Survival and disruption of subsystems during cold collapse

Cold collapse of a cluster consisting of small identical clumps, each of which is in equilibrium, is considered. At the beginning the clumps have no relative motion, and then the cluster collapses by its gravity. At the first collapse most of the clumps are destroyed, but some clumps survive. From numerical simulations, we obtained a empirical condition of the number and the size of the clumps for survival. A simple analytic estimate agree with the numerical result. When it is applied to cosmological clustering, the condition suggests that many of the first collapsed objects which are formed from the density fluctuation with the power spectrum index nk ≥ −1 survive if many objects collapse simultaneously.