Stability of hierarchical triples comprising a central massive body and a tight binary: the effect of inner and outer eccentricities on the binary breakup condition

TL;DR

This paper investigates the stability of hierarchical triple systems with a central massive body and a tight binary, focusing on how inner and outer eccentricities influence the binary's breakup condition, using extensive N-body simulations.

Contribution

It provides an improved Hill-type stability criterion that accounts for eccentricities, mutual inclination, mass ratios, and breakup timescales, based on long-term N-body simulations.

Findings

Derived an empirical formula for binary breakup conditions.

Demonstrated the impact of eccentricities on stability.

Extended stability analysis to longer timescales.

Abstract

We explore the stability of gravitational triple systems comprising a central massive body and a tight binary of less massive pairs. In the present paper, we focus on improving the Hill-type stability criterion for the binary in those systems, with particular attention to the effects of the eccentricities of the inner and outer orbits. We perform direct Newtonian N-body simulations over much longer integration times than previous studies, which is essential to determine the stability and breakup timescale distributions of those systems in a reliable fashion. As a result, we obtain an empirical fitting formula of the binary breakup condition that incorporates effects of the inner and outer eccentricities, the mutual inclination of the inner and outer orbits, the mass ratios of the three bodies, and the breakup timescale.