Survival and disruption of subsystems during a cold collapse Free

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 under its own 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 a systematic study in two-parameter space: the number of the clumps N_c and the size of the clump r_v. We obtained the condition N_c ≫ 1 and n_k ≥ 1, where n_k is related to r_v and the initial radius of the cluster R_ini through the relation R_ini/r_v = 2N^(nk+5)/6_c. A simple analytical argument supports the numerical result. This n_k 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/Ωh²)Mpc, the first violent collapse is strong enough to sweep away all the substructures that exist before the collapse.