A safety net for fast migrators: Interactions between gap-opening and sub-gap-opening bodies in a protoplanetary disk

Abstract

Young planets interact with their parent gas disks through tidal torques. An imbalance between inner and outer torques causes bodies of mass $\ga 0.1$ Earth masses to lose angular momentum and migrate inward rapidly relative to the disk; this is known as ``Type I'' migration. However, protoplanets that grow to gas giant mass, O($10^2) M_\oplus$, open a gap in the disk and are subsequently constrained to migrate more slowly, locked into the disk's viscous evolution in what is called "Type II" migration. In a young planetary system, both Type I and Type II bodies likely coexist; if so, differential migration ought to result in close encounters when the former originate on orbits exterior to the latter. We investigate the resulting dynamics, using two different numerical approaches: an N-body code with dissipative forces added to simulate the effect of the gas disk, and a hybrid code which combines an N-body component with a 1-dimensional viscous disk model, treating planet-disk interactions in a more self-consistent manner. In both cases, we find that sub-gap-opening bodies have a high likelihood of being resonantly captured when they encounter a gap-opening body. A giant planet thus tends to act as a barrier in a protoplanetary disk, collecting smaller protoplanets outside of its orbit. Such behavior has two important implications for giant planet formation: First, for captured protoplanets it mitigates the problem of the migration timescale becoming shorter than the growth timescale. Secondly, it suggests one path to forming systems with multiple giant planets: Once the first has formed, it traps/accretes the future solid core of the second in an exterior mean-motion resonance, and so on. The most critical step in giant planet formation may thus be the formation of the very first one.