A Simple Random-Walk Model Explains the Disruption Process of Hierarchical, Eccentric 3-Body Systems

We study the disruption process of hierarchical 3-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 3-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 timescale. 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 life-time, instead of answering the binary question (stable/unstable), set by case-specific criteria.