Towards a Concordant Model of Halo Occupation Statistics

We use the conditional luminosity function (CLF) and data from the 2dFGRS to constrain the average relation between light and mass in a LCDM cosmology with Omega_m=0.23 and sigma_8=0.74 (hereafter WMAP3 cosmology). Reproducing the observed luminosity dependence of the galaxy two-point correlation function results in average mass-to-light ratios that are about 35 percent lower than in a LCDM cosmology with Omega_m=0.3 and sigma_8=0.9 (hereafter WMAP1 cosmology). This removes an important problem with previous halo occupation models which had a tendency to predict cluster mass-to-light ratios that were too high. For the WMAP3 cosmology our model yields average mass-to-light ratios, central galaxy luminosities, halo occupation numbers, satellite fractions, and luminosity-gap statistics, that are all in excellent agreement with those obtained from a 2dFGRS group catalogue and from other independent studies. We also use our CLF model to compute the probability distribution P(M|L_cen), that a central galaxy of luminosity L_cen resides in a halo of mass M. We find this distribution to be much broader than what is typically assumed in HOD models, which has important implications for the interpretation of galaxy-galaxy lensing data. Finally, reproducing the luminosity dependence of the pairwise velocity dispersions in the 2dFGRS requires relatively low mass-to-light ratios for clusters and a satellite fraction that decreases strongly with increasing luminosity. This is only marginally consistent with our CLF constraints. We argue that a cosmology with parameters between those of the WMAP1 and WMAP3 cosmologies is likely to yield results with a higher level of consistency.