The Physics of Galaxy Clustering. I. A Model for Subhalo Populations

(Abridged) We present a semi-analytic model for Cold Dark Matter halosubstructure that can be used as a framework for studying galaxy formation andan ingredient in halo models of galaxy clustering. We perform a comprehensivecomparison of the model to the results of a suite of high-resolutioncosmological simulations. The comparisons reveal that subhalo statistics, suchas velocity and mass functions, radial distributions, and the halo occupationdistributions, agree well over three orders of magnitude in host halo mass atvarious redshifts. Both in the simulations and in our model, the radialdistributions of subhalos are significantly shallower than that of the darkmatter density. The abundance of subhalos in a host is set by competitionbetween destruction and new accretion. High mass halos and halos at highredshift tend to host more subhalos because the subhalos have, on average, beenaccreted more recently. Similarly, at fixed mass, halos that formed morerecently host more subhalos. Observed "fossil groups" may represent an extremetail of this correlation. We find a related correlation between host haloconcentration and subhalo abundance at fixed host mass, Nsat ~ c^-a, where achanges with redshift and host-to-subhalo mass ratio. Lastly, we use our modelto populate host halos in one of our high-resolution cosmological simulations,replacing the subhalos resolved in the simulation with subhalos computedaccording to our model. We show that the resulting 2pt correlation function ofsuch a "hybrid" halo ensemble is indistinguishable from that measured directlyin the simulation. This supports one of the key tenets of the standard halomodel -- the assumption that the halo occupation distribution is statisticallyindependent of host halo environment.Comment: 23 pages, 16 figures. Replaced with revised version accepted for publication in ApJ. Last revision corrects typo in Eq. 8 which is incorrect in published versio