Resonance Trapping in Protoplanetary Disks. I. Coplanar Systems

Abstract

Mean-motion resonances (MMRs) are likely to play an important role both during and after the lifetime of a protostellar gas disk. We study the dynamical evolution and stability of planetary systems containing two giant planets on circular orbits near a 2:1 resonance and closer. We find that by having the outer planet migrate inward, the two planets can capture into either the 2:1, 5:3, or 3:2 MMR. We use direct numerical integrations of ~1000 systems in which the planets are initially locked into one of these resonances and allowed to evolve for up to ~10^7 yr. We find that the final eccentricity distribution in systems which ultimately become unstable gives a good fit to observed exoplanets. Next, we integrate ~500 two-planet systems in which the outer planet is driven to continuously migrate inward, resonantly capturing the inner; the systems are evolved until either instability sets in or the planets reach the star. We find that although the 5:3 resonance rapidly becomes unstable under migration, the 2:1 and 3:2 are very stable. Thus the lack of observed exoplanets in resonances closer than 2:1, if it continues to hold up, may be a primordial signature of the planet formation process.

10 pages, 8 color figures. Accepted to the Astrophysical Journal. v2 - Added new figure, reflects accepted version

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• Retired A Stars and Their Companions VI. A Pair of Interacting Exoplanet Pairs Around the Subgiants 24 Sextanis and HD200964
• Hydrodynamic outcomes of planet scattering in transitional discs
• Relativistic Astrophysics with Resonant Multiple Inspirals
• Effects of an eccentric inner Jupiter on the dynamical evolution of icy body reservoirs in a planetary scattering scenario
• Confirming the 3:2 Resonance Chain of K2-138
• Resonant Trapping of Stars by Merging Massive Black Hole Binaries
• Relativistic Resonant Relations between Massive Black Hole Binary and Extreme Mass Ratio Inspiral
• On the orbital evolution of a pair of giant planets in mean motion resonance
• Detecting planet pairs in mean motion resonances via astrometry method