Model of Angular Momentum Transport at the Protoplane-tary Disk Evolution and Disk Surface Density

Abstract

We consider how the tidal effect of a protoplanetary disk interaction can be incorporated into calculations of its viscous evolution. The evolution of the disk occurs under the action of both internal viscous torques and external torques resulting from the presence of one or more embedded planets. The planets migrate under the effect of their tidal interaction with the disk (in the type-II migration regime). Torques on a planet are caused by its gravitational interaction with the density waves which occupy the Lindblad resonances in the disk. Our model simplifies the functional form of the rate of injection of the angular momentum Λ(r) to construct and solve the evolution equation for a disk and an embedded protoplanet. The functional Λ(r) depends on the tidal dissipation distribution in the disk which is concentrated in a vicinity of the protoplanet’s orbit. We have found an analytic solution for the disk surface density.