The E ect of Encounters on the Eccentricity of Binaries in Clusters Douglas

We derive analytical expressions for the change in the orbital eccentricity of a binary following a distant encounter with a third star on a hyperbolic or parabolic orbit. To establish the accuracy of these expressions, we present detailed comparisons with the results of direct numerical integrations of the equations of motion for the three bodies. We treat with particular care the di cult case of a binary with zero initial eccentricity. In this case, we show that the eccentricity e induced by the encounter declines in general as a power-law, e / (a=rp) , where a is the binary semi-major axis and rp is the periastron distance of the encounter. This power-law arises from the octupole-level secular perturbation of the binary. In contrast, non-secular quadrupolelevel perturbations induce an eccentricity change that declines exponentially with rp. These non-secular e ects can become dominant at su ciently small rp, for a su ciently high relative velocity, or for a su ciently massive perturber. We also derive cross sections for eccentricity change and compare our results with those of previous studies based on numerical scattering experiments. Our results have important implications for a number of astrophysical problems including, in particular, the evolution of binary millisecond pulsars in globular clusters.