Growth of eccentric modes in disc-planet interactions

TL;DR

This paper develops a linear model to analyze how small eccentricities evolve in a disc-planet system, revealing conditions for mode growth and the influence of disc properties on eccentricity excitation.

Contribution

It introduces a comprehensive set of linear equations for eccentricity evolution in disc-planet systems, including 3D effects and mode growth analysis.

Findings

Inner disc modes can grow rapidly within system lifetime

Eccentricity can be excited through resonances and viscosity

Mode growth depends on disc properties and structure

Abstract

We formulate a set of linear equations that describe the behaviour of small eccentricities in a protoplanetary system consisting of a gaseous disc and a planet. Eccentricity propagates through the disc by means of pressure and self-gravity, and is exchanged with the planet via secular interactions. Excitation and damping of eccentricity can occur through Lindblad and corotation resonances, as well as viscosity. We compute normal modes of the coupled disc-planet system in the case of short-period giant planets orbiting inside an inner cavity, possibly carved by the stellar magnetosphere. Three-dimensional effects allow for a mode to be trapped in the inner parts of the disc. This mode can easily grow within the disc's lifetime. An eccentric mode dominated by the planet can also grow, although less rapidly. We compute the structure and growth rates of these modes and their dependence on the assumed properties of the disc.