Studying Statistical Properties Of Dark Matter And Galaxy Distribution Based On Halo Model

In this PhD thesis,we study the three-point correlation function(3PCF) and bispectrum of both dark matter and galaxies,based on the halo model.And we build a new scaling relation between the stellar mass M_*,the observational radius R₉₀ and the stellar velocity dispersionσ_v(Hereafter,the MRD relation) for early-type galaxies.We probe its dependence for early-type galaxies on the enviroment and the intrinsic properties of individual galaxies.The thesis contents include four chapters.In the first chapter,we introduce the background of the large scale structure formation.Firstly,we briefly review the basic frame of the standard cosmology. Then,we introduce the linear theory of the gravitational perturbation,the initial power spectrum and the linear transfer function,the simplest nonlinear gravitational collapse model:the spherical collapse model.In chapter 2,we briefly introduce some usual statistical tools on studying statistical properties of both simulation samples and observation samples,especially reviewing the two-point correlation function(2PCF),3PCF and their Fourier transform(Power spectrum & Bispectrum).In addition,we introduce some redshift survey observations and how to construct mock galaxy redshift surveys with the same selection criterias as in the redshift surveys.In chapter 3,firstly,we introduce briefly the halo model ingredients:halo mass function,halo density profile,bias model and occupation number model. Then,we present models for the 3PCF of both dark matter and galaxies.We show that models based on the halo model can reasonably match the dark matter 3PCF obtained from high-resolution N-body simulations.On small scales(r≤0.5h^-1 Mpc) the 3PCF is sensitive to details regarding the density distributions of dark matter halos.On larger scales(r≥2.0h^-1 Mpc) the results are very sensitive to the abundance of the few most prominent halos.Using the conditional luminosity function,we also construct models for the 3PCF of galaxies,which we test against large mock galaxy samples.The bias of the galaxy distribution with respect to the dark matter,and the finite number of galaxies that can be hosted by individual halos,significantly reduce the normalized three-point correlation function with respect to that of dark matter.Contrary to the 3PCF of the dark matter,the galaxy 3PCF is much less sensitive to details regarding the spatial number density distribution of galaxies in individual halos or to the abundance of the few most massive systems.Finally,we show that our model based on the conditional luminosity function is in good agreement with results obtained from the 2-degree Field Galaxy Redshift Survey.In particular,the model nicely reproduces the observational finding that the 3PCF for early-type galaxies is slightly higher than that of late-type galaxies,and that there is no significant dependence of the 3PCF on galaxy luminosity.The chapter 4,we build a new scaling relation between the stellar mass M_*, the observational radius R₉₀ and the stellar velocity dispersionσ_v(Hereafter,the MRD relation) for early-type galaxies.We probe its dependence for early-type galaxies on the enviroment and the intrinsic properties of individual galaxies.The investigations are based on two early-type galaxy samples selected from the SDSS DR2 and the SDSS group catalogue constructed with a halo-based group finder. We probe the dependence of the MRD on the host halo masses and find that the stellar velocity dispersion of,whether central galaxies or satellite galaxies,is higher in larger halos than in small halos.Especially,the MRD relation of central galaxies in the super massive halos is evidently different from the one in small halos.And there is no significant radial dependence on the MRD relations for satellite galaxies.But the MRD relation of central galaxies is evidently different from that of satellite galaxies and the stellar velocity dispersion of central galaxies is higher than that of satellite galaxies.We also investigate the dependence of the MRD on the galaxy luminosity and color.The brighter galaxies have significantly higher stellar velocity dispersions and the color dependence of early-type galaxies' MRD relation is weak.