MERGER RATES IN HIERARCHICAL-MODELS OF GALAXY FORMATION .2. COMPARISON WITH N-BODY SIMULATIONS

We have made a detailed comparison of the results of N-body simulation s with the analytical description of the merging histories of dark mat ter haloes presented in Lacey and Cole, which is based on an extension of the Press-Schechter method. We find the analytical predictions for the halo mass function, merger rates and formation times to be remark ably accurate. The N-body simulations used 128(3) particles and were o f self-similar clustering, with Omega = 1 and initial power spectra P( k) proportional to k(n), with spectral indices n = -2, -1, 0. The anal ytical model is, however, expected to apply for arbitrary Omega and mo re general power spectra. Dark matter haloes were identified in the si mulations using two different methods and at a range of overdensities. For haloes selected at mean overdensities -similar to 100-200, the an alytical mass function was found to provide a good fit to the simulati ons with a collapse threshold close to that predicted by the spherical collapse model, with a typical error of less than or equal to 30 per cent over a range of 10(3) in mass, which is the full dynamical range of our N-body simulations. This was insensitive to the type of filteri ng used. Over a range of 10(2)-10(3) in mass, there was also good agre ement with the analytical predictions for merger rates, including thei r dependence on the masses of the two haloes involved and the time int erval being considered, and for formation times, including the depende nce on halo mass and formation epoch. The analytical Press-Schechter m ass function and its extension to halo lifetimes and merger rates thus provide a very useful description of the growth of dark matter haloes through hierarchical clustering, and should provide a valuable tool i n studies of the formation and evolution of galaxies and galaxy cluste rs.