Precollapse Evolution of Globular Clusters

Abstract

The dynamical evolution of a cluster in which N, the number of stars, is large, results primarily from encounters between pairs of stars; these tend to modify the system so that it approaches a more probable configuration. In statistical equilibrium, the distribution of stars among states of different energy, E_i, per unit mass would be determined to a first approximation by the probability P_i, where

$${P_i} \propto {g_i}\exp ( - B{E_i});$$

((1))

here g_i is the statistical weight of each state, proportional to the amount of phase space available, and B is a constant. Evidently dynamical evolution tends a) towards stellar states which are more tightly bound by their mutual gravitational attraction and have a correspondingly lower E_i, and b) towards the free state, where the volume of available phase space is very large. The only relatively stable state for an isolated cluster is one in which a central, non-evolving massive configuration (a compact object, or tight binary, or a hierarchical multiple system) has all the initial binding energy of the cluster and all other stars have escaped.