Dynamical Friction. III. A more exact theory of the rate of escape of stars from clusters

Abstract

A more exact estimate of the rate of escape of stars from clusters is made than in an earlier paper by properly allowing for the dependence of the coefficient of dynamical friction on the velocity. It is found that the probability that a star will have acquired the necessary velocity of escape (assumed to be equal to twice the root mean square velocity of the stars in the system) in a time κ (measured in units of the time of relaxation of the system) is given by Q(κ)=(1-e^-O.0075κ). On this basis, half-lives for galactic clusters of the order of 3×10⁹ years are provided for, and it is further concluded that dynamical friction provides the principal mechanism for the continued existence of galactic clusters like the Pleiades for times of the order of 3×10⁹ years.