Survival and disruption of subsystems during a cold collapse

Cold collapse of a cluster composed of small identical clumps, each of which is in virial equilibrium, is considered. Since the clumps have no relative motion with respect to each other initially, the cluster collapses by its gravity. At the first collapse of the cluster, most of the clumps are destroyed, but some survive. In order to find the condition for the clumps to survive, we made systematic study in two-parameter space: the number of the clumps Nc and the size of the clump rv. We obtained the condition, Nc ≫ 1 and nk ≥ 1, where nk is related to rv and the initial radius of the cluster Rini through the relation Rini/rv = 2N (nk+5)/6 c . A simple analytic argument supports the numerical result. This nk corresponds to the index of the power spectrum of the density fluctuation in the cosmological hierarchical clustering, and thus our result may suggest that in the systems smaller than 2/(Ωh)Mpc, the first violent collapse is strong enough to sweep away all substructures which exist before the collapse.