Analytic modelling of binary-single encounters: non-thermal eccentricity distribution and gravitational-wave source formation

Chaotic three-body interactions may lead to the formation of gravitational-wave sources. Here, by modelling the encounter as a series of close non-hierarchical triple approaches, interspersed with hierarchical phases, in which the system consists of an inner binary and a star that orbits it, we compute the pericentre probability distribution, and thereby the in-spiral probability in any given binary-single encounter. We then consider the indirect influence of binary-single encounters on the population of gravitational-wave sources, by changing the eccentricity distribution of hard binaries in clusters; we calculate this distribution analytically, by requiring that it be invariant under interactions with single stars.