Extreme eccentricities of triple systems: Analytic results

Triple stars and compact objects are ubiquitously observed in nature. Their long-term evolution is complex; in particular, the von-Zeipel-Lidov-Kozai (ZLK) mechanism can potentially lead to highly eccentric encounters of the inner binary. Such encounters can lead to a plethora of interacting binary phenomena, as well as stellar and compact-object mergers. Here we find explicit analytical formulae for the maximal eccentricity, $e_{\rm max}$, of the inner binary undergoing ZLK oscillations, where both the test particle limit (parametrised by the inner-to-outer angular momentum ratio $η$) and the double-averaging approximation (parametrised by the period ratio, $ε_{\rm SA}$) are relaxed, for circular outer orbits. We recover known results in both limiting cases (either $η$ or $ε_{\rm SA} \to 0$) and verify the validity of our model using numerical simulations. We test our results with two accurate numerical N-body codes, $\texttt{Rebound}$ for Newtonian dynamics and $\texttt{Tsunami}$ for general-relativistic (GR) dynamics, and find excellent correspondence. We discuss the implications of our results for stellar triples and both stellar and supermassive triple black hole mergers.

No reviews yet.

No comments yet.