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 compa re the predictions of the extended Press & Schechter (P&S) formalism w ith several conditional statistics of the protocluster matter: the mas s distribution and relative abundance of progenitor haloes at differen t redshifts, the infall rate of progenitors within the protocluster, t he formation redshift of the most massive cluster progenitor, and the accretion rates of other haloes on to it. The high duality of our simu lations allows an unprecedented resolution in the mass range of the st udied distributions. We also present the global mass function for the same cosmological model. We find that the P&S formalism and its extens ions 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 underpredict ing the number of high-mass progenitors at high redshift. Although the P&S formalism can provide a good qualitative description of the globa l evolution of hierarchical clustering, particular attention is needed when applying the theory to the mass distribution of progenitor objec ts at high redshift.