1 research outputs found
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, , of the inner binary
undergoing ZLK oscillations, where both the test particle limit (parametrised
by the inner-to-outer angular momentum ratio ) and the double-averaging
approximation (parametrised by the period ratio, ) are
relaxed, for circular outer orbits. We recover known results in both limiting
cases (either or ) and verify the validity of
our model using numerical simulations. We test our results with two accurate
numerical N-body codes, for Newtonian dynamics and
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