Binary--single-star scattering VI. Automatic Determination of Interaction Cross Sections

Abstract

Scattering encounters between binaries and single stars play a central role in determining the dynamical evolution of a star cluster. In addition, three-body scattering can give rise to many interesting exceptional objects: merging can produce blue stragglers; exchange can produce binaries containing millisecond pulsars in environments quite different from those in which the pulsars were spun up; various types of X-ray binaries can be formed, and their activity can be either shut off or triggered as a result of triple interactions. To date, all published results on three-body scattering have relied on human guidance for determining the correct parameter range for the envelope within which to perform Monte--Carlo scattering experiments. In this paper, we describe the first fully automatic determination of cross sections and reaction rates for binary--single-star scattering. Rather than relying on human inspection of pilot calculations, we have constructed a feedback system that ensures near-optimal coverage of parameter space while guaranteeing completeness. We illustrate our approach with a particular example, in which we describe the results of a three-body encounter between three main-sequence stars of different masses. We provide total cross sections, as well as branching ratios for the various different types of two-body mergers, three-body mergers, and exchanges, both non-resonant and resonant. The companion paper in this series, Paper VII, provides a full survey of unequal-mass three-body scattering for hard binaries in the point-mass limit.