Numerical calculations of the linear response of a gaseous disk to a protoplanet

Numerical calculations of the linear response of a 2D gaseous disk to the perturbations induced by a protoplanet and the corresponding torque are presented. When the pressure gradient is taken into account, torques are increased in disks with gradients in either surface density and sound speed, the effect of the latter being much greater for the same-sized gradient as measured by the power law index. The torques in turn may be used to calculate timescales for orbital migration of protoplanets.