The mass and luminosity functions of galaxies and their evolution

We set up a model for the evolution of the galaxy luminosity function, taki ng advantage of recent work that brought in some better understanding of th e mass function for gravitationally condensed objects. We add to this a sim ple model of star formation that reproduces the behaviour of the Tully-Fish er relation, in order to attach a luminosity to a massive halo with a given velocity dispersion. The physics of cooling of the gravitationally heated baryonic component allows us to distinguish halos that become groups or clu sters from those that eventually form galaxies (possibly within the former objects). With our new mass function and our new application of the cooling criteria - which motivated this paper - we get a satisfactory and natural cutoff at the bright end of the luminosity function, the needed flat slope for faint magnitudes and the correct trend in colors (brighter galaxies are redder) within the framework of the hierarchical clustering picture. This infirms earlier claims that the latter was inadequate to reproduce the form er observations. We find the velocity dispersion to be a much better parame ter than mass or radius to characterize galaxies. This model of the salient features that may describe galaxies allows one to discuss galaxy evolution as a function of redshift, in number as well as in luminosity. We find tha t bright galaxies form at z similar to 2 from mergers with a rather quiet e volution afterwards, whereas small galaxies are the result of a continuous merging process active up to the present epoch. The transition is found to occur at the observed transition between bright spirals and small dwarf ell ipticals or irregulars. The galaxy luminosity was larger in a recent past f or bright galaxies, as has been observed in the CFRS survey. This is becaus e the mass of gas in a typical L* galaxy such as the Milky Way is a small f raction of the total baryonic mass and thus star formation is already slowi ng down. The evolution in number, which is quite well controlled in our mod el, agrees reasonably well with the counts as a function of apparent magnit ude. The quasar multiplicity as a function of redshift is also discussed.