The Effect of Encounters on the Eccentricity of Binaries in Clusters
Abstract
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, deltae~(a/r_p)^5/2, where a is the binary semimajor axis and r_p is the periastron distance of the encounter. This power law arises from the octupolelevel secular perturbation of the binary. In contrast, nonsecular quadrupolelevel perturbations induce an eccentricity change that declines exponentially with r_p. These nonsecular effects can become dominant at sufficiently small r_p, for a sufficiently high relative velocity, or for a sufficiently massive perturber. We also derive crosssections 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.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 October 1996
 DOI:
 10.1093/mnras/282.3.1064
 arXiv:
 arXiv:astroph/9506082
 Bibcode:
 1996MNRAS.282.1064H
 Keywords:

 CELESTIAL MECHANICS;
 STELLAR DYNAMICS;
 BINARIES: CLOSE;
 PULSARS: GENERAL;
 GLOBULAR CLUSTERS: GENERAL;
 Astrophysics
 EPrint:
 final version with minor revisions, uses MNRAS TeX macros, 23 pages, to appear in MNRAS, also available from http://ensor.mit.edu/~rasio/papers/