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.

arXiv comment5 pages, 2 figures

References in corpus (18)

• Shrinking binary and planetary orbits by Kozai cycles with tidal friction
• The Eccentric Kozai-Lidov Effect and Its Applications
• Hot Jupiters from Secular Planet--Planet Interactions
• Secular evolution of compact binaries near massive black holes: gravitational wave sources and other exotica
• Accelerating Compact Object Mergers in Triple Systems with the Kozai Resonance: A Mechanism for "Prompt" Type Ia Supernovae, Gamma-Ray Bursts, and Other Exotica
• Long-Term Cycling of Kozai-Lidov Cycles: Extreme Eccentricities and Inclinations Excited by a Distant Eccentric Perturber
• Greatly enhanced merger rates of compact-object binaries in non-spherical nuclear star clusters
• Enhanced Black-Hole Mergers in Binary-Binary Interactions
• Greatly Enhanced Eccentricity Oscillations in Quadruple Systems Composed of Two Binaries: Implications for Stars, Planets, and Transients
• Secular chaotic dynamics in hierarchical quadruple systems, with applications to hot Jupiters in stellar binaries and triples
• Dynamics of Quadruple Systems Composed of Two Binaries: Stars, White Dwarfs, and Implications for Ia Supernovae
• 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?
• Compact-Object Mergers in the Galactic Center: Evolution in Triaxial Clusters

Cited by in corpus (4)

• Irregular Fixation: I. Fixed points and librating orbits of the Brown Hamiltonian
• Librating Kozai-Lidov Cycles with a Precessing Quadrupole Potential are Analytically Approximately Solved
• 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