Testing the modified Press-Schechter model against N-body simulations

A modified version of the extended Press-Schechter model for the growth of dark-matter haloes was introduced in two previous papers, with the aim of e xplaining the mass-density relation shown by haloes in high-resolution cosm ological simulations. In this model, major mergers are well separated from accretion, thereby allowing a natural definition of halo formation and dest ruction. This makes it possible to derive analytic expressions for halo for mation and destruction rates, the mass accretion rate and the probability d istribution functions of halo formation times and progenitor masses. The st ochastic merger histories of haloes can be readily derived and easily incor porated into semi-analytical models of galaxy formation, thus avoiding the usual problems encountered in the construction of Monte Carlo merger trees from the original extended Press-Schechter formalism. Here we show that the , predictions of the modified Press-Schechter model are in good agreement w ith the results of N-body simulations for several scale-free cosmologies.