Effects of Turbulence, Eccentricity Damping, and Migration Rate on the Capture of Planets into Mean Motion Resonance

TL;DR

This study investigates how turbulence, eccentricity damping, and migration rate influence the likelihood of extrasolar planets capturing into mean motion resonance during convergent migration, using both numerical simulations and semi-analytic models.

Contribution

It provides a detailed analysis of the factors affecting resonance capture probability, highlighting the roles of turbulence and damping in planetary migration models.

Findings

Resonance capture probability decreases with higher migration rates.

Turbulence reduces the likelihood of resonance locking.

Eccentricity damping increases the chance of resonance capture.

Abstract

Pairs of migrating extrasolar planets often lock into mean motion resonance as they drift inward. This paper studies the convergent migration of giant planets (driven by a circumstellar disk) and determines the probability that they are captured into mean motion resonance. The probability that such planets enter resonance depends on the type of resonance, the migration rate, the eccentricity damping rate, and the amplitude of the turbulent fluctuations. This problem is studied both through direct integrations of the full 3-body problem, and via semi-analytic model equations. In general, the probability of resonance decreases with increasing migration rate, and with increasing levels of turbulence, but increases with eccentricity damping. Previous work has shown that the distributions of orbital elements (eccentricity and semimajor axis) for observed extrasolar planets can be reproduced by migration models with multiple planets. However, these results depend on resonance locking, and this study shows that entry into -- and maintenance of -- mean motion resonance depends sensitively on migration rate, eccentricity damping, and turbulence.