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 CDM 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 \sim 35 percent lower than in a \Lambda CDM 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 halo occupation distribution ( HOD ) 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 ( PVDs ) 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 consistency .