Three-body capture, ejection, and the demographics of bound objects in binary systems

TL;DR

This paper develops a geometric framework to analyze the capture and ejection of objects in binary systems, providing insights into their orbital distributions, lifetimes, and implications for dark matter populations.

Contribution

It introduces a simple geometric model for capture cross sections and ejection rates in binary systems, extending previous solar system studies to a broader context.

Findings

Derived a geometric characterization of capture cross sections.

Provided a closed-form estimate for ejection rates matching numerical results.

Applied the framework to estimate dark matter populations in binaries.

Abstract

We study the capture of light objects of arbitrary velocity by binary systems. Extending results for the capture of comets in the solar system, we develop a simple geometric characterization of the capture cross section, leading directly to the distribution of orbital parameters of captured objects. We use the same framework to study the lifetimes of these bound orbits prior to ejection, and find that a simplified version of the \"Opik--Arnold approach readily yields a closed-form estimate for the ejection rate that agrees well with numerical experiments. Without any detailed-balance assumptions, our results make manifest the characteristics of close encounters leading to capture and ejection. As an application of our results, we demonstrate the estimation of the equilibrium population of captured dark matter particles in a binary system.