Planet migration and gap formation by tidally-induced shocks

Gap formation in a gas disk triggered by disk-planet tidal interaction is considered. Density waves launched by the planet are assumed to be damped as a result of their nonlinear evolution leading to shock formation and its subsequent dissipation. As a consequence wave angular momentum is transferred to the disk,leading to evolution of its surface density. Planetary migration is an important ingredient of the theory; effects of the planet-induced surface density perturbations on the migration speed are considered. A gap is assumed to form when a stationary solution for the surface density profile is no longer possible in the frame of reference migrating with the planet. An analytical limit on the planetary mass necessary to open a gap in an inviscid disk is derived. The critical mass turns out to be smaller than mass M_1 for which planetary Hill's radius equals disk scaleheight by a factor of at least Q^{5/7} (Q is the Toomre stability parameter) depending on the strength of the migration feedback. In viscous disks the critical planetary mass could vary from about 0.1M_1 to M_1, depending on the disk viscosity. This implies that a gap could be formed by a planet with mass 1-10 times bigger than the Earth mass depending on the disk aspect ratio, viscosity, and planet's location in the nebula.