A simple random walk model explains the disruption process of hierarchical, Eccentric three-body systems
Jonathan Mushkin, Boaz Katz
Abstract
ABSTRACT We study the disruption process of hierarchical three-body systems with bodies of comparable mass. Such systems have long survival times that vary by orders of magnitude depending on the initial conditions. By comparing with three-body numerical integrations, we show that the evolution and disruption of such systems can be statistically described as a simple random walk process in the outer orbit’s energy, where the energy exchange per pericenter passage (step size) is calculated from the initial conditions. In our derivation of the step size, we use previous analytic results for parabolic encounters, and average over the (Kozai–Lidov) oscillations in orbital parameters, which are faster then the energy diffusion time-scale. While similar random walk models were studied before, this work differs in two manners: (a) this is the first time that the Kozai–Lidov averaged step size is derived from first principles and demonstrated to reproduce the statistical evolution of numerical ensembles without fitting parameters, and (b) it provides a characteristic lifetime, instead of answering the binary question (stable/unstable), set by case-specific criteria.