Dynamical Disruption Timescales and Chaotic Behavior of Hierarchical Triple Systems

Abstract

We examine the stability of hierarchical triple systems using direct N-body simulations without adopting a secular perturbation assumption. 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 Mardling & Aarseth 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 109 times the inner orbital period. The timescales follow the scaling predicted by Mushkin & Katz, especially at high e 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 tiny changes of the initial parameters, reflecting the genuine chaotic nature of the dynamics of those systems.

A Stability Timescale for Nonhierarchical Three-body Systems

“…The stability of three massive objects has a generalized, hierarchy-based stability condition often used in the literature (e.g., Mardling & Aarseth 2001), and similar stable-unstable boundaries were derived by Eggleton & Kiseleva (1995), Petrovich (2015), Tory et al (2022), Vynatheya et al (2022), and Hayashi et al (2022). Considering hierarchical systems, where one mass orbits on a tight configuration about the primary and a tertiary is on a wider orbit, a condition is often used to estimate the long-term stability against high-eccentricity excitations due to secular dynamics (e.g., Ivanov et al 2005;Lithwick & Naoz 2011;Katz & Dong 2012;Antonini et al 2014;Bode & Wegg 2014;Naoz & Silk 2014) and nonsecular perturbations to secular dynamics (e.g., Antognini et al 2014;Luo et al 2016;Grishin et al 2018;Bhaskar et al 2020).…”

“…Additionally, Mushkin & Katz (2020) developed a stability timescale for the outer orbit in hierarchical systems, based on formulae for secular energy exchange (e.g., Roy & Haddow 2003). Further studies on the time-dependence of stability were done by Hayashi et al (2022Hayashi et al ( , 2023, using N-body simulations of mildly hierarchical triples.…”

Constraining the Binarity of Black Hole Candidates: A Proof-of-concept Study of Gaia BH1 and Gaia BH2

“…In order to predict the short-term RV modulations for Gaia BH1 and Gaia BH2 more quantitatively, we perform threebody simulations using TSUNAMI (see Trani & Spera 2023). The details of the procedure are described in , ), and Hayashi et al (2022.…”

“…Condition (6) turned out to be a good approximation for coplanar triples (i mut = 0°). Hayashi et al (2022Hayashi et al ( , 2023 examined the Lagrange stability timescales of triples in general and found that condition (6) needs to be improved especially for inclined triples that exhibit the ZKL oscillations.…”

Quadruple-star systems are not always nested triples: a machine learning approach to dynamical stability

“…Lalande & Trani (2022) trained a convolutional neural network on a limited time series of orbital parameters to predict the long-term stability of triples. Hayashi et al (2022b) conducted a detailed study on the disruption timescales of triples, rather than just classifying them as stable or unstable. Tory et al (2022) came up with an updated triple-stability criterion which takes into account the varying dependence on outer mass ratio.…”