BinarySingleStar Scattering. IV. Analytic Approximations and Fitting Formulae for Cross Sections and Reaction Rates
Abstract
An overview of research on the threebody scattering problem is presented. Emphasis is placed on stars with the same mass, and suitable random distributions of initial conditions, including eccentricity. The change in the binding energy of the binary is highlighted. The qualitative theoretical aspects of the problem, including the fundamental distinction between fast and slow encounters and also between wide and close encounters, are discussed. A simple seminumerical formula which can be used to calculate the probability of a given change in the binding energy of a binary, given the speed of the encounter, is provided. The results are applied to three aspects of binary interactions: the mean and mean square changes in the binding energy of a soft binary, the differential cross section for hard binaries, and the mean rate at which energy is generated by a mixture of single stars and hard binaries.
 Publication:

The Astrophysical Journal Supplement Series
 Pub Date:
 April 1993
 DOI:
 10.1086/191768
 Bibcode:
 1993ApJS...85..347H
 Keywords:

 Binary Stars;
 Celestial Mechanics;
 Gravitational Effects;
 Scattering Cross Sections;
 Stellar Gravitation;
 Three Body Problem;
 Adiabatic Conditions;
 Asymptotic Properties;
 Energy Conservation;
 FokkerPlanck Equation;
 Astrophysics;
 STARS: BINARIES: GENERAL;
 CELESTIAL MECHANICS;
 STELLAR DYNAMICS