Institute for Advanced Study Informal Astrophysics Seminar - Note Special Date

The general Newtonian three-body problem is notoriously resistant to analytic solution. Various implementations of perturbation theory provide analytic solutions in portions of parameter space, but only where hierarchies of masses or separations exist. Qualitatively, non-hierarchical three-body systems of Newtonian point particles will almost always disintegrate into a single escaping star and a stable, bound binary system. The chaotic nature of the three-body problem has prevented the derivation of tractable analytic formulae deterministically mapping initial conditions to final outcomes. However, chaos also motivates the assumption of thermodynamic ergodicity. Using this assumption, we derive a complete statistical solution to the non-hierarchical three-body problem, one which provides distributions of outcomes (e.g. binary and escaper orbital elements) given the conserved integrals of motion. We compare our closed form distributions to large ensembles of numerical three-body integrations, and find good agreement, so long as we restrict ourselves to "resonant" encounters (the ~50% of scatterings that do not resolve promptly). In analyzing our scattering experiments, we identify "scrambles" (periods in time where no pairwise binaries exist) as the key dynamical state that ergodicizes a three-body system. The generally super-thermal distributions of survivor binary eccentricity we predict have notable applications to astrophysical scenarios, such as the formation of gravitational wave sources in globular clusters.