Analytic Modelling of Binary-Single Encounters: Non-Thermal Eccentricity Distribution and Gravitational-Wave Source Formation

TL;DR

This paper develops an analytical model for binary-single star encounters, focusing on their impact on eccentricity distributions and the formation of gravitational-wave sources, providing insights into dynamical processes in star clusters.

Contribution

It introduces a novel analytical approach to model non-thermal eccentricity distributions resulting from binary-single encounters and their role in gravitational-wave source formation.

Findings

Derived the pericentre probability distribution for binary-single encounters.

Calculated the invariant eccentricity distribution of hard binaries in clusters.

Linked encounter dynamics to gravitational-wave source populations.

Abstract

Chaotic three-body interactions may lead to the formation of gravitational-wave sources. Here, by modelling the encounter as a series of close, non-hierarchical, triple approaches, interspersed with hierarchical phases, in which the system consists of an inner binary and a star that orbits it, we compute the pericentre probability distribution, and thereby the in-spiral probability in any given binary-single encounter. We then consider the indirect influence of binary-single encounters on the population of gravitational-wave sources, by changing the eccentricity distribution of hard binaries in clusters; we calculate this distribution analytically, by requiring that it be invariant under interactions with single stars.