A New Statistical Solution to the Chaotic Three-Body Problem
by Dr. Nick Stone
at Astrophysics and Cosmology Seminar
Wed, 06 May 2020, 11:00
Sacta-Rashi Building for Physics (54), room 207
The three-body problem is arguably the oldest open question in astrophysics and has resisted a general analytic solution for centuries. Various implementations of perturbation theory provide solutions in portions of parameter space, but only where hierarchies of masses or separations exist. Numerical integrations show that bound, non-hierarchical triple systems of Newtonian point particles will almost always disintegrate into a single escaping star and a stable bound binary, but the chaotic nature of the three-body problem prevents the derivation of tractable analytic formulae that deterministically map initial conditions to final outcomes. Chaos, however, also motivates the assumption of ergodicity. I will present a new statistical solution to the non-hierarchical three-body problem that is derived using the ergodic hypothesis and that provides closed-form distributions of outcomes (for example, binary orbital elements) when given the conserved integrals of motion. We compare our outcome distributions to large ensembles of numerical three-body integrations and find good agreement, so long as we restrict ourselves to "resonant" encounters (the roughly 50% of scatterings that undergo chaotic evolution). In analysing our scattering experiments, we identify "scrambles" (periods of time in which no pairwise binaries exist) as the key dynamical state that ergodicizes a non-hierarchical triple system. Finally, I will discuss how the generally super-thermal distributions of survivor binary eccentricity that we predict have applications to many astrophysical scenarios. For example, non-hierarchical triple systems produced dynamically in globular clusters are a primary formation channel for black-hole mergers, but the rates and properties of the resulting gravitational waves depend on the distribution of post-disintegration eccentricities.
Created on 04-05-2020 by Zitrin, Adi (zitrin)
Updaded on 04-05-2020 by Zitrin, Adi (zitrin)