Testing the flux-based statistical prediction of the three-body problem. Issue 1 (12th June 2021)

• Record Type: Journal Article
• Authors: Manwadkar, Viraj; Kol, Barak; Trani, Alessandro A; Leigh, Nathan W C
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 506:Issue 1(2021)
• Page Start: 692
• Page End: 708
• Publication Date: 2021-06-12
• Subjects: chaos -- gravitation -- celestial mechanics -- planets and satellites: dynamical evolution and stability; Astronomy -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnras/stab1689
• Languages: English
• ISSNs: 0035-8711

Abstract

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.