The increase of computational resources has recently allowed high resolution , three dimensional calculations of planets embedded in gaseous protoplanetary disks .
They provide estimates of the planet migration timescale that can be compared to analytical predictions .
While these predictions can result in extremely short migration timescales for cores of a few Earth masses , recent numerical calculations have given an unexpected outcome : the torque acting on planets with masses between 5 M _ { \oplus } and 20 M _ { \oplus } is considerably smaller than the analytic , linear estimate .
These findings motivated the present work , which investigates existence and origin of this discrepancy or “ offset ” , as we shall call it , by means of two and three dimensional numerical calculations .
We show that the offset is indeed physical and arises from the coorbital corotation torque , since ( i ) it scales with the disk vortensity gradient , ( ii ) its asymptotic value depends on the disk viscosity , ( iii ) it is associated to an excess of the horseshoe zone width .
We show that the offset corresponds to the onset of non-linearities of the flow around the planet , which alter the streamline topology as the planet mass increases : at low mass the flow non-linearities are confined to the planet ’ s Bondi sphere whereas at larger mass the streamlines display a classical picture reminiscent of the restricted three body problem , with a prograde circumplanetary disk inside a “ Roche lobe ” .
This behavior is of particular importance for the sub-critical solid cores ( M \lesssim 15 M _ { \oplus } ) in thin ( H / r \lesssim 0.06 ) protoplanetary disks .
Their migration could be significantly slowed down , or reversed , in disks with shallow surface density profiles .