Galaxy Groups in the SDSS DR4: III. the luminosity and stellar mass   functions
  Using a large galaxy group catalogue constructed from the Sloan Digital Sky Survey Data Release 4 (SDSS DR4) with an adaptive halo-based group finder, we investigate the luminosity and stellar mass functions for different populations of galaxies (central versus satellite; red versus blue; and galaxies in groups of different masses) and for groups themselves. The conditional stellar mass function (CSMF), which describes the stellar distribution of galaxies in halos of a given mass for central and satellite galaxies can be well modeled with a log-normal distribution and a modified Schechter form, respectively. On average, there are about 3 times as many central galaxies as satellites. Among the satellite population, there are in general more red galaxies than blue ones. For the central population, the luminosity function is dominated by red galaxies at the massive end, and by blue galaxies at the low mass end. At the very low-mass end ($M_\ast \la 10^9 h^{-2}\Msun$), however, there is a marked increase in the number of red centrals. We speculate that these galaxies are located close to large halos so that their star formation is truncated by the large-scale environments. The stellar-mass function of galaxy groups is well described by a double power law, with a characteristic stellar mass at $\sim 4\times 10^{10}h^{-2}\Msun$. Finally, we use the observed stellar mass function of central galaxies to constrain the stellar mass - halo mass relation for low mass halos, and obtain $M_{\ast, c}\propto M_h^{4.9}$ for $M_h \ll 10^{11} \msunh$. 
Xiaohu Yang (SHAO), H.J. Mo (UMass), Frank C. van den Bosch (MPIA)