THE EFFECT OF ENCOUNTERS ON THE ECCENTRICITY OF BINARIES IN CLUSTERS

We derive analytical expressions for the change in the orbital eccentr icity of a binary following a distant encounter with a third star on a hyperbolic or parabolic orbit. To establish the accuracy of these exp ressions, we present detailed comparisons with the results of direct n umerical integrations of the equations of motion for the three bodies. We treat with particular care the difficult case of a binary with zer o initial eccentricity. In this case, we show that the eccentricity de lta e induced by the encounter declines in general as a power law, del ta e proportional to (a/r(p))(5/2), where a is the binary semi-major a xis and r(p) is the periastron distance of the encounter. This power l aw arises from the octupole-level secular perturbation of the binary. In contrast, non-secular quadrupole-level perturbations induce an ecce ntricity change that declines exponentially with r(p). These non-secul ar effects can become dominant at sufficiently small r(p), for a suffi ciently high relative velocity, or for a sufficiently massive perturbe r. We also derive cross-sections for eccentricity change and compare o ur results with these of previous studies based on numerical scatterin g experiments. Our results have important implications for a number of astrophysical problems including, in particular, the evolution of bin ary millisecond pulsars in globular clusters.