Planetary Torques as the Viscosity of Protoplanetary Disks

@article{Goodman2001PlanetaryTA,
  title={Planetary Torques as the Viscosity of Protoplanetary Disks},
  author={Jeremy Goodman and Roman R. Rafikov},
  journal={The Astrophysical Journal},
  year={2001},
  volume={552},
  pages={793 - 802}
}
We revisit the idea that density wave wakes of planets drive accretion in protostellar disks. The effects of many small planets can be represented as a viscosity if the wakes damp locally but the viscosity is proportional to the damping length. Damping occurs mainly because of shocks even for Earth-mass planets. The excitation of the wake follows from standard linear theory including the torque cutoff. We use this as input to an approximate but quantitative nonlinear theory based on Burger's… 
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