Constraining galaxy formation and cosmology with the conditional luminosity function of galaxies

We use the conditional luminosity function Phi(L \ M) dL, which gives the number of galaxies with luminosities in the range L +/- d L/2 that reside in a halo of mass M, to link the distribution of galaxies to that of dark matter haloes. Starting from the number density of dark matter haloes predicted by current models of structure formation, we seek the form of Phi(L \ M ) that reproduces the galaxy luminosity function and the luminosity dependence of the galaxy clustering strength. We test the models of Phi(L \ M ) by comparing the resulting mass-to-light ratios with constraints from the Tully-Fisher (TF) relation and from galaxy clusters. A comparison between model predictions and current observations yields a number of stringent constraints on both galaxy formation and cosmology. In particular, this method can break the degeneracy between Omega(0) and the power-spectrum normalization sigma(8), inherent in current weak-lensing and cluster-abundance studies. For flat LambdaCDM cosmogonies with sigma(8) normalized by recent weak gravitational lensing observations, the best results are obtained for Omega(0) similar to 0.3; Omega(0) less than or similar to 0.2 leads to too large galaxy correlation lengths, while Omega(0) greater than or similar to 0.4 gives too high mass-to-light ratios to match the observed TF relation. The best-fitting model for the LambdaCDM concordance cosmology with Omega(0) = 0.3 and Omega(Lambda) = 0.7 predicts mass-to-light ratios that are slightly too high to match the TF relation. We discuss a number of possible effects that might remedy this problem, such as small modifications of sigma(8) and the Hubble parameter with respect to the concordance values, the assumption that the Universe is dominated by warm dark matter, systematic errors in current observational data, and the existence of dark galaxies. We use the conditional luminosity function derived from the present data to predict several statistics about the distribution of galaxy light in the local Universe. We show that roughly 50 per cent of all light is produced in haloes less massive than 2 x 10(12) h(-1) M-circle dot. We also derive the probability distribution P (M \ L) dM that a galaxy of luminosity L resides in a halo with virial masses in the range M +/- dM/2.