Testing the flux-based statistical prediction of the three-body problem
Abstract
We present an extensive comparison between the statistical properties of non-hierarchical three-body systems and the corresponding three-body theoretical predictions. We perform and analyse 1 million realizations for each different initial condition considering equal and unequal mass three-body systems to provide high-accuracy statistics. We measure four quantities characterizing the statistical distribution of ergodic disintegrations: escape probability of each body, the characteristic exponent for escapes by a narrow margin, predicted absorptivity as a function of binary energy and binary angular momentum, and, finally, the lifetime distribution. The escape probabilities are shown to be in agreement down to the 1 per cent level with the emissivity-blind flux-based theoretical prediction. This represents a leap in accuracy compared to previous three-body statistical theories. The characteristic exponent at the threshold for marginally unbound escapes is an emissivity-independent flux-based prediction, and the measured values are found to agree well with the prediction. We interpret both tests as strong evidence for the flux-based three-body statistical formalism. The predicted absorptivity and lifetime distributions are measured to enable future tests of statistical theories.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- September 2021
- DOI:
- 10.1093/mnras/stab1689
- arXiv:
- arXiv:2101.03661
- Bibcode:
- 2021MNRAS.506..692M
- Keywords:
-
- chaos;
- gravitation;
- celestial mechanics;
- planets and satellites: dynamical evolution and stability;
- Astrophysics - Earth and Planetary Astrophysics;
- Astrophysics - Solar and Stellar Astrophysics;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 17 pages, 11 figures