We revisit some fundamental aspects of the theory of disk-satellite interaction and address the questions of how is the tidal torque exerted by a massive perturber distributed troughout the accretion disk (i.e. the torque density). This is a general astrophysical setup, but probably the most interesting applications are in the theory of disk-planet interactions and supermassive black hole binaries (SMBHs) embedded by gaseous disks.
Most remarkably, in Rafikov & Petrovich 2012 we find that the excitation torque density in a uniform density disk changes sign beyond ~3.2 scale heights away from the perturber as a result of superposition of Lidblad resonances - a result qualitatively different from the conventional wisdom (e.g. the classical paper by Goldreich & Tremaine 1980, GT80). This confirms remarkably well what was previously seen in the numerical simulations carried out by Dong, Rafikov, Stone & Petrovich 2011 (see figure above).
When the perturber is massive enough, the tidal torque can expell the gas around it as it is the case of density gaps around planets (Type II migration) and disk cavities around SMBH binaries. It is customary that theoretical works modelling the tidal torques use a prescription similar that in GT80, where given our previous revision in uniform density disks one could expect that it gives an inadequate description for the torque density.
In fact, by self-consistently including the density gradients in the fluid equations we found in Petrovich & Rafikov 2012 that the excited torque is more concentrated towards the gap edge, compared to the classical prescriptions, falling-off exponentially with distance. We understand this as a result of accumulation of Lindblad resonances in regions with large density gradients. This effect might facilitate the process of gap opening around planets and clearing cavities around SMBHs.