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, Ei, per unit mass would be determined to a first approximation by the probability Pi, where here gi 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 Ei, 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.