Dynamical disruption timescales and chaotic behavior of hierarchical triple systems

TL;DR

This study uses direct N-body simulations to analyze the stability and disruption timescales of hierarchical triple systems, revealing the significant influence of mutual inclination and chaotic dynamics on their stability.

Contribution

It provides an improved empirical stability criterion and disruption timescale estimates, emphasizing the role of mutual inclination and chaotic behavior in triple system dynamics.

Findings

Stability boundary is highly sensitive to mutual inclination.

Disruption timescales follow predicted scaling, especially at high outer eccentricity.

Retrograde coplanar triples are more stable than previously thought.

Abstract

We examine the stability of hierarchical triple systems using direct $N$-body simulations without adopting a secular perturbation approximation. We estimate their disruption timescales in addition to the mere stable/unstable criterion, with particular attention to the mutual inclination between the inner and outer orbits. First, we improve the fit to the dynamical stability criterion by \citet{Mardling1999,Mardling2001} widely adopted in the previous literature. Especially, we find that that the stability boundary is very sensitive to the mutual inclination; coplanar retrograde triples and orthogonal triples are much more stable and unstable, respectively, than coplanar prograde triples. Next, we estimate the disruption timescales of triples satisfying the stability condition up to $10^9$ times the inner orbital period. The timescales follow the scaling predicted by \citet{Mushkin2020}, especially at high $e_\mathrm{out}$ where their random walk model is most valid. We obtain an improved empirical fit to the disruption timescales, which indicates that the coplanar retrograde triples are significantly more stable than the previous prediction. We furthermore find that the dependence on the mutual inclination can be explained by the energy transfer model based on a parabolic encounter approximation. We also show that the disruption timescales of triples are highly sensitive to the tiny change of the initial parameters, reflecting the genuine chaotic nature of the dynamics of those systems.