  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_Earth and 20 M_Earth 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 <~ 15 M_Earth) in thin (H/r <~0.06) protoplanetary disks. Their
migration could be significantly slowed down, or reversed, in disks with
shallow surface density profiles.
