A New Statistical Solution to the Chaotic Three-Body Problem

The three-body problem is arguably the oldest open question in astrophysics and has resisted a general analytic solution for centuries. Various forms of perturbation theory provide solutions in portions of parameter space, but only where hierarchies of masses and/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 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. I will briefly 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 dense star 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.

Nick Stone (Hebrew University)
Zoom Link: https://zoom.us/j/86426763198?pwd=S0d1Sm5NemFzWGpwZUlHazZldFVTdz09 Meeting ID: 864 2676 3198 Passcode: 689647
Kohei Inayoshi
Thursday, November 18, 2021 - 3:30PM to Thursday, November 18, 2021 - 4:30PM
I am a Senior Lecturer (US equivalent is Assistant Professor) at the Hebrew University of Jerusalem, and have been since 2019. Earlier in my career, I was a postdoctoral researcher and then Einstein Fellow at Columbia University in NYC (2013-2018). I did my PhD at Harvard University with Avi Loeb as my PhD advisor; before that, I did my undergraduate studies at Cornell University in Physics/Mathematics/Economics.