  The torque felt by a non-accreting protoplanet on a circular orbit embedded
in a uniform surface density protoplanetary disk is analyzed by means of
time-dependent numerical simulations. Varying the viscosity enables one to
disentangle the Lindblad torque (which is independent of viscosity) from the
corotation torque, which saturates at low viscosity and is unsaturated at high
viscosity. The dependence of the corotation torque upon the viscosity and upon
the width of the librating zone is compared with previous analytical
expressions, and shown to be in agreement with those. The effect of the
potential smoothing respectively on the Lindblad torque and on the corotation
torque is investigated, and the question of whether 3D effects and their impact
on the total torque sign and magnitude can be modeled by an adequate smoothing
prescription in a 2D simulation is addressed. As a side result, this study
shows that the total torque acting on a Neptune-sized protoplanet is positive
in a sufficiently thin, viscous disk (H/r < 4%, \alpha > 10^-2), but the inward
migration time of smaller bodies is still very short, making it unlikely that
they reach the torque reversal mass before having migrated all the way to the
central object.

Astrophysics