A statistical solution to the chaotic, non-hierarchical three-body problem.

Area of Science:

• Astrophysics
• Dynamical Systems
• Statistical Mechanics

Background:

• The three-body problem remains a centuries-old challenge in astrophysics, lacking a general analytic solution.
• Perturbation theory and numerical integrations offer partial solutions but struggle with non-hierarchical systems and chaotic dynamics.
• The chaotic nature prevents deterministic analytic solutions, yet suggests ergodicity.

Purpose of the Study:

• To develop a statistical solution for the non-hierarchical three-body problem using the ergodic hypothesis.
• To provide closed-form distributions for outcomes, such as binary orbital elements.
• To compare theoretical predictions with numerical integrations and identify key dynamical states.

Main Methods:

• Application of the ergodic hypothesis to the non-hierarchical three-body problem.
• Derivation of closed-form outcome distributions based on conserved integrals of motion.
• Comparison with large ensembles of numerical three-body integrations, focusing on resonant encounters.

Main Results:

• Good agreement found between statistical predictions and numerical integrations for chaotic, resonant encounters.
• Identification of 'scrambles' as the crucial dynamical state that leads to ergodicity in non-hierarchical triples.
• Prediction of generally super-thermal distributions for survivor binary eccentricity.

Conclusions:

• The ergodic hypothesis provides a viable statistical solution to the non-hierarchical three-body problem.
• The findings have significant implications for understanding astrophysical scenarios, including black-hole mergers.
• Accurate prediction of post-disintegration eccentricities is crucial for modeling gravitational wave events.