Dissipation in planar resonant planetary systems

TL;DR

This paper presents an analytical model explaining why many Kepler-detected close-in planetary pairs are just outside mean-motion resonances, showing that dissipation causes these systems to appear resonant but are actually non-resonant.

Contribution

The authors develop a low-eccentricity analytical model for dissipation in resonant planetary systems, clarifying the origin of observed period ratio distributions and the apparent libration of resonant angles.

Findings

Dissipation explains the excess of near-resonant pairs observed by Kepler.

Final planetary pairs are non-resonant, with no separatrices in the dissipative phase space.

Apparent libration of resonant angles is due to damping of secular eigenmodes.

Abstract

Close-in planetary systems detected by the Kepler mission present an excess of periods ratio that are just slightly larger than some low order resonant values. This feature occurs naturally when resonant couples undergo dissipation that damps the eccentricities. However, the resonant angles appear to librate at the end of the migration process, which is often believed to be an evidence that the systems remain in resonance. Here we provide an analytical model for the dissipation in resonant planetary systems valid for low eccentricities. We confirm that dissipation accounts for an excess of pairs that lie just aside from the nominal periods ratios, as observed by the Kepler mission. In addition, by a global analysis of the phase space of the problem, we demonstrate that these final pairs are non-resonant. Indeed, the separatrices that exist in the resonant systems disappear with the dissipation, and remains only a circulation of the orbits around a single elliptical fixed point. Furthermore, the apparent libration of the resonant angles can be explained using the classical secular averaging method. We show that this artifact is only due to the severe damping of the amplitudes of the eigenmodes in the secular motion.