When do star clusters become multiple star systems? II. Toward a half-life formalism with four bodies

TL;DR

This paper introduces a half-life formalism to predict the disruption times and decay product distributions of gravitational four-body systems, validated through simulations and applicable to astrophysical contexts like black hole populations.

Contribution

It develops a novel half-life approach for four-body gravitational interactions, extending chaos theory analogies to larger N-body systems.

Findings

Half-lives predict decay product fractions accurately.

Good agreement between simulations and the half-life hypothesis.

Potential applications to black hole populations in clusters.

Abstract

We present a half-life formalism for describing the disruption of gravitationally-bound few-body systems, with a focus on binary-binary scattering. For negative total encounter energies, the four-body problem has three possible decay products in the point particle limit. For each decay product and a given set of initial conditions, we obtain directly from numerical scattering simulations the half-life for the distribution of disruption times. As in radioactive decay, the half-lives should provide a direct prediction for the relative fractions of each decay product. We test this prediction with simulated data and find good agreement with our hypothesis. We briefly discuss applications of this feature of the gravitational four-body problem to populations of black holes in globular clusters. This paper, the second in the series, builds on extending the remarkable similarity between gravitational chaos at the macroscopic scale and radioactive decay at the microscopic scale to larger-N systems.