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

Abstract

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.

arXiv comment11 pages, 14 figures;

References in corpus (8)

• A Survey of Stellar Families: Multiplicity of Solar-Type Stars
• Accelerating Compact Object Mergers in Triple Systems with the Kozai Resonance: A Mechanism for "Prompt" Type Ia Supernovae, Gamma-Ray Bursts, and Other Exotica
• Head-on collisions of white dwarfs in triple systems could explain type Ia supernova
• A class of symplectic integrators with adaptive timestep for separable Hamiltonian systems
• Type Ia Supernovae with Bi-Modal Explosions Are Common -- Possible Smoking Gun for Direct Collisions of White-Dwarfs
• The rate of WD-WD head-on collisions may be as high as the SNe Ia rate
• Stability criteria for hierarchical triple systems
• Extreme close approaches in hierarchical triple systems with comparable masses

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