Low-mass protoplanet migration in T Tauri α-disks

We present detailed estimates of type I-migration rates for low-mass protoplanets embedded in steady state T Tauri alpha-disks, based on Lindblad torque calculations ignoring feedback on the disk. Differences in migration rates for several plausible background disk models are explored and we compare results obtained using the standard two-dimensional formalism of spiral density wave theory with those obtained from a simple treatment of three-dimensional effects. Opacity transitions in the disk result in sudden radial variations of the migration rates. Regions with minimal migration rates may be preferred sites of gravitational interactions between protoplanets. Three-dimensional torques are significantly weaker than two-dimensional ones, and they are sensitive to the surface density profile of the background disk. We find that migration times in excess of runaway-envelope-accretion times or T Tauri disk lifetimes are possible for Earth-mass protoplanets in some background disk models, even at sub-AU distances. We conclude that an understanding of the background disk structure and viscosity, as well as a proper treatment of three-dimensional effects in torque calculations, is necessary to obtain reliable estimates of type I-migration rates.