The Binding-Energy Distribution of the Binaries in a Star Cluster

Abstract

In order to study the development of the binding-energy distribution of hard binaries in a star cluster, solutions of the appropriate kinetic equation have been obtained, using the three-body encounter rates calculated by Heggie (1975). The binaries in a homogeneous, time-independent stellar medium are considered first. We calculate an analytical solution, of self-similar form, that can be applied to very hard binaries. Integrated forward in time from an initial state containing no hard binaries, a numerical solution of the kinetic equation rapidly approaches the equilibrium ‘Saha’ form of the energy distribution at small energies, while at high energies the numerical solution behaves like our analytical self-similar solution. The fluctuations in the distribution, due to the stochastic nature of binary creation and evolution, are analyzed. We calculate the rate of exchange encounters when stars of different masses are present; these rates are then combined with the other Heggie rates to find the binary distribution in a multi-mass environment. Next, the creation rate as a function of energy is obtained for the binaries that form in two-body, tidally dissipative encounters. This rate is combined with the three-body encounter rates to calculate how the energy distribution of the tidal binaries evolves. Finally, the binding-energy distribution of hard binaries is obtained in a more realistic inhomogeneous, time-dependent cluster model. Although the evolution of the cluster is governed primarily by the effects of two-body relaxation, the influence of the binaries on the cluster is considered as well. A detailed report of this study has been submitted to The Astronomical Journal.