The Mass and Luminosity Functions of Galaxies and their Evolution

We set up a model for the evolution of the galaxy luminosity function, taking advantage of recent work that brought in some better understanding of the mass function for gravitationally condensed objects. The physics of cooling of the baryonic component allows us to distinguish halos that become groups or clusters 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 former observations. We find the velocity dispersion to be a much better parameter than mass or radius to characterize galaxies. We find that bright galaxies form at z~2 from mergers with a rather quiet evolution 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 ellipticals or irregulars. The quasar multiplicity as a function of redshift is also discussed.