smaller amount of ( but warmer ) dust , which can be found by surveys at shorter wavelengths . a series of surveys using bright _ spitzer _ 24@xmath2 m emission combined with optically faint photometry have been carried out to probe the ulirg population with emission from smaller and warmer dust grains ( e.g. , rigby et al . 2004 , donley et al . 2007 , yan et al . 2007 , farrah et al . 2008 , soifer et al . 2008 , lonsdale et al . 2009 , huang et al . one of the simplest search criteria is given as @xmath14 mjy , and @xmath15 > 14 $ ] ( where @xmath16 and [ 24 ] are vega magnitudes for @xmath16 band and _ spitzer _ 24 @xmath2 m ) , or roughly @xmath17 ( dey et al . 2008 , fiore et al . 2008 ) , leading to a well defined @xmath182 population which is referred to as dust obscured galaxies ( dey et al . 2008 , hereafter d08 ) . the most luminous dogs have star formation rates ( 500 - 1000 m@xmath11yr@xmath12 or more ) and infrared luminosities ( @xmath19 , bussmann et al 2009 , tyler et al . 2009 , melbourne et al . 2012 ) that are comparable to smgs . it has been proposed that both smgs and dogs are an early phase of galaxy merging , with smgs representing an earlier , starburst - dominant phase , while luminous dogs are in a transitional phase from starburst - dominated to agn - dominated ( e.g. narayanan 2010 ) . the bolometric luminosities also reach their maximum during these phases , making the most luminous galaxies in these phases also among the most luminous objects in the universe . looking for the most luminous galaxies in the universe is one of the major goals of nasa s wide - field infrared survey explorer ( wise , wright et al . wise surveyed the entire sky at 3.4 , 4.6 , 12 and 22 @xmath2 m ( hereafter w1 , w2 , w3 , w4 ) in 2010 . the wise dataset is well suited to investigate the starburst - agn phase of distant , infrared luminous galaxies . at @xmath18 2 - 3 , starburst- or agn - heated hot dust can be traced by 12 and 22 @xmath2 m emission , while the rest near infrared ( nir ) obscuration is sampled by 3.4 and 4.6 @xmath2 m continuum . studies of luminous infrared galaxies with the wise w1 , w2 and w4 bands can take advantage of existing knowledge and techniques developed by earlier studies with _ spitzer _ at similar wavelengths ( irac at 3.6 and 4.5 @xmath2 m , and mips at 24 @xmath2 m ) . observing w4 selected galaxies with wise is similar to observing 24 @xmath2 m bright galaxies with _ spitzer _ , but with the surveyed area enlarged from a few tens of square degrees covered by existing dog surveys to the entire sky . in order to search for hyperluminous infrared galaxies ( hylirgs , @xmath20 ) from the wise dataset , the wise team has explored multiple methods to select candidates . the most productive method so far has been to search for more heavily obscured galaxies , whose w1 ( 3.4 @xmath2 m ) and w2 ( 4.6 @xmath2 m ) flux densities become faint or undetected by wise , while remaining easily detectable at 12 and/or 22 @xmath2 m , with typical w4 ( 22 @xmath2 m ) flux densities @xmath21 . we call this population `` w1w2-dropouts '' ( eisenhardt et al 2012 ) or for brevity `` w12drops '' . follow - up spectroscopy of more than 100 w12drop galaxies at large telescopes ( this paper , eisenhardt et al . ( 2012 ) , see also bridge et al . 2012 ) reveals that a large fraction ( @xmath22 ) of these galaxies are at high redshift ( @xmath23 ) , with the highest at @xmath1=4.6 . most of the redshifts are between 2 and 3 , suggesting they also trace the peak epoch of cosmic star formation and qso activity . at these redshifts , such high flux densities at 22 @xmath2 m imply extremely high luminosities . they are potentially hyperluminous galaxies . in order to understand the dust properties and calculate the total luminosities of these unusual galaxies , continuum measurements at longer wavelengths are crucial . as the first high redshift examples were identified , we began follow - up 0.35 - 1.1 mm continuum observations using the caltech submillimeter observatory ( cso ) , in order to construct their seds and to explore the nature of w12drop galaxies . in this paper , we report the initial results of this follow - up study . the wise data are described in section 2.1 , and the w12drop population followed up with the cso and reported here is listed in table 1 . sections 2.2 and 2.3 describe the cso data , while section 2.4 describes the follow - up optical spectroscopy , which is summarized in table 2 . section 2.5 describes spitzer follow - up observations at 3.6 @xmath2 m and 4.5 @xmath2 m of the w12drops , which were selected to be difficult to detect by wise at w1 ( 3.4 @xmath2 m ) and w2 ( 4.6 @xmath2 m ) , and the photometry for the sources is presented in table 3 . section 3 presents luminosity and dust temperatures constraints from the photometry , while section 4 compares w12drop properties to those of dogs and smgs , and section 5 summarizes the findings . throughout this paper we assume a cdm cosmology with @xmath24 km s@xmath12 mpc@xmath12 , @xmath25 , and @xmath26 .

we have used the caltech submillimeter observatory ( cso ) to follow - up a sample of wise - selected , hyperluminous galaxies , so called w1w2-dropout galaxies . this is a rare ( all - sky ) population of galaxies at high redshift ( peaks at=2 - 3 ) , that are faint or undetected by wise at 3.4 and 4.6 m , yet are clearly detected at 12 and 22 m . follow - up of 25 targets at 3.6 and 4.5 , as well as optical spectra of 12 targets are also presented in the paper . combining wise data with observations from warm _ they are likely among the most luminous galaxies in the universe .

we have used the caltech submillimeter observatory ( cso ) to follow - up a sample of wise - selected , hyperluminous galaxies , so called w1w2-dropout galaxies . this is a rare ( all - sky ) population of galaxies at high redshift ( peaks at=2 - 3 ) , that are faint or undetected by wise at 3.4 and 4.6 m , yet are clearly detected at 12 and 22 m . the optical spectra of most of these galaxies show significant agn activity . we observed 14 high - redshift ( ) w1w2-dropout galaxies with sharc - ii at 350 to 850 m , with 9 detections ; and observed 18 with bolocam at 1.1 mm , with five detections . warm _ spitzer _ follow - up of 25 targets at 3.6 and 4.5 , as well as optical spectra of 12 targets are also presented in the paper . combining wise data with observations from warm _ spitzer _ and cso , we constructed their mid - ir to millimeter spectral energy distributions ( seds ) . these seds have a consistent shape , showing significantly higher mid - ir to submm ratios than other galaxy templates , suggesting a hotter dust temperature . we estimate their dust temperatures to be k using a single - temperature model . their infrared luminosities are well over 10l . these seds are not well fitted with existing galaxy templates , suggesting they are a new population with very high luminosity and hot dust . they are likely among the most luminous galaxies in the universe . we argue that they are extreme cases of luminous , hot dust - obscured galaxies ( dogs ) , possibly representing a short evolutionary phase during galaxy merging and evolution . a better understanding of their long - wavelength properties needs alma as well as _ herschel _ data .

1208.5518

r

of the 14 high redshift w12drop galaxies observed with sharc - ii at 350 @xmath2 m , nine were detected at @xmath38 3 @xmath27 or above . the relatively high detection rate of these w12drop galaxies at 350 @xmath2 m implies they are a submillimeter bright population with high infrared luminosity . we also observed three of the 14 targets using the sharc - ii 450 @xmath2 m band , with one detection and one marginal detection ( 2@xmath27 - 3@xmath27 ) ; and observed one ( w0410@xmath300913 , which has the brightest 350@xmath2 m flux density ) in the 850 @xmath2 m band , with a detection . the flux densities of the detections are presented in table 3 . we used bolocam to follow - up 18 w12drop galaxies at z@xmath281.7 in the 1.1 mm band , including six of the galaxies that were observed with sharc - ii . we obtained five detections , and 13 useful upper limits . flux densities of the detected targets and 95@xmath39 confidence ( 2 @xmath27 ) upper limits for undetected targets are presented in table 3 . we also tabulate in table 3 _ _ spitzer _ _ 3.6 and 4.5 @xmath2 m , and wise 12 and 22 @xmath2 m measurements . w0149 + 2350 was observed with the submillimeter array ( sma ) at 1.3 mm ( wu , bussmann , et al . in prep ) . we list this sma measurement in the 1.1 mm column in table 3 . taking the 3.6 @xmath2 m to 1.1 mm measurements from table 3 , we construct the mid - ir to millimeter sed for w12drop galaxies . figure 3 shows seds for the 9 sharc - ii detected w12drop galaxies compared with galaxy models . in the first panel we overlay a wide range of templates at the corresponding redshift for one w12drop galaxy , normalized to the same w4 flux densities . these templates include the starburst - dominated galaxy arp220 , the agn - starburst blend mrk231 , type i ( unobscured ) , type ii ( obscured ) agn models ( qso 1 and qso 2 ) from polletta et al . ( 2007 ) , a torus model ( polletta et al . 2006 ) , and simulation models of dogs ( narayanan et al . 2010 ) . in the remaining panels we overlay only the arp220 and mark231 templates . the most notable feature is the apparently flat seds extending from the mid - ir to the submillimeter in all of these w12drop galaxies . at 3.6 and 4.5 @xmath2 m , large visual extinction must be added to the comparison templates to match the data , suggesting they are highly obscured . if we normalize all seds at their 22 @xmath2 m flux densities , then the submm emission of w12drop galaxies is much fainter than expected for any other population , indicating their mid - ir to submm flux ratio is unusually high . starburst models miss these seds by a large margin . qso models are better , and the closest match is from the agn dust torus model , but the fit is still poor . to quantitatively show the high mid - ir to submm ratio , we compare @xmath68l@xmath68(24@xmath4)/@xmath68l@xmath68(350@xmath4 ) in w12drops to this ratio in smgs and dogs in figure 4a . figure 5 shows the seds of all submm detected w12drops plotted at their rest frame wavelength in @xmath68l@xmath69 units , normalized by their total luminosity ( see the next section ) . this figure shows a fairly consistent sed for all the w12drop galaxies reported in this paper . this sed has a power - law in the mid - ir ( 1 - 5 @xmath2 m ) , a mid - ir bump that dominates the total luminosity contribution , and becomes flat in the mid - ir to submm . the typical sed of w12drops is quite different from any existing galaxy templates , indicating they may be a new type of galaxy . their seds apparently peak at significantly shorter wavelengths than other galaxy templates , indicating hotter average dust temperatures . in order to understand the nature of the w12drop galaxies , we need to estimate their luminosities and dust temperatures . the standard method to do this is to fit several black - body models with wavelength - dependent opacities to fit sed points along a large range of wavelengths , to constrain both temperatures and luminosities . we already know that w12drop galaxies have unusually high mid - ir to submm ratios , and that the major luminosity comes from 24@xmath4 to 350@xmath4 emission ( see figure 5 ) , so this is clearly the key wavelength range to characterize . at redshift 2 - 3 , the irac [ 3.6 ] and [ 4.5 ] bands ( rest wavelength 0.8 - 1.5 @xmath2 m ) may be significantly affected by stellar light , and at longer wavelengths , we see indications that these w12drop galaxies may have components in addition to a hot - dust component ( see section 4 ) . in many cases infrared - luminous galaxies are dominated by one major dust component , and can be approximated by a single - temperature modified blackbody model . for example , a single dust temperature model provides a good description of the far - ir and submm / mm seds of smgs ( e.g. magnelli et al . 2012 ) , with typical dust temperatures of 30 - 40 k ( chapman et al . 2005 , kovcs et al . 2006 , coppin et al . 2008 , wu et al . 2009 , magnelli et al . 2012 ) . most dogs can also be described by a single - temperature model with dust temperatures of 20 - 40 k ( melbourne et al . 2012 ) . because the peak of the w12drop seds is not well sampled in the data presented here , it is unclear whether their 24@xmath4 to 350@xmath4 emission can be well described by a single - temperature model , and we are obtaining _ herschel _ data to better determine this . in this paper we use a single - temperature model to describe the bulk of the emission from w12drops . we apply a single temperature , modified black - body model combined with a power - law model , to fit the mid - ir to mm seds . at lower frequencies we use @xmath70 , where @xmath71 is the plank function and @xmath72 is the dust emissivity index with @xmath73 , attached smoothly to which at higher frequencies is a power - law with @xmath74 . the two portions are joined at the frequency when the modified black - body slope equals that of the power - law ( @xmath57 ) . the @xmath57 parameter and dust temperature @xmath75 are constrained by w3 , w4 and 350@xmath2 m data , as well as 450@xmath2 m , 850@xmath2 m and 1.1 mm data when available . these data do not absolutely determine the shape of the sed , but the combination of the @xmath57 and @xmath75 parameters provide a reasonable measure of the peak frequency of the sed . in table 4 , we give the derived dust temperatures and mid - ir power - law indexes from this model . the derived dust temperatures of w12drops range from 60 k to 123 k , with a median value of 94 k. we applied this same model to calculate dust temperatures for dogs in bo@xmath76tes field , using similar data from melbourne et al . we used their reported irac 8@xmath4 and mips 24@xmath4 data in place of w3 and w4 to calculate @xmath57 , together with their spire 350 and 500 @xmath4 data to estimate the dust temperature . we obtained similar dust temperatures to the 20 - 40 k reported by melbourne et al . this confirms that w12drop galaxies are much hotter than typical dogs . our single - temperature model also provides a luminosity when @xmath57 , @xmath72 and t are fixed . however this luminosity is sensitive to the data points close to the peak , which is not well sampled here . therefore instead , we use a simple , but conservative method to estimate the total luminosity , which is to simply connect the data points of all the available sed points with power - laws , and integrate the total flux densities . this method may miss the luminosity close to the peak of the sed , so it provides a lower bound to the true luminosity . we list the conservative total luminosity calculated between 2 - 1000 @xmath2 m in table 4 . the derived total luminosities range from 1.7 @xmath77 ( w0211@xmath302242 ) , to 1.8 @xmath78 ( w0410@xmath300913 ) , confirming that these galaxies are very luminous , well above the @xmath79 threshold for hylirgs .

the optical spectra of most of these galaxies show significant agn activity . we observed 14 high - redshift ( ) w1w2-dropout galaxies with sharc - ii at 350 to 850 m , with 9 detections ; and observed 18 with bolocam at 1.1 mm , with five detections . warm _ spitzer _ spitzer _ and cso , we constructed their mid - ir to millimeter spectral energy distributions ( seds ) . herschel _ data .

we have used the caltech submillimeter observatory ( cso ) to follow - up a sample of wise - selected , hyperluminous galaxies , so called w1w2-dropout galaxies . this is a rare ( all - sky ) population of galaxies at high redshift ( peaks at=2 - 3 ) , that are faint or undetected by wise at 3.4 and 4.6 m , yet are clearly detected at 12 and 22 m . the optical spectra of most of these galaxies show significant agn activity . we observed 14 high - redshift ( ) w1w2-dropout galaxies with sharc - ii at 350 to 850 m , with 9 detections ; and observed 18 with bolocam at 1.1 mm , with five detections . warm _ spitzer _ follow - up of 25 targets at 3.6 and 4.5 , as well as optical spectra of 12 targets are also presented in the paper . combining wise data with observations from warm _ spitzer _ and cso , we constructed their mid - ir to millimeter spectral energy distributions ( seds ) . these seds have a consistent shape , showing significantly higher mid - ir to submm ratios than other galaxy templates , suggesting a hotter dust temperature . we estimate their dust temperatures to be k using a single - temperature model . their infrared luminosities are well over 10l . these seds are not well fitted with existing galaxy templates , suggesting they are a new population with very high luminosity and hot dust . they are likely among the most luminous galaxies in the universe . we argue that they are extreme cases of luminous , hot dust - obscured galaxies ( dogs ) , possibly representing a short evolutionary phase during galaxy merging and evolution . a better understanding of their long - wavelength properties needs alma as well as _ herschel _ data .

1208.5518

i

wise has discovered a possibly new type of object , the w12drop galaxies . the results of our cso submm / mm follow - up observations for a subsample of w12drop galaxies are as follows : \2 . the seds constructed from wise , warm _ spitzer _ and cso data reveal consistent features for w12drop galaxies . these seds show a power - law shape in the mid - ir , and are apparently flat from the mid - ir to submm / mm . their seds have unusually high mid - ir to submm luminosity ratios , indicating a hotter dust temperature than other populations . their seds can not be well fit with existing galaxy templates , indicating they are likely a new population . using power - laws to connect the sed data points , we estimate their total luminosities to be at least 1.7 @xmath77 to 1.8 @xmath78 . using a single - temperature modified blackbody model with @xmath72=1.5 , we estimate their dust temperatures to be 60 k to 120 k , much hotter than other infrared luminous galaxies . besides the hot dust component , they may also have colder dust components that are similar to starburst galaxies . w12drop galaxies in this paper would also be selected as dogs , but are at least 10 times more luminous and 10000 times rarer . they may be the extreme cases of very luminous , hot dogs , and may represent a short evolutionary phase during galaxy merging , following the phase of smg , bump dog and power - law dog . j. wu and r. assef were supported by an appointment to the nasa postdoctoral program at the jet propulsion laboratory , administered by oak ridge associated universities through a contract with nasa . n. evans acknowledges support from nsf grant ast-1109116 . this publication makes use of data products from the wide - field infrared survey explorer , which is a joint project of the university of california , los angeles , and the jet propulsion laboratory / california institute of technology , funded by the national aeronautics and space administration . this work is based on observations made with the caltech submillimeter observatory , which is operated by the california institute of technology under funding from the national science foundation , contract ast 90 - 15755 . this work uses data obtained from the _ spitzer _ space telescope , which is operated by the jet propulsion laboratory , california institute of technology under contract with nasa . some of the data presented herein were obtained at the w.m . keck observatory , which is operated as a scientific partnership among caltech , the university of california and nasa . the keck observatory was made possible by the generous financial support of the w.m . keck foundation . some data reported here were obtained at the mmt observatory , a joint facility of the university of arizona and the smithsonian institution . this paper uses data from sdss ( dr 8) . funding for sdss - iii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , and the u.s . department of energy office of science . the sdss - iii web site is http://www.sdss3.org/. dey , a. , soifer , b. t. , desai , v. , brand , k. , le floch , e. , brown , m. j. i. , jannuzi , b. t. , armus , l. , bussmann , s. , brodwin , m. , bian , c. , eisenhardt , p. , higdon , s. j. , weedman , d. , willner , s. p. 2008 , , 677 , 943 sayers , j. , golwala , s. r. , rossinot , p .. , ade , p. a. r. , aguirre , j. e. , bock , j. j. , edgington , s. f. , glenn , j. , goldin , a. , haig , d. , lange , a. e. , laurent , g. t. , mauskopf , p. d. , nguyen , h. t. 2009 , , 690 , 1597 w0026 + 2015 & 00:26:09.24 & + 20:15:56.2 & 1.990 & 350 @xmath2 m & 2011 sep 9 & 1.0 & 0.045 + w0116@xmath300505 & 01:16:01.41 & -05:05:04.1 & 3.173 & 350 @xmath2 m & 2011 sep 10 & 1.0 & 0.045 + & & & & 1100 @xmath2 m & 2011 sep 18 & 2.3 & 0.15 w0149 + 2350 & 01:49:46.16 & + 23:50:14.6 & 3.228@xmath93 & 350 @xmath2 m & 2010 jul 28,31 & 2.0 & 0.05 + & & & & 450 @xmath2 m & 2010 sep 12 & 0.7 & 0.04 w0211@xmath302242 & 02:11:34.63 & -22:42:23.4 & 1.746@xmath93 & 350 @xmath2 m & 2011 sep 10 & 1.0 & 0.05 + w0220 + 0137 & 02:20:52.12 & + 01:37:11.6 & 3.122 & 350 @xmath2 m & 2010 sep 12 , 2011 sep 10 & 1.8 & 0.045 + & & & & 1100 @xmath2 m & 2011 sep 19,20 & 3.7 & 0.16,0.07 w0243 + 4158 & 02:43:44.18 & + 41:58:09.1 & 2.010 @xmath93 & 350 @xmath2 m & 2011 sep 10 & 0.8 & 0.05 + w0248 + 2705 & 02:48:58.81 & + 27:05:29.8 & 2.210 & 350 @xmath2 m & 2010 sep 13 , 2011 sep 9 & 2.8 & 0.045 + & & & & 1100 @xmath2 m & 2011 feb 19,20,22 , sep 18 - 20 & 7.4 & 0.15,0.07 w0338 + 1941 & 03:38:51.33 & + 19:41:28.6 & 2.123 & 350 @xmath2 m & 2011 sep 10 & 0.8 & 0.05 + w0410@xmath300913 & 04:10:10.60 & -09:13:05.2 & 3.592 & 350 @xmath2 m & 2011 feb 21 , 2011 sep 9 & 2.3 & 0.95 , 0.045 + & & & & 850 @xmath2 m & 2011 feb 16 - 18 & 4.3 & 0.12 & & & & 1100 @xmath2 m & 2010 dec 12 - 14 & 7.3 & 0.14,0.1 w0422@xmath301028 & 04:22:48.82 & -10:28:32.0 & 2.227@xmath93 & 1100 @xmath2 m & 2011 sep 17 & 2.7 & 0.21 + w0542@xmath302705 & 05:42:30.90 & -27:05:40.5 & 2.532 & 350 @xmath2 m & 2010 sep 13 & 0.4 & 0.05 + w0757 + 5113 & 07:57:25.07 & + 51:13:19.7 & 2.277 @xmath93 & 1100 @xmath2 m & 2011 feb 18,22 & 4.0 & 0.21 + w0851 + 3148 & 08:51:24.78 & + 31:48:56.1 & 2.640 & 1100 @xmath2 m & 2010 dec 13,14 & 5.3 & 0.13,0.1 + w0856 + 0005 & 08:56:28.08 & + 00:05:48.7 & 2.519 @xmath93 & 1100 @xmath2 m & 2011 feb 20 & 2.7 & 0.20 + w0859 + 4823 & 08:59:29.94 & + 48:23:02.3 & 3.245@xmath93 & 1100 @xmath2 m & 2010 dec 13 - 14,2011 feb 16 - 18 & 6.7 & 0.11,0.13 + w0926 + 4232 & 09:26:25.44 & + 42:32:51.9 & 2.498 & 1100 @xmath2 m & 2011 feb 19 & 4.0 & 0.28 + w1146 + 4129 & 11:46:12.87 & + 41:29:14.3 & 1.772 @xmath93 & 1100 @xmath2 m & 2011 feb 16 & 3.0 & 0.15 + w1316 + 3512 & 13:16:28.53 & + 35:12:35.1 & 1.956 @xmath93 & 1100 @xmath2 m & 2011 feb 19 & 2.7 & 0.21 + w1409 + 1335 & 14:09:25.56 & + 13:35:02.1 & 3.048 @xmath93 & 1100 @xmath2 m & 2011 feb 17,22 & 2.3 & 0.1 , 0.2 + w1422 + 5613 & 14:22:28.86 & + 56:13:55.6 & 2.524 & 1100 @xmath2 m & 2011 feb 18,20,21 & 9.0 & 0.2 + w1603 + 2745 & 16:03:57.39 & + 27:45:53.3 & 2.633 @xmath93 & 350 @xmath2 m & 2010 sep 13 & 0.5 & 0.04 + w1814 + 3412 & 18:14:17.30 & + 34:12:25.0 & 2.452 @xmath94 & 350 @xmath2 m & 2010 jul 13,23 & 2.7 & 0.06 , 0.04 + & & & & 450 @xmath2 m & 2010 sep 12,13 & 1.8 & 0.045 & & & & 1100 @xmath2 m & 2010 jun 17,18 & 6.0 & 0.1 w1830 + 6504 & 18:30:13.53 & + 65:04:20.5 & 2.653 & 350 @xmath2 m & 2011 sep 9,10 & 2.7 & 0.05 + w1835 + 4355 & 18:35:33.71 & + 43:55:49.1 & 2.298 @xmath93 & 350 @xmath2 m & 2010 sep 12 & 1.0 & 0.04 + & & & & 450 @xmath2 m & 2010 sep 13 & 0.6 & 0.04 w2207 + 1939 & 22:07:43.84 & + 19:39:40.3 & 2.022 @xmath93 & 1100 @xmath2 m & 2010 dec 14 & 1.8 & 0.1 + w2238 + 2653 & 22:38:10.20 & + 26:53:19.8 & 2.405 & 1100 @xmath2 m & 2011 sep 20 & 1.7 & 0.075 + w0026@xmath952015 & keck / lris & 2010 nov 08 & 600 + 300 & 1.990 & ly@xmath57 , nv , civ , heii , [ neiv ] , mgii + w0116@xmath300505 & mmt / bcs & 2010 dec 04 & @xmath96 & 3.173 & ly@xmath72,ly@xmath57,nv , siiv / oiv + w0220@xmath950137 & mmt / bcs & 2010 dec 04 & @xmath96 & 3.122 & ly@xmath72,ly@xmath57,nv , siiv / oiv + w0248@xmath952705 & keck / lris & 2010 nov 09 & @xmath97 & 2.210 & ly@xmath57,cii],mgii + w0338@xmath951941 & keck / lris & 2011 feb 02 & @xmath98 & 2.123 & ly@xmath57 + w0410@xmath300910 & keck / lris & 2010 nov 08 & @xmath99 & 3.592 & civ , heii ( ly@xmath57 at dichroic ) + w0542@xmath302705 & keck / lris & 2010 nov 08 & @xmath97 & 2.532 & ciii , ovi , ly@xmath57,nv , ... + w0851@xmath953148 & keck / lris & 2011 nov 08 & @xmath97 & 2.640 & ovi , ly@xmath57,civ , heii , ciiii],cii ] + w0926@xmath954232 & keck / lris & 2011 feb 02 & @xmath98 & 2.498 & absorption lines only + w1422@xmath955613 & keck / lris & 2010 jul 15 & @xmath97 & 2.524 & ly@xmath57,nv , civ + w1830@xmath956504 & keck / lris & 2010 jul 13 & @xmath99 & 2.653 & likely ly@xmath57 + w2238@xmath952653 & keck / lris & 2010 nov 08 & @xmath98 & 2.405 & ly@xmath57 , nv , siiv / oiv , civ + llcccccccc w0026 + 2015 & 22.10 & 40.1(2.0 ) & 80.5(2.0 ) & 2.77(0.13 ) & 15.05(0.97 ) & @xmath100 & ... & ... & ... + w0116@xmath300505 & 21.38 & 50.7(2.2 ) & 89.4(2.3 ) & 2.39(0.13 ) & 12.96(1.00 ) & 36(12 ) & ... & ... & @xmath101 + w0149 + 2350 & @xmath3122.9 & 19.7(1.7 ) & 34.7(1.5 ) & 1.77(0.10 ) & 9.18(0.76 ) & 29(8 ) & 35(9 ) & ... & 2(0.4)@xmath94 + w0211@xmath302242 & & 30.5(11)@xmath102 & 78.0(10)@xmath102 & 3.31(0.11 ) & 11.31(0.73 ) & 56(15 ) & ... & ... & ... + w0220 + 0137 & 21.84 & 25.2(1.8 ) & 38.4(1.4 ) & 1.78(0.10 ) & 11.98(0.81 ) & 43(9 ) & ... & ... & 6.2(2.0 ) + w0243 + 4158 & ... & 23.1(1.7 ) & 70.7(2.0 ) & 2.56(0.13 ) & 9.02(0.93 ) & 38(13 ) & ... & ... & ... + w0248 + 2705 & ... & 31.5(1.9 ) & 52.0(1.6 ) & 2.04(0.14 ) & 11.11(1.05 ) & 32(8 ) & ... & ... & @xmath103 + w0338 + 1941 & & 12.2(1.6 ) & 37.5(1.6 ) & 1.97(0.14 ) & 10.27(0.99 ) & @xmath104 & ... & ... & ... + w0410@xmath300913 & ... & 26.7(1.8 ) & 46.1(1.5 ) & 2.45(0.14 ) & 12.35(0.99 ) & 118(17 ) & ... & 40(14 ) & 13.6(2.6 ) + w0422@xmath301028 & ... & 18.0(1.6 ) & 55.0(1.6 ) & 2.74(0.13 ) & 10.70(1.02 ) & ... & ... & ... & @xmath105 + w0542@xmath302705 & & 24.6(1.7 ) & 29.2(1.2 ) & 2.55(0.11 ) & 14.08(0.90 ) & @xmath106 & ... & ... & ... + w0757 + 5113 & 22.27 & 20.0(1.7 ) & 35.0(1.4 ) & 1.46(0.11 ) & 9.31(0.84 ) & ... & ... & ... & @xmath107 + w0851 + 3148 & 21.64 & 41.4(2.0 ) & 88.5(2.2 ) & 3.51(0.16 ) & 14.73(1.02 ) & ... & ... & ... & @xmath108 + w0856 + 0005 & @xmath3122.9 & 52.7(2.2 ) & 74.2(2.0 ) & 2.94(0.13 ) & 15.06(0.96 ) & ... & ... & ... & @xmath109 + w0859 + 4823 & @xmath3122.9 & 16.4(1.6 ) & 44.8(1.4 ) & 2.22(0.10 ) & 11.83(0.91 ) & ... & ... & ... & 6.2(1.5 ) + w0926 + 4232 & @xmath3122.9 & 18.6(1.6 ) & 28.6(1.2 ) & 1.45(0.11 ) & 7.78(0.93 ) & ... & ... & ... & @xmath110 + w1146 + 4129 & @xmath3122.9 & 23.6(1.7 ) & 45.7(1.5 ) & 3.90(0.13 ) & 20.35(1.05 ) & ... & ... & ... & @xmath111 + w1316 + 3512 & 22.56 & 22.0(1.7 ) & 49.4(1.5 ) & 3.00(0.12 ) & 12.62(0.94 ) & ... & ... & ... & @xmath112 + w1409 + 1335 & @xmath3122.9 & 6.9(0.4 ) & 16.4(1.0 ) & 1.63(0.09 ) & 9.44(0.73 ) & ... & ... & ... & 5.7(2.1 ) + w1422 + 5613 & @xmath3122.9 & 28.6(1.8 ) & 74.3(1.9 ) & 3.07(0.09 ) & 11.95(0.68 ) & ... & ... & ... & @xmath113 + w1603 + 2745 & @xmath3122.9 & 29.9(1.8 ) & 47.6(1.5 ) & 3.15(0.12 ) & 9.53(0.87 ) & @xmath114 & ... & ... & @xmath115 + w1814 + 3412 & 23.00 & 20.8(2.1 ) & 26.5(1.9 ) & 1.86(0.10 ) & 14.38(0.86 ) & 33(9 ) & @xmath116 & ... & @xmath117 + w1830 + 6504 & @xmath3122.9 & 14.2(1.6 ) & 41.9(1.4 ) & 2.25(0.05 ) & 7.56(0.34 ) & @xmath104 & ... & ... & ... + w1835 + 4355 & ... & 51.5(2.2 ) & 142.8(3.0 ) & 6.13(0.13 ) & 27.05(0.87 ) & 46(16 ) & 31(14 ) & ... & ... + w2207 + 1939 & @xmath3122.9 & 41.7(2.0 ) & 57.8(1.7 ) & 1.49(0.11 ) & 10.27(0.90 ) & ... & ... & ... & @xmath101 + w2238 + 2653 & 22.77 & 42.2(2.0 ) & 58.8(1.6 ) & 2.35(0.11 ) & 17.15(0.98 ) & ... & ... & ... & 6.0(2.2 ) + w0116@xmath300505 & 123@xmath1188 & 2.42@xmath1180.15 & 7.4 @xmath119 + w0149 + 2350 & 100@xmath1185 & 2.05@xmath1180.10 & 5.7 @xmath119 + w0211@xmath302242 & 60@xmath1185 & 1.73@xmath1180.10 & 1.7 @xmath119 + w0220 + 0137 & 118@xmath1186 & 2.50@xmath1180.15 & 7.1 @xmath119 + w0243 + 4158 & 68@xmath1185 & 1.81@xmath1180.20 & 2.0 @xmath119 + w0248 + 2705 & 87@xmath1188 & 2.28@xmath1180.10 & 2.8 @xmath119 + w0410@xmath300913 & 82@xmath1185 & 2.16@xmath1180.10 & 1.8 @xmath120 + w1814 + 3412 & 113@xmath1187 & 2.89@xmath1180.10 & 4.0 @xmath119 + w1835 + 4355 & 94@xmath11810 & 1.96@xmath1180.10 & 6.5 @xmath119 +

these seds have a consistent shape , showing significantly higher mid - ir to submm ratios than other galaxy templates , suggesting a hotter dust temperature . we estimate their dust temperatures to be k using a single - temperature model . these seds are not well fitted with existing galaxy templates , suggesting they are a new population with very high luminosity and hot dust . we argue that they are extreme cases of luminous , hot dust - obscured galaxies ( dogs ) , possibly representing a short evolutionary phase during galaxy merging and evolution .

we have used the caltech submillimeter observatory ( cso ) to follow - up a sample of wise - selected , hyperluminous galaxies , so called w1w2-dropout galaxies . this is a rare ( all - sky ) population of galaxies at high redshift ( peaks at=2 - 3 ) , that are faint or undetected by wise at 3.4 and 4.6 m , yet are clearly detected at 12 and 22 m . the optical spectra of most of these galaxies show significant agn activity . we observed 14 high - redshift ( ) w1w2-dropout galaxies with sharc - ii at 350 to 850 m , with 9 detections ; and observed 18 with bolocam at 1.1 mm , with five detections . warm _ spitzer _ follow - up of 25 targets at 3.6 and 4.5 , as well as optical spectra of 12 targets are also presented in the paper . combining wise data with observations from warm _ spitzer _ and cso , we constructed their mid - ir to millimeter spectral energy distributions ( seds ) . these seds have a consistent shape , showing significantly higher mid - ir to submm ratios than other galaxy templates , suggesting a hotter dust temperature . we estimate their dust temperatures to be k using a single - temperature model . their infrared luminosities are well over 10l . these seds are not well fitted with existing galaxy templates , suggesting they are a new population with very high luminosity and hot dust . they are likely among the most luminous galaxies in the universe . we argue that they are extreme cases of luminous , hot dust - obscured galaxies ( dogs ) , possibly representing a short evolutionary phase during galaxy merging and evolution . a better understanding of their long - wavelength properties needs alma as well as _ herschel _ data .

1204.1535

i

stars form in a diverse range of environments within molecular clouds . these cloud environments include crowded , massive clusters heated by o stars ( e.g. in orion ) , smaller clusters without high mass stars ( e.g. in ophiuchus ) , or isolated , cold dark clouds containing low mass stars ( e.g. in taurus ) . the temperatures , densities , and turbulent linewidths of the natal molecular gas can vary systematically between these regions @xcite , and the surface density of young stellar objects ( ysos ) can vary by over two orders of magnitude @xcite . this motivates us to study how these different environments affect the outcomes of the star formation process . despite significant differences in gas temperature , column density , and the turbulent velocities , the star forming regions and clusters in our galaxy exhibit remarkably similar initial mass functions . there may be a few exceptions : @xcite have compared the imfs from taurus with chamaeleon i and ic-348 and find that taurus has a significant excess of stars between 0.6 and 0.8 m@xmath2 . nevertheless , the similarity between the imfs of dark clouds like chamaeleon i , clusters with b - stars such as ic 348 , and massive clusters with o and b stars such as the orion nebula cluster suggests that the imf is remarkably invariant . although the imf averaged over a star forming region or cluster may be universal , there is some evidence that masses are initially segregated within clouds or within clusters . massive stars are found primarily in the center of clusters , although it not clear whether this is the result of primordial mass segregation or dynamical evolution @xcite . the detection of compact groups of massive protostars in the centers of clusters is evidence for primordial mass segregation since such objects would have little time for dynamical evolution @xcite . mass segregation is also observed in small groups of young stars : @xcite studied groups of 20 and 40 stars in the taurus and perseus molecular clouds and found that the most massive members ( in some cases with a mass of only 1 m@xmath2 ) are found preferentially near the centers of the groups . in such small groups , it is unlikely that dynamical evolution has occurred since the relaxation time of the group exceeds 5 myr , longer than the estimated ages of the groups @xcite . these observations are evidence for primordial mass segregation , with the imf in the centers of clusters biased towards higher mass stars . an understanding of the origin of the imf , and the potential primordial mass segregation within star forming regions , requires a better knowledge of both the initial conditions leading to the formation of stars as well as the process by which the gas is subsequently accreted onto the star . work on the initial conditions has focused on the determining the mass function of dense molecular cores that collapse into stars ( hereafter : core mass function or cmf ) . the similarity in the shapes of the imf and cmf has led to the suggestion that the imf reflects the cmf at later stages if a fixed percentage of the core mass is accreted onto the central protostar . although this provides an attractive model for a universal imf , there are several questions regarding this model . first , completeness and signal - to - noise issues may contribute to the observed shape of the cmf @xcite . second , it is unclear whether many of the observed star - less cores are gravitationally bound and capable of forming stars @xcite . third , the most massive cores are observed to form groups of stars , not single stars , and consequently , the high mass end of the cmf may describe a mass function for small stellar groups and not individual stars @xcite . fourth , the collapse of the core may be followed by the infall of gas from the surrounding molecular cloud resulting in a final stellar mass greater than that of the initial core @xcite . finally , it is known that young stars have stellar outflows and winds that mediate the infall of gas onto the central system and the accretion of gas onto the central protostar , thus the final mass must be in part determined by protostellar evolution @xcite . like the imf , a number of investigations have found that the cmf is also remarkably invariant in star forming clouds ( e.g. * ? ? ? . however , these studies may not be able to detect variations in the cmf due to the limited angular resolution of the observations and the relatively small number of detected cores . furthermore , it remains to be seen if the core masses are segregated within molecular clouds . the study presented in this paper is part of a larger effort to build a bridge between the initial conditions of star formation ( the cmf ) and the resulting ensemble properties of the nascent stars ( the imf ) . it is in the protostellar phase that the mass from the collapsing core is accreted onto a star ; thus , protostellar evolution must play a key role in determining the properties of a nascent star . our understanding of protostars is limited by the difficulty in measuring their basic properties . the radiation from the accreting protostar is reprocessed or scattered by a non - spherical infalling envelope and disk . consequently , observations spanning near- to far - ir wavelength coupled with radiative transfer codes are needed to constrain fundamental attributes such as the emitted protostar luminosity , the inner envelope density , and the geometry of the envelope and outflow cavities . for this reason , current work has focused on the most readily measured property of a protostar : its observed luminosity . the determination of the protostellar luminosity function in the nearest clouds by the _ spitzer c2d legacy program has motivated several theoretical studies showing that the luminosity functions provide an important constraint on protostellar evolution @xcite . we present here an observational study of protostellar luminosity functions in nine nearby ( @xmath3 1 kpc ) molecular clouds : orion ( combining the orion a and b clouds ) , mon r2 , cep ob3 , taurus , and the _ c2d _ mapped regions of serpens , perseus , ophiuchus , lupus i , lupus iii , and lupus iv , and chamaeleon ii . this study is motivated by the availability of _ spitzer _ @xmath4 @xmath5 surveys of each of these clouds . with spitzer _ , we are capable of identifying and classifying young stellar objects ( ysos ) and , specifically , protostars using mid - infrared photometry . the protostellar sed peaks longward of the j , h , and k@xmath6 bands , making it imperative to utilize the longer wavelength photometry to identify and characterize protostars @xcite . we utilize photometry from the 3.6 , 4.5 , 5.8 , 8.0 @xmath1 m bands from the infrared array camera ( _ irac _ ) and the 24 @xmath1 m band on the multiband imaging photometer for _ spitzer _ ( _ mips _ ) instruments aboard _ spitzer _ these wavelengths are highly sensitive to the infrared excess exhibited by ysos , with the excess even more pronounced at wavelengths longer than 24 @xmath1 m . after using the mid - ir colors to identify protostars , we use the slope of the sed and the mid - ir luminosity to estimate the bolometric luminosity of the member protostars and construct luminosity functions for each of the clouds . we then estimate the amount of contamination in our protostar sample due to reddened class ii sources , edge - on disks , and galaxies . this study expands on previous work in several ways . the chosen sample of clouds spans a range of environments , from crowded clusters with massive stars to relatively isolated regions of star formation . we present the first protostellar luminosity functions constructed from the _ spitzer _ surveys of the orion , mon r2 and cep ob3 clouds , each of which is forming massive stars . we then compare luminosity functions to test whether the luminosity function is universal , or whether it shows distinct differences between clouds as first suggested in a comparison of the taurus and ophiuchus clouds by @xcite . we also look for spatial variations in the luminosity function within individual clouds by comparing regions of high and low stellar density . finally , we compare our luminosity function with recent models of protostellar accretion . variations in the protostellar luminosity function are of key interest , since they may trace how differences in the environment affect the star formation process . the luminosity of a protostar is the sum of the intrinsic luminosity of the central protostar and the accretion luminosity generated by matter falling onto the protostar . the accretion luminosity is proportional to the mass accretion rate , and the mass accretion rate is dependent on the rate of mass infall from the envelope ( although the accretion rate may not equal the infall rate due to episodic accretion ; * ? ? ? the mass infall rate , in turn , can depend on the properties of the surrounding gas and the physical mechanism driving infall . for example , if the mass infall results from the collapse of thermally supported cores , the infall rate increases with increasing sound speed , and hence , increasing temperature @xcite . on the other hand , if the infall is the result of bondi - hoyle accretion from a larger reservoir of gas , the infall rate increases with gas density and stellar mass @xcite . alternatively , if interactions between protostars are important , the luminosity may depend on the degree of clustering . thus , variations in the luminosity function can be used to understand the physics that mediates infall and accretion . furthermore , variations in the luminosity function may give us some insight into mass segregation . higher protostellar luminosities may imply either higher accretion rates - which can result in higher masses , or higher intrinsic luminosities - which may imply more massive protostars . although the relationship between the current luminosity and the ultimate mass is uncertain for protostars , they have the advantage of being at their birth sites . in contrast , stars used to determine imfs have typically dispersed their birth environment and have moved form their birthsites ( i.e. orion , ic 348 , * ? ? ? * ) . thus , protostars provide the means to more directly connect the properties of a forming star and the environment in which it forms . in section 2 , we overview the data reduction and photometry . the identification of protostars and the determination of their bolometric luminosities is described in section 3 . after estimating the contamination in section 4 , the protostellar luminosity functions are presented and analyzed in section 5 . there we present evidence that the protostellar luminosity functions vary not only between molecular clouds , but also within clouds . section 6 compares our luminosity functions with predicted luminosity functions from a variety of accretion models and speculates on the implication of a spatially varying luminosity function for primordial mass segregation .

we combine near- and mid - infrared photometry from 2mass j , h , and bands and _ spitzer _ 3.6 , 4.5 , 5.8 , 8.0 , and 24 m bands to create 1 - 24 m spectral energy distributions ( seds ) . using protostars from the _ c2d _ survey with well - determined bolometric luminosities , we derive a relationship between bolometric luminosity , mid - ir luminosity ( integrated from 1 - 24 m ) , and sed slope . estimations of the bolometric luminosities for protostar candidates are combined to create luminosity functions for each cloud . = 1

we identify protostars in _ spitzer _ surveys of nine star - forming molecular clouds within 1 kpc : serpens , perseus , ophiuchus , chamaeleon , lupus , taurus , orion , cep ob3 , and mon r2 , which combined host over 700 protostar candidates . these clouds encompass a variety of star forming environments , including both low mass and high mass star forming regions , as well as dense clusters and regions of sparsely distributed star formation . our diverse cloud sample allows us to compare protostar luminosity functions in these varied environments . we combine near- and mid - infrared photometry from 2mass j , h , and bands and _ spitzer _ 3.6 , 4.5 , 5.8 , 8.0 , and 24 m bands to create 1 - 24 m spectral energy distributions ( seds ) . using protostars from the _ c2d _ survey with well - determined bolometric luminosities , we derive a relationship between bolometric luminosity , mid - ir luminosity ( integrated from 1 - 24 m ) , and sed slope . estimations of the bolometric luminosities for protostar candidates are combined to create luminosity functions for each cloud . contamination due to edge - on disks , reddened class ii sources , and galaxies is estimated and removed from the luminosity functions . we find that luminosity functions for high mass star forming clouds ( orion , mon r2 , and cep ob3 ) peak near 1 l and show a tail extending toward luminosities above 100 l . the luminosity functions of the low mass star forming clouds ( serpens , perseus , ophiuchus , taurus , lupus , and chamaeleon ) do not exhibit a common peak , however the combined luminosity function of these regions peaks below 1 l . finally , we examine the luminosity functions as a function of the local surface density of ysos . in the orion molecular cloud , we find a significant difference between the luminosity functions of protostars in regions of high and low stellar density , the former of which is biased toward more luminous sources . this may be the result of primordial mass segregation , although this interpretation is not unique . we compare our luminosity functions to those predicted by models and find that our observed luminosity functions are best matched by models which invoke competitive accretion , although we do not find strong agreement of the high mass star forming clouds with any of the models . = 1

1204.1535

i

we identify 727 protostar candidates in _ spitzer _ surveys of nine star forming clouds within 1 kpc of the sun . the sample includes both nearby dark clouds forming primarily low mass stars , clouds with moderate sized clusters forming intermediate mass stars , and clouds with large clusters forming massive stars . the clouds are ophiuchus , chamaeleon ii , lupus i , iii , and iv , taurus , perseus , serpens , orion , cep ob3 , and mon r2 . with this sample , we have done the following analysis : * we estimate bolometric luminosities based on sed 3 - 24 @xmath1 m slope ( @xmath15 ) and the 1 - 24 @xmath1 m luminosity , @xmath16 . we do this by determining a relationship between @xmath17 and log(@xmath15 ) using _ sources with known bolometric luminosities , then applying the relationship to all protostars in our sample and estimating bolometric luminosities for each of our protostar candidates . * we estimate the amount of contamination from reddened class iis , edge - on disks , and background galaxies . we find that up to 20@xmath18 of our protostar candidate sample are likely edge - on disks , 4@xmath18 are likely reddened class ii objects , and 2@xmath18 are likely galaxies . these contaminating objects are removed from our sample using a statistical approach . * the resulting protostellar luminosity functions for clouds that for high mass stars ( orion , cep ob , and mon r2 ) peak near 1 l@xmath2 . the luminosity functions of each high mass sf cloud has a tail extending toward luminosities upward of 100 l@xmath2 . * the protostellar luminosity function of the low mass sf clouds ( those without high mass stars ) do not show a common peak . the combined taurus / lupus / chamaeleon luminosity function shows a marginal peak near 1 l@xmath2 , the ophiuchus luminosity function shows a marginal peak below 1 l@xmath2 , serpens shows a broad peak near 2.6 l@xmath2 , and perseus do not show a well - defined peak . none of the low mass sf clouds contain protostars at luminosities above 1000 l@xmath2 nor do they show a tail above 100 l@xmath2 . * we find significant differences between the combined low mass sf cloud luminosity function and the combined high mass sf cloud luminosity function . the median probability that they are from the same parent distribution is @xmath14 = -4.66 . thus , we do not expect the luminosity function of protostars in high mass sf clouds are from the same parent distribution as the luminosity function of protostars in low mass sf clouds . * in the orion clouds , there is a very low probability that the protostellar luminosity functions from high and low stellar density regions are drawn from the same parent distribution ; instead the luminosity function becomes increasingly biased to higher luminosities with increasing stellar density . this may be evidence for primordial mass segregation , although there are other possible explanations . a similar tend is seen in mon r2 , but the trend is weak or non - existent in cep ob3 and not present in the low mass star forming clouds . * we compare our luminosity functions with models of protostellar accretion . we do not find a good match between the model luminosity function incorporating episodic accretion of @xcite and our low mass sf cloud luminosity function . the combined luminosity function of both the high mass and low mass sf clouds are best matched by the competitive accretion model as implemented by @xcite , although other models can not be formally ruled out . competitive accretion also predicts a dependence of the accretion rate with stellar density , consistent with the variations of the luminosity function with environment we find in our high mass sf clouds . we conclude that models like competitive accretion which predict mass accretion rates that vary with both the mass of the protostar and the density of stars and gas in the surrounding environment , are best able to describe our observations .

we identify protostars in _ spitzer _ surveys of nine star - forming molecular clouds within 1 kpc : serpens , perseus , ophiuchus , chamaeleon , lupus , taurus , orion , cep ob3 , and mon r2 , which combined host over 700 protostar candidates . these clouds contamination due to edge - on disks , reddened class ii sources , and galaxies is estimated and removed from the luminosity functions . we find that luminosity functions for high mass star forming clouds ( orion , mon r2 , and cep ob3 ) peak near 1 l and show a tail extending toward luminosities above 100 l .

we identify protostars in _ spitzer _ surveys of nine star - forming molecular clouds within 1 kpc : serpens , perseus , ophiuchus , chamaeleon , lupus , taurus , orion , cep ob3 , and mon r2 , which combined host over 700 protostar candidates . these clouds encompass a variety of star forming environments , including both low mass and high mass star forming regions , as well as dense clusters and regions of sparsely distributed star formation . our diverse cloud sample allows us to compare protostar luminosity functions in these varied environments . we combine near- and mid - infrared photometry from 2mass j , h , and bands and _ spitzer _ 3.6 , 4.5 , 5.8 , 8.0 , and 24 m bands to create 1 - 24 m spectral energy distributions ( seds ) . using protostars from the _ c2d _ survey with well - determined bolometric luminosities , we derive a relationship between bolometric luminosity , mid - ir luminosity ( integrated from 1 - 24 m ) , and sed slope . estimations of the bolometric luminosities for protostar candidates are combined to create luminosity functions for each cloud . contamination due to edge - on disks , reddened class ii sources , and galaxies is estimated and removed from the luminosity functions . we find that luminosity functions for high mass star forming clouds ( orion , mon r2 , and cep ob3 ) peak near 1 l and show a tail extending toward luminosities above 100 l . the luminosity functions of the low mass star forming clouds ( serpens , perseus , ophiuchus , taurus , lupus , and chamaeleon ) do not exhibit a common peak , however the combined luminosity function of these regions peaks below 1 l . finally , we examine the luminosity functions as a function of the local surface density of ysos . in the orion molecular cloud , we find a significant difference between the luminosity functions of protostars in regions of high and low stellar density , the former of which is biased toward more luminous sources . this may be the result of primordial mass segregation , although this interpretation is not unique . we compare our luminosity functions to those predicted by models and find that our observed luminosity functions are best matched by models which invoke competitive accretion , although we do not find strong agreement of the high mass star forming clouds with any of the models . = 1

1005.4854

i

the present paper addresses a constrained optimization problem , subsuming and extending optimization tasks which arise in various areas of applications such as ( i ) low - rank tensor approximation problems from signal processing and data compression , ( ii ) geometric measures of pure state entanglement from quantum computing , ( iii ) subspace reconstruction problems from image processing and ( iv ) combinatorial problems . the problem can be stated as follows : given a collection of integer pairs @xmath2 with @xmath3 for @xmath4 and a hermitian @xmath5 matrix @xmath6 with @xmath7 , find the global maximizer of the trace function @xmath8 . here , @xmath9 is restricted to the set of all hermitian projectors @xmath10 of rank @xmath11 , which can be represented as a tensor product @xmath12 of hermitian projectors @xmath13 of rank @xmath14 . thus , one is faced with the constrained optimization task @xmath15 where @xmath1 denotes the set of all hermitian projectors of the above tensor type and @xmath16 is a shortcut for @xmath17 . we will see that it makes sense to call the above objective function @xmath18 the _ generalized rayleigh - quotient _ of @xmath6 with respect to the partitioning @xmath16 . to the best of the authors knowledge , problem ( [ grq1 ] ) has not been discussed in the literature in this general setting . however , depending on the structure of @xmath6 as well as on the choice of @xmath16 , problem ( [ grq1 ] ) relates to well - known numerical linear algebra issues : \(i ) for hermitian matrices of rank-@xmath19 , i.e. @xmath20 , it reduces to a best low - rank approximation problem for the tensor @xmath21 which satisfies @xmath22 , cf . @xcite . classical application areas of such low - rank approximations can be found in statistics , signal processing and data compression @xcite . \(ii ) a recent application in quantum computing plays a central role in characterizing and quantifying pure state entanglement . here , the distance of a pure state ( tensor ) to the set of all product states ( rank-@xmath19 tensors ) provides a geometric measure for entanglement @xcite . \(iii ) moreover , the challenging task of recovering subspaces of possibly different dimensions from noisy data known as subspace detection or subspace clustering problem in computer vision and image processing @xcite can also be cast into the above setting . more precisely , for an appropriately chosen hermitian matrix @xmath6 the subspace clustering task can be characterized by problem ( [ grq1 ] ) in the sense that for unperturbed data the global minima of the generalized rayleigh - quotient are in unique correspondence with the sought subspaces . numerical experiments in section 4 support that even for noisy data the proposed optimization yields reliable approximations of the unperturbed subspaces . \(iv ) in @xcite a certain class of combinatorial problems are recast as optimization problems for trace functions on the special unitary group . for the case when @xmath6 is a diagonal matrix , optimization task is a generalization of the applications mentioned in @xcite . our solution to problem ( @xmath23 ) is based on the fact that the constraint set @xmath24 can be equipped with a riemannian submanifold structure . this admits the use of techniques from riemannian optimization a rather new approach towards constrained optimization exploiting the geometrical structure of the constraint set in order to develop numerical algorithms @xcite . in particular , we pursue two approaches : a newton and a conjugated gradient method . on a riemannian manifold , the intrinsic newton method is usually described by means of the levi - civita connection , performing iterations along geodesics , see @xcite . a more general approach via local coordinates was initiated by shub in @xcite and further discussed in @xcite . here , we follow the ideas in @xcite and use a pair of local parametrizations normal coordinates for the push - forward and qr - type coordinates for the pull - back satisfying an additional compatibility condition to preserve quadratic convergence . thus we obtain an intrinsically defined version of the classical newton algorithm with some computational flexibility . nevertheless , for high - dimensional problems its iterations are expensive , both in terms of computational complexity and memory requirements . therefore , we alternatively propose a conjugated gradient method , which has the advantage of algorithmic simplicity at a satisfactory convergence rate . in doing so , we suggest to replace the global line - search of the classical conjugated gradient method by a one - dimensional newton - step , which yields a better convergence behavior near stationary points than the commonly used armijo - rule . as mentioned earlier , depending on the structure of @xmath6 , the above - specified problems ( i ) , ( ii ) , ( iii ) and ( iv ) are particular cases of the optimization task ( @xmath23 ) . for the best low - rank approximation of a tensor the standard numerical approach is an alternating least - squares algorithm , known as higher - order orthogonal iteration ( hooi ) @xcite . recently , several new methods also exploiting the geometric structure of the problem have been published . newton algorithms have been proposed in @xcite , quasi - newton methods in @xcite , conjugated gradient and trust region methods in @xcite . for high - dimensional tensors , all riemannian newton algorithms manifest similar problems : too high computational complexity and memory requirements . our conjugated gradient method is however , a good candidate to solve large scale problems . it exhibits locally a good convergence behavior , comparable to that of the quasi - newton methods in @xcite at much lower computational costs , which considerably reduces the necessary cpu time . for the problem of estimating a mixture of linear subspaces from sampled data points , cf . ( iii ) , our numerical approach is an efficient alternative to the classical ones : _ ad - hoc _ type methods such as k - subspace algorithms @xcite , or probabilistic methods using a maximum likelihood framework for the estimation @xcite . the paper is organized as follows . in section 2 , we familiarize the reader with the basic ingredients of riemannian optimization . in particular , we address the following topics : the riemannian submanifold structure of the constraint set @xmath1 , its isometry to the @xmath25-fold cartesian product of grassmannians , geodesics and parallel transport and the computation of the intrinsic gradient and hessian for smooth objective functions . section 3 is dedicated to the problem of optimizing the generalized rayleigh - quotient @xmath0 , including also a detailed discussion on its relation to problems ( i ) , ( ii ) , ( iii ) and ( iv ) . moreover , an analogy to the classical rayleigh - quotient is also the subject of this section . we compute the gradient and the hessian of the generalized rayleigh - quotient and derive critical point conditions . we end the section with a result on the generic non - degeneracy of its critical points . in section 4 , a newton - like and a conjugated gradient algorithm as well as numerical simulations tailored to the previously mentioned applications are given .

we introduce a generalized rayleigh - quotient on the tensor product of grassmannians enabling a unified approach to well - known optimization tasks from different areas of numerical linear algebra , such as best low - rank approximations of tensors ( data compression ) , geometric measures of entanglement ( quantum computing ) and subspace clustering ( image processing ) . we briefly discuss the geometry of the constraint set , we compute the riemannian gradient of , we characterize its critical points and prove that they are generically non - degenerated . moreover , we derive an explicit necessary condition for the non - degeneracy of the hessian . finally , we present two intrinsic methods for optimizing a newton - like and a conjugated gradient and compare our algorithms tailored to the above - mentioned applications with established ones from the literature .

we introduce a generalized rayleigh - quotient on the tensor product of grassmannians enabling a unified approach to well - known optimization tasks from different areas of numerical linear algebra , such as best low - rank approximations of tensors ( data compression ) , geometric measures of entanglement ( quantum computing ) and subspace clustering ( image processing ) . we briefly discuss the geometry of the constraint set , we compute the riemannian gradient of , we characterize its critical points and prove that they are generically non - degenerated . moreover , we derive an explicit necessary condition for the non - degeneracy of the hessian . finally , we present two intrinsic methods for optimizing a newton - like and a conjugated gradient and compare our algorithms tailored to the above - mentioned applications with established ones from the literature . riemannian optimization , grassmann manifold , multilinear rank , best approximation of tensors , subspace clustering , entanglement measure , newton method , conjugated gradient method . 14m15 , 15a69 , 65d19 , 65f99 , 65k10 , 81p68

1405.2773

i

each group can be obtained by quotienting a free group by a normal subgroup generated by a set of relators . in @xcite gromov introduced the notion of a random finitely presented group on @xmath5 generators at density @xmath6 . the idea was to fix a set of @xmath7 generators and consider presentations with @xmath8 relators , each of which is a random reduced word of length @xmath9 . gromov investigated the properties of random groups when @xmath9 goes to infinity . we say that a property occurs in the gromov density model with _ overwhelming probability _ if the probability that a random group has this property converges to @xmath10 when @xmath11 . significant results of this theory are the following : for densities @xmath1 a random group is trivial with overwhelming probability ( * ? ? ? * theorem 11 ) ; for densities @xmath12 a random group is , with overwhelming probability , infinite , hyperbolic and torsion - free ( * ? ? ? * theorem 11 ) ; for densities @xmath13 a random group does not have property ( t ) with overwhelming probability ( * ? ? ? * corollary 7.5 ) . one modification of gromov s idea is the triangular model : length of relators in the presentation is always 3 , but we let the number of generators go to infinity . precisely , for a fixed density @xmath14 , we consider a presentation on @xmath0 generators with @xmath15 relations , each of which is a random reduced word of length @xmath16 . we say that some property occurs in the triangular model with _ overwhelming probability _ if the probability that a random group has this property converges to @xmath10 when @xmath17 . this model was introduced in @xcite and further studied in @xcite . the triangular model was a way to prove that random groups in the gromov density model for densities @xmath18 have property ( t ) with overwhelming probability ( * ? ? ? * theorem b ) , @xcite . we introduce a new random group model by considering a random set of relations , each of which is a random reduced word of length four . the following notation will be used in the whole paper consider the set @xmath19 , which we will treat as an alphabet . let @xmath20 be the set of positive words of length 4 over @xmath21 and @xmath22 be the set of all cyclically reduced words of length 4 over @xmath21 . note that @xmath23 and @xmath24 up to a multiplicative constant . by @xmath25 we will denote the free group generated by the elements of @xmath21 . by _ relators _ we will understand words over generators and by _ relations _ equalities holding in the group . [ def : gcar ] for @xmath6 let us choose randomly , with uniform distribution , a subset @xmath26 such that @xmath27 . quotienting @xmath25 by the normal closure of the set @xmath28 , we obtain a _ random group in the positive square model at density d_. [ def : overwhelming ] we say that property @xmath29 occurs in the positive square model with _ overwhelming probability _ if the probability that a random group has property @xmath29 converges to @xmath10 when @xmath17 . the most important group properties which we consider are : being trivial , being free , being hyperbolic and having property ( t ) . we prove , as in the gromov model , that for densities @xmath30 a random group in the positive square model is trivial with overwhelming probability ( theorem [ thm : triv ] ) and that for densities @xmath2 a random group is with overwhelming probability hyperbolic ( corollary [ cor : hyp ] ) . moreover we show that for densities @xmath31 a random group in the positive square model does not have property ( t ) ( theorem [ thm : nt ] ) . inspired by the results in the triangular model we prove that for densities @xmath4 in the positive square model a random group is free with overwhelming probability ( theorem [ thm : free ] ) . we also introduce abstract diagrams with fixed edges ( definition [ def : fix ] ) and prove a generalization of the isoperimetric inequality ( theorem [ thm : lab ] ) . it is not known what is the optimal density threshold for a property of not having property ( t ) in the gromov density model . this model seems to be much harder to analyze than the triangular model , where we know that for densities @xmath32 a random group is free with overwhelming probability ( * ? ? ? * proposition 30 ) and that for densities @xmath18 a random group has property ( t ) with overwhelming probability ( * ? ? ? * theorem a ) , @xcite . in our model we expect to find the critical density threshold for having property ( t ) in further research . we also expect that for densities @xmath32 a random group in the square model can be cubulated ( see @xcite for discussion about cubulating random groups in the gromov density model ) . the advantage of the positive square model is that since the length of relators is even , we can consider the hypergraphs in the presentation complex and cayley complex of the random group ( definition [ def : hyp ] ) , which is not possible in the triangular model . as we will see , hypergraphs are a useful tool to investigate many group theoretic and topological properties . we have decided to consider as relators only positive words to avoid technical annoyances , but we will show that all of our results remain true in a model where we allow non - positive words . firstly , we will define this model : [ def : gcar ] for @xmath6 let us choose randomly , with uniform distribution , a subset @xmath33 such that @xmath34 . quotienting @xmath25 by the normal closure of the set @xmath28 , we obtain a _ random group in the square model at density d_. * acknowledgment*. i would like to thank piotr przytycki for suggesting the topic of this thesis , for his help , valuable suggestions and many interesting discussions . i am also grateful to irena danilczuk jaworska , jerzy trzeciak and micha kotowski for improving this paper and many corrections .

we introduce a new random group model called the _ square model _ : we quotient a free group on generators by a random set of relations , each of which is a reduced word of length four . we prove , as in the gromov model introduced in , that for densities a random group in the square model is trivial with overwhelming probability and for densities a random group is with overwhelming probability hyperbolic . moreover we show that for densities a random group in the square model does not have property ( t ) . inspired by the results for the triangular model we prove that for densities in the square model , a random group is free with overwhelming probability . we also introduce abstract diagrams with fixed edges and prove a generalization of the isoperimetric inequality .

we introduce a new random group model called the _ square model _ : we quotient a free group on generators by a random set of relations , each of which is a reduced word of length four . we prove , as in the gromov model introduced in , that for densities a random group in the square model is trivial with overwhelming probability and for densities a random group is with overwhelming probability hyperbolic . moreover we show that for densities a random group in the square model does not have property ( t ) . inspired by the results for the triangular model we prove that for densities in the square model , a random group is free with overwhelming probability . we also introduce abstract diagrams with fixed edges and prove a generalization of the isoperimetric inequality .

1008.0828

i

our study concerns the combinatorics behind the character of the space of diagonal harmonics @xmath6 and identities involving macdonald polynomials that can be used to form expressions for this character . at the root of this theory is a linear operator @xmath1 , introduced in @xcite , under which the modified macdonald polynomials @xmath7 $ ] are eigenfunctions . @xcite proved that the frobenius image of the character of @xmath6 equals @xmath8 . this gives an explicit expression involving rational functions in @xmath0 for the multiplicity of an irreducible indexed by a partition @xmath9 in the character of @xmath6 . an important open problem in this area is the shuffle conjecture " of @xcite which asserts that the coefficient of @xmath10 in @xmath8 simplifies to a @xmath0 statistic on lattice paths . a major breakthrough in this direction was made with the conjectured combinatorial formula of @xcite for the coefficient of @xmath11 in @xmath8 . in this case , the coefficient is a bi - graded version of the sign character and it is called the @xmath0-catalan @xmath12 since it reduces to the @xmath13th catalan number when @xmath14 . the combinatorial formula for @xmath12 was proven in @xcite,@xcite and pursuant work @xcite also settled the shuffle conjecture for partitions of hook - shape . however , the general case remains a mystery . an unrelated study of macdonald polynomials led to the discovery @xcite of a new family of symmetric functions called @xmath15-schur functions @xmath16 $ ] which were conjectured to refine the special combinatorial properties held by schur functions . the @xmath15-schur functions have a number of conjecturally equivalent characterizations and it has now been established in @xcite that those introduced in @xcite refine combinatorial , geometric and representation theoretic aspects of schur theory . this prompted bergeron , descouens , and zabrocki to explore the role of @xmath15-schur functions in the @xmath0-catalan theory . to this end , they conjectured in @xcite that the coefficient of @xmath17 in @xmath18 $ ] is a positive polynomial in @xmath0 and they proved their conjecture for the case that @xmath19 . our work here was initially motivated by a desire to find a combinatorial description for this coefficient in general , ideally in terms of a @xmath0-statistic on lattice paths as with the @xmath0-catalans . we found such a description , but more remarkably this led us to discover that a natural setting for the combinatorial theory of @xmath20 is created by applying @xmath1 to the general set of hall - littlewood polynomials indexed by compositions . to be precise , it was proven in @xcite that the @xmath15-schur function @xmath21 $ ] is merely a certain hall - littlewood polynomial . this led us to study @xmath1 on a hall - littlewood polynomial indexed by any partition @xmath9 . but in fact , our work carries through to the family of polynomials @xmath22 $ ] , for any composition @xmath23 , defined in terms of operators similar to jing operators . a key component in the proof of the @xmath0-catalan conjecture @xcite is the use of symmetric functions @xmath24 $ ] which decompose @xmath25 into pieces that remain positive under the action of @xmath1 . we have discovered that the @xmath22 $ ] can be used as building blocks in the @xmath0-catalan theory that decompose the @xmath24 $ ] into finer pieces , still positive under the action of @xmath1 . our conjectures on these building blocks thus refine earlier conjectures involving @xmath24 $ ] , the conjectures in @xcite , the shuffle conjecture , and the conjectures in @xcite asserting that @xmath1 applied to hall - littlewood functions have @xmath0-positive schur coefficients . loehr and warrington @xcite introduced an intricate conjecture for the combinatorics of @xmath1 applied to a schur function @xmath26 . our conjecture is extremely simple , describes the action of @xmath1 on a larger set of symmetric functions than just a basis , and refines the conjecture of loehr and warrington when @xmath1 acts on the schur function @xmath27 ( * ? ? ? * conjecture 3 ) as explained at the end of section [ nab ] . garsia , xin , and zabrocki @xcite using work of hicks @xcite have now proven our generalized @xmath0-catalan conjecture and expanded the result giving a `` compositional @xmath0-schrder '' theorem .

our conjecture refines several earlier conjectures concerning the space of diagonal harmonics including the shuffle conjecture " ( duke j. math . ( ) , pp . ) for $ ] . we bring to light that certain generalized hall - littlewood polynomials indexed by compositions are the building blocks for the algebraic combinatorial theory of-catalan sequences and we prove a number of identities involving these functions .

we introduce a-enumeration of dyck paths which are forced to touch the main diagonal at specific points and forbidden to touch elsewhere and conjecture that it describes the action of the macdonald theory operator applied to a hall - littlewood polynomial . our conjecture refines several earlier conjectures concerning the space of diagonal harmonics including the shuffle conjecture " ( duke j. math . ( ) , pp . ) for $ ] . we bring to light that certain generalized hall - littlewood polynomials indexed by compositions are the building blocks for the algebraic combinatorial theory of-catalan sequences and we prove a number of identities involving these functions .

quant-ph0508218

i

quantum computing offers a way to realize certain algorithms exponentially more efficiently than with the best known classical solutions @xcite . a substantial effort has therefore been made to develop the corresponding quantum technologies . proof - of - principle experiments demonstrating the feasibility of quantum computing have already been performed : using nuclear magnetic resonance techniques , vandersypen _ et al . _ @xcite realized a simple instance of shor s algorithm by factoring @xmath0 . a two qubit gate has been implemented in a color center in diamond , utilizing the electron spin state of the nitrogen - vacancy defect center together with a nearby nuclear spin as qubits @xcite . groups in innsbruck and boulder implemented a universal two - qubit gate in an ion trap @xcite , and the three - qubit teleportation protocol @xcite . adding more qubits to this `` proto quantum computer '' will increase the density of the motional states used for the two - qubit interaction . consequently , it will become even harder to implement clean two - qubit gates . scaling ion trap quantum computers much further therefore seems to require some form of distributed quantum information processing , possibly involving ion transport @xcite . the schemes mentioned above are based on manipulating _ stationary _ qubits such as atoms , molecules , or trapped ions . an alternative route to finding a feasible and scalable technology for building quantum computers is based on _ flying _ qubits , such as photons . the main advantage of photons is their extremely long coherence time : in vacuum and in simple dielectric media , photons do not interact with their environment , and hence do not lose their quantum information . this is why photons are usually the qubits of choice for quantum communication @xcite . however , at the same time this lack of interaction means that it is very hard to create two - photon entangling gates . it therefore came as a surprise that the bosonic symmetry requirement of the electromagnetic field , together with photon counting and proper single - photon sources , is sufficient for implementing scalable quantum computing @xcite . the overhead cost for linear optical quantum computing ( loqc ) has subsequently been brought down significantly . in particular , the one - way or cluster - state model for quantum computing @xcite has allowed for drastic improvements in the scalability @xcite . recently , a four - qubit cluster state was realized experimentally by walther _ et al_.@xcite . the main drawbacks of loqc are the difficulties of maintaining interferometric stability , the lack of practical ` on demand ' single - photon sources and the lack of quantum memories for photonic qubits @xcite . in this paper , we consider the practical advantage of combining stationary and flying qubits for the realisation of scalable quantum computing . the stationary qubits ( single photon sources ) are arranged in a network of nodes with each node processing and storing a small number of qubits . to achieve scalability , the concept of distributed quantum computing was introduced and it was proposed that distant qubits communicate with each other through the means of flying qubits ( i.e. photons ) @xcite . initial schemes for the implementation of this idea relied on entangled ancillas as a resource @xcite . others required that the photon from one source is fed into another source @xcite or a photon - mediated interaction between two fiber - coupled distant cavities needed to be established @xcite . more hybrid approaches to quantum computing can be found in refs . @xcite . other authors developed schemes for the probabilistic generation of highly entangled states between distant single photon sources @xcite . in these schemes , one generates a photon in each of the sources and then performs an entangling photon measurement . by virtue of entanglement swapping , this results in entangled stationary qubits . it has been shown that similar ideas can also result in the implementation of probabilistic remote two - qubit gates @xcite . at this point , it was believed that scalable quantum computing with distant photon sources requires additional resources such as local entangling gates @xcite or entangled ancillas in order to become deterministic . the concrete setup that we consider in this paper has recently been introduced by lim _ _ @xcite and allows for the more efficient implementation of universal two - qubit gates than previous proposals . the presented scheme consists of a network of single stationary qubits ( like trapped atoms , molecules , ions , quantum dots and nitrogen vacancy color centers ) inside optical cavities , which act as a source for the generation of single photons on demand . read - out measurements and single qubit rotations can be performed on the stationary qubits using laser pulses and standard quantum optics techniques as employed in the recent ion trap experiments in innsbruck and boulder @xcite . the main building block for the realization of a two - qubit gate , which qualifies the setup for universal quantum computing , is shown in figure [ moon ] . it requires the simultaneous generation of a photon in each source involved in the operation . afterwards the photons should pass through a linear optics setup , where a pair measurement is performed in the output ports . this photon pair measurement results either in the completion of the gate or indicates the presence of the original qubits . in the later event , the gate should be repeated . the qubits are never lost in the computation and the presented scheme has therefore been called _ repeat - until - success _ quantum computing @xcite . under realistic conditions , i.e. in the presence of finite detector efficiencies and finite success rates for the generation of a single photon on demand , the setup in figure 1 can still be used for the implementation of probabilistic gates with a very high fidelity . as shown recently by barrett and kok @xcite , it is possible to use probabilistic gates to efficiently generate graph states for one - way quantum computing @xcite . both schemes , @xcite and @xcite overcome the limitations to scalable quantum computing faced before when using the same resources . in ref . @xcite this is achieved with an eventually deterministic gate . @xcite introduced a so - called double - heralding scheme , in which the entangling photo - detection stage was employed twice to eliminate unwanted separable contributions to the density matrix . in this paper , we combine the ideas presented in our previous work @xcite . in this way , we obtain a truly scalable design for quantum computing , i.e. even in the presence of imperfect components , with several key advantages : 1 . since our system uses _ no direct qubit - qubit interactions _ , the qubits can be well isolated . not only does this allow us to address the individual qubits easily , it also means that there are fewer decoherence channels and hence fewer errors in the computation . we achieve _ robustness to photon loss_. in the presence of photon loss , the two qubit gates become non - deterministic . however , the gate failures are heralded , and so the gates can still be used to build high - fidelity entangled states , albeit in a non - deterministic manner . photon loss thus increases the overall overhead cost associated with the scheme , but does not directly reduce the fidelity of the computation . when realistic photo - detectors and optical elements are used , photon loss is inevitable and this built - in robustness is essential . our scheme largely relies only on _ components that have been demonstrated in experiments _ like atom - photon entanglement @xcite . apart from linear optics , we require only relatively good sources for the generation of single photons on demand @xcite , preferrably at a high rate @xcite , and relatively efficient but not necessarily number resolving photon detectors @xcite . combining these in a working quantum computer will be challenging , but the basic physics has been shown to be correct . 4 . the photon pair measurement is _ interferometrically stable_. since each generated photon contributes equally to the detection of a photon in the linear optics setup , fluctuations in the length between the photon source and the detectors can at most result in an overall phase factor with no physical consequences . this constitutes a significant advantage compared to previous schemes based on one - photon measurements ( the only interferometrically stable schemes are @xcite ) , since the photons do not need to arrive simultaneously in the detectors as long as they overlap within their coherence time in the setup . the basic ideas presented in this paper are _ implementation independent _ and the stationary qubits can be realised in a variety of ways . any system with the right energy - level structure and able to produce encoded flying qubits may be used . our scheme is inherently _ distributed_. hence , it can be used in applications which integrate both quantum computation and quantum communication . we show that entanglement can be generated directly between any two stationary qubits in the physical quantum computer . this significantly reduces the computational cost compared to architectures involving only nearest - neighbor interactions between the qubits @xcite . this paper is organized as follows . in the next section , we give an overview on the basic principles of measurement - based quantum computing , since the described hybrid approach to quantum computing constitutes a novel implementation of these ideas . section iii details the general principle of a remote two - qubit gate implementation . in section [ rea ] , we discuss possible gate implementations with polarization and time - bin encoded photons . in section [ cluster ] , we describe how to overcome imperfections of inefficient photon generation and detection with the help of pre - fabricated graph states . finally , we state our conclusions in section [ conc ] .

we introduce an architecture for robust and scalable quantum computation using both stationary qubits ( e.g. single photon sources made out of trapped atoms , molecules , ions , quantum dots , or defect centers in solids ) and flying qubits ( e.g. photons ) . our scheme solves some of the most pressing problems in existing non - hybrid proposals , which include the difficulty of scaling conventional stationary qubit approaches , and the lack of practical means for storing single photons in linear optics setups . we combine elements of two previous proposals for distributed quantum computing , namely the efficient photon - loss tolerant build up of cluster states by barrett and kok [ phys . rev . a * 71 * , 060310 ( 2005 ) ] with the idea of repeat - until - success ( rus ) quantum computing by lim _ et al . _ rev . the resulting gates can still be used to build graph states for one - way quantum computing . in this paper , we describe the rus method , present possible experimental realizations , and analyse the generation of graph states .

we introduce an architecture for robust and scalable quantum computation using both stationary qubits ( e.g. single photon sources made out of trapped atoms , molecules , ions , quantum dots , or defect centers in solids ) and flying qubits ( e.g. photons ) . our scheme solves some of the most pressing problems in existing non - hybrid proposals , which include the difficulty of scaling conventional stationary qubit approaches , and the lack of practical means for storing single photons in linear optics setups . we combine elements of two previous proposals for distributed quantum computing , namely the efficient photon - loss tolerant build up of cluster states by barrett and kok [ phys . rev . a * 71 * , 060310 ( 2005 ) ] with the idea of repeat - until - success ( rus ) quantum computing by lim _ et al . _ [ phys . rev . lett . * 95 * , 030505 ( 2005 ) ] . this idea can be used to perform eventually deterministic two - qubit logic gates on spatially separated stationary qubits via photon pair measurements . under non - ideal conditions , where photon loss is a possibility , the resulting gates can still be used to build graph states for one - way quantum computing . in this paper , we describe the rus method , present possible experimental realizations , and analyse the generation of graph states .

1406.7490

i

a large body of work has evolved concerning the problem of identifying an `` intruder '' vertex in a graph . as examples , one might seek to identify a malfunctioning processor in a multiprocessor network , or the location of an intruder such as a thief , saboteur or fire in a graph - modeled facility . in this paper , we introduce the new model of _ centroidal detection _ as such a graph identification problem . an early model considered the case where one could place detection devices like sonar or loran stations at vertices in a graph ; each detection device could determine the distance to the intruder s vertex location . as introduced independently in slater @xcite and harary and melter @xcite , vertex set @xmath8 is a _ locating set _ ( also called _ resolving set _ in the literature ) if for each vertex @xmath9 , the ( ordered ) @xmath10-tuple @xmath11 of distances between the detector s locations and the intruder vertex @xmath12 uniquely determines @xmath12 . a minimum cardinality locating set is called a _ metric basis _ ( also called _ reference set _ in the literature ) , and its order is the _ metric dimension _ of @xmath0 , denoted by @xmath13 . other studies involving metric bases include for example @xcite . carson @xcite and , independently , delmas , gravier , montassier and parreau @xcite ( for the latter authors , under the name of _ light @xmath14-codes _ ) considered the case in which each detection device at @xmath15 can only detect an intruder at distance at most @xmath14 . in another model , the presence of any edge @xmath16 indicates that a detection device at @xmath17 is able to detect an intruder at @xmath12 . let us denote by @xmath18 and @xmath19 $ ] the open and the closed neighbourhood of vertex @xmath17 , respectively . a set @xmath20 is a _ dominating set _ if @xmath21=v(g)$ ] . clearly , in the latter model , if every possible intruder location must be detectable , the set of detector locations must form a dominating set . the concepts of locating and dominating set were merged in slater @xcite : when a detection device at vertex @xmath17 can distinguish between there being an intruder at @xmath17 or at a vertex in @xmath18 ( but which precise vertex in @xmath18 can not be determined ) , then we have the concept of a _ locating - dominating set_. more precisely , a set @xmath22 of vertices is locating - dominating if it is dominating and every vertex in @xmath23 is dominated by a distinct subset of @xmath22 . the minimum cardinality of a locating - dominating set of graph @xmath0 is denoted @xmath24 . when one can only decide if there is an intruder somewhere in @xmath19 $ ] , one is interested in an _ identifying code _ , as introduced by karpovsky , chakrabarty and levitin @xcite . haynes , henning and howard @xcite added the condition that the locating - dominating set or identifying code not have any isolated vertices . when a detection device at @xmath17 can determine that an intruder is in @xmath18 , but will not report if the intruder is at @xmath17 itself , one is interested in _ open - locating - dominating sets _ , as introduced for the hypercube by honkala , laihonen and ranto @xcite and for all graphs by seo and slater @xcite . a bibliography of related papers is maintained by lobstein @xcite . in what follows , we will denote the path and the cycle on @xmath3 vertices by @xmath25 and @xmath26 , respectively . in this paper , we introduce the study of _ centroidal bases_. in this model , we assume that detection devices have unlimited range , as for metric bases . however , exact distances to the intruder are not known , but for detection devices @xmath27 , if there is an intruder at vertex @xmath28 , then the presence of the intruder in the graph is determined earlier by @xmath17 than by @xmath12 when @xmath17 is closer to @xmath28 than @xmath12 , that is , when @xmath29 . when @xmath30 we assume that @xmath17 and @xmath12 report simultaneously . for example , consider @xmath31 ( see figure [ fig : p8 ] ) . for vertex @xmath32 , the order in which the detectors of @xmath33 report is @xmath34 because @xmath35 . for vertex @xmath36 , we have @xmath37 , hence the order of reporting is @xmath38 . the smallest size of a set @xmath39 for which the order of reporting uniquely identifies each vertex is , in fact , four . in 1869 , jordan @xcite showed that each of the center and the ( branch weight ) centroid of a tree either consists of one vertex , or of two adjacent vertices . eccentricity _ of vertex @xmath17 is the maximum distance from @xmath17 to another vertex in graph @xmath0 , @xmath40 , and the _ center _ @xmath41 of @xmath0 is the set of vertices of minimum eccentricity . for a tree @xmath42 , the _ branch weight _ of @xmath17 , @xmath43 , is the maximum number of edges in a subtree with @xmath17 as an endpoint . the _ branch weight centroid _ of @xmath42 is the set @xmath44 of vertices with minimum branch weight in @xmath42 . in 1964 , hakimi @xcite considered two facility location problems , one involving the center . the second one involved the _ distance _ @xmath45 , measuring the total response time at @xmath17 ( this notion was called _ status _ of @xmath12 by harary in 1959 @xcite ) . the _ median _ of @xmath0 , @xmath46 , is the set of vertices of minimum distance in @xmath0 . in 1968 , zelinka @xcite showed that for any tree @xmath42 , @xmath47 , which seemed to imply that the median would be a good generalization of the branch weight centroid of a tree to an arbitrary graph . however ( with details in slater @xcite and slater and smart @xcite ) , note that components of @xmath48 of the same order , one being a path and the other a star , contribute the same value of a branch weight , but have much different distances . in trying to keep closer to the spirit of what the branch weight centroid measures , the _ centroid _ @xmath49 of an arbitrary graph @xmath0 was defined in terms of competitive facility location @xcite . for facilities located at vertices @xmath17 and @xmath12 , a customer at vertex @xmath28 is interested in which of the facilities is the closer . as defined in slater @xcite , the set @xmath50 is the set of vertex customer locations strictly closer to @xmath17 than to @xmath12 . then , @xmath51 rates how well @xmath17 does as a facility location , in comparison to @xmath12 . letting @xmath52 , the _ centroid _ of a graph @xmath0 is the set @xmath53 . when @xmath0 is a tree , the centroid and branch weight centroid are easily seen to coincide . interestingly , there are graphs @xmath0 for which @xmath54 for all @xmath55 . note that in our context of centroidal bases , detectors located at @xmath17 and @xmath12 enable us to determine if an intruder is in @xmath56 , in @xmath57 , or in @xmath58 . let @xmath59 be a set of vertices of graph @xmath0 with detection devices located at each @xmath15 . as noted , we will assume that each detection device has an unlimited range an intruder entering at any vertex @xmath28 will , at some point , have its presence noted at each @xmath15 . simply the presence will be noted , with no information about the location of the intruder . in particular , unlike in the setting of metric bases , @xmath60 will not be known . however , the time it takes before @xmath15 detects the intruder at @xmath28 will be an increasing function of the distance @xmath60 . that is , @xmath15 will indicate an intruder presence before @xmath61 whenever @xmath62 ( in our previous terminology , @xmath63 ) . we will say that @xmath28 is _ located _ first by @xmath15 , and then by @xmath61 . thus , each vertex @xmath28 has a rank ordering @xmath64 of the elements of a partition of @xmath65 ( in fact , @xmath64 is an _ ordered partition _ of @xmath65 , that is , an ordered set of disjoint subsets of @xmath65 whose union is @xmath65 ) . this ordering lists all the elements of @xmath65 in non - decreasing order by their distance from @xmath28 , with ties noted . note that the number of ordered partitions of a set @xmath65 of @xmath10 elements is the _ @xmath10-th ordered bell number _ , denoted @xmath66 ( see the book of wilf ( * ? ? ? * section 5.2 , example 1 ) ) . for @xmath67 in path @xmath68 ( see figure [ fig : p8 ] ) , @xmath69 , @xmath70 , @xmath71 , @xmath72 , @xmath73 , @xmath74 , @xmath75 and @xmath76 . vertex set @xmath77 is called a _ centroidal locating set _ of graph @xmath0 if @xmath78 for every pair @xmath79 of distinct vertices . a _ centroidal basis _ of @xmath0 is a centroidal locating set of minimum cardinality . the _ centroidal dimension _ of @xmath0 , denoted @xmath2 , is the cardinality of a centroidal basis . in our example , @xmath67 is the unique centroidal basis of path @xmath68 , and @xmath80 . observe that every graph @xmath0 has a centroidal locating set , for example , @xmath81 : each vertex @xmath28 is the only vertex having @xmath28 as the first element of @xmath64 . a useful reformulation of the definition of a centroidal locating set is as follows : [ obs : otherdef ] a set @xmath65 of vertices of a graph @xmath81 is a centroidal locating set if and only if for every pair @xmath79 of distinct vertices of @xmath81 , there exist two vertices @xmath82 in @xmath65 such that either @xmath83 but @xmath84 , or @xmath85 and @xmath86 ( in other words , @xmath87 but not @xmath28 , or @xmath88 , but not @xmath89 ) . we start in section [ sec : prelim ] by stating some preliminary observations and lemmas , and by giving bounds on parameter @xmath90 involving the order , the diameter , and other parameters of graphs ; in particular , we show that @xmath91 when @xmath0 has @xmath3 vertices and maximum degree at least 2 . in section [ sec : tightness ] , we discuss the tightness of the two aforementioned bounds by constructing graphs with small centroidal dimension , and by fully characterizing the graphs having centroidal dimension @xmath92 . in section [ sec : paths - cycles ] , we give a lower bound @xmath93 when @xmath0 has @xmath94 edges and every pair of vertices is connected by a small number , @xmath10 , of paths . we show that the bound is tight ( up to a constant factor ) for paths and cycles . finally , in section [ sec : complex ] , we discuss the computational complexity of finding a centroidal basis ; we show that for graphs with @xmath3 vertices , it is -hard to compute an @xmath95-approximate solution , and describe an @xmath96-approximation algorithm . we also remark that the problem is fixed - parameter - tractable when parameterized by the solution size .

we introduce the notion of a centroidal locating set of a graph , that is , a set of vertices such that all vertices in are uniquely determined by their relative distances to the vertices of . a centroidal locating set of of minimum size is called a centroidal basis , and its size is the centroidal dimension . this notion , which is related to previous concepts , gives a new way of identifying the vertices of a graph . the centroidal dimension of a graph is lower- and upper - bounded by the metric dimension and twice the location - domination number of , respectively . the latter two parameters are standard and well - studied notions in the field of graph identification . we show that for any graph with vertices and maximum degree at least 2 , . we discuss the tightness of these bounds and in particular , we characterize the set of graphs reaching the upper bound . we finally investigate the computational complexity of determining for an input graph , showing that the problem is hard and can not even be approximated efficiently up to a factor of . we also give an-approximation algorithm .

we introduce the notion of a centroidal locating set of a graph , that is , a set of vertices such that all vertices in are uniquely determined by their relative distances to the vertices of . a centroidal locating set of of minimum size is called a centroidal basis , and its size is the centroidal dimension . this notion , which is related to previous concepts , gives a new way of identifying the vertices of a graph . the centroidal dimension of a graph is lower- and upper - bounded by the metric dimension and twice the location - domination number of , respectively . the latter two parameters are standard and well - studied notions in the field of graph identification . we show that for any graph with vertices and maximum degree at least 2 , . we discuss the tightness of these bounds and in particular , we characterize the set of graphs reaching the upper bound . we then show that for graphs in which every pair of vertices is connected via a bounded number of paths , , the bound being tight for paths and cycles . we finally investigate the computational complexity of determining for an input graph , showing that the problem is hard and can not even be approximated efficiently up to a factor of . we also give an-approximation algorithm .

1407.6299

i

if black hole evaporation is assumed to preserve unitarity , a range of arguments based on quantum correlations @xcite suggest that physics at the slowly - shrinking horizon may differ significantly from the innocuous picture that underlies hawking s original derivation of black hole radiation within curved spacetime quantum field theory @xcite . in particular , almheiri _ et al _ @xcite have argued that the horizon will be replaced by a region of high curvature , a `` firewall '' , which will destroy any observer who attempts to fall into the black hole . reviews with extensive references can be found in @xcite . a key element in the firewall argument as formulated in @xcite is that the conventional quantum field theory picture of black hole evaporation involves strong quantum correlations between the black hole interior and exterior , and the assumption of unitary evolution of the full system turns out to preclude such correlations . in this paper we examine the consequences of severing closely similar correlations across a killing horizon in a system in which the requisite quantum state can be readily written down : a conformal scalar field in @xmath5 spacetime dimensions . for concreteness , we take the spacetime to be minkowski , so that the sense of thermality is that of the unruh effect of uniform acceleration @xcite , and we induce a firewall by breaking the correlations across the rindler horizon . the killing horizon in @xmath0-dimensional black hole spacetimes with a kruskal - like global structure could be treated in the same manner , with similar conclusions . we shall not attempt to examine how the spacetime geometry might react to the firewall singularity of the scalar field on the rindler horizon , but we shall examine how the singularity of the scalar field affects a particle detector that falls through the horizon . we consider a two - level unruh - dewitt ( udw ) detector that couples linearly to the scalar field @xcite , and its modification that couples linearly to the proper time derivative of the field @xcite . the reasons to consider the derivative - coupling detector are twofold . first , for quantum states that are regular in the hadamard sense @xcite , the derivative - coupling detector is insensitive to the infrared ambiguity in the wightman function of the @xmath0-dimensional conformal field . second , the short - distance behaviour of the @xmath0-dimensional derivative - coupling udw detector is similar to that of the @xmath6-dimensional udw detector with a non - derivative coupling @xcite . we may hence expect a derivative - coupling detector in @xmath5 dimensions to be a good model for a non - derivative detector that crosses a @xmath6-dimensional firewall . we recall that the non - derivative udw detector in @xmath6 dimensions models the @xmath7 term by which an atomic electron couples to the quantised electromagnetic field when there is no angular momentum exchange @xcite . we shall show that crossing the rindler firewall has a nonzero and sudden but _ finite _ effect on the detector s transition probability , within first - order perturbation theory . in terms of the detector s energy gap @xmath3 , the difference from the minkowski vacuum transition probability is proportional to @xmath1 for the non - derivative detector and to @xmath2 for the derivative - coupling detector both in the limit of a large energy gap and in the limit of adiabatic switching . we consider also a generalisation to a quantum state in which rindler excitations are added behind the rindler horizon in a way that has been suggested @xcite to model the `` energetic curtain '' of @xcite in a black hole spacetime . we show that in this state the response across the horizon is again finite but can be made arbitrarily large by increasing the temperature parameter that characterises the added excitations . we begin by reviewing in sections [ sec : detector ] and [ sec : minkowski ] the two - level udw detector and its derivative - coupling generalisation , coupled to a massless scalar field in @xmath0-dimensional minkowski spacetime . the rindler firewall quantum state is constructed in section [ sec : firewallstate - def ] , and we discuss the sense in which it models the stationary aspects of the black hole firewall of @xcite . the response of an inertial detector that crosses the rindler horizon in this state is analysed in section [ sec : resp - across ] , deferring technical steps to two appendices . section [ sec : curtain ] addresses the generalisation to a state in which excitations have been added behind the rindler horizon . section [ sec : conc ] presents a summary and concluding remarks , including a discussion of detectors with multiple levels . we use metric signature @xmath8 in which a timelike vector has negative norm squared , and we set @xmath9 . spacetime points are denoted by sans serif letters ( @xmath10 ) and complex conjugation is denoted by an overline .

the difference from the minkowski vacuum response is proportional to for the non - derivative detector and to for the derivative - coupling detector , both in the limit of a large energy gap and in the limit of adiabatic switching . adding to the quantum state high rindler temperature excitations behind the horizon increases the detector s response proportionally to the temperature ; this situation has been suggested to model the energetic curtain proposal of braunstein _ et al_. we speculate that the-dimensional derivative - coupling detector may be a good model for a non - derivative detector that crosses a firewall in dimensions .

we investigate a two - level unruh - dewitt detector coupled to a massless scalar field or its proper time derivative in-dimensional minkowski spacetime , in a quantum state whose correlation structure across the rindler horizon mimics the stationary aspects of a firewall that almheiri _ et al _ have argued to ensue in an evaporating black hole spacetime . within first - order perturbation theory , we show that the detector s response on falling through the horizon is sudden but finite . the difference from the minkowski vacuum response is proportional to for the non - derivative detector and to for the derivative - coupling detector , both in the limit of a large energy gap and in the limit of adiabatic switching . adding to the quantum state high rindler temperature excitations behind the horizon increases the detector s response proportionally to the temperature ; this situation has been suggested to model the energetic curtain proposal of braunstein _ et al_. we speculate that the-dimensional derivative - coupling detector may be a good model for a non - derivative detector that crosses a firewall in dimensions .

1407.6299

i

we have shown that a two - level udw detector in @xmath0-dimensional minkowski spacetime , coupled linearly to a massless scalar field or its proper time derivative , has a finite response on crossing inertially the rindler horizon in a firewall - type quantum state in which the minkowski vacuum correlations between the right and left rindler wedges have been fully severed . in the limit of a large detector energy gap @xmath3 , the leading contribution to the difference from the minkowski vacuum response is proportional to @xmath166}^2\omega^{-2}\ln(|\omega|)$ ] for the non - derivative detector and to @xmath166}^2\ln(|\omega|)$ ] for the derivative - coupling detector , where @xmath167 is the coupling strength at the horizon - crossing moment . the same leading contributions arise also in the limit of adiabatic switching . if the detector operates both before and after the horizon - crossing moment but not at the horizon - crossing moment , and the coupling strength changes smoothly in time , the effect is weaker : for a detector whose coupling vanishes in any open interval containing the horizon - crossing moment , the difference from the minkowski vacuum response dies off at large @xmath67 faster than any inverse power of @xmath3 . our construction of the rindler firewall state @xmath78 relied on the fact that the right - moving and left - moving components of a massless field are decoupled in @xmath5 dimensions . ( related consequences of this decoupling for past - future correlations have been investigated in @xcite . ) @xmath78 is not hadamard at the rindler horizon , and we found that the wightman function of @xmath78 contains a heightened version of the @xmath0-dimensional infrared ambiguity . in particular we found that the response of the derivative - coupling detector is ambiguous by an additive lorentz - noninvariant constant , even though this detector is free from infrared ambiguities in hadamard states @xcite . it could be interesting to investigate whether such ambiguities are present for the derivative - coupling detector in firewall - type states in which a severing of correlations evolves from an initially regular state by some dynamical mechanism . we emphasise that @xmath78 is undoubtedly singular at the rindler horizon , as seen from the non - hadamard form of the wightman function , and from the way in which the detector s response hinges on the coupling strength at the horizon - crossing moment . @xmath78 is hence qualitatively different from an evaporating @xmath0-dimensional black hole in the cghs model , where the outcome is a long - lived remnant @xcite , and from a @xmath0-dimensional moving - mirror system that models a remnant @xcite . we have not attempted to characterise the singularity in @xmath78 in terms of a stress - energy tensor , or by other means that might indicate how the spacetime responds to the singularity when allowed to become dynamical . however , our main observation is that when the spacetime is assumed to be unaffected by the singularity in @xmath78 , the response of the detector that falls across the horizon is , while sudden , nevertheless finite . our udw detector had two internal states . if the detector s internal hilbert space is generalised to that of a harmonic oscillator , it would be usual to take @xmath22 in to be the oscillator s position operator , @xmath168 , where @xmath169 is the oscillator s angular frequency and @xmath170 are the annihilation and creation operator pair @xcite . for the non - derivative detector in @xmath4 dimensions , this choice for @xmath22 models the @xmath171 term by which an atomic electron couples to the quantised electromagnetic field when there is no angular momentum exchange @xcite . with this choice , @xmath22 has nonvanishing matrix elements only between neighbouring energy eigenstates , and the only nonvanishing first - order transition probabilities from detector state @xmath172 are to detector states @xmath173 and @xmath174 , given by our formulas with @xmath175 . the conclusion about a finite detector response on crossing the firewall hence still holds . if however @xmath22 were chosen to have matrix elements of equal magnitude between each pair of the harmonic oscillator eigenstates , the sum of the first - order transition probabilities from state @xmath172 to all other states would diverge for the derivative - coupling detector , because of the leading term proportional to @xmath176 at large @xmath177 , but be still finite for the non - derivative detector , because the leading term is only proportional to @xmath178 . we considered also a generalisation of @xmath78 in which excitations are added behind the rindler horizon in a way that has been suggested @xcite to model the energetic curtain of @xcite . we found that the response is qualitatively similar to that in @xmath78 but can be made arbitrarily large by increasing the temperature - like parameter that characterises the added excitations . finally , recall that the short - distance behaviour of the wightman function becomes more singular as the spacetime dimension increases . one may hence expect an udw detector in dimensions higher than @xmath5 to react to a firewall more violently @xcite . however , the short - distance behaviour of the derivative - coupling detector in @xmath5 dimensions is similar to that of the non - derivative detector in @xmath4 dimensions @xcite . this suggests that our results for the @xmath5 derivative - coupling udw detector may faithfully reflect the response of a non - derivative udw detector that crosses a @xmath6-dimensional firewall .

we investigate a two - level unruh - dewitt detector coupled to a massless scalar field or its proper time derivative in-dimensional minkowski spacetime , in a quantum state whose correlation structure across the rindler horizon mimics the stationary aspects of a firewall that almheiri _ et al _ have argued to ensue in an evaporating black hole spacetime . within first - order perturbation theory , we show that the detector s response on falling through the horizon is sudden but finite .

we investigate a two - level unruh - dewitt detector coupled to a massless scalar field or its proper time derivative in-dimensional minkowski spacetime , in a quantum state whose correlation structure across the rindler horizon mimics the stationary aspects of a firewall that almheiri _ et al _ have argued to ensue in an evaporating black hole spacetime . within first - order perturbation theory , we show that the detector s response on falling through the horizon is sudden but finite . the difference from the minkowski vacuum response is proportional to for the non - derivative detector and to for the derivative - coupling detector , both in the limit of a large energy gap and in the limit of adiabatic switching . adding to the quantum state high rindler temperature excitations behind the horizon increases the detector s response proportionally to the temperature ; this situation has been suggested to model the energetic curtain proposal of braunstein _ et al_. we speculate that the-dimensional derivative - coupling detector may be a good model for a non - derivative detector that crosses a firewall in dimensions .

1301.6031

i

recent progress in the field of dynamical quantum transport @xcite opens new and fascinating perspectives for exploring and understanding mesoscopic and nanoscopic conductors . with the implementation of an on - demand single - electron emitter @xcite not relying on electron - electron interaction it is possible to address directly dynamic properties of a single - electron state in solids . the single - particle nature of emitted wave - packets was demonstrated using the noise measurements.@xcite to investigate the coherence properties of emitted wave - packets an approach based on the measurement of current correlations at a beam splitter @xcite and an approach based on the measurement of current at the output of an interferometer @xcite have already been proposed . the state of an electron depends crucially on the way it is emitted , see fig . [ fig1 ] . in most experiments with such high - speed single - electron sources see , e.g. , refs . , also the theoretical proposal in ref . and the analysis of a single - electron capture in ref . electrons are emitted from the quantum dot with energy far above the fermi level . on the other hand in theory many effects were predicted for electrons emitted adiabatically almost at the surface of the fermi sea : the shot - noise quantization @xcite ; the shot - noise suppression effect @xcite ; a two - particle interference and entanglement generation @xcite interesting for quantum information applications @xcite ; a particle reabsorption @xcite ; the suppression of a single - particle interference by collisions . @xcite recently also single and few - electron sources based on the generation of lorentzian voltage pulses applied to a ballistic conductor as proposed in refs . , and discussed in detail in ref . , have now been realized experimentally in ref . . the properties of a single - electron state generated by such a source are similar to those of the state emitted adiabatically by a single lead mesoscopic capacitor.@xcite . b ) non - adiabatic emission : the ses is driven by a pulsed periodic potential , the pulse as a function of time has an exponential shape characterized by the dwell time @xmath0.,width=264 ] our aim here is to answer the question of whether one can expect similar effects with particles emitted non - adiabatically or not . for this purpose we analyze the single - electron source of ref . because it can operate in both adiabatic and non - adiabatic emission conditions . moreover it seems that its properties are well described by a non - interacting theory . @xcite that makes it possible to develop a relatively simple analytical theory which describes both operating conditions . we use a non - interacting model @xcite , in which the source consists of a single circular edge state , a fabry - prot cavity , weakly coupled to a linear edge state , which plays the role of an electron waveguide . this analytical model is in good agreement with actual experiments . in the weak coupling limit , the transparency of the quantum point contact connecting the cavity and the electron waveguide is small , @xmath1 . all relevant energies are smaller than the fermi energy , @xmath2 and the energy spectrum of electrons can be linearized in the vicinity of @xmath2 . that results in the equidistant spectrum of the cavity with level spacing @xmath3 defined by the time of flight , @xmath4 , around the circular edge state of the cavity . a metallic top - gate with potential @xmath5 periodically changes the position of the quantum levels in the cavity . we assume optimal operating conditions @xcite which require that the fermi level is positioned in the middle of two levels of the cavity and the gate potential changes with amplitude @xmath6 . in this case only one level crosses the fermi energy : when it raises above the fermi level an electron is emitted from the cavity into the waveguide , whereas when the level sinks below the fermi level an electron is absorbed by the cavity hence a hole appears in the stream of electrons within the waveguide . such a source generates no dc current and is often referred to as a quantum capacitor . @xcite to get an intuitive estimate of both the shape and the duration of a single - particle wave - packet we look at the current pulse emitted by the cavity . the sudden change of a potential , @xmath7 , results in a transient current pulse ( an expectation value),@xcite @xmath8 + with highly asymmetric shape ( we ignore a fine structure @xcite on the scale of @xmath4 ) . here @xmath9 is the electron charge and @xmath10 the heaviside theta - function . the time @xmath11 denotes the time at which the potential changes , leading to the emission of an electron and the label `` @xmath12 '' stands for non - adiabatic . indeed , as explained below , such an emission process corresponds to non - adiabatic emission conditions . the time @xmath0 , @xmath13 + the dwell time of an electron in the cavity . therefore the dwell time sets a relevant time - scale of the problem under consideration . first , the period @xmath14 of the gate voltage , @xmath15 , should be long enough for the driven cavity to work as a single - particle source,@xcite @xmath16 + note that to operate the source periodically , the energy level needs to be returned back to its initial position by applying the opposite potential @xmath17 . here , @xmath18 denotes the time at which the emission of a hole starts . the delay between subsequent potential steps should be longer than the duration of a current pulse , @xmath19 , to allow an electron emission to be completed : the emitted charge @xmath20 should be equal to an electron charge , @xmath21 . at time @xmath22 a hole can be emitted . second , the dwell time , @xmath23 , defines the condition of adiabatic or non - adiabatic emission . if the potential @xmath5 changes fast on the scale of @xmath23 , then we speak about a non - adiabatic emission . in this case the shape of an emitted current pulse is asymmetric and given by eq . ( [ pulse - na ] ) . in contrast , if @xmath5 changes smoothly compared to @xmath0 , the current pulse is predicted to be symmetric . @xcite close to @xmath11 , the corresponding current pulse @xmath24 reads : @xmath25 + now the duration @xmath26 of a current pulse is defined by the time of crossing , @xmath27 + where @xmath28 is the width of a quantum level in the weakly coupled cavity . in the model used @xmath29 . for @xmath30 , where @xmath31 , and @xmath32 we find @xmath33 + remarkably , it was shown in ref . that the pulse duration @xmath26 also sets the single - particle coherence time of an electron emitted adiabatically . this shows that the source , described by this analytical model , has no intrinsic dephasing processes.@xcite this makes the emitted single electron states of particular interest for further applications in quantum information processing . equation ( [ pulse - a ] ) is calculated assuming that @xcite @xmath34 + it means that the level of the cavity crosses the fermi sea level so slowly that an electron has enough time to leave the cavity once his energy becomes larger than the fermi energy . from eq . ( [ ad ] ) it also follows that the width of a wave - packet emitted adiabatically is much larger than the width of a wave - packet emitted non - adiabatically . apparently with decreasing crossing time @xmath35 , keeping the period @xmath36 large compared to @xmath23 , the shape of the pulse evolves from adiabatic , eq . ( [ pulse - a ] ) , to non - adiabatic , eq . ( [ pulse - na ] ) . for a level driven with a constant speed , an analysis describing this crossover can be found in ref . . the current pulses @xmath37 , eq . ( [ pulse - na ] ) , and @xmath38 , eq . ( [ pulse - a ] ) , have both similar and different features . on one hand , they both carry a quantized charge . therefore , we anticipate that they both should show similar quantization effects @xcite and effects arising due to the overlap of wave - packets @xcite . we use below the shot noise suppression effect as an example . and the dc heat flow @xmath39 nullify . ( b ) non - adiabatic emission : the cavities are driven by pulsed potentials and electron - hole pairs are emitted . since this pair is neutral , the time - dependent current is zero , @xmath40 . however , both the electron and the hole carry energy . because of the asymmetric shape of the pulses reabsorption can not be a time - reversed emission process . there is no absorption effect , the generated dc heat flow is not zero : @xmath41.,width=264 ] on the other hand for some effects the shape of a wave - packet is crucial . as an example below we use the effect of reabsorption @xcite predicted for the adiabatic regime : if two cavities are coupled to the same edge state , then the electron emitted adiabatically by one cavity can be reabsorbed by another cavity emitting a hole at the same time , see fig . [ fig2 ] ( a ) . first of all , in this regime the time - dependent current is zero , @xmath40 . @xcite this current consists of two parts , electron , @xmath42 , and hole , @xmath43 , which compensates each other : @xmath44 . to clarify whether it is merely a compensation effect or a reabsorption effect , additionally the heat generated by the two cavities was analyzed . @xcite it was shown that each particle , either an electron or a hole , carries an excess energy ( over the fermi energy ) @xmath45 + this energy can be understood as the work done by the potential @xmath5 on the particle during its escape from the cavity . the particle starts to escape when its energy becomes equal to the fermi energy . the time it takes to escape is the dwell time , @xmath46 , given in eq . ( [ taud ] ) . we use eq . ( [ gam ] ) and find @xmath47 . notice the energy of a particle in the cavity has an uncertainty @xmath48 ( the level width ) . this results in the uncertainty @xmath35 of the time when a particle starts to escape the cavity . that in turns defines the width of the current pulse , eq . ( [ pulse - a ] ) . if two cavities emit an electron and a hole at different times , then these two particles together carry the energy @xmath49 . however , if an electron and a hole are emitted at the same time ( the time of flight between the cavities should be trivially taken into account ) then the extra energy flowing out of the system is zero.@xcite clearly this means that an electron emitted by the cavity @xmath50 and carrying an energy @xmath51 was reabsorbed by the cavity @xmath52 . this effect is paradoxical : on one hand , in fact , the hole emission is an electron absorption . on the other hand , the cavity @xmath52 can absorb any electrons in the waveguide passing it . why does it absorb the electron emitted by the cavity @xmath50 ? possibly this effect can be understood using time - reversal symmetry arguments . first , let us take only one cavity and let it emit an electron . after that let us reverse time . apparently the emitted electron will be reabsorbed . importantly , the portion of the wave - packet emitted last will be reabsorbed first . now let us take two identical cavities and let us drive them with potentials @xmath53 and @xmath54 related by the time - reversal symmetry , @xmath55 . note with such potentials if the first cavity emits an electron the second cavity emits a hole and vice versa . we can expect the second cavity to be an analogue of the time - reversal twin of the first cavity . to make such an analogy complete , the shape of the wave - packet does matter . because the second cavity will first reabsorb ( if possible ) the part of the wave - packet , which was emitted first . in contrast , the true time - reversal twin will first absorb what was emitter last . if the shape of a wave - packet is symmetric , as in the adiabatic emission regime , ( for the corresponding current pulse see eq . ( [ pulse - a ] ) ) , then there is no difference between what was emitted first and what was emitted last . consequently the second cavity can play the role of the time - reversal twin and reabsorb what was emitted by the first cavity . however , if the shape of a wave - packet is non - symmetric , as in the non - adiabatic emission regime , ( for the corresponding current pulse see eq . ( [ pulse - na ] ) ) , then there is a striking difference between what was emitted first and last . as a consequence what the second cavity sees is different from what the time - reversal twin would see . therefore , adiabatic and non - adiabatic cavities work differently . as we show below , in the non - adiabatic emission regime both cavities emit together an electron - hole pair , which carries no charge , @xmath40 , but carries a non - zero energy . the paper is organized as follows : in sec . [ shot ] we discuss the shot noise quantization and the shot noise suppression effect for electrons emitted non - adiabatically . in sec . [ two ] the dc heat flow generated by the two - particle emitter working in the non - adiabatic regime is analyzed . we conclude with a brief discussion in sec . [ concl ] . details of the calculations are in appendices . in appendix [ scat ] we derive the floquet scattering amplitude for a cavity driven by the pulsed potential . in appendix [ shn ] the zero frequency correlation function for currents flowing through the electron collider circuit is found . in appendix [ twope ] we discuss the dc heat flow generated by the two - cavity emitter .

we investigate adiabatic and non - adiabatic emission of single particles into an edge state using an analytically solvable dynamical scattering matrix model of an on - demand source . most effects observed for adiabatic emitters also occur for non - adiabatic emitters . in particular this applies to effects arising due to the overlap of wave - packets colliding at a quantum point contact . whereas the squared average charge current can be nullified for both operating conditions , the heat current can be made to vanish only with adiabatic emitters .

we investigate adiabatic and non - adiabatic emission of single particles into an edge state using an analytically solvable dynamical scattering matrix model of an on - demand source . we compare adiabatic and non - adiabatic emissions by considering two geometries : a collider geometry where two emitters are coupled to two different edge states and a series geometry where two emitters are coupled to the same edge state . most effects observed for adiabatic emitters also occur for non - adiabatic emitters . in particular this applies to effects arising due to the overlap of wave - packets colliding at a quantum point contact . specifically we compare the pauli peak ( the fermionic analog of the bosonic hong - ou - mandel dip ) for the adiabatic and non - adiabatic collider and find them to be similar . in contrast we find a striking difference between the two operating conditions in the series geometry in which particles are emitted into the same edge state . whereas the squared average charge current can be nullified for both operating conditions , the heat current can be made to vanish only with adiabatic emitters .

1201.1617

i

the present understanding of galaxy formation in a cosmological context is based upon the collapse via gravitational instability of tiny dark matter ( dm ) perturbations dominating the matter contribution @xmath4 to the energy density of the universe , with baryons contributing only a fraction @xmath5 . in such a context , the number density and the properties of galaxies with different mass ultimately arise from the power spectrum of dm perturbations at the epoch of recombination . for example , in a universe dominated by cold dark matter ( cdm ) the low thermal speed of dm particles makes the density perturbations gravitationally unstable down to mass scales negligible for galaxy formation , and structure formation proceeds bottom - up with the progressive collapse of larger and larger regions ; massive galaxies , groups and clusters form by subsequent aggregations . when coupled with the evidences for a positive vacuum energy @xmath6 dominating the energy - density of the universe ( with @xmath7 see spergel et al . 2007 ) , such a @xmath6cdm scenario appears to be consistent with a wide range of observables ; from the temperature anisotropies in the microwave background radiation ( komatsu et al . 2011 ) to the clustering of galaxies on large scales ( cole et al . . however , such observables directly probe scales from@xmath8 gpc down to @xmath9 mpc . at galactic and sub - galactic scales @xmath10 mpc , the computations based on n - body simulations pose several problems to the @xmath6cdm scenario . for example , the cdm haloes are predicted to have inner density profiles much steeper than those inferred from the rotation curves of real galaxies ( moore et al . 1999 , abadi et al . 2003 , reed et al . 2005 ; madau , diemand , kuhlen 2008 ; for observations see , e.g. , gentile et al . 2007 , mcgaugh et al . 2007 ) , the discrepancy being larger for dwarf galaxies ( see governato et al . 2007 ; abadi et al . 2003 ; de blok et al . 2008 ) . in addition , cdm haloes are predicted to contain a wealth of substructure , which we expect to observe as satellite galaxies within the haloes of galaxies and groups , in contrast with observations ( see klypin et al . 1999 , moore et al . 1999 ; see also mateo et al . 1998 ) . since at such small scales the model predictions depend on the complex physics involved in the process of galaxy formation , part of the solutions to the above problems may be of astrophysical nature . feedback processes such as heating or winds caused by supernovae explosions and heating due to the uv background may be effective in suppressing star formation in the low - mass haloes of satellite galaxies ( bullock et al . 2000 ; benson et al . 2002 ; somerville et al . 2002 ; kravtsov , gnedin & klypin 2004 ; governato et al . 2007 ; mashchenko , wadsley & couchman 2008 ) , and in flattening the the inner density profiles in both spirals and dwarfs ( see governato et al . 2007 ; 2010 ) . however , the origin of the above problems may also lie , at least partially , in the shape of the cdm power spectrum , which could over predict the amplitude of small - scale ( @xmath11 mpc ) perturbations . indeed , a strong indication that this may be the case comes from the statistical properties of galaxies and active galactic nuclei ( agn ) , usually investigated in the framework of @xmath6cdm through semi - analytic models of galaxy formation ( sams , see kauffman , white & guiderdoni 1993 , cole et al . 1994 ; monaco , salucci & danese 2000 , kauffmann & haenhelt 2000 ; granato et al . 2004 ; menci et al . 2006 ; croton et al . 2006 ; bower et al . 2006 ; marulli et al . 2008 ) , which connect the physical processes involving gas and star formation to the merging histories ( and hence to the power spectrum ) of dm haloes . all such models ( including different astrophysical feedback process ) concur in predicting an excess of small - mass galaxies compared to observations . in particular : i ) the predicted galaxy luminosity functions at low redshift are much steeper than observed unless a strong feedback is assumed ( see , e.g. , somerville , primack 1999 ; cole et al . 2000 ; menci et al . 2002 ) , while at high redshifts the larger escape velocities of galaxies ( due to their larger densities ) make the feedback inefficient in suppressing star formation in low - mass objects . this results into an over - prediction of faint galaxies increasing with redshift when compared , e.g. , with the evolution of the k - band luminosity function for @xmath12 ( see cirasuolo et al . 2010 ) or with the faint lyman - break galaxies ( lo faro et al . 2009 ) at @xmath13 ; the excess of star - forming low - mass galaxies at @xmath13 reflects into an excess of red low - mass galaxies at @xmath14 ( see , e.g. , croton et al . 2006 ; salimbeni et al . ii ) the number of galaxies with stellar mass @xmath15 m@xmath16 in the universe is systematically over predicted by all theoretical cdm models ( fontana et al . 2006 ; fontanot et al . 2009 ; marchesini et al . 2009 ) in the whole redshift range @xmath17 where the small - mass end of the mass function has been measured ( see also santini et al . 2012 ) . thus , the baryonic processes ( and the feedback in particular ) implemented so far in all galaxy formation models do not seem able to provide an explanation for the _ predicted _ excess . while it is still possible that the problem stems from a poor understanding of the laws governing star formation especially at high redshifts @xmath18 ( see , e.g. , krumholz & dekel 2011 ) , it is interesting to note that the over - predictions of low - mass objects in the cdm scenario concerns also the agn population ; recent estimates of the x - ray luminosity functions of agn extending down to log @xmath19(2 -10 kev)@xmath20 ( fiore et al . 2011 ) are in sharp contrast with the large density of faint agn predicted by analytic ( shankar 2009 ) or semi - analytic ( menci et al . 2006 , 2008 ) models for the co - evolution of galaxies and agns ( se also shankar & mathur 2007 ; wyithe & loeb 2003 ; lapi et al . 2006 , shen 2009 ; shankar 2010 and references therein ) , even when the observed luminosity functions are corrected for the estimated fraction of obscured objects ( e.g. , la franca et al . 2005 ) . although , individually , the above problems do not definitely rule out the cdm model due to the complexity of the baryonic physics relating dm haloes with observable properties , the concurring evidences listed above call for a more radical approach , to investigate the possibility that the conflicts are rooted in an excess of power of the cdm spectrum at small scales , and that density perturbations could be dumped below same characteristic scale @xmath21 . a natural mechanism for such a suppression is the free - streaming of dm particles on scales @xmath22 , where @xmath23 is the dm thermal speed at the time of matter - radiation equality @xmath24 . for large dm velocities @xmath25 ( corresponding to a neutrino with mass @xmath26 ev ) this leads to the well - known hot dm scenario ( for a review see primack & gross 2000 ) which would yield @xmath27 mpc , well above the most recent observational limits @xmath28 set by the comparison of the lyman-@xmath2 forest spectra at @xmath29 with the n - body simulations ( viel et al . 2005 ; 2008 ) . however , for dm particles with larger mass @xmath30 the streaming speed could be reduced so as to bring @xmath21 close to @xmath31 mpc ( corresponding to a mass scale @xmath32 ) , consistent with present bounds but still large enough to affect galaxy formation . if constituted by thermal relic particles , such warm dm ( wdm ) would have streaming velocities @xmath33 , where @xmath34 is the effective temperature determining the value of the wdm density @xmath35 , so that @xmath36 . thus , to lower the smoothing scale @xmath37 of a factor @xmath38 compared to the above hot dm case , the wdm particles should have @xmath39 kev if their density has to match the observed dm density parameter @xmath40 . this type of relic wdm was discussed by peebles ( 1982 ) , bond , szalay & turner ( 1982 ) , and could have a physical counterpart in the gravitino , the supersymmetric partner of the graviton , in gauge - mediated supersymmetry breaking models ( pagels , & primack 1982 ; see steffen 2006 for a recent review ) . another possibility is that wdm particles have never been in thermal equilibrium , as is the case , e.g. , for sterile neutrinos created from oscillations with active neutrinos ( olive & turner 1982 ; dodelson & widrow 1994 ; shi & fuller 1999 ; abazajian , fuller & patel , 2001 ; dolgov & hansen 2002 ) . a discussion on the wdm candidates can be found in colombi , dodelson , lawrence ( 1996 , and references therein ) . for scenarios based on composite dm see khlopov et al . ( 2008 ) . previous studies based on n - body simulations have shown that wdm can resolve some of the tension between theoretical predictions and observations ( bode et al . 2001 ; avila - reese et al . some simulations suggest that the density profiles of wdm haloes are shallower in the inner regions ( colin , valenzuela , avila - reese 2008 ; see also de vega , salucci , sanchez 2010 ) , and that wdm can provide an explanation for the observed kinematics of satellites of massive galaxies ( lovell et al . simulations focussed on the halo properties and mass distribution in wdm scenario ( see knebe et al . 2002 ; zavala et al . 2009 ; polisensky & ricotti 2011 , smith & markovic 2011 ) have shown that there is a sensible suppression in the number of haloes with @xmath41 . however , the effects of a wdm spectrum on the properties of galaxies at such mass scales would be best investigated with sams , since not only they allow to probe in detail the effects on the halo statistics for @xmath41 , but also they can investigate the chain of effects that such a suppression has on the baryonic processes involved in galaxy formation : a modification of the power spectrum changes the number and the formation epoch ( and hence the internal densities ) of the of high - redshift progenitors of local galaxies , an effect which propagates to gas cooling , to the disk sizes , and to star formation ; this also affects both dynamical friction and binary merging , the processes determining the fate of sub - haloes associated to satellite galaxies ( see , e.g. , somerville & primack 1999 ; menci 2002 ) , and consequently the stellar mass growth of large galaxies due to accretion of smaller objects ; finally , starbursts and agn accretion and feedback ( included in almost all state - of - the - art sams ) induced by galaxy interactions are affected by the change in the number and in the properties of sub - haloes . in the present paper we investigate for the first time the effects of a wdm power spectrum on the statistical properties of galaxy using a sam of galaxy formation . we adopt a wdm power spectrum with a power suppression ( compared to the cdm spectrum ) below a cut - off scale @xmath42 mpc , to retain consistency with present bounds provided by the microwave background wmap data and by the comparison of hydrodynamical n - body simulations with observed lyman-@xmath2 forest ( see viel et al . 2005 ) . in terms of the properties of the wdm particles , such a cut off scale @xmath42 mpc is achieved for a mass of dm particles @xmath39 kev ( see sect . 2 ) whose free streaming length is @xmath43 mpc , corresponding to the wavelength of the mode for which the linear perturbation amplitude is suppressed by a factor of 2 . we run our fiducial semi - analytic model ( menci et al . 2006 , 2008 ) with such a wdm power spectrum to derive galaxy luminosity functions ( in b , uv , and k bands ) and the stellar mass distributions over a wide range of cosmic epochs , to compare with recent observations ( sect . 3 ) ; the predicted color distribution of galaxies in the wdm model is also checked against the data . our results are discussed in sect . 4 , while sect . 5 is devoted to conclusions .

we investigate for the first time the effects of a warm dark matter ( wdm ) power spectrum on the statistical properties of galaxies using a semi - analytic model of galaxy formation . the wdm spectrum we adopt as a reference case is suppressed - compared to the standard cold dark matter ( cdm ) case - below a cut - off scale mpc corresponding ( for thermal relic wdm particles ) to a mass kev . this ensures consistency with present bounds provided by the microwave background wmap data and by the comparison of hydrodynamical n - body simulations with observed lyman- forest . we run our fiducial semi - analytic model with such a wdm spectrum to derive galaxy luminosity functions ( in b , uv , and k bands ) and the stellar mass distributions over a wide range of cosmic epochs , to compare with recent observations and with the results in the cdm case . cosmology : theory cosmology : dark matter galaxies : formation

we investigate for the first time the effects of a warm dark matter ( wdm ) power spectrum on the statistical properties of galaxies using a semi - analytic model of galaxy formation . the wdm spectrum we adopt as a reference case is suppressed - compared to the standard cold dark matter ( cdm ) case - below a cut - off scale mpc corresponding ( for thermal relic wdm particles ) to a mass kev . this ensures consistency with present bounds provided by the microwave background wmap data and by the comparison of hydrodynamical n - body simulations with observed lyman- forest . we run our fiducial semi - analytic model with such a wdm spectrum to derive galaxy luminosity functions ( in b , uv , and k bands ) and the stellar mass distributions over a wide range of cosmic epochs , to compare with recent observations and with the results in the cdm case . the predicted color distribution of galaxies in the wdm model is also checked against the data . when compared with the standard cdm case , the luminosity and stellar mass distributions we obtain assuming a wdm spectrum are characterized by : i ) a flattening of the faint end slope and ii ) a sharpening of the cutoff at the bright end for . we discuss how the former result is directly related to the smaller number of low - mass haloes collapsing in the wdm scenario , while the latter is related to the smaller number of satellite galaxies accumulating in massive haloes at low redshift , thus suppressing the accretion of small lumps on the central , massive galaxies . these results shows how a adopting a wdm power spectrum may contribute to solve two major problems of cdm galaxy formation scenarios , namely , the excess of predicted faint ( low mass ) galaxies at low and - most of all - high redshifts , and the excess of bright ( massive ) galaxies at low redshifts . cosmology : theory cosmology : dark matter galaxies : formation

1201.1617

i

in this paper we investigated the effect of assuming a wdm power spectrum on galaxy formation using a sam , leaving unchanged the baryonic mechanisms already implemented in our previous cdm model ( in particular the stellar and the agn feedback ) ; this allows to single out the effects of changing the dm spectrum with the same baryon physics . we focussed on the statistical distribution of luminosity and stellar masses , leaving to next paper a full study of the effects of wdm on other properties of the galaxy population ( e.g. , chemical abundances , ages of stellar populations , effects of the environment ) . within the present study , we find that adopting power spectrum corresponding to wdm particles with mass @xmath123 kev may contribute to solve two major problems of cdm galaxy formation scenarios , namely , the excess of predicted faint ( low mass ) galaxies at low and especially at high redshifts , and the excess of bright ( massive ) galaxies at low redshifts . in fact , adopting a wdm spectrum on the one hand results in a smaller number of collapsed low - mass haloes ; on the other hand it results into a smaller number of satellite galaxies accumulating in massive haloes at low redshifts , thus suppressing the accretion of small lumps on the central , massive galaxies for @xmath3 . such conclusions are robust with respect to the uncertainties in the modelling of the wdm halo abundance around the free streaming mass scale , as discussed in sect . 4 . our results on the luminosity and stellar mass distributions of galaxies concur to indicate that particles with mass @xmath42 kev constitute interesting candidates for dm ; such an indication adds to the existing astrophysical evidences from ( see references in the introduction ) : a ) the observed galaxy structures at small scales ( @xmath124 kpc ) ; b ) the cored profiles of galaxies ; c ) the number of sub haloes and satellites in the haloes of massive galaxies . directly testing whether dm is constituted by such particles , is a realistic possibility for the near future . a cosmological direct probe of wdm could be provided by cosmic shear ( weak gravitational lensing ) , which has the advantage of being weakly dependent on baryonic physics . first results in the simple relic scenario indicate that future lensing surveys like euclid could see wdm signals for @xmath125 kev ( smith & markovic 2011 ) , close to the mass adopted here . if the wdm is constituted by sterile neutrinos , as advocated to account for the non - zero active neutrino mass ( for a review see boyarsky , ruchayskiy & shaposhnikov 2009 ) , astrophysical bounds on its mass can be placed because it would decay in a standard neutrino plus a photon with energy of the order of the kev , thus producing narrow line emission in x - rays . claims for detection of lines hardly identifiable with known transitions have been published using both chandra and suzaku observations of dwarf galaxies and the galactic centre ( loewenstein & kuseno 2010 , prokhorov & silk 2010 ) . both the claimed lines are at energies where the effective area is strongly reducing ( 8.7 kev suzaku ) or near the gold m edge feature of the chandra mirror ( 2.51 kev ) . in the case wdm is constituted by sterile neutrinos direct detection is also possible through triple beta decay experiments like mare and katrin ( see de vega et al . 2011 ) . as for the case of thermal wdm , the favourite candidate is the gravitino . it emerges as a natural candidates for the lightest supersymmetric ( lsp ) particle in gauge - mediated supersymmetry breaking models ( see dine , nelson , nir , shirman 1996 ) with conserved r parity . contrary to the gravity - mediated supersymmetry breaking case , where the lsp ( typically the neutralino ) has masses exceeding the 10 tev scale , the gravitino mass can range from a fraction of ev up to o(gev ) . however , if it constitutes the lsp with mass @xmath123 kev , a large value @xmath126 for the degrees of freedom would be needed at the time of its decoupling to comply with the observed matter density @xmath127 ( pagels & primack 1982 ) ; this is larger than @xmath128 expected in minimal supersymmetric standard model ( mssm ) . of course , scenarios with @xmath129 exceeding the mssm expectations are conceivable , as well as scenarios where entropy - producing processes could dilute the gravitino abundance ( fujiii and yanagida 2002 ) , or where vanishing gauge coupling at high temperature suppresses the gravitino production ( buchmuller , hamaguchi & ratz 2003 ; see also lemoine , moultaka , jedamzik 2006 ) . a gravitino mass @xmath123 kev effective to provide a viable wdm scenario for galaxy formation would correspond to a relatively low energy scale for supersymmetry breaking @xmath130 gev ( here @xmath131 is the reduced plank mass ) . while its extremely weak coupling with matter ( @xmath132 , see lee & wu , 1999 ) makes gravitino dm inaccessible to direct searches , upcoming data from colliders may allow for signals from light gravitinos with mass in the ev to mev range ( see feng , kamionkowski & lee 2010 ) . light gravitinos would be produced primarily in the decays of the next - to - lightest supersymmetric particle , resulting in a variety of signals , including di - photons , delayed and nonpointing photons , kinked charged tracks , and heavy metastable charged particles . if light gravitino constitutes wdm , the 7 tev lhc with 1 fb@xmath133 could see evidence for hundreds of light - gravitino events . our results have straightforward implications concerning the growth of supermassive black holes and the evolution of agns . in cosmological galaxy formation theories , these are tightly related to the evolution of their host galaxies , as indicated also by the observed correlation between the mass of supermassive black holes and global properties of their host galaxies , like the stellar mass or the velocity dispersion ( kormendy & richstone 1995 ; magorrian et al . 1998 ; gebhardt et al . 2000 ; ferrarese & merritt 2000 ) . as recalled in the introduction ( see references therein ) , the over - predictions of low - mass objects in the cdm scenario concerns also the agn population ; assuming a wdm power spectrum could substantially alleviate the problem , analogously to what we showed to happen for the galaxy population . note that , contrary to what we derived for low redshift massive galaxies , we do not expect bright agns to be affected by assuming a wdm spectrum . this is because such objects are thought to be powered by gas accretion triggered by galaxy encounters with partners of comparable mass ( extremely rare at low redshift ) , only mildly affected by the abundance of low mass satellites . we shall investigate this points in a next paper . abadi , m. g. , navarro , j. f. , steinmetz , m. eke , v. r. 2003 , apj 591 , 499 abazajian , k. , fuller , g.m . , patel , m. 2001 , phys . d , 64 , 02351 avila - reese , v. , colin , p. , valenzela , o. , donghia , e. , firmani , c. , 2001 , apj , 559 , 516 baldry , i.k . , glazebrook , k. , brinkmann , j. , zeljko , i. , lupton , r.h . , nichol , r.c . , szalay , a.s . 2004 , apj , 600 , 681 bardeen j. m. , bond j. r. , kaiser n. , szalay a. s. , 1986 , apj , 304 , 15 baugh , c.m . 2006 , rep . prog . phys . 69 , 3101 bell , e. , wolf , c. , meisenheimer , k. , rix , h .- w . , borch , a. , dye , s. , kleineinrich , m. , mcintosh , d. 2004 , apj , 608 , 752 benson , a.j . , frenk , c.s . , lacey , c.g . , baugh , c.m . , cole , s. 2002 , mnras , 333 , 177 blanton , m.r . 2001 , apj , 121 , 2358 bode , p. , ostriker , j.p . , turok , n. 2001 , apj , 556 , 93 bond , j.r . , szalay , a.s . , turner , m. s. 1982 , phys . 48 , 1636 bond , j.r . , cole , s. , efstathiou , g. , & kaiser , n.,1991 , apj , 379 , 440 bower , r.g . , benson , a.j . , malbon , r. , helly , j.c . , frenk , c.s . , baugh , c.m . , cole , s. , lacey , c.g . 2006 , mnras , 370 , 645 boyarsky , a. , ruchayskiy , o. , shaposhnikov , m. 2009 , annual review of nuclear and particle science , 59 , 191 bouwens , r.j . , illingworth , g.d . , franx , m. , ford , h. 2007 , apj , 670 , 928 buchmuller , w. , hamaguchi , k. & ratz , m. 2003 , phys . b , 574 , 156 bullock , j.s . , kravstov , a.v . , weinberg , d.h . 2000 , apj , 539 , 517 cattaneo , a. , dekel , a. , devriendt , j. , guiderdoni , b. , blaizot , j. , mnras , 370 , 1651 cavaliere , a. , & vittorini , v. 2000 , apj , 543 , 599 cirasuolo m. , mclure r. j. , dunlop j. s. , almaini o. , foucaud s. , simpson c. , 2010 , mnras , 401 , 1166 cole , s. , aragon - salamanca , a. , frenk , c.s . , navarro , j.f . , zepf , s.e . , 1994 , mnras , 271 , 781 cole , s. , lacey , c.g . , baugh , c.m . , frenk , c.s . , 2000 , mnras , 319 , 168 cole , s. et al . 2005 , mnras , 362 , 505 colin , p. , valenzuela , o. , avila - reese , v. , 2000 , apj , 673 , 203 colombi , s. , dodelson , s. , widrow , l.m . 1996 , apj , 458 , 1 croton , d.j , springel , v. , white , s.d.m . , de lucia , g.,frenk , c.s . , gao , l. , jenkins , a. , kauffmann , g. , navarro , j.f . , yoshida , n. , 2006 , mnras , 365 , 11 de blok , w.j.g . ; 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we discuss how the former result is directly related to the smaller number of low - mass haloes collapsing in the wdm scenario , while the latter is related to the smaller number of satellite galaxies accumulating in massive haloes at low redshift , thus suppressing the accretion of small lumps on the central , massive galaxies . these results shows how a adopting a wdm power spectrum may contribute to solve two major problems of cdm galaxy formation scenarios , namely , the excess of predicted faint ( low mass ) galaxies at low and - most of all - high redshifts , and the excess of bright ( massive ) galaxies at low redshifts .

we investigate for the first time the effects of a warm dark matter ( wdm ) power spectrum on the statistical properties of galaxies using a semi - analytic model of galaxy formation . the wdm spectrum we adopt as a reference case is suppressed - compared to the standard cold dark matter ( cdm ) case - below a cut - off scale mpc corresponding ( for thermal relic wdm particles ) to a mass kev . this ensures consistency with present bounds provided by the microwave background wmap data and by the comparison of hydrodynamical n - body simulations with observed lyman- forest . we run our fiducial semi - analytic model with such a wdm spectrum to derive galaxy luminosity functions ( in b , uv , and k bands ) and the stellar mass distributions over a wide range of cosmic epochs , to compare with recent observations and with the results in the cdm case . the predicted color distribution of galaxies in the wdm model is also checked against the data . when compared with the standard cdm case , the luminosity and stellar mass distributions we obtain assuming a wdm spectrum are characterized by : i ) a flattening of the faint end slope and ii ) a sharpening of the cutoff at the bright end for . we discuss how the former result is directly related to the smaller number of low - mass haloes collapsing in the wdm scenario , while the latter is related to the smaller number of satellite galaxies accumulating in massive haloes at low redshift , thus suppressing the accretion of small lumps on the central , massive galaxies . these results shows how a adopting a wdm power spectrum may contribute to solve two major problems of cdm galaxy formation scenarios , namely , the excess of predicted faint ( low mass ) galaxies at low and - most of all - high redshifts , and the excess of bright ( massive ) galaxies at low redshifts . cosmology : theory cosmology : dark matter galaxies : formation

1507.05688

c

as presented in the previous sections , we parameterize the gas inflow and outflow rates in mwlgs in terms of @xmath62 and @xmath63 as described in equation ( [ eq : fit ] ) . the properties of these parameters are summarized as follows . * both @xmath64 and @xmath65 are a decreasing function of time . * the index @xmath67 is almost unity at all epochs , implying that the inflow rate can be regarded to be proportional to the sfr . * the index @xmath68 for the frmg model is about 0.5 at all epochs , whereas that for the srmg model evolves from @xmath69 1 at @xmath60 to @xmath69 0.5 at @xmath48 . therefore the evolution of @xmath68 is expected to depend on the adopted evolution of the rmg . these results reflect basic baryonic physics associated with gas inflow and outflow processes in the disk . in this section , we discuss how the above properties of @xmath62 and @xmath63 are related to and deduced from such baryonic physics . the most remarkable difference between the results of the srmg and frmg models is the redshift evolution of @xmath68 . this difference suggests that the dependence of outflow process on star formation activity affects the chemical evolution over the galactic disk significantly . the relation between @xmath68 and the rmg can be simply interpreted as follows . for an ordinary galactic disk that has more active star formation in its inner region , @xmath74 means that the ratio of the outflow rate to sfr becomes higher toward the inner region . therefore , the enrichment process driven by active star formation in the inner region of the disk is suppressed by the effect of much higher outflow rate of gas , so that the steepening of the rmg with time is suppressed , although the actual situation is expected to depend on the nucleosynthetic yield and initial distribution of heavy elements in the disk . in contrast , for @xmath75 the chemical evolution always progresses faster in the inner disk region , so that the rmg is steepened with time . therefore , for the srmg model @xmath76 at high @xmath26 leads to the flat rmg and the gradual decrease of @xmath68 accompanies the steepening of the rmg . on the other hand , for the frmg model @xmath77 at all redshifts makes the rmg steeper at earlier epochs . thus the chemical evolution over the galactic disk strongly depends on the properties of the outflow process , whereby the physical origin of the evolution of @xmath68 is a key to understanding the chemical evolution of the galactic disk . in the next subsection , we present possible models for explaining these properties of the outflow process . previous studies with both analytical models and numerical simulations have suggested that gas outflows from a galactic disk are driven by the injection of kinetic energy ( e.g. , springel & hernquist 2003 ; okamoto et al . 2010 ) or momentum ( e.g. , murray et al . 2005 ; oppenheimer & dav 2006 ; hopkins et al . 2012 ) from stellar feedback into ism . the former and latter outflow mechanisms are called the energy - driven wind ( edw ) and momentum - driven wind ( mdw ) , respectively . recently okamoto et al . ( 2014 ) showed that a baryonic feedback model including both edw and mdw successfully reproduces the various properties of galaxies , for example stellar mass function , stellar mass - halo mass relation and their redshift evolutions from @xmath26 = 4 to 0 . however , which wind mechanism is actually the main source of galactic outflow is not well understood . in this section we consider these edw and mdw models as the origin of the relation between @xmath56 and @xmath13 obtained in our analysis , which will provide valuable insights into the main mechanism of galactic outflow . first , we attempt to describe @xmath56 as a function of @xmath13 in the framework of the edw model . here we consider a star cluster with stellar mass of @xmath78 . because the energy injected from the star cluster into ism is proportional to @xmath78 in the edw model , the mass of outflow ejected from the star cluster , @xmath79 , is described by using a typical velocity of outflowing gas when leaving the disk , @xmath80 , as follows , @xmath81 we assume that @xmath80 corresponds to the escape velocity of the disk defined as , @xmath82 where @xmath83 , and @xmath84 is the scale height of the disk and is assumed to be constant along the radius . as the number of star clusters with @xmath78 in the region where stars are formed in the rate of @xmath13 is estimated as @xmath85 , we can describe @xmath56 in terms of @xmath13 as follows , @xmath86 by substituting equations ( [ eq : edw1 ] ) and ( [ eq : vw ] ) into ( [ eq : out ] ) and adopting the ks relation , @xmath36 , we express @xmath56 as functions of @xmath87 and @xmath13 as follows , @xmath88 we regard the factor @xmath89 in this equation depends only on time , because the variation of @xmath87 along the radius is much smaller than that of @xmath13 . therefore @xmath89 and @xmath90 in this equation correspond to @xmath65 and @xmath68 in equation ( [ eq : fit ] ) , respectively . this formulation reveals that @xmath68 is independent of time and that by adopting @xmath91 as observed in local star - forming galaxies we find @xmath92 . these properties of @xmath68 are basically in agreement with our results obtained for the frmg model . moreover , since @xmath87 is generally much higher at higher redshifts , we reproduce @xmath65 as a decreasing function of time . to confirm the validity of equation ( [ eq : edw2 ] ) , in figure [ fig : e / m ] we show @xmath65 divided by the factor @xmath89 with blue solid line for the frmg model . in this figure we also show the undivided @xmath65 with blue dashed line for comparison . we note that each @xmath65 is normalized by the value at @xmath26 = 0 , and @xmath87 used in this procedure is derived by using the total gas and stellar mass at each redshift . we find that the divided @xmath65 for the frmg model is only slightly smaller than unity at all redshifts and is approximately constant at @xmath93 . thus the edw model can well represent the properties of gas outflow obtained for the frmg model . in contrast , the properties of @xmath68 in the srmg model are not understood in the framework of the edw model but the mdw model is at work as explained below . divided by @xmath94 and @xmath89 for the srmg model ( red solid line ) and frmg model ( blue solid line ) , respectively . the parameter @xmath87 used here is calculated from the total gas and stellar mass at each redshift . for comparison , we also show the undivided @xmath65 for the srmg model ( red dashed line ) and frmg model ( blue dashed line ) . each line is normalized by the value at @xmath26 = 0.,width=302,height=188 ] we now derive the relation between @xmath56 and @xmath13 based on the mdw model . we consider that the radiation emitted from a star cluster drives the ambient gas as outflow . the momentum injected into the ambient gas from a star cluster via the radiation during the time scale of @xmath95 , which should roughly correspond to the lifetime of massive stars , i.e. , @xmath69 10 myr , is described as follows , @xmath96 where @xmath97 and @xmath98 are the luminosity of the star cluster and the optical depth of the ambient gas to the infrared emission by dust grains , respectively . we note that @xmath98 is proportional to the surface gas density of giant molecular clouds ( gmcs ) surrounding the star cluster , @xmath99 , rather than @xmath11 as in equations ( [ eq : dm1 ] ) and ( [ eq : dm2 ] ) . therefore , in order to discuss the result in figure [ fig:3 ] , we need to explicitly describe the relation between @xmath99 and @xmath11 . we consider here that each of a gmc is originally a fragment of the galactic gas disk with @xmath11 and the scale of fragmentation is roughly consistent with the scale height of the gas disk . then the mass of a gmc can be described as @xmath100 , where @xmath101 is the radius of a gmc . assuming that the ratio of @xmath84 to @xmath101 is nearly constant , as in murray et al . ( 2011 ) , we obtain @xmath102 . in this manner , we connect the physics in a galactic disk scale with that in a gmc scale in this discussion . here we consider the optically thin ( @xmath103 ) and thick ( @xmath104 ) limits , and the mass of outflow ejected from the star cluster for each limit is described as follows , @xmath105 where we assume that @xmath97 is proportional to @xmath78 . from equations ( [ eq : vw ] ) , ( [ eq : out ] ) and ( [ eq : mdw1 ] ) , @xmath56 for the mdw model can be presented as follows ; @xmath106 thus , we find that @xmath56 for the mdw model can also be expressed in the same functional form as equation ( [ eq : fit ] ) , similarly to the edw model . the remarkable difference from the case of the edw model is that @xmath68 depends on the optical depth of the ambient gas and thus the surface gas density . adopting @xmath91 leads to @xmath107 0.64 and 1.36 for the optically thin and thick limit , respectively , which roughly reproduce the values of @xmath68 for the srmg model at @xmath27 0 and 2 , respectively . therefore , we suggest that the evolution of @xmath68 obtained for the srmg model is understood in the framework of the mdw model , as the transition from the optically thick to thin limit in the galactic gas disk . this transition occurs at the gas density of @xmath108 ( murray et al . 2011 ) , which would be sufficiently lower than the gas densities in high-@xmath26 mwlgs . equation ( [ eq : mdw2 ] ) also predicts the decreasing @xmath65 with time . the red solid and dashed lines in figure [ fig : e / m ] show @xmath65 for the srmg model divided and undivided by the factor @xmath94 , respectively . from this figure , we find that the divided @xmath65 remains nearly unity and constant in comparison with the undivided @xmath65 . thus mdw appears to explain well the properties of gas outflow in the srmg model . from the above discussion , we conclude that clarifying how the time evolution of the rmg in mwlgs proceeds , i.e. , more steepened or flattened with time , distinguishes which wind - blowing mechanism , injection of momentum or kinetic energy from stellar feedback , is actually at work . thus , future observational constraints on the rmg in mwlgs will be important to understand the main mechanism driving galactic outflows . in section 3 , we have shown the linear relation between @xmath55 and @xmath13 , which is almost independent of the difference in the rmg evolutions . a similar proportionality was also confirmed by recchi et al . ( 2008 ) , who compared a chemical evolution model including gas inflow being proportional to sfr with a model assuming exponentially decreasing inflow rate with time . we show here that this proportionality is indeed universal for all the galactic evolution models with various gas inflow histories . following the results of this work as well as previous works , gas inflow is always systematically larger than outflow , thereby we assume here @xmath109 as a working hypothesis in the following discussion . then equation ( [ eq : dm1 ] ) for the conservation of gas mass is rewritten as , @xmath110 since @xmath111 is described with @xmath87 as follows , @xmath112 then , by substituting this equation into equation ( [ eq : sgmin1 ] ) , @xmath55 can be expressed as , @xmath113 the second term in the bracket on the right hand side corresponds to the ratio of gas consumption timescale , @xmath114 ( @xmath115 ) , to the timescale on which @xmath87 is changing , @xmath116 ( @xmath117 ) . we note here that @xmath116 depends on both sfr and inflow rate , whereas @xmath114 depends only on sfr . this implies that while @xmath118 in the closed - box model , the model taking into account inflow yields @xmath119 , because the gas supply by inflow cancels out the decrease of the gas mass due to star formation . therefore we find from equation ( [ eq : sgmin3 ] ) that @xmath55 is basically proportional to @xmath13 for @xmath120 , which is in particular the case at high redshifts . then the property of @xmath64 is dominated by the factor @xmath121 , which is a decreasing function of time , thereby reproducing the time evolution of @xmath64 presented in section 3 . for @xmath122 , as expected at most of the lower redshifts , the second term in the bracket on the right hand side of equation ( [ eq : sgmin3 ] ) provides the deviation from the simple proportionality , which may reproduce @xmath67 being slightly smaller than unity as derived in our analysis . thus the proportionality of @xmath55 to @xmath13 as revealed by our analysis is simply understood from the conservation of gas mass . this proportionality may imply that gas inflow regularly controls the gas budget and sfr in the galactic disk . as noted in section 2.1 , our analysis does not include the effect of radial redistributions of metals inside the galactic disk . however , the recent observations of nearby galaxies having extended gas disks show that the star formation activities observed at their outskirts are too weak to produce their metallicities observed in such regions , and therefore suggest the need of significant transportations of heavy elements from their inner to outer disk regions ( werk et al . 2010 , 2011 ; bresolin et al . such transportations of heavy elements may be driven by radial flows of gas inside galactic disks due to gravitational instabilities or re - accretion of metal - enriched galactic wind into the galactic disk . in this subsection we discuss the possible impacts of such radial redistributions of heavy elements on our results . radial flow of gas may be frequently driven by non - axisymmetric structures such as bar / spiral and significantly affect the structural and chemical evolutions of disk galaxies ( e.g. , schnrich & binney 2009 ; minchev et al . 2013 ; kubryk et al . we here attempt to simply evaluate to what extent such radial flows can actually change our results . it is worth noting , however , that the answer may sensitively depend on the detailed properties of given radial flow . the effect of radial flow on the evolution of a surface gas mass density at each radius is represented by adding an advection term to the right side of equation ( 1 ) , @xmath123 , where @xmath124 is the velocity of radial flow . taking into account @xmath125 as obtained above , we write @xmath126 several chemical evolution models for our galaxy including radial flow suggested the advection term in equation ( [ eq : rf ] ) to be of the order of @xmath127 ( e.g. , schnrich & binney 2009 ; kubryk et al . 2014 ) , which is comparable to @xmath55 at @xmath128 as followed from figure [ fig:1 ] . therefore the influence of radial flow on the estimate of @xmath55 may be significant only at @xmath128 . we also note that in our analysis all the terms except for those of @xmath55 and advection in equation ( [ eq : rf ] ) are derived independently from the latter two terms , so that the change of @xmath55 associated with radial flow simply reflects the sign and amplitude of the advection term . we now consider the effect of bar / spiral structures , which generally drive radial flow with negative ( positive ) @xmath124 for the gas at @xmath6 smaller ( larger ) than the co - rotation radius of bar / spiral , @xmath129 . then the last term of the right hand side of equation ( [ eq : rf ] ) is negative at @xmath6 around @xmath129 , thereby to compensate this export of gas due to the radial flow , @xmath55 becomes larger than that for the case without radial flow . in contrast , the advection term is positive in both the central and outer disk regions , so @xmath55 becomes lower . then @xmath67 in the case of non - zero @xmath124 at @xmath130 ( @xmath131 ) becomes smaller ( larger ) than that in the case of @xmath132 . thus radial flow will provide non - monotonous changes in the relation between @xmath55 and @xmath13 . however when considering the effects of radial flow over the entire disk , the difference of @xmath67 between the case of zero and non - zero @xmath124 may be small , implying that @xmath55 is on average proportional to @xmath13 even including the effect of radial flow . thus the effect of radial flow on the derived properties of gas inflow is expected to be insignificant . the effect on the outflow rate , @xmath56 , by the presence of radial flow can be inferred as follows . for the disk with the negative rmg , because metal - poor ( rich ) gas present in the outer ( inner ) disk regions flow inward ( outward ) , the rmg tends to be flattened by such radial flow . then @xmath68 may become smaller in response to this flattened rmg since the outflow with smaller @xmath68 works so as to steepen the rmg more efficiently , as mentioned in section 4.1 . recent hydro - dynamical simulations for galaxy evolution suggest that some fraction of gas ejected from the galactic disk by feedback processes remain in the host halo and accrete back into the disk ( oppenheimer & dav 2008 ; dav et al . 2011 ) . moreover outflowing gas may acquire additional angular momentum via feedback processes and preferentially re - accrete into outer disk regions than the radii where they originally resided ( bekki et al . . therefore re - accretion of metal - enriched galactic wind , if it occurs , may play a role in transporting heavy elements from the inner to outer disk regions , thereby strongly affecting the radial distribution of heavy elements inside the galactic disk ( e.g. , tsujimoto et al . 2010 ; gibson et al . 2013 ) . to investigate this influence on our results , we consider the case that inflowing gas consists of not only primordial one , but also re - accreting enriched one , for which we adopt a non - zero @xmath17 to solve equation ( [ eq : dm2 ] ) . for this experiment , we assume that the metallicity of inflowing gas at each radius is proportional to the total metallicity of the galaxy , @xmath133 , where the proportional coefficient , @xmath134 , is assumed to increase linearly along the radius so as to represent re - accretion of metals preferentially into the outer disk regions . as a fiducial example , we adopt @xmath135 so that it changes from 0.1 at @xmath6 = 0 kpc to 0.2 at @xmath6 = 10 kpc . we believe that this case provides sufficiently large @xmath17 to examine the effect , because the actually observed metallicities in high velocity clouds presently falling into our galactic disk are estimated as only 0.09 times the solar metallicity ( e.g. , wakker et al . 1999 ) . we perform this calculation for both the srmg and frmg models and find that this form of non - zero @xmath136 makes about 20 % of metals ejected from the entire disk eventually fall back at later epochs . we also find that the results from these calculations are basically the same as those shown in section 3 : the change in the parameters @xmath62 and @xmath63 by adopting this non - zero @xmath17 are typically only about 10 % and generally confined to less than 30 % at all epochs for both the srmg and frmg models , so the redshift evolutions of these parameters remain the same as those shown in figure [ fig:3 ] . therefore we conclude that the effect of re - accretion of metal - enriched galactic wind does not significantly modify our conclusions in this paper . the total inflow and outflow rates at each redshift are obtained by integrating the inflow and outflow profiles along the radius shown in figure [ fig:1 ] . the information on these total gas flow rates , which are to be compared with the observations of distant mwlgs , can place useful constraints on galactic chemical evolution models . we here present the integrated inflow and outflow masses obtained from our analysis , and discuss their roles in galaxy evolution . figure [ fig : tin ] shows the total inflow rates ( solid lines ) and cumulative inflow masses after @xmath60 ( dashed lines ) derived by integrating the inflow profile within @xmath6 = 10 kpc , which is the outer boundary of the disk in our analysis as mentioned in section 2 , where the results from the srmg and frmg models are shown with red and blue lines , respectively . we find that the total inflow rates are highest at @xmath60 and decrease rapidly with time at later epochs . it is clear that the total inflow rates for two models are remarkably similar , although the internal properties of gas inflow between the models are largely different . this result suggests that the total mass of inflowing gas into a galaxy is determined by the cumulative properties of the galaxy , such as its total stellar mass , sfr and mass budget of heavy elements , rather than the spatially resolved properties , such as the radial distributions of baryonic components and their metallicities . the total masses accreted on the galactic disk after @xmath60 are @xmath137 and @xmath138 for the srmg and frmg models , respectively . these masses correspond to the present stellar disk mass in mwlgs . = 10 kpc ( solid line ) and the cumulative inflow mass after @xmath60 ( dashed line ) as a function of redshift . the red and blue lines show the results for the srmg and frmg models , respectively . for comparison , the case for the ideal baryonic accretion is shown with black lines.,width=302,height=188 ] in figure [ fig : tin ] we also show the ideal baryonic accretion into the halo of mwlgs with black lines , which is obtained by multiplying the cosmic baryonic fraction , @xmath139 , by the average virial mass growth rate for mwlgs ( bouch et al . 2010 , and references therein ) . we find that this ideal accretion is clearly different from the actual inflows presented by our analysis , as the latter decline much faster than the former . this difference implies that not all the gas existing in the halo of mwlgs has been supplied on the galactic disk , in particular at lower redshifts . this suppression of gas infall may be caused by feedback from supernovae or active galactic nucleus in the galaxy , which makes halo gas heated up before accreting on the galactic disk . recently , lu et al . ( 2015 ) investigated the semi - analytic model , which includes the effects of preheating mechanisms , and found that the model can reproduce remarkably well various observational scaling relations such as the cold gas fraction - virial mass relation , disk size - stellar mass relation and its evolution . thus the feedback processes in a galaxy may be linking up not only to the production of outflow , but also to the several properties of star - forming galaxies including baryonic accretion . figure [ fig : tout1 ] is the same as figure [ fig : tin ] , but for the total outflow rates . we find that these rates show nearly the same evolution for both models , i.e. , declining rapidly with time , similarly to the total inflow rates . the total masses ejected from the galactic disk after @xmath60 are @xmath140 and @xmath141 for the srmg and frmg models , respectively . figure [ fig : tout2 ] shows the total outflow rate of metals and their cumulative mass . this flow is also decreasing with time , but this decreasing rate is somewhat slower than that for gas outflow because the chemical abundance of the galactic disk is a increasing function of time . the total masses of metals ejected from the galactic disk after @xmath60 are @xmath142 and @xmath143 for the srmg and frmg models , respectively . these masses correspond to about 40 % of the mass of all metals synthesized in the star formation history of mwlgs , @xmath144 . similar results were reported by the previous works , which compared the mass of metals still contained in the galactic disk with that produced by all the star formation processes ( e.g. , zahid et al . according to peeples et al . ( 2014 ) , about 80 % of metals are already lost from the galactic disk in mwlgs probably due to outflow . thus these works including our current analysis imply that galactic outflows have provided significant effects on the chemical evolution of galaxies . = 10 kpc ( solid line ) and the cumulative outflow mass after @xmath60 ( dashed line ) as a function of redshift . the red and blue lines show the results for the srmg and frmg models , respectively.,width=302,height=188 ] = 10 kpc ( solid line ) and the cumulative metal outflow mass after @xmath60 ( dashed line ) as a function of redshift . the red and blue lines show the results for the srmg and frmg models , respectively.,width=302,height=188 ]

we find that the efficiency of gas inflow for a given sfr decreases with time and that the inflow rate is always nearly proportional to the sfr . for gas outflow , although its efficiency for a given sfr is a decreasing function of time , similarly to gas inflow , the outflow rate is not necessarily proportional to the sfr and the relation between the outflow rate and sfr strongly depends on the evolution of the adopted rmg . we also find that the results on the outflow rate can be reproduced in the framework of momentum - driven ( energy - driven ) wind mechanism if the rmg is steepening ( flattening ) with time .

we investigate gas inflow and outflow histories in milky way - like disk galaxies , to get new insights into the baryonic processes in galaxy formation and evolution . for this purpose , we solve the equations for the evolutions of the surface mass densities of gas and metals at each radius in a galactic disk , based on the observed structural properties of distant star - forming galaxies , including the redshift evolution of their stellar mass distribution , their scaling relation between the mass of baryonic components , star formation rate ( sfr ) and chemical abundance , as well as the supposed evolution of their radial metallicity gradients ( rmgs ) . we find that the efficiency of gas inflow for a given sfr decreases with time and that the inflow rate is always nearly proportional to the sfr . for gas outflow , although its efficiency for a given sfr is a decreasing function of time , similarly to gas inflow , the outflow rate is not necessarily proportional to the sfr and the relation between the outflow rate and sfr strongly depends on the evolution of the adopted rmg . we also find that the results on the outflow rate can be reproduced in the framework of momentum - driven ( energy - driven ) wind mechanism if the rmg is steepening ( flattening ) with time . therefore if the well measured rmgs and their evolution for milky way - like galaxies are obtained from future observations , then our results will be useful to constrain the main driving mechanism for their galactic outflows .

1507.05688

i

we have investigated the gas inflow and outflow rate densities in milky way - like galaxies as a function of the sfr density , in order to get new insights into the baryonic processes tightly relating to galaxy formation and evolution . for this purpose , we solve equations ( [ eq : dm1 ] ) and ( [ eq : dm2 ] ) for the evolutions of the surface mass densities of gas and metals at each radius in a galactic disk , based on the observational studies of distant star - forming galaxies , such as the redshift evolution of their stellar mass distribution , their fundamental metallicity relation and the evolution of their radial metallicity gradients . the solutions of these equations allow us to evaluate the efficiency of inflow and outflow rate densities , @xmath55 and @xmath56 , and their dependence on the sfr density parameterized with @xmath62 and @xmath63 as presented in equation ( [ eq : fit ] ) . we have found that @xmath67 is approximately unity at all redshifts , representing the proportionality of the inflow rate to the sfr , and @xmath64 is a decreasing function of time . such properties of gas inflow can be understood based on the equation of gas mass evolution . therefore gas inflow dominates the budget of gas and star formation activity in a galactic disk . for gas outflow , while @xmath65 decreases with decreasing redshift , similarly to @xmath64 , @xmath68 deviates largely from unity at most redshifts , indicating that gas outflow rate is not necessarily proportional to sfr . moreover , we have found that the relation between the outflow rate and sfr strongly depends on the evolution of the adopted radial metallicity gradient . thus galactic outflow provides the significant influence on the distribution of heavy elements in disk galaxies . the relation between the outflow rate and sfr is understood based on the momentum and energy - driven wind models . it is found that momentum - driven ( energy - driven ) wind mechanisms can well reproduce the redshift evolution of @xmath68 based on the steepening ( flattening ) radial metallicity gradients with time . however , the detailed spatial distribution of metallicity in milky way - like galaxies has not been constrained well from the observations of distant galaxies . future observations armed with the state - of - the - art surface - spectroscopic instruments such as vlt / kmos will be important to unveil the detailed spatial distribution of metallicity in distant galaxies at several redshifts . if the well measured radial metallicity gradients and their evolution are available from such observations , then the method that we have presented in this work will be useful to constrain the main driving mechanism for their galactic outflows . we are grateful for the referee for her / his constructive comments that have helped us to improve our paper . this work is supported in part by a grants - in - aid for scientific research from the japan society for the promotion of science ( jsps ; no . 27 - 2450 for dt ) and by a grant - in - aid for scientific research ( 25287062 ) of the ministry of education , culture , sports , science and technology in japan . 1 athanassoula , e. 1992 , , 259 , 345 bekki , k. , tsujimoto , t. , & chiba , m. 2009 , , 692 , l24 belfiore , f. , maiolino , r. , & bothwell , m. 2015 , arxiv:1503.06823 bigiel , f. , leroy , a. , walter , f. , et al . 2008 , , 136 , 2846 bouch , n. , dekel , a. , genzel , r. , et al . 2010 , , 718 , 1001 bouch , n. , lehnert , m. d. , & proux , c. 2005 , , 364 , 319 bouch , n. , lehnert , m. d. , & proux , c. 2006 , , 367 , l16 bouch , n. , lehnert , m. d. , aguirre , a. , proux , c. , & bergeron , j. 2007 , , 378 , 525 bresolin , f. , kennicutt , r. c. , & ryan - weber , e. 2012 , , 750 , 122 casagrande , l. , schnrich , r. , asplund , m. , et al . 2011 , , 530 , a138 chiappini , c. , matteucci , f. , & gratton , r. 1997 , , 477 , 765 cresci , g. , mannucci , f. , maiolino , r. , et al . 2010 , , 467 , 811 dav , r. , finlator , k. , & oppenheimer , b. d. 2011 , , 416 , 1354 dayal , p. , ferrara , a. , & dunlop , j. s. 2013 , , 430 , 2891 genzel , r. , tacconi , l. j. , gracia - carpio , j. , et al . 2010 , , 407 , 2091 gibson , b. k. , pilkington , k. , brook , c. b. , stinson , g. s. , & bailin , j. 2013 , , 554 , a47 hayden , m. r. , bovy , j. , holtzman , j. a. , et al . 2015 , arxiv:1503.02110 hopkins , p. f. , quataert , e. , & murray , n. 2012 , , 421 , 3522 kennicutt , r. c. , jr . 1998 , , 498 , 541 kordopatis , g. , binney , j. , gilmore , g. , et al . 2015 , , 447 , 3526 kubryk , m. , prantzos , n. , & athanassoula , e. 2014 , arxiv:1412.0585 kudritzki , r .- , ho , i .- t . , schruba , a. , et al . 2015 , , 450 , 342 leitner , s. n. , & kravtsov , a. v. 2011 , , 734 , 48 lilly , s. j. , carollo , c. m. , pipino , a. , renzini , a. , & peng , y. 2013 , , 772 , 119 lu , y. , mo , h. j. , & wechsler , r. h. 2015 , , 446 , 1907 luck , r. e. , & lambert , d. l. 2011 , , 142 , 136 mannucci , f. , cresci , g. , maiolino , r. , marconi , a. , & gnerucci , a. 2010 , , 408 , 2115 minchev , i. , chiappini , c. , & martig , m. 2013 , , 558 , a9 morishita , t. , ichikawa , t. , noguchi , m. , et al . 2015 , arxiv:1502.05713 murray , n. , mnard , b. , & thompson , t. a. 2011 , , 735 , 66 murray , n. , quataert , e. , & thompson , t. a. 2005 , , 618 , 569 navarro , j. f. , & steinmetz , m. 2000 , , 538 , 477 noguchi , m. 1998 , , 392 , 253 okamoto , t. , frenk , c. s. , jenkins , a. , & theuns , t. 2010 , , 406 , 208 okamoto , t. , shimizu , i. , & yoshida , n. 2014 , , 66 , 70 oman , k. a. , navarro , j. f. , fattahi , a. , et al . 2015 , arxiv:1504.01437 oppenheimer , b. d. , & dav , r. 2006 , , 373 , 1265 oppenheimer , b. d. , & dav , r. 2008 , , 387 , 577 pagel , b. e. j. 1989 , rev . mexicana astron . astrofis . , 18 , 161 peeples , m. s. , werk , j. k. , tumlinson , j. , et al . 2014 , , 786 , 54 recchi , s. , spitoni , e. , matteucci , f. , & lanfranchi , g. a. 2008 , , 489 , 555 rupke , d. s. , veilleux , s. , & sanders , d. b. 2005 , , 160 , 115 snchez , s. f. , rosales - ortega , f. f. , iglesias - pramo , j. , et al . 2014 , , 563 , a49 sawala , t. , frenk , c. s. , fattahi , a. , et al . 2014 , arxiv:1412.2748 schmidt , m. 1959 , , 129 , 243 schnrich , r. , & binney , j. 2009 , , 396 , 203 sellwood , j. a. , & binney , j. j. 2002 , , 336 , 785 shapley , a. e. , steidel , c. c. , pettini , m. , & adelberger , k. l. 2003 , , 588 , 65 snaith , o. n. , haywood , m. , di matteo , p. , et al . 2014 , , 781 , l31 sparre , m. , hayward , c. c. , springel , v. , et al . 2014 , arxiv:1409.0009 springel , v. , & hernquist , l. 2003 , , 339 , 289 stott , j. p. , sobral , d. , swinbank , a. m. , et al . 2014 , , 443 , 2695 toyouchi , d. , & chiba , m. 2014 , , 788 , 89 tremonti , c. a. , moustakas , j. , & diamond - stanic , a. m. 2007 , , 663 , l77 troncoso , p. , maiolino , r. , sommariva , v. , et al . 2014 , , 563 , a58 tsujimoto , t. , bland - hawthorn , j. , & freeman , k. c. 2010 , , 62 , 447 van dokkum , p. g. , leja , j. , nelson , e. j. , et al . 2013 , , 771 , l35 vila - costas , m. b. , & edmunds , m. g. 1992 , , 259 , 121 vogelsberger , m. , genel , s. , springel , v. , et al . 2014 , , 444 , 1518 wakker , b. p. , howk , j. c. , savage , b. d. , et al . 1999 , , 402 , 388 weiner , b. j. , coil , a. l. , prochaska , j. x. , et al . 2009 , , 692 , 187 werk , j. k. , putman , m. e. , meurer , g. r. , et al . 2010 , , 715 , 656 werk , j. k. , putman , m. e. , meurer , g. r. , & santiago - figueroa , n. 2011 , , 735 , 71 white , s. d. m. , & frenk , c. s. 1991 , , 379 , 52 yabe , k. , ohta , k. , akiyama , m. , et al . 2015 , , 798 , 45 zahid , h. j. , dima , g. i. , kewley , l. j. , erb , d. k. , & dav , r. 2012 , , 757 , 54

we investigate gas inflow and outflow histories in milky way - like disk galaxies , to get new insights into the baryonic processes in galaxy formation and evolution . for this purpose , we solve the equations for the evolutions of the surface mass densities of gas and metals at each radius in a galactic disk , based on the observed structural properties of distant star - forming galaxies , including the redshift evolution of their stellar mass distribution , their scaling relation between the mass of baryonic components , star formation rate ( sfr ) and chemical abundance , as well as the supposed evolution of their radial metallicity gradients ( rmgs ) . therefore if the well measured rmgs and their evolution for milky way - like galaxies are obtained from future observations , then our results will be useful to constrain the main driving mechanism for their galactic outflows .

we investigate gas inflow and outflow histories in milky way - like disk galaxies , to get new insights into the baryonic processes in galaxy formation and evolution . for this purpose , we solve the equations for the evolutions of the surface mass densities of gas and metals at each radius in a galactic disk , based on the observed structural properties of distant star - forming galaxies , including the redshift evolution of their stellar mass distribution , their scaling relation between the mass of baryonic components , star formation rate ( sfr ) and chemical abundance , as well as the supposed evolution of their radial metallicity gradients ( rmgs ) . we find that the efficiency of gas inflow for a given sfr decreases with time and that the inflow rate is always nearly proportional to the sfr . for gas outflow , although its efficiency for a given sfr is a decreasing function of time , similarly to gas inflow , the outflow rate is not necessarily proportional to the sfr and the relation between the outflow rate and sfr strongly depends on the evolution of the adopted rmg . we also find that the results on the outflow rate can be reproduced in the framework of momentum - driven ( energy - driven ) wind mechanism if the rmg is steepening ( flattening ) with time . therefore if the well measured rmgs and their evolution for milky way - like galaxies are obtained from future observations , then our results will be useful to constrain the main driving mechanism for their galactic outflows .

cond-mat0109011

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we have introduced a range of schematic models that are capable of exhibiting a form of jamming under an imposed stress @xmath1 . the models are based on the sgr model of sollich _ et al . _ , but differ in that the effective temperature @xmath0 is no longer constant , and can instead vary with the state of the system through either the global stress @xmath1 or the local strain @xmath2 . we have considered choices of @xmath0 that decrease for increasing @xmath1 or @xmath2 , which is relevant to the study of shear thickening materials . these models have no spatial definition , and thus by construction can not exhibit any form of spatial heterogeneity . for @xmath3 , the flow curves can be extracted from the known curves for constant @xmath0 . many choices of @xmath5 produce flow curves with non monotonic regions , which exhibit hysteresis in @xmath79 under ramping the strain rate @xmath19 first upwards and then downwards . furthermore , a subset of these @xmath5 also give rise to a _ jammed _ state for a range of applied stresses , in that the strain @xmath17 creeps logarithmically , @xmath165 . the criterion for this to arise is that the curve of @xmath5 drops below the sgr yield stress curve @xmath84 when they are plotted on the same axes . for an imposed strain rate that decays to zero at late times , a jammed configuration was defined as one with a finite asymptotic stress , @xmath166 as @xmath167 and @xmath18 . it was found that whether or not a jammed configuration was reached depends on the entire strain history of the system , a situation that was referred to as _ history dependent jamming_. for @xmath10 , the flow curves are always monotonic , and steady flow is always reached under a constant imposed strain rate @xmath58 . however , for a range of imposed stresses and some choices of @xmath11 , steady flow is not realised . numerical integration of the master equation demonstrated that @xmath19 oscillated around a well defined mean with a single period of oscillation . the possibility of more complex non steady behaviour in some regions of parameter space could not be ruled out . a similar oscillatory behaviour occurs with a simpler model in which every element has the same energy barrier @xcite , which suggests that this phenomenon is robust . finally , we discussed the relationship between this oscillatory behaviour and that observed in experiments , and considered analogous phenomena from fields outside of rheology .

lett . * 78 * , 2020 ( 1997 ) ] , but with an effective temperature that is a decreasing function of either the global stress or the local strain . for appropiate , it is shown that the flow curves include a region of negative slope , around which the stress exhibits hysteresis under a cyclically varying imposed strain rate . these same systems may produce a finite asymptotic yield stress under an imposed strain , in a manner that depends on the entire stress history of the sample , a phenomenon we refer to as _ history dependent jamming_. in contrast , when the flow curves are always monotonic , but we show that some generate an oscillatory strain response for a range of steady imposed stresses .

we investigate shear thickening and jamming within the framework of a family of spatially homogeneous , scalar rheological models . these are based on the ` soft glassy rheology ' model of sollich _ et al . _ [ phys . rev . lett . * 78 * , 2020 ( 1997 ) ] , but with an effective temperature that is a decreasing function of either the global stress or the local strain . for appropiate , it is shown that the flow curves include a region of negative slope , around which the stress exhibits hysteresis under a cyclically varying imposed strain rate . a subclass of these have flow curves that touch the axis for a finite range of stresses ; imposing a stress from this range _ jams _ the system , in the sense that the strain creeps only logarithmically with time , . these same systems may produce a finite asymptotic yield stress under an imposed strain , in a manner that depends on the entire stress history of the sample , a phenomenon we refer to as _ history dependent jamming_. in contrast , when the flow curves are always monotonic , but we show that some generate an oscillatory strain response for a range of steady imposed stresses . similar spontaneous oscillations are observed in a simplified model with fewer degrees of freedom . we discuss this result in relation to the temporal instabilities observed in rheological experiments and stick slip behaviour found in other contexts , and comment on the possible relationship with ` delay differential equations ' that are known to produce oscillations and chaos . 2

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supermassive black holes ( smbh ) are believed to reside in nearly all galaxies @xcite and the masses of these smbh ( @xmath5 ) show correlations with host galaxy properties , implying that smbh and galaxy formation processes are closely linked @xcite . previous studies have shown correlations between @xmath5 and galaxy s effective stellar velocity dispersion ( @xmath9 ) , bulge luminosity ( @xmath10 ) , s@xmath1rsic index ( _ n _ ) and stellar mass of the bulge component ( @xmath11 ) @xcite . some of the challenges faced by current models of smbh formation and evolution include reproducing and maintaining these scaling relations regardless of the events that take place during galaxy evolution driven by the process of hierarchical mass assembly @xcite . these scaling relations are not only important tests of the models of smbh formation and evolution but also powerful predictive tools from which we can infer smbh masses of galaxies that are located at higher redshifts . in this paper , we examine the evidence for a scaling relation between @xmath5 and the _ total _ mass of the host galaxy ( denoted as @xmath0 ) . most self regulating theoretical models of smbh formation predict a fundamental connection between @xmath5 and @xmath0 of the host galaxy @xcite . one of the most important predictions of the galaxy models , which study the interaction between the dark matter haloes of galaxies and baryonic matter settling into the gravitational potential to form the bulge and smbh , is that halo properties determine those of the bulge component and smbh @xcite . however , observational evidence for such a scaling relation has been sparse since measurement of the total mass is non - trivial . results from @xcite examined some of the first _ indirect _ observational evidence for the existence of a @xmath8 relation . in @xcite , the correlation between bulge velocity dispersion ( @xmath12 ) and the observed circular velocity ( @xmath13 ) , for a sample of 20 elliptical galaxies and 16 spiral galaxies , is translated into an equivalent @xmath8 correlation . although @xmath12 can be translated into @xmath5 through @xmath14 relation in a straightforwards manner , an estimate of @xmath0 is dependent on the conversion between @xmath13 and virial velocity , the velocity of the galactic halo at the virial radius . @xcite uses results from @xmath15cdm cosmological simulations to derive @xmath0 . following @xcite , several studies have examined the @xmath16 relation and its implications for galaxy formation and evolution @xcite . the primary goal of this study is to extend the observational evidence to support the @xmath17 relation using an attractive , alternative , and _ direct _ method to measure the total mass of the host galaxy . in recent years , strong gravitational lensing has emerged as a powerful tool to probe the mass profiles , ranging from individual galaxies to clusters of galaxies @xcite . due to the fact deflection of a photon passing an intervening massive object is independent of the deflector s dynamical state , gravitational lensing does not suffer from difficulties associated with dynamical mass measurements of galaxies , where assumptions regarding orbital motions of tracers can lead to complications . thus , gravitational lensing is a more robust method to estimate the total mass , including dark matter , around early - type galaxies and infer the existence of an isothermal mass profile ( @xmath18 ) in various systems @xcite the mass enclosed within the einstein radius ( @xmath19 ) which is measured from the lens model that produces the best fit to the observed multiple images , is a direct probe of both luminous and dark mass in a galaxy . in conjunction with velocity dispersion and surface brightness profiles of the lens galaxy , measurement of @xmath19 from a lens model can be used effectively to constrain the luminous and dark matter profiles . in this study , we utilize the @xmath19 as a tracer of the total mass and use the @xmath20 mass profile of the lensing galaxy to determine the mass contained within a redshift - independent circular aperture . we also attempt to derive the @xmath8 relation using purely photometric tracers of @xmath5 and @xmath0 . therefore , we examine the possibility of using @xmath2 relation @xcite as the primary method to estimate black hole masses . surface brightness profiles of the bulge component of most galaxies , in particular e / s0 , can be described by the s@xmath1rsic law @xcite as follows : @xmath21 } ) } \label{eq : sersic}\end{aligned}\ ] ] where @xmath22(r ) is the surface brightness at radius @xmath23 and s@xmath1rsic index ( @xmath24 ) is the degree of light concentration . previous studies in the literature indicate that the quantity _ n _ varies monotonically with galaxy magnitude . therefore , the existence of a @xmath25 relation can be inferred given the dependence of @xmath5 on the galaxy magnitude @xcite and the connection between galaxy magnitude and s@xmath1rsic index @xcite . @xcite discuss the most recent version of the @xmath25 relation and indicate that the dependence between the quantities @xmath26 and @xmath27 can be best represented by a log - quadratic relation . the main motivation for using this relation is that measurement of _ n _ requires only imaging data , which is easier to acquire than spectroscopic data at a given redshift ; therefore , @xmath8 could be easily extended to large samples of higher redshift gravitational lenses , which may not have spectroscopic measurements . furthermore , _ n _ is a distant - independent quantity , an added advantage for estimating black hole masses of high redshift galaxies that may not have secure redshift measurements . this paper is structured as follows . in 2 we present a brief description of the target selection . in 3 we describe the following analysis procedures : 3.1 measurements of @xmath0 ; 3.2 : deriving the connection between @xmath5 and @xmath0 using @xmath3 relation ; 3.3 : deriving the connection between @xmath5 and @xmath0 using @xmath2 relation . in 4 we present the results of our analysis . in 5 and 6 we discuss the implications of our results and give some concluding remarks regarding this project . we assume the following cosmological terms for all computations in the paper : @xmath28 , @xmath29 , @xmath30 and @xmath31 . unless otherwise noted all scaling relations in this paper are defined as linear relationships in log - log space and all logarithms assume a base of 10 .

the best fit correlation , where is determined from relation , is over 2 orders of magnitude in . from a variety of tests the relation provides some of the first , direct observational evidence to test the prediction that supermassive black hole properties are determined by the halo properties of the host galaxy .

we investigate the correlation between the mass of a central supermassive black hole and the total gravitational mass of the host galaxy ( ) . the results are based on 43 galaxy - scale strong gravitational lenses from the sloan lens acs ( slacs ) survey whose black hole masses were estimated through two scaling relations : the relation between black hole mass and srsic index ( ) and the relation between black hole mass and stellar velocity dispersion ( ) . we use the enclosed mass within , the radius within which the density profile of the early type galaxy exceeds the critical density of the universe by a factor of 200 , determined by gravitational lens models fitted to hst imaging data , as a tracer of the total gravitational mass . the best fit correlation , where is determined from relation , is over 2 orders of magnitude in . from a variety of tests , we find that we can not reliably infer a connection between and from the relation . the relation provides some of the first , direct observational evidence to test the prediction that supermassive black hole properties are determined by the halo properties of the host galaxy .

0909.0269

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we use a sample of 43 early - type galaxies , which exhibit galaxy - scale strong gravitational lensing , to derive the scaling relation between black hole mass , @xmath5 , and the total mass , @xmath0 , of the host galaxy . in this study , we use gravitational lens modeling to directly measure the total mass and the mass profile of the galaxy rather than converting the observed circular velocity into a total mass , the traditional method that is used in black hole studies . we use two alternative scaling relations , @xmath3 and @xmath25 to estimate the black hole masses of the lens sample . we obtain a tight correlation between @xmath9 and @xmath0 in the log - log space . in conjunction with the @xmath3 relation , we derive the observational form of the @xmath8 relation that is consistent with no intrinsic scatter . we do not find a significant correlation between @xmath90 and @xmath0 . from a variety of tests , we find that we can not confidently estimate black hole masses with the @xmath98 relation . the scaling relation we observe between @xmath5 and @xmath0 is non - linear and is in agreement with theoretical predictions of the growth of black holes and observational studies of the local @xmath8 relation . the observed @xmath8 relation is also consistent with the studies of the fundamental plane of slacs lenses @xcite , which is suggestive of a unified scenario where the properties of the host halo determine those of the resulting galaxy and black hole formed through hierarchical merging . the observed non - linear correlation between @xmath5 and @xmath0 indicates that massive halos are more efficient in forming black holes and the slope of the @xmath8 relation is suggestive of a merger - driven , feed - back regulated process for the growth of black holes . we wish to thank laura ferrarese , chien peng , christopher pritchet , jon willis , and the members of the slacs team for valuable discussions and useful comments . we also wish to thank the anonymous referee whose helpful comments improved this paper . this research used the facilities of the canadian astronomy data centre operated by the national research council of canada with the support of the canadian space agency . the authors gratefully acknowledge the support from the national research council of canada and nserc through discovery grants . adams , f.c . , graff , d.s . , mbonye , m. , & richstone , d.o . 2003 , , 591 , 125 adams , f.c . , graff , d.s . , & richstone , d.o . 2001 , , 551 , l31 baes , m. , buyle , p. , hau , g.k.t . , & dejonghe , h. 2003 , , 341 , l44 bertin , e. , & arnouts , s. 1996 , , 117 , 393 bolton , a. , burles , s. , koopmans , l.v.e . , treu , t. , gavazzi , r. , moustaka , l.a . , wayth , r. , & + schlegel , d.j . 2008 , , 682 , 946 bolton , a. , treu , t. , koopmans , l.v.e . , gavazzi , r. , moustakas , l.a . , burles , s. , schlegel , d.j . , & wayth , r. 2008 , , 684 , 248 bolton , a. , burles , s. , koopmans , l.v.e . , treu , t. , & moustakas , l.a . 2006 , , 638 , 703 bullock , j.s . , kolatt , t.s . , sigad , y. , somerville , r.s . , kravtsov , a.v . , klypin , a.a . , primack , j.r . , & dekel , a. 2001 , , 321 , 559 buyle , p. , ferrarese , l. , gentile , g. , dejonghe , h. , baes , m. , & klein , u. 2006 , , 373 , 700 cattaneo , a. 2001 , , 324 , 128 cattaneo , a. , haehnelt , m.g . , rees , m.j . 1999 , , 308 , 77 courteau , s. , mcdonald , m. , widrow , l.m . , & holtzman , j. 2007 , , 655 , l21 croton , d.j . 2009 , , 394 , 1109 croton , d.j . , 2006 , , 365 , 11 di matteo , t. , springel , v. , & hernquist , l. 2005 , , 433 , 604 di matteo , t. , croft , r.a.c . , springel , v. , & hernquist , l. 2003 , , 593 , 56 djorgovski , s. , & davis , m. 1987 , , 313 , 59 dye , s. & warren , s. 2007 , arxiv:0708.0787 eisenstein , d.j . , et al . 2001 , , 122 , 2267 el - 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tim psf ( panel 2 ) , natural psf ( panel 3 ) and acs - library generated psf ( panel 4 ) is subtracted from the observed image . residual image where the galaxy model is convolved with a tiny - tim psf shows artifacts such as boxy - core feature , due to the finite size of the tiny - tim psf , evident in panel 2 . statistics of the pixels in panel 2 show that the mean value of the core residuals is comparable to the background level ; therefore , the artifact introduced by the finite tiny - tim psf does not significantly affect the quality of the overall fit . in general , we find that both natural and acs - library generated psfs produce minimal core residuals . however , most slacs fields are relatively devoid of stars , suitable for convolution ; therefore , we use acs - library generated psf for gim2d galaxy modeling . ] ) , i - band magnitude of the bulge ( @xmath63 ) and aperture corrected bulge velocity dispersion ( @xmath130 ) . the scaling relations between bulge structural parameters for sdss early type galaxies are constructed from a sample 77523 galaxies and are shown in gray - scale . the gray - scale is scaled to 20% of the peak value of the central distribution to show that the structural parameters of the slacs lenses lie well within the distribution that encompasses the sdss galaxies . the outlier in this figure is sdss j0959 + 0410 . ] and @xmath0 , for the sample of early type slacs lenses . velocity dispersion values from sdss pipeline are corrected to an aperture of radius equal to @xmath151 using the empirical relation @xcite . the error bars correspond to the 1-@xmath130 error of the aperture corrected velocity dispersion , from gaussian error propagation , taking the measurement errors of sdss velocity dispersions into account . total masses of the slacs lenses are derived from strong lens modeling parameters of @xcite . the 1-@xmath130 errors of @xmath0 , which are smaller than the data points , are incorporated into the fitting routines but not shown in this plot . the solid line correspond to the best - fit @xmath72 relation for all slacs lenses in the logarithmic space . ] with @xmath9 converted into @xmath5 using @xmath8 relation @xcite . the error bars correspond to 1-@xmath50 error on the quantity @xmath152 . the solid line corresponds to the @xmath8 relation for all slacs lenses derived using the @xmath72 and @xmath8 relations . the dashed line represents the resulting @xmath153 relation obtained by @xcite , where @xmath0 is computed from cosmological simulations @xcite relating the the observed circular velocity ( @xmath154 ) to the virial velocity of the host halo ( @xmath155 ) . the dotted line shows the resulting @xmath153 relation if @xmath0 is computed using @xmath156 @xcite . ] and @xmath0 , for the sample of early type slacs lenses . the s@xmath1rsic indices are derived from the best - fit bulge+disk decomposition of the slacs lenses . the error bars correspond to the measurement errors on the quantity @xmath90 . total masses of the slacs lenses are derived from strong lens modeling parameters of @xcite . the 1-@xmath50 errors of @xmath0 , which are smaller than the data points , are incorporated into the fitting routines but not shown in this plot . ] with @xmath90 converted into @xmath5 using @xmath25 relation @xcite . the error bars correspond to 1-@xmath50 error on the quantity @xmath152.the 1-@xmath50 error of @xmath0 is smaller than the data points , and is not shown in the plot . ] relation to slacs data . @xmath5 values are derived from the @xmath3 relation and s@xmath1rsic indices are best - fit results from the gim2d bulge - disk decomposition . error bar on the legend represent the typical 1-@xmath50 uncertainty of @xmath157 , derived from gaussian error propagation using measurement errors from the sdss velocity dispersions ( @xmath158 ) , and a measurement error of 20% on the quantity @xmath24 . the log - quadratic relation by @xcite is shown by the solid black line . ] versus @xmath159 for slacs lens sample . the values of @xmath90 are the best fit @xmath160 s@xmath1rsic indices from the bulge+disk decomposition using gim2d . the values of @xmath101 are the best - fit , extinction - corrected , i - band @xmath160 magnitudes from the bulge+disk decomposition . ] relation from various analytical predictions for @xmath161 . the pale blue , solid lines are predictions from @xcite , where @xmath162 . the dashed lines are predictions from @xcite , where @xmath127 , for the same epochs as @xcite ( epochs increasing in the same order as shown in the labels for @xcite ) . the thick , solid black line is a comparison of the observed @xmath8 relation from the slacs lens sample ( equation [ eq : observational ] ) , at @xmath128 . ] relation to theoretical predictions of the @xmath8 relation at @xmath129 , the mean redshift of the slacs lens sample . the solid black line correspond to the best - fit result from this study and the shaded region shows the 1-@xmath50 upper and lower limits of the @xmath8 relation . the solid red and blue lines correspond to the theoretical predictions of @xcite and @xcite of the @xmath8 relation respectively . ] lccccccc sdss j0029 - 0055 & 0.23 & 0.76 & @xmath163 & 7.29@xmath164 & @xmath165 & 2.65@xmath164 & 1.04@xmath166 + sdss j0037 - 0942 & 0.20 & 0.94 & @xmath167 & 3.38@xmath164 & @xmath168 & 5.69@xmath164 & 2.40@xmath166 + sdss j0216 - 0812 & 0.33 & 0.43 & @xmath169 & 8.50@xmath170 & @xmath171 & 1.52@xmath172 & 4.03@xmath166 + sdss j0252 + 0039 & 0.28 & 0.58 & @xmath173 & 1.19@xmath172 & @xmath174 & 6.48@xmath170 & 1.27@xmath166 + sdss j0330 - 0020 & 0.35 & 0.88 & @xmath175 & 9.65@xmath164 & @xmath176 & 1.88@xmath164 & 1.51@xmath166 + sdss j0728 + 3835 & 0.21 & 0.95 & @xmath177 & 7.21@xmath164 & @xmath178 & 1.90@xmath164 & 1.73@xmath166 + sdss j0737 + 3216 & 0.32 & 0.85 & @xmath179 & 6.70@xmath164 & @xmath180 & 1.28@xmath172 & 2.41@xmath166 + sdss j0822 + 2652 & 0.24 & 0.81 & @xmath181 & 4.41@xmath164 & @xmath182 & 4.67@xmath164 & 2.00@xmath166 + sdss j0912 + 0029 & 0.16 & 1.00 & @xmath183 & 1.35@xmath164 & @xmath184 & 1.09@xmath172 & 4.36@xmath166 + sdss j0935 - 0003 & 0.35 & 0.27 & @xmath185 & 6.89@xmath170 & @xmath186 & 3.33@xmath172 & 4.46@xmath166 + sdss j0936 + 0913 & 0.19 & 0.79 & @xmath187 & 6.27@xmath164 & @xmath188 & 3.42@xmath164 & 1.48@xmath166 + sdss j0946 + 1006 & 0.22 & 0.40 & @xmath189 & 2.61@xmath170 & @xmath190 & 5.91@xmath164 & 2.32@xmath166 + sdss j0955 + 0101 & 0.11 & 0.77 & @xmath191 & 1.05@xmath172 & @xmath192 & 1.14@xmath164 & 1.21@xmath166 + sdss j0956 + 5100 & 0.24 & 0.90 & @xmath193 & 9.48@xmath164 & @xmath194 & 1.11@xmath172 & 3.24@xmath166 + sdss j0959 + 0410 & 0.13 & 0.14 & @xmath195 & 2.10@xmath170 & @xmath196 & 2.25@xmath164 & 1.08@xmath166 + sdss j0959 + 4416 & 0.24 & 0.64 & @xmath197 & 1.87@xmath164 & @xmath198 & 3.99@xmath164 & 1.65@xmath166 + sdss j1020 + 1122 & 0.28 & 0.58 & @xmath199 & 3.20@xmath164 & @xmath200 & 7.16@xmath164 & 2.76@xmath166 + sdss j1029 + 0420 & 0.10 & 0.84 & @xmath201 & 6.24@xmath164 & @xmath202 & 1.81@xmath164 & 9.82@xmath203 + sdss j1106 + 5228 & 0.10 & 0.79 & @xmath204 & 5.90@xmath164 & @xmath205 & 4.94@xmath164 & 1.49@xmath166 + sdss j1112 + 0826 & 0.27 & 0.67 & @xmath206 & 5.63@xmath170 & @xmath207 & 1.32@xmath172 & 3.08@xmath166 + sdss j1134 + 6027 & 0.15 & 0.53 & @xmath208 & 1.55@xmath164 & @xmath209 & 3.80@xmath164 & 1.51@xmath166 + sdss j1142 + 1001 & 0.22 & 0.48 & @xmath210 & 1.98@xmath164 & @xmath211 & 2.81@xmath164 & 1.68@xmath166 + sdss j1143 - 0144 & 0.11 & 0.90 & @xmath212 & 1.46@xmath164 & @xmath213 & 4.70@xmath164 & 2.52@xmath166 + sdss j1204 + 0358 & 0.16 & 0.72 & @xmath214 & 4.37@xmath164 & @xmath215 & 5.78@xmath164 & 1.72@xmath166 + sdss j1205 + 4910 & 0.22 & 0.78 & @xmath216 & 5.66@xmath164 & @xmath217 & 6.17@xmath164 & 2.37@xmath166 + sdss j1213 + 6708 & 0.12 & 0.89 & @xmath218 & 1.19@xmath172 & @xmath219 & 5.76@xmath164 & 1.70@xmath166 + sdss j1250 + 0523 & 0.23 & 0.70 & @xmath191 & 1.05@xmath172 & @xmath220 & 3.89@xmath164 & 1.46@xmath166 + sdss j1402 + 6321 & 0.20 & 1.00 & @xmath221 & 6.38@xmath164 & @xmath222 & 4.40@xmath164 & 2.61@xmath166 + sdss j1403 + 0006 & 0.19 & 0.66 & @xmath223 & 1.18@xmath172 & @xmath224 & 1.74@xmath164 & 1.18@xmath166 + sdss j1416 + 5136 & 0.30 & 0.55 & @xmath225 & 6.07@xmath170 & @xmath226 & 4.04@xmath164 & 2.31@xmath166 + sdss j1420 + 6019 & 0.06 & 0.75 & @xmath227 & 1.29@xmath164 & @xmath228 & 1.74@xmath164 & 9.39@xmath203 + sdss j1430 + 4105 & 0.29 & 0.74 & @xmath229 & 3.00@xmath164 & @xmath230 & 1.18@xmath172 & 3.76@xmath166 + sdss j1443 + 0304 & 0.13 & 0.89 & @xmath231 & 1.17@xmath172 & @xmath232 & 1.74@xmath164 & 9.46@xmath203 + sdss j1451 - 0239 & 0.13 & 0.93 & @xmath233 & 5.46@xmath164 & @xmath234 & 2.21@xmath164 & 1.17@xmath166 + sdss j1525 + 3327 & 0.36 & 0.58 & @xmath235 & 3.23@xmath164 & @xmath236 & 5.06@xmath164 & 3.03@xmath166 + sdss j1531 - 0105 & 0.16 & 1.00 & @xmath237 & 5.37@xmath164 & @xmath238 & 5.55@xmath164 & 2.35@xmath166 + sdss j1538 + 5817 & 0.14 & 0.86 & @xmath239 & 1.12@xmath172 & @xmath240 & 1.06@xmath164 & 1.17@xmath166 + sdss j1627 - 0053 & 0.21 & 0.67 & @xmath241 & 3.27@xmath164 & @xmath242 & 7.91@xmath164 & 2.11@xmath166 + sdss j1630 + 4520 & 0.25 & 0.86 & @xmath243 & 2.68@xmath164 & @xmath244 & 6.15@xmath164 & 3.02@xmath166 + sdss j1636 + 4707 & 0.23 & 0.64 & @xmath245 & 1.33@xmath164 & @xmath246 & 3.23@xmath164 & 1.53@xmath166 + sdss j2238 - 0754 & 0.14 & 0.80 & @xmath247 & 3.41@xmath164 & @xmath248 & 1.47@xmath164 & 1.44@xmath166 + sdss j2303 + 1422 & 0.16 & 0.97 & @xmath249 & 2.71@xmath164 & @xmath250 & 3.83@xmath164 & 2.57@xmath166 + sdss j2341 + 0000 & 0.19 & 0.52 & @xmath251 & 9.02@xmath164 & @xmath252 & 1.44@xmath164 & 1.87@xmath166

we investigate the correlation between the mass of a central supermassive black hole and the total gravitational mass of the host galaxy ( ) . the results are based on 43 galaxy - scale strong gravitational lenses from the sloan lens acs ( slacs ) survey whose black hole masses were estimated through two scaling relations : the relation between black hole mass and srsic index ( ) and the relation between black hole mass and stellar velocity dispersion ( ) .

we investigate the correlation between the mass of a central supermassive black hole and the total gravitational mass of the host galaxy ( ) . the results are based on 43 galaxy - scale strong gravitational lenses from the sloan lens acs ( slacs ) survey whose black hole masses were estimated through two scaling relations : the relation between black hole mass and srsic index ( ) and the relation between black hole mass and stellar velocity dispersion ( ) . we use the enclosed mass within , the radius within which the density profile of the early type galaxy exceeds the critical density of the universe by a factor of 200 , determined by gravitational lens models fitted to hst imaging data , as a tracer of the total gravitational mass . the best fit correlation , where is determined from relation , is over 2 orders of magnitude in . from a variety of tests , we find that we can not reliably infer a connection between and from the relation . the relation provides some of the first , direct observational evidence to test the prediction that supermassive black hole properties are determined by the halo properties of the host galaxy .

1604.02823

c

in this paper , we have presented an extensive study of so melting , namely of the sudden disappearance of so after a quantum quench . we have highlighted the fact that non - local order can be particularly fragile in a dynamical context , in the presence of a perturbation which breaks the symmetry to which so is related . this is qualitatively different from what would happen in the presence of a local order parameter in the manner of landau , where the continuity of the evolution rules out the disappearance of order in an infinitesimal time we analyzed this phenomenon by considering a quantum quench in a spin-1 chain initialized in the aklt state . we focused on the coupling constant , time and string - length evolution of the expectation value of the string operator after the quench , and related the presence of so after the quench to the symmetries of the post - quench hamiltonian . in our simulations , we observed a first exponential decay of the expectation value of the string operator as a function of the string length , which we identify as the thermalization region . this region can be followed either by a plateau ( when the system displays so ) or by a second exponential decay . this second regime is what it is associated to so melting . a short - time expansion allowed to predict the behavior of so just after the quench at short times and distances . at longer times , where thermalization occurs , non - perturbative effects come into play and we resorted only on the numerical results . the features that we studied in our simulations ( e.g. , light - cone effects ) could also be observed when quenching from non - topological states and measuring string correlations ( see , e.g. , the non - topological mott insulating phase of the bose - hubbard model @xcite or the fermionic correlations in the ising chain @xcite ) . the melting phenomenon is related to the non - locality of the observable , more than the topology of the state . however , in the aklt chain , so is related to the presence of topological order , and thus this out - of - equilibrium analysis can be linked to the survival or disappearance of topological properties in the system . so is only one of the features which characterize the properties of one - dimensional symmetry - protected phases of matter @xcite . as long as the properties of the ground state are concerned , it is known that different indicators , such as so , the presence of edge modes or the existence of degeneracies in the entanglement spectrum , may behave differently @xcite . we leave as an open intriguing perspective the characterization of the behavior of such indicators in an out - of - equilibrium context , as well as the extension of this discussion to higher dimensions . generally speaking , it would be interesting to assess whether symmetry - protected topological phases can disappear abruptly after a quantum quench . r.f . was supported by eu ( ip - siqs and strep - quic ) , and by scuola normale superiore ( progetto interno non - equilibrium dynamics of one - dimensional quantum systems " ) . r.f . also acknowledges the oxford martin school for support . l.m . was supported by labex ens - icfp : anr-10-labx-0010/anr-10-idex-0001 - 02 psl*. l.m . and d.r . acknowledge support by the italian miur ( firb project rbfr12nlna ) .

depending on which of these two situations arises , string order is either preserved or lost even at infinitesimal times in the thermodynamic limit . the fact that non - local order may be abruptly destroyed , what we call _ string - order melting _ , makes it qualitatively different from typical order parameters in the manner of landau .

we investigate the evolution of string order in a spin-1 chain following a quantum quench . after initializing the chain in the affleck - kennedy - lieb - tasaki state , we analyze in detail how string order evolves as a function of time at different length scales . the hamiltonian after the quench is chosen either to preserve or to suddenly break the symmetry which ensures the presence of string order . depending on which of these two situations arises , string order is either preserved or lost even at infinitesimal times in the thermodynamic limit . the fact that non - local order may be abruptly destroyed , what we call _ string - order melting _ , makes it qualitatively different from typical order parameters in the manner of landau . this situation is thoroughly characterized by means of numerical simulations based on matrix product states algorithms and analytical studies based on a short - time expansion for several simplified models .

0807.0012

i

cosmological gamma - ray bursts ( grbs ) have released a tremendous amount of energy in the past and present universe . their emission covers very wide range of frequencies : a highly variable prompt phase radiates @xmath3100 kev gamma rays , while a subsequent afterglow radiates radio to x - ray photons . it is likely that the bulk of these photons are emitted by gyration of relativistic electrons in magnetic fields e.g . , synchrotron radiation . the relativistic electrons are accelerated in either internal dissipation ( for prompt emission ) or external shocks ( for afterglows ) . for reviews , see , @xcite . gev photons were detected as well from several grbs by the energetic gamma ray experimental telescope ( egret ) on board the _ compton gamma ray observatory ( cgro ) _ the data are still not sufficient for us to firmly infer emission mechanisms of these gev gamma rays , but the most promising mechanism is synchrotron self - compton ( ssc ) scattering ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? this is because the relevant emission parameters such as the energy fraction of the grb jets going to electrons ( @xmath4 ) and magnetic fields ( @xmath5 ) are relatively well measured from the afterglow spectra as well as light curves ; the typical values are @xmath6 and @xmath7 ( e.g. , * ? ? ? * ; * ? ? ? * ) . in the prompt emission , @xmath4 is similar or even higher , as evident from the high efficiency of this phase , while @xmath5 is not well constrained . thus , there should be a significant inverse - compton ( ic ) component accompanying the synchrotron radiation in both the afterglow and prompt emission . the luminosities of the synchrotron and ic are expected to be comparable as ic - to - synchrotron luminosity ratio is roughly given by @xmath8 , according to theory ( e.g. , * ? ? ? * ) . in this paper , we explore the gev gamma - ray emission of grbs in the context of ssc mechanism . besides the several grbs detected by egret , there are many others for which upper bounds on the fluence were obtained @xcite . these @xmath3100 grbs should also be compared with the predictions of ssc model , because the fluence upper limits in the egret energy band are comparable to the fluence of prompt emission collected by burst and transient source experiment ( batse ) instrument onboard _ cgro_. as the experimental bound is already strong , while theoretical models of ssc process predict a large fluence for the egret energy range , we derive meaningful constraints from egret data analysis on the physics of the high - energy emission mechanisms of grbs . this approach is different from ( and therefore complementary with ) that in previous studies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) , where the prediction of gamma - ray flux relies only on theoretical models and sub - gev observations . we instead use egret data in order to infer the gev emission and constrain the theoretical models . we use our results to predict the expected number of grbs that would be detected by the _ gamma - ray large area space telescope ( glast)_. the _ glast _ satellite is equipped with the large area telescope ( lat ) , which is an upgraded version of egret . since revealing the high - energy emission mechanisms of grbs are one of the important objectives of _ glast _ , our prediction should give a useful guideline . finally , we apply our results to estimate the contribution of grbs to the diffuse extragalactic gamma - ray background ( egb ) , which was also measured by egret ( * ? ? ? * ; * ? ? ? * see , however , @xcite for a subtle issue of galactic foreground subtraction ) . this paper is organized as follows . in [ sec : ic ] , we summarize the predictions of ssc model for the prompt ( [ sub : prompt ] ) and afterglow ( [ sub : afterglow ] ) phases . section [ sec : constraint on high - energy emission with egret ] is devoted for analysis of the grb fluence data by egret , from which distributions of fluence in the gev band are derived . we then use these distributions to argue prospects for grb detection with _ glast _ in [ sec : glast ] , and implications for egb from grb emissions in [ sec : egb ] . in [ sec : conclusions ] , we give a summary of the present paper .

we investigate the gev emission from gamma - ray bursts ( grbs ) , using the results from the energetic gamma ray experimental telescope ( egret ) , and in view of the _ gamma - ray large area space telescope ( glast)_. assuming that the conventional prompt and afterglow photons originate from synchrotron radiation , we compare an accompanying inverse - compton component with egret measurements and upper limits on gev fluence , taking klein - nishina feedback into account . glast _ glast _ will enable a more precise test of the high - energy emission mechanism . finally , we show that the contribution of grbs to the flux of the extragalactic gamma - ray background measured with egret is at least 0.01% and likely around 0.1% .

we investigate the gev emission from gamma - ray bursts ( grbs ) , using the results from the energetic gamma ray experimental telescope ( egret ) , and in view of the _ gamma - ray large area space telescope ( glast)_. assuming that the conventional prompt and afterglow photons originate from synchrotron radiation , we compare an accompanying inverse - compton component with egret measurements and upper limits on gev fluence , taking klein - nishina feedback into account . we find that egret constraints are consistent with the theoretical framework of the synchrotron self - compton model for both prompt and afterglow phases , and discuss constraints on microphysical parameters in both phases . based on the inverse - compton model and using egret results , we predict that _ glast _ would detect grbs with gev photons at a rate yr from each of the prompt and afterglow phases . this rate applies to the high - energy tail of the prompt synchrotron emission and to the inverse - compton component of the afterglow . theory predicts that in a large fraction of the cases where synchrotron gev prompt emission would be detected by _ glast _ , inverse - compton photons should be detected as well at high energies ( gev ) . therefore _ glast _ will enable a more precise test of the high - energy emission mechanism . finally , we show that the contribution of grbs to the flux of the extragalactic gamma - ray background measured with egret is at least 0.01% and likely around 0.1% .

1508.03241

i

the migration of protoplanets embedded in accretion discs has been extensively studied in recent years ( see , e.g. , review by @xcite ) . a low - mass protoplanet excites density waves in the disc at the lindblad resonances and migrates toward the star if no other torques are exerted ( e.g. , @xcite ) . however , a corotation torque originating near the planet can slow or even reverse the migration ( e.g. , @xcite ) . another possible cause of slowed or reversed migration is the excitation of magnetic resonances in the disc when a relatively strong ( @xmath4 , where @xmath5 and @xmath6 are the pressure and magnetic field in the disc , respectively ] ) azimuthal magnetic field is present @xcite . these magnetic resonances can halt or reverse the migration of the planet if the magnetic field is sufficiently strong and it has a steep gradient toward the star the action of this mechanism has been shown in numerical simulations by @xcite . on the other hand , accretion discs threaded with a weak magnetic field are prone to the magneto - rotational instability ( mri ; @xcite ) . numerical simulations of planet migration in a turbulent disc have shown that the semimajor axis of the planet changes stochastically due to the planet s interaction with the turbulent cells in the disc . the migration rate can increase or decrease , and the direction of the migration can reverse @xcite . an initial goal of this paper was to more deeply investigate the effect of magnetic resonances on the migration of a low - mass embedded planet following the methods used by @xcite , albeit that we explored a larger parameter space with regards to the mass of the planet and the density distribution in the disc , as well as the magnetic field strength and its distribution in the disc . while exploring this expanded parameter space , we noticed the development of mri - driven turbulence in the disc in many cases . in particular , when the magnetic field is weak , non - axisymmetric density waves excited by the planet lead to perturbations in the initially - azimuthal magnetic field and , subsequently , to growth of the radial component of the magnetic field near the planet . the azimuthal field grows with time due to the stretching of the radial field lines by the differential rotation of the keplerian disc . as a result , an mri - type instability develops and propagates to larger distances from the planet , and the disc becomes turbulent . the planet interacts with the turbulent cells , and the torque associated with this interaction is much larger than the torque seen prior to the development of turbulence ( i.e. , the torque due to magnetic resonances ) . therefore , we also studied the parameter space describing the transition from a laminar to a turbulent disc , as well as the migration of a planet in a turbulent disc in detail . we first describe how the migration rate and direction of a low - mass planet are affected by the planet mass , as well as the distribution of surface density and magnetic field in the laminar disc . we also show how these parameters alter the time at which the onset of turbulence occurs in magnetized discs . finally , to better understand the interaction between the planet and turbulent cells in the disc , we study the torque on the planet by ( 1 ) an ordered , low - amplitude density wave generated at the inner boundary and ( 2 ) a high - amplitude wave that is excited in a turbulent mhd disc . the plan for this paper is as follows . in [ sec : theoretical background ] we overview the theory of the different sources of torque on the planet . in [ sec : model ] we describe our physical model and numerical setup . in [ sec : parameter space ] we describe our main parameters . we describe our test simulations in the hydrodynamical disc in [ sec : migration hydro ] and simulations in a laminar magnetic disc in [ sec : magres migration ] . migration in turbulent discs is shown in [ sec : migration turbulent ] , and migration under the influence of density waves is shown in [ sec : migration in waves ] . we conclude in [ sec : conclusions ] .

however , when the magnetic field is weaker ( i.e. , the plasma parameter is relatively large ) , then non - axisymmetric density waves excited by the planet lead to growth of the radial component of the field and , subsequently , to development of the magneto - rotational instability , such that the disc becomes turbulent . = 1 accretion , accretion discs magnetic fields mhd waves planets and satellites : dynamical evolution and stability planet - disc interactions

we investigate the migration of low - mass planets ( and ) in accretion discs threaded with a magnetic field using 2d mhd code in polar coordinates . we observed that , in the case of a strong azimuthal magnetic field where the plasma parameter is , density waves at the magnetic resonances exert a positive torque on the planet and may slow down or reverse its migration . however , when the magnetic field is weaker ( i.e. , the plasma parameter is relatively large ) , then non - axisymmetric density waves excited by the planet lead to growth of the radial component of the field and , subsequently , to development of the magneto - rotational instability , such that the disc becomes turbulent . migration in a turbulent disc is stochastic , and the migration direction may change as such . to understand migration in a turbulent disc , both the interaction between a planet and individual turbulent cells , as well as the interaction between a planet and ordered density waves , have been investigated . = 1 accretion , accretion discs magnetic fields mhd waves planets and satellites : dynamical evolution and stability planet - disc interactions

0811.3873

c

it had been established by several authors , that red samples defined by cmr cuts do not only contain passively evolving spheroidal galaxies , but are contaminated with spiral galaxies both in clusters @xcite and in the field @xcite . there is also evidence for a large population of star - forming and at least moderately dusty galaxies in clusters ( wgm05 ) or the field @xcite , who report average fractions of 30 - 40% in red samples , or fractions as a function of mass and environment : we see the most extreme environmental dependence at low mass , where fractions range from @xmath60% in cores to @xmath66% in the field , in excellent agreement with @xcite . while @xcite find red spirals in the field to be mostly edge - on galaxies , we emphasise that in dense environments inclination is not the dominant explanation for their colour : instead lower specific sfrs cause the red colour irrespective of a galaxy s orientation . the key is to look not at contamination fraction in red samples , but at the ratio of red to blue spirals instead : if red spirals were purely due to high inclination , random orientation statistics would suggest in a given mass bin , that the red fraction among spirals ( or star - forming galaxies ) should be independent of environment . in fact , the @xmath76 field sample in wgm05 has a 1:8 ratio of dusty red to blue galaxies , indistinguishable from the red spiral to blue galaxy ratio at @xmath77 reported by @xcite . it is entirely plausible that one in eight spiral galaxies have inclinations high enough to extinguish most of the light from young disk stars due to the increased optical depth of dust projected on the disk . however , the red spiral fraction in our cluster sample exceeds dramatically the small geometric fraction , as it has _ more red spirals than blue galaxies _ at @xmath70 . the majority of these show reduced star formation but do not show enhanced dust extinction of the overall stellar population . their morphologies are also clearly not edge - on , but they have smoothed substructure as expected for a low - sfr system and seen in fig . [ csseq ] . given that these galaxies are the major constituent of the star - forming population , we would like to include them when studying a star - forming sample . as a result , star - forming samples show different colour and star - formation properties than pure blue cloud samples . wgm05 report an average equivalent width of [ oii ] emission in a901 dusty red galaxies of @xmath78 , compared to 17.5 in the blue cloud . [ oii ] line fluxes are an order of magnitude reduced in dusty red compared to blue galaxies . hence , their [ oii ] emission would be undetectable in the cluster studies of @xcite or in the vvds field survey @xcite . their spectra otherwise appear similar to those of truly passive galaxies . it is thus no surprise that spectroscopic surveys have found red spirals _ without optical signatures of star formation_. @xcite point out that the sdss fiber spectra at low redshift target a small nuclear region and fail to detect young stellar populations in many cases , a bias that enhances red - sequence contamination . in order to identify virtually all star - forming galaxies , they suggest to combine nuv data with an h@xmath79-line sensitivity of 2 ( equivalent width ) . finally we note , that @xcite report a fraction of star - forming red galaxies ( their intermediate types ) among all galaxies in their sdss sample ( @xmath80 ) of 20% . surprisingly , it appears to be entirely independent of the galaxy luminosity and its environment ( halo mass , location in a galaxy group ) . a number of works have established two independent observations that are in apparent conflict : \(1 ) the proximity of the virgo cluster has permitted the discovery of a substantial population of spiral galaxies , which have truncated star - forming disks . the idea is that gas is gradually being stripped from galaxies , perhaps via ism - icm interaction , whereby the outer regions of a galaxy are swept first given their lower column densities @xcite , and the truncation radius shrinks with time . at intermediate redshifts there is further evidence that cluster spirals have more centrally - concentrated star formation than field galaxies @xcite . seeing such transition objects abundantly requires a long time scale for the sf - suppressing process . \(2 ) most studies of sfr in star - forming galaxies report an independence of sfr on environment ; they only find that the fraction of star - forming galaxies declines with density , thus requiring a fast transition ( e.g. * ? ? ? the average equivalent width of the [ oii ] line in star - forming galaxies is found by @xcite at @xmath81 $ ] to be @xmath82 in the field , groups or clusters alike ; in @xmath83 clusters @xcite find @xmath84 , and at @xmath85 @xcite find 15 in bright @xmath86 galaxies . why this number should be constant across such a wide range in redshift is unclear , and may coincidentally arise from the mass - dependence of the s - sfr evolution with redshift and the redshift dependence of mass limits in the galaxy samples . our results show that at @xmath4 $ ] the mean s - sfr of star - forming galaxies declines almost by 50% from field to cores , but by much less in lower - mass galaxies . thus , we have found a significant sfr decline with density , as a result of including dusty red galaxies in our star - forming sample and using more reliable sfr estimates . had we restricted ourselves to blue galaxies alone , we would have seen only a 20% decline with very large errors due to the smaller sample , instead of a clear 50% decline . also , our blue sample has [ oii ] properties similar to the literature samples above . the comparison between blue and star - forming samples helps to resolve the contradiction posed between observations of slow transformation in virgo and apparently rapid truncation in more distant clusters : the inclusion of semi - passive spirals in the star - forming sample of cluster galaxies produces a decline of sfr in star - forming galaxies with density , which is consistent with slow quenching in clusters . in contrast , considerations of only blue - cloud galaxies require to invoke nearly instantaneous sf suppression given that their sfrs are apparently constant over density . we note that @xcite report a 20% sfr decline across density in their faintest sample bin at @xmath87 $ ] . their brighter bins show no trends but are affected by an aperture bias , which they argue may hide evolution that may only play out in an extended star - forming disk outside the aperture . we believe that their judgement is correct ; we have a smaller aperture bias in our data , given that our aperture has 4.25 kpc fwhm as opposed to the on average sub - kpc fiber aperture in @xcite . in @xmath88 clusters @xcite reported seeing numerous _ optically passive _ spirals , i.e. spiral galaxies with an absorption - line spectrum characteristic of older stellar populations , and no [ oii ] emission or otherwise apparent star formation . they also found a population of _ k+a galaxies _ characterised by abrupt sf truncation and asked why these quiescent infall populations are so prevalent at @xmath88 , but apparently lacking at low @xmath89 . in the virgo cluster , star formation was still observed and spatially resolved in spirals , and it was later shown that the anemic spirals discovered by @xcite were not the most abundant cluster - specific phenomenon @xcite ; instead , the principal effect of the virgo cluster on infalling spirals seemed to be a slow outside - in truncation of the star - forming disk . in our young @xmath90 cluster environment , we see again a very abundant infall population with similar optical properties as poggianti s _ optically passive _ spirals , except that we have shown them to be on average only _ semi - passive _ : they still form stars at a substantial rate , as shown consistently from either our ir data or from our optical estimates of dust extinction and star formation . their specific sfr , however , is on average lower by 0.6 dex in comparison to regular blue galaxies of the same mass . given an s - sfr scatter in the blue cloud of @xmath91 dex @xcite , these semi - passive spirals are @xmath92-outliers from the regular star - forming sequence in field galaxy samples ( see also the discussion in * ? ? ? altogether , we see spirals in the cluster to span the whole range from normally star - forming to virtually passive . we note that we do not see a star - bursting population in a901 , and wgm05 found no evidence for an abundant post - starburst population either , although that was concluded from stacked spectra , and they could not reliably measure h@xmath93 equivalent widths in individual galaxies . wgm05 showed the optical spectral signatures of dusty red galaxies to be almost indistinguishable from passively evolving ( old red ) galaxies on the basis of high - s / n stacked spectra . individual spectra were too noisy to find the weak [ oii ] lines and were otherwise dominated by the absorption - line spectrum of the older stars . it is now clear that the drop in star formation combined with an increase in the obscuration of star - forming regions , is sufficient to make the optical detection of star - formation signatures a challenge . but although the @xmath94 colours of red spirals and red spheroids are indistinguishable , this is only a coincidence of choosing two bands in which the effects of age and dust are ambiguous . choosing a wider range of colour , it turns out that red spirals are redder than spheroids at the red end and bluer at the blue end of the spectrum , which was the critical differentiation used by wgm05 . in fig . [ ssfrm ] we saw how e.g. the use of a near - uv colour discriminates dusty red from old red galaxies . we thus suggest that the red , or optically passive , spirals in cluster environments discussed by various authors are the same phenomenon as our semi - passive dusty red galaxies . the differentiating criterion for separating them from canonical red - sequence galaxies was the spiral morphology in @xcite and despite similar @xmath94 colour the signature of dust and younger ages in the sed in wgm05 . in some more star - forming and less obscured cases [ oii ] lines could be strong enough to appear above detection limits @xcite ; @xcite also used mir colours to trace star formation in red galaxies . in this paper , the morphology , the spiral - typical dust extinction , the brighter uv luminosity and the substantial ir fluxes all came together to form a consistent picture of semi - passive spirals . finally , we believe we can consider the sf - truncated virgo spirals to be local counterparts to the dusty red galaxies as their properties match at least in global respects : @xcite find the s - sfr in their virgo spirals to be on average @xmath95 reduced compared to the field , with an overall range from 10-fold reduction to slight enhancement ; this echoes the s - sfr properties of our dusty red galaxies . also , the star formation in the virgo spirals is on average more obscured , just as in dusty red galaxies again ; in virgo this is a consequence of the less obscured star formation in the outer disk being much reduced while the more obscured star formation in the central parts remains normal or is even enhanced . their appearance in large numbers suggests that spirals in many clusters undergo only slow quenching of their star formation , and that the time scale of morphological evolution must be longer than that of the spectral evolution . all this applies only in the mass regime of @xmath4 $ ] , where the sfr decline from blue galaxies in the field to dusty red galaxies in the infall region is not accompanied by morphological changes . morphology seems to change only further into the cluster alongside further sf decline that replaces dusty red galaxies by old red ones . at lower masses , in contrast , sfr decline and morphological changes appear more synchronised , and virtually no red spirals are found , except for a near - constant fraction of @xmath96% that may result from high - inclination spirals following random orientation statistics . this situation appears to be similar in the virgo cluster where @xcite find dwarf galaxies ( defined by @xmath97 ) to be either star - forming or quiescent with no intermediate objects being found . already kennicutt ( 1983 ) observed that at fixed hubble type virgo galaxies were redder and less star - forming than their cousins in the field . @xcite confirmed the colour difference for further clusters . however , whether these trends are due to nature ( hidden in the past ) or due to nurture ( change during cluster infall ) could not be identified from snapshot pictures of individual galaxies or clusters , because a snapshot will show the effects of infall and cosmic evolution of the progenitors intertwined . if we can not see the histories of the individual galaxies , we have no means to assess whether the progenitors of present - day cluster galaxies looked like the present - day infall galaxies do . only if this is the case , could we map the density axis onto a time axis and interpret the environmental trends as evolutionary tracks . however , there is strong evidence , e.g. , that higher - redshift clusters have fewer s0s and more spirals @xcite , so for s0s the link is established that a build - up in time corresponds to a build - up in density . higher - redshift cluster cores have similarities with lower - redshift cluster outskirts giving rise to a double downsizing picture where star formation moves progressively to lower - mass objects as you move either forward in cosmic time or higher in density of the environment @xcite . our results for a901/2 suggest , that empirically there are three mass domains with different behaviour along density : * at high mass ( @xmath98 , but certainly at @xmath99 ) only little change is observed with density , as most galaxies are red and spheroidal in all environments . * at intermediate mass ( @xmath100 $ ] ) we see a sequence with density whereby blue spirals in the field are replaced by red spirals in the infall region , which are then replaced by s0s in the core . * at low mass ( @xmath101 ) we see a sequence from blue field spirals and irregulars directly to red cluster spheroids . let us assume that the density axis can be mapped on a time arrow in the evolution of infalling galaxies , and the environmental trends are mostly due to nurture . an average galaxy falling in at 600 km / sec ( the velocity dispersion of a901a / b dusty red galaxies listed , see wgm05 ) needs @xmath102 gyr to fall from the virial radius to the core assuming a plunging orbit . there is thus no need to assume that they have already passed through the core . the results then say that star formation is suppressed at all densities and masses , and already between the field and the outermost infall region in our data , i.e. outside the virial radius of the cluster . this agrees with observations of galaxy pre - processing in infalling groups ( e.g. * ? ? ? * ; * ? ? ? morphological transformation appears in step with the sfr decline in low - mass galaxies , but is delayed for intermediate - mass galaxies . the delay gives rise to spiral galaxies in the infall region that appear red due to a combination of moderate extinction and reduced star formation . they appear broadly less clumpy and have less well - defined spiral arms than their blue cousins in the field , and they are the only progenitor candidates of similar - mass s0 galaxies . the steeper s - sfr decline for massive galaxies demonstrates that they transform slowly and remain visible in transformation for long . in contrast , the near - absence of a trend in mean s - sfr at lower mass requires more abrupt conversions that leave little chance to observe transforming objects , while giving rise to the steep trends in the sf / non - sf composition . we roughly find ( with large errors ) that the red fraction of spirals is increased in the infall region by perhaps 10% over the field value at a mass of @xmath103 and by maybe 50% at @xmath104 . at equal infall velocity this would imply @xmath105 longer quenching time - scales at @xmath105 higher mass or @xmath106 . the time - scale for ram - pressure stripping though is @xmath107 assuming constant surface mass density of disk galaxies @xcite and equal infall velocity . while we do not have the data to be very quantitative here , we argue that at least the quenching time - scale is unlikely to decline with mass . @xcite model the evolution of dwarf galaxies in virgo ( with @xmath108 ) assuming interaction with the intracluster medium , and derive sf quenching time scales of @xmath109 myr . such a rapid sf truncation would be consistent with the absence of a noticeable transition population . also , @xcite see k+a galaxies in the coma cluster only fainter than @xmath110 : the k+a signature requires a sharp truncation in star formation , which argues in favour of a faster shutdown of star formation at lower mass . in higher - mass spirals , gas stripping by hot icm would first remove gas from the outer disks where the gas column densities are lower , and the slow truncation of star - forming disks seen by @xcite would leave morphology largely intact over a slow sf quenching process , and would hence not lead to a k+a signature . it then may remain as puzzling that @xcite found many k+a spirals of normal mass in clusters at @xmath88 . however , the transformation time scale must depend not only on galaxy mass but also on the icm properties . already @xcite found higher s0 fractions with increasing x - ray luminosity of the clusters , although the presence of a residual relation at fixed cluster mass is unclear ( see discussion in * ? ? ? * ) . however , the basic effect has been studied by comparing two @xmath111 clusters with very different icm properties representing a low - mass ( cl0024 ) and high - mass ( ms0451 ) prototype in cluster evolution @xcite . low - mass clusters are irregular with several sub - clumps , perhaps young and still assembling , and have little volume occupied by hot icm ( e.g. virgo and a901/2 ) ; higher - mass clusters are more regular in structure and have a large volume occupied by hot icm ( e.g. coma ) . the galaxies in the two clusters compared by @xcite are on two different tracks of s - sfr - vs .- age as seen from [ oii]-vs.-@xmath112 , showing that ram pressure from the well - developed icm in ms0451 shuts down star formation rapidly even in larger galaxies , while the less developed icm in cl0024 means the transition is a lot slower and may even be driven predominantly by factors other than stripping by the icm , so that many transitioning red spirals with low s - sfr are seen . in line with this picture , we already see variation between our four cluster cores : the most x - ray - luminous core a901b has not only the most prominent icm but also the lowest red spiral and the highest s0 fraction . the discussion whether the observed s0 galaxies have evolved from spiral progenitors has continued for three decades now @xcite . we suggest to tackle the question with a mass - resolved approach , motivated by the strong trends seen at intermediate mass in our cluster . several authors ( e.g * ? ? ? * ) have argued that present - day s0s are too luminous to be made from present - day infalling spirals . in a901/2 we admittedly find s0 galaxies , but no infalling spirals at @xmath46 ; we suggest that these would have formed in the more distant past of this cluster from more massive progenitors that we do not observe in the present snapshot due to downsizing . we have no evidence against this picture , and note the absence of massive star - forming galaxies that could further enrich the massive s0 sample in a901/2 in the near future . in contrast , at @xmath113 $ ] we find a very strong trend of red spirals disappearing towards the core and s0s appearing in comparable numbers ; the s0 concentration towards the cores of a901/2 is markedly different from the flat s0 fraction within a virial radius seen in ensembles of more evolved clusters @xcite . this is consistent with a901/2 being a young clusters with weaker icm , and it suggests that a901/2 has much progenitor material to form more intermediate - mass s0s over the next few gyrs to fill the virial volume more evenly . a further obstacle in the understanding of s0 formation is the difference in the structural properties of s0s compared to their progenitor spirals : s0s are claimed to have larger concentrations or bulges and thicker disks than their progenitors , although recent works claim a smaller degree of difference @xcite . we are not aware of a mass - resolved study of progenitors and s0s that evaluates the effects of gradual gas stripping and continuing centrally concentrated star formation . @xcite studied residual morphological trends in the sdss data after eliminating the primary trend of the dominant colour - density relation and found only a weak trend towards higher concentration with density , and applying only to more luminous galaxies . this would be entirely consistent with a picture where low - mass galaxies experience more abrupt sf shutoff in dense environments , while high - mass galaxies continue forming stars in their inner regions . however , @xcite find no change in concentration with density at @xmath98 , and only a weak trend below .

we note , that edge - on spirals play a minor role ; despite being dust - reddened they form only a small fraction of spirals independent of environment . surveys ; galaxies : evolution ; galaxies : spiral ; galaxies : clusters : general ; stars : formation ; infrared : galaxies

we investigate the properties of optically passive spirals and dusty red galaxies in the a901/2 cluster complex at redshift using restframe near - uv - optical seds , 24 m ir data and hst morphologies from the stages dataset . the cluster sample is based on combo-17 redshifts with an rms precision of km / sec . we find that dusty red galaxies and optically passive spirals in a901/2 are largely the same phenomenon , and that they form stars at a substantial rate , which is only lower than that in blue spirals at fixed mass . this star formation is more obscured than in blue galaxies and its optical signatures are weak . they appear predominantly in the stellar mass range of $ ] where they constitute over half of the star - forming galaxies in the cluster ; they are thus a vital ingredient for understanding the overall picture of star formation quenching in clusters . we find that the mean specific sfr of star - forming galaxies in the cluster is clearly lower than in the field , in contrast to the specific sfr properties of blue galaxies alone , which appear similar in cluster and field . such a rich red spiral population is best explained if quenching is a slow process and morphological transformation is delayed even more . at , such galaxies are rare , suggesting that their quenching is fast and accompanied by morphological change . we note , that edge - on spirals play a minor role ; despite being dust - reddened they form only a small fraction of spirals independent of environment . surveys ; galaxies : evolution ; galaxies : spiral ; galaxies : clusters : general ; stars : formation ; infrared : galaxies

0811.3873

c

we have investigated the properties of galaxies , especially those of optically passive spirals , in a cluster complex at redshift @xmath0 , which consists of four cores ( a901a , a901b , a902 and sw group ) . we have used the stages dataset published by @xcite , exploiting the restframe near - uv - optical seds , ir 24@xmath1 m data and hst morphologies . the cluster sample is defined on the basis of combo-17 redshifts with an rms precision of @xmath2 km / sec ( at @xmath114 ) . we draw the following conclusions : 1 . optically passive spirals in clusters , dusty red galaxies in a901/2 and virgo spirals with truncated star - formation disks @xcite appear to be basically the same phenomenon . however , these objects are not truly passive galaxies despite their integrated optical appearance from large distances . 2 . they form stars at a substantial rate but reduced in comparison to field spirals ( on average @xmath3 lower sfr at fixed mass in our sample ) . however , their star formation is more obscured and its optical signatures are weak . they appear predominantly in the mass range @xmath4 $ ] where they constitute over half of the star - forming galaxies in the cluster , and thus form an important transition population . we find that the mean s - sfr of star - forming galaxies in the cluster is clearly lower than in the field , in contrast to the s - sfr properties of blue galaxies alone , which appear unchanged . the dusty red spirals are thus a vital ingredient for understanding the overall picture of sf quenching in clusters . 5 . at lower mass the dusty red sample consists mostly of edge - on spirals , which are a small fraction of all spirals with no environmental dependence . there is limited room for a cluster - specific contribution . physically , it seems that star formation quenching is fast in low - mass galaxies and accompanied by morphological change ; hence , no cluster - specific red spiral phenomenon is observed at @xmath5 . at larger masses , sf quenching is a slower process and strong morphological transformation is even more delayed , thus giving rise to abundant red spirals . 7 . the currently observed red spirals are expected to turn into s0s with time when their star formation is terminated by hot icm , although they may end up with different detailed properties from those s0s that are already in place .

we investigate the properties of optically passive spirals and dusty red galaxies in the a901/2 cluster complex at redshift using restframe near - uv - optical seds , 24 m ir data and hst morphologies from the stages dataset . the cluster sample is based on combo-17 redshifts with an rms precision of km / sec . this star formation is more obscured than in blue galaxies and its optical signatures are weak . they appear predominantly in the stellar mass range of $ ] where they constitute over half of the star - forming galaxies in the cluster ; they are thus a vital ingredient for understanding the overall picture of star formation quenching in clusters . we find that the mean specific sfr of star - forming galaxies in the cluster is clearly lower than in the field , in contrast to the specific sfr properties of blue galaxies alone , which appear similar in cluster and field . such a rich red spiral population is best explained if quenching is a slow process and morphological transformation is delayed even more . at , such galaxies are rare , suggesting that their quenching is fast and accompanied by morphological change .

we investigate the properties of optically passive spirals and dusty red galaxies in the a901/2 cluster complex at redshift using restframe near - uv - optical seds , 24 m ir data and hst morphologies from the stages dataset . the cluster sample is based on combo-17 redshifts with an rms precision of km / sec . we find that dusty red galaxies and optically passive spirals in a901/2 are largely the same phenomenon , and that they form stars at a substantial rate , which is only lower than that in blue spirals at fixed mass . this star formation is more obscured than in blue galaxies and its optical signatures are weak . they appear predominantly in the stellar mass range of $ ] where they constitute over half of the star - forming galaxies in the cluster ; they are thus a vital ingredient for understanding the overall picture of star formation quenching in clusters . we find that the mean specific sfr of star - forming galaxies in the cluster is clearly lower than in the field , in contrast to the specific sfr properties of blue galaxies alone , which appear similar in cluster and field . such a rich red spiral population is best explained if quenching is a slow process and morphological transformation is delayed even more . at , such galaxies are rare , suggesting that their quenching is fast and accompanied by morphological change . we note , that edge - on spirals play a minor role ; despite being dust - reddened they form only a small fraction of spirals independent of environment . surveys ; galaxies : evolution ; galaxies : spiral ; galaxies : clusters : general ; stars : formation ; infrared : galaxies

0909.0265

i

we have performed cosmological hydro - chemodynamic simulations of galaxy formation in 3 milky way - sized haloes taken from the aquarius project @xcite . a primary aim of our study has been to constrain the nature of some of the feedback processes that must have operated during galaxy formation . we have done this by focusing on satellite galaxies whose shallow potential wells make them particularly sensitive to feedback effects . as a byproduct , we have been able to explore some of the controversial properties of satellite galaxies , such as their luminosity function , in the context of the @xmath5cdm cosmology which we have assumed in our simulations . although our simulations are amongst the largest of their kind performed to date , they lack the resolution to follow the physics of the interstellar medium directly . such processes must be included as ` sub - grid physics ' . in particular , we have assumed that energy injected by sne generate galactic winds . we have assumed further that all the energy released by sne is deposited as kinetic energy in the winds . early studies , as well as more recent ones have shown that many observed galaxy properties can not be reproduced unless most of the sn energy is used to blow gas out of galaxies ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? since a large fraction of sn energy must be radiated away , other sources of energy seem to be required to power strong winds such as radiation from young stars @xcite . in this study we have included these unresolved processes in a purely phenomenological way by assuming two types of ` energy - conserving ' winds . in the first type , the initial wind speed is taken to be proportional to the local velocity dispersion of the dark matter , @xmath69 , as suggested by recent data @xcite , and thus , the wind mass - loading , @xmath3 ( ` vw ' models ) . in the second type , the initial wind speed and the wind mass - loading are assumed to be constant for all galaxies ( ` cw ' models ) , as suggested by earlier data @xcite . disc - dominated galaxies formed in several of our simulations . in some of our simulations , we included a multiphase model for star - forming gas , but we found that this made little difference to the outcome ( see also * ? ? ? * ) , apart from the overall morphology of the central galaxy . the use of a stiff equation of state for the ism tends to promote the formation of disc - dominated galaxies by stabilising gaseous discs against gravitational instability . the key to the diversity of behaviours that we find is not the treatment of the ism , but rather the treatment of the sn - driven winds . the ` vw ' models give a reasonable match to the observed luminosity function of local group satellites . a major factor in this success is the behaviour of the mass - loading in the wind which becomes increasingly large in smaller galaxies . if the mass - loading is kept constant as in the ` cw ' case , galaxy formation is not sufficiently suppressed in small haloes resulting in a satellite luminosity function which rises much too steeply at the faint end . previous sph simulations had already shown that an acceptable match to the abundance of bright satellites can be obtained from @xmath5cdm initial conditions @xcite , thus confirming the conclusion from early semi - analytic studies that the so - called ` satellite problem ' in the cdm cosmology @xcite disappears when proper account is taken of the baryonic processes involved in galaxy formation @xcite . our high - resolution simulation , however , extends the comparison with the luminosity function to much fainter magnitudes than previous sph simulations . the ` vw ' feedback model that produces an acceptable satellite luminosity function , also produces an acceptable luminosity - metallicity relation for the satellites . by contrast , the ` cw ' model fails to reproduce this relation for the same reasons that it fails to reproduce the luminosity function : the constant mass - loading leads to an iron abundance in satellites with @xmath149 which is essentially independent of luminosity , contrary to what is observed . none of our ` vw ' models reproduces the oxygen - to - iron abundance ratio measured for dwarf satellites . there are several possible reasons for this discrepancy : the star formation timescale may be too long , the model of sne ia or the imf that we have adopted may be incorrect , or our assumed oxygen yield may be too low . given the large uncertainties in the value of the yield , the imf and sne ia rates , we do not consider this shortcoming of our models to be fatal although further work is required . for example , a top - heavy imf in these metal - poor objects could provide the solution although it is unclear whether such a radical assumption would destroy the agreement of the model with other observables . based on our estimate of the minimum resolved circular velocity of subhaloes in the simulations , we find that subhaloes hosting satellites in the ` vw ' models are reliably resolved down to the faintest magnitude . thus , the faint - end slope of the satellite luminosity function and the luminosity - metallicity relation in the ` vw ' models are robust . this conclusion is confirmed by a direct convergence study of one model ( ` vw5@xmath2 ' of the aq - d ) : low- and high - resolution simulations give consistent results . on the other hand , in the ` cw ' models in which the smaller wind mass - loading factor allows satellites to form in halos with small values of @xmath70 , the faint - end slope of the satellite luminosity function could be affected by limited numerical resolution although we estimate that any such effects would be restricted to the extreme faint end . barring the alpha - to - iron ratio , we conclude that an energy - conserving wind model in which the mass loading scales inversely with square of velocity dispersion provides a viable model for feedback as judged by the properties of satellite galaxies . our preferred wind model is different from the ` momentum - driven ' wind models favoured by @xcite in order to explain the mass - metallicity relation of large galaxies . in this kind of model , the wind speed is proportional to @xmath2 as in our ` vw ' models , but the mass - loading scales as @xmath150 ( rather than as @xmath113 ) . it could be that the mechanisms that drive galactic outflows in small and large galaxies are different . in ` vw ' models with wind speed , @xmath151 , the mass loading is large in small galaxies . winds therefore remove substantial amounts of star - forming gas , but much of this material eventually falls back onto the galaxy . as a result , the star formation in small satellites is episodic and has a much longer timescale than in the ` cw ' models in which the gas is expelled from the small halo , never to return . these general properties underlie the different predictions for the number density of faint galaxies and their chemical properties in the different models . the star formation histories of the satellites retain no obvious imprint of the reionization of gas at early times . accretion onto larger haloes , on the other hand , often affects subsequent star formation and , in low mass satellites ( @xmath152 ) , it truncates it altogether . only 5% of subhaloes whose circular velocities are higher than the minimum resolved value ( @xmath153 ) in the high - resolution simulation ( aq - d - hr ) host satellites . the vast majority of subhaloes do not manage to make a visible galaxy and remain dark . the mechanisms that distinguish visible from dark satellites are investigated in a companion paper @xcite .

we investigate the properties of satellite galaxies in cosmological-body / sph simulations of galaxy formation in milky way - sized haloes . because of their shallow potential wells , satellite galaxies are very sensitive to heating processes which affect their gas content . their properties can therefore be used to constrain the nature of feedback processes that regulate galaxy formation . in our simulations , we assume that all the energy produced by supernovae is used as kinetic energy to drive galactic winds . several of our simulations produce bright , disc - dominated galaxies . we find that wind models in which the wind speed , , is proportional to the local velocity dispersion of the dark matter , ( and thus the wind mass - loading , ) , make star formation in satellites sporadic , reproduce the observed satellite luminosity function reasonably well ( down to ) and match the luminosity - metallicity relation observed in the local group satellites . by contrast , models that assume a constant wind speed overproduce faint satellites and predict an incorrect luminosity - metallicity relation .

we investigate the properties of satellite galaxies in cosmological-body / sph simulations of galaxy formation in milky way - sized haloes . because of their shallow potential wells , satellite galaxies are very sensitive to heating processes which affect their gas content . their properties can therefore be used to constrain the nature of feedback processes that regulate galaxy formation . in our simulations , we assume that all the energy produced by supernovae is used as kinetic energy to drive galactic winds . several of our simulations produce bright , disc - dominated galaxies . we find that wind models in which the wind speed , , is proportional to the local velocity dispersion of the dark matter , ( and thus the wind mass - loading , ) , make star formation in satellites sporadic , reproduce the observed satellite luminosity function reasonably well ( down to ) and match the luminosity - metallicity relation observed in the local group satellites . by contrast , models that assume a constant wind speed overproduce faint satellites and predict an incorrect luminosity - metallicity relation . our simulations therefore suggest that the feedback processes that operate on the scale of satellite galaxies should generate galactic outflows whose mass - loading varies inversely with the depth of the potential . [ firstpage ] methods : numerical galaxies : evolution galaxies : formation cosmology : theory .

1407.0570

i

we consider a permutation to be simply an arrangement of the numbers @xmath2 for some positive @xmath3 . a permutation @xmath4 is said to be _ contained _ in another permutation @xmath5 if @xmath5 has a subsequence whose terms have the same relative ordering as those of @xmath4 . for example , @xmath6 is contained in @xmath7 because the subsequence @xmath8 is ordered in the same way as @xmath6 . if @xmath4 is not contained in @xmath5 then we say that @xmath5 _ avoids _ @xmath4 . for example , @xmath7 avoids @xmath9 . in the context of containment and avoidance , a permutation is often called a _ pattern_. the containment relation is a partial order on the set of all permutations , and a set of permutations closed downwards ( a down - set ) in this partial order is called a _ permutation class_. it is natural to define a permutation class by the minimal set of permutations that it avoids . this minimal forbidden set of patterns is known as the _ basis _ of the class . the class with basis @xmath10 is denoted @xmath11 . given a permutation class @xmath12 , we denote by @xmath13 the set of permutations in @xmath12 of length @xmath3 . the ( univariate ) _ generating function _ of @xmath12 is then @xmath14 , where @xmath15 is the length of @xmath5 . the _ growth rate _ of @xmath12 is defined by the limit @xmath16{|\ccc_n| } , $ ] if it exists . it is widely believed ( see the first conjecture in @xcite ) that all permutation classes have a growth rate . in the study of permutation classes , there has been significant interest in deriving the generating functions for classes with a few small basis elements ( see @xcite for an up - to - date list of results ) . this has led to the enrichment of the theory of permutation classes due to the requisite development of a variety of enumeration techniques . we add to this work by proving the following two theorems : * hasse graphs * corresponding to each permutation @xmath5 , we define an ordered plane graph @xmath17 , which we call its _ hasse graph_. if @xmath18 is the poset on the points @xmath19 in which @xmath20 if both @xmath21 and @xmath22 , then @xmath17 is the graph corresponding to the hasse diagram of @xmath18 . see the figures throughout this paper for illustrations showing the hasse graphs of permutations . in practice , we tend not to distinguish between a permutation and its hasse graph . the minimal elements of the poset @xmath18 are known as the _ left - to - right minima _ of the permutation @xmath5 . similarly , maximal elements of @xmath18 are called _ right - to - left maxima _ of @xmath5 . hasse graphs of permutations were previously considered by bousquet - mlou & butler @xcite , who determined the algebraic generating function of the family of _ forest - like _ permutations whose hasse graphs are acyclic . more recently , they have been used by the present author @xcite to establish a new lower bound for the growth rate of @xmath23 . given a permutation @xmath5 , we partition the vertices of @xmath17 by spanning it with a sequence of graphs , which we call the _ source graphs _ of @xmath5 . there is one source graph for each left - to - right minimum of @xmath5 . suppose @xmath24 are the vertices of @xmath17 corresponding to the left - to - right minima of @xmath5 , listed from left to right . then the @xmath25th source graph @xmath26 is the graph induced by @xmath27 and those vertices of @xmath17 lying above and to the right of @xmath27 that are not in @xmath28 . we refer to @xmath27 as the _ root _ of source graph @xmath26 . see figure [ figfperm ] for an illustration . the structure of the source graphs of permutations in a specific permutation class is constrained by the need to avoid the patterns in the basis of the class . if the source graphs for some class are acyclic , we refer to them as _ source trees_. the _ bottom subgraph _ of a hasse graph is the graph induced by its lowest vertex ( the least entry in the permutation ) and all the vertices lying above and to its right . observe that the bottom subgraph may contain vertices from more than one source graph . for example , the bottom subgraph of the hasse graph in figure [ figfperm ] contains vertices from three source graphs . bottom subgraphs of permutations in a specific permutation class satisfy the same structural restrictions as do the source graphs . we refer to an acyclic bottom subgraph as a _ bottom subtree_. we build the hasse graph of a permutation by starting with a source graph and then repeatedly adding another source graph to the lower right . the technique is similar to that of `` adding a slice '' , which has been used to enumerate constrained compositions and other classes of polyominoes , a topic of interest in statistical mechanics ( see , for example , bousquet - mlou s review paper @xcite , the books of van rensburg @xcite and guttmann @xcite , and flajolet & sedgewick ( * ? ? ? * examples iii.22 and v.20 ) ) . when a source graph is added , its vertices are interleaved horizontally with the non - root vertices of the bottom subgraph of the graph built from the previous source graphs . typically , the positioning of the vertices of the new source graph is constrained by the need to avoid forbidden patterns . in order to derive the univariate generating functions we require , we make use of multivariate functions involving additional `` catalytic '' variables that record certain parameters of the bottom subgraph of the permutations . these additional variables enable us to establish recurrence relations which we can then solve using the kernel method . typically , when employing a multivariate generating function , we treat it simply as a function of the relevant catalytic variable , writing , for example , @xmath29 rather than @xmath30 . occasionally , we also make use of a variant of the symbolic structural notation presented in flajolet & sedgewick @xcite to establish functional equations . in particular , @xmath31 is the atomic class consisting of a single vertex , and we use @xmath32 to represent a possibly empty sequence of elements of @xmath33 and @xmath34 to represent a non - empty sequence of elements of @xmath33 . the two classes we enumerate are quite distinct structurally . a source graph in @xmath35 consists of a root together with a @xmath36avoider formed from the non - root vertices . however , the presence of a @xmath36 forces any subsequent source graph to be simply a fan . in contrast , @xmath37 has plane source graphs and a much more uniform structure . we enumerate @xmath35 in section [ sectf ] . in doing so , the kernel method is used six times to solve the relevant functional equations . the class @xmath37 is enumerated in section [ secte ] . this requires an unusual simultaneous double application of the kernel method .

we investigate the structure of the two permutation classes defined by the sets of forbidden patterns and . by considering our approach is similar to that of `` adding a slice '' , used previously to enumerate various classes of polyominoes and other combinatorial structures . to solve the relevant functional equations , we make extensive use of the kernel method

we investigate the structure of the two permutation classes defined by the sets of forbidden patterns and . by considering how the hasse graphs of permutations in these classes can be built from a sequence of rooted source graphs , we determine their algebraic generating functions . our approach is similar to that of `` adding a slice '' , used previously to enumerate various classes of polyominoes and other combinatorial structures . to solve the relevant functional equations , we make extensive use of the kernel method

1507.08550

c

we here concisely summarise the main conclusions of this work . * the [ cm]@xmath3 dust model can very precisely match all the isecs observed in the mcs , yielding estimates for the total dust mass column density versus total hydrogen column density that are fully consistent with those obtained by @xcite in a completely different , independent way . * abundance of elements locked up in [ cm]@xmath3 models fitting the isecs in the mcs are at least as compatible with abundance constraints as those for the mwg @xcite . * when isecs have vanishingly weak bump and faruv nonlinear rise , they can be equally well fitted either by classical dust alone or by classical dust _ and _ pahs . in such cases models without pahs use much more si and c atoms , which may put them at odds with abundance constraints . * carbonaceous mantles in the mcs resulting from the [ cm]@xmath3 model fits are overwhelmingly aliphatic , whereas those in the mwg are predominantly aromatic . together with the observational constraint that radiation fields in mcs are typically 10 times stronger than the average in the mwg @xcite , in the [ cm]@xmath3 model this implies that mantleshattering events must be @xmath99 times more frequent in the mcs than in the mwg , and/or much more efficient . desorption from such mantles can not be a significant source of pahs in the mcs . * bumpless isecs with large nonlinear faruv rises can be fitted within the [ cm]@xmath3 model , but this requires a finely tuned match of the gap in the size distribution of classical dust grains , resulting in a dip in the extinction they produce that precisely cancels with the bump . either there is some hitherto not understood physical relation connecting the population of pahs with the size distribution of silicate grains in the diffuse interstellar medium , or this hints that the [ cm]@xmath3 model must be missing some component different from pahs that can can produce a nonlinear faruv rise without simultaneously contributing to the bump .

we find that in the magellanic clouds the extinction produced by classic grains is generally larger than absorption by polycyclic aromatic hydrocarbons . within this model , this hints either a physical connection between ( e.g. , a common cause for ) polycyclic aromatic hydrocarbons and the absence of middlesized dust particles , or the need for an additional component in the model , that can account for the nonlinear faruv rise without contributing to the uv bump at nm , e.g. , nanodiamonds .

we model the extinction profiles observed in the small and large magellanic clouds with a synthetic population of dust grains consisting by core - mantle particles and a collection of freeflying polycyclic aromatic hydrocarbons . all different flavors of the extinction curves observed in the magellanic clouds can be described by the present model , that has been previously ( successfully ) applied to a large sample of diffuse and translucent lines of sight in the milky way . we find that in the magellanic clouds the extinction produced by classic grains is generally larger than absorption by polycyclic aromatic hydrocarbons . within this model , the nonlinear faruv rise is accounted for by polycyclic aromatic hydrocarbons , whose presence in turn is always associated to a gap in the size distribution of classical particles . this hints either a physical connection between ( e.g. , a common cause for ) polycyclic aromatic hydrocarbons and the absence of middlesized dust particles , or the need for an additional component in the model , that can account for the nonlinear faruv rise without contributing to the uv bump at nm , e.g. , nanodiamonds .

1004.4728

i

the inclusion of nanometric conductive fillers such as carbon nanotubes @xcite , nanofibers @xcite , and graphene @xcite into insulating matrices allows to obtain electrically conductive nanocomposites with unique properties which are widely investigated and have several technological applications ranging from antistatic coatings to printable electronics @xcite . a central challenge in this domain is to create composites with an overall conductivity @xmath0 that can be controlled by the volume fraction @xmath1 , the shape of the conducting fillers , their dispersion in the insulating matrix , and the local inter - particle electrical connectedness . understanding how these local properties affect the composite conductivity is therefore the ultimate goal of any theoretical investigation of such composites . a common feature of most random insulator - conductor mixtures is the sharp increase of @xmath0 once a critical volume fraction @xmath2 of the conductive phase is reached . this transition is generally interpreted in the framework of percolation theory @xcite and associated with the formation of a cluster of electrically connected filler particles that spans the entire sample . the further increase of @xmath0 for @xmath3 is likewise understood as the growing of such a cluster . in the vicinity of @xmath2 , this picture implies a power - law behavior of the conductivity of the form @xmath4 where @xmath5 is a critical exponent . values of @xmath5 extracted from experiments range from its expected universal value for three - dimensional percolating systems , @xmath6 , up to @xmath7 , with little or no correlation to the critical volume fraction @xmath2,@xcite or the shape of the conducting fillers @xcite . in the dielectric regime of a system of nanometric conducting particles embedded in a continuous insulating matrix , as is the case for conductor - polymer nano - composites,@xcite the particles do not physically touch each other , and the electrical connectedness is established through tunneling between the conducting filler particles . in this situation , the basic assumptions of percolation theory are , a priori , at odds with the inter - particle tunneling mechanism.@xcite indeed , while percolation requires the introduction of some sharp cut - off in the inter - particle conductances , i.e. , the particles are either connected ( with given non - zero inter - particle conductances ) or disconnected,@xcite the tunneling between particles is a continuous function of inter - particle distances . hence , the resulting tunneling conductance , which decays exponentially with these distances , does not imply any sharp cut - off or threshold . quite surprisingly , this fundamental incompatibility has hardly been discussed in the literature,@xcite and basically all the measured conductivity dependencies on the fractional volume content of the conducting phase , @xmath8 , have been interpreted in terms of eq . assuming the `` classical '' percolation behavior.@xcite in this article , we show instead that the inter - particle tunneling explains well all the main features of @xmath8 of nanocomposites without imposing any _ a priori _ cut - off , and that it provides a much superior description of @xmath8 than the `` classical '' percolation formula . in order to specify our line of reasoning and to better appreciate the above mentioned incompatibility , it is instructive to consider a system of particle dispersed in an insulating continuum with a tunneling conductance between two of them , @xmath9 and @xmath10 , given by : @xmath11 where @xmath12 is a constant , @xmath13 is the characteristic tunneling length , and @xmath14 is the minimal distance between the two particle surfaces . for spheres of diameter @xmath15 , @xmath16 where @xmath17 is the center - to - center distance . there are two extreme cases for which the resulting composite conductivity has qualitatively different behaviors which can be easily described . in the first case the particles are so large that @xmath18 . it becomes then clear from eq . that the conductance between two particles is non - zero only when they essentially touch each other . hence , removing particles from the random closed packed limit is equivalent to remove tunneling bonds from the system , in analogy to sites removal in a site percolation problem in the lattice.@xcite the system conductivity will have then a percolation - like behavior as in eq . with @xmath6 and @xmath2 being the corresponding percolation threshold.@xcite the other extreme case is that of sites ( @xmath19 ) randomly dispersed in the continuum . in this situation , a variation of the site density @xmath20 does not change the connectivity between the particles and its only role is to vary the distances @xmath21 between the sites.@xcite the corresponding @xmath0 behavior was solved by using the critical path ( cp ) method@xcite in the context of hopping in amorphous semiconductors yielding @xmath22$].@xcite for sufficiently dilute system of impenetrable spheres this relation can be generalized to @xmath23$].@xcite it is obvious then from the above discussion that the second case is the low density limit of the first one , but it turns out that the variation of @xmath8 between the two types of situations , which is definitely pertinent to nanocomposites , has not been studied thus far . following the above considerations we turned to study here the @xmath8 dependencies by extending the low - density ( hopping - like ) approach to higher densities than those used previously.@xcite specifically , we shall present numerical results obtained by using the global tunneling network ( gtn ) model , where the conducting fillers form a network of globally connected sites via tunneling processes . this model has already been introduced in ref . [ ] for the case of impenetrable spheres , but here we shall generalize it in order to describe also anisotropic fillers such as rod - like and plate - like particles , as to apply to cases of recent interest ( _ i.e. _ , nanotube , nanofiber , nanosheet , and graphene composites ) . in particular , the large amount of published experimental data on these systems allows us to test the theory and to extract the values of microscopic parameters directly from macroscopic data on the electrical conductivity . the structure of the paper is as follows . in sec . [ gen ] we describe how we generate particle dispersions and in sec . [ cond ] we calculate numerically the composite conductivities within the gtn model and compare them with the conductivities obtained by the cp approximation . in sec . [ critical ] we present our results on the critical tunneling distance which are used in sec . [ formulas ] to obtain analytical formulas for the composite conductivity . these are applied in sec . [ compa ] to several published data on nanocomposites to extract the tunneling distance . section [ concl ] is devoted to discussions and conclusions .

we noted that the tunneling - percolation framework is quite well understood at the extreme cases of percolation - like and hopping - like behaviors but that the intermediate regime has not been previously discussed , in spite of its relevance to the intensively studied electrical properties of nanocomposites . following that we study here the conductivity of dispersions of particle fillers inside an insulating matrix by taking into account explicitly the filler particle shapes and the inter - particle electron tunneling process . furthermore , we demonstrate that our numerical results are fully reproduced by the critical path method , which is generalized here in order to include the particle filler shapes . by exploiting this method these results are concluded then to be not only useful for the understanding of the intermediate regime but also for tailoring the electrical properties of nanocomposites .

we noted that the tunneling - percolation framework is quite well understood at the extreme cases of percolation - like and hopping - like behaviors but that the intermediate regime has not been previously discussed , in spite of its relevance to the intensively studied electrical properties of nanocomposites . following that we study here the conductivity of dispersions of particle fillers inside an insulating matrix by taking into account explicitly the filler particle shapes and the inter - particle electron tunneling process . we show that the main features of the filler dependencies of the nanocomposite conductivity can be reproduced without introducing any _ a priori _ imposed cut - off in the inter - particle conductances , as usually done in the percolation - like interpretation of these systems . furthermore , we demonstrate that our numerical results are fully reproduced by the critical path method , which is generalized here in order to include the particle filler shapes . by exploiting this method , we provide simple analytical formulas for the composite conductivity valid for many regimes of interest . the validity of our formulation is assessed by reinterpreting existing experimental results on nanotube , nanofiber , nanosheet and nanosphere composites and by extracting the characteristic tunneling decay length , which is found to be within the expected range of its values . these results are concluded then to be not only useful for the understanding of the intermediate regime but also for tailoring the electrical properties of nanocomposites .

1004.4728

m

in considering the overall conductivity arising in such composites , we attributed to each spheroid pair the tunneling conductance given in eq . where , now , for @xmath31 the inter - particle distance @xmath14 depends also on the relative orientation of the spheroids . the @xmath14 values were obtained here from the numerical procedure described in ref . [ ] . on the other hand , in writing eq . we neglect any energy difference between spheroidal particles and disregard activation energies since , in general , these contributions can be ignored at relatively high temperatures,@xcite which is the case of interest here . for the specific case of extreme prolate objects ( @xmath24 ) the regime of validity of this approximation has been studied in ref . [ ] . the full set of bond conductances given by eq . was mapped as a resistor network with @xmath32 and the overall conductivity was calculated through numerical decimation of the resistor network.@xcite to reduce computational times of the decimation procedure to manageable limits , an artificial maximum distance was introduced in order to reject negligibly small bond conductances . it is important to note that this artifice is not in conflict with the rationale of the gtn model , since the cutoff it implies neglects conductances which are completely irrelevant for the global system conductivity . we chose the maximum distance to be generally fixed and equal to four times the spheroid major axis ( i.e. @xmath26 in the prolate case and @xmath27 in the oblate case ) , which is equivalent to reject inter - particle conductances below @xmath33 for @xmath34 case ( and considerably less for smaller @xmath13 values ) . however , for the high aspect - ratios and high densities the distance had to be reduced . moreover , since the maximum distance implies in turn an artificial geometrical percolation threshold of the system , for the high aspect - ratios , at low volume fractions the distance had to be increased to avoid this effect . by comparing the results with the ones obtained with significantly larger maximum distances we verified that the effect is undetectable . in fig . [ fig2](a ) we show the so - obtained conductivity @xmath0 values ( symbols ) as a function of the volume fraction @xmath1 of prolate spheroids with aspect - ratio @xmath35 and different values of @xmath36 , where @xmath37 . each symbol is the outcome of @xmath38 realizations of a system of @xmath39 spheroids . the logarithm average of the results was considered since , due to the exponential dependence of eq . , the distribution of the computed conductivities was approximately of the log - normal form.@xcite the strong reduction of @xmath0 for decreasing @xmath1 shown in fig . [ fig2](a ) is a direct consequence of the fact that as @xmath1 is reduced , the inter - particle distances get larger , leading in turn to a reduction of the local tunneling conductances [ eq . ] . in fact , as shown in fig . [ fig2](b ) , this reduction depends strongly on the shape of the conducting fillers . specifically , as the shape anisotropy of the particles is enhanced , the composite conductivity drops for much lower values of @xmath1 for a fixed @xmath13 . having the above result we turn now to show that the strong dependence of @xmath8 on @xmath28 and @xmath13 in fig . [ fig2 ] can be reproduced by cp method @xcite when applied to our system of impenetrable spheroids . for the tunneling conductances of eq . , this method amounts to keep only the subset of conductances @xmath40 having @xmath41 , where @xmath42 , which defines the characteristic conductance @xmath43 , is the largest among the @xmath14 distances , such that the so - defined subnetwork forms a conducting cluster that span the sample . next , by assigning @xmath44 to all the ( larger ) conductances of the subnetwork , a cp approximation for @xmath0 is @xmath45,\ ] ] where @xmath46 is a pre - factor proportional to @xmath12 . the significance of eq . is that it reduces the conductivity of a distribution of hard objects that are electrically connected by tunneling to the computation of the geometrical critical " distance @xmath42 . in practice , @xmath42 can be obtained by coating each impenetrable spheroid with a penetrable shell of constant thickness @xmath47 , and by considering two spheroids as connected if their shells overlap . @xmath42 is then the minimum value of @xmath48 such that , for a given @xmath1 , a cluster of connected spheroids spans the sample . to extract @xmath42 we follow the route outlined in ref . [ ] with the extended distribution generation algorithm described in sec . [ gen ] . specifically , we calculated the spanning probability as a function of @xmath1 for fixed @xmath28 and @xmath42 by recording the frequency of appearance of a percolating cluster over a given number of realizations @xmath49 . the realization number varied from @xmath50 for the smallest values of @xmath42 up to @xmath51 for the largest ones . each realization involved distributions of @xmath52 spheroids , while for high aspect - ratio prolate spheroids this number increased to @xmath53 in order to be able to maintain the periodic boundary conditions on the simulation cell . relative errors on @xmath42 were in the range of a few per thousand . results of the cp approximation are reported in fig . [ fig2 ] by dotted lines . the agreement with the full numerical decimation of the resistor network is excellent for all values of @xmath28 and @xmath36 considered . this observation is quite important since it shows that the cp method is valid also beyond the low - density regime , for which the conducting fillers are effectively point particles , and that it can be successfully used for systems of particles with impenetrable volumes . besides the clear practical advantage of evaluating @xmath0 via the geometrical quantity @xmath42 instead of solving the whole resistor network , the cp approximation is found then , as we shall see in the next section , to allow the full understanding of the filler dependencies of @xmath0 and to identify asymptotic formulas for many regimes of interest . before turning to the analysis of the next section , it is important at this point to discuss the following issue . as shown in fig . [ fig2 ] , the gtn scenario predicts , in principle , an indefinite drop of @xmath0 as @xmath54 because , by construction , there is not an imposed cut - off in the inter - particle conductances . however , in real composites , either the lowest measurable conductivity is limited by the experimental set - up,@xcite or it is given by the intrinsic conductivity @xmath55 of the insulating matrix , which prevents an indefinite drop of @xmath0 . for example , in polymer - based composites @xmath55 falls typically in the range of @xmath56 s / cm , and it originates from ionic impurities or displacement currents.@xcite since the contributions from the polymer and the inter - particle tunneling come from independent current paths , the total conductivity ( given by the polymer and the inter - particle tunneling ) is then simply @xmath57.@xcite as illustrated in fig . [ fig3 ] , where @xmath58 is plotted for @xmath59 , @xmath60 , and @xmath61 and for @xmath62 , the @xmath1-dependence of @xmath58 is characterized by a cross - over concentration @xmath2 below which @xmath63 . as seen in this figure , fillers with larger shape - anisotropy entail lower values of @xmath2 , consistently with what is commonly observed.@xcite we have therefore that the main features of nanocomposites ( drop of @xmath0 for decreasing @xmath1 , enhancement of @xmath0 at fixed @xmath1 for larger particle anisotropy , and a characteristic @xmath2 below which the conductivity matches that of the insulating phase ) can be obtained without invoking any microscopic cut - off , leading therefore to a radical change of perspective from the classical percolation picture . in particular , in the present context , the conductor - insulator transition is no longer described as a true percolation transition ( characterized by a critical behavior of @xmath0 in the vicinity of a definite percolation threshold , _ i.e. _ , eq . ) , but rather as a cross - over between the inter - particle tunneling conductivity and the insulating matrix conductivity .

we show that the main features of the filler dependencies of the nanocomposite conductivity can be reproduced without introducing any _ a priori _ imposed cut - off in the inter - particle conductances , as usually done in the percolation - like interpretation of these systems . , we provide simple analytical formulas for the composite conductivity valid for many regimes of interest .

we noted that the tunneling - percolation framework is quite well understood at the extreme cases of percolation - like and hopping - like behaviors but that the intermediate regime has not been previously discussed , in spite of its relevance to the intensively studied electrical properties of nanocomposites . following that we study here the conductivity of dispersions of particle fillers inside an insulating matrix by taking into account explicitly the filler particle shapes and the inter - particle electron tunneling process . we show that the main features of the filler dependencies of the nanocomposite conductivity can be reproduced without introducing any _ a priori _ imposed cut - off in the inter - particle conductances , as usually done in the percolation - like interpretation of these systems . furthermore , we demonstrate that our numerical results are fully reproduced by the critical path method , which is generalized here in order to include the particle filler shapes . by exploiting this method , we provide simple analytical formulas for the composite conductivity valid for many regimes of interest . the validity of our formulation is assessed by reinterpreting existing experimental results on nanotube , nanofiber , nanosheet and nanosphere composites and by extracting the characteristic tunneling decay length , which is found to be within the expected range of its values . these results are concluded then to be not only useful for the understanding of the intermediate regime but also for tailoring the electrical properties of nanocomposites .

astro-ph0407061

c

from the application of karhunen - love transform , an objective classification of @xmath88170,000 galaxy spectra in the sdss is performed . with a quantitative convergence criteria defined , gappy galaxy spectra can be repaired and kl eigenspectra and eigencoefficients derived . for most of the galaxy types , three eigenspectra are sufficient for describing the continua and emission lines to a high degree of accuracy with a maximum error in line - reconstructions of approximately 10% . typically ten modes are needed in the reconstruction of galaxies with extreme emission lines with errors of @xmath109% in the line fluxes . we find that a two - parameter @xmath161-classification scheme can discriminate between spectra corresponding to all spectral types used in the current classification scheme ( including galaxies with extreme emission lines ) . this classification is robust to repeat observations ( at a level of a few degrees in the classification angles ) due to the accurate spectrophotometric calibration of the sdss data set . we find a weak dependence in the classification on the signal - to - noise of the spectra . this effect is , however , smaller than the typical dispersion between repeat observations and is negligible at signal - to - noise levels at which the sdss spectra are defined as being of survey quality . we find that there exists a minimum number of randomly selected spectra that are necessary to statistically represent the information within the full sample ( i.e. , to be representative of the true distribution of galaxies ) . for a set of ten eigenspectra ( i.e. , ten eigenspectra enable the reproduction of both quiescent and active galaxies ) the number of spectra required is around @xmath74 to @xmath75 . this is due to the need to sample a minimum number of randomly selected galaxies in order to include galaxies with extreme emission line properties in our data set ( as they comprise only 0.1% of the full galaxy sample ) . we find that the bias on the spectral classification due to the fixed aperture spectroscopy is , on average , small and is negligible for all galaxies except for the reddest galaxies that are very close by ( @xmath162 ) and for those galaxies that are large physically ( @xmath163 kpc ) with prominent emission lines . a look - up table is constructed for the correction of this bias . there are several future directions related to this work . with the present continuous classification scheme , which simplifies the distribution of galaxies into a handful of parameters , studies of the statistics of the physical properties of galaxies become more tractable . the clustering and spectral properties of these classifications will be addressed in a future paper . the generality of these techniques are applicable to any set of spectra and has been recently applied to the sdss qso catalog ( yip et al . 2003 , 2004 ) . we thank mariangela bernardi , ravi sheth and michael blanton for comments and discussions . cwy is partially supported by zaccheus daniel fellowship . ajc and cwy acknowledge partial support from an nsf career award ast99 84924 , a nasa ltsa grant nag5 8546 and a nsf itr award 0121671 . funding for the creation and distribution of the sdss archive has been provided by the alfred p. sloan foundation , the participating institutions , the national aeronautics and space administration , the national science foundation , the u.s . department of energy , the japanese monbukagakusho , and the max planck society . the sdss web site is http://www.sdss.org/. the sdss is managed by the astrophysical research consortium ( arc ) for the participating institutions . the participating institutions are the university of chicago , fermilab , the institute for advanced study , the japan participation group , the johns hopkins university , los alamos national laboratory , the max - planck - institute for astronomy ( mpia ) , the max - planck - institute for astrophysics ( mpa ) , new mexico state university , university of pittsburgh , princeton university , the united states naval observatory , and the university of washington . connolly a. j. , budavri t. , szalay a. s. , csabai i. & brunner r. j. 1999b , in asp conf . 191 , _ photometric redshifts and high redshift galaxies _ , ed . weymann r. j. , storrie - lombardi l. j. , sawicki m. , & brunner r. j. ( san francisco : asp ) , 13 . lupton r. , gunn j. e. , ivezi z. , knapp g. r. & kent s. 2001 , in asp conf . 238 , _ astronomical data analysis software and systems x _ , ed . harnden f. r. jr . , primini f. a. , & payne h. e. ( san francisco : astr . spc . pac . ) , p. 269 . .the number of galaxies in the range ( @xmath164 ) . these data are a subset of the full sample . the galaxy types listed are the possible morphological types , estimated by comparing the spectral features of the mean spectrum constructed in each range with spectra in @xcite and therefore they are for reference only . [ tab : number ] [ cols="^,^,^,^,^",options="header " , ]

we perform an objective classification of 170,000 galaxy spectra in the sloan digital sky survey ( sdss ) using the karhunen - love ( kl ) transform . with about one - sixth of the total set of galaxy spectra which will be obtained by the survey , we are able to carry out the most extensive analysis of its kind to date . bias in the spectral classifications due to the aperture spectroscopy in the sdss is small and within the signal - to - noise limit for majority of galaxies except for the reddest nearby galaxies and large galaxies ( kpc ) with prominent emissions .

we perform an objective classification of 170,000 galaxy spectra in the sloan digital sky survey ( sdss ) using the karhunen - love ( kl ) transform . with about one - sixth of the total set of galaxy spectra which will be obtained by the survey , we are able to carry out the most extensive analysis of its kind to date . the formalism proposed by connolly and szalay ( 1999a ) is adopted to correct for gappy regions in the spectra , and to derive eigenspectra and eigencoefficients . from this analysis , we show that this gap - correction formalism leads to a converging set of eigenspectra and kl - repaired spectra . furthermore , kl eigenspectra of galaxies are found to be convergent not only as a function of iteration , but also as a function of the number of randomly selected galaxy spectra used in the analysis . from these data a set of ten eigenspectra of galaxy spectra are constructed , with rest - wavelength coverage . the eigencoefficients describing these galaxies naturally place the spectra into several classes defined by the plane formed by the first three eigencoefficients of each spectrum . spectral types , corresponding to different hubble - types and galaxies with extreme emission lines , are identified for the 170,000 spectra and are shown to be complementary to existing spectral classifications . from a non - parametric classification technique , we find that the population of galaxies can be divided into three classes which correspond to early late- through to intermediate late - types galaxies . this finding is believed to be related to the color separation of sdss galaxies discussed in earlier works . bias in the spectral classifications due to the aperture spectroscopy in the sdss is small and within the signal - to - noise limit for majority of galaxies except for the reddest nearby galaxies and large galaxies ( kpc ) with prominent emissions . the mean spectra and eigenspectra derived from this work can be downloaded from http://www.sdss.org .

nucl-th9810026

i

quantum hadrodynamics ( qhd ) and the relativistic treatment of nuclear systems has been a subject of growing interest during recent years @xcite . the model of walecka @xcite and its non - linear extensions with cubic and quartic self - interactions of the scalar - meson field @xcite have been widely used to this end . this model contains dirac nucleons together with neutral scalar and vector mesons as well as isovector - vector @xmath0 mesons . at the mean field ( hartree ) level , it already includes the spin orbit force , the finite range and the density dependence which are essential ingredients of the nuclear interaction . this simple model has become very popular in relativistic calculations and describes successfully many properties of the atomic nucleus . from a theoretical point of view , the non - linear model with cubic and quartic scalar self - interactions was classed within renormalizable field theories which can be characterized by a finite number of coupling constants . however , very recently , generalizations of this model that include other non - linear interactions among the meson fields and tensor couplings have been presented on the basis of effective field theories by serot et al.@xcite . the effective theory contains many couplings of non - renormalizable form that are consistent with the underlying symmetries of qcd . consequently , one must find some suitable expansion parameters and develop a systematic truncation scheme . for this purpose the concept of naturalness has been employed : it means that the unknown couplings of the theory should all be of the order of unity when written in appropriate dimensionless form using naive dimensional analysis @xcite . then , one can estimate the contributions coming from different terms by counting powers in the expansion parameters and truncating the lagrangian at a given level of accuracy . one important fact is the observation that at normal nuclear densities the scalar and vector meson fields , denoted by @xmath1 and @xmath2 , are small as compared with the nucleon mass @xmath3 and that they change slowly in finite nuclei . this implies that the ratios @xmath4 , @xmath5 , @xmath6 and @xmath7 are useful expansion parameters when the effective field theory is applied to the nuclear many - body problem . from this viewpoint , if all the terms involving scalar and meson self - interactions are retained in the lagrangian up to fourth order , one recovers the well - known non - linear model plus some additional terms @xcite . for the truncation to be consistent , the corresponding coupling constants should exhibit naturalness and can not be arbitrarily dropped out without an additional symmetry argument . the effective lagrangian truncated at fourth order contains thirteen free parameters that have been fitted to reproduce twenty - nine finite nuclei observables @xcite . remarkably , the fitted parameters turn out to be natural and the results are not dominated by the last terms retained . this evidence confirms the utility of the principles of naive dimensional analysis and naturalness and shows that truncating the effective lagrangian at the first lower orders is justified . the term with a vector - meson quartic self - interaction has been considered previously in relativistic mean field ( rmf ) calculations from a phenomenological point of view . bodmer @xcite considered this coupling to avoid the negative coefficient of the quartic scalar self - interaction that appears in many non - linear parametrizations that correctly describe the atomic nucleus @xcite . in some special situations this negative term can lead to a pathological behaviour of the scalar potential . on the other hand , the equation of state is softened at moderate high densities when the vector non - linearity is taken into account . the quartic vector self - interaction has also been phenomenologically used by gmuca @xcite in a non - linear model for parametrizing dirac brueckner fock calculations of nuclear matter . the same idea was developed by toki et al . and applied to study finite nuclei @xcite and neutron stars @xcite . recently , the properties of high - density nuclear and neutron matter have been analyzed in the rmf approach taking into account scalar and vector non - linearities @xcite . the tensor couplings of the vector @xmath8 and @xmath0 mesons to the nucleon were investigated by reinhard et al . @xcite as an extension of the rmf model , and more recently by furnstahl et al.@xcite from the point of view of relativistic effective field theory . in these works it was shown that the tensor coupling of the @xmath8 meson has an important bearing on the nuclear spin orbit splitting . the surface properties of nuclei play a crucial role in certain situations . this is the case , for instance , of saddle - point configurations in nuclear fission or fragment distributions in heavy - ion collisions . within a context related to the liquid droplet model ( ldm ) and the leptodermous expansion @xcite , the surface properties can be extracted from semi - infinite nuclear matter calculations either quantally or semiclassically ( though the total curvature energy coefficient can only be computed semiclassically @xcite ) . in the non - relativistic case most of the calculations of the surface properties have been carried out using skyrme forces , quantally @xcite or semiclassically with the help of the extended thomas fermi ( etf ) method @xcite . in the relativistic case the nuclear surface has been analyzed within the model since a long time ago . the calculations have been performed semiclassically using the relativistic thomas fermi ( tf ) method or its extensions ( retf ) , for symmetric @xcite and asymmetric @xcite matter , and also in the quantal hartree approach @xcite . in the framework of the relativistic model and effective field theory , the main purpose of the present work is to carefully analyze the influence on surface properties of the quartic vector non - linearity , of the newly proposed scalar - vector self - interactions and of the tensor coupling . we shall investigate quantities such as the surface energy coefficient , surface thickness , spin orbit strength , surface stiffness coefficient and neutron skin thickness obtained from hartree calculations of symmetric and asymmetric semi - infinite nuclear matter . the paper is organized as follows . section 2 is devoted to the basic theory . the results on the surface properties of symmetric matter are discussed in section 3 . section 4 addresses the case of asymmetric systems . the summary and conclusions are given in the last section .

we perform hartree calculations of symmetric and asymmetric semi - infinite nuclear matter in the framework of relativistic models based on effective hadronic field theories as recently proposed in the literature . we investigate the implications of these terms on nuclear surface properties such as the surface energy coefficient , surface thickness , surface stiffness coefficient , neutron skin thickness and the spin orbit force . = 22.5 cm = 16.4 cm = -0.4 cm = -0.5 cm addtoresetequationsection tempcntc citex[#1]#2@filesw auxout tempcnta@tempcntb@neciteaciteforciteb:=#2citeo#1 citeotempcnta > tempcntbciteacitea , tempcnta = tempcntbtempcnta * nuclear surface properties in + relativistic effective field theory * + m. del estal , m. centelles , x. vias + _ departament destructura i constituents de la matria , facultat de fsica , + universitat de barcelona , diagonal _ 647 _ , e-_08028 _ barcelona , spain _ _ pacs : _ 21.60.-n , 21.30.-x , 21.10.dr , 21.65.+f _ keywords : _ nuclear surface properties ; spin orbit potential ; semi - infinite nuclear matter ; non - linear self - interactions ; quantum hadrodynamics ; effective field theory .

we perform hartree calculations of symmetric and asymmetric semi - infinite nuclear matter in the framework of relativistic models based on effective hadronic field theories as recently proposed in the literature . in addition to the conventional cubic and quartic scalar self - interactions , the extended models incorporate a quartic vector self - interaction , scalar - vector non - linearities and tensor couplings of the vector mesons . we investigate the implications of these terms on nuclear surface properties such as the surface energy coefficient , surface thickness , surface stiffness coefficient , neutron skin thickness and the spin orbit force . = 22.5 cm = 16.4 cm = -0.4 cm = -0.5 cm addtoresetequationsection tempcntc citex[#1]#2@filesw auxout tempcnta@tempcntb@neciteaciteforciteb:=#2citeo#1 citeotempcnta > tempcntbciteacitea , tempcnta = tempcntbtempcnta * nuclear surface properties in + relativistic effective field theory * + m. del estal , m. centelles , x. vias + _ departament destructura i constituents de la matria , facultat de fsica , + universitat de barcelona , diagonal _ 647 _ , e-_08028 _ barcelona , spain _ _ pacs : _ 21.60.-n , 21.30.-x , 21.10.dr , 21.65.+f _ keywords : _ nuclear surface properties ; spin orbit potential ; semi - infinite nuclear matter ; non - linear self - interactions ; quantum hadrodynamics ; effective field theory .

1311.6515

i

the galactic supernova remnant ( snr ) kes 73 ( g27.4 + 0.0 ) has been classified as a shell - type snr and hosts the anomalous x - ray pulsar ( axp ) 1e 1841@xmath0045 ( helfand et al . 1994 ; vasisht & gotthelf 1997 ) . radio studies of the remnant show an incomplete , small diameter ( @xmath205@xmath21 ) , shell characterized by a steep spectral index ( @xmath22 @xmath20 0.68 ) , a flux density of 6 jy at 1 ghz , and with no detection of the central compact source with a flux limit @xmath23 @xmath24 0.45 mjy and @xmath25 @xmath24 0.60 mjy ( green 2009 ; kriss et al . 1985 ; helfand et al . 1994 ) . the infrared studies , carried out as part of the galactic snr surveys , clearly detected the remnant in the 24 @xmath26 m band ( wachter et al . 2007 ; carey et al . 2009 ; pinheiro goncalves et al . the infrared emission originating from the snr with an estimated dust mass of 0.11 @xmath19 has been explained by pinheiro goncalves et al . ( 2011 ) as likely due to grains heated by collisions in the hot plasma , while carey et al . ( 2009 ) suggested that the 24 @xmath26 m emission may be mostly due to nebular emission lines such as [ o iv ] ( 25.89 @xmath26 m ) and [ fe ii ] ( 25.99 @xmath26 m ) with a small contribution to the continuum emission from dust produced in the remnant . the snr kes 73/axp system was previously observed and studied using many x - ray observatories including _ einstein _ , _ rosat _ , _ asca _ , _ chandra _ , and _ xmm - newton_. the _ asca _ spectrum was described by a thermal bremsstrahlung model with @xmath27 @xmath20 0.6 kev plus gaussian emission lines with evidence for enhanced mg , and possibly o and ne , abundances , with the snr age estimated to be @xmath282000 years ( gotthelf & vasisht 1997 ) . observation of the snr was briefly studied by morii et al . ( 2010 ) in connection with the _ suzaku _ studies of axp 1e 1841@xmath0045 , where the entire snr spectrum was modeled by a vsedov model . the _ xmm - newton _ study of the remnant was performed by vink & kuiper ( 2006 ) using the mos data . they fitted the spectrum using either a two - component non - equilibrium ionization ( nei ) model under the spex fitting package ( kaastra & mewe 2000 ) or a one - component vsedov model , both of which yielded solar metal abundances . their study , primarily targeted to determine the supernova explosion energy , argued against the millisecond proto - neutron star model for magnetar formation . recently , lopez et al . ( 2011 ) also reported x - ray results on kes 73 as part of a survey study aimed at typing snrs using their x - ray morphology as well as to set observational constraints on the hydrodynamical models . their study , which made use of one of the available _ chandra _ observations of kes 73 , yielded a mean temperature of @xmath27 = 0.84 @xmath16 0.49 kev using a one - component vpshock model and detected enhanced abundances from mg , si , and s for some of the small scale regions extracted from within the remnant . the above mentioned x - ray studies lack a detailed imaging and spectroscopic analysis of the remnant using all available data . hence , in the following work , we extend the earlier studies to include multi - wavelength data and in particular , the previously unpublished _ chandra _ and _ xmm - newton _ observations . we provide a detailed x - ray imaging - spectroscopic analysis to investigate the snr s multi - wavelength morphology ( radio , infrared , and x - rays ) , map the spectral parameters across the remnant , revisit the supernova explosion properties , and address the mass of its progenitor star . the latter goal is motivated by addressing the nature of the progenitors and the environment of highly magnetized neutron stars ( with a surface dipole magnetic field @xmath29 @xmath18 4@xmath310@xmath30 g ) through studying their hosting snrs ( see safi - harb & kumar 2012 ) . kes 73 is one of only a few snrs associated with high-@xmath29 pulsars . the x - ray emission from its associated axp , the slowest ( @xmath31 = 11.8 s ) known magnetar with a characteristic age of @xmath204.7 kyr , was first decoupled from the diffuse emission from the snr using _ asca _ ( helfand et al . 1994 ; gotthelf & vasisht 1997 ) . this source has been manifesting itself as a quiescent magnetar since the time of its discovery until recently , when it exhibited the first magnetar - like burst caught by the _ swift _ x - ray observatory ( beardmore et al . 2010 ; kumar & safi - harb 2010 ) followed by a few more bursts ( lin et al . 2011 ) , further establishing its magnetar nature with @xmath29 @xmath20 7@xmath310@xmath32 g. although the axp s emission will not be further discussed in this paper , the study of snr kes 73 , because of its relative youth and brightness , provides a unique opportunity to shed light on the progenitor of highly magnetized neutron stars . the paper is organized as follows : section 2 describes the _ chandra _ and _ xmm - newton _ observations and data reduction . in sections 3 and 4 , we present the details of the x - ray imaging analysis and spectral fitting of the remnant , respectively . section 5 discusses the results and finally , we summarize our study in section 6 .

we present a _ chandra _ and _ xmm - newton _ study of the supernova remnant ( snr ) kes 73 hosting the anomalous x - ray pulsar 1e 1841 . we also discuss the possible scenario for kes 73 expanding into the late red supergiant wind phase of its massive progenitor . comparing the inferred metal abundances to core - collapse nucleosynthesis model yields , we estimate a progenitor mass , adding a candidate to the growing list of highly magnetized neutron stars proposed to be associated with very massive progenitors .

we present a _ chandra _ and _ xmm - newton _ study of the supernova remnant ( snr ) kes 73 hosting the anomalous x - ray pulsar 1e 1841 . the chandra image reveals clumpy structures across the remnant with enhanced emission along the western rim . the x - ray emission fills the radio shell and spatially correlates with the infrared image . the global x - ray spectrum is described by a two - component thermal model with a column density = 2.6 and a total luminosity of = 3.3 ergs s ( 0.510 kev , at an assumed distance of 8.5 kpc ) . the soft component is characterized by a temperature = 0.5 kev , a high ionization timescale , and enhanced si and s abundances suggesting emission that is dominated by shocked ejecta . the hard component has a temperature = 1.6 kev , a relatively low ionization timescale , and mostly solar abundances suggesting emission that is dominated by interstellar / circumstellar shocked material . a spatially resolved spectroscopy study reveals no significant variations in the spectral properties . we infer an snr age ranging between 750 yr and 2100 yr , an explosion energy of 3.0 ergs and a shock velocity of ( 1.2 0.3) km s ( under the sedov phase assumption ) . we also discuss the possible scenario for kes 73 expanding into the late red supergiant wind phase of its massive progenitor . comparing the inferred metal abundances to core - collapse nucleosynthesis model yields , we estimate a progenitor mass , adding a candidate to the growing list of highly magnetized neutron stars proposed to be associated with very massive progenitors .

1311.6515

i

in this paper , we have performed the first detailed imaging and spectral analysis of the snr kes 73 , using all archival _ chandra _ and _ xmm - newton _ data , to determine the intrinsic properties of the supernova explosion and the physical properties of the remnant . the main results are summarized as follows : 1 . the high resolution x - ray images confirm a spherical morphology of @xmath205@xmath35 size with several clumpy and knotty structures , and bright diffuse emission originating from the snr interior . the multi - wavelength morphology of the remnant in the radio , infrared , and x - rays shows the western limb to be much brighter than all other regions . the infrared image spatially correlates well with the x - ray image while the radio shell appears to extend slightly beyond the x - ray emission and displays a thin filamentary feature along the edges , which likely represents the location of the forward shock . the spectra obtained from different diffuse emission regions are best fit with a vpshock+vpshock model . the western limb of the snr showed a slightly higher column density given by @xmath160 = 3.3@xmath48@xmath310@xmath4 @xmath5 . the soft component is dominated by enhanced metal abundances mainly for si and s in all the regions , with plasma temperatures of 0.30.5 kev and ionization timescales @xmath3710@xmath142 @xmath76 s ( except for regions 2 and 7 ) . the hard component is dominated by solar abundances , with plasma temperatures of 1.11.7 kev and ionization timescales of ( 0.53.2)@xmath310@xmath75 @xmath76 s. this indicates that the soft component plasma for most regions has reached ionization equilibrium earlier than the plasma associated with the hard component . 3 . the global x - ray emission from kes 73 is best described by a two - component vsedov+vpshock model , with a column density @xmath160 = 2.6@xmath2@xmath310@xmath4 @xmath5 and the soft and hard components characterized by plasma temperatures of 0.5@xmath11 kev ( @xmath141 @xmath37 6.1@xmath310@xmath142 @xmath76 s ) and 1.6@xmath13 kev ( @xmath74 = 0.8@xmath57 @xmath3 10@xmath75 @xmath76 s ) , respectively . the presence of enhanced abundances in the soft component suggests that this component is dominated by shock - heated ejecta , while the hard component characterized mostly by solar abundances is dominated by shocked interstellar / circumstellar material . we have also refined the snr age ranging between 750 @xmath175 yr for the free expansion phase ( assuming an expansion velocity of 5000 km s@xmath9 ) and 2100 @xmath175 yr assuming a sedov phase of evolution . the sedov phase yields a shock velocity of ( 1.2 @xmath16 0.3)@xmath310@xmath17 km s@xmath9 , an explosion energy of @xmath264 = 3.0@xmath14@xmath310@xmath269 ergs , and a swept - up mass of 16@xmath309 m@xmath251 under the assumption of an explosion in a uniform ambient medium . considering kes 73 to be still expanding into the dense wind of its late phase rsg evolution , we infer a shock velocity of ( 1.6@xmath160.7)@xmath310@xmath262 km s@xmath9 , an age of 2.6@xmath160.6 @xmath175 kyr , and explosion energy @xmath264 = ( 1.1@xmath310@xmath310@xmath301 @xmath197@xmath289 ergs . these derived values are consistent with the predictions of a very massive progenitor for kes 73 . 4 . although the abundances are not well - constrained , the abundance ratios , when compared to core - collapse nucleosynthesis models , suggest a progenitor mass @xmath1820@xmath311 for kes 73 . a much deeper exposure with existing x - ray missions , and high - resolution spectroscopy with the soft x - ray spectrometer of _ astro - h _ ( takahashi et al . 2012 ) , are needed for an accurate measurement of the abundances and shock velocities , and to further motivate the development of the existing nucleosynthesis models . we thank ken@xmath21ichi nomoto for helpful discussions on the nucleosynthesis yield models for core - collapse supernovae and the referee for useful comments that helped improved the paper . this research made use of nasa s astrophysics data system ( ads ) and of nasa s heasarc maintained at the goddard space flight center ( gsfc ) . s. safi - harb acknowledges support by a discovery grant from the natural sciences and engineering research council of canada ( nserc ) , the canada research chairs ( crc ) program , the canada foundation for innovation , the canadian institute for theoretical astrophysics , and the canadian space agency . pos acknowledges support from nasa contract nas8 - 03060 .

the global x - ray spectrum is described by a two - component thermal model with a column density = 2.6 and a total luminosity of = 3.3 ergs s ( 0.510 kev , at an assumed distance of 8.5 kpc ) . the hard component has a temperature = 1.6 kev , a relatively low ionization timescale , and mostly solar abundances suggesting emission that is dominated by interstellar / circumstellar shocked material . we infer an snr age ranging between 750 yr and 2100 yr , an explosion energy of 3.0 ergs and a shock velocity of ( 1.2 0.3) km s ( under the sedov phase assumption ) .

we present a _ chandra _ and _ xmm - newton _ study of the supernova remnant ( snr ) kes 73 hosting the anomalous x - ray pulsar 1e 1841 . the chandra image reveals clumpy structures across the remnant with enhanced emission along the western rim . the x - ray emission fills the radio shell and spatially correlates with the infrared image . the global x - ray spectrum is described by a two - component thermal model with a column density = 2.6 and a total luminosity of = 3.3 ergs s ( 0.510 kev , at an assumed distance of 8.5 kpc ) . the soft component is characterized by a temperature = 0.5 kev , a high ionization timescale , and enhanced si and s abundances suggesting emission that is dominated by shocked ejecta . the hard component has a temperature = 1.6 kev , a relatively low ionization timescale , and mostly solar abundances suggesting emission that is dominated by interstellar / circumstellar shocked material . a spatially resolved spectroscopy study reveals no significant variations in the spectral properties . we infer an snr age ranging between 750 yr and 2100 yr , an explosion energy of 3.0 ergs and a shock velocity of ( 1.2 0.3) km s ( under the sedov phase assumption ) . we also discuss the possible scenario for kes 73 expanding into the late red supergiant wind phase of its massive progenitor . comparing the inferred metal abundances to core - collapse nucleosynthesis model yields , we estimate a progenitor mass , adding a candidate to the growing list of highly magnetized neutron stars proposed to be associated with very massive progenitors .

1002.2226

i

a new era of galaxy cluster surveys , based on measuring distortions in the cosmic microwave background ( cmb ) , has begun . these distortions , known as the sunyaev - zeldovich effect @xcite , have been detected for the first time in untargeted surveys over large areas of the sky by two new mm - band experiments : the atacama cosmology telescope ( act ) and the south pole telescope ( spt ) . first results from act @xcite and spt @xcite offer a taste of the future potential these experiments hold for obtaining large samples of essentially mass - selected clusters to arbitrary redshifts and have also provided the first measurement of the microwave background at arc - minute angular scales @xcite . both act and spt aim to provide unique samples of massive clusters of galaxies , selected by mass nearly independently of redshift , over a large area of the southern sky . while the number density of sze - selected clusters can be used as a potentially strong probe of dark energy as well as for studies of cluster physics , it is crucial to understand the systematics of sze surveys by comparing with cluster identification using independent methods before the new cluster samples can be effectively used . for example the low amplitude of the sz component in the high-@xmath2 cmb power spectrum @xcite or stacked clusters in wmap @xcite are recent issues that provide additional motivation for an independent search for clusters over the region being surveyed in the sz . furthermore , although the new mm - band telescopes can be used to identify clusters , coordinated optical data are necessary for confirmation and to determine redshifts and other fundamental properties of the new clusters . the last decade has seen significant effort to produce large and well - selected optical catalogs of cluster of galaxies that can be used in cosmological , large - scale structure and galaxy evolution studies . the first systematic attempts to generate large samples of clusters , and to define their richness , came from the abell catalogs @xcite which searched for projected galaxy overdensities through visual inspection of photographic plates successfully identifying thousands of clusters . although optical catalogs can be relatively inexpensive and efficient at detecting low mass systems , early attempts were known to suffer from significant projection effects along the line of sight . the advent of ccd cameras and the digitization of large photographic plates has enabled the development of new search algorithms for galaxy clusters using a combination of space , brightness and color information ( i.e. photometric redshifts ) , minimizing projection issues ( see * ? ? ? * for a historical review of search methods ) . among these algorithms are the pioneering implementation of a spatial matched filter technique @xcite and its variants @xcite , the adaptive kernel technique @xcite , voronoi tessellation @xcite and methods exploiting the tight ridgeline in color - magnitude space of galaxies in clusters @xcite such as the red cluster sequence ( rcs ) @xcite and the maxbcg @xcite techniques . this new wave of studies have produced large sets of well - defined optical cluster catalogs covering thousands of square - degrees ( i.e. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) providing reliable richness - mass correlations @xcite and establishing independent cosmological constraints @xcite using optical catalogs . in this article we present new results from the southern cosmology survey ( scs ) , our on - going multi - wavelength survey coordinated with act . our first paper in this series , @xcite , described our scs imaging pipeline and presented a sample of new galaxy clusters from an @xmath3 deg@xmath4 optical imaging survey of the southern sky acquired at the blanco 4-m telescope . here , we complete our cluster analysis using all the 70 deg@xmath4 contiguous imaging available , which represents a comoving volume of 0.076 gpc@xmath5 at @xmath6 . throughout this paper we assume a flat cosmology with @xmath7 km s@xmath8 mpc@xmath8 , @xmath9 and matter density @xmath10 .

we present a catalog of 105 rich and massive ( ) optically - selected clusters of galaxies extracted from 70 square - degrees of public archival imaging from the blanco 4-m telescope acquired over 45 nights between 2005 and 2007 . a strong motivation for this study is to identify the massive clusters that are expected to display prominent signals from the sunyaev - zeldovich effect ( sze ) and therefore be detected in the wide - area mm - band surveys being conducted by both the atacama cosmology telescope and the south pole telescope .

we present a catalog of 105 rich and massive ( ) optically - selected clusters of galaxies extracted from 70 square - degrees of public archival imaging from the blanco 4-m telescope acquired over 45 nights between 2005 and 2007 . we use the clusters optically - derived properties to estimate photometric redshifts , optical luminosities , richness , and masses . we complement the optical measurements with archival xmm - newton and rosat x - ray data which provide additional luminosity and mass constraints on a modest fraction of the cluster sample . two of our clusters show clear evidence for central lensing arcs ; one of these has a spectacular large - diameter , nearly - complete einstein ring surrounding the brightest cluster galaxy . a strong motivation for this study is to identify the massive clusters that are expected to display prominent signals from the sunyaev - zeldovich effect ( sze ) and therefore be detected in the wide - area mm - band surveys being conducted by both the atacama cosmology telescope and the south pole telescope . the optical sample presented here will be useful for verifying new sze cluster candidates from these surveys , for testing the cluster selection function , and for stacking analyzes of the sze data .

1002.2226

r

the observational quantities required as input to the cluster mass scaling relation are 200 , 200 , and . the cluster richness , 200 , is the number of e and e / s0 galaxies within a given radius , originally defined by @xcite as @xmath46 mpc , with colors and luminosities that satisfy specific conditions for membership . similarly , @xmath42 is the total rest - frame integrated @xmath47-band luminosity , @xmath48-corrected to @xmath49 , of all member galaxies included in 200 , and @xmath50 is the similarly defined rest - frame @xmath47-band luminosity of the bcg . @xcite provide power - law functions for both the luminosity - mass and richness - mass relations ( see section 5.2.1 in their paper ) . both @xcite and @xcite found that the luminosity - mass and richness - mass relations were well described by power - law functions and they measured the normalizations and slopes in these relations using @xmath51 minimization . we computed the two fitting functions based on @xmath42 and 200 , ( see section 5.2.1 from @xcite for full details ) , which are described as : @xmath52 and @xmath53 where @xmath54 is the mass observational equivalent of @xmath55 ( i.e. the halo mass enclosed within a radius of spherical volume within which the mean density is 200 times the average density ) in units of @xmath56 , @xmath42 is in units of @xmath57 and the dependence is normalized by its mean value . this is also described by a power - law function for a given value of 200 and 200 : @xmath58 and @xmath59 the published best - fitting parameters for @xmath60 , @xmath61 and @xmath62 in eqs . ( [ eq : m1 ] ) and ( [ eq : m2 ] ) as well as the new erratum - corrected values of @xmath63 and @xmath64 ( r. reyes , private communication ) for eqs . ( [ eq : l1 ] ) and ( [ eq : l2 ] ) are shown in table [ tab : pars ] . these recent changes in the values of the @xmath63 and @xmath64 parameters in @xcite have implications for our mass estimation . specifically , the changes translate into a decrease in mass when compared to our previous analysis of @xcite which used the initial parameters from their pre - print paper . as we discuss below , this change also affects the recovery of clusters in @xcite for the sky region that overlaps with this study . band observed magnitude for the bcgs in our sample as a function of the redshift of the cluster ( filled circles ) . we also show the @xmath65 bcg - redshift relationship from @xcite as the dashed curve.,width=384 ] we use this parametrization to obtain the optical mass estimates 200 and 200 , based on 200 and 200 , respectively , for all of the visually inspected clusters . based on these estimates we defined our catalog of massive clusters by selecting all systems with either @xmath66 or @xmath67 and @xmath68 . this defines the sample : 61 systems in the 5hr region and 44 in the 23hr region for a total of 105 clusters over @xmath69 deg@xmath4 of multi - band imaging . this mass threshold is aimed to include the upcoming @xmath70 significant sze detections from spt and act . in tables [ tab : clustes23hr ] and [ tab : clustes05hr ] we display the optical properties , photometric redshifts , positions and mass estimates for all clusters at 23hr and 5hr respectively . in these tables we provide for each cluster the photometric redshift of the bcg as well as the mean photometric redshift for the system which was estimated using galaxies within 250 kpc of the bcg . as we discussed in @xcite the expected luminosity range of bcgs in rich clusters has been already observationally established from the sdss @xcite and it can be used as an additional probe to confirm the presence of a massive cluster . to this end in figure [ fig : magz ] we compare the observed @xmath71band magnitudes of all bcgs in our sample as a function of redshift to a parametrization of the observed @xmath71band of sdss bcgs ( dashed curve ) . this corresponds to the @xmath72 prescription from @xcite where we have used @xmath73 from @xcite and allowed it to evolve passively with redshift . we see in the figure that all of the sources lie very close or well below ( i.e. , are intrinsically brighter ) than the model curve as we would expect for the bcg in a rich cluster . in our previous study @xcite we presented a similar cluster analysis and mass estimation over @xmath3 deg@xmath4 area in the 23hr region which is fully contained in the current 70 deg@xmath4 dataset . however , due to the changes in the mass parametrization prescription we did not recover all the massive clusters from @xcite even though the nominal mass threshold was the same ( @xmath0 ) as here . therefore , only 3 out of 8 clusters from table 5 of @xcite are massive enough to appear in the current paper s table [ tab : clustes23hr ] , while the remaining clusters , although detected , now have masses that fall below the @xmath74 mass limit . similarly , when comparing with the weak lensing mass estimates of @xcite we can only match the same 3 sources with clusters in their analysis ( see table 2 of their paper ) . on the other hand , there is now better agreement between the updated @xmath75 values and the weak lensing masses for the matched clusters . out of the 105 massive clusters in the sample we report two systems ( see the two lower panels of figure [ fig : clusters23hr ] ) with obvious evidence of arcs near the bcg . of these two lensing clusters , scso 235138@xmath76545253 at @xmath77 is a potentially unique system in that it shows a large diameter ( @xmath78 ) , nearly complete einstein ring embedded in a massive cluster . although our density of lensing clusters is not widely different from the @xcite rcs sample of 5 lensing clusters over @xmath79 deg@xmath4 , all of the gladders et al . clusters are at @xmath80 , while both of our systems are at @xmath81 making them completely exclusive in redshift . moreover , none of the @xcite sample shows anything close to a complete einstein ring . rrrrrrrrrrr[b ] @xmath82 & 1.54 & 0.61 & 0.41 & 0.67 & @xmath83 & @xmath84 & @xmath85 & @xmath86 & @xmath87 & @xmath88 + @xmath89 & 1.64 & 0.58 & 0.43 & 0.66 & @xmath90 & @xmath91 & @xmath92 & @xmath93 & @xmath94 & @xmath95 + [ tab : pars ] rrrccrrrr scso j231340@xmath76521919 & 0.21 & 0.21 & @xmath96 & @xmath97 & @xmath98 & @xmath99 & @xmath100 + scso j231403@xmath76564710 & 0.60 & 0.60 & @xmath101 & @xmath102 & @xmath103 & @xmath104 & @xmath105 + scso j231455@xmath76555308 & 0.21 & 0.23 & @xmath106 & @xmath107 & @xmath108 & @xmath109 & @xmath110 + scso j231511@xmath76523322 & 0.36 & 0.39 & @xmath111 & @xmath112 & @xmath113 & @xmath114 & @xmath115 + scso j231629@xmath76554535 & 0.51 & 0.53 & @xmath116 & @xmath117 & @xmath118 & @xmath119 & @xmath120 + scso j231651@xmath76545356 & 0.36 & 0.36 & @xmath121 & @xmath122 & @xmath123 & @xmath114 & @xmath124 + scso j231717@xmath76565723 & 0.74 & 0.73 & @xmath125 & @xmath126 & @xmath127 & @xmath128 & @xmath129 + scso j231848@xmath76561711 & 0.51 & 0.51 & @xmath130 & @xmath131 & @xmath132 & @xmath133 & @xmath119 + scso j231930@xmath76563858 & 0.36 & 0.37 & @xmath134 & @xmath135 & @xmath136 & @xmath105 & @xmath100 + scso j232001@xmath76565222 & 0.80 & 0.80 & @xmath137 & @xmath138 & @xmath139 & @xmath140 & @xmath109 + scso j232423@xmath76565705 & 0.75 & 0.75 & @xmath141 & @xmath142 & @xmath143 & @xmath144 & @xmath145 + scso j232437@xmath76530047 & 0.73 & 0.75 & @xmath146 & @xmath147 & @xmath148 & @xmath114 & @xmath110 + scso j232529@xmath76532420 & 0.74 & 0.71 & @xmath149 & @xmath150 & @xmath151 & @xmath152 & @xmath153 + scso j232612@xmath76531858 & 0.15 & 0.13 & @xmath154 & @xmath155 & @xmath156 & @xmath157 & @xmath99 + scso j232627@xmath76531512 & 0.74 & 0.74 & @xmath158 & @xmath159 & @xmath160 & @xmath161 & @xmath162 + scso j232637@xmath76533911 & 0.76 & 0.77 & @xmath163 & @xmath164 & @xmath165 & @xmath153 & @xmath166 + scso j232653@xmath76524149 & 0.11 & 0.11 & @xmath167 & @xmath168 & @xmath169 & @xmath99 & @xmath104 + scso j232724@xmath76533553 & 0.74 & 0.74 & @xmath170 & @xmath171 & @xmath172 & @xmath173 & @xmath174 + scso j232800@xmath76535152 & 0.74 & 0.75 & @xmath175 & @xmath147 & @xmath176 & @xmath177 & @xmath178 + scso j232811@xmath76533847 & 0.74 & 0.74 & @xmath179 & @xmath180 & @xmath181 & @xmath133 & @xmath119 + scso j232825@xmath76522814 & 0.73 & 0.70 & @xmath182 & @xmath183 & @xmath184 & @xmath185 & @xmath186 + scso j232827@xmath76531414 & 0.36 & 0.35 & @xmath187 & @xmath188 & @xmath189 & @xmath190 & @xmath177 + scso j232856@xmath76552428 & 0.57 & 0.57 & @xmath191 & @xmath192 & @xmath103 & @xmath193 & @xmath105 + scso j232916@xmath76522910 & 0.73 & 0.74 & @xmath194 & @xmath195 & @xmath196 & @xmath153 & @xmath173 + scso j233006@xmath76524035 & 0.73 & 0.71 & @xmath197 & @xmath198 & @xmath199 & @xmath161 & @xmath200 + scso j233227@xmath76535827 & 0.35 & 0.32 & @xmath201 & @xmath202 & @xmath203 & @xmath177 & @xmath204 + scso j233232@xmath76522016 & 0.36 & 0.37 & @xmath205 & @xmath206 & @xmath207 & @xmath208 & @xmath204 + scso j233329@xmath76521513 & 0.51 & 0.50 & @xmath175 & @xmath209 & @xmath210 & @xmath211 & @xmath109 + scso j233420@xmath76542732 & 0.56 & 0.55 & @xmath212 & @xmath213 & @xmath214 & @xmath124 & @xmath211 + scso j233544@xmath76535115 & 0.51 & 0.51 & @xmath215 & @xmath216 & @xmath217 & @xmath218 & @xmath219 + scso j233556@xmath76560602 & 0.64 & 0.63 & @xmath220 & @xmath221 & @xmath222 & @xmath157 & @xmath110 + scso j233607@xmath76535235 & 0.54 & 0.53 & @xmath223 & @xmath224 & @xmath225 & @xmath226 & @xmath227 + scso j233726@xmath76565655 & 0.50 & 0.52 & @xmath228 & @xmath229 & @xmath230 & @xmath124 & @xmath190 + scso j233807@xmath76531223 & 0.47 & 0.49 & @xmath231 & @xmath232 & @xmath233 & @xmath234 & @xmath235 + scso j233931@xmath76544525 & 0.73 & 0.71 & @xmath236 & @xmath112 & @xmath237 & @xmath124 & @xmath238 + scso j234012@xmath76541907 & 0.59 & 0.62 & @xmath239 & @xmath240 & @xmath214 & @xmath152 & @xmath241 + scso j234138@xmath76545210 & 0.55 & 0.56 & @xmath242 & @xmath243 & @xmath244 & @xmath178 & @xmath105 + scso j234156@xmath76530848 & 0.49 & 0.49 & @xmath245 & @xmath246 & @xmath247 & @xmath248 & @xmath249 + scso j234703@xmath76535051 & 0.56 & 0.55 & @xmath250 & @xmath251 & @xmath252 & @xmath193 & @xmath190 + scso j234917@xmath76545521 & 0.73 & 0.72 & @xmath253 & @xmath254 & @xmath255 & @xmath140 & @xmath161 + scso j235055@xmath76530124 & 0.46 & 0.48 & @xmath256 & @xmath257 & @xmath258 & @xmath234 & @xmath211 + scso j235138@xmath76545253 & 0.33 & 0.31 & @xmath259 & @xmath260 & @xmath160 & @xmath120 & @xmath261 + scso j235233@xmath76564348 & 0.74 & 0.72 & @xmath262 & @xmath263 & @xmath264 & @xmath128 & @xmath99 + scso j235454@xmath76563311 & 0.51 & 0.50 & @xmath265 & @xmath266 & @xmath267 & @xmath268 & @xmath200 + [ tab : clustes23hr ] rrrccrrrr[b ] scso j050854@xmath76513048 & 0.70 & 0.70 & @xmath141 & @xmath269 & @xmath270 & @xmath204 & @xmath268 + scso j050857@xmath76535837 & 0.76 & 0.78 & @xmath271 & @xmath272 & @xmath273 & @xmath200 & @xmath274 + scso j050902@xmath76520704 & 0.58 & 0.58 & @xmath275 & @xmath271 & @xmath276 & @xmath178 & @xmath234 + scso j050926@xmath76522227 & 0.67 & 0.70 & @xmath277 & @xmath278 & @xmath279 & @xmath157 & @xmath208 + scso j051023@xmath76544455 & 0.39 & 0.37 & @xmath280 & @xmath281 & @xmath282 & @xmath105 & @xmath144 + scso j051112@xmath76523112 & 0.73 & 0.73 & @xmath212 & @xmath163 & @xmath283 & @xmath129 & @xmath162 + scso j051136@xmath76561045 & 0.70 & 0.71 & @xmath277 & @xmath182 & @xmath284 & @xmath161 & @xmath285 + scso j051144@xmath76511416 & 0.48 & 0.48 & @xmath286 & @xmath287 & @xmath279 & @xmath100 & @xmath177 + scso j051145@xmath76515430 & 0.70 & 0.70 & @xmath288 & @xmath289 & @xmath290 & @xmath104 & @xmath105 + scso j051207@xmath76514204 & 0.48 & 0.46 & @xmath291 & @xmath292 & @xmath293 & @xmath105 & @xmath114 + scso j051225@xmath76505913 & 0.70 & 0.70 & @xmath294 & @xmath295 & @xmath296 & @xmath297 & @xmath173 + scso j051240@xmath76513941 & 0.66 & 0.66 & @xmath298 & @xmath299 & @xmath300 & @xmath104 & @xmath105 + scso j051245@xmath76502028 & 0.62 & 0.62 & @xmath301 & @xmath302 & @xmath303 & @xmath178 & @xmath304 + scso j051258@xmath76542153 & 0.67 & 0.68 & @xmath305 & @xmath306 & @xmath307 & @xmath193 & @xmath208 + scso j051400@xmath76512635 & 0.72 & 0.73 & @xmath308 & @xmath309 & @xmath310 & @xmath311 & @xmath312 + scso j051412@xmath76514004 & 0.67 & 0.66 & @xmath313 & @xmath314 & @xmath315 & @xmath316 & @xmath317 + scso j051457@xmath76514345 & 0.69 & 0.69 & @xmath197 & @xmath205 & @xmath318 & @xmath238 & @xmath319 + scso j051542@xmath76514017 & 0.73 & 0.73 & @xmath320 & @xmath321 & @xmath322 & @xmath208 & @xmath323 + scso j051558@xmath76543906 & 0.66 & 0.64 & @xmath324 & @xmath135 & @xmath325 & @xmath178 & @xmath105 + scso j051613@xmath76542620 & 0.38 & 0.36 & @xmath326 & @xmath327 & @xmath328 & @xmath329 & @xmath319 + scso j051637@xmath76543001 & 0.23 & 0.25 & @xmath330 & @xmath331 & @xmath332 & @xmath312 & @xmath333 + scso j051755@xmath76555727 & 0.66 & 0.66 & @xmath334 & @xmath335 & @xmath336 & @xmath128 & @xmath133 + scso j051933@xmath76554243 & 0.69 & 0.70 & @xmath141 & @xmath337 & @xmath338 & @xmath100 & @xmath339 + scso j051935@xmath76554916 & 0.75 & 0.75 & @xmath340 & @xmath242 & @xmath341 & @xmath104 & @xmath185 + scso j052051@xmath76561804 & 0.74 & 0.73 & @xmath342 & @xmath343 & @xmath344 & @xmath345 & @xmath219 + scso j052113@xmath76510418 & 0.64 & 0.61 & @xmath346 & @xmath347 & @xmath348 & @xmath349 & @xmath350 + scso j052200@xmath76502700 & 0.50 & 0.47 & @xmath351 & @xmath352 & @xmath353 & @xmath304 & @xmath120 + scso j052533@xmath76551818 & 0.72 & 0.72 & @xmath354 & @xmath355 & @xmath356 & @xmath357 & @xmath234 + scso j052608@xmath76561114 & 0.14 & 0.15 & @xmath358 & @xmath359 & @xmath360 & @xmath105 & @xmath161 + scso j052803@xmath76525945 & 0.68 & 0.69 & @xmath361 & @xmath362 & @xmath363 & @xmath329 & @xmath274 + scso j052810@xmath76514839 & 0.65 & 0.64 & @xmath364 & @xmath365 & @xmath366 & @xmath144 & @xmath200 + scso j052858@xmath76535744 & 0.70 & 0.70 & @xmath205 & @xmath367 & @xmath368 & @xmath316 & @xmath218 + scso j052951@xmath76551611 & 0.66 & 0.65 & @xmath228 & @xmath369 & @xmath370 & @xmath129 & @xmath218 + scso j053052@xmath76552056 & 0.73 & 0.71 & @xmath149 & @xmath371 & @xmath372 & @xmath373 & @xmath219 + scso j053154@xmath76552031 & 0.23 & 0.21 & @xmath374 & @xmath375 & @xmath376 & @xmath349 & @xmath162 + scso j053327@xmath76542016 & 0.23 & 0.25 & @xmath377 & @xmath378 & @xmath379 & @xmath129 & @xmath133 + scso j053437@xmath76552312 & 0.76 & 0.80 & @xmath380 & @xmath381 & @xmath382 & @xmath383 & @xmath384 + scso j053448@xmath76543534 & 0.65 & 0.65 & @xmath385 & @xmath386 & @xmath387 & @xmath204 & @xmath114 + scso j053500@xmath76532018 & 0.59 & 0.57 & @xmath388 & @xmath389 & @xmath390 & @xmath100 & @xmath274 + scso j053632@xmath76553123 & 0.72 & 0.72 & @xmath391 & @xmath392 & @xmath393 & @xmath235 & @xmath120 + scso j053638@xmath76553854 & 0.74 & 0.71 & @xmath394 & @xmath395 & @xmath396 & @xmath114 & @xmath234 + scso j053645@xmath76553302 & 0.74 & 0.71 & @xmath397 & @xmath398 & @xmath399 & @xmath241 & @xmath297 + scso j053655@xmath76553809 & 0.76 & 0.72 & @xmath400 & @xmath401 & @xmath402 & @xmath109 & @xmath403 + scso j053715@xmath76541530 & 0.49 & 0.51 & @xmath404 & @xmath405 & @xmath406 & @xmath193 & @xmath99 + scso j053732@xmath76542521 & 0.62 & 0.61 & @xmath407 & @xmath408 & @xmath409 & @xmath157 & @xmath166 + scso j053952@xmath76561423 & 0.36 & 0.36 & @xmath410 & @xmath411 & @xmath412 & @xmath238 & @xmath100 + scso j054012@xmath76561700 & 0.38 & 0.38 & @xmath413 & @xmath414 & @xmath325 & @xmath200 & @xmath114 + scso j054022@xmath76541622 & 0.51 & 0.48 & @xmath415 & @xmath231 & @xmath416 & @xmath129 & @xmath185 + scso j054052@xmath76551943 & 0.76 & 0.78 & @xmath417 & @xmath418 & @xmath296 & @xmath153 & @xmath218 + scso j054228@xmath76525002 & 0.65 & 0.66 & @xmath126 & @xmath419 & @xmath366 & @xmath140 & @xmath153 + scso j054332@xmath76505651 & 0.35 & 0.36 & @xmath420 & @xmath421 & @xmath422 & @xmath238 & @xmath178 + scso j054358@xmath76531349 & 0.24 & 0.25 & @xmath423 & @xmath424 & @xmath425 & @xmath99 & @xmath144 + scso j054401@xmath76511254 & 0.28 & 0.28 & @xmath131 & @xmath426 & @xmath427 & @xmath133 & @xmath190 + scso j054407@xmath76530924 & 0.25 & 0.26 & @xmath428 & @xmath429 & @xmath430 & @xmath129 & @xmath104 + scso j054436@xmath76550319 & 0.35 & 0.36 & @xmath431 & @xmath432 & @xmath433 & @xmath211 & @xmath434 + scso j054721@xmath76554906 & 0.59 & 0.59 & @xmath117 & @xmath435 & @xmath436 & @xmath316 & @xmath329 + scso j054742@xmath76554836 & 0.50 & 0.50 & @xmath437 & @xmath340 & @xmath307 & @xmath157 & @xmath114 + scso j054811@xmath76555601 & 0.64 & 0.64 & @xmath438 & @xmath439 & @xmath440 & @xmath178 & @xmath162 + scso j054931@xmath76522655 & 0.38 & 0.39 & @xmath441 & @xmath251 & @xmath442 & @xmath124 & @xmath443 + scso j054949@xmath76513503 & 0.28 & 0.28 & @xmath135 & @xmath413 & @xmath444 & @xmath316 & @xmath129 + scso j055017@xmath76534601 & 0.49 & 0.47 & @xmath299 & @xmath445 & @xmath446 & @xmath157 & @xmath211 + [ tab : clustes05hr ] we queried the nasa / ipca extragalactic database ( ned ) for catalogued clusters from _ rosat _ , @xcite , act @xcite and spt @xcite within a 3@xmath447 radius of the location of each scs cluster ( see table [ tab : clustersid ] ) . in some cases there was a catalogued galaxy from the 2 micron all sky survey ( * ? ? ? * ned i d : 2masx ) , which we report if it is within @xmath448 of the bcg . we also take note of radio sources within @xmath449 of our cluster positions since these could potentially bias the cluster sz signal . we only found radio sources from the sydney university molonglo sky survey ( sumss ) at 843 mhz @xcite . finally we find one unidentified bright x - ray source from the _ rosat _ all sky survey ( rass ) @xcite that is coincident with one of our clusters . it is interesting to note that although we recover two of the sze - selected clusters from the first spt results @xcite , there are two others from that study which we do not recover . one of these ( spt - cl 0509@xmath765342 ) falls below the mass threshold used here with mass estimates of @xmath450 and @xmath451 for 200 and 200 respectively . these are lower than the optical mass quoted in @xcite due to the change in the @xcite mass parametrization but still are comparable to the weak lensing mass range , @xmath452 , obtained by @xcite using the same optical dataset . the other cluster ( spt - cl0547@xmath765345 ) has a photometric redshift of 0.88 @xcite that puts it beyond the redshift threshold ( @xmath453 ) we use here . we searched for x - ray counterparts to the scs optical clusters using the _ rosat _ all sky survey ( rass ) data following the same procedure as in @xcite . the raw x - ray photon event lists and exposure maps were downloaded from the mpe _ rosat _ archive and queried with our own custom software . at the position of each scs cluster , rass count rates in the 0.52 kev band ( corresponding to pi channels 52201 ) were extracted from within a 3@xmath447 radius for the source emission and from within a surrounding annulus ( 5@xmath447 to 25@xmath447 inner and outer radii ) for the background emission . the background - subtracted count rates were converted to x - ray luminosity ( in the 0.52.0 kev band ) assuming a thermal spectrum ( @xmath454 kev ) and the galactic column density of neutral hydrogen appropriate to the source position , using data from the leiden / argentine/ hi bonn survey @xcite . x - ray masses within an overdensity of 500 times the critical density were then determined using the @xmath455 vs. @xmath456 scaling relation from @xcite . these were then converted to an overdensity of 200 with respect to the average density of the universe for comparison to the optically - derived masses using a simple multiplicative scaling factor of 1.77 . this factor is good to 10% over the redshift and mass range of our sample . in table [ tab : clustersrass ] we show redshifts , column densities , rates , luminosities , and masses only for those clusters with x - ray emission significant at 2 @xmath457 or higher , while figure [ fig : masses ] shows all the scs clusters with either actual values for the x - ray mass or ( for most cases ) upper limits . we also show points corresponding to a simple stacking of the x - ray and the optical masses for clusters in three redshift and three optical mass bins as the green and red dots , respectively . each point represents an average of @xmath45820 clusters each with some positive x - ray count rate , excluding the several higher significance individual cases plotted in the figure . it is encouraging that the points scatter by about a factor of two around the line of equal optical and x - ray masses , suggesting that the x - ray emission is in fact associated with hot gas in the potential well of a massive cluster . in at least two cases , we have recovered known clusters ( scso j051637@xmath76543001 and scso j232653@xmath76524149 ) . and two of the rass - correlated clusters ( scso j053154@xmath76552031 and scso j233227@xmath76535827 ) are among those shown in the color images ( i.e. , see the bottom left panel of fig.[fig : clusters05hr ] and the top panel of fig . [ fig : clusters23hr ] ) . -@xmath455 scaling relation . clusters with x - ray emission are shown as the box symbols , while the others are shown as upper limits . the solid line denotes equality ; the dashed lines indicate a factor of two range in mass . the green points show the average optical and x - ray masses for clusters stacked in three redshift bins ( 0.0 - 0.4 , 0.4 - 0.6 , 0.6 - 0.8 ) ordered from bottom to top , while the red points were stacked in three optical mass bins ( @xmath4593.2@xmath460 , 3.2@xmath461 - 4.5@xmath460 , and @xmath4624.5@xmath461 ) ordered from left to right . , width=336 ] there are a number of _ xmm - newton _ pointings that overlap with the scs especially in the 23-hr region . table [ tab : clustersxmm ] lists all the optical clusters from this study ( tables [ tab : clustes23hr ] and [ tab : clustes05hr ] ) that are located within the field of view of an archival _ xmm - newton _ pointing ( specifically the following obsids : 0205330301 , 0505380601 , 0505381801 , 0505382201 , and 0505383601 ) . in several cases , there is an associated x - ray source detected by the pipeline processing system ( pps ) which is run on all _ xmm - newton _ pointings to produce standard results and are provided to the observer . if a pps source exists , we list its i d , the offset in arcseconds between the x - ray source and the optical cluster position and whether or not the pps has flagged the x - ray source are being extended . to determine fluxes and luminosities , we extract spectra from circular regions chosen to maximize the extracted count rate for the extended x - ray sources . for the other sources we use a 1@xmath447 radius circle . background spectra come from a surrounding annular region with sufficient area to obtain good photon statistics . the rate , summed over the single pn and both mos detectors , is quoted in column 7 of table [ tab : clustersxmm ] . we also used standard _ xmm - newton _ software tools to calculate the instrumental response functions ( i.e. , the arf and rmf files ) for each cluster . x - ray luminosity values were determined using the extracted spectra and response files assuming a simple source emission model consisting of an absorbed thermal plasma model . for the absorption component we fixed the column density of neutral hydrogen to the galactic value toward the cluster position ( obtained in the same way as for the rass discussed above ) . three clusters have enough signal that their mean temperatures can be measured ( see below ) ; for the others we assume @xmath454 kev for the luminosity calculation . the final column lists the cluster mass inferred from the x - ray luminosity as discussed above . the _ xmm - newton _ spectra constrain the cluster temperatures for and to values of @xmath463 kev and @xmath464 kev , respectively ( errors are at the 68% confidence interval ) , assuming a metal abundance of 0.3 times the solar value . scso j051637@xmath76543001 ( abell s0520 ) is a bright cluster that was the target of a specific _ xmm - newton _ program . our analysis finds a best fit temperature of @xmath465 kev and metal abundance of @xmath466 relative to solar , which are both consistent with previous work ( e.g. , * ? ? ? the x - ray masses for these three systems just mentioned agree quite well with the optically - derived masses and , in the case of scso j051637@xmath76543001 , with the rosat - derived mass as well . for the three other clusters in the 23hr region in table [ tab : clustersxmm ] the x - ray masses are all lower than the optical masses by factors of 35 . for the remaining system ( scso j051613@xmath76542620 ) there is a catastrophic disagreement between the inferred optical and x - ray masses with the x - ray mass being more than an order of magnitude below the optical one . this is likely due to significant contamination of the optical number counts by cluster members from the nearby , rich system abell s0520 which is also close in redshift ( 0.2952 vs. 0.36 ) .

we use the clusters optically - derived properties to estimate photometric redshifts , optical luminosities , richness , and masses . we complement the optical measurements with archival xmm - newton and rosat x - ray data which provide additional luminosity and mass constraints on a modest fraction of the cluster sample . two of our clusters show clear evidence for central lensing arcs ; one of these has a spectacular large - diameter , nearly - complete einstein ring surrounding the brightest cluster galaxy . the optical sample presented here will be useful for verifying new sze cluster candidates from these surveys , for testing the cluster selection function , and for stacking analyzes of the sze data .

we present a catalog of 105 rich and massive ( ) optically - selected clusters of galaxies extracted from 70 square - degrees of public archival imaging from the blanco 4-m telescope acquired over 45 nights between 2005 and 2007 . we use the clusters optically - derived properties to estimate photometric redshifts , optical luminosities , richness , and masses . we complement the optical measurements with archival xmm - newton and rosat x - ray data which provide additional luminosity and mass constraints on a modest fraction of the cluster sample . two of our clusters show clear evidence for central lensing arcs ; one of these has a spectacular large - diameter , nearly - complete einstein ring surrounding the brightest cluster galaxy . a strong motivation for this study is to identify the massive clusters that are expected to display prominent signals from the sunyaev - zeldovich effect ( sze ) and therefore be detected in the wide - area mm - band surveys being conducted by both the atacama cosmology telescope and the south pole telescope . the optical sample presented here will be useful for verifying new sze cluster candidates from these surveys , for testing the cluster selection function , and for stacking analyzes of the sze data .

0709.0813

r

we describe here the analysis performed over each of the different collected data . the data included in the final sample of night - sky spectra for moonless dark nights described in section [ spec_data ] were combined to create a typical moonless night - sky spectrum at the observatory . for doing so each spectrum was normalized to the mean intensity ( of the sample ) at 5200 ( 0.13 10@xmath11 erg s@xmath12 cm@xmath4 @xmath12 ) . then the final spectrum was produced by averaging the flux of these normalized spectra at each sampled wavelength . figure [ spec ] shows the resulting spectrum , covering a wavelength range between 3700 and 7933 . this is the first time that a typical night - sky spectrum is published for the calar alto observatory . the emission lines clearly identified in the spectrum have been labeled with its corresponding atomic name and wavelength . several of the distinctive features of the night - sky spectrum are due to airglow , although a substantial fraction is due to light - pollution . the airglow is emitted by atoms and molecules in the upper atmosphere which are excited by solar uv radiation during the day and twilight ( ingham 1972 ) . airglow is the most important component of the light of night - sky . it produces the 5577 and 6300 lines from oi ( which are stronger near the twilight ) . it contributes to the ubiquitious 5890 - 6 nad doublet , although this line is heavely contaminated by light - pollution from low and high preassure street - lamps . airglow is also responsible for the oh rotation / vibration bands in the red and ir , known as the meinel bands ( meinel 1950 ) , visible at the redder wavelengths of the spectrum ( see fig . [ spec ] ) . in addition it produces a pseudo - continuum in the blue from overlapping o@xmath16 bands ( 2600 - 3800 ) and in the green from no@xmath16 bands ( 5000 - 6000 ) . a more detailed description of the effects of the airglow on the night - sky emission can be found in benn & ellison ( 1998a ) . an atlas of the airglow from 3100 to 10000 was presented by ingham ( 1962 ) and broadfoot & kendell ( 1968 ) . other contributions to the night - sky spectrum are the zodiacal light , the starlight , and the extragalactic light , which increases the background continuum emission ( see benn & ellison 1998a and references therein for a more detailed explanation on their effects ) . all of them , including the airglow , comprises the natural processes that produce the night - sky spectrum in any astronomical site . in addition to them , the night - sky spectrum can be affected by the light - pollution due mostly to the street - lights of populated areas near the observatories . light pollution arises principally from troposheric scattering of light emitted by sodium and mercury - vapour and incandescent street lamps ( mcnally 1994 ; holmes 1997 ) . typical spectra of the three more used types of street - lamps were presented by osterbrock et al . ( 1976 ) : the sodium low - pressure lamps , the sodium high - pressure lamps and the mercury lamps . the first of the three is the one with less impact in astronomical observations , since its produces most of its light concentrated in the 5890 - 6 nad and 8183 - 95 nad emission lines . therefore only a very reduced number of astronomical observations are strongly affected by them . on the other hand the high - pressure sodium lamps emitt most of its light in a broad nad line centred in @xmath05890 , with a fwhm of @xmath0400 , that shows a central reversal . they also show a strong 8183 - 95 emission line , and fainter emission lines at 4494 - 8 , 4665 - 9 , 4758 - 52 , 4979 - 83 , 5149 - 53 , 5683 - 88 , 6154 - 61 and 7665,7699 . the high - pressure sodium lamps may affect strongly the quality of any astronomical observation . finally the mercury lamps produce narrow lines at 3651/63 , 4047 , 4358 , 5461 , 5770 and 5791 , together with broad features at 6200 and 7200 of fwhm@xmath0100 , from the phosphor used to convert uv to visible light . they also produce a weak continuum emission over the whole visible range . some mercury pollution lines can strongly affect certain astronomical studies : ( i ) the 4358 hg line strongly affect any attempt to measure the emission of the 4364 [ oiii ] line in any object in the galaxy . this line is fundamental for the estimation of the electron temperature of galactic nebulae . ( ii ) the 5460 hg line lies in the centre of the @xmath17-band of the @xmath18 strmgren photometric system , which may affect the programs devoted to the study of stellar populations that use this filter set . other sources of light pollution are the incandescent lamps and the high - pressure metal halide lamps . the spectrum of the former consists of continuum emission only , and it is difficult to identify in a night - spectrum . the latter are nowadays frequently used in the illumination of sport stadiums and arquitectonical monuments ( which can be considerable , since they are normally oriented towards the sky ) . these high - pressure metal halide lamps exhibit some scandium , titanium and litium emission lines , that are charactezed by a blue edge due to molecular bands ( general electric 1975 ; lane & garrison 1978 ; osterbrock et al . 1976 ) . the night - sky spectrum shown in fig.[spec ] shows clear evidence of strong light pollution from all the street - lamps described before . it shows strong mercury lines all over the spectrum , the typical emission lines and features of high - pressure sodium lamps , with a well detected broad emission at @xmath05900 , and a strong nai emission line at 5893 indicative of low - pressure sodium lamps . evenmore , it also presents the typical emission lines corresponding to high - pressure metal halide lamps . all this pollution comes from the populations nearby the observatory , in particular from almeria ( @xmath0250000 habitants ) , at 40 km towards the south , and smaller towns at the north ( like baza , @xmath021000 habitants , and macael , @xmath06000 habitants ) . there are well established estimations of the contribution of city lighting to dark - sky brightness ( e.g. , treanor 1973 , walker 1973 , yocke et al . 1986 , garstang 1991 , and reference therein ) . however , its contribution to the spectrum is more complex , since it depends on the particular kind of lamps used for street illumination . most major observatories nearby populated areas have some kind of night - sky protection laws with the aim of reducing the effects of light pollution by controlling the fraction of light that escapes towards the sky and the kind of lamps used ( normally they promote the use of low - pressure sodium lamps ) . the calar alto observatory does not benefit yet from any local sky - protection law which regulates the street illumination , with the corresponding effects that can be appreciated in the night - sky spectrum . to estimate the contribution of light pollution to the night - sky spectrum we derive the flux intensity corresponding to each of the detected emission lines . each line was fitted with a single gaussian function using fit3d @xcite , using the same procedure described in @xcite . table [ tab_line ] lists the integrated flux for each of the detected emission lines shown in fig.[spec ] , together with the identification of the line and the nominal wavelength . in addition to the emission lines , the flux intensity of the sodium broad - band emission at @xmath05900 was also estimated by fitting the feature with a single broad gaussian function . the result is also listed in table [ tab_line ] . all the fluxes were converted to rayleighs following the conversion formulae by benn & ellison ( 1998a ) . these values can be compared to those ones obtained for another astronomical sites . e.g. , pedani ( 2005 ) presented a study of the night - sky spectrum at the observatory of the roque de los muchachos , la palma . the intensity of the lines produced by the mercury and low - pressure sodium lamps found in our spectrum are only comparable to those ones in la palma when pointing in the directions towards the most polluting towns in this island . on the other hand , the contribution of the lines produced by the high - pressure sodium lamps is much lower , being comparable to that of the less polluted areas of the sky in la palma . this may indicate that most of the street lamps used in almeria are mercury and low - pressure sodium lamps , rather than high - pressure sodium ones , and therefore they only affect specific wavelength ranges ( and science programs ) . finally we clearly see lines produced by high pressure metal halide lamps , only marginally ( and recently ) detected in the sky spectrum at la palma ( pedani 2005 ) . once determined the contribution of each emission line to the night - sky spectrum it is possible to decontaminate it by the effect of the pollution lines ( ie . , all but the oi ones ) , creating a _ clean _ night - sky spectrum . this can be done directly for the mercury , scandium , titanium and litium lines , since all its emission is produced by light pollution . however , in the case of the sodium lines there is a natural contribution due to the airglow . we lack a direct measurement of this natural contribution at calar alto , that can only be achived nowadays with a general blackout . however its natural contribution must not be significantly larger than in other astronomical sites . benn & ellison ( 1998a ) estimated the natural contribution by the broad sodium emission band in @xmath00.03 mag in v and @xmath00.02 mag in r for la palma observatory . similar contributions are expected by the nai 5893,6 emission lines . therefore , the natural contribution by the sodium due to the airglow is expected to be of the order of @xmath00.04 mag in both bands . thus , as a first order we can assume that all the detected emission by sodium in our sky - emission spectrum is due to pollution , and once determined its contribution we can correct it by the expected contribution of natural emission , if needed . table [ tab_cont ] lists the estimated contribution of the light pollution to the sky background in different bands . it includes the @xmath1 , @xmath2 and @xmath3-johnson filters , and a set of medium band filters selected from those ones used by the alhambra survey ( moles et al . 2007 ) , a major imaging survey currently on going at the calar alto observatory . they are included to illustrate the effects of the pollution lines in the background sky when using median / narrow - band filters affected by these lines . the contamination from light pollution is clearly stronger in the @xmath1-band than in other astronomical sites : e.g , @xmath00.02 mag at la palma ( benn & ellison 1998a ) , 0.02 - 0.04 mag at kitt peak ( massey et al . although there are astronomical sites with similar or stronger contaminations : e.g. mount hopkins ( see fig . 2 , from massey & foltz 2000 ) . this contamination can be reduced by a proper light pollution law that limits the use of the mercury street lamps . strong benefits from such laws has been experienced in different sites ( e.g. , benn & ellison 1998a ; massey & foltz 2000 ) . the contamination in the @xmath2 and @xmath3-bands is slightly stronger than in some other places , like la palma : 0.05 - 0.10 mag at the @xmath2-band and 0.07 - 0.12 mag at the @xmath3-band ( pedani et al . 2005 ) , but it is similar or smaller than in other astronomical sites , like kitt peak : 0.19 - 0.33 mag in the @xmath2-band ( massey et al . 1990 ) or mount hopkings : 0.17 mag in the @xmath2-band ( massey & foltz 2000 ) . one of the two recomendations of the iau for a dark place is that the contribution of the pollution to the sodium emission should not exceed in intensity the natural airglow one ( smith 1979 ) . if we consider that the airglow emission is similar in calar alto than in la palma ( or at least of the same order ) , it is clear that the contribution from the light pollution is much stronger . in these regards calar alto does not fulfill the iau recomendations for a dark place . a proper light - pollution law , that increases the use of low - preasure sodium lamps rather than high - presure ones , will not reduce the net effect of the light pollution to the sky - background in these bands , but it will concentrate it in a more reduced wavelength range , affecting less observing programs . most of the lamps that cause the light pollution also produce a certain level of continuum emission . in particular mercury and high pressure metal halide ones . however its contribution is difficult to estimate . although we donecannot quantify its effect , the reduction of the use of mercury , high - pressure sodium lamps and high pressure metal halide lamps in the vicinity of the observatory will certainly also reduce the sky - background continuum . the lack of previous similar studies of the night sky spectrum at the calar alto observatory ( to our knowledge ) does not let us to analyze the evolution of the light pollution along the time . the night sky brightness was determined by using both the imaging and spectrocopic data described before . in the case of the imaging data , the calibration fields contain at least 5 calibration starts per frame . the magnitude zeropoint for each image was determined by measuring the counts intensity of each of these stars within a fixed aperture of 8@xmath8 radius , using imexam task of iraf package , and applying the formula : @xmath19 where @xmath20 is the magnitude zeropoint , @xmath21 is the apparent magnitude of the calibration star in the corresponding band , @xmath22 is the extinction , derived from the correponding value measured by the cavex this night and the airmass of the image , @xmath23 are the measured counts within the indicated aperture , and @xmath24 is the exposure time . since the measured seeing of the images ( fwhm of the field stars ) , ranges between 0.9@xmath8 and 1.3@xmath8 , this aperture ensures that most of the flux is contained within it , and no aperture correction was applied . the average of the values derived for each calibration star in the field is considered the zeropoint of the image , and the standard deviation from this mean value is considered as the photometric error . this standard deviation ranges between 0.02 mag and 0.06 mag for each band and each night . the sky brightness was then determined in each image by measuring the mean counts level in several ( @xmath25 ) square apertures of @xmath050@xmath8@xmath950@xmath8 , in areas free of targets , using imexam task of iraf package . the mean value of these measurements is considered as the count level of the sky brightness , and the standard deviation with respect to this mean value the error in the count level estimation . finally , the sky surface brightness was determined using the formula : @xmath26 where @xmath27 is the surface brightness in magnitudes per square arcsec , @xmath20 is the zeropoint described before , @xmath28 is the sky counts level estimated and @xmath29 is the pixel scale in arcseconds ( ie . , 0.53@xmath8 for cafos ) . it is noticed that the magnitude zeropoint was corrected by the extinction , but the sky brightness was not , following the convention adopted in most of the recent studies of sky brightness ( e.g. , walker 1988b ; krisciunas 1990 ; lockwood et al 1990 ; leinert et al . 1995 ; mattila et al . 1996 ; benn & ellison 1998a , b ) . correcting the sky brightness for extinction would be appropiate only if the extinguishing layer were known to be below all sources of sky brightness , which is not the case ( benn & ellison 1998a , b ) . in addition to the estimations of the sky surface brighness obtained using direct imaging we also derived the sky surface brightness by using the ppak spectroscopic information for the only full moonless night of our sample ( 02/06/2005 ) . the two night - sky spectra obtained this night cover the wavelength range of the @xmath1 , @xmath2 and @xmath3-band filters . we derived the sky flux intensity for each of these filters by convolving each spectrum with the corresponding filter tranmission curves listed in the asiago database on photometric systems ( moro & manuri 2000 ) . then the fluxes were transformed to magnitudes by using the zero - pointings listed in fukugita et al . the mean value of the two derived magnitudes in each filter is adopted as the sky surface brightness of that night , and the absolute difference between both magnitudes as the error . table [ tab_mag ] lists the sky - surface brightness obtained from both the imaging and spectroscopic data at the different bands for each moonless night . in addition , it lists previous results on the sky - brightness at different astronomical sites , including the results presented by leinert et al . ( 1995 ) for calar alto , derived from broad - band photometry obtained along three nights in 1990 . there is a wide range of sky surface brightness values for the different bands , considering that all the measurements were obtained in full moonless nights , without twilight contamination . the data from the first night , derived using ppak data , are very similar to those ones from the third night , derived using cafos data , being the sky in the former slightly brigher in the @xmath1-band . the sky brightness of the second night is brighter in all the bands . looking back to the data , we realize that the airmass of the images of the 1st night ( @xmath01.7 ) , corresponds to an elevetion much lower than that of the 2nd and 3rd night data ( @xmath01.3 and @xmath01.2 , respectively ) . the sky brightness increases with the airmass for two different reasons . one is a natural effect of the airglow , which is brighter at low elevations cause the line of sight intercepts a larger number of atoms in the airglow layer ( garstang 1989 ; benn & ellison 1998a , and references therein ) . a second effect is the increase of light pollution when pointing towards high populated areas at low airmass . walker ( 1971,1991 ) and garstang ( 1989 ) estimate that the increase in the brightness at an air mass of @xmath01.4 , in the direction of a populated area of p inhabitants at a distance d km to be @xmath30 mag . that would correspond to @xmath00.3 mag when pointing directly towards the south , where is the largest populated city nearby ( almeria ) . however since our observed fields are mostly pointing towards the east its contribution is more difficult to estimate . it is not possible to know which is the actual contribution of the light pollution to the continuum brightness at the zenith . therefore we do not know if calar alto fulfill ( or not ) the other iau recomendation for a dark site , that is that this contribution must be lower than @xmath00.1 mag ( smith 1979 ) . it is possible to derive an approximate expression of the sky brightness dependecy on the zenith distance due to natural effects based on the results by garstang ( 1989 ) , as already pointed out by krisciunas & schaefer ( 1991 ) . this expression can be used to correct the measured values and derive a much appropiate estimation of the zenithal sky brightness ( benn & ellison 1998a ; patat 2003 ) . patat ( 2003 ) derive the following formula ( appendix c of that article ) for this correction : @xmath31+\kappa ( x-1)\ ] ] where @xmath32 is the increase in sky brightness at a certain band and airmass ( @xmath33 ) , @xmath34 is the fraction of the total sky brightness generated by airglow , being ( 1-@xmath34 ) the fraction produced outside the atmosphere ( hence including zodiacal light , faint stars and galaxies ) and @xmath35 is the extinction coefficient at the corresponding wavelength . we applied this correction to our data , using the typical extinction curve at calar alto ( following sections ) normalized to the corresponding @xmath36 extinction coefficient of each night . a typical value of @xmath370.6 was used for this correction ( patat 2003 ) . once applied there is a significant reduction of the dispersion between the values obtained for each night . this indicates that the correction works pretty well , despite the fact that it does not take into account the effects of light pollution . the mean values of the sky brightness at the zenit after correction for each band are also listed in table [ tab_mag ] . the night sky - brightness at calar alto shows no significant change in the last 15 years , when comparing with the results by leinert et al . they did not applied any correction for the dependecy on the zenith distance to their data ( table 6 of that article ) . therefore we must compare with the mean values without correction . the only band where it is appreciated an increase of the sky - brightness is the @xmath5-band ( @xmath00.4 mag brigther ) . however , if we take into account that we only have data for this band at low elevation , we can not consider these results conclusive . for the remaining bands the sky seems to be @xmath00.2 mag brighter in the @xmath1-band , @xmath00.2 mag fainter in the @xmath3-band and without changes in the @xmath2- and @xmath6-bands , when comparing with the mean values derived for the three nights of our sample . however none of these differences seems to be significative , lying withing the errors of our measurements . when comparing with the two darkest nights with data obtained at high elevation the differences ( if any ) disappear for the @xmath1 and @xmath2-bands , and the sky seems to be even darker in the @xmath3 and @xmath6-band . a possible caveat to this comparison is that the results listed in leinert et al . ( 1995 ) were obtained not exactly in the solar minimun , which may produce an increase of the sky - brightness . however , although their broad - band data were obtained in the 1990 , they also obtained intermediate - band data in the 1993 and their sinthetized broad - band surface sky - brightness are similar to those obtained in the nights of the 1990 . the sky surface brightnesses at the calar alto observatory at different bands , listed in table [ tab_mag ] , are remarkable similar to those ones at many other different astronomical sites . in the optical wavelength range ( @xmath5,@xmath1,@xmath2 and @xmath3-bands ) , calar alto seems to be a particular dark site , comparible to mauna kea . the fact that both places seem darker than paranal may be an artifact since the data presented by patat et al . ( 2003 ) were taken during the maximun of solar activity . this result is in anycase remarkable , considering the strong light pollution present in the calar alto spectra , which effect is particularly strong in the @xmath1 , @xmath2 and @xmath3-bands ( tab . [ tab_cont ] ) . most of the listed observatories have little light pollution or they benefit of specific protection laws against it . this has been demonstrated as a tremendous useful tool to preserve or increase the quality of the night - sky ( eg . , benn & ellison 1998a , b ; massey & foltz 2000 ; walker & schwarz 2007 ) . if the effects of light pollution could be reduced in the vicinity of calar alto it would become a particularly dark site for optical observations . on the other hand , the sky is clearly brighter in the @xmath6-band than in any other astronomical site listed in this table . despite the fact that the observatory is located in the most arid place in europe , in the vecinity of a desert ( the tabernas desert ) , the water vapor meinel bands are particularly strong . the humidity at calar alto is higher than in other astronomical sites , like paranal or mauna kea , although there are frequent epochs of low humidity ( @xmath1520% ) in the summer . the height of the observatory , @xmath02200 m over the sea level , normally places it under the inversion layer , which has a particular strong impact in the strength of the water vapor emission lines . both combined effects can explain the rise of the sky - brightness in the @xmath6-band . it is important to note here that this effect has a relatively reduced effect over near - infrared observations in the @xmath38 , @xmath39 and @xmath40-band . the median @xmath2-band extinction at the calar alto observatory for the time period covered by the cavex data ( section [ ext_data ] ) was @xmath00.18 mag , with a mean value of @xmath00.21@xmath410.08 mag . this value is slightly smaller than the previously reported by hopp & fernandez ( 2002 ) , which was based on a much smaller sample of data ( comprising 74 nights spanned between 1986 and 2000 ) . they found that there was an increase of the extinction at the summer season , that was most probably associated with an increase of the aerosols ( ie . dust ) in this period of the year . similar seasonal pattern has been appreciated in another major observatories : e.g. , la palma observatory is strongly affected by dust extinction in the summer when dust from the sahara desert ( @xmath0400 km away ) blows over the canary islands ( benn & ellison 1998a ) . although the calar alto observatory is nearer to the sahara desert ( @xmath0250 km away ) than la palma , it is normally out of its main wind streams , being shielded by the altas mountains . on the other hand , it is located in an arid region nearby a much smaller desert , the tabernas desert ( @xmath015 km away ) . figure [ cavex ] shows the evolution of the average @xmath2-band extinction for each night along the period of time sampled by the dataset . as already suspected by hopp & fernandez ( 2002 ) , there is a clear seasonal pattern . the typical extinction in the winter nights is @xmath70.15 mag , being mostly restricted to values lower than @xmath420.2 mag . in summer time there is a wider range of extinctions , although in most of the cases the extinction is lower than @xmath420.4 mag . as indicated before this increase of the extinction is most probably associated with a rise of the aerosols ( dust ) in the atmosphere . we will explore that possibility latter . this seasonal pattern is somehow similar to the one seen in la palma . indeed the fraction of nights with @xmath430.25 mag is similar in both observatories , @xmath020% of the nights . however there is a major difference : the fraction of nights with high extinction , @xmath430.4 mag , at calar alto is very reduced , @xmath03% , while at la palma this fraction is @xmath010% of the nights , with frequent peaks of extinction over @xmath430.6 mag ( benn & ellison 1998a , figure 3 ) . based on the fraction of nights that the cavex was operative and derived realiable measurements of the @xmath2-band extinction ( @xmath36 ) , it is estimated that @xmath070% of the nights were astronomically useful in the period covered by these data ( 4 complete years ) . this fraction is remarkable similar to that one in many other astronomical sites ( eg . , la palma , benn & ellison 1998a ) . the fraction of fully photometric nights , defined as nights where the @xmath2-band extinction varies less than a 20% along all the night , was @xmath030% . the excalibur data described in section [ ext_data ] were used to determine the typical extinction curve at calar alto . this curve was previously studied by hopp & fernandez ( 2002 ) , using an inhomogenous dataset . the extinction coefficients were analyzed separately for the summer and winter seasons due to the observed seasonal pattern . first , it was derived the mean extinction coefficients per night by averaging all the measured extinction coefficients per band obtained along each night ( @xmath0160 values ) . then , the mean extinction coefficients per season were determined by averaging all the measured extinction coefficients per band obtained along each season nights . table [ tab_ext ] lists the average extinctions coefficients obtained for each season for each of the 6 bands sampled by the instrument , including their central wavelengths and the standard deviation with respect to these mean values . as expected the standard deviation in the extinction coefficients is larger for the summer data than for the winter ones , in agreement with the results shown in the previous section . the excalibur results are consistent with the cavex ones for the wavelength covered by both instruments , ie . , @xmath0500 nm . this indicates that the extinction coefficients listed in table [ tab_ext ] are a good representation of the typical values for each season . the total extinction is mostly due to three contributions , the rayleigh scattering at the atmospheric atoms and molecules , the extinction due to aerosol particles ( mostly dust ) , and extinction due to ozone ( walker 1987b ) . the rayleigh scattering can be described by @xmath44 where @xmath45 is the wavelength and @xmath1 is a constant that mostly depends on the pressure , the temperature and the normalized refractive index of the air ( @xmath46 , slightly wavelength dependent ) . in general @xmath1 can be replaced by its average value for the mean conditions in a certain astronomical site ( e.g. , rufener 1986 ) . the aerosol particles produce a similar absorption , that can be described by @xmath47 where @xmath48 is a parameter that depends mostly on the height of the observatory ( @xmath49 ) , and @xmath10 is a power law index that depends on the size of the aerosol grains . although an @xmath501.3 , derived by siedentopf ( 1948 ) , is widely used , we adopted a value of @xmath510.8 for consistency with the previous study of the extinction curve at calar alto ( hopp & fernandez 2002 ) . the ozone extinction is a selective absorption by molecular bands . it can be approximately described by a broad gaussian function centred in @xmath526000 ( matching the shape shown in runefer 1986 and hopp & fernandez 2002 ) : @xmath53\ ] ] each single contribution to the extinction depends on the wavelength and a particular constant that , in the case of the two first , depends on the height and the average atmospheric conditions in the observatory . we adopted the values listed for @xmath545400 in rufener ( 1986 ) , consitent with those derived by tg ( 1977 ) , obtained for la silla observatory . a similar approach was followed by hopp & fernandez ( 2002 ) . the height and average weather conditions in this observatory are very similar to those of calar alto , which justifies the use of these constants . therefore the total extinction curve is a linear combination of these three contributions : @xmath55 the extinction coefficients for the two seasons were fitted to this linear combination , deriving the relative contribution of each one ( @xmath56 ) to the total extinction . table [ tab_ecurve ] lists the results from this fitting analysis , including the relative contribution ( @xmath56 ) derived for each component for each season . for comparison it also includes the same relative contributions derived for calar alto by hopp & fernandez ( 2002 ) , and their compilation of similar results for different astronomical sites . the contribution of the rayleigh scattering seems to be rather constant for the two considered seasons , like the ozone absorption . on the other hand , the aerosol contribution rises considerable in the summer time , being responsible of the increase of the extinction in this season , as it was thought . the estimated contributions of the rayleigh scattering and the aerosol extinction are very similar to the values reported by hopp & fernandez ( 2002 ) for the winter season , which may indicate that both contributions have not changed considerably with time ( their data corresponds to 1986 - 2000 ) . both contributions are also similar to the ones derived for other major astronomical sites . on the other hand the contribution of the ozone absorption seems to be stronger than in previous measurements and other astronomical sites . unfortunally the coverage of excalibur when mounted at calar alto did not allow to perform an accurate sampling of the wavelength range affected more strongly by the ozone absorption , which did not let us to be conclusive on this respect . figure [ ext_curve ] shows the distribution of the extinction coefficients along the wavelength for the two season datasets . it also includes the best fitted linear combination of the three components to the extinction and each of these components scaled to its relative contribution to the total extinction . despite the apparent increase of the ozone absorption its actual contribution to the total extinction at any wavelength is very limited , being neglectible in comparison with the other two contributions . indeed the fitting process derives equally good results when this contribution is removed . as already indicated the rayleigh scattering contribution is very similar for both datasets , being the dominant contribution in the winter season , ie . , in conditions of low extinction . in winter time is responsible of the @xmath085% of the extinction in the @xmath2-band , only @xmath011% is due to aerosol extinction and @xmath04% to ozone absorption . on the other hand , in summer its contributions drops to @xmath063% , with @xmath035% due to aerosol extinction and @xmath02% due to ozone absorption . curiously , the contribution of aerosols to the extinction in the conditions of minimun extinction are much reduced than the one found in other astronomical sites , like la silla ( burki et al . 1995 ) . as we shown in the previous section the extinction curve depends strongly on the relative contribution of each of the three major components to the extinction . each of them has a different dependecy with the wavelength , and two of them depends also on the particular atmospheric conditions at the observatory . therefore , it is difficult to derive a precise extinction curve valid for every night that depends only in a reduced number of parameters . however it is still possible to look for an approximate expression for the extinction curve that provide an useful estimation of the extinction at any wavelength and that depends only in a single parameter : the @xmath2-band extinction , measured each night by the cavex . based on the results of the previous section it is known that the ozone absorption have a marginal effect in the total extintion at any wavelength . therefore we have not considered it for our approximate expression . it is also known that the contribution of the rayleigh scattering is almost contant along the year , and therefore the variations in the extinction are controlled by the amount of aerosol particles ( ie . , dust ) . based on this assumption an approximate expression for the extinction curve can be derived by considering that the extinction in the @xmath2-band is due to a fix contribution of rayleigh scattering ( the average for both seasons ) and a variable contribution due to aerosol extinction . the derived expression is : @xmath57 the typical differences found in the extinction coefficients derived using this formula and the more precise decomposition presented in the previous section are of the order of @xmath010% . the seeing data described in section [ seeing_data ] were used to determine an average seeing for each night comprised in the dataset ( spanned along @xmath02 years ) . the median atmospheric seeing for all the time period was @xmath00.90@xmath8 , with a @xmath070% of the nights under subarcsecond seeing ( @xmath151@xmath8 ) . figure [ seeing1 ] shows the nightly averaged seeing distribution along the time . the epochs without data in april 2005 and march 2006 were due to reparations in the hut of the dimm . there is a mild seasonal pattern in the seeing distribution , with the best seeing concentrated in the summer season . to further investigate this possibility we created the seeing histogram for all the data comprised in the dataset and for two different subsets of data corresponding to the summer season ( may - september ) and the winter season ( the rest of the months ) . figure [ seeing2 ] shows the three histograms . the differences in the seeing distribution for the summer ( median seeing @xmath00.87@xmath8 ) and the winter seasons ( median seeing @xmath00.96@xmath8 ) are clearly appreciated . not only the median seeing is better in the summer season , the chances of having better seeing in a summer night are larger . table [ tab_seeing ] lists the median seeing estimated for both the total sample and the two season subsamples . for comparison purposes it also lists the atmospheric seeing measured at different astronomical sites world - wide , ordered by increasing seeing . although the median seeing at calar alto is larger than that of some major astronomical observatories ( mauna kea , la palma ) , it is actually better than in many other astronomical sites ( eg . , mtgraham , paranal ) .

we derive , for the first time , the typical moonless night - sky optical spectrum for the observatory . regarding the strength of the sodium pollution line in comparison with the airglow emission , the observatory does not fulfill the iau recomendations of a dark site . the zenith - corrected values of the moonless night - sky surface brightness are 22.39 , 22.86 , 22.01 , 21.36 and 19.25 mag arcsec in , , , and , which indicates that calar alto is a particularly dark site for optical observations up to the-band . the typical extinction at the observatory is.15 mag in the winter season , with little dispersion . in summer the extinction has a wider range of values , although it does not reach the extreme peaks observed at other sites .

we present a characterization of the main properties of the night - sky at the calar alto observatory for the time period between 2004 and 2007 . we use optical spectrophotometric data , photometric calibrated images taken in moonless observing periods , together with the observing conditions regularly monitored at the observatory , such as atmospheric extinction and seeing . we derive , for the first time , the typical moonless night - sky optical spectrum for the observatory . the spectrum shows a strong contamination by different pollution lines , in particular from mercury lines , which contribution to the sky - brightness in the different bands is of the order of.09 mag ,.16 mag and.10 mag in , and respectively . regarding the strength of the sodium pollution line in comparison with the airglow emission , the observatory does not fulfill the iau recomendations of a dark site . the zenith - corrected values of the moonless night - sky surface brightness are 22.39 , 22.86 , 22.01 , 21.36 and 19.25 mag arcsec in , , , and , which indicates that calar alto is a particularly dark site for optical observations up to the-band . the fraction of astronomical useful nights at the observatory is% , with a% of photometric nights . the typical extinction at the observatory is.15 mag in the winter season , with little dispersion . in summer the extinction has a wider range of values , although it does not reach the extreme peaks observed at other sites . the analysis of the winter and summer extinction curves indicates that the rayleigh scattering is almost constant along the year . the rise of the extinction in the summer season is due to an enhance of the aerosol extinction , most probably associated with an increase of dust in the atmosphere . the median seeing for the last two years ( 2005 - 6 ) was.90 , being smaller in the summer (.87 ) than in the winter (.96 ) . we conclude in general that after 26 years of operations calar alto is still a good astronomical site . its main properties are similar in many aspects to those of other major observatories where 10m - like telescopes are under operation or construction , being a natural candidate for future large aperture optical telescopes .

0709.0813

c

we have characterized the main properties of the night - sky at the calar alto observatory , comparing them , when possible , with similar properties of other different astronomical sites . the main results of this article can be summarized in the following points : * an average night - sky spectrum for the moonless dark - time at the observatory has been presented for the first time . this spectrum , which covers the optical wavelength range ( 3700 - 7933 ) , is distributed freely to the community . airglow and light - pollution emission lines are detected in this spectrum . the strength of the light - pollution lines has been measured , estimating their contribution to the emission in different bands . in comparison with other sites the mercury lines are particularly strong . the contribution of the light pollution to the sodium emission is far stronger than its natural emission . in this regards calar alto does not fulfill the iau recomendations for a dark astronomical site ( smith 1979 ) , like other major astronomical sites ( eg . , la palma , pedani 2005 ) . * the moonless night - sky brightness at the zenith has been determined for the @xmath5 , @xmath1 , @xmath2 , @xmath3 and @xmath6-bands . there was no appreciable change in the sky - brightness over the last 15 years . in comparison with other astronomical sites , calar alto shows a particularly dark sky in the optical bands , similar to that of mtgraham or mauna kea . the sky brightness could be even darker if it was possible to reduce the light pollution in the optical bands , which would place calar alto as a very dark astronomical site . on the other hand , the sky is brighter in the @xmath6-band , mostly due to the strength of the water - vapor meinel bands . * the extinction , measured along the last 4 years , shows a seasonal dependency with a typical value of @xmath580.15 mag in winter time and a wide range of values in summer , most of them restricted to @xmath590.4 mag . this seasonal pattern , caused by saharan dust , is similar to the one found in la palma , but with a smaller range of values in summer time . the analysis of the typical extinction coefficients at different wavelenghts for each season indicates that the rise of the extinction in summer is due to an increase of aerosols ( dust ) in this period of the year . due to the reduced contribution of the ozone absorption to the extinction , and the stability of the contribution of the rayleigh scattering along the year it was possible to derive an aproximate expression for the extinction curve parametrized only by the @xmath2-band extinction . * the fraction of astronomical useful nights , when the weather was good enough to allow an acurate measurement of the extinction , was @xmath070% of the nights in the last 4 years . this fraction is similar to the one found in la palma ( benn & ellison 1998 ) . the fraction of these nights that were photometric was a @xmath030% . * the median seeing along the last 2 years was 0.90@xmath8 , being slightly better in summer ( 0.87@xmath8 ) than in winter ( 0.96@xmath8 ) . the seeing was better than 1@xmath8 in a @xmath070% of the nights . although this seeing is slightly worse than in some astronomical sites ( eg . mauna kea , la palma ) , it is better than the currently seeing at paranal or mtgraham , two astronomical sites where 10m - like telescope are currently in operation or under construction . we conclude that calar alto remains a good astronomical site , similar in many aspects to places where there are 10m - like telescopes under operation or construction . it will strongly benefit from a sky protection law that would reduce the light pollution , particularly due to mercury and high - pressure sodium street lamps . such a law has been under discussion by the local andalusian goverment during the last few years and we hope it will be soon operative . the fact that calar alto is placed in continental europe is a major advantage in comparison with other european observatories away from the continent , since both the operational and development costs are significantly smaller . for both reasons we consider that this observatory is a good candidate for the location of future large aperture optical telescopes .

we present a characterization of the main properties of the night - sky at the calar alto observatory for the time period between 2004 and 2007 . the analysis of the winter and summer extinction curves indicates that the rayleigh scattering is almost constant along the year . the rise of the extinction in the summer season is due to an enhance of the aerosol extinction , most probably associated with an increase of dust in the atmosphere . the median seeing for the last two years ( 2005 - 6 ) was.90 , being smaller in the summer (.87 ) than in the winter (.96 ) . we conclude in general that after 26 years of operations calar alto is still a good astronomical site . its main properties are similar in many aspects to those of other major observatories where 10m - like telescopes are under operation or construction , being a natural candidate for future large aperture optical telescopes .

we present a characterization of the main properties of the night - sky at the calar alto observatory for the time period between 2004 and 2007 . we use optical spectrophotometric data , photometric calibrated images taken in moonless observing periods , together with the observing conditions regularly monitored at the observatory , such as atmospheric extinction and seeing . we derive , for the first time , the typical moonless night - sky optical spectrum for the observatory . the spectrum shows a strong contamination by different pollution lines , in particular from mercury lines , which contribution to the sky - brightness in the different bands is of the order of.09 mag ,.16 mag and.10 mag in , and respectively . regarding the strength of the sodium pollution line in comparison with the airglow emission , the observatory does not fulfill the iau recomendations of a dark site . the zenith - corrected values of the moonless night - sky surface brightness are 22.39 , 22.86 , 22.01 , 21.36 and 19.25 mag arcsec in , , , and , which indicates that calar alto is a particularly dark site for optical observations up to the-band . the fraction of astronomical useful nights at the observatory is% , with a% of photometric nights . the typical extinction at the observatory is.15 mag in the winter season , with little dispersion . in summer the extinction has a wider range of values , although it does not reach the extreme peaks observed at other sites . the analysis of the winter and summer extinction curves indicates that the rayleigh scattering is almost constant along the year . the rise of the extinction in the summer season is due to an enhance of the aerosol extinction , most probably associated with an increase of dust in the atmosphere . the median seeing for the last two years ( 2005 - 6 ) was.90 , being smaller in the summer (.87 ) than in the winter (.96 ) . we conclude in general that after 26 years of operations calar alto is still a good astronomical site . its main properties are similar in many aspects to those of other major observatories where 10m - like telescopes are under operation or construction , being a natural candidate for future large aperture optical telescopes .

astro-ph0006218

i

the cold dark matter ( cdm ) family of cosmological models provides an excellent description of a wide variety of observational results , from the earlier observable epochs detected via microwave background fluctuations to present - day observations of galaxies and large - scale structure . a concordance model " with roughly one - third matter and two - thirds vacuum energy , either a cosmological constant or quintessence ( @xcite ) , is consistent with almost all current observations on scales @xmath2 mpc ( @xcite ) . recently , improving observations and numerical techniques have enabled a comparison of cdm scenarios to observations on galactic scales of @xmath3 few kpc . the results have not been encouraging . there are a number of distinct observations that may be in conflict with predictions of cdm : * the density profile of galaxies in the inner few kiloparsecs appears to be much shallower than predicted by numerical simulations ( navarro , frenk & white 1996 , hereafter @xcite ) . for density profiles characterized by @xmath4 as @xmath5 , cdm predicts @xmath6 with little scatter ( @xcite 1999 ) , while current h@xmath7 observations suggest @xmath8 with significant scatter ( @xcite ; @xcite , though see @xcite ) . * the central density of dark matter halos is observed to be @xmath9 roughly independent of halo mass ( @xcite ) , while cdm predicts halos with @xmath10 at dwarf galaxy masses , increasing to larger masses ( @xcite 1999 ) . * the number of dwarf galaxies in the local group is an order of magnitude fewer than predicted by cdm simulations , with the discrepancy growing towards smaller masses ( @xcite ; @xcite ) . * hydrodynamic simulations produce galaxy disks that are too small and have too little angular momentum , yielding a tully - fisher relation whose zero - point is off by several magnitudes from observations ( @xcite ) . * the robustness of rapidly rotating bars in high surface brightness spiral galaxies implies lower density cores than predicted by cdm ( @xcite ) . * cluster cl 0024 + 1654 is nearly spherical with a large , soft core , while cdm typically predicts triaxial clusters with cuspy cores ( @xcite , though see miralda - escud 2000 for a counterexample ) . each piece of evidence taken individually is perhaps not convincing enough to claim that cdm has failed on galactic scales . for instance , until recently there was controversy amongst simulators regarding inner profiles ( @xcite ) , but more careful simulations have converged on a consistent prediction ( @xcite ) . observationally , inner galactic profiles are uncertain due to beam smearing effects in observations ( @xcite ; @xcite ) , though samples of high - resolution h@xmath7 observations continue to show shallower profiles than predicted by cdm ( @xcite ) . the number of observed local group dwarf galaxies may be reconciled with cdm via plausible scenarios for suppressed galaxy formation ( e.g. @xcite ) , or else compact high - velocity clouds could represent the missing satellites " that are seen in @xmath0-body simulations ( @xcite ) . hydrodynamic simulations of disk galaxy formation are fraught with the usual concerns about the effects of feedback , artificial viscosity and resolution , though it appears the discrepancies above are due to the underlying dark matter distribution ( @xcite ) . it becomes more interesting to consider alternatives to conventional cdm when one recognizes that all these discrepancies may be symptomatic of a single cause : _ dark matter halos in cdm simulations appear to be more centrally concentrated than observed . _ recognizing this , various authors have recently forwarded a plethora of alternative dark matter theories that suppress the central concentration of dark matter in galaxy halos . among such theories are that the dark matter is warm ( @xcite ; @xcite ; @xcite ) , repulsive ( @xcite ) , fluid ( @xcite ) , fuzzy ( @xcite ) , decaying ( @xcite ) , annihilating ( @xcite ) , and the alternative we investigate here , self - interacting ( sidm ; spergel & steinhardt 2000 ) . interestingly , all theories may be tuned to solve the problems mentioned above ( at least in analytic approximations ) , all theories may be motivated from particle physics considerations , and all theories retain the desirable properties of cdm on extragalactic scales ( though warm dark matter is non - trivially constrained by this requirement ; see @xcite ) . sidm is governed by a single free parameter , the cross section per unit mass @xmath11 of the interacting dark matter particle . @xcite suggested @xmath12 in order to reduce the central concentration of galaxy halos by a sufficient amount to alleviate the above problems . intriguingly , this value is close to the cross section of ordinary hadrons , motivating some particular particle physics candidates for sidm ( steinhardt et al . , in preparation ) . if @xmath11 is significantly smaller than this range , then the optical depth at galactic densities is much less than unity , implying that sidm would have a negligible effect on the dark matter distribution in halos . a qualitative picture of the evolution of an sidm halo is as follows : at early times there is no difference between sidm and cdm since the densities and peculiar velocities are sufficiently low that collisions are rare ; hence sidm makes identical predictions to cdm regarding cosmic microwave background fluctuations and the lyman alpha forest . as the halo forms and grows via gravitational instability , the central density increases . eventually , collisions are so frequent that dark matter particles scatter out of the center as fast as they are accreted , and the density growth is halted , forming a core . such a limit is not present in the cdm model , where the central density grows unchecked . the sidm core then begins to extend while retaining constant central density . heat transfer from the outer parts of the halo raises the temperature in the halo core . if the halo is truly isolated , then eventually the core thermalizes with the exterior resulting in an isothermal halo with a steep density profile . this initiates gravothermal collapse , where the direction of heat transfer is reversed and the exterior begins to cool the halo center . however , in a realistic cosmological setting , galaxies constantly accrete material , keeping the outer halo hot and heat flowing inwards , thus delaying core collapse . the interplay between collisional heat transfer and accretion determines whether a halo will undergo core collapse in a hubble time . it is important to appreciate that the transport behavior does not change monotonically with @xmath11 . for small cross - sections , heat transfer increases with @xmath11 since the frequency of collisions increases ; however , for large cross - sections , the conductivity @xmath13 and no heat transfer occurs . thus , as we discuss in [ sec : comparison ] , the fluid approximation is a poor decription of sidm in the moderate cross - section regime proposed by spergel and steinhardt . furthermore , the behavior in the moderate cross - section regime can not be surmised by interpolating between the fluid and the non - interacting cdm regimes . a proper treatment of the sidm proposal , which includes the interplay of accretion and heat transfer , its non - monotonic dependence @xmath11 , and the effects of merging demands numerical simulations designed to explore the moderate cross - section regime . in this paper we investigate the statistical properties of halos in sidm and cdm in cosmological @xmath0-body simulations . our spatial and mass resolutions are sufficient to probe the inner regions ( @xmath14 ) of small halos ( @xmath15 few@xmath16 ) , while maintaining sufficient volume so as to have a significant sample of such halos . we use a monte carlo technique similar to @xcite ( 2000 ) to model collisions . the primary difference between our simulations and prior investigations ( discussed in more detail in [ sec : comparison ] ) is that we model a cosmologically - significant random volume of the universe with self - interaction cross sections in the range favored by @xcite , enabling us to characterize the statistical properties of halos as we vary @xmath11 . [ sec : sim ] describes our initial conditions and simulation techniques using a monte carlo @xmath0-body approach . in [ sec : structure ] we compare the structural properties of halos in cdm versus sidm models with several cross sections . in particular we examine their central densities , inner profile slopes @xmath7 , the mass dependence of @xmath7 , concentrations , phase space densities , and ellipticities , and where possible compare to observations . in [ sec : res ] we use lower resolution simulations to test the effects of finite particle numbers in our monte carlo method . in [ sec : subhalo ] we examine the subhalo population around the largest halo in our simulations . in [ sec : comparison ] we compare our findings to the simulations of other groups who have conducted numerical studies of self - interacting dark matter , and examine results from a wider range of @xmath11 . we summarize our results and discuss observational constraints in [ sec : disc ] . we find that sidm with @xmath1 produces halos that are in better agreement than collisionless cdm for a wide variety of observations .

we find , in agreement with various authors , that cdm yields cuspy halos that are too centrally concentrated as compared to observations . conversely , sidm simulations using a monte carlo-body technique produce halos with significantly reduced central densities and flatter cores with increasing cross section . we discuss our findings in relation to various relevant observations as well as sidm simulations of other groups . taking proper account of simulation limitations , we find that a dark matter cross section per unit mass of is consistent with all current observational constraints .

we present a comparison of halo properties in cosmological simulations of collisionless cold dark matter ( cdm ) and self - interacting dark matter ( sidm ) for a range of dark matter cross sections . we find , in agreement with various authors , that cdm yields cuspy halos that are too centrally concentrated as compared to observations . conversely , sidm simulations using a monte carlo-body technique produce halos with significantly reduced central densities and flatter cores with increasing cross section . we introduce a concentration parameter based on enclosed mass that we expect will be straightforward to determine observationally , unlike that of navarro , frenk & white , and provide predictions for sidm and cdm . sidm also produces more spherical halos than cdm , providing possibly the strongest observational test of sidm . we discuss our findings in relation to various relevant observations as well as sidm simulations of other groups . taking proper account of simulation limitations , we find that a dark matter cross section per unit mass of is consistent with all current observational constraints . 3m_^-3 200r_200 200v_200

astro-ph0006218

i

we present a set of cosmological self - interacting dark matter simulations having cross - sections in the range favored by @xcite ( 2000 ) . our simulations include the growth of halos from linear fluctuations in a random volume of the universe , with sufficient volume and resolution to obtain a statistical sample of galactic halos resolved to @xmath83 . we compare the resulting halos on a case - by - case basis to those in a collisionless cdm simulation having the same initial conditions . 1 . the inner slopes of sidm with @xmath200 typical halos have @xmath201 at @xmath202 , with some scatter in @xmath7 . our cdm halos have @xmath6 , in agreement with previous studies ( e.g. @xcite 1999 ) . sidm with @xmath203 is intermediate between these cases , with median @xmath204 . sidm is in better agreement with a preliminary analysis of h@xmath7 rotation curves of low surface brightness galaxies ( @xcite ) . 2 . sidm with @xmath200 produces central densities @xmath205 at @xmath83 , and shows no trend with halo mass . sidm with @xmath206 has somewhat higher @xmath80 values , but remains fairly independent of mass . conversely , @xmath80 in cdm halos is much larger than observed , typically @xmath207 at @xmath83 , and shows a strong trend with halo mass . with their steep profiles , cdm halos are in significantly worse agreement at smaller radii . sidm is thus is in better agreement with observations , as has also been argued by @xcite . 3 . simulations with sidm having @xmath206 are intermediate between cdm and sidm with @xmath200 , indicating a smooth increase in the effect of sidm with cross section , a result that extends ( using lower - resolution simulations ) from @xmath208 . in particular , the generation of singular isothermal halos is not seen in any of the massive halos simulated , even for @xmath209 . this suggests that the dynamical process of halo growth in a cosmological setting helps keep outer regions of halos hot and prevents core collapse in a hubble time . we introduce a new mass concentration parameter @xmath106 based on a more directly observable quantity , the enclosed mass within tens of kpc . this halo concentration is significantly lower in sidm models as compared to cdm , providing an observationally accessible discriminant that is not dependent on fitting a particular profile form . a rough estimate of @xmath106 for the milky way , with large corrections for baryonic effects , favors sidm over cdm . the central phase space density is lower in sidm vs. cdm mostly due to the reduction in @xmath80 . the velocity dispersions in the inner regions are quite similar . both sidm and cdm are consistent with observations shown in @xcite , though sidm is mildly favored . sidm produces halos that are more spherical , especially in their inner regions , as compared to cdm . in principle , this is one of the strongest tests of the sidm paradigm , as near the center _ any _ value of @xmath11 that has a non - negligible effect on the dark matter distribution will increase the core sphericity , while cdm cores are almost always significantly triaxial . however , baryons are likely to dominate the shapes of the inner parts of halos , complicating a direct comparison , and in the outer parts the differences between sidm and cdm are less pronounced . the number of subhalos around our largest ( milky way - sized ) halo is somewhat reduced with increasing @xmath11 , but due to discreteness effects in our monte carlo @xmath0-body technique , we can not put robust quantitative estimates on the strength of this effect . based on these simulations , our currently favored value for @xmath11 is somewhere between @xmath59 and @xmath73 . such a cross section simultaneously reproduces both the observed central density and inner slope , as well as being consistent with various observations considered here , which is non - trivial . in contrast , for instance , warm dark matter has difficulty simultaneously reproducing the observed central densities , inner slopes and subhalo population ( @xcite ) . as stated before , inner halo shapes may provide a strong discriminant between cdm and sidm . on galactic scales , they are difficult to observe and confused by baryonic contributions . conversely , clusters provide a cleaner test because they have large cores that are not baryon - dominated , and their mass distributions are directly observable via lensing . @xcite uses the asphericity of cluster ms 2137 - 23 to ( analytically ) argue that @xmath210 , effectively ruling out sidm as a solution to halo concentration problems . on the other hand , cl 0024 + 1654 is very spherical , much more so than cdm models generally predict ( @xcite ) . our simulations can not directly address the shapes of clusters , as we have no cluster - sized objects in our volume . however , sidm shows some range of halo shapes due to asymmetric infall and unrelaxed mass distributions , so it is unclear whether a single object can definitively rule out sidm . support for this statement is provided by @xcite , whose cluster has enough triaxiality to be consistent with ms 2137 - 23 even for @xmath195 ( their model s1wb ) , contradicting miralda - escud s scaling argument . we note that halo shapes are unaffected by annihilating ( @xcite ) or decaying ( @xcite ) dark matter , thus they also provide a discriminant between these variants and sidm . the cluster core sizes in the simulations of @xcite are larger than observed ( @xmath211 , @xcite ; @xcite ) , certainly for @xmath191 ( @xmath192 ) , and probably even for @xmath195 ( @xmath196 ) . so it may be that sidm has difficulty matching observations at both dwarf galaxy and cluster scales . however , adiabatic contraction of baryons during the formation of the cd galaxy will reduce the cluster core radius from @xmath0-body predictions , so the discrepancy may not be that large . in any case , sidm with @xmath212 comes remarkably close to matching dwarf galaxies , @xmath213 galaxies and clusters given the @xmath214 range in mass scales , so we reserve judgement pending a more careful comparison with observations . @xcite mention that sidm core sizes would be in better agreement with observations if @xmath215 , which would result in the effects of self - interactions being diminished in hot cluster environments as compared to galaxies . such a scenario occurs naturally if the dark matter dark matter scattering has low - lying resonance or bound state contributions , as is the case for ordinary nucleons . another theoretical avenue explored in relation to sidm has been modeling the tully - fisher relation . hydrodynamic simulations show that the simulated tully - fisher zero point may be brought into agreement with observations only if halos are less centrally concentrated than predicted by cdm ( @xcite ) . @xcite determine that a cross section of @xmath216 would produce a correct tully - fisher relation for @xmath217 km / s halos . thus it is conceivable that the cross section preferred from halo structure constraints may also alleviate the tully - fisher discrepancies . @xcite suggested that dark matter interactions in the centers of halos naturally produce central black holes with a mass scaling @xmath218 , in agreement with observations ( @xcite ; @xcite ) , and he estimates @xmath219 in order to avoid central black holes that are too large . however , this estimate is based on an @xmath220 profile all the way in to the black hole . if such a dense center never arises because collisions inhibit its formation , then the limits on @xmath11 are weakened considerably . observations of dark matter halos promise to improve significantly in the coming years , particularly constraints on halo core shapes from lensing and on inner profiles and concentrations of halos from h@xmath7 rotation curves . if the inner parts of dark matter halos are found to be generically triaxial , this would be the high place of sacrifice for self - interacting dark matter ; conversely , spherical halos would provide strong support for this scenario . the main modeling work yet to be is done is an improved examination of the subhalo populations in sidm , as well as simulations of a larger range of mass scales . the @xmath0-body monte carlo approach has difficulty achieving a large dynamic range due to the stringent monte carlo resolution limit ( i.e. discreteness effects in the probabalistic description of collisions ) , therefore a different approach may be necessary . the sidm simulations presented here are a first attempt at examining the effect of self - interacting dark matter within the context of a realistic halo formation scenario . the results are quite encouraging that this simple variant of the cold dark matter paradigm will alleviate a wide range of difficulties faced by cdm on galactic scales . we look forward to further investigations and comparisons with observations . we thank julianne dalcanton , lars hernquist , jerry ostriker , penny sackett , scott tremaine , martin white , and naoki yoshida for helpful discussions . we thank greg bryan for sharing his unpublished results . weinberg , d. h. , dav , r. , gardner , j. p. , hernquist , l. , & katz , n. 1999 in `` photometric redshifts and high redshift galaxies '' , eds . r. weymann , l. storrie - lombardi , m. sawicki & r. brunner ( sf : asp conf series )

we present a comparison of halo properties in cosmological simulations of collisionless cold dark matter ( cdm ) and self - interacting dark matter ( sidm ) for a range of dark matter cross sections . we introduce a concentration parameter based on enclosed mass that we expect will be straightforward to determine observationally , unlike that of navarro , frenk & white , and provide predictions for sidm and cdm .

we present a comparison of halo properties in cosmological simulations of collisionless cold dark matter ( cdm ) and self - interacting dark matter ( sidm ) for a range of dark matter cross sections . we find , in agreement with various authors , that cdm yields cuspy halos that are too centrally concentrated as compared to observations . conversely , sidm simulations using a monte carlo-body technique produce halos with significantly reduced central densities and flatter cores with increasing cross section . we introduce a concentration parameter based on enclosed mass that we expect will be straightforward to determine observationally , unlike that of navarro , frenk & white , and provide predictions for sidm and cdm . sidm also produces more spherical halos than cdm , providing possibly the strongest observational test of sidm . we discuss our findings in relation to various relevant observations as well as sidm simulations of other groups . taking proper account of simulation limitations , we find that a dark matter cross section per unit mass of is consistent with all current observational constraints . 3m_^-3 200r_200 200v_200

1507.00374

i

a review of nmr studies performed on the three nanoscale molecular magnets with peculiarly - structured frustrated systems has been presented . \(i ) v15 : a model system of @xmath25=1/2 heisenberg triangular antiferromagnet . the @xmath13v nmr spectrum measurements at very low temperatures below 0.1 k and as a function of the external applied field have allowed the determination of the local microscopic spin configuration in the frustrated ground state . it is found that the pure chiral states described by eq . ( 3 ) are broken down in the v15 nanomagnet . the two quasidegenerate @xmath15 = 1/2 ground states correspond to two different spin configurations which can be described by the two eigenfunctions @xmath59 and @xmath60 . we also found that the lower energy of the two @xmath15 = 1/2 split states is the one pertaining to the eigenfunction @xmath59 . the local spin configuration is consistent with a small structural distortion from an equilateral triangle to a nearly isosceles one . the dynamical magnetic properties of v15 were investigated by proton spin - lattice relaxation rate ( 1/@xmath18 ) measurements . in the @xmath15 = 3/2 state , 1/@xmath18 shows thermally activated behavior as a function of temperature . on the other hand , a temperature independent behavior of 1/@xmath18 at very low temperatures is observed in frustrated @xmath15 = 1/2 ground state below 2.7 tesla . possible origins for the peculiar behavior of 1/@xmath18 have been discussed in terms of magnetic fluctuations due to spin frustrations . \(ii ) fe30 : a spin ball . static and dynamical properties of fe@xmath19 ( @xmath20 ) have been investigated by proton nmr spectra and 1/@xmath18 measurements . from the temperature dependence of 1/@xmath18 , the fluctuation frequency of the fe@xmath19 spins is found to decrease with decreasing temperature , indicating spin freezing at low temperatures . the spin freezing is also evidenced by the observation of a sudden broadening of @xmath21h nmr spectra below 0.6 k. the origin of the spin freezing in fe30 has been suggested to be the distribution of the exchange interactions . \(iii ) cu3 : a twisted spin tube . @xmath21h nmr and dc magnetization data in the cu spin tube were described . an observation of magnetic broadening of @xmath21h nmr spectra at low temperatures below 1 k directly revealed a gapless ground state of the system . the dc magnetization data below 1 k are also consistent with the gapless ground state . we also found the clear change in the slope of the magnetization curves around 5 t attributed to the so - called 1/3 plateau in magnetization . the temperature dependence of @xmath22 under various magnetic fields revealed an usual slow spin dynamics in the cu3 spin tube . the temperature dependence of 1/@xmath18 was not simply explained by the spin - phonon interactions model , nor is it the tomonaga - luttinger liquid model . further theoretical studies are required to understand the peculiar behavior of 1/@xmath18 in the quasi one dimensional cu3 spin tube . it is important to point out that nmr appears to be a unique tool for determination of the local spin configuration , ground state properties and low energy spin dynamics of frustrated systems . the author would like to acknowledge collaborations and fruitful discussions with ferdinando borsa , ken - ichi kumagai , alessandro lasscialfari , yusuke nishisaka , yuri fujiyoshi , yuzuru sumida , yuichi hatanaka , edoardo micotti , marshall luban , ruslan prozorov , christian schrder , jrgen schnack , and hiroyuki nojiri . special thanks go to paul kgerler , xikui fang , and leroy cronin who have been succeeded in synthesizing valuable crystals which makes it possible for us to carry out this research . monte carlo simulation for the fe30 magnetization has been performed by christian schrder . dc magnetization for the cu spin tube at low temperatures below 1 k was measured by hiroshi amitsuka , ken - ichi tenya , and yusei shimizu at hokkaido university , japan . a part of nmr work has been performed at hokkaido university in japan , which is supported by 21@xmath159 century coe programs `` topological science and technology '' at hokkaido university and grant - in - aid from the ministry of education , culture , sports , science and technology of japan . the work at ames laboratory was supported by the u.s . department of energy ( doe ) , office of basic energy sciences , division of materials sciences and engineering . ames laboratory is operated for the u.s . doe by iowa state university under contract no . de - ac02 - 07ch11358 . 99 , edited by h. t. deip , world scientific , singapore , 2005 . , edited by c. lacroix , p. mendels , and f. mila , springer - berlin heidelberg , 2011 . p. w. anderson , mater . * 8 * , 153 ( 1973 ) . e. f. schender and p. c. holdsworth , in _ fluctuations and order : the new synthesis _ , springer - verlag , berlin , 1994 , and references therein ; a. keren , phys . lett . * 72 * , 3254 ( 1994 ) . j. n. reimers and a. j. berlinsky , phys . b * 48 * , 9539 ( 1993 ) . t. inami , t. morimoto , m. nishiyama , s. maegawa , y. oka , and h. okumura , phys . b * 64 * 2001 ) 054421 . d. gatteschi , l. pardi , a. l. barra , a. muller , j. doring , nature * 354 * , 463 - 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the dynamical magnetic properties of v15 were investigated by proton spin - lattice relaxation rate ( 1/ ) measurements . in the = 3/2 state , 1/ shows thermally activated behavior as a function of temperature . on the other hand , a temperature independent behavior of 1/ at very low temperatures is observed in the frustrated = 1/2 ground state below 2.7 tesla . possible origins for the peculiar behavior of 1/ will be discussed in terms of magnetic fluctuations due to spin frustrations . in fe30 spin ball , static and dynamical properties of fe ( ) have been investigated by proton nmr spectra and 1/ measurements . from the temperature dependence of 1/ , the fluctuation frequency of the fe spins is found to decrease with decreasing temperature , indicating spin freezing at low temperatures . the spin freezing is also evidenced by the observation of a sudden broadening ofh nmr spectra below 0.6 k. finallyh nmr data in the cu spin tube will be described . an observation of magnetic broadening ofh nmr spectra at low temperatures below 1 k directly revealed a gapless ground state of the system . the measurements revealed an usual slow spin dynamics in the quasi one dimensional cu3 spin tube .

we present a comprehensive review of nuclear magnetic resonance ( nmr ) studies performed on three nanoscale molecular magnets with different configurations of geometrically frustrated antiferromagnetic ( afm ) triangles , new spin frustration systems with different novel structures : ( 1 ) the isolated single afm triangle k[vaso(ho)]ho ( in short v15 ) , ( 2 ) the spin ball [ mofeo(moo(ho)) ( mooh(ho))(chcoo)(ho)ho ( in short fe30 spin ball ) , and ( 3 ) the twisted triangular spin tube [ ( cucltachh)cl]cl ( in short cu3 spin tube ) . in the v15 nanomagnet , fromv nmr spectra observed at only below 0.1 k , we directly determined the local spin configuration in both the nonfrustrated total spin = 3/2 state at higher magnetic fields ( t ) and the two nearly degenerate = 1/2 ground states at lower magnetic fields ( t ) . the dynamical magnetic properties of v15 were investigated by proton spin - lattice relaxation rate ( 1/ ) measurements . in the = 3/2 state , 1/ shows thermally activated behavior as a function of temperature . on the other hand , a temperature independent behavior of 1/ at very low temperatures is observed in the frustrated = 1/2 ground state below 2.7 tesla . possible origins for the peculiar behavior of 1/ will be discussed in terms of magnetic fluctuations due to spin frustrations . in fe30 spin ball , static and dynamical properties of fe ( ) have been investigated by proton nmr spectra and 1/ measurements . from the temperature dependence of 1/ , the fluctuation frequency of the fe spins is found to decrease with decreasing temperature , indicating spin freezing at low temperatures . the spin freezing is also evidenced by the observation of a sudden broadening ofh nmr spectra below 0.6 k. finallyh nmr data in the cu spin tube will be described . an observation of magnetic broadening ofh nmr spectra at low temperatures below 1 k directly revealed a gapless ground state of the system . the measurements revealed an usual slow spin dynamics in the quasi one dimensional cu3 spin tube .

astro-ph9707169

c

we have shown that detailed absolute number counts , color and redshift distributions can be computed for lensed galaxies through an accurate modelling of the cluster - lens mass distribution . the framework for galaxy evolution has been chosen to fairly reproduce the observed number counts and redshift distribution of field galaxies . the interest in applying these calculations to arclets is to use cluster - lenses as filters to select faint distant galaxies . we have applied this procedure to two different cluster - lenses , a2218 and a370 , for which the mass distribution is fairly well known , and we have studied the impact of the different sources of uncertainty on the predicted number counts and redshift distributions , taking into account the observational conditions . the main result is that arcs at redshifts between 0.5 and 1 are correctly predicted by the modelling as observed . nevertheless , an important population of high redshift arclets ( @xmath0 ) is also revealed by the simulations , which is not observed in spectroscopic surveys of arclets . this disagreement could result partly from a bias in the spectroscopy of arclets , but the main contribution is probably due to uncertainties in the evolutionary models for galaxies at high redshift . in summary , our results show that a detailed model for the cluster - lens , including galaxy - scale mass components , is absolutely needed to interpret the observed distribution of arcs and arclets in terms of general properties of the background population of galaxies . a good agreement between model and observed absolute number counts can be obtained by a fine tuning parametrization of the evolutionary models for galaxies and/or the cosmological parameters . in this respect , the present work joins the problems encountered in the modelling of faint field galaxy samples ( pbz , @xcite ) . nevertheless , the difference in this case is that we are selecting high redshift galaxies and rejecting the faint neighbouring population . as evolutionary effects are extremely sensitive to the behaviour of sources at high redshift , the more distant the lens is , easier it will be to constrain them , provided one is able to detect a cluster lens with a sufficient number of arclets . in a more prospective way , observing distant cluster - lenses could help on disentangle the role of pure geometrical effects , giving constraints on the world model , from pure spectromorphological evolution . in any case , the piece of work presented here is just the beginning of a study , an example on two single clusters at moderate redshift , but the effort has to be pursued on a complete sample of lenses in order to minimize the fluctuations and possible clustering along the line of sight , which is difficult to avoid . for this reason , it is essential to define a homogeneous sample of cluster - lenses in order to derive reliable constraints on the absolute number of background galaxies . this could be explored by using the sample of distant clusters selected from the emss catalog ( @xcite ) , but it would require an analysis of hst images for each cluster combined with an accurate modelling for all those identified as cluster - lenses . another interesting effect which is amplified when selecting high redshift objects is the role of elliptical galaxies . they are responsible for the bulk of the presently undetected population of high redshift arclets at @xmath174 . changing the redshift of formation modifies the expected n(z ) distribution at such redshifts , but it does not reduce significantly the total excess in number . the most straightforward way to solve the problem is to break down the hypothesis that ellipticals form in a unique burst . this idea is also supported by the deep hst images ( see also a discussion in @xcite ) , where the distant galaxies seem rather irregular , deviating from the pure elliptical shape assumed here . in a more general way , there is no observational reason to assert that the progenitors of present day galaxies follow the simple evolutionary law used here ( spectrophotometric evolution + @xmath175 dimming in surface brightness ) , and the first results on the arclet sample strongly support this idea . there is more probably a strong relationship between morphology and spectrophotometry , the two aspects being both interdependent and wavelength dependent . in any case , the identification of the distant progenitors of ellipticals remains an exciting challenge . computing the 2d distributions in number counts or mean redshift seems to be an important tool to build up independent samples of high redshift galaxies . we propose to couple together the computational tool presented here with photometric redshift techniques in order to select the spectroscopic samples . it is worth noting that arcs and arclets correspond to a sample of galaxies much less affected by biases in intrisic luminosity . besides , the brightest galaxies at any ( high ) redshift will be seen through lens magnification before being detected somewhere else . we thank ptit lu van waerbeke , jp . kneib , y. mellier , g. bruzual and b. fort for useful discussions and helpful comments . this work was partly supported by the groupe de recherche cosmologie and by the french centre national de la recherche scientifique . allen s.w . , fabian a.c . , kneib j.p . , 1996 , mnras , 279 , 615 bartelmann m. , steinmetz m. , weiss a. , 1995 , a&a , 297 , 1 baugh c.m . , cole s. , frenk c.s . , lacey c.g . , 1997 , preprint astro - 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we present a detailed model of the absolute number counts , color and redshift distributions of gravitational arclets observed in clusters of galaxies . the framework adopted for galaxy evolution is chosen to fairly reproduce the observed number counts and redshift distribution of field galaxies . then , the spectrophotometric evolutionary code is coupled with an accurate modelling of the cluster - lens mass distribution . the interest in applying these calculations to arclets is to use cluster - lenses as filters to select faint distant galaxies . this procedure is applied on two different cluster - lenses , abell 2218 and abell 370 , for which the mass distribution is well constrained . we have studied the impact of the different sources of uncertainty on the predicted number counts and redshift distributions , taking into account the observational conditions for two sets of data , hst and ground - based images . the main result is that arcs at redshifts between 0.5 and 1 are correctly predicted by the modelling as observed . nevertheless , an important population of high redshift arclets ( ) is also revealed by the simulations , which is not observed in spectroscopic surveys of arclets . we discuss the nature of this disagreement , probably due to uncertainties in the evolutionary models adopted here for galaxies at high redshift .

we present a detailed model of the absolute number counts , color and redshift distributions of gravitational arclets observed in clusters of galaxies . the framework adopted for galaxy evolution is chosen to fairly reproduce the observed number counts and redshift distribution of field galaxies . then , the spectrophotometric evolutionary code is coupled with an accurate modelling of the cluster - lens mass distribution . the interest in applying these calculations to arclets is to use cluster - lenses as filters to select faint distant galaxies . this procedure is applied on two different cluster - lenses , abell 2218 and abell 370 , for which the mass distribution is well constrained . we have studied the impact of the different sources of uncertainty on the predicted number counts and redshift distributions , taking into account the observational conditions for two sets of data , hst and ground - based images . we investigate in details the influence of the mass modelling on the counts and we show that simple cluster - scale potentials can no longer be used for arcs statistics . the main result is that arcs at redshifts between 0.5 and 1 are correctly predicted by the modelling as observed . nevertheless , an important population of high redshift arclets ( ) is also revealed by the simulations , which is not observed in spectroscopic surveys of arclets . we discuss the nature of this disagreement , probably due to uncertainties in the evolutionary models adopted here for galaxies at high redshift . the spatial distribution of arclets in number density and the local mean redshift of the sample are also derived . these maps can be used as a tool to optimize the search for high redshift galaxies magnified by the clusters of galaxies .

1504.01888

c

in this paper , we study coronal events that occurred in active region noaa 10646 on 2004 july 14 . we observed large - scale contraction of higher active region loops for a time span of @xmath130 minutes which was followed by an m6.2 flare and associated failed eruption of a flux rope . table [ tab1 ] presents a summary of the different phases of flare evolution and associated phenomena . p1.6inp1.4inp3 in + phases & time & observations + + pre - flare activity & 4:30 05:17 ut & three small goes flare events , euv loop contraction for @xmath130 min , drastic change in speed of contraction during third peak of pre - flare phase , pre - flare events showing localized brightenings in euv 171 , mw and x - ray sources at the core region underneath the contracting coronal loops . + contraction phase & 04:47 05:17 ut & large overlying coronal loops observed at euv 171 undergo contraction by @xmath020 mm ( 40% of original height ) , loop contraction continues through all three episodes of pre - flare activity . + flare impulsive phase and rapid activation of flux rope & 05:17 05:25 ut & peak hxr emission up to 100 kev with electron spectral index @xmath59 @xmath05 , multiple peaks in hxr and mw ( 17 and 34 ghz ) emission , rapid rise of flux rope by @xmath040 mm . + decay phase and confinement of eruption & 05:25 05:35 ut & braking and successive disruption of eruption front , multiple mw sources from footpoint and coronal regions , compact hxr footpoint source . + [ tab1 ] although the active region noaa 10646 had a relatively simple bipolar magnetic structure in the photosphere , it exhibited very complex structures of overlying loops in the corona ( see figure [ loops ] ) . the euv images at 171 clearly show large - scale contraction of a system of higher coronal loops that started @xmath130 minute prior to the m6.2 flare . it is important to note that the loop contraction was observed throughout the pre - flare phase and ceased with the onset of the flare impulsive phase . we observed three small events during the pre - flare phase ( events i , ii , and iii ; figures [ goes_profile ] and [ pre-2 ] ) which are characterized by localized brightenings in the core region of the overlying loops . the speed of loop contraction increased drastically ( from @xmath15 km s@xmath9 to @xmath125 km s@xmath9 ; figure [ imp_ht ] ) just @xmath15 minute prior to the impulsive phase of the m - class flare , i.e. , during the pre - flare event iii . rhessi measurements during the pre - flare events reveal hxr emission up to 20 kev . from the x - ray spectra , we find that the x - ray emission was predominantly thermal during this phase with plasma temperatures @xmath6020 mk during pre - flare peaks ( see e.g. , figure [ hsi_spectra](a ) ) . these observations indicate that the flaring site was already enveloped by hot plasma before the onset of filament activation and associated m6.2 flare . it is worth to emphasize that the m6.2 flare occurred at the location of pre - flare brightenings which was enveloped by the large contracting coronal loop system . although the phenomenon of loop contraction has been observed in several recent studies , the contraction reported here is remarkable in several aspects . first , the contraction was observed in overlying coronal loops at large - scales both at spatial and temporal domains during which the loop height decreased by @xmath120 mm ( @xmath140% of original height ) . the total duration of loop contraction is @xmath130 minutes which is the longest period of loop contraction reported so far . further , the contraction phase ends with the onset of the impulsive phase of the m6.2 flare , i.e. , the onset of the impulsive phase can be treated as the transition from inward to outward motion of coronal loops . the investigations of loop contraction have emerged as a very important aspect of solar eruptions in recent times . these studies are essentially inspired by the rhessi discovery of altitude decrease in the hxr loop top ( lt ) source during the early impulsive phase in sol2002 - 04 - 15 of class m1.2 @xcite . this phenomenon of downward motion of hxr lt source was established by many subsequent rhessi observations in flares of different intensity classes ( i.e. , from class c to x ) during their earliest stages to the impulsive phase @xcite . motivated by the rhessi observations , the dynamics of complex coronal loop system over the flaring core was extensively investigated in euv images . these studies reveal a significant contraction of coronal loops that envelop the flaring region before and during the flare ( e.g. , * ? ? ? ? * ; * ? ? ? * ) which was attributed to ` magnetic implosion ' @xcite by many authors @xcite . @xcite provided the first evidence for the contraction of euv coronal loops that lasted for @xmath15 minutes from trace 195 images which was temporarily and spatially correlated with the shrinkage in rhessi 1225 kev lt source during the early impulsive phase of sol2002 - 04 - 16 flare of class m2.5 . the study of a long duration m7.6 event ( sol2003 - 10 - 24 ) , characterized by a prolonged rise phase of @xmath120 minutes , provided one of the best examples for the contraction of coronal loops @xcite . in this event , trace 195 loops and hxr lt sources underwent a shrinkage of @xmath135% of initial height during @xmath111 minutes . more importantly , the downward motion was observed simultaneously with speed of @xmath115 km s@xmath9 in euv loops as well as hxr lt sources in different energy bands , viz . , 612 , 1225 , and 2550 kev . due to observational limitations , it is usually not possible to probe the motions of flare associated lt and footpoint ( fp ) sources simultaneously . nevertheless some uniquely observed events have given us the opportunity to examine the relationship between the dynamics of lt and fp sources in the early flare phases @xcite . these studies indicate that shrinkage in lt sources are associated with converging fp motions , making us to predict that simultaneity of the two phenomena could be part of the coronal implosion . @xcite presented observations of contraction of large coronal loops during the early impulsive phase of sol2005 - 07 - 30 of class c8.9 . this contraction was found in three clusters of euv loops observed at 171 that sustained for a longer interval with relatively slower speed ( @xmath110 minutes with an average speed of @xmath15 km s@xmath9 ) . recently , @xcite reported loop contraction in euv 171 images during the impulsive phase of m6.4 flare sol2012 - 03 - 09 that was associated with loop oscillations . it is widely believed that coronal transients derive their energy from the energy stored locally in the coronal magnetic fields . @xcite conjectured that the energy conversion process during transient events would involve a magnetic implosion when the following assumptions hold : ( 1 ) the energy required for the event must come from the corona directly ; ( 2 ) gravitational potential energy plays no significant role ; ( 3 ) low plasma @xmath61 in the corona . with these assumptions , the conservation of energy implies that magnetic energy decreases between the static states before and after the energy release . the reduction of magnetic energy , @xmath62 dv , and consequently the reduction of the magnetic pressure , b@xmath63 , would inevitably result in the contraction of overlying field lines so as to achieve a new force balance . the observations of the contraction of overlying coronal loops during and before the impulsive phase of flares by high temporal cadence images from trace and sdo support the predictions of the conjecture by @xcite . however , the observational evidences for the contraction in coronal loops are uncommon for the majority of flares that exhibit explosive rather than implosive behaviour . we note that in our observations prolonged coronal implosion displays three distinct stages with varying speed of loop contraction ( figure [ imp_ht](a ) ) . here it is important to focus on the brief and localized x - ray and mw emissions that were observed from the core region of the overlying loop system a few minute before the onset of contraction ( figures [ pre-2](b)(d ) ) . later on this region brightened up in euv images also with the localized brightening of multiple low - lying loops . more importantly , the contraction speed rapidly increased @xmath15 minute before the flare onset and this phase is co - temporal with the sequential brightenings of low - lying coronal loops at the core region during which x - ray and mw emissions intensified ( figure [ pre-2 ] ) . the observations of sequential and localized brightenings during pre - flare phase imply episodic release of small amount of energy which can be considered as the signature of magnetic reconnection at relatively small - scales ( in contrast to large - scale reconnection during the flare impulsive phase ) @xcite . rhessi observations of this phase further indicate that this interval is mostly dominated by the thermal emission . the slow and gradual energy release over the prolonged pre - flare phase will cause the magnetic pressure of the coronal loop system to decrease . it is likely that during this slow preheating phase , the increase of the thermal pressure is mainly due to localized heating and gentle evaporation which is not enough to compensate for the decrease of the magnetic pressure ( see * ? ? ? this will result in the implosion of the surrounding flaring region consisting of euv coronal loops . we therefore conjecture that multiple small - scale , localized events of energy release at the core region over the prolonged preheating phase favourably contributed to sustain a large - scale contraction of coronal loops . with the onset of the ` standard flare reconnection ' during the impulsive energy release , the implosion becomes insignificant as the large - scale magnetic reconnection proceeds successively in higher coronal loops stretched by the eruption of the prominence or magnetic flux rope . we examine the temporal and morphological evolution of mw and hxr emission during the impulsive phase ( i.e. , shaded area in figure [ flux_profile ] ) and their associations with the prominence activation . the comparisons of spatial and temporal structures of hxr and mw emission offer us crucial information on different aspects of conditions in the solar atmosphere where the flare occurs as both types of emissions are produced by highly energetic electrons but with different emission mechanisms . the hxr emission most likely arises from bremsstrahlung produced when energetic electrons are decelerated by coulomb forces in collisions with the ambient ions , either in the chromosphere or in the corona . bremsstrahlung hxr emission is proportional to the product of the non - thermal electron density and the ambient ion density . on the other hand , non - thermal mw emission is produced by the gyrosynchrotron mechanism which depends on the magnetic field intensity and its direction . the gyrosynchrotron production mechanism is very efficient and allows us to detect electrons at energies of hundreds of kev , even when their numbers are very low . microwave emission can also be produced by thermal electrons through bremsstrahlung in sufficiently dense thermal plasma ( for a review see * ? ? ? the impulsive phase is characterized by three events of flux enhancements in mw emission denoted by ` a ' , ` b ' , and ` c ' . it is worth to note that the events ` a ' and ` c ' occurred simultaneously in mw and hxr profiles while ` b ' is largely missing in hxr measurements . the spatial evolution of hxr emission with respect to euv images ( see figure [ mainevent ] ) provides some important insights to understand the relationship between flare emission and phases of prominence activity . we find that at the very beginning of the impulsive phase ( @xmath05:17 ut ; figure [ mainevent](a ) ) , two distinct 1225 kev hxr sources are observed and at this time the flare related euv brightening at hxr source locations is insignificant . soon afterwards , non - thermal high energy hxr emission ( at 40@xmath64100 kev energy band ) was observed from the same location with two distinct , well separated emission centroids ( see figure [ mainevent](b ) ) . this phase corresponds to the first peak of the impulsive phase ( i.e. , event ` a ' marked in figure [ flux_profile ] ) . at this time , plasma temperature ( estimated from rhessi spectra ; figure [ hsi_spectra](b ) ) raised to @xmath032 mk which also corresponds to the maximum temperature during the flare ( figure [ plasma_param](a ) ) . the high temperature and low emission measure ( figure [ plasma_param](a ) and ( b ) ) indicate impulsive heating of plasma within a small volume which is also consistent with corresponding euv images that show localized brightening . we also note that this very epoch is associated with significant non - thermal characteristics with an electron spectral index @xmath59 @xmath05 ( figures [ hsi_spectra ] and [ plasma_param ] ) . it is further noteworthy that during event ` a ' , high energy hxr source at 40@xmath64100 kev resembles the mw source at 34 ghz ; both show emission from an extended region with the appearance of two distinct well separated emission centroids ( see also figures [ mainevent](b ) and [ tr_norh](a ) ) . in figure [ mdi_hsi ] , these conjugate emission centroids are indicated on combined wl / magnetogram image as s1 and s2 . the associations of s1 and s2 with opposite polarity magnetic regions suggest that they probably represent emissions from the footpoints of a flaring loop . on the other hand the 17 ghz source resembles the hxr emitting structure at relatively lower energies ( @xmath6540 kev ) . we also note that event ` a ' is followed by the rise and subsequent eruption of the prominence . the peak of the impulsive phase ( i.e. , event ` c ' ) occurred simultaneously in hxr and mw emission . at this time , hxr sources at energies @xmath1525 kev exhibit a single structure ( figure [ mainevent](d ) ) . the non - thermal hxr emission is generally believed to originate from footpoint locations of coronal loops by thick - target bremsstrahlung , thus observations of pairs of hxr sources are expected . the single hxr source implies that the two footpoints are very close indicating energy release in small low - lying loops ( e.g. , * ? ? ? it should be noted that the present event occurred close to the limb , so due to projection effects the footpoint sources may appear much closer than their actual separation . although this hxr peak ( event ` c ' ) is much broader and intense than the first peak ( event ` a ' ) , the non - thermal electron spectral indices during the two peaks are comparable ( @xmath05 ; see figures [ hsi_spectra ] and [ plasma_param ] ) . p3.2inp2.0 in + flare characteristics & parameters + + total duration of hxr peaks & 430 s + no . of hxr peaks & 2 + & 94 s and 336 s + total non - thermal energy ( ( e@xmath66)@xmath67 ) & 3.03 @xmath6810@xmath69erg + thermal energy ( e@xmath70 ) & + (e@xmath71)@xmath72 & 3.89 @xmath6810@xmath73 erg + (e@xmath71)@xmath74 & 0.33 @xmath710@xmath73 erg + @xmath75 & @xmath17.5 + [ tab2 ] in table [ tab2 ] , we summarize various aspects of energy release during the impulsive phase of the flare ( see also figure [ plasma_param2 ] ) . the total duration of hxr impulsive phase ( as revealed by hxr flux profile @xmath6025 kev ) is 430 s which is composed of two peaks of 94 s and 336 s durations ( see figure [ plasma_param2](d ) ) . we find that the power delivered by the non - thermal electrons ( p@xmath76 ) was maximum during the peak of hxr impulsive phase ( event ` c ' ) while the thermal energy e@xmath70 maximized @xmath12 min later which nearly coincides with the peak of thermal sxr emission ( figures [ plasma_param2](a ) and ( c ) ) . the total non - thermal energy ( ( e@xmath76)@xmath67 ) emitted during this whole impulsive phase was @xmath13.0@xmath710@xmath69erg while the maximum thermal energy ( ( e@xmath77)@xmath72 ) was noted at the end of impulsive phase as @xmath13.9@xmath710@xmath73ergs , yielding a ratio of ( e@xmath78)@xmath67/(e@xmath77)@xmath72 @xmath17.5 . @xcite examined the ratio of non - thermal to thermal energies for a set of c- and m - class flares and found that this ratio varies in the range of @xmath11.56 . it was also noted the flares with longer hxr peaks ( @xmath15200 s ) display larger ratios of non - thermal to thermal energy . considering that the present event displays a longer hxr impulsive phase of 430 s with two sequential hxr peaks , the ratio of @xmath17.5 is in good agreement with the results of @xcite . in order to understand the relationship between the flare - accelerated electron beam and the flare - associated emission from thermal plasma , we compare the hxr profile ( rhessi 25100 kev ) with the derivative of sxr flux ( goes 18 ) in figure [ plasma_param2](d ) . we obtained a good temporal consistency between the two curves which suggests that this flare , associated with confined eruption , follows the neupert effect @xcite . the consistency with the neupert effect is further complemented by the fact that the curve showing the evolution of cumulative non - thermal energy ( figure [ plasma_param2](c ) ) exhibits a good temporal correspondence with the evolution of thermal energy ( figure [ plasma_param2](a ) ) indicating that the non - thermal energy is eventually converted into the thermal energy @xcite . the validity of the neupert effect implies that the energetic electrons responsible for the hxr emission by thick - target collisional bremsstrahlung ( imaged as high energy hxr sources ) are the main source of heating and mass supply of the sxr emitting hot coronal plasma @xcite . we also note that with the onset of prominence activation and increase of flare emission after event ` a ' , there is an enhancement in the density and pressure of the thermal plasma ( figure [ plasma_param](c ) ) . with the onset of event ` c ' , we observe a rapid increase in the speed of the erupting prominence ( figure [ exp_ht ] ) . it is important to note that hxr images at high energies ( @xmath1525 kev ) do not show significant changes in the location and structure of the hxr source , i.e. , a single compact source is observed that remained at the same location . we note that the eruption proceeded symmetrically till @xmath105:24 ut with the distinct appearance of an intact eruption front ( shown by arrow in figure [ mainevent](f ) and ( g ) ) . thereafter , the eruption front evolved into an asymmetrical structure ( first seen in euv image at 05:24:30 ut ) with the disruption of the south - west part of the eruption front ( marked by arrow in figure [ mainevent](h ) ) . in the successive images , we clearly observe the downfall of the erupted material which eventually leads to the complete failure of the filament eruption without any cme . @xcite and @xcite have carried out detailed investigations to understand the reason for the confinement of the prominence for this event . they found strong evidence that the interaction between overlying coronal magnetic fields with the erupting prominence was capable to suppress the eruption completely . we have recognized some interesting morphological structures associated with the erupting prominence that overlap the flare s impulsive phase ( @xmath005:21 - 05:23 ut ) and highlighted in euv 171 images in figure [ kink ] . here we emphasize that this phase corresponds to the interval when the erupting prominence attained the maximum speed of @xmath0242 km s@xmath14 ( figure [ exp_ht ] ) . these structures consists of rapidly expanding bright twisted loops at the front and spiky patterns at the following part which very likely represent the helically twisted loops associated with the erupting prominence . these structures can be attributed to the portions of the heated prominence within the flux rope . the hxr source at 2540 kev along with corresponding spectrum ( figure [ hsi_spectra](f ) ) presents evidence for non - thermal emission from accelerated electrons in that region in addition to hot plasma . further , from the euv images , it is apparent that the magnetic field lines underwent curving toward the bright central region after being stretched by the erupting prominence - flux rope system ( shown by arrows in figures [ kink](b ) , ( c ) , and ( e ) ) . flux ropes are considered to be an important structural component in the models of solar eruptions . many recent studies validate the existence of flux ropes in the lower corona in euv observations , mostly in hot euv channels @xcite . here we emphasize that evidence for a flux rope was found just after the peak ` c ' ( the largest peak ) of the flare impulsive phase ( figure [ flux_profile ] ) . it is probable that the flux rope was formed following this most violent episode of energy release . @xcite presented a very clear example of formation and rise of an euv flux rope structure during the impulsive phase of an x - class flare . these observations suggest that a flux rope has a multi - temperature structure that possesses several structural components , such as , sigmoid , hot plasma blob or plasmoid , leading edge , etc . in our observations , the flux rope structure was seen in euv 171 ( which represents plasma at a temperature of @xmath01 mk ) presumably due to the heating of the prominence that lies within the flux rope . @xcite illustrated three kinds of magnetic topology that can lead to the diversity of eruptive phenomena : full , partial and nil @xcite . according to this study , magnetic reconnection can occur completely above the system of a prominence and its supporting flux rope or within it leading to nil or partial eruption of the filament . we believe that , the eruption of bright prominence material along with the helically twisted loops represents the case of magnetic reconnection occurring within the system of prominence and supporting magnetic flux rope . however , we believe that this is just a part of the flux rope which contain the prominence body . it is very likely that the remaining part of the flux rope , devoided of the prominence , might exist at a very high temperature which is not visible in 171 euv images . mw sources at 17 and 34 ghz show an interesting evolution from lower as well as higher coronal regions ( figure [ tr_norh ] ) . in general , we note significant differences in the morphology of mw and hxr sources although one of the mw sources ( which appeared at the early impulsive phase ; see figure [ mainevent](h ) ) exhibits spatial correlation with the hxr source throughout the flare . during event ` a ' ( i.e. , between 05:1805:19 ut ) , we observe a 34 ghz mw source with two distinct centroids having a separation of @xmath118@xmath8 ( see figure [ tr_norh](a ) and ( b ) ) . on the other hand , 17 ghz images ( note that 17 ghz images have lower spatial resolution than 34 ghz images ) show a relatively extended single source . as discussed earlier , the conjugate centroids ( s1 and s2 ; figures [ mdi_hsi ] and [ tr_norh](a ) ) , observed at high energy hxr ( 40@xmath64100 kev ) and 34 ghz mw emissions , exhibit structural similarities and co - spatiality during event ` a ' . at the second peak ( event ` b ' ; see figure [ flux_profile ] ) , images at both mw frequencies present similar source structures with a single centroid ( see figure [ tr_norh](c ) ) . during the third mw burst at 05:21 ut ( event ` c ' ; figure [ flux_profile ] ) , a new mw source originated at a distance of @xmath533@xmath79 toward the south - west of the pre - existing source ( see figure [ tr_norh](d)-(i ) ) . we mark the newly developed source as s3 ( figure [ tr_norh](d ) ) and show its location on wl / magnetogram in figure [ mdi_hsi ] . this new source s3 prevailed till the end of the flare ( @xmath105:30 ut ) with more prominent appearance at 17 ghz over 34 ghz . we also note the source s3 never appeared in hxrs . the temporal and spatial associations of hxr and mw sources ( also see figure [ mdi_hsi ] ) indicate that the main energy release site lies in coronal loops close to the magnetic neutral line , probably formed by connecting footpoints s1 and s2 . it is also likely that the distant mw source s3 resulted from the injection of flare accelerated electrons onto an overlying coronal loop ( which probably connects s1 and s3 regions ) as the rising flux rope interacted with overlying loop systems . we note that norh has much better dynamic range than rhessi and therefore it is capable of detecting secondary sources @xcite . more importantly , we find multiple mw sources from higher coronal regions that intermittently appear at several locations after @xmath005:22 ut ( figures [ tr_norh](e)(i ) ) . it is also important to note that the whole flaring region ( i.e. , footpoint and coronal regions associated with the prominence eruption and its subsequent confinement ) brightened up in 17 ghz mw emission following the impulsive phase of the flare . in particular , distinct mw sources appeared along the narrow , bright region seen in euv images where bright blobs of plasma were observed following the confinement of the eruption ( marked by arrows in figures [ tr_norh](g)-(i ) ) . these multiple coronal mw sources were observed after the beginning of disruption of the eruption front , i.e. , when the ejected prominence and its supporting flux rope were subjected to confinement by the overlying field lines . in view of this , we conclude that the distinct mw sources in the corona presumably represent emission from hot plasma blobs formed within the collapsing magnetic flux rope .

the pre - flare phase of this event is characterized by spectacular large - scale contraction of overlying extreme ultraviolet ( euv ) coronal loops during which the loop system was subjected to an altitude decrease of mm ( 40% of the initial height ) for an extended span of min . , we detect mw emission from the extended coronal region with multiple emission centroids which likely represent emission from hot blobs of plasma formed after the collapse of the expanding flux rope and entailing prominence material .

we present a detailed multi - wavelength study of the m6.2 flare which was associated with a confined eruption of a prominence using trace , rhessi , and norh observations . the pre - flare phase of this event is characterized by spectacular large - scale contraction of overlying extreme ultraviolet ( euv ) coronal loops during which the loop system was subjected to an altitude decrease of mm ( 40% of the initial height ) for an extended span of min . this contraction phase is accompanied by sequential euv brightenings associated with hard x - ray ( hxr ) ( up to 25 kev ) and microwave ( mw ) sources from low - lying loops in the core of the flaring region which together with x - ray spectra indicate strong localized heating in the source region before the filament activation and associated m - class flare . with the onset of the impulsive phase of the m6.2 flare , we detect hxr and mw sources that exhibit intricate temporal and spatial evolution in relation with the fast rise of the prominence . following the flare maximum , the filament eruption slowed down and subsequently confined within the large overlying active region loops ; the event did not lead to a coronal mass ejection ( cme ) . during the confinement process of the erupting prominence , we detect mw emission from the extended coronal region with multiple emission centroids which likely represent emission from hot blobs of plasma formed after the collapse of the expanding flux rope and entailing prominence material . rhessi observations reveal high plasma temperature ( mk ) and substantial non - thermal characteristics with electron spectral index ( ) during the impulsive phase of the flare . the time - evolution of thermal energy exhibits a good correspondence with the variations in cumulative non - thermal energy which suggest that the energy of accelerated particles efficiently converted to hot flare plasma implying an effective validation of the neupert effect .

1504.01888

i

we have presented a comprehensive multi - wavelength study of an m6.2 flare which is associated with a confined eruption of a prominence - flux rope system . the availability of a wide range of multi - wavelength data ( euv , mw , x - ray ) from the beginning of the pre - flare to the end of the impulsive phase of the event provided us with a unique opportunity to probe several flare associated phenomena in detail : large - scale loop contraction , small - scale loop brightenings , eruption of prominence - flux rope system and its subsequent confinement . in the following , we summarize the important results of this study : 1 . we have reported implosion of overlying coronal loops that continued over 30 minute during which overlying loops underwent contraction by 20 mm ( @xmath140 % of their original height ) during the pre - flare phase . such a large - scale contraction has been reported for the first time . we observe episodic and localized events of energy release in low - lying loops at the core of the large overlying loops . by synthesizing the multi - wavelength data , we propose that prolonged loop contraction is a manifestation of localized events of energy release that occurred intermittently during the pre - flare phase of the m6.2 flare . the pre - flare phase was dominated by thermal emission with temperatures beyond 20 mk . this indicates that the plasma was already substantially preheated at the flare core before the onset of impulsive phase . we believe that the strong preheating at the flare core will contribute favorably toward efficient particle acceleration during the subsequent impulsive phase of the event . the impulsive phase of the flare is characterized by multiple non - thermal peaks . after the first impulsive peak , associated with strong hxr emission up to 40 - 100 kev , we observe the activation of the prominence and its supporting flux rope . our observations imply that the onset of impulsive flare emission ( which probably corresponds to large - scale magnetic reconnection ) has triggered the eruption of the flux rope . 4 . rhessi spectroscopy reveals high plasma temperatures ( @xmath130 mk ) and substantial non - thermal characteristics with electron spectral index ( @xmath805 ) during the impulsive phase of the flare . during this phase , characterized by two sequential hxr peaks , the ratio of total non - thermal energy to maximum thermal energy was found to be @xmath17.6 which is consistent with earlier studies . more importantly , the time - evolution of thermal energy nicely correlates with the variations of the cumulative non - thermal energy throughout the impulsive phase of the flare . this can be interpreted in terms of conversion of the energy of accelerated particles to hot flare plasma and is well consistent with the neupert effect . the prominence along with its supporting flux rope could not have a successful escape through the overlying coronal loops and therefore leads to a confined eruption . the observations of the confinement process of the flux rope are remarkable ; we detect multiple coronal mw sources along the trajectory of the eruption . the euv images show hot plasma blobs on the location of these coronal sources . in our opinion , the coronal mw sources represent emission from hot plasma blobs which are formed within the collapsing magnetic flux rope as a result of its interaction with the overlying and surrounding magnetic field lines . this paper highlights the importance of studying the pre - flare activity . this study also underlines that confined eruptions form a very interesting category of solar eruptive phenomena . their investigations provide a unique opportunity to probe the interaction among different magnetic field systems in the corona besides exploring the triggering mechanisms and energy releases processes . we acknowledge rhessi , trace , norh , soho , and goes for their open data policy . rhessi and trace are nasa s small explorer missions . soho is a joint project of international cooperation between the esa and nasa . this work was supported by the bk21 plus program through the national research foundation ( nrf ) funded by the ministry of education of korea . a.m.v . gratefully acknowledges the austrian science fund ( fwf ) : p27292-n20 . we sincerely thank the anonymous referee for providing constructive comments and valuable suggestions that have enhanced the quality and presentation of this paper .

we present a detailed multi - wavelength study of the m6.2 flare which was associated with a confined eruption of a prominence using trace , rhessi , and norh observations . this contraction phase is accompanied by sequential euv brightenings associated with hard x - ray ( hxr ) ( up to 25 kev ) and microwave ( mw ) sources from low - lying loops in the core of the flaring region which together with x - ray spectra indicate strong localized heating in the source region before the filament activation and associated m - class flare . with the onset of the impulsive phase of the m6.2 flare , we detect hxr and mw sources that exhibit intricate temporal and spatial evolution in relation with the fast rise of the prominence . following the flare maximum , the filament eruption slowed down and subsequently confined within the large overlying active region loops ; the event did not lead to a coronal mass ejection ( cme ) . during the confinement process of the erupting prominence rhessi observations reveal high plasma temperature ( mk ) and substantial non - thermal characteristics with electron spectral index ( ) during the impulsive phase of the flare . the time - evolution of thermal energy exhibits a good correspondence with the variations in cumulative non - thermal energy which suggest that the energy of accelerated particles efficiently converted to hot flare plasma implying an effective validation of the neupert effect .

we present a detailed multi - wavelength study of the m6.2 flare which was associated with a confined eruption of a prominence using trace , rhessi , and norh observations . the pre - flare phase of this event is characterized by spectacular large - scale contraction of overlying extreme ultraviolet ( euv ) coronal loops during which the loop system was subjected to an altitude decrease of mm ( 40% of the initial height ) for an extended span of min . this contraction phase is accompanied by sequential euv brightenings associated with hard x - ray ( hxr ) ( up to 25 kev ) and microwave ( mw ) sources from low - lying loops in the core of the flaring region which together with x - ray spectra indicate strong localized heating in the source region before the filament activation and associated m - class flare . with the onset of the impulsive phase of the m6.2 flare , we detect hxr and mw sources that exhibit intricate temporal and spatial evolution in relation with the fast rise of the prominence . following the flare maximum , the filament eruption slowed down and subsequently confined within the large overlying active region loops ; the event did not lead to a coronal mass ejection ( cme ) . during the confinement process of the erupting prominence , we detect mw emission from the extended coronal region with multiple emission centroids which likely represent emission from hot blobs of plasma formed after the collapse of the expanding flux rope and entailing prominence material . rhessi observations reveal high plasma temperature ( mk ) and substantial non - thermal characteristics with electron spectral index ( ) during the impulsive phase of the flare . the time - evolution of thermal energy exhibits a good correspondence with the variations in cumulative non - thermal energy which suggest that the energy of accelerated particles efficiently converted to hot flare plasma implying an effective validation of the neupert effect .

0902.4383

i

early - type galaxies are observed to obey a set of scaling relations that connect their photometric and kinematic properties ( e.g. kormendy relation , kormendy 1977 , faber - jackson relation , faber @xmath13 jackson 1976 ) . among these , the most notable , due to its surprising small scatter ( @xmath14dex ) , is the relation between effective radius @xmath15 , mean surface brightness within the effective radius @xmath16 and central velocity dispersion @xmath5 @xcite . in the three - dimensional space ( @xmath17@xmath15 , @xmath18 , @xmath19 ) , elliptical galaxies populate a tight plane known as the fundamental plane ( fp ) and usually expressed in the form : @xmath20 if elliptical galaxies formed a homologous family , i.e. systems with density , luminosity and kinematical structures equal over the entire early - type sequence and with constant mass - to - light ratios , then the virial theorem predicts a correlation with @xmath21 , @xmath22 . however , observations show that the plane is somewhat `` tilted '' with respect to virial expectations , with best - fit scalings @xmath23 , @xmath24 ( e.g. * ? ? ? the origin of the fp tilt has been much debated and can be interpreted as the breakdown of either of the two assumptions in the virial expectation . a systematic variation in the mass - to - light ratio along the fp could be due to variations in the stellar content ( age , metallicity or imf ) and/or the amount of dark matter among ellipticals . performing detailed dynamical analyses of 25 galaxies with sauron integral - field stellar kinematics to @xmath15 , @xcite find the `` tilt '' almost exclusively due to real m / l variations of the form @xmath25 , while structural and dynamical non - homologies have negligible effects . they also find the variation of the dynamical m / l ratio to correlate with the h@xmath26 line - strength , and ascribe most of the tilt to stellar population ( age ) effects . on the other hand ( e.g. la barbera et al . @xcite , trujillo et al . @xcite ) other authors find that the tilt is not primarily driven by stellar populations , but instead results from other effects , such as non - homology . although the fp relation is quite tight , there is none the less a significant scatter around the plane that can not be attributed to measurement errors . the origin of this intrinsic component has been investigated by many authors . @xcite found that they were unable to reduce the scatter by introducing additional parameters , such as ellipticity or isophotal shape of the galaxies , into the fp relation . variations in stellar populations along the sequence of early - type galaxies are found to be partially responsible for the intrinsic scatter ( e.g. gregg 1992 ; guzman @xmath13 lucey 1993 ; guzman , lucey , bower 1993 ) . prugniel and simien ( 1996 ) studying the correlation between the residuals from the fp and the residuals from the colour and mg@xmath27 line - strength vs. luminosity relations , found that blue and low - mg@xmath27 elliptical galaxies deviate systematically from the value predicted by the fp . following this evidence forbes et al . ( 1998 ) , studying a sample of non - cluster galaxies , found that the residuals of the fp correlate with the ages of the galaxies , i.e. that the scatter of the fp is partly due to variation in galaxy age at a given mass , and in particular to variations in the time of the last starburst . on the contrary , they found that the effect of changes in metallicity is negligible . similar results were obtained by reda et al . ( 2005 ) analysing a sample of isolated galaxies : some objects deviate from the fp relation having lower m / l ratio and this was interpreted as due to their younger stellar populations , probably induced by recent gaseous merger . the same conclusions were reached by wuyts et al . ( 2004 ) for two high - redshift clusters . they found that the residuals from the fp correlate with the residuals from the h@xmath26 - @xmath5 relation . this confirms the role played by stellar populations in determining the appearance of the fp , with relations appearing more dispersed for samples of galaxies that are more dispersed in age . the existence of the fp , its small observed scatter and the tilt have presented a long standing challenge to theoretical models explaining the origin of early - type galaxies . in fact , whatever the scenario of formation and evolution of early - type galaxies is , it has to be able to explain the existence of such a tight correlation and its deviation from virial expectations and therefore to link galaxy structure and dynamics with their star - formation histories . in the recent years , observations and simulations have broadly supported the galaxy merging scenario which fits naturally into the @xmath28cdm hierarchical cosmology ( e.g. steinmetz & navarro , 2002 ) . in the hierarchical scenario ellipticals form through the merging of disk galaxies @xcite . in the merging context , significant new insights have been made through large - scale gas dynamical simulations of galaxy mergers @xcite , indicating that for lower mass galaxies , dissipation becomes increasingly important , driving nuclear starbursts that contribute larger mass fractions , and producing systematic trends with mass in both the structures and stellar populations of the remnant ellipticals @xcite . the fp tilt then arises as a direct consequence of the systematic trends with mass of the importance of dissipation during mergers . in the same scenario of galaxy formation , the origin of the intrinsic scatter in the fp arises as a combination of the scatter in the total baryon - to - dark matter content of the progenitor galaxies , and variations in the dissipational fractions at fixed stellar mass . this latter factor should be observable as correlations between the residuals from the fp and the stellar population parameters , and represents a critical test of the merger scenario @xcite , through the predicted coevolution of the stellar populations and structures of elliptical galaxies . the increasing importance of dissipation in the formation of low - mass galaxies and the different mechanisms that drive the evolution and the star - formation histories for low- and high - mass galaxies ( haines et al . 2007 ) should be reflect in variations with mass of the structural and kinematical properties and hence in variations both in the shape and orientation of the fp for these two families of galaxies . it should also be noted that non - merger origins may be important for lower mass galaxies , whose evolution turns out to be primarly driven by the mass of their host halo , probably through the combined effects of tidal forces and ram - pressure stripping ( haines et al . 2007 ) . + to date no large homogeneous sample of galaxies covering both the giant and dwarf regime exists . although many fp datasets for systems as different as bcgs , normal es , des , dsphs have been analysed and compared to look for changes in @xmath8 @xcite , these studies suffer from the non - homogenity of the samples both in terms of differences in measuring the quantities entering the fp ( for example different fits to derive structural parameters , different apertures to measure the velocity dispersion ) as well as the selection of galaxies themselves . the form of the fp obtained can be influenced by all of these criteria . in this paper we present a fp analysis of 141 early - type galaxies from the shapley supercluster ( @xmath29 ) with both new @xmath4-band surface photometry measurements and published velocity dispersion measurements from @xcite . the sample is randomly selected down to @xmath30 and represents the largest homogeneous sample of low - mass early - type galaxies with reliable velocity dispersions down to @xmath31kms@xmath2 . in section 2 , we present the photometric and spectroscopic data ( including velocity dispersion measurements and spectral indices ) and the catalogue of `` newly derived '' structural parameters ; the morphological classification is described in section 3 . our fp fits for the overall and high-@xmath10 ( @xmath32kms@xmath2 ) samples are presented in section 4 , which discusses how the selection criteria can affect the values of the fp coefficients and mimic a possible curvature of the plane . in section 5 we quantify the contribution of stellar population to the intrinsic scatter . we discuss our results in section 6 and give a summary in section 7 . the origin of the tilt of the fp will be investigated in a forthcoming paper . throughout this paper we use h@xmath33kms@xmath2mpc@xmath2 , @xmath34 and @xmath35 . with this cosmology 1 arcsec@xmath36kpc at @xmath0 and the distance modulus is 36.69 .

we present a fundamental plane ( fp ) analysis of 141 early - type galaxies in the shapley supercluster at based on spectroscopy from the aaomega spectrograph at the aat and photometry from the wfi on the eso / mpi 2.2 m telescope . thus , variations in/fe account for of the total variance around the fp , and of the estimated intrinsic variance . our results appear to be consistent with the merger hypothesis for the formation of ellipticals which predicts that a significant fraction of the scatter is due to variations in the importance of dissipation in forming merger remnants of a given mass . [ firstpage ] galaxies : abundances , galaxies : ellipticals , galaxies : formation , galaxies : fundamental parameters , galaxies : structure

we present a fundamental plane ( fp ) analysis of 141 early - type galaxies in the shapley supercluster at based on spectroscopy from the aaomega spectrograph at the aat and photometry from the wfi on the eso / mpi 2.2 m telescope . the key feature of the survey is its coverage of low - mass galaxies down tokms . we obtain a best - fitting fp relation in the band . the shallow exponent of is a result of the extension of our sample to low velocity dispersions . considering the subsample of km s galaxies , the fp relation is , consistent with previous studies in the high - luminosity regime . we investigate the origin of the intrinsic fp scatter , using estimates of age , metallicity and/fe . we find that the fp residuals anti - correlate ( ) with the mean stellar age in agreement with previous work . however , a stronger ( ) correlation with/fe is also found . these correlations indicate that galaxies with effective radii smaller than those predicted by the fp have stellar populations systematically older and with over - abundances larger than average , for their . including/fe as a fourth parameter in the fp , the total scatter decreases from 0.088dex to 0.075dex and the estimated intrinsic scatter decreases from 0.068 dex to 0.049dex . thus , variations in/fe account for of the total variance around the fp , and of the estimated intrinsic variance . this result indicates that the distribution of galaxies around the fp are tightly related to the enrichment , and hence to the timescale of star - formation . our results appear to be consistent with the merger hypothesis for the formation of ellipticals which predicts that a significant fraction of the scatter is due to variations in the importance of dissipation in forming merger remnants of a given mass . [ firstpage ] galaxies : abundances , galaxies : ellipticals , galaxies : formation , galaxies : fundamental parameters , galaxies : structure

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we have derived the fp of a sample of 141 early - type @xmath37 galaxies in the shapley supercluster at @xmath0 . velocity dispersions and stellar population parameters were derived from the spectroscopic data of smith et al . ( 2007 ) , while r - band photometry is from the shapley optical survey @xcite . the final sample extends down to m@xmath167 + 3 in magnitude and 50 km s@xmath2 in @xmath5 . using the software 2dphot ( la barbera et al . 2008b ) we derived for each galaxy the structural parameters @xmath15 , @xmath63 , @xmath64 , and @xmath168 by fitting a 2d psf - convolved sersic model . the morphological classification was performed by eye and checked with those of @xcite for a subsample of 54 galaxies finding complete agreement . adopting a weighted fit ( see eq . [ fp_weighted ] ) we derived the fp : @xmath15@xmath169@xmath170 for the 141 early - type r@xmath10718 galaxies . the low value of @xmath8 can be related to the extension of our sample towards very low values of velocity dispersion and and also to the method used to determine @xmath10 . considering the subsample of @xmath6 km s@xmath2 galaxies the fp turns out to follow the relation @xmath171@xmath169@xmath172 which is consistent with the coma fp obtained by jfk96 . observing the significant change in the @xmath8 value between the total and the high-@xmath5 samples , we investigate the possible curvature of the fp . applying the same cuts to a simulated sample following a linear fp relation , we ascertain that the observed curvature can be explained by selection effects . departure from a linear trend of the fp relation has been claimed by donofrio et al . ( 2008 ) , and desroches et al . ( 2001 ) found that the faint - end luminosity cut influences the coefficient @xmath8 of the fp , in agreement with nigoche - netro ( 2008 ) . similar results were found by hyde @xmath13 bernardi ( 2008 ) studying the fp residuals along the plane . however , these works pointed out that conclusive evidence of the fp curvature needs either more robust statistics or higher accuracy in the velocity dispersion estimates for low mass systems . the most important result of this work is our demonstration that the fp residuals are correlated with stellar population characteristics ( line- strength indices and derived ssp parameters ) . in particular , fp residuals are anti - correlated both with the @xmath8-element abundance ratio , @xmath8/fe , and with galaxy age resulting in trends whereby galaxies more compact than expected from the fp relation have stellar pupulations systematically older and with higher abundances than average . previous studies have reported correlations of the fp residuals with stellar age ( e.g. forbes et al . 1998 ; reda et al . although our fp residual do show a correlation with age , we recover a much stronger signal for @xmath8/fe than for age , suggesting that this is the more fundamental dependence . indeed , a multiple regression analysis suggests there is no age correlation at fixed @xmath8/fe , but a very strong @xmath8/fe correlation at fixed age . the correlation between @xmath8/fe and fp residuals does not indicate a direct _ causal _ effect , since varying @xmath8/fe at fixed age and z / h has little effect on the stellar mass - to - light . instead , the correlation suggests that the structural properties and the star - formation history are both dependent on some unobserved aspect of the galaxy assembly process . at face value , our results are broadly consistent with recent galaxy merger simulations , which predict a sequence of formation mechanisms governed by the varying importance of dissipation ( hopkins et al . 2008 ) . in this scenario , mergers with a higher initial gas - fraction trigger more centrally - concentrated starbursts , and higher @xmath8 abundances due to the short duration of star - formation in the burst .

the shallow exponent of is a result of the extension of our sample to low velocity dispersions . considering the subsample of km s galaxies , the fp relation is , consistent with previous studies in the high - luminosity regime . however , a stronger ( ) correlation with/fe is also found .

we present a fundamental plane ( fp ) analysis of 141 early - type galaxies in the shapley supercluster at based on spectroscopy from the aaomega spectrograph at the aat and photometry from the wfi on the eso / mpi 2.2 m telescope . the key feature of the survey is its coverage of low - mass galaxies down tokms . we obtain a best - fitting fp relation in the band . the shallow exponent of is a result of the extension of our sample to low velocity dispersions . considering the subsample of km s galaxies , the fp relation is , consistent with previous studies in the high - luminosity regime . we investigate the origin of the intrinsic fp scatter , using estimates of age , metallicity and/fe . we find that the fp residuals anti - correlate ( ) with the mean stellar age in agreement with previous work . however , a stronger ( ) correlation with/fe is also found . these correlations indicate that galaxies with effective radii smaller than those predicted by the fp have stellar populations systematically older and with over - abundances larger than average , for their . including/fe as a fourth parameter in the fp , the total scatter decreases from 0.088dex to 0.075dex and the estimated intrinsic scatter decreases from 0.068 dex to 0.049dex . thus , variations in/fe account for of the total variance around the fp , and of the estimated intrinsic variance . this result indicates that the distribution of galaxies around the fp are tightly related to the enrichment , and hence to the timescale of star - formation . our results appear to be consistent with the merger hypothesis for the formation of ellipticals which predicts that a significant fraction of the scatter is due to variations in the importance of dissipation in forming merger remnants of a given mass . [ firstpage ] galaxies : abundances , galaxies : ellipticals , galaxies : formation , galaxies : fundamental parameters , galaxies : structure

astro-ph9804194

c

we have presented hst observations of the nuclear gas and dust disk in the e4 radio galaxy ngc 7052 . wfpc2 broad- and narrow - band images were used to constrain the stellar surface brightness profile , the optical depth of the dust , and the flux distribution of the ionized gas . we have built axisymmetric models in which the gas and dust reside in the equatorial plane , and in which the gas moves on circular orbits with an additional velocity dispersion due to turbulence ( or otherwise non - gravitational motion ) . these models were used to interpret the ionized gas kinematics inferred from our new fos spectra and from existing ground - based spectra . the models fit the observed central rotation gradient only if there is a central bh with mass @xmath27 . models without a black hole are ruled out at @xmath14% confidence . the models provide an adequate fit to the available observations with a minimum number of free parameters . the assumptions that we make are similar to those that have been made in hst studies of other galaxies with nuclear gas disks . in several areas our models are in fact more sophisticated than some of the previous work . in particular : we use our multi - colour photometry in order to constrain the central cusp steepness of the stellar mass distribution ; we explicitly take into account the contribution of the axisymmetric stellar mass distribution to the circular velocity of the gas , and we do not assume the rotation field to be purely keplerian ; we explicitly model the convolution with the hst / fos psf and the binning over the size of the aperture ; we model the full line profile shapes , and fit the widths of the emission lines as well as their mean ; and we fit gaussians to the models as we do the data , to properly take into account the fact that gaussian fits to lines that may be skewed or have broad wings yield biased estimate of the true moments . still , our models remain only an approximation to the true structure of ngc 7052 . in particular : the thickness of the gas disk may not be negligible ; the mean motion of the gas may not be circular ; and the observed rotation curve may not perfectly reflect the intrinsic rotation curve , because of partial absorption of the emission line flux by dust . the limited sky coverage of the fos spectra prevents a direct check on whether the gas motions in ngc 7052 are indeed circular . however , several consistency checks are available that may have signaled errors in our assumptions ; none did . the stellar mass - to - light ratio and systemic velocity inferred with our models from the nuclear gas kinematics agree with those inferred from stellar kinematical measurements outside the region influenced by dust absorption . the best - fitting model for the gas kinematics reproduces the shapes of the emission lines on the nucleus , despite the fact that these shapes were not included as constraints in the fit . these agreements do not rule out a conspiracy of some sort , but they do make it less likely that the observed gas kinematics are the result of vastly non - circular motion , or have been strongly modified by dust absorption . models of adiabatic bh growth for the stellar surface brightness cusp provide another successful check : the bh mass implied by these models is fully consistent with that inferred from the gas kinematics . figure [ f : allbhs ] shows a scatter plot of @xmath20 versus @xmath0-band spheroid luminosity @xmath230 for all galaxies with reasonably secure bh mass determinations ( adapted from van der marel 1998 , with the addition of ngc 7052 ; all for @xmath28 ) . there is a trend of increasing @xmath20 with increasing @xmath230 , although it remains difficult to rule out that systematic biases play some role in this relation ( van der marel 1998 ) . besides ngc 7052 , the other galaxies for which the bh detections are based on kinematical studies of nuclear gas disks with the hst are m87 ( harms et al . 1994 ; macchetto et al . 1997 ) , m84 ( bower et al . 1998 ) , ngc 6251 and ngc 4261 ( ferrarese , ford & jaffe , 1998 , 1996 ) . the @xmath20 in these galaxies are @xmath231 , @xmath232 , @xmath233 and @xmath234 , respectively . ngc 7052 falls at the low end of this range . the five galaxies with bh evidence from nuclear gas disks form a very homogeneous set . each of these galaxies is a radio source and is morphologically classified as an elliptical . the luminosities are identical to within @xmath17% ( @xmath235 in the range @xmath236@xmath237 for all five galaxies ) . by contrast , the black hole masses span a range of a factor @xmath16 . the results for these galaxies therefore show that any relation between @xmath20 and @xmath230 must have a scatter of at least a factor @xmath16 , even if the comparison is restricted to galaxies of similar type . the authors are grateful to tim de zeeuw and tony keyes for helpful discussions , and to bill workman and jean surdej for successful scheduling and implementation of the observations . gerry quinlan kindly allowed us to use his adiabatic bh growth software . fvdb thanks the institute for advanced study in princeton for its hospitality during a visit in 1996 . support for this work was provided by nasa through grant number # go-05848.01 - 94a , through hubble fellowships # hf-01065.01 - 94a and # hf-01102.11 - 97a , and through an stsci fellowship , all awarded by the space telescope science institute which is operated by the association of universities for research in astronomy , incorporated , under nasa contract nas5 - 26555 .

we present a hubble space telescope ( hst ) study of the nuclear region of the e4 radio galaxy ngc 7052 , which has a nuclear disk of dust and gas . the images yield the stellar surface brightness profile , the optical depth of the dust , and the flux distribution of the ionized gas . the emission lines yield the rotation curve of the ionized gas and the radial profile of its velocity dispersion . in which the gas and dust reside in a disk in the equatorial plane of the stellar body , and are viewed at an inclination of . it is assumed that the gas moves on circular orbits , with an intrinsic velocity dispersion due to turbulence ( or otherwise non - gravitational motion ) . the latter is required to fit the observed increase in the line widths towards the nucleus , and must reach a value in excess of in the central . the black hole masses inferred for m87 , m84 , ngc 6251 , ngc 4261 and ngc 7052 span a range of a factor , with ngc 7052 falling on the low end . by contrast , the luminosities of these galaxies are identical to within% . any relation between black hole mass and luminosity , as suggested by independent arguments , must therefore have a scatter of at least a factor .

we present a hubble space telescope ( hst ) study of the nuclear region of the e4 radio galaxy ngc 7052 , which has a nuclear disk of dust and gas . the second wide field and planetary camera ( wfpc2 ) was used to obtain , and broad - band images and an h+[nii ] narrow - band image . the images yield the stellar surface brightness profile , the optical depth of the dust , and the flux distribution of the ionized gas . the faint object spectrograph ( fos ) was used to obtain h+[nii ] spectra at six different positions along the major axis , using a diameter circular aperture . the emission lines yield the rotation curve of the ionized gas and the radial profile of its velocity dispersion . the observed rotation velocity at from the nucleus is . the gaussian dispersion of the emission lines increases from at , to on the nucleus . to interpret the gas kinematics we construct axisymmetric models in which the gas and dust reside in a disk in the equatorial plane of the stellar body , and are viewed at an inclination of . it is assumed that the gas moves on circular orbits , with an intrinsic velocity dispersion due to turbulence ( or otherwise non - gravitational motion ) . the latter is required to fit the observed increase in the line widths towards the nucleus , and must reach a value in excess of in the central . the circular velocity is calculated from the combined gravitational potential of the stars and a possible nuclear black hole . models without a black hole predict a rotation curve that is shallower than observed ( at ) , and are ruled out at% confidence . models with a black hole of mass provide an acceptable fit . the best - fitting model with a black hole adequately reproduces the observed emission line shapes on the nucleus , which have a narrower peak and broader wings than a gaussian . ngc 7052 can be added to the list of active galaxies for which hst spectra of a nuclear gas disk provide evidence for the presence of a central black hole . the black hole masses inferred for m87 , m84 , ngc 6251 , ngc 4261 and ngc 7052 span a range of a factor , with ngc 7052 falling on the low end . by contrast , the luminosities of these galaxies are identical to within% . any relation between black hole mass and luminosity , as suggested by independent arguments , must therefore have a scatter of at least a factor . [ s : intro ]

1210.2617

i

a fundamental problem in finance , economics and management science is to determine the optimal time to invest in a project in a random environment and to address these types of problems the theory of discretionary stopping has been widely employed following karlin @xcite . in order to solve some problems of this type we fix a filtered probability space , @xmath1 , satisfying the usual conditions and carrying a standard one - dimensional @xmath2-brownian motion , @xmath3 . we assume that the stochastic system we study is driven by the it diffusion given by the stochastic differential equation @xmath4 and the functions @xmath5 satisfy assumptions [ a1][a2 ] . our objective is to select the @xmath2-stopping - time , @xmath6 , that maximises @xmath7 , \end{aligned}\ ] ] where @xmath8 is subject to the conditions in assumption [ a4 ] and @xmath9 is a state - dependent discounting factor defined by @xmath10 for some function @xmath0 satisfying the conditions of assumption [ a3 ] . the majority of financial and economic models in the literature assume that the underlying asset s value dynamics are modelled by a geometric brownian motion , the associated payoff function is affine and the discounting rate is constant . the approach we employ relaxes all these assumptions . considering more general payoff functions allows for utility based decision making , which , apart from the work of henderson and hobson @xcite , and despite its fundamental importance , has not been widely discussed . however , the main benefit of accommodating general payoffs in the modelling framework is the ability to incorporate compound payoffs into the payoff function , such as running payoffs or reversible decisions , as in johnson and zervos @xcite or guo and tomecek @xcite . for example , consider the case where a project is initiated at a cost @xmath11 and provides a running payoff given by @xmath12 . in this case we have that @xmath13 , \label{init}\ ] ] for a stopping - time @xmath14 . here , for example , @xmath15 could represent the demand for electricity and @xmath16 is the ` stack ' , a discontinuous function , representing the price of supplying the demand , or @xmath15 could be the value of an asset that is taxed at banded rates , modelled by @xmath17 and @xmath16 . in both these , practically important , cases @xmath8 will not be @xmath18 and the classical approach to solving stopping problems using variational inequalities can not be used . the framework we present accommodates systems driven by general it diffusions . this is essential in economics given that not all asset price processes should be modelled by a geometric brownian motion , which , on average , grows exponentially . beyond decisions driven by prices , extending the theory to a wider class of diffusions is important , for example in regime switching models such as in dai , zhang and zhu @xcite where the driving stochastic process represents a probability that the market is a bull or bear , and @xmath190,1[$ ] . employing state dependent discounting enables a more realistic modelling framework for investment decisions in the presence of default risk and the events following 2007 have highlighted the importance of including this feature in decision making . one approach to addressing discretionary stopping problems is through dynamic programming and involves a set of variational inequalities . this is discussed by , amongst many others , el - karoui @xcite , krylov @xcite , bensoussan and lions @xcite , davis and karatzas @xcite , and guo and shepp @xcite . the technique has become widespread in finance and economics since the introduction of so - called ` real options ' theory by mcdonald and siegel @xcite , and has been described in merton @xcite , dixit and pindyck @xcite and trigorgis @xcite . however , taking this approach often involves making strong assumptions about the problem data in order to obtain explicit results . a different approach has been to employ @xmath20-excessive functions , functions that satisfy @xmath21,\quad\textrm{for } x\in{\mathcal{i}}.\ ] ] this approach has been adopted by dynkin @xcite , shiryaev @xcite , salminen @xcite , alvarez @xcite and lempa @xcite , while dayanik and karatzas @xcite and dayanik @xcite use a certain characterisation of @xmath20-excessive functions , as the difference of two convex functions , to solve the stopping problem . these techniques , while powerful , are technical and are less accessible to a general audience in finance and economics unfamiliar with the details of probability theory . another approach uses martingale theory to locate the optimal boundaries between the stopping and continuation regions and is taken by , for example , beibel and lerche ( @xcite , @xcite ) , lerche and urusov @xcite , and christensen and irle @xcite and is described informally in shreve ( * ? ? ? * sec 8.3.2 ) . this approach , while relatively straightforward , is based on assuming the diffusion starts in the continuation region and considers the first time it hits the stopping region . however , as well as relying on the explicit problem data , this approach depends on the continuation region existing and an intuitive understanding of where it is located . the approach we adopt is based on the familiar dynamic programming approach while providing the power of the probabilistic techniques . the connection between the different approaches is provided by johnson and zervos @xcite , where the it - tanaka - meyer formula is used to analyse the solution to the variational inequality as the difference of two convex functions , rather than as a function in @xmath18 . in using this result , the strong assumptions associated with the dynamic programming framework can be relaxed and explicit solutions that rely , only , on the problem data can be easily obtained . this approach has been taken in rschendorf and urusov @xcite , lamberton @xcite , johnson and zervos @xcite and has been developed fully in lamberton and zervos @xcite . the contribution of this paper is to demonstrate how the general theory , developed in lamberton and zervos @xcite , can be applied to obtain explicit solutions to a variety of discretionary stopping problems . this paper is organised as follows . section [ problem ] is concerned with a formulation of the optimal stopping problem and a set of assumptions for our problem to be well - posed while in section [ implications ] we discuss the practical implications of these assumptions . in section [ soln ] we present the methodology for identifying the boundaries for six ` elementary ' problems and then , in section [ ex ] , we demonstrate how these ` elementary ' problems can be employed in solving more complex stopping problems . an appendix provides a proof of a key result in solving the problem when a continuation region lies between two stopping regions .

this is done within a framework based on dynamic programming techniques employing variational inequalities and links to the probabilistic approaches employing-excessive functions and martingale theory . the aim of this paper is to facilitate the the solution of a wide variety of problems , particularly in finance or economics . + + _ keywords _ : stochastic control , optimal stopping , dynamic programming , finance + + _ 2000 mathematics subject classifications _ : 60g40 , ( 93e20 , 49k45 , 91b70 , 90c39 ) = 1 [ section ] [ section ] [ section ] [ section ] [ section ] [ section ] [ section ] [ section ] [ section ]

we present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general , one - dimensional , it diffusions , payoff functions that need not be smooth and state - dependent discounting . this is done within a framework based on dynamic programming techniques employing variational inequalities and links to the probabilistic approaches employing-excessive functions and martingale theory . the aim of this paper is to facilitate the the solution of a wide variety of problems , particularly in finance or economics . + + _ keywords _ : stochastic control , optimal stopping , dynamic programming , finance + + _ 2000 mathematics subject classifications _ : 60g40 , ( 93e20 , 49k45 , 91b70 , 90c39 ) = 1 [ section ] [ section ] [ section ] [ section ] [ section ] [ section ] [ section ] [ section ] [ section ]

cond-mat0509262

c

in this paper we have presented a microscopic theory of skyrmions in qh ferromagnets . we have shown that the skyrmion is a w@xmath1(2)-rotated state of a hole - excited state . because of an intrinsic entanglement between the electron density and the spin density implied by the w@xmath1(2 ) algebra , a w@xmath1(2 ) rotation modulates not only the spin configuration but also the electron density around a hole , thus decreasing the coulomb energy . similarly , the antiskyrmion is a w@xmath1(2)-rotated state of an electron - excited state . there is a simple type of skyrmion state characterized by the fact that its wave function is factorizable in the electron coordinates . we call it the factorizable skyrmion . it corresponds to the nonlinear - sigma - model skyrmion previously derived in the semiclassical approximation . we have analyzed the skyrmion state in the realistic coulomb system with the zeeman interaction . by minimizing the excitation energy we have estimated the activation energy of a skyrmion - antiskyrmion pair . the result is found to explain the experimental data@xcite remarkably well .

we present a microscopic theory of skyrmions in the monolayer quantum hall ferromagnet . it is a peculiar feature of the system that the number density and the spin density are entangled intrinsically as dictated by the w algebra . they are spin textures accompanied with density modulation that decreases the coulomb energy .

we present a microscopic theory of skyrmions in the monolayer quantum hall ferromagnet . it is a peculiar feature of the system that the number density and the spin density are entangled intrinsically as dictated by the w algebra . the skyrmion and antiskyrmion states are constructed as w-rotated states of the hole - excited and electron - excited states , respectively . they are spin textures accompanied with density modulation that decreases the coulomb energy . we calculate their excitation energy as a function of the zeeman gap and compared the result with experimental data .

1107.0860

i

optically thin , two - temperature accretion flows have been considered as an explanation of a variety of black hole systems and a substantial work has been done for investigation of their dynamical and spectral properties ( see , e.g. , narayan & mcclintock 2008 for a review ) . however , the developed models still involve several approximations which significantly reduce their accuracy . these involve the use of a pseudo - newtonian potential of paczyski & wiita ( 1980 ) , which fails in the innermost region ( particularly if rotation of the black hole is considered ) , where most of the gravitational energy is dissipated , as well as local approximations of comptonization , which appear to be particularly incorrect in optically thin flows ( see xie et al . 2010 ; hereafter x10 ) . previous attempts to improve these two weaknesses are discussed in section [ previous ] . in this paper , we extend our previous treatment of global comptonization from x10 by using the hydrodynamical model from manmoto ( 2000 ; hereafter m00 ) , and develop a self - consistent model involving a fully general - relativistic ( gr ) description of both the hydrodynamical and the radiative processes . we consider moderate values of accretion rate , at which coulomb coupling between ions and electrons is relatively weak compared to the viscous heating of ions and , therefore , the ion temperature ( and hence the total pressure ) is not affected significantly by the details of the description of radiative processes . this allows for a slightly simplified treatment of the flow structure in our computations leading to a self - consistent solution . already the foundational papers proposed that tenuous , two - temperature flows may be responsible for the hard spectral states of black - hole binaries ( ichimaru 1977 ; see also narayan & yi 1995 ) and for the low nuclear luminosities in radio galaxies with large radio lobes ( rees et al . 1982 ) . we consider two ranges of the key parameters ( black hole mass and accretion rate ) which should be relevant for these two major application areas . for each of these two cases , we illustrate the impact of the black hole spin by considering a non - rotating and a maximally - rotating black hole . on the other hand , we neglect here the dependence on some other parameters of hot - flow models . in particular , we consider only weakly magnetized flows , with the magnetic pressure of 1/10th of the total pressure , and we neglect the direct viscous heating of electrons ; see section [ delta ] for a discussion of these two assumptions . furthermore , we neglect outflows , which may play an important role in some systems ( e.g. yuan , quataert & narayan 2003 ) . then , our solutions are strongly dominated by the advection of energy by ions , as in the original formulation of the advection - dominated accretion flow ( adaf ) model by , e.g. , narayan & yi ( 1995 ) . in this paper , we focus on modelling an innermost part of an accretion flow , namely inside @xmath7 , where @xmath8 is the gravitational radius and @xmath9 is the black - hole mass , where the bulk of the observed radiation is produced . global comptonization has a net effect of compton heating outside @xmath10 ( e.g. park & ostriker 2001 , yuan , xie & ostriker 2009 , yuan & li 2011 ) , which effect is not considered here .

we present a model of optically thin , two - temperature , accretion flows using an exact monte carlo treatment of global comptonization , with seed photons from synchrotron and bremsstrahlung emission , as well as with a fully general relativistic description of both the radiative and hydrodynamic processes . we consider accretion rates for which the luminosities of the flows are between and of the eddington luminosity . the consequent reduction of effects related to the value of the black spin is more significant at smaller accretion rates . for a non - rotating black hole

we present a model of optically thin , two - temperature , accretion flows using an exact monte carlo treatment of global comptonization , with seed photons from synchrotron and bremsstrahlung emission , as well as with a fully general relativistic description of both the radiative and hydrodynamic processes . we consider accretion rates for which the luminosities of the flows are between and of the eddington luminosity . the black hole spin parameter strongly affects the flow structure within the innermost gravitational radii . the resulting large difference between the coulomb heating in models with a non - rotating and a rapidly rotating black hole is , however , outweighed by a strong contribution of compression work , much less dependent on spin . the consequent reduction of effects related to the value of the black spin is more significant at smaller accretion rates . for a non - rotating black hole , the compressive heating of electrons dominates over their coulomb heating , and results in an approximately constant radiative efficiency of per cent in the considered range of luminosities . for a rapidly rotating black hole , the coulomb heating dominates , the radiative efficiency is per cent and it slightly increases ( but less significantly than estimated in some previous works ) with increasing accretion rate . our study neglects the direct heating of electrons , which effect can lead to larger differences between the radiative properties of models with a non - rotating and a rapidly rotating black hole than estimated here . flows with the considered parameters produce rather hard spectra , with the photon spectral index , and with high energy cut - offs at several hundred kev . we find an agreement between our model , in which the synchrotron emission is the main source of seed photons , and observations of black - hole binaries in their hard states and agns at low luminosities . in particular , our model predicts a hardening of the x - ray spectrum with increasing luminosity , as indeed observed below or so in both black - hole binaries and agns . also , our model approximately reproduces the luminosity and the slope of the x - ray emission in cen a. [ firstpage ] accretion , accretion discs black hole physics x - rays : binaries x - rays : general .

1107.0860

r

figs [ fig : rates ] and [ fig : rates_stel ] show the change of the heating and cooling rates , and the electron temperature , between our initial and final solutions . figs [ fig : flow ] and [ fig : flow_stel ] show the remaining parameters of the flow these are assumed to be the same in the initial and final solutions . we can clearly see how the value of the spin parameter , @xmath83 , affects the flow properties . rotation of the black hole stabilizes the circular motion of the innermost part of the flow ( an effect directly related with properties of test particle motion , analogous to the well - known dependence of the innermost stable orbit on @xmath83 in keplerian discs ) which yields a higher density ( through the continuity equation ) . this , in turn , implies both a stronger coulomb coupling ( see figs [ fig : rates]f and [ fig : rates_stel]f ) and a larger optical depth ( see figs [ fig : flow]a and [ fig : flow_stel]a ) in the innermost region in models with @xmath28 . on the other hand , heating by the compression work is typically stronger than , or comparable to , heating by the coulomb energy transfer from ions ( cf . nakamura et al . 1997 , mahadevan & quataert 1997 ) , which effect partly reduces the differences between the high and low @xmath83 models . these effects , and their impact on the radiative properties of the flow , are discussed in detail below . figs [ fig : rates](f ) and [ fig : rates_stel](f ) show also the dissipative heating rate of ions , @xmath61 . the stabilized rotation results in a much stronger dissipative heating in the inner region for @xmath28 , however , this property is rather unimportant for effects investigated in this paper ( neglecting both the direct heating of electrons and hadronic processes ) . we discuss here in some details the initial solutions although they are not self - consistent , because most of models available in literature use the same local approximation for comptonization . moreover , we amend some conclusions regarding the accuracy of local approximations , derived previously in x10 . we find the initial solutions using the prescription for the compton cooling rate in a slab geometry with initial photon energies of 1 ev , given in dermer et al . ( 1991 ; hereafter d91 ) . in x10 , we found that it gives a reasonably good approximation for the innermost region . for the models considered here , the slab approximation appears to be less accurate , however , our choice of the slab case allows for a direct comparison with previous studies , a number of which used the slab approximation based on d91 , or its modification introduced in esin et al . ( 1996 ) . figs [ fig : rates](a , c ) and [ fig : rates_stel](a , c ) show the heating and cooling rates in the initial solution . comptonization of synchrotron photons is the most efficient radiative cooling process . however , the synchrotron emissivity decreases rapidly beyond its transition radius , @xmath40 ( @xmath84 for @xmath23 and @xmath85 for @xmath86 ) . then , in the local model , the radiative cooling at @xmath87 is dominated by the ( much weaker ) bremsstrahlung and its comptonization . then , two regions can be distinguished in terms of the _ electron _ energy equation ( ions are always advection dominated ) . ( i ) at @xmath87 , the flow is adiabatically compressed , which is reflected in the increase of @xmath69 with decreasing @xmath21 ( see figs [ fig : rates]e and [ fig : rates_stel]e ) ; both the radiative cooling and the coulomb heating are much weaker than the advective terms . ( ii ) at @xmath88 , the radiative cooling becomes efficient and @xmath69 decreases ; the coulomb heating is more efficient in this region and it exceeds the compression work in the innermost part ( except for the model with @xmath27 and @xmath89 ) . in this region , the advection of the internal energy contributes also to the heating of electrons , however , this effect is rather weak . the solid curves in figs [ fig : rates](a , c ) and [ fig : rates_stel](a , c ) show the gr global compton cooling rate obtained in our initial mc simulations , i.e. with the @xmath69 satisfying the energy equation ( [ eq : energy ] ) with the compton cooling rate , @xmath90 , given by the local slab ( d91 ) prescription . as we can see , there are significant deviations between the local ( dotted curves ) and global cooling rates , resulting from several effects . two of these effects should be generic to models of black - hole flows regardless of specific values of parameters of the flow . first , the input of seed photons from the inner region strongly enhances the compton cooling beyond @xmath40 . the second one involves the presence of the event horizon ( neglected in the local approximation ) . the presence of an inner boundary of the flow at the event horizon results in an obvious difference with respect to the semi - infinite slab ; namely , a large fraction of photons generated in the innermost region is captured , reducing the input of seed photons . another effect affecting the structure of the flow is the dependence of the optical depth from a given point on direction . this strongly depends on the flow parameters and assumptions about heating and outflow . in particular , the flows for our parameters have the optical depth from a point in the equatorial plane along the outward radial direction , @xmath91 , similar to the vertical one , @xmath92 , at any @xmath21 , whereas @xmath93 in the model of x10 . furthermore , for @xmath28 , both @xmath91 and @xmath92 are much smaller than the optical depth in the inward radial direction , @xmath94 , except for the very innermost region ; in these models @xmath95 ( @xmath96 for @xmath97 and @xmath4 for @xmath80 ) at @xmath98 . for @xmath27 , @xmath95 ( @xmath99 for @xmath97 and @xmath100 for @xmath80 ) at @xmath101 ; in these models the difference between @xmath94 and @xmath91 typically does not exceed a factor of 2 . then , for a non - rotating black hole , the local radiative properties would be more accurately described by the spherical geometry , while for a rapidly rotating black hole the local properties are intermediate between the sphere and the slab . then , the assumption of the slab geometry overestimates the initial cooling rate in all models considered here . finally , as we note in x10 , the d91 formula is accurate for only two values of seed photon energies , 1 ev and 1 kev , and we use here the lower one . with this value , the formula gives a reasonable approximation for flows around a stellar black hole , where seed photons have energies @xmath102 ev . for flows around a supermassive black hole , however , with typical seed photon energies of @xmath1 ev ( for @xmath103 ) , it underestimates the cooling rate . specifically , for this @xmath9 we found deviations by a factor of @xmath104 between the formula of d91 for 1 ev and the results of our _ local _ slab mc simulation using the exact energy distribution of seed photons ( given by the synchrotron and bremsstrahlung emission distributions ; see x10 for the description of our local mc model ) . the initial solutions are qualitatively similar at both values of @xmath26 considered here , the most significant dependence on @xmath105 involves the increase of the value of @xmath40 with increasing @xmath26 . in contrary , detailed properties of the self - consistent , final solutions are more sensitive to @xmath26 . figs [ fig : rates](b , d ) show the heating and cooling rates of the final solutions for @xmath23 . at @xmath106 , a significant fraction of the power heating electrons is stored as their internal energy rather than radiated away . this is qualitatively similar to the initial solution , although @xmath43 is larger at @xmath106 in the global cooling model and hence @xmath38 is smaller than in the local cooling model ; therefore , the temperature gradient is smaller in the outer region in our final solutions ( see discussion below ) . we note that the strong contribution of the @xmath38 term significantly complicates the procedure for finding the self - consistent solution at this lower @xmath26 , as both the global compton cooling and the electron advection are strongly sensitive to , and affect , the electron temperature profile . [ fig : rates](e ) shows the electron temperature profiles for the initial and the final solutions . we see that , in the final solution , @xmath69 increases compared to the initial solution , by a factor of @xmath107 in the inner region , and up to a factor of 3 at several hundred @xmath67 . the increase of @xmath69 at @xmath108 is an obvious effect , related with the overestimation of the cooling rate by the slab approximation , combined with - crucial in that region - capturing of seed photons by the black hole , as discussed in section [ initial ] . somewhat surprisingly , the global solution requires higher @xmath69 also at @xmath109 , where the global radiative cooling is significantly enhanced . the temperature must remain high in this outer region because the energy balance could not be achieved for @xmath69 decreasing too rapidly . namely , we found that such a ( too rapid ) decrease of temperature at @xmath109 would yield a large positive @xmath110 term in the electron energy equation ( [ eq : energy ] ) , which , added to the ( increased in global cooling ) @xmath43 term , could not be balanced by the heating terms . we emphasise that this property is related to strong contribution of advective terms and it should not necessarily occur in the whole range of parameters , in particular at higher accretion rates . for @xmath25 ( fig . [ fig : rates_stel ] ) , the self - consistent @xmath69 is higher in the innermost part than @xmath69 in the initial solution , due to the same reasons as for @xmath23 . however , the compton cooling is relatively more important in the outer region , which results in an approximately isothermal structure at @xmath111 ; in particular , we do not find a local maximum of @xmath69 , marking the transition ( at @xmath112 ) from an adiabatically compressed flow to an efficiently cooled flow in global solutions with @xmath23 and in all our local solutions . the temperature at which the energy balance is achieved is twice lower for @xmath28 , due to a much larger input of seed photons from the central region . the strong contribution of the compressive heating has crucial consequences for the radiative efficiency , @xmath113 , where @xmath51 is the total observed luminosity of the flow , and for its scaling with @xmath26 . we compare here our models with the same @xmath83 for different @xmath26 , although we note that they have also different @xmath9 , which may slightly affect such a comparison ( the main dependence on the value of @xmath9 concerns the energy of synchrotron photons , influencing the cooling rate ) . comparing our results for @xmath23 and 0.5 , we find that the fraction of an accretion power transferred to electrons via coulomb collisions varies approximately as @xmath114 for @xmath28 and for @xmath27 we note even stronger dependence on @xmath26 . then , heating dominated by the coulomb coupling would lead to an approximately linear scaling of the radiative efficiency with @xmath26 , as derived in previous works on this subject ( see , e.g. , eq . 12 and references in narayan & mcclintock 2008 ; see also table 3 in rajesh & mukhopadhyay 2010 ) . however , @xmath115 is much less dependent , moreover negatively , on @xmath26 ; specifically , it is higher by a factor of @xmath104 for @xmath23 than for @xmath25 . as a result , the dependence of @xmath116 on @xmath26 is significantly reduced . for @xmath27 , @xmath117 at @xmath23 and @xmath118 at @xmath25 . the decrease of @xmath115 with increasing @xmath26 is partially balanced by the increased contribution of coulomb heating . two further effects decrease the radiative efficiency at lower @xmath26 : ( 1 ) the increase of the fraction of the energy given to electrons which is not radiated away ( and increases the internal energy advected with the flow ) , and ( 2 ) the increase of the fraction of photons captured by the black hole ( section [ collimation ] ) . as a result , the radiative efficiency for @xmath27 is approximately the same for both considered values of @xmath26 . more specifically , @xmath119 ( with @xmath120 erg s@xmath121 and @xmath122 ) for @xmath23 and @xmath123 ( @xmath124 erg s@xmath121 and @xmath125 ) for @xmath25 . for @xmath28 , @xmath48 exceeds @xmath49 at both @xmath23 and 0.5 . radiative efficiencies at these @xmath26 differ only by a factor of 2 , due to relatively stronger contribution of compressive heating at @xmath23 and very strong reduction of the observed @xmath51 by gr effects ( section [ collimation ] ) at @xmath25 . specifically , for @xmath23 , @xmath126 ( @xmath127 erg s@xmath121 and @xmath128 ) and for @xmath25 , @xmath129 ( @xmath130 erg s@xmath121 and @xmath131 ) . we note that for @xmath28 the apparent luminosity depends on @xmath132 , see section [ anisotropy ] , and the above values of @xmath51 are averaged over all viewing angles . and @xmath23 . the solid ( black ) and dashed ( red ) curves are for @xmath28 and @xmath27 , respectively . ( b ) the angular dependence of spectra for the final solution with @xmath28 ; the spectra from bottom to top are for @xmath1331 , 0.50.6 and 00.1 . , width=302 ] and @xmath23 . the solid ( black ) and dashed ( red ) curves are for @xmath28 and @xmath27 , respectively . ( b ) the angular dependence of spectra for the final solution with @xmath28 ; the spectra from bottom to top are for @xmath1331 , 0.50.6 and 00.1 . , width=302 ] figs [ fig : spectra](a ) and [ fig : spectra_stel](a ) show the angle - averaged spectra for the initial and final solution . in all models , the normalization of the spectra of the final solution is much higher than that of the initial solution , due to the increase of the synchrotron emissivity resulting from the increase of @xmath69 . the x - ray spectra are relatively hard , with the photon index @xmath134 , for both ( @xmath23 , @xmath28 ) and ( @xmath25 , @xmath27 ) and @xmath135 for ( @xmath25 , @xmath28 ) ; the last value is determined in the 210 kev range , as at higher energies a rather pronounced wien peak leads to further hardening of the spectrum . for ( @xmath136 , @xmath27 ) , the relativistic @xmath69 and small optical depth result in pronounced scattering bumps seen in this model spectrum ; the average slope in the 2200 kev range is @xmath137 . thus , we see that the spectra harden with the increasing luminosity , for @xmath26 increasing from 0.1 to 0.5 , from @xmath138 to @xmath139 at @xmath27 and from @xmath140 to @xmath141 at @xmath28 . in all models , the @xmath142 spectra have the maxima at several hundred kev . the electron temperature reaches the maximum values of @xmath143 mev for @xmath23 and @xmath144 kev for @xmath25 . note , however , that although these flows produce photons with energies @xmath145 , we do not expect an efficient e@xmath146 pair production in photon - photon collisions . the probability that a @xmath147-ray produces a pair is approximately given by the compactness parameter for this process , @xmath148 , where @xmath149 is the radiative power in photons with @xmath150 kev produced within @xmath151 . it is @xmath152 for all @xmath151 in all models except for @xmath25 and @xmath28 , where @xmath153 in the innermost few @xmath67 . the same conclusion was reached in previous studies of pair equilibria in advection - dominated flows ( e.g. esin 1999 ) where additional pair creation processes , namely electron - electron and photon - particle collisions , were also taken into account . but for @xmath154 and @xmath25 . , width=302 ] but for @xmath154 and @xmath25 . , width=302 ] the nature of the space - time metric ( specified by the value of @xmath83 ) affects the radiative properties of hot flows through various effects . as noted above , the stabilized circular motion results in a much larger density in the innermost region in models with large @xmath83 . this affects the radiative efficiency in a manner discussed in section [ final ] ; here we restate some of these results with the emphasis on the dependence on @xmath83 . two further effects , discussed in sections [ collimation][anisotropy ] , concern the properties of photon motion in curved space - time . higher density implies a stronger coulomb coupling for large @xmath83 . for @xmath27 , @xmath48 is smaller than for @xmath28 by a factor of 200 and 35 for @xmath23 and 0.5 , respectively . the difference between the heating of electrons for high and low @xmath83 is , however , strongly reduced by the high efficiency of compression , which shows very weak dependence on the value of @xmath83 . then , the total heating , @xmath155 , is higher in models with @xmath28 only by a factor of 3.5 ( @xmath156 ) and 16 ( @xmath25 ) . extrapolating our results we can expect that at @xmath157 the difference between the heating efficiencies in high and low @xmath83 models vanishes . on the other hand , a much larger difference between the heating rates for large and small values of @xmath83 could be expected in models involving the direct transfer of the dissipated energy to electrons ; compare @xmath47 and @xmath37 with @xmath61 shown in figs [ fig : rates](f ) and [ fig : rates_stel](f ) . higher density implies also a larger optical depth for large @xmath83 . then , despite a stronger heating in these models , the energy balance in the innermost region is achieved at smaller electron temperatures than for small @xmath83 . on the hand , the highly efficient comptonization occurs at very small @xmath21 , therefore , a much more centrally concentrated emissivity of comptonized radiation is achieved in models with @xmath28 and the _ observed _ luminosity is subject to stronger reduction by gr effects , discussed below . different velocity fields result in a different strength of collimation toward the black hole horizon . in principle , larger values of the radial velocity , @xmath158 , imply a stronger collimation for @xmath27 , which could give rise to a larger fraction of photons being captured by the black hole . however , the radiation is produced , on average , at a smaller radial distance for @xmath28 and , therefore , the reduction of the observed luminosity due to gr effects , including the photon capture and the gravitational redshift , turns out to be larger in that case . specifically , in models with @xmath28 , @xmath159 for @xmath25 and 0.3 for @xmath156 ; the large reduction for @xmath25 results from @xmath160 ( and trapping of photons ) in the central region . for @xmath27 , @xmath161 ( for @xmath23 ) and 0.9 ( for @xmath86 ; in this case the emissivity profile is flatter ) . for high values of @xmath83 , effects unique for the kerr metric , i.e. bending of photon trajectories to the equatorial plane combined with a dependence of the gravitational shift of energy on the direction of photon escape , result in an intrinsic anisotropy of radiation produced within the innermost few @xmath67 ( see piran & shaham 1977 , niedwiecki 2005 ) . the comptonized component from that region is softer ( i.e. has a larger spectral index and a smaller cut - off energy ) and has a smaller normalization when observed at a smaller @xmath132 . the gravitational effects , underlying this property , are strong only within @xmath162 , then , the magnitude of the anisotropy in the total spectrum depends on the proportion between contributions from the innermost and the surrounding ( beyond @xmath163 ) regions . figs [ fig : spectra](b ) and [ fig : spectra_stel](b ) show the @xmath132-dependence of the observed spectra in our models with @xmath28 ( in models with @xmath27 the dependence on @xmath132 is negligible ) . as we can see , the spectra indeed show some anisotropy but the effect is relatively moderate . for @xmath23 , the total flux emitted face - on ( @xmath1331 ) and edge - on ( @xmath1640.1 ) corresponds to the isotropic luminosity of @xmath165 and @xmath166 erg s@xmath121 , respectively . in this model , the compressive heating results in a rather flat emissivity profile , then , mixing of relatively weak contribution from @xmath167 with radiation produced at more distant regions washes out the anisotropic properties . for @xmath25 , the face - on and edge - on fluxes correspond to @xmath168 erg s@xmath121 and @xmath169 erg s@xmath121 , respectively . in this model , the emissivity is strongly centrally concentrated ; however , the optical depth of the inner region is large and a large fraction of photons produced there get reprocessed at larger distances or captured . at both @xmath26 , the spectral indices differ by @xmath170 between a face - on and an edge - on observer . we expect that a much larger anisotropy would be produced in a model with moderate @xmath26 ( yielding @xmath171 ) and strong direct heating of electrons ( giving a very centrally concentrated emissivity ) . an optically thick disc may extend to relatively low radii in some objects observed at @xmath172 similar to these characterising our models . the best example concerns xte j1118 + 480 , in which the derived truncation radius of the outer cold disc is @xmath173 ( esin et al . we consider here the cooling of the inner hot flow due to comptonization of thermal photons emitted by such a surrounding , cold disc . for this we take the innermost part , within @xmath174 , of our self - consistent solutions described in section [ final ] . we use our mc method to compute the comptonization of the seed photons emitted by a cold , keplerian disc extending from @xmath175 to @xmath176 . the local black - body temperature of its thermal emission is found using page & thorne ( 1974 ) ; note that this approach gives the largest possible luminosity of the outer disc as it involves the assumption that the rate of the outward transport of mechanical energy , which is the dominant source of the radiated energy at @xmath177 , is the same as in an untruncated keplerian disc . we do not look for self - consistent solutions including this additional source of seed photons . instead , we compute the total rate of the compton cooling by the outer disc photons , @xmath178 , and compare it with the total compton cooling rate due to the synchrotron and bremsstrahlung emission , @xmath179 , of our self - consistent solutions . we find that in models with @xmath27 the effect is small , with @xmath180 , and for @xmath28 it is negligible , @xmath181 . we note that the weakness of this effects results from the following properties . first , the total luminosity of the disc truncated at @xmath182 is relatively small ( specifically , it is approximately equal to the luminosity of the hot flow ) . second , the solid angle subtended by the flow as seen by the outer disc is rather small . third , the optical thickness of the outer parts of the flow is very small at the values of @xmath26 considered here , so a small fraction of photons illuminating the flow get scattered . our results are consistent with the conclusion of esin et al . ( 2001 ) that the outer disc is not an important source for compton cooling in this range of parameters . obviously , the effect would be more important for a smaller truncation radius ( cf . esin 1997 ) , at which the luminosity of the disc would be larger , as well as at higher @xmath26 , at which a larger fraction of photons irradiating the flow would be scattered . most of the specific properties discussed in this paper have been studied in previous works . however , their quantitative importance could not be assessed properly as neither of previous studies considered self - consistently all relevant effects . the solution of a hot - flow structure based on a self - similar model ( e.g. , narayan & yi 1995 ) is commonly used due to its relative simplicity . however , this simple solution introduces inaccuracies of up to an order of magnitude even for the basic flow parameters ( e.g. , the density given by eq . 1 in mahadevan & quataert ( 1997 ) is @xmath183 times larger than the density in our solutions ) , which leads to further inaccuracies in papers based on this model ; e.g. , we find that compressive heating dominates over coulomb heating at much higher accretion rates than the critical value given by eq . ( 35 ) in mahadevan & quataert ( 1997 ) . gammie & popham ( 1998 ) and popham & gammie ( 1998 ) presented an extensive study of various aspects of gr hydrodynamical description of a flow in the kerr metric and they show that the black hole spin has a large effect on the velocity field , density and temperature of the flow ( in ways also discussed in the present paper ) ; however , their study neglected radiative processes , so a more detailed impact on the observed spectrum could not be established . manmoto , mineshige & kusunose ( 1997 ) included an explicit description of radiative processes with local approximation of compton cooling in a pseudo - relativistic model . the same model including outflows and direct electron heating was used by yuan et al . ( 2003 , 2005 ) . then , m00 improved such models by including a fully gr treatment of the hydrodynamical processes ( but still with local approximation of compton cooling ) . we have fully reproduced their results in our initial solutions ; the accuracy of these models is directly illustrated by comparison of our initial and final ( global ) solutions . in an alternative ( to mc ) method for the treatment of global comptonization in an optically thin flow , developed by narayan , barret & mcclintock ( 1997 ) , the flow is divided into a set of nested spherical shells and the iterative scattering method is used to describe their mutual interactions . the model was used , e.g. by esin , mcclintock & narayan ( 1997 ) , quataert & narayan ( 1999 ) and esin et al . neither of these papers presents any details which could allow us to compare our cooling rates and only the produced spectra can be compared . the results of esin et al . ( 2001 ) , who use the gr hydrodynamical model from gammie & popham ( 1998 ) and include the special relativistic effects and the gravitational redshift in the calculation of radiative processes , is of particular interest for such a comparison . it appears that the model of narayan et al . ( 1997 ) yields a higher cooling rate than our monte carlo model , as the spectrum computed in esin et al . ( 2001 ) for parameters similar to these in our models ( see the solid curve in their fig . 1 ) has a break energy at @xmath184 kev , significantly lower than our model spectra . we do not know the cause of this difference . among previous studies of hot flows , the fully gr adaf model of kurpiewski & jaroszyski ( 1999 , 2000 ) , with a mc computation of global comptonization , seems to be the closest to our present work . their spectra show a much stronger dependence on @xmath83 , see e.g. figure 4 in kurpiewski & jaroszyski ( 2000 ) , which may be due to their values of @xmath26 significantly smaller than in our models . yuan et al . ( 2009 ) used an iteration method , similar to ours but with a different approach to computing global comptonization , to find the radiative cooling rate mutually consistent between the dynamics and radiation of the flow in a non gr model including strong outflows and electron heating . taking into account significant differences between the results of our present work and x10 , pointed out below , we speculate that gr flows with a different strength of these two effects may be characterised by different critical accretion rates , and different maximum luminosities , than those found in the model of yuan et al . ( 2009 ) . finally , we compare our results with the pseudo - relativistic model of x10 . first , we note that models based on the pseudo - newtonian potential fail to properly describe the innermost region even for the @xmath27 case . specifically , the pseudo - relativistic model predicts a decrease of the optical depth at @xmath185 ( see the dot - dashed curve in fig . 2b in x10 ) while the fully gr model with the same parameters ( see our fig . [ fig : flow]a ) yields the optical depth monotonically increasing with decreasing @xmath21 . the reason for this discrepancy can be traced to the ( unphysically ) large radial velocity in the pseudo - relativistic model , formally exceeding @xmath186 at small @xmath21 , which implies a much smaller density than that in the gr model . second , in the present work we use the equation for vertical equilibrium in the form derived for the kerr metric by abramowicz , lanza & percival ( 1997 ) . in x10 we used its simplified version , @xmath187 , where @xmath188 is the sound speed and @xmath189 is the keplerian angular velocity , and we note significant differences in scale heights derived in these two approaches . specifically , the equation from abramowicz et al . ( 1997 ) yields a larger scale height , up to a factor of @xmath190 , for the flow parameters describing our models . third , additional effects included in x10 , namely the strong outflow and direct viscous heating of electrons affect the flow structure in a complex manner and lead to a qualitatively different effect of taking into account the global nature of the comptonization process . obviously , the outflow leads to a reduction of @xmath191 at small @xmath21 . therefore , @xmath191 is much smaller , by a factor of @xmath183 at @xmath66 , in the model of x10 than in our present model with @xmath27 and @xmath25 ( which parameters are the same as those in x10 ) . then , the outflow reduces the compressive heating of ions via reducing the density gradient , and the direct heating of the electrons reduces the viscous heating of ions . also , the outflow reduces the viscous heating rate per unit volume , flattening its radial profile , but the viscous heating rate per ion remains unchanged . we note that the compressive heating of ions exceeds their viscous heating in our models , and it is much larger , by a factor of @xmath192 , than the compressive heating of electrons . together , both reductions of the ion heating cause a reduction of @xmath68 , which , in turn , leads to a decrease of @xmath78 by @xmath193 per cent ( with respect to the pseudo - relativistic model without both an outflow and electron heating ) within the innermost several @xmath67 . the simplified hydrostatic equilibrium condition together with the outflow and electron heating considered in x10 yield a much smaller @xmath78 than our present model ( compare our fig . [ fig : flow_stel]b with fig . 3b in x10 ) . as a result , in spite of the strong mass loss to the outflow , the total _ radial _ optical depth in the model of x10 is still higher than that in our model with @xmath27 and @xmath25 . also , the radial optical depth of x10 is much larger than @xmath191 ; then , the geometry of the flow resembles that of a slab . fourth , comparing the radiative efficiencies of the x10 model and the present one with @xmath27 , @xmath25 illustrates the strong impact of the direct heating of electrons . namely , in x10 the value of @xmath116 is three times larger , although most of the potential energy of the flow is lost to the outflow in their model . we discuss here briefly our assumption on the strength of the magnetic field as well as our neglect of the viscous heating of electrons . our assumption of rather weak magnetic field , with the magnetic pressure of @xmath194 , is supported by results of the magnetohydrodynamic ( mhd ) simulations in which amplification of magnetic fields by the mri typically saturates at such a ratio of the magnetic to the total pressure ( e.g. machida , nakamura & matsumoto 2004 and references therein ) . it is rather easy to assess changes of the flow structure and the spectrum resulting from a change of this assumption . namely , a stronger magnetic field would result in a stronger synchrotron emission and this would cause a decrease of the electron temperature and a softening of the comptonization spectrum ( see , e.g. , esin et al . 1997 ) . an issue of the direct viscous heating of electrons is more uncertain . current applications of adaf models typically assume large values of electron heating to total heating , @xmath195 ( e.g. , yuan et al . 2003 ) , however , the model has a degeneracy between the value of @xmath196 and the strength of an outflow ( quataert & narayan 1999 ) . various attempts to assess this effect on theoretical grounds seem to favour small values of @xmath196 for weak magnetic fields and rather high @xmath26 , which are considered in our models . analytic investigation of particle heating by mhd turbulence in adafs indicates that the turbulence primarily heats protons for weak magnetic fields , while electrons are primarily heated for strong magnetic fields ( see quataert & gruzinov 1999 ) . however , large uncertainties in the division between electron and proton heating result from uncertainties in the description of the turbulence ; @xmath197 , assumed in our models , may correspond to the values of @xmath196 between @xmath198 and 0.6 ( see fig . 2 in quataert & gruzinov 1999 ) . details of another potential mechanism of electron heating discussed by bisnovatyi - kogan & lovelace ( 1997 ) and quataert & gruzinov ( 1999 ) , i.e. reconnection , remain even more uncertain . simulations of mri turbulence by sharma et al . ( 2007 ) indicate that pressure anisotropy , created in turbulent plasmas , may give an additional mechanism for particle heating ; they approximate the fraction of the viscous energy which heats electrons as @xmath199 . however , their model assumes a fully collisionless plasma , which approximation is valid only for @xmath200 . at higher accretion rates , coulomb collisions suppress the electron pressure anisotropy and electron heating is negligible . then , their prescription for @xmath196 seems to be not relevant for our models . we note that the direct viscous heating would exceed the coulomb and compressive heating of electrons for @xmath201 in models with @xmath27 , and for @xmath202 in models with @xmath28 . for these values of @xmath196 , flows should have larger luminosities than these assessed in our models . we can also expect that flows with such values of @xmath196 produce harder x - ray spectra , with higher cut - off energies , than obtained in our models . however , we note also that large values of @xmath196 , for which the heating of ions is significantly reduced , may have a strong impact on the flow structure , especially if a strong outflow is also present , which may lead to enhanced global compton cooling ( as discussed in section [ previous ] ) . then , the above simple estimation of spectral changes related to the increase of @xmath196 may be incorrect ; in particular , we note that the spectrum obtained in our model with @xmath203 in x10 has a smaller cut - off energy than our spectra computed here with @xmath204 .

, the coulomb heating dominates , the radiative efficiency is per cent and it slightly increases ( but less significantly than estimated in some previous works ) with increasing accretion rate . flows with the considered parameters produce rather hard spectra , with the photon spectral index , and with high energy cut - offs at several hundred kev .

we present a model of optically thin , two - temperature , accretion flows using an exact monte carlo treatment of global comptonization , with seed photons from synchrotron and bremsstrahlung emission , as well as with a fully general relativistic description of both the radiative and hydrodynamic processes . we consider accretion rates for which the luminosities of the flows are between and of the eddington luminosity . the black hole spin parameter strongly affects the flow structure within the innermost gravitational radii . the resulting large difference between the coulomb heating in models with a non - rotating and a rapidly rotating black hole is , however , outweighed by a strong contribution of compression work , much less dependent on spin . the consequent reduction of effects related to the value of the black spin is more significant at smaller accretion rates . for a non - rotating black hole , the compressive heating of electrons dominates over their coulomb heating , and results in an approximately constant radiative efficiency of per cent in the considered range of luminosities . for a rapidly rotating black hole , the coulomb heating dominates , the radiative efficiency is per cent and it slightly increases ( but less significantly than estimated in some previous works ) with increasing accretion rate . our study neglects the direct heating of electrons , which effect can lead to larger differences between the radiative properties of models with a non - rotating and a rapidly rotating black hole than estimated here . flows with the considered parameters produce rather hard spectra , with the photon spectral index , and with high energy cut - offs at several hundred kev . we find an agreement between our model , in which the synchrotron emission is the main source of seed photons , and observations of black - hole binaries in their hard states and agns at low luminosities . in particular , our model predicts a hardening of the x - ray spectrum with increasing luminosity , as indeed observed below or so in both black - hole binaries and agns . also , our model approximately reproduces the luminosity and the slope of the x - ray emission in cen a. [ firstpage ] accretion , accretion discs black hole physics x - rays : binaries x - rays : general .

1107.0860

c

we have developed a fully gr model with global compton scattering of hot , tenuous accretion flows . the dominant source of seed photons in our model is the synchrotron process . we assume that an outer , optically - thick , accretion disc is truncated at large radii , so irradiation of the hot flow by it is negligible . we have also neglected direct viscous electron heating and outflows . we have considered the accretion rates of @xmath97 and 0.5 , for which our model gives the bolometric luminosities of @xmath227@xmath228 . in this range of @xmath172 , we find our models predict x - ray spectra hardening with increasing @xmath51 , which is in agreement with the correlation observed at @xmath235 in both black - hole binaries in the hard state and agns . this is also in agreement with the suggestion of sobolewska et al . ( 2011 ) that synchrotron seed photons dominate in this range of @xmath172 , whereas an optically - thick accretion disc overlapping with the hot flow provide dominant source of seed photons at higher @xmath51 . we have compared our models to the low-@xmath51 fr i radio galaxy cen a. we have found a good agreement with the observed x - ray spectral slope , but the position of the high - energy break , observed at @xmath217200 kev , is lower than the model cut - off energy . this may be possibly explained by the hadronic processes , which would be present if the black hole in this source has a high spin . we have studied the impact of the black hole spin and we find that despite a very strong influence of this parameter on the dynamical properties of the inner part of the flow , the difference between the observed radiation from a flow surrounding a maximally rotating and a non - rotating black hole , with other parameters unchanged , is rather moderate . in particular , their luminosities differ only by a factor of 23 ( i.e. smaller than a factor of @xmath238 in keplerian discs ) . we find this is due to a strong role of the compressive electron heating , which process only weakly depends on the black - hole spin . we note , however , that a much larger dependence on the spin value is expected in models involving direct heating of electrons , or taking into account hadronic processes . we stress that a proper treatment of global compton scattering is crucial for accurate modelling of the flow structure , most importantly , for the electron temperature profile , and for the spectral formation in optically thin flows . in models with @xmath80 , we find the entire inner flow is efficiently cooled by comptonization when the non - local nature of this process is taken into account . at @xmath97 , global comptonization is important , but also electron advection effects are strong at @xmath239 , giving rise to large temperature gradients . as compared to the results with the global comptonization , the local model assuming a slab geometry provides in general a very poor approximation , overestimating the cooling rate by an order of magnitude in the innermost region .

the black hole spin parameter strongly affects the flow structure within the innermost gravitational radii . the resulting large difference between the coulomb heating in models with a non - rotating and a rapidly rotating black hole is , however , outweighed by a strong contribution of compression work , much less dependent on spin . our study neglects the direct heating of electrons , which effect can lead to larger differences between the radiative properties of models with a non - rotating and a rapidly rotating black hole than estimated here . we find an agreement between our model , in which the synchrotron emission is the main source of seed photons , and observations of black - hole binaries in their hard states and agns at low luminosities . in particular , our model predicts a hardening of the x - ray spectrum with increasing luminosity , as indeed observed below or so in both black - hole binaries and agns .

we present a model of optically thin , two - temperature , accretion flows using an exact monte carlo treatment of global comptonization , with seed photons from synchrotron and bremsstrahlung emission , as well as with a fully general relativistic description of both the radiative and hydrodynamic processes . we consider accretion rates for which the luminosities of the flows are between and of the eddington luminosity . the black hole spin parameter strongly affects the flow structure within the innermost gravitational radii . the resulting large difference between the coulomb heating in models with a non - rotating and a rapidly rotating black hole is , however , outweighed by a strong contribution of compression work , much less dependent on spin . the consequent reduction of effects related to the value of the black spin is more significant at smaller accretion rates . for a non - rotating black hole , the compressive heating of electrons dominates over their coulomb heating , and results in an approximately constant radiative efficiency of per cent in the considered range of luminosities . for a rapidly rotating black hole , the coulomb heating dominates , the radiative efficiency is per cent and it slightly increases ( but less significantly than estimated in some previous works ) with increasing accretion rate . our study neglects the direct heating of electrons , which effect can lead to larger differences between the radiative properties of models with a non - rotating and a rapidly rotating black hole than estimated here . flows with the considered parameters produce rather hard spectra , with the photon spectral index , and with high energy cut - offs at several hundred kev . we find an agreement between our model , in which the synchrotron emission is the main source of seed photons , and observations of black - hole binaries in their hard states and agns at low luminosities . in particular , our model predicts a hardening of the x - ray spectrum with increasing luminosity , as indeed observed below or so in both black - hole binaries and agns . also , our model approximately reproduces the luminosity and the slope of the x - ray emission in cen a. [ firstpage ] accretion , accretion discs black hole physics x - rays : binaries x - rays : general .

1603.08673

r

we estimated the statistical uncertainty of our stellar parameters from the distribution of best fit values relative to their multi - epoch means . we used the results from the second stage of our fitting pipeline ( where stellar properties are allowed to vary from epoch to epoch , c.f sec . [ modelfittingsec ] ) , exclusive of spectroscopic binaries , to obtain fits to 2283 spectra of 214 targets ( see table [ prectargtable ] ) with which we computed the differences between the single epoch values and the adopted multi - epoch values of the stellar parameter . we then performed kernel density estimation on each parameter and computed confidence intervals . the resulting pdfs are shown in figures [ teffprecision ] , [ fehprecision ] , [ alphaprecision ] , and [ vsiniprecision ] and the @xmath90 confidence intervals given in table [ stellarpropprectable ] . in addition to the overall pdfs , the plots give pdfs for subsamples grouped by spectral type and rotation rate ( @xmath91 km / s ) . the selection of 8 km / s as a grouping is largely arbitrary , though corresponds with the point where @xmath5 becomes the dominate source of line broadening relative to the instrumental psf . though we do not explicitly show pdfs for groupings in s / n , the pdfs for spectral type show this by proxy ; later spectral types are fainter and have lower s / n spectra . we saw no evidence that the psf form ( e.g. gaussian vs. hermite series ) affected the measured values or their uncertainties . we estimated the accuracy of our technique for determining @xmath1 , [ fe / h ] , and [ @xmath3/fe ] by comparing the values we measured with those in the literature . tables [ stdparvals ] gives our values for the six standard stars along with those from the literature . tables [ stderrors ] then reports the differences in these values : we adopt the averages therein as an estimate of our systematic uncertainties . as an additional check we fitted @xmath92 twilight spectra and report the values and differences thereby obtained . though these values are of comparable quality , we excluded them from our average as the large number of spectra would heavily bias the results . we tested our @xmath5 accuracy by comparing our values with those reported in @xcite , with which we have thirty - seven targets in ngc 2516 in common . our values agree to within 5 km / s for all but four stars , which are all spectroscopic binaries . for the remaining 33 stars our adopted , multi - epoch mean values agree with a standard deviation of 2.2 km / s . we recovered the correct @xmath5 to better than 0.1 km / s in fits to our twilight spectra . our code is not able to reliably measure @xmath5 values below @xmath93 km / s ( roughly one third of our velocity resolution ) . based on this analysis , we report our fits yield typical single - epoch precisions of 75 k , 0.05 dex , and 0.75 km / s for @xmath1 , [ fe / h ] and [ @xmath3/fe ] , and @xmath5 . we find this translates to mean multi - epoch precisions of @xmath2 k , @xmath4 dex for both [ fe / h ] and [ @xmath3/fe ] , and @xmath60.3 km / s for @xmath5 . our @xmath1 values are typically cooler than available literature data for our standards by @xmath025 k and we find a similar offset when fitting twilight spectra . iron abundance values appear elevated by a tenth dex but are driven entirely by hip 48331 : excluding hip 48331 @xmath94[fe / h ] becomes @xmath95 dex , consistent with our twilight fits . we do not see any evidence of a systematic offset in [ @xmath3/fe ] or @xmath5 . lccccc ngc 2516 & 11.68 15.09 & 0.46 1.17 & 108 & 18 + ngc 2422 & 12.19 16.05 & 0.45 1.31 & 106 & 19 + total & 11.68 16.05 & 0.45 1.31 & 214 & 37 + lcccccccc @xmath1 ( k ) & @xmath2844 & + 59 & @xmath2862 & + 74 & @xmath2895 & + 121 & @xmath2882 & + 163 + @xmath96 $ ] ( dex ) & @xmath280.06 & + 0.05 & @xmath280.05 & + 0.06 & @xmath280.07 & + 0.06 & @xmath280.07 & + 0.05 + @xmath97 $ ] ( dex ) & @xmath280.04 & + 0.04 & @xmath280.05 & + 0.04 & @xmath280.07 & + 0.04 & @xmath280.07 & + 0.04 + @xmath5 ( km / s ) & @xmath280.5 & + 0.5 & @xmath280.3 & + 0.4 & @xmath280.5 & + 0.7 & @xmath281.0 & + 0.9 + + mean s / n & & & & lrrrrr + this work & @xmath98 & ( 4.7 ) & @xmath99 & @xmath100 + s05 & @xmath101 & @xmath102 & @xmath103 & ... + s08 & @xmath104 & @xmath105 & @xmath106 & ... + n09 & s08 & s08 & s08 & @xmath107 + c11 & @xmath30 & @xmath108 & ... & ... + a12 & s08 & s08 & s08 & @xmath109 + t13 & @xmath110 & @xmath111 & @xmath112 & ... + + + this work & @xmath113 & ( 4.6 ) & @xmath114 & @xmath115 + c11 & @xmath116 & @xmath117 & @xmath118 & @xmath119 + s08 & @xmath120 & @xmath121 & @xmath122 & ... + n09 & s08 & s08 & s08 & @xmath123 + + + this work & @xmath124 & ( 4.6 ) & @xmath125 & @xmath126 + v05 & @xmath127 & @xmath128 & @xmath129 & ... + c11 & @xmath34 & @xmath130 & @xmath131 & @xmath132 + + + this work & @xmath133 & ( 4.5 ) & @xmath134 & @xmath135 + c11 & @xmath136 & @xmath137 & @xmath138 & @xmath139 + + + this work & @xmath140 & ( 4.5 ) & @xmath141 & @xmath142 + c11 & @xmath38 & @xmath143 & @xmath144 & @xmath145 + k13 & @xmath146 & @xmath147 & @xmath148 & @xmath149 + + + this work & @xmath150 & ( 4.4 ) & @xmath151 & @xmath152 + c11 & @xmath40 & @xmath153 & @xmath154 & @xmath155 + + + this work & @xmath156 & ( 4.5 ) & @xmath157 & @xmath158 lcrrrr hip 48331 & k5v & @xmath159 & @xmath160 & @xmath161 + hip 13388 & k1v & @xmath162 & @xmath163 & @xmath164 + hip 10798 & g8v & @xmath165 & @xmath166 & @xmath167 + hip 22278 & g5v & @xmath168 & @xmath169 & @xmath170 + hip 19589 & g0v & @xmath171 & @xmath172 & @xmath173 + hip 31415 & f6v & @xmath174 & @xmath175 & @xmath176 + + average & & @xmath177 & @xmath178 & @xmath179 + + twilights & g2v & @xmath180 & @xmath181 & @xmath182 + radial velocity variations of stars without a companion stem from one of five sources : ( 1 ) an inherent photon noise error ( @xmath183 ) arising from the s / n and the number and shape of the stellar and telluric lines , ( 2 ) an instrumental error ( @xmath184 ) based on the characteristics of m2fs spectra , ( 3 ) an error contribution due to our analysis ( @xmath185 ) , ( 4 ) intrinsic stellar variability ( @xmath186 ) caused by stellar activity ( e.g. stellar flares or star spots ) , and ( 5 ) variability in the bulk atmospheric motion along the line of sight that introduces a doppler shift on our wavelength reference ( @xmath187 ) . we assume that all five sources add in quadrature to produce the observed dispersion ( @xmath188 ) , as follows : @xmath189 under this assumption , the observed velocity dispersion of a star with a known @xmath186 and observed under conditions with a known @xmath187 can be used to estimate the quadrature sum of the first three error terms , which we refer to as an effective measurement error , @xmath190 , @xmath191 here we focus on estimating @xmath190 as a function of s / n , based on observations of the standard star hip 48331 . we observed hip 48331 35 times on 19 different nights ; 9 nights have more than 1 epoch . of these we use the 31 spectra with s / n above 200 and r @xmath192 . eighteen spectra were obtained using the red m2fs arm and 13 using the blue arm . the s / n of these spectra span between 200 and 300 , with a median of 240 . the resolving power of these spectra range from 40,000 to 64,000 , with a median of 55,000 due to variations in the psf width across the m2fs detector and soft instrument focus during early observing runs . the rv measurements of hip 48331 are illustrated in figure [ rvmeasures ] ; these values have a standard deviation ( @xmath188 ) of 23 m / s . to simulate lower s / n spectra that are more representative of the open cluster stars surveyed here , we generated lower s / n versions of these 31 spectra and recomputed the best fit models and rvs from which new @xmath188 can be calculated . we generated the the lower s / n spectra by sampling a poisson process at each pixel with expectation value of the measured electrons multiplied by the desired fractional reduction in mean s / n : e. g. @xmath193 where @xmath194 is the number of electrons measured at the @xmath195 pixel and prime denotes the new values . we also ensured that the simulated variance spectra included in an appropriate amount of gaussian noise to include the effects of detector read noise . the resulting spectra have s / n levels of @xmath0150 , 100 , 80 , 60 , 50 , 40 , and 15 . the spectra were then fit as described in section [ analysis ] , treating each s / n level independently . this resulted in eight rv time - series ( one for each s / n level ) with each standard deviation yielding a measurement of @xmath188 at that s / n level . we also computed @xmath183 for each of the 248 spectra by applying the algorithm described in @xcite to the telluric and stellar components of each best - fit model , adding the results in quadrature . to obtain @xmath190 from the eight @xmath188 values calculated above , we subtracted off a stellar variability of @xmath196 m / s @xcite and an atmospheric variability of @xmath197 m / s ( determined as shown later in this section , see also figure [ noaawindfig ] ) . these values can be compared directly to the the mean @xmath183 values for each of the eight s / n bins . oddly , we found that would result in imaginary errors below a s / n of @xmath198 . in figure [ rvprecisionmeas ] we plot both @xmath190 and @xmath183 , which shows that we measure our rvs with greater precision that anticipated at low s / n . in figure [ rvprecisionmeas ] , we also show the ratio of @xmath190 to the mean of @xmath183 at each s / n bin . as an additional reference we also plot the ratio of each bin @xmath190 to each of the @xmath183 in that bin . this suggests an approximately linear relation between our measurement error and the @xmath183 value we computed for each spectrum . we adopted errors for the ratio from two sources : ( 1 ) the standard deviation of @xmath183 in each s / n bin contributes directly and ( 2 ) an estimate of the error in @xmath188 that was obtained by computing our best - fit models with a small number of slightly perturbed initial rvs for each spectrum in each bin , adopting the standard deviations of the resulting @xmath188 values as an uncertainty on @xmath190 in each s / n bin . we fit the ratio of @xmath190 to the mean of the @xmath183 for each s / n bin and use the result as a scaling relation to convert @xmath183 to @xmath190 provided a s / n . this technique allows us to account for some , if not all , of the increased uncertainty in spectra that are at a lower resolution ( e.g. due to mis - focus ) than the typical rv standard observation , are of more rapidly rotating stars , or otherwise possess a different number or strength of stellar lines . the errors in figure [ rvmeasures ] have been scaled in this manner . from this analysis we find m2fs has a limiting rv precision of about 25 m / s , though the @xmath183 values we computed at high s / n suggest an additional 15 m / s precision gain may be possible at higher s / n ratios . a potential culprit in our modeling process is as yet unclear . in figures [ rvprecisionpsf ] and [ rvprecisionspt ] we use the same process to show the impact various modifications to our analysis have on achievable precision , some of which are discussed in further detail in the following paragraphs . finally , figure [ rvprecision2 ] shows an updated version of figure [ precisionfig ] with the corrections discussed above . [ [ atmospheric - variability ] ] atmospheric variability + + + + + + + + + + + + + + + + + + + + + + + we estimated the impact bulk atmospheric motions have on our wavelength reference by integrating the water vapor weighted wind speed along the line of sight using data from the noaa gfs forecast models @xcite . using the gfs model closest in time to our data the forecast is within 3 hours of the model s initial conditions . these models have an rmse wind vector error of about 3 m / s three days ( ! ) in the future . perturbing the integrals by this error has a maximum impact of about 1 m / s , with typical values less than a tenth of that . the resulting contributions for our data on hip 48331 , ngc 2516 , and ngc 2422 are shown in figure [ noaawindfig ] . while pointing directly into or along the jet - stream would exhibit a clear signature at the @xmath199 m / s level , typical values are not particularly significant to our efforts . as mentioned , we adopt @xmath197 m / s . [ [ sky - emission-1 ] ] sky emission + + + + + + + + + + + + ideally the spectra we obtained of our rv standard would be completely representative of our program stars . our cluster targets are , however , significantly fainter than our rv standard and so many of them exhibit a number of strong sky emission lines ( c.f . figure [ exampleextractions ] and [ fitexamplefig ] ) . to better asses their impact on our rv precision we took a subset of 60 spectra and extracted and fit the spectra from images prior to stacking . this gave us a sample of 4 or 5 rvs from spectra obtained consecutively . these spectra spanned a s / n of about 15 45 for targets of spectral type @xmath0 k3 - f5 . the @xmath188 for these rvs was in agreement with that expected based on our @xmath190 relation . we see some evidence that our better - than - anticipated rv precision stems from our use of the mean rv as a prior . if fit with an initial rv far from the multi - epoch mean we observe an increased @xmath188 at low s / n , though still somewhat below that predicted by ( * ? ? ? figure [ rvprecisionmeas ] ) . [ [ psf - effects ] ] psf effects + + + + + + + + + + + we found very little difference in the results of the multi - gaussian parameterization of @xcite and a gauss - hermite kernel when the center of its enclosed power is not constrained to the central pixel undergoing convolution . the latter is faster with many fewer parameters and once the enclosed power is constrained to the central sub - pixel we find it exhibits enhanced stability ( c.f . figure [ rvprecisionpsf ] ) . both yielded slightly worse performance than a simple gaussian and we did not find an improvement in rv precision by using a variable , but symmetric psf . it may be worth investigating a hybrid approach where the components of the hermite parametrization are allowed to vary with pixel . [ [ model - spectra ] ] model spectra + + + + + + + + + + + + + as an additional test on rv precision and the impact our use of the phoenix grid has we model the twilight spectra both with the phoenix grid and using the empiric solar spectrum of @xcite as the template . we select the @xmath0 600 twilight spectra in images with mean s / n above 100 ( 100 650 , mean of 320 ) . for these spectra we measured a @xmath90 rv scatter within each twilight image of @xmath200 m / s when fitting with the phoenix models and @xmath201 m / s using kurucz s empiric solar spectra . this strongly suggests that the phoenix templates are not limiting our rv precision . we see evidence of a slight quadratic dependence of the measured rv on the spectrum s ccd position . this suggests that the rv zero point and wavelength zero points are slightly affecting our dispersion , though we note that program stars are typically observed in the same fiber . fitting and removing this effect reduced the scatter to @xmath202 m / s and @xmath203 m / s , respectively . we estimated the accuracy of our rvs by looking at the differences between our values and those in the literature for each of our six standard stars . we report these differences in table [ stdrverrors ] and find an offset of @xmath204 m / s from the scale of @xcite , albeit with significant scatter . we also saw a slight indication that rvs measured in our lowest s / n bin are slightly shifted relative to the higher s / n bins by @xmath205 m / s . lccr hip 48331 & k5v & 30 & @xmath206 + hip 13388 & k1v & 2 & @xmath207 + hip 10798 & g8v & 5 & @xmath208 + hip 22278 & g5v & 3 & @xmath209 + hip 19589 & g0v & 1 & @xmath210 + hip 31415 & f6v & 1 & @xmath211 + + average & & & @xmath204

we show our approach can attain a single - epoch velocity precision of 25 m / s to 60 m / s over a broad range of s / n throughout our observational baseline of 1.1 years . subsequent papers will provide results for stars observed in the target clusters , analyze our dataset of rv time - series for stellar jitter and stellar and sub - stellar companions , and consider the implications of our findings on the clusters themselves .

we present a multiplexed , high - resolution ( r,000 median ) spectroscopic survey designed to detect exoplanet candidates in two southern star clusters ( ngc 2516 and ngc 2422 ) using the michigan / magellan fiber system ( m2fs ) on the magellan / clay telescope at las campanas observatory . with 128 available fibers in our observing mode , we are able to target every star in the core half - degree of each cluster that could plausibly be a solar - analog member . our template - based spectral fits provide precise measurements of fundamental stellar properties ( k ) , [ fe / h ] and [/fe ] ( dex ) , and (.3 km / s)and radial velocities ( rvs ) by using telluric absorption features from 7160 to 7290 as a wavelength reference for 251 mid - f to mid - k stars ( 126 in ngc 2516 and 125 in ngc 2422 ) that comprise our survey . in each cluster we have obtained epochs of our targets . using repeat observations of an rv standard star we show our approach can attain a single - epoch velocity precision of 25 m / s to 60 m / s over a broad range of s / n throughout our observational baseline of 1.1 years . our technique is suitable for non - rapidly rotating stars cooler than mid - f . in this paper we describe our observational sample , analysis methodology , and present a detailed study of the attainable precision and measurement capabilities of our approach . subsequent papers will provide results for stars observed in the target clusters , analyze our dataset of rv time - series for stellar jitter and stellar and sub - stellar companions , and consider the implications of our findings on the clusters themselves .

astro-ph0108470

i

we present a near - infrared extinction study of the protostellar collapse candidate b335 using deep integrations from hst / nicmos supplemented by data from the w.m . keck observatory . in summary : 1 . we determine transformations between the nicmos filters f160w and f222 m and the standard h and k bands in the cit photometric system for a range of @xmath41 color from 0 to 3 . at the accuracy of our data , the derived transformations do not have significant slopes or color terms . 2 . the nicmos mosaic image of the central @xmath26 region of b335 shows a dramatic fall off in the number of stars detected towards the protostar location , where the extinction increases due to the central concentration of dense core material . the nicmos mosaic image contains a total of 119 stars detected in both filters , the innermost of which is at a radius of @xmath70 . the photometry shows a steep gradient in the @xmath41 colors toward the central protostar . in addition , there is a strong asymmetry in the colors superimposed on the overall gradient that coincides with the bipolar outflow . we compare a series of models of dense core stucture to the extinction data , including the previously proposed models of inside - out collapse derived from molecular line observations . the _ shape _ of the @xmath136 radial profile is well matched by the inside - out collapse model , in particular the density fall - off as @xmath129 for the envelope and a flattening within the purported infall zone . an unstable bonnor - ebert sphere with dimensionless outer radius @xmath0 provides an equally good description of the density profile , and is indistinguishable from the collapse model over the range in radius where there are stars to fit . the inside - out collapse model is not unique . the power law index for the density distribution derived from extinction is consistent with recent determinations from dust emission measurements at millimeter and submillimeter wavelengths . the bipolar outflow appears to be responsible for the dominant asymmetry in the extinction data . stars whose line of sight fall within @xmath137 of the outflow axis show lower extinction than those further away from the outflow . the effect of the outflow on the extinction data is reproduced very well by models that consider a hollowed out bipolar cone of constant opening angle . in the context of the inside - out collapse models , the observed asymmetry is too large to be explained by either rotation , or a weak magnetic field . 5 . the entire extinction dataset can be well fitted by a model that includes infall , bipolar outflow , and an additional @xmath140 dispersion that mimics residual turbulent motions . the best fit outflow semi - opening angle is @xmath3 and the best fit infall radius is @xmath1 . the fitted value of the infall radius is consistent with those derived from molecular line studies of b335 , and supports the inside - out collapse interpretation of the density structure . the fitted opening angle for the bipolar outflow is somewhat larger than has been observed in high velocity co emission , perhaps because the molecular line studies do not recover the full outflow width due to confusion with ambient emission at low velocities . the normalization of the observed color excess is a factor of @xmath179@xmath180 higher than the value predicted using the nominal 250 pc distance to b335 , and the standard gas - to - dust ratio and near - infrared reddening law . the discepancy can conceivably be explained by a combination of a closer distance and a lower gas - to - dust ratio . partial support for this work was provided by nasa through grant number hst - go-07843.01-a from the space telescope science institute , which is operated by aura , inc . , under nasa contract nas5 - 26555 we thank bob goodrich and randy campbell for invaluable assistance with the observations obtained at the w.m . keck observatory . dwah thanks brian mcleod for his help in running the nicreduce software , and alex wilson for his assistance with idl graphics .

we present a near - infrared extinction study of the dark globule b335 , a protostellar collapse candidate , using data from hst / nicmos and the w.m . we find that the _ shape _ of the density profile is well matched by the collapse model , but that the _ amount _ of extinction corresponds to larger column densities than predicted . an unstable bonnor - ebert sphere with dimensionless outer radius provides an equally good description of the density profile , and is indistinguishable from the collapse model over the range in radius sampled by the extinction data . the bipolar outflow driven by the embedded young stellar object has an important effect on the extinction through the core , and modeling the outflow as a hollowed - out bipolar cone of constant opening angle provides a good match to the observations . the complete exinction map is well reproduced by a model that includes both infall and outflow , and an additional 20% dispersion that likely results from residual turbulent motions . the fitted infall radius is consistent with those derived from molecular line observations and supports the inside - out collapse interpretation of the density structure . the fitted opening angle for the outflow is slightly larger than observed in high velocity co emission , perhaps because the full extent of the outflow cone in co becomes confused with ambient core emission at low velocities .

we present a near - infrared extinction study of the dark globule b335 , a protostellar collapse candidate , using data from hst / nicmos and the w.m . keck observatory . these data allow a new quantitative test of the `` inside - out '' collapse model previously proposed to explain molecular line profiles observed toward this region . we find that the _ shape _ of the density profile is well matched by the collapse model , but that the _ amount _ of extinction corresponds to larger column densities than predicted . an unstable bonnor - ebert sphere with dimensionless outer radius provides an equally good description of the density profile , and is indistinguishable from the collapse model over the range in radius sampled by the extinction data . the bipolar outflow driven by the embedded young stellar object has an important effect on the extinction through the core , and modeling the outflow as a hollowed - out bipolar cone of constant opening angle provides a good match to the observations . the complete exinction map is well reproduced by a model that includes both infall and outflow , and an additional 20% dispersion that likely results from residual turbulent motions . this fitted model has an infall radius of ( pc for 250 pc distance ) , and an outflow cone semi - opening angle of . the fitted infall radius is consistent with those derived from molecular line observations and supports the inside - out collapse interpretation of the density structure . the fitted opening angle for the outflow is slightly larger than observed in high velocity co emission , perhaps because the full extent of the outflow cone in co becomes confused with ambient core emission at low velocities .

1105.3061

i

we have presented a new numerical scheme for solving the advection equation and the vlasov equation . the present scheme solves not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables , for better conservation of the information entropy . we have developed one- and two - dimensional schemes , and have shown their high capabilities . the present scheme provides quite accurate solutions even with smaller numbers of grid points , although it requires a higher memory cost than other existing schemes . we have shown that , however , the total memory usage of the present scheme is smaller than the others for the same accuracy of solutions applications of the one - dimensional scheme to the electrostatic vlasov simulations ( linear landau damping and two stream instability ) , and the two - dimensional scheme to the electromagnetic vlasov simulations ( perpendicular wave propagation and harris current sheet equilibrium ) have been presented . the two - dimensional scheme allows us to solve the gyro motion and the @xmath251 drift motion for a long time with little numerical heating . since the present scheme treats the zeroth to second order moments and advances them on the basis of their governing equations , the particle momentum and energy as well as mass are conserved very well . this is important for studying plasma phenomena such as convection , heating , and acceleration . although the present scheme correctly solves the moments up to the second order , the entropy is numerically increased in the two stream instability ( section [ sec : two - stre - inst ] ) , by the dissipation of fine structures in velocity space . this is understood that the perturbation of lower order moments decreases and higher order moments contribute to the entropy when the so - called filamentation phenomena proceed ( e.g. , * ? ? ? since the filamentation is inevitable as long as discretizing velocity space , it is essentially impossible to exactly conserve the entropy with finite information . the present scheme is designed specifically to solve the advection and rotation in velocity space in the vlasov equation . in our vlasov simulation code , the cip - csl2 scheme has been employed to solve the advection in configuration space . we note that , however , another scheme can be applied to the advection in configuration space and be combined with the present scheme . several advection schemes proposed for vlasov simulations are designed to preserve positivity and non - oscillatory property , in order to suppress a non - physical growth of plasma waves caused by numerically - produced positive gradient in velocity space . @xcite argued that the positivity - preserving and non - oscillatory are important properties for reliable vlasov simulations . on the other hand , it may cause a non - physical global evolution driven by plasma pressure gradient that is increased by the numerical diffusion in velocity space , even when the plasma should be in an equilibrium state . although the present scheme is not positivity - preserving or non - oscillatory , we have shown that the obtained results are better than the others . we thus consider that preserving high order moments is another important property for vlasov simulations . magnetized plasma phenomena that allow to assume the two dimensionality in velocity space are limited , e.g. , strictly perpendicular shocks @xcite and the two - dimensional kelvin - helmholtz instability @xcite . even considering the one dimension in configuration space , there are many phenomena that should treat the full three - dimensional velocity space . we are now developing a three - dimensional scheme and its application to the full electromagnetic vlasov simulation , which will enable us to study a wide variety of collisionless plasma phenomena .

we present a new numerical scheme for solving the advection equation and its application to vlasov simulations . the scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables , for better conservation of the information entropy . applications of the one- and two - dimensional schemes to electrostatic and electromagnetic vlasov simulations are presented with some benchmark tests .

we present a new numerical scheme for solving the advection equation and its application to vlasov simulations . the scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables , for better conservation of the information entropy . we have developed one- and two - dimensional schemes and show that they provide quite accurate solutions within reasonable usage of computational resources compared to other existing schemes . the two - dimensional scheme can accurately solve the solid body rotation problem of a gaussian profile for more than hundred rotation periods with little numerical diffusion . this is crucially important for vlasov simulations of magnetized plasmas . applications of the one- and two - dimensional schemes to electrostatic and electromagnetic vlasov simulations are presented with some benchmark tests . advection equation , conservative form , multi - moment , information entropy , vlasov simulations , magnetized plasmas