The halo occupation distribution (HOD) describes the relation between galaxies and dark matter at the level of individual dark matter halos. The properties of galaxies residing at the centers of halos differ from those of satellite galaxies because of differences in their formation histories. Using a smoothed particle hydrodynamics (SPH) simulation and a semi-analytic (SA) galaxy formation model, we examine the separate contributions of central and satellite galaxies to the HOD, more specifically to the probability P(N|M) that a halo of virial mass M contains N galaxies of a particular class. In agreement with earlier results for dark matter subhalos, we find that the mean occupation function for galaxies above a baryonic mass threshold can be approximated by a step function for central galaxies plus a power law for satellites, and that the distribution of satellite numbers is close to Poisson at fixed halo mass. For galaxy samples defined by different baryonic mass thresholds, there is a nearly linear relation between the minimum halo mass Mmin required to host a 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 of young galaxies exhibits a local minimum at M ~ 10 Mmin where halos are too massive to host a young central galaxy but not massive enough to host satellites. We show that the conditional galaxy mass function at fixed halo mass cannot be described by a Schechter function because central galaxies produce a "bump" at high masses. We suggest parameterizations for the HOD and the conditional luminosity function that can be used to model observed galaxy clustering. Many of our predictions are in good agreement with recent results inferred 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
We investigate the physical mechanisms that shape the luminosity function. Beginning with the mass function of dark matter halos, we show how gas cooling, photoionization, feedback, merging and thermal conduction affect the shape of the luminosity function. We consider three processes whereby supernovae can affect the forming galaxy: (1) reheating of disk gas to the halo temperature; (2) expansion of the diffuse halo gas; (3) expulsion of cold disk gas from the halo. While feedback of form (1) is able to flatten the faint end of the luminosity function, this alone does not produce the sharp cut-off observed at large luminosities. Feedback of form (2) is also unable to solve this problem. The relative paucity of very bright galaxies can only be explained if cooling in massive halos is strongly suppressed. Conduction is a promising mechanism, but an uncomfortably high efficiency is required to suppress cooling to the desired level. If, instead, superwinds are responsible for the lack of bright galaxies, then the total energy budget required to obtain a good match to the galaxy luminosity function greatly exceeds the energy available from supernova explosions. The mechanism is only viable if the formation of central supermassive black holes play a crucial role in limiting the amount of stars that form in the host galaxy. (abridged)Comment: 10 pages, 5 figures. Submitted to Ap
1 September 2001 in Monthly Notices of the Royal Astronomical Society