On the Migration of Protogiant Solid Cores

The increase of computational resources has recently allowed high resolution,three dimensional calculations of planets embedded in gaseous protoplanetarydisks. They provide estimates of the planet migration timescale that can becompared to analytical predictions. While these predictions can result inextremely short migration timescales for cores of a few Earth masses, recentnumerical calculations have given an unexpected outcome: the torque acting onplanets with masses between 5 M_Earth and 20 M_Earth is considerably smallerthan the analytic, linear estimate. These findings motivated the present work,which investigates existence and origin of this discrepancy or ``offset'', aswe shall call it, by means of two and three dimensional numerical calculations.We show that the offset is indeed physical and arises from the coorbitalcorotation torque, since (i) it scales with the disk vortensity gradient, (ii)its asymptotic value depends on the disk viscosity, (iii) it is associated toan excess of the horseshoe zone width. We show that the offset corresponds tothe onset of non-linearities of the flow around the planet, which alter thestreamline topology as the planet mass increases: at low mass the flownon-linearities are confined to the planet's Bondi sphere whereas at largermass the streamlines display a classical picture reminiscent of the restrictedthree body problem, with a prograde circumplanetary disk inside a ``Rochelobe''. This behavior is of particular importance for the sub-critical solidcores (M <~ 15 M_Earth) in thin (H/r <~0.06) protoplanetary disks. Theirmigration could be significantly slowed down, or reversed, in disks withshallow surface density profiles.Comment: Accepted for publication in Ap