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We study the capture of light objects of arbitrary velocity by binarysystems. Extending results for the capture of comets in the solar system, wedevelop 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 toejection, and find that a simplified version of the \"Opik--Arnold approachreadily yields a closed-form estimate for the ejection rate that agrees wellwith numerical experiments. Without any detailed-balance assumptions, ourresults make manifest the characteristics of close encounters leading tocapture and ejection. As an application of our results, we demonstrate theestimation of the equilibrium population of captured dark matter particles in abinary system.

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