Abstract
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 explaining the mass–density relation shown by haloes in high-resolution cosmological simulations. In this model, major mergers are well separated from accretion, thereby allowing a natural definition of halo formation and destruction. This makes it possible to derive analytic expressions for halo formation and destruction rates, the mass accretion rate and the probability distribution functions of halo formation times and progenitor masses. The stochastic merger histories of haloes can be readily derived and easily incorporated 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 with the results of N-body simulations for several scale-free cosmologies.
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