Linking early- and late-type galaxies to their dark matter haloes

Using data from the 2 Degree Field Galaxy Redshift Survey (2dFGRS) we compute the conditional luminosity functions (CLFs) of early- and late-type galaxies. These functions give the average number of galaxies with luminosities in the range L +/- dL/2 that reside in a halo of mass M , and are a powerful statistical tool to link the distribution of galaxies to that of dark matter haloes. Although some amount of degeneracy remains, the CLFs are well constrained. They indicate that the average mass-to-light ratios of dark matter haloes have a minimum of similar to100 h (M/L). around a halo mass of similar to3 x 10(11) h(-1) M.. Towards lower masses [M/L] increases rapidly, and matching the faint-end slope of the observed luminosity function (LF) requires that haloes with M < 10(10) h(-1) M. are virtually devoid of galaxies. At the high-mass end, the observed clustering properties of galaxies require that clusters have b(J)-band mass-to-light ratios in the range 500-1000 h (M/L).. Finally, the fact that early-type galaxies are more strongly clustered than late-type galaxies requires that the fraction of late-type galaxies is a strongly declining function of halo mass. We compute two-point correlation functions as a function of both luminosity and galaxy type. The agreement with observations, in terms of normalization and power-law slope, is remarkably good. When including predictions for the correlation functions of faint galaxies we find a weak (strong) luminosity dependence for the late- (early-) type galaxies. We also investigate the inferred halo occupation numbers. Late-type and faint galaxies reveal a shallower [N](M) than bright, early-type galaxies, which explains why [N](M) transforms from a single power law for bright galaxies to a more complicated form when fainter galaxies are included. Finally, we compare our CLFs with predictions from several semi-analytical models for galaxy formation. As long as these models accurately fit the 2dFGRS luminosity function the agreement with our predictions is remarkably good. This indicates that the technique used here has recovered a statistical description of how galaxies populate dark matter haloes, which is not only in perfect agreement with the data, but which in addition fits nicely within the standard framework for galaxy formation.