MERGER RATES IN HIERARCHICAL-MODELS OF GALAXY FORMATION

We present an analytical description of the merging of virialized halo es which is applicable to any hierarchical model in which structure gr ows via gravitational instability. The formulae are an extension of th e Press-Schechter model. The dependence of the merger rate on halo mas s, epoch, the spectrum of initial density fluctuations and the density parameter OMEGA0 is explicitly quantified. We calculate the distribut ion of halo formation times and survival times. We also describe a Mon te Carlo method for constructing representative histories of merger ev ents leading to formation of haloes of a prescribed mass. Applying the se results to the age distribution of rich clusters of galaxies, we in fer that a high value of the density parameter (OMEGA0 greater than or similar to 0.5) is required to reproduce the substantial fraction of rich clusters that exhibit significant substructure, if such substruct ure only persists for a time 0. 2 t0 after a merger, where t0 is the p resent age of the universe. We also investigate the rate of infall of satellite galaxies into galactic discs, by combining our Monte Carlo t echnique for halo mergers with an estimate of the time required for dy namical friction to erode the orbits of the baryonic cores of the accr eted galaxies. We find that, even for OMEGA0 = 1, the infall rate is l ow (provided that the satellite orbits are not too eccentric), and tha t we would expect only a modest fraction of stellar discs to be thicke ned or disrupted by this process.