The Effect of Encounters on the Eccentricity of Binaries in Clusters

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 difficult case of a binary with zero initial eccentricity. In this case, we show that the eccentricity $\delta e$ induced by the encounter declines in general as a power-law, \delta e\propto (a/\rp)^{5/2}, 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 quadrupole-level perturbations induce an eccentricity change that declines exponentially with \rp. These non-secular effects can become dominant at sufficiently small \rp, for a sufficiently high relative velocity, or for a sufficiently 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.Comment: final version with minor revisions, uses MNRAS TeX macros, 23 pages, to appear in MNRAS, also available from http://ensor.mit.edu/~rasio/papers

The density and drag of the accretion wake of a massive body moving through a uniform stellar distribution

We calculate the change in density within a uniform distribution of field stars (point masses) caused by a single massive body passing through with a constant velocity. Starting with the simplest case in which the field stars are initially stationary this leads to an infinite density wake behind the body. Introducing a small thermalisation within the field stars removes this infinity whilst leading to similar results off the path of the massive body. Results are in good agreement with those previously derived. An approximation can be made for the density in the thermalised case and this can be used to deduce the force exerted on the massive body due to the drag caused by the accretion wake