Planetary Torques as the Viscosity of Protoplanetary Disks

We revisit the idea that density-wave wakes of planets drive accretion inprotostellar disks. The effects of many small planets can be represented as aviscosity if the wakes damp locally, but the viscosity is proportional to thedamping length. Damping occurs mainly by shocks even for earth-mass planets.The excitation of the wake follows from standard linear theory including thetorque cutoff. We use this as input to an approximate but quantitativenonlinear theory based on Burger's equation for the subsequent propagation andshock. Shock damping is indeed local but weakly so. If all metals in aminimum-mass solar nebula are invested in planets of a few earth masses each,dimensionless viscosities [alpha] of order dex(-4) to dex(-3) result. Wecompare this with observational constraints. Such small planets would haveescaped detection in radial-velocity surveys and could be ubiquitous. If so,then the similarity of the observed lifetime of T Tauri disks to thetheoretical timescale for assembling a rocky planet may be fate rather thancoincidence.Comment: 23 pages, 3 figures. Uses aastex50