Extreme Eccentricities of Triple Systems: Analytic Results

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