Dynamical friction. II. The rate of escape of stars from clusters and the evidence for the operation of dynamical friction

Abstract

In this paper a general method is described for determining the rate of escape of stars from galactic and globular clusters which is based on certain general statistical principles. Essentially the method consists in reducing the problem to a boundary-value problem in partial differential equations and in making use of the interpretation of the stochastic process in the velocity space as a diffusion process of a rather general type. The rate of escape has been evaluated, first, ignoring dynamical friction, and, second, making due allowance for it. It appears that the rate of escape of stars predicted on the first basis is too rapid to be compatible with a life for galactic clusters even of the order of 5×10⁸ years. However, the rates of escape are drastically reduced when dynamical friction is allowed for and permits a time scale of the order of 3×10⁹ years. It is concluded that in the very existence of galactic clusters like the Pleiades we can look for direct evidence for the operation of dynamical friction which was predicted on theoretical grounds in the preceding paper.