Galaxy Occupation Statistics of Dark Matter Haloes: Observational Results

Abstract

We study the occupation statistics of galaxies in dark matter haloes using galaxy groups identified from the 2-degree Field Galaxy Redshift Survey with the halo-based group finder of Yang et al. The occupation distribution is considered separately for early and late type galaxies, as well as in terms of central and satellite galaxies. The mean luminosity of the central galaxies scales with halo mass approximately as $L_c\propto M^{2/3}$ for haloes with masses $M<10^{13}h^{-1}\msun$, and as $L_c\propto M^{1/4}$ for more massive haloes. The characteristic mass of $10^{13} h^{-1} \Msun$ is consistent with the mass scale where galaxy formation models suggest a transition from efficient to inefficient cooling. Another characteristic halo mass scale, $M\sim 10^{11} h^{-1}\msun$, which cannot be probed directly by our groups, is inferred from the conditional luminosity function (CLF) that matches the observed galaxy luminosity function and clustering. For a halo of given mass, the distribution of $L_c$ is rather narrow. The satellite galaxies are found to follow a Poissonian number distribution. The central galaxies in low-mass haloes are mostly late type galaxies, while those in massive haloes are almost all early types. We also measure the CLF of galaxies in haloes of given mass. Over the mass range that can be reliably probed with the present data ($13.3 \lta {\rm log}[M/(h^{-1}\Msun)] \lta 14.7$), the CLF is reasonably well fit by a Schechter function. Contrary to recent claims based on semi-analytical models of galaxy formation, the presence of central galaxies does not show up as a strong peak at the bright end of the CLF. (Abridged)