Eccentricity pumping of a planet on an inclined orbit by a disc

TL;DR

This paper demonstrates that a disc's gravitational potential can significantly increase a planet's orbital eccentricity on inclined or crossing orbits, extending the Kozai effect and affecting planetary evolution.

Contribution

It introduces a new mechanism for eccentricity pumping of inclined planets via disc gravity, extending the classical Kozai effect to crossing orbits.

Findings

Eccentricity can be pumped up to high values by disc gravity.

The process depends on the initial inclination and disc mass distribution.

Planets can remain on eccentric orbits after disc dissipation.

Abstract

In this paper, we show that the eccentricity of a planet on an inclined orbit with respect to a disc can be pumped up to high values by the gravitational potential of the disc, even when the orbit of the planet crosses the disc plane. This process is an extension of the Kozai effect. If the orbit of the planet is well inside the disc inner cavity, the process is formally identical to the classical Kozai effect. If the planet's orbit crosses the disc but most of the disc mass is beyond the orbit, the eccentricity of the planet grows when the initial angle between the orbit and the disc is larger than some critical value which may be significantly smaller than the classical value of 39 degrees. Both the eccentricity and the inclination angle then vary periodically with time. When the period of the oscillations of the eccentricity is smaller than the disc lifetime, the planet may be left on an eccentric orbit as the disc dissipates.