Towards a concordant model of halo occupation statistics

We use the conditional luminosity function (CLF) and data from the 2-degree Field Galaxy Redshift Survey (2dFGRS) to constrain the average relation between light and mass in a Lambda cold dark matter (ΛCDM) cosmology with Ωm= 0.23 and σ8= 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 ∼35 per cent lower than those in a ΛCDM cosmology with Ωm= 0.3 and σ8= 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 | Lcen), that a central galaxy of luminosity Lcen resides in a halo of mass M. We find this distribution to be much broader than what is typically assumed in halo occupation distribution models, which has important implications for the interpretation of satellite kinematics and galaxy-galaxy lensing data. Finally, reproducing the luminosity dependence of the pairwise peculiar 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 the constraints obtained from the luminosity dependence of the galaxy two-point correlation function. 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 consistenc