Binary-single star scattering. II - Analytic approximations for high velocity

Binary-single star scattering is discussed in the asymptotic limit of high field-star energies, extending Heggie's (1975) analysis for soft binaries where necessary to interpret the numerical results of Hut and Bahcall (1983). Different regimes of analytic approximations are discussed, and previous results by Heggie are compared with data from Hut and Bahcall. Differential cross sections are derived with respect to energy exchange between binary and field star, using an impulsive approximation. This analysis is given for arbitrary eccentricity of the initial binary orbit. Flyby scattering and ionization is treated for the case of a field star which does not disrupt the binary and after the encounter travels to infinity and for the case where all three stars become unbounded. Exchange scattering, where the incoming star is captured by one of the old binary members to form a new binary, forcing the third star to escape, is treated. Total cross sections are derived for both exchange scattering and ionization.