Avoiding resonance capture in multi-planet extrasolar systems

A commonly noted feature of the population of multi-planet extrasolar systems is the rarity of planet pairs in low-order mean-motion resonances. We revisit the physics of resonance capture via convergent disk-driven migration. We point out that for planet spacings typical of stable configurations for Kepler systems, the planets can routinely maintain a small but nonzero eccentricity due to gravitational perturbations from their neighbors. Together with the upper limit on the migration rate needed for capture, the finite eccentricity can make resonance capture difficult or impossible in Sun-like systems for planets smaller than ~Neptune-sized. This mass limit on efficient capture is broadly consistent with observed exoplanet pairs that have mass determinations: of pairs with the heavier planet exterior to the lighter planet -- which would have been undergoing convergent migration in their disks -- those in or nearly in resonance are much more likely to have total mass greater than two Neptune masses than to have smaller masses. The agreement suggests that the observed paucity of resonant pairs around sun-like stars may simply arise from a small resonance capture probability for lower-mass planets. Planet pairs that thereby avoid resonance capture are much less likely to collide in an eventual close approach than to simply migrate past one another to become a divergently migrating pair with the lighter planet exterior. For systems around M stars we expect resonant pairs to be much more common, since there the minimum mass threshhold for efficient capture is about an Earth mass.