RESONANCE TRAPPING IN PROTOPLANETARY DISKS. I. COPLANAR SYSTEMS

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 similar to 1000 systems in which the planets are initially locked into one of these resonances and allowed to evolve for up to similar 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 similar to 500 two-planet systems in which the outer planet is driven to continuously migrate inward, resonantly capturing the inner planet; 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.