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The halo occupation distribution (HOD) describes the relation betweengalaxies and dark matter at the level of individual dark matter halos. Theproperties of galaxies residing at the centers of halos differ from those ofsatellite galaxies because of differences in their formation histories. Using asmoothed particle hydrodynamics (SPH) simulation and a semi-analytic (SA)galaxy formation model, we examine the separate contributions of central andsatellite galaxies to the HOD, more specifically to the probability P(N|M) thata halo of virial mass M contains N galaxies of a particular class. In agreementwith earlier results for dark matter subhalos, we find that the mean occupationfunction <N> for galaxies above a baryonic mass threshold can be approximatedby a step function for central galaxies plus a power law for satellites, andthat the distribution of satellite numbers is close to Poisson at fixed halomass. For galaxy samples defined by different baryonic mass thresholds, thereis a nearly linear relation between the minimum halo mass Mmin required to hosta central galaxy and the mass M1 at which an average halo hosts one satellite,with M1 ~ 14 Mmin (SPH) or M1 ~ 18 Mmin (SA). The mean occupation number ofyoung galaxies exhibits a local minimum at M ~ 10 Mmin where halos are toomassive to host a young central galaxy but not massive enough to hostsatellites. We show that the conditional galaxy mass function at fixed halomass cannot be described by a Schechter function because central galaxiesproduce a "bump" at high masses. We suggest parameterizations for the HOD andthe conditional luminosity function that can be used to model observed galaxyclustering. Many of our predictions are in good agreement with recent resultsinferred from clustering in the Sloan Digital Sky Survey.Comment: 38 pages, 13 figures. Figures are added to show model predictions on  CLF and the conditional mass distribution of halos hosting galaxies at fixed  luminosity. Accepted for publication in Ap

Theoretical Models of the Halo Occupation Distribution: Separating Central and Satellite Galaxies