Orbital evolution of a planet on an inclined orbit interacting with a disc

TL;DR

This paper investigates how inclined planets interact with protoplanetary discs, revealing that gravitational and frictional forces can cause Kozai cycles, affecting orbital alignment and eccentricity over disc lifetimes.

Contribution

It demonstrates the role of Kozai cycles and damping forces in the orbital evolution of inclined planets, highlighting mass-dependent outcomes for planet-disc interactions.

Findings

Kozai cycles induce high eccentricity and inclination oscillations.

Frictional forces dampen inclination and eccentricity over time.

Mass determines whether planets align and circularize or remain inclined.

Abstract

We study the dynamics of a planet on an orbit inclined with respect to a disc. If the initial inclination of the orbit is larger than some critical value, the gravitational force exerted by the disc on the planet leads to a Kozai cycle in which the eccentricity of the orbit is pumped up to large values and oscillates with time in antiphase with the inclination. On the other hand, both the inclination and the eccentricity are damped by the frictional force that the planet is subject to when it crosses the disc. We show that, by maintaining either the inclination or the eccentricity at large values, the Kozai effect provides a way of delaying alignment with the disc and circularization of the orbit. We find the critical value to be characteristically as small as about 20 degrees. Typically, Neptune or lower mass planets would remain on inclined and eccentric orbits over the disc lifetime, whereas orbits of Jupiter or higher mass planets would align and circularize. This could play a significant role in planet formation scenarios.