The assembly of matter in galaxy clusters

We study the merging history of dark matter haloes that end up in rich clusters, using N-body simulations of a scale-free universe. We compare the predictions of the extended Press & Schechter (P&S) formalism with several conditional statistics of the protocluster matter: the mass distribution and relative abundance of progenitor haloes at different redshifts, the infall rate of progenitors within the protocluster, the formation redshift of the most massive cluster progenitor, and the accretion rates of other haloes on to it. The high quality of our simulations allows an unprecedented resolution in the mass range of the studied distributions. We also present the global mass function for the same cosmological model. We find that the P&S formalism and its extensions cannot simultaneously describe the global evolution of clustering and its evolution in a protocluster environment. The best-fitting P&S model for the global mass function is a poor fit to the statistics of cluster progenitors. This discrepancy is in the sense of underpredicting the number of high-mass progenitors at high redshift. Although the P&S formalism can provide a good qualitative description of the global evolution of hierarchical clustering, particular attention is needed when applying the theory to the mass distribution of progenitor objects at high redshift.