The Eccentric Kozai Mechanism for a Test Particle

TL;DR

This paper explores how the eccentric Kozai mechanism causes test particles orbiting a star to flip their orbital direction and reach high eccentricities due to an eccentric exterior planet, significantly affecting dynamical evolution models.

Contribution

It introduces the eccentric Kozai mechanism (EKM), extending the standard Kozai mechanism to eccentric planetary orbits and mapping conditions for extreme orbital behavior.

Findings

EKM causes orbit flips and high eccentricities in test particles.

High planetary eccentricity increases likelihood of extreme orbital changes.

Approximately half of randomly oriented orbits flip and reach high eccentricity when planetary eccentricity exceeds a few percent of semi-major axis ratio.

Abstract

We study the dynamical evolution of a test particle that orbits a star in the presence of an exterior massive planet, considering octupole-order secular interactions. In the standard Kozai mechanism (SKM), the planet's orbit is circular, and so the particle conserves vertical angular momentum. As a result, the particle's orbit oscillates periodically, exchanging eccentricity for inclination. However, when the planet's orbit is eccentric, the particle's vertical angular momentum varies and its Kozai oscillations are modulated on longer timescales---we call this the eccentric Kozai mechanism (EKM). The EKM can lead to behavior that is dramatically different from the SKM. In particular, the particle's orbit can flip from prograde to retrograde and back again, and it can reach arbitrarily high eccentricities given enough time. We map out the conditions under which this dramatic behavior (flipping and extreme eccentricities) occurs, and show that when the planet's eccentricity is sufficiently high, it occurs quite generically. For example, when the planet's eccentricity exceeds a few percent of the ratio of semi-major axes (outer to inner), around half of randomly oriented test particle orbits will flip and reach extreme eccentricities. The SKM has often been invoked for bringing pairs of astronomical bodies (star-star, planet-star, compact-object pairs) close together. Including the effect of the EKM will enhance the rate at which such matchmaking occurs.