On formation of close binaries by two-body tidal capture

Abstract

We calculate in detail the two-body tidal capture mechanism of Fabian, Pringle, and Rees: when two unbound stars have a close encounter, they may become bound by the energy that each deposits into nonradial oscillations of the other. After dimensional scalings are removed, the process depends only on a single dimensionless parameter, and on the dimensionless envelope structure of the stars. General formulae are derived; for definiteness, we apply them to the specific case of stars with an n = 3 polytropic structure. Capture cross sections as a function of velocity and capture rates for an isothermal distribution are given for the case of equal-mass stars; other cases can easily be computed from the formulae given.