The Dark Side of the Halo Occupation Distribution

We analyze the halo occupation distribution (HOD), the probability for a halo of mass M to host a number of subhalos N, and two-point correlation function of galaxy-size dark matter halos using high-resolution dissipationless simulations of the concordance flat LCDM model. The halo samples include both the host halos and the subhalos, distinct gravitationally-bound halos within the virialized regions of larger host systems. We find that the first moment of the HOD, <N>(M), has a complicated shape consisting of a step, a shoulder, and a power law high-mass tail. The HOD can be described by a Poisson statistics at high halo masses but becomes sub-Poisson for <N><4. We show that the HOD can be understood as a combination of the probability for a halo of mass M to host a central galaxy and the probability to host a given number Ns of satellite galaxies. The former can be approximated by a step-like function, while the latter can be well approximated by a Poisson distribution, fully specified by its first moment <Ns>(M). We find that <Ns>~M^b with b~1 for a wide range of number densities, redshifts, and different power spectrum normalizations. This formulation provides a simple but accurate model for the halo occupation distribution found in simulations. At z=0, the two-point correlation function (CF) of galactic halos can be well fit by a power law down to ~100/h kpc with an amplitude and slope similar to those of observed galaxies. At redshifts z>~1, we find significant departures from the power-law shape of the CF at small scales. If the deviations are as strong as indicated by our results, the assumption of the single power law often used in observational analyses of high-redshift clustering is likely to bias the estimates of the correlation length and slope of the correlation function.