In 2D simulations with beta-cooling, an accreting Jupiter-mass planet migrates outward when beta is small and inward when beta exceeds the local dynamical timescale.
A torque formula for non-isothermal Type I planetary migration - I. Unsaturated horseshoe drag
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abstract
We study the torque on low-mass planets embedded in protoplanetary discs in the two-dimensional approximation, incorporating non-isothermal effects. We couple linear estimates of the Lindblad (or wave) torque to a simple, but non-linear, model of adiabatic corotation torques (or horseshoe drag), resulting in a simple formula that governs Type I migration in non-isothermal discs. This formula should apply in optically thick regions of the disc, where viscous and thermal diffusion act to keep the horseshoe drag unsaturated. We check this formula against numerical hydrodynamical simulations, using three independent numerical methods, and find good agreement.
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Effects of Thermodynamics on the Concurrent Accretion and Migration of Gas Giants in Protoplanetary Disks
In 2D simulations with beta-cooling, an accreting Jupiter-mass planet migrates outward when beta is small and inward when beta exceeds the local dynamical timescale.