Statistics of N-Body Simulations. II. Equal Masses after Core Collapse

Abstract

This paper presents and analyses statistical results from a large number of $N$-body simulations of isolated systems with equal masses, in which $250\le N\le 2000$. It concentrates on the phase starting around the end of core collapse, when binaries start to play a crucial role. Interactions of hard binaries are consistent with the Spitzer (1987) cross section. The evolution of the half-mass radius after core collapse nearly follows classical theory, The evolution of the inner parts of the system around the time of core bounce is consistent with these simplified models provided that the continuous production of energy, as usually assumed, is replaced by a model of {\sl stochastic} energy production. Similarly, post-collapse evolution of the core requires a modest recalibration of the coefficient of energy generation, especially for small $N$. The distributions of velocity dispersion and anisotropy become remarkably homologous soon after core bounce. The bound mass of the systems very nearly follows a power law with time. A small number of escapers, presumed to be those associated with binary activity, dominate the energy which is carried off. The ``internal" energy of escaping binaries is consistent with theoretical expectations.