Evolution of binaries in the field of light particles and the problem of two black holes

Abstract

Numerical experiments in the framework of the elliptic restricted three-body problem have been applied to obtain the effects of dynamical friction on the evolution of a binary in the field of light particles. We derive rate coefficients for the evolution of the energy and angular momentum of the heavy binary. The results are compared with an N-body simulation and also with recent theoretical estimates for the case of high-velocity particles. Good agreement is observed in all the comparisons. The angular momentum transfer rate allows us to estimate the evolution of the eccentricity of the binary. A fast increase occurs if the particle velocities are very small, but for moderate and large velocities the eccentricity is virtually unaffected. Application of the results to the motion of black hole binaries in galactic centers is discussed.