The binding-energy distribution of the binaries in a star cluster. I - Time-independent, homogeneous cluster models

Abstract

In order to study the development of the binding-energy distribution of the hard binaries in a star cluster, solutions of the appropriate kinetic equation have been obtained, using the three-body encounter rates of Heggie. The binaries in a homogeneous, time-independent stellar medium are considered in this paper. 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 multimass environment. Finally, 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.