The origin of the negative torque density in disk-satellite interaction
  Tidal interaction between a gaseous disk and a massive orbiting perturber is
known to result in angular momentum exchange between them. Understanding
astrophysical manifestations of this coupling such as gap opening by planets in
protoplanetary disks or clearing of gas by binary supermassive black holes
(SMBHs) embedded in accretion disks requires knowledge of the spatial
distribution of the torque exerted on the disk by a perturber. Recent
hydrodynamical simulations by Dong et al (2011) have shown evidence for the
tidal torque density produced in a uniform disk to change sign at the radial
separation of $\approx 3.2$ scale heights from the perturber's orbit, in clear
conflict with the previous studies. To clarify this issue we carry out a linear
calculation of the disk-satellite interaction putting special emphasis on
understanding the behavior of the perturbed fluid variables in physical space.
Using analytical as well as numerical methods we confirm the reality of the
negative torque density phenomenon and trace its origin to the overlap of
Lindblad resonances in the vicinity of the perturber's orbit - an effect not
accounted for in previous studies. These results suggest that calculations of
the gap and cavity opening in disks by planets and binary SMBHs should rely on
more realistic torque density prescriptions than the ones used at present.
