Testing the Flux-based statistical prediction of the Three-Body Problem

TL;DR

This paper rigorously tests flux-based statistical predictions for three-body systems by analyzing one million simulations, confirming the theory's high accuracy in predicting escape probabilities, exponents, and distributions.

Contribution

It provides the first high-precision validation of flux-based three-body statistical theory against extensive numerical simulations.

Findings

Escape probabilities match theoretical predictions within 1%.

Characteristic exponents agree with flux-based predictions.

Measured distributions support the validity of the statistical formalism.

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 analyze 1 million realizations for each different initial condition considering equal and unequal mass three-body systems to provide high accuracy statistics. We measure 4 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% 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.