Migration of two massive planets into (and out of) first order mean motion resonances

TL;DR

This study investigates how two massive planets can temporarily enter and exit first order mean motion resonances during migration, influenced by eccentricity damping and mass ratios, affecting observed planetary configurations.

Contribution

It introduces a generalized model showing the dependence of resonance overstability on planetary mass ratios and damping timescales, and discusses implications for observed exoplanet distributions.

Findings

Resonance overstability depends on mass ratio and damping timescales.

Escape from resonance can be long, making planets likely to be observed in resonance.

Overstability alone cannot explain the scarcity of Kepler planet pairs near resonances.

Abstract

We consider the dynamical evolution of two planets orbiting in the vicinity of a first order mean motion reso- nance while simultaneously undergoing eccentricity damping and convergent migration. Following Goldreich & Schlichting (2014), we include a coupling between the dissipative semimajor axis evolution and the damping of the eccentricities. In agreement with past studies, we find that this coupling can lead to overstability of the resonance and that for a certain range of parameters capture into resonance is only temporary. Using a more general model, we show that whether overstable motion can occur depends in a characteristic way on the mass ratio between the two planets as well as their relative eccentricity damping timescales. Moreover, we show that even when escape from resonance does occur, the timescale for escape is long enough such at any given time a pair of planets is more likely to be found in a resonance rather than migrating between them. Thus, we argue that overstability of resonances cannot singlehandedly reconcile convergent migration with the observed lack of Kepler planet pairs found near resonances. However, it is possible that overstable motion in combination with other effects such as large scale orbital instability could produce the observed period ratio distribution.