Type I Planet Migration in Nearly Laminar Disks

We describe 2D hydrodynamic simulations of the migration of low-mass planets (30 M_) in nearly laminar disks (viscosity parameter < 10^-3) over timescales of several thousand orbit periods. We consider disk masses of 1, 2, and 5 times the minimum mass solar nebula, disk thickness parameters of H/r = 0. 035 and 0. 05, and a variety of values and planet masses. Disk self-gravity is fully included. Previous analytic work has suggested that Type I planet migration can be halted in disks of sufficiently low turbulent viscosity, for 10^-4. The halting is due to a feedback effect of breaking density waves that results in a slight mass redistribution and consequently an increased outward torque contribution. The simulations confirm the existence of a critical mass (M₂ₑ 10 M_) beyond which migration halts in nearly laminar disks. For 10^-3, density feedback effects are washed out and Type I migration persists. The critical masses are in good agreement with the analytic model of Rafikov (2002). In addition, for 10^-4 steep density gradients produce a vortex instability, resulting in a small time-varying eccentricity in the planet's orbit and a slight outward migration. Migration in nearly laminar disks may be sufficiently slow to reconcile the timescales of migration theory with those of giant planet formation in the core accretion model.