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

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.

43 pages including 14 figures; accepted for publication in The Astrophysical Journal

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• Analytical Treatment of Planetary Resonances
• Disk-planets interactions and the diversity of period ratios in Kepler's multi-planetary systems
• Condition for Capture into First-order Mean Motion Resonances and Application to Constraints on Origin of Resonant Systems
• Dynamical Evolution of Multi-Resonant Systems: the Case of GJ876
• An Analytic Criterion for Turbulent Disruption of Planetary Resonances
• Origin Scenarios for the Kepler 36 Planetary System
• Planetesimal and Protoplanet Dynamics in a Turbulent Protoplanetary Disk: Ideal Stratified Disks
• Mean motion resonance capture in the context of type-I migration
• Effects of Collisions with Rocky Planets on the Properties of Hot Jupiters
• On the dynamics of resonant super-Earths in disks with turbulence driven by stochastic forcing
• Mean Motion Resonances in Exoplanet Systems: An Investigation Into Nodding Behavior
• Running The Gauntlet -- Survival of Small Circumbinary Planets Migrating Through Destabilising Resonances
• On the migration of three planets in a protoplanetary disc and the formation of chains of mean motion resonances
• Sculpting the circumbinary planet size distribution through resonant interactions with companion planets
• On the Ages of Planetary Systems with Mean Motion Resonances
• The architecture and formation of the Kepler-30 planetary system
• Kepler-80 Revisited: Assessing the Participation of a Newly Discovered Planet in the Resonant Chain
• Tides Tighten the Hycean Habitable Zone
• Accretion of Rocky Planets by Hot Jupiters