Luminosity dependence of the spatial and velocity distributions of galaxies: Semi-analytic models versus the Sloan Digital Sky Survey

By comparing semi-analytic galaxy catalogues with data from the Sloan Digital Sky Survey (SDSS), we show that current galaxy formation models reproduce qualitatively the dependence of galaxy clustering and pairwise peculiar velocities on luminosity, but some subtle discrepancies with the data still remain. The comparisons are carried out by constructing a large set of mock galaxy redshift surveys that have the same selection function as the SDSS Data Release Four (DR4). The mock surveys are based on two sets of semi-analytic catalogues presented by Croton et al. and Kang et al. From the mock catalogues, we measure the redshift-space projected two-point correlation function, the power spectrum, and the pairwise velocity dispersion (PVD) in Fourier space and in configuration space, for galaxies in different luminosity intervals. We then compare these theoretical predictions with the measurements derived from the SDSS DR4. On large scales and for galaxies brighter than L*, both sets of mock catalogues agree well with the data. For fainter galaxies, however, both models predict stronger clustering and higher pairwise velocities than observed. We demonstrate that this problem can be resolved if the fraction of faint satellite galaxies in massive haloes is reduced by ~30% compared to the model predictions. A direct look into the model galaxy catalogues reveals that a signifcant fraction (15%) of faint galaxies ($-18<M_{^{0.1}r}<-17$) reside in haloes with $M_{vir}>10^{13}\msun$, and this population is predominantly red in colour. These faint red galaxies are responsible for the high PVD values of low-luminosity galaxies on small scales.