### 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 δe induced by the encounter declines in general as a power law, δe α (a/r_{p})^{5/2}, where a is the binary semi-major axis and r_{p} 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 r_{p}. These non-secular effects can become dominant at sufficiently small r_{p}, 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.

Original language | English (US) |
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Pages (from-to) | 1064-1084 |

Number of pages | 21 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 282 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1996 |

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### Keywords

- Binaries: close
- Celestial mechanics, stellar dynamics
- Globular clusters: general
- Pulsars: general

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Monthly Notices of the Royal Astronomical Society*,

*282*(3), 1064-1084. https://doi.org/10.1093/mnras/282.3.1064