On the migration of two planets in a disc and the formation of mean motion resonances

Abstract

We study the dynamics of a system of two super-Earths embedded in a protoplanetary disc. We build a simple model of an irradiated viscous disc and use analytical prescriptions for the planet-disc interactions which lead to migration. We show that depending on the disc parameters, planets' masses and their positions in the disc, the migration of each planet can be inward or outward and the migration of a two-planet system can be convergent (which may lead to formation of a first order mean motion resonance, MMR) or divergent (a system moves away from MMR). We performed $3500$ simulations of the migration of two-planet systems with various masses and initial orbits. Almost all of them end up as resonant configurations, although the period ratios may be very distant from the nominal values of a given MMR. We found that almost all the systems resulting from the migration are periodic configurations.

accepted to MNRAS, 12 pages, 10 figures

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• An exact, generalised Laplace resonance in the HR 8799 planetary system
• The role of dissipative evolution for three-planet, near-resonant extrasolar systems
• Migration of Planets Into and Out of Mean Motion Resonances in Protoplanetary Disks: Analytical Theory of Second-Order Resonances
• Long live the disk: lifetimes of protoplanetary disks in hierarchical triple star systems and a possible explanation for HD 98800 B
• Dynamics and Origins of the Near-Resonant Kepler Planets
• Migration of Planets Into and Out of Mean Motion Resonances in Protoplanetary Discs: Overstability of Capture and Nonlinear Eccentricity Damping
• Two Super-Earths in the 3:2 MMR around KOI-1599
• The origin and 9:7 MMR dynamics of the Kepler-29 system
• Radial migration of gap-opening planets in protoplanetary disks. II. The case of a planet pair
• On the migration of three planets in a protoplanetary disc and the formation of chains of mean motion resonances
• The formation of giant planets in wide orbits by photoevaporation-synchronised migration
• The architecture and formation of the Kepler-30 planetary system
• Period Ratio Sculpting Near Second-Order Mean-Motion Resonances
• A periodic configuration of the Kepler-25 planetary system?
• The PAIRS project: a global formation model for planets in binaries. I. Effect of disc truncation on the growth of S-type planets
• On the migration-induced formation of the 9:7 mean motion resonance