A Simplified Model for the Secular Dynamics of Eccentric Discs and Applications to Planet-Disc Interactions

TL;DR

This paper introduces a simplified, computationally efficient model for analyzing the long-term eccentricity evolution of planets and discs in protoplanetary systems, aligning well with previous detailed simulations.

Contribution

The authors develop a linearized ODE-based model for secular planet-disc interactions that simplifies complex dynamics while maintaining accuracy, enabling faster long-term evolution studies.

Findings

Model reproduces behaviors from hydrodynamical simulations

Eccentricity excitation via secular resonance is influenced by disc dynamics

Eccentric disc effects can significantly alter planetary eccentricity evolution

Abstract

We develop a simplified model for studying the long-term evolution of giant planets in protoplanetary discs. The model accounts for the eccentricity evolution of the planets and the dynamics of eccentric discs under the influences of secular planet-disc interactions and internal disc pressure, self-gravity and viscosity. Adopting the ansatz that the disc precesses coherently with aligned apsides, the eccentricity evolution equations of the planet-disc system reduce to a set of linearized ODEs, which allows for fast computation of the evolution of planet-disc eccentricities over long timescales. Applying our model to "giant planet + external disc" systems, we are able to reproduce and explain the secular behaviours found in previously published hydrodynamical simulations. We re-examine the possibility of eccentricity excitation (due to secular resonance) of multiple planets embedded in a dispersing disc, and find that taking into account the dynamics of eccentric discs can significantly affect the evolution of the planets' eccentricities.