Chaos in the Test Particle Eccentric Kozai-Lidov Mechanism

TL;DR

This paper systematically analyzes the chaotic and quasiperiodic behaviors in the test particle limit of the Kozai-Lidov mechanism at the octupole level, revealing how resonances induce orbital flips and eccentricity excitation.

Contribution

It provides a detailed characterization of the parameter space for large eccentricity and inclination oscillations in the octupole-level Kozai-Lidov mechanism, highlighting chaos and resonance effects.

Findings

Resonances cause orbital flips between prograde and retrograde.

High mutual inclination leads to chaotic orbital evolution.

Parameter space for large eccentricity oscillations is mapped.

Abstract

The Kozai-Lidov mechanism can be applied to a vast variety of astrophysical systems involving hierarchical three-body systems. Here, we study the Kozai-Lidov mechanism systematically in the test particle limit at the octupole level of approximation. We investigate the chaotic and quasiperiodic orbital evolution by studying surfaces of section and the Lyapunov exponents. We find that the resonances introduced by the octupole level of approximation cause orbits to flip from prograde to retrograde and back as well as cause significant eccentricity excitation, and the chaotic behaviors occur when the mutual inclination between the inner and the outer binary is high. We characterize the parameter space that allows large amplitude oscillations in eccentricity and inclination.