http://arxiv.org/abs/2303.13579
The very long-term evolution of the hierarchical restricted three-body problem with a precessing quadruple 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{arXiv:1705.02334v2, arXiv:1705.05848v2}. 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. We show that a central ingredient of the dynamics is a resonance between the perturbation frequency and the precession frequency of the eccentricity vector in the regime where the eccentricity vector, the precession axis and the quadruple direction are closely aligned. By averaging the secular equations of motion over the Kozai-Lidov Cycles we solve the problem analytically in this regime.
Y. Klein and B. Katz
Mon, 27 Mar 23
9/59
Comments: 5 pages, 2 figures