Modelling galaxy clustering: halo occupation distribution versus subhalo
  matching

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Abstract

We model the luminosity-dependent projected and redshift-space two-point correlation functions (2PCFs) of the Sloan Digital Sky Survey (SDSS) DR7 Main galaxy sample, using the halo occupation distribution (HOD) model and the subhalo abundance matching (SHAM) model and its extension. All the models are built on the same high-resolution \(N\)-body simulations. We find that the HOD model generally provides the best performance in reproducing the clustering measurements in both projected and redshift spaces. The SHAM model with the same halo-galaxy relation for central and satellite galaxies (or distinct haloes and subhaloes), when including scatters, has a best-fitting \(\chi^2/\rm{dof}\) around \(2\)--\(3\). We therefore extend the SHAM model to the subhalo clustering and abundance matching (SCAM) by allowing the central and satellite galaxies to have different galaxy--halo relations. We infer the corresponding halo/subhalo parameters by jointly fitting the galaxy 2PCFs and abundances and consider subhaloes selected based on three properties, the mass \(M_{\rm acc}\) at the time of accretion, the maximum circular velocity \(V_{\rm acc}\) at the time of accretion, and the peak maximum circular velocity \(V_{\rm peak}\) over the history of the subhaloes. The three subhalo models work well for luminous galaxy samples (with luminosity above \(L_*\)). For low-luminosity samples, the \(V_{\rm acc}\) model stands out in reproducing the data, with the \(V_{\rm peak}\) model slightly worse, while the \(M_{\rm acc}\) model fails to fit the data. We discuss the implications of the modeling results.

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Halo occupation numbers and galaxy bias

R Smith, J. Peacock (2000)

We propose a heuristic model that displays the main features of realistic theories for galaxy bias. We show that the low-order clustering statistics of the dark-matter distribution depend almost entirely on the locations and density profiles of dark-matter haloes. A hypothetical galaxy catalogue depends on (i) the efficiency of galaxy formation, as manifested by the halo occupation number -- the number of galaxies brighter than some sample limit contained in a halo of a given mass; (ii) the location of these galaxies within their halo. The first factor is constrained by the empirical luminosity function of groups. For the second factor, we assume that one galaxy marks the halo centre, with any remaining galaxies acting as satellites that trace the halo mass. These simple assumptions amount to a recipe for non-local bias, in which the probability of finding a galaxy is not a simple function of its local mass density. We have applied this prescription to some CDM models of current interest, and find that the predictions are close to the observed galaxy correlations for a flat \(\Omega=0.3\) model (\(\Lambda\)CDM), but not for an \(\Omega=1\) model with the same power spectrum (\(\tau\)CDM). This is an inevitable consequence of cluster normalization for the power spectra: cluster-scale haloes of given mass have smaller core radii for high \(\Omega\), and hence display enhanced small-scale clustering. Finally, the pairwise velocity dispersion of galaxies in the \(\Lambda\)CDM model is lower than that of the mass, allowing cluster-normalized models to yield a realistic Mach number for the peculiar velocity field. This is largely due to the strong variation of galaxy-formation efficiency with halo mass that is required in this model.