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

TL;DR

Zheng et al. address how the halo occupation distribution of galaxies arises when separating central and satellite populations. They apply both SPH hydrodynamic and semi-analytic GALFORM models to quantify the mean occupation $\langle N\rangle_M$ as a central-step plus satellite power-law with $\langle N_{sat}\rangle_M \propto (M/M_1)^\alpha$ and $\alpha \approx 1$, and show $P(N_{sat}|M)$ is near-Poisson. They find $M_1/M_{min} \approx 14$ (SPH) or $\approx 18$ (SA) across mass, and that CMF/CLF exhibit a central 'bump' that breaks a Schechter form, motivating 5-parameter HOD/CLF fits. The results are broadly in line with SDSS clustering analyses and provide practical parameterizations to model observed galaxy clustering, with implications for constraining cosmology.

Abstract

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 <N> 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.

Figures (13)

• Figure 1: Mean occupation number and scatter as a function of halo mass, separated into central and satellite galaxies. Predictions are shown for the $\bar{n}_g=0.02 h^3 {\rm Mpc}^{-3}$ samples from the SPH simulation (left panels) and from the SA model (right panels). Lower panels plot the mean occupation numbers of central, satellite, and all galaxies. In the upper panels, circles show $\langle N(N-1)\rangle^{1/2}/\langle N\rangle$, indicating the width of the probability distribution, for all galaxies (filled circles) and satellite galaxies (open circles). For Poisson $P(N|M)$, this ratio would be one (dotted line). This figure can be compared to Fig. 4 of K04.
• Figure 2: Probability distributions of satellite numbers as a function of the mean occupation number of satellites, predicted by the SPH simulation (left panels) and by the SA model (right panels). Points are predictions of the models, and the Poisson error in each bin is assigned as the error bar. The dotted histogram in each panel shows the Poisson distribution of the same mean.
• Figure 3: Parameterized fits to mean occupation functions (top panels) and predicted numbers of galaxy pairs and triplets (middle and bottom panels) for the SPH simulation (left) and the SA model (right). For each model, left panels show results based on 3-parameter fits, which assume sharp cutoff profiles of $\langle N_{\rm cen}\rangle_M$ and $\langle N_{\rm sat}\rangle_M$, and right panels show results of fits with more parameters to model the cutoff profiles (see eqs. [\ref{['eqn:Ncenerf']}] and [\ref{['eqn:Nsat']}]). Fits and predictions are plotted as curves, and circles are measurements from the models.
• Figure 4: Age dependence of the HOD predicted by the SPH simulation (left panels) and by the SA model (right panels). For each model, the mean occupation functions of old and young galaxies are shown in the top panel, contributions from central and satellite galaxies to the mean occupation number are plotted in the middle panel, and the fraction of young galaxies (in central, satellite, and all galaxies) is plotted in the bottom panel.
• Figure 5: Same as Fig. \ref{['fig:parfit']}, but for each model the left panels show the young galaxy sample and right panels the old galaxy sample. Points show the model results and lines show fits using the 5-parameter model for all galaxies and the blue fraction parameterization described in the text.