Statistical Solution to the 3-Body Problem, and Dynamical Formation of Gravitational-Wave Sources

Chaotic three-body interactions are a dynamical pathway of gravitational-wave source production. Any such encounter terminates when one of the three stars is ejected to infinity, leaving behind a remnant binary; the problem of binary-single star-scattering consists of finding the probability distribution of the orbital parameters of the remnant binary, as a function of the total energy and the total angular momentum. We model 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 -- this turns the evolution of the entire encounter to a random walk between consecutive hierarchical phases. We generalise the study to account for dissipative processes, such as tides and gravitational-wave emission. Our solution can reproduce the results of the extensive body of past
numerical simulations.