Protoplanet Migration by Nebula Tides

Abstract

The tidal interaction of a protoplanet with a circumstellar gaseous disk results in mutual angular momentum exchange that modifies both the disk and the orbit of the secondary. There are two, conceptually distinct circumstances wherein nebula torques can cause a secular variation in a protoplanet's semimajor axis. (I) The net torque exerted on a secondary by an undisturbed disk is not, in general, zero. Although gradients in the disk density and temperature can contribute to this torque, it is mostly due to asymmetries in the disk/planet interaction that are inherent to a Keplerian disk. For a relatively thick disk, the differential torque can be a significant fraction of the torque from either its exterior or its interior portion. In this case, the protoplanet drifts relative to disk material on a time scale inversely proportional to its mass. (II) The protoplanet opens a gap in the disk that establishes a flow barrier to disk material. A density discontinuity that locks the protoplanet into the disk's viscous evolution develops across the orbit. The protoplanet migrates on a time scale set by the disk's viscosity. A unified model that clarifies the relationship between these migration types and reveals under what circumstances a given type is selected is presented. In both cases, orbital decay is the prevailing outcome, although type I migration rates can be between one and two orders of magnitudes faster than type II. Estimates of orbital lifetimes are given and are generally shorter than the expected lifetime of the disk. Some implications to the issue of planetary formation are discussed.