Resonant Capture by Inward-migrating Planets

We investigate resonant capture of small bodies by planets that migrate inward, using analytic arguments and three-body integrations. If the orbits of the planet and the small body are initially circular and coplanar, the small body is captured when it crosses the 2 : 1 resonance with the planet. As the orbit shrinks, it becomes more eccentric until, by the time its semimajor axis has shrunk by a factor of 4, its eccentricity reaches nearly unity (1 - e ≪ 10^-4). In typical planetary systems, bodies in this high-eccentricity phase are likely to be consumed by the central star. If they can avoid this fate, as migration continues the inclination flips from 0° to i = 180°; thereafter the eccentricity declines until the semimajor axis is a factor of 9 smaller than at capture, at which point the small body is released from the 2 : 1 resonance on a nearly circular retrograde orbit. Small bodies captured into resonance from initially inclined or eccentric orbits can also be ejected from the system, or released from the resonance on highly eccentric polar orbits (i ≃ 90°) that are stabilized by a secular resonance. We conclude that migration could drive much of the inner planetesimal disk into the star, and that postmigration multiplanet systems may not be coplanar.