THE MASS-DISTRIBUTION OF GROUPS AND CLUSTERS OF GALAXIES

We reformulate the collapse theories for the mass distribution of cosmic structures-of which the theory of Press and Schechter constitutes the archetype-in terms of a rate equation with finite collapse and survival times. We then derive the mass distribution and the optical luminosity function expected for groups and clusters of galaxies in these hierarchical clustering scenarios, considering both the collapse of high peaks in the initial overdensity field and the subsequent mass infall. We finally discuss the transition from direct collapse to merging and aggregation theories.