Analytic understanding of the resonant nature of Kozai Lidov Cycles with a precessing quadrupole potential

Abstract

The very long-term evolution of the hierarchical restricted three-body problem with a slightly aligned precessing quadrupole potential is studied analytically. This problem describes the evolution of a star and a planet which are perturbed either by a (circular and not too inclined) binary star system or by one other star and a second more distant star, as well as a perturbation by one distant star and the host galaxy or a compact-object binary system orbiting a massive black hole in non-spherical nuclear star clusters \citep{hamers2017,petrovich2017}. Previous numerical experiments have shown that when the precession frequency is comparable to the Kozai-Lidov time scale, long term evolution emerges that involves extremely high eccentricities with potential applications for a broad scope of astrophysical phenomena including systems with merging black holes, neutron stars or white dwarfs. By averaging the secular equations of motion over the Kozai-Lidov Cycles (KLCs) we solve the problem analytically in the neighborhood of the KLC fixed point where the eccentricity vector is close to unity and aligned with the quadrupole axis and for a precession rate similar to the Kozai Lidov time scale. In this regime the dynamics is dominated by a resonance between the perturbation frequency and the precession frequency of the eccentricity vector. While the quantitative evolution of the system is not reproduced by the solution far away from this fixed point, it sheds light on the qualitative behaviour.

5 pages, 2 figures

References in corpus (7)

• Secular chaotic dynamics in hierarchical quadruple systems, with applications to hot Jupiters in stellar binaries and triples
• Chaotic dynamics of wide triples induced by galactic tides: a novel channel for producing compact binaries, mergers, and collisions
• Enhanced Lidov-Kozai migration and the formation of the transiting giant planet WD1856+534b
• Formation and merging of Mass Gap Black Holes in Gravitational Wave Merger Events from Wide Hierarchical Quadruple Systems
• Kozai Migration Naturally Explains the White Dwarf Planet WD1856b
• Chaotic quadruple secular evolution and the production of misaligned exomoons and Warm Jupiters in stellar multiples
• Was GW190412 born from a hierarchical 3+1 quadruple configuration?

Cited by in corpus (4)

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• Short-Range Forces Can Catalyze Extreme Orbital Evolution in Hierarchical Triples
• The evolution of a supermassive binary black hole in an non-spherical nuclear star cluster