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 ~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. 
Aaron T. Lee, Edward W. Thommes, Frederic A. Rasio