TYPE I PLANET MIGRATION IN NEARLY LAMINAR DISKS

Abstract

We describe two-dimensional hydrodynamic simulations of the migration of low-mass planets ( 30 M⊕) in nearly laminar disks (viscosity parameter α< 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 α 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 α ∼ 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 (Mcr ∼ 10M⊕) beyond which migration halts in nearly laminar disks. For α 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. In addition, for α 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.