Planet Migration and Gap Formation by Tidally Induced Shocks

Gap formation in a gas disk triggered by disk-planet tidal interaction isconsidered. Density waves launched by the planet are assumed to be damped as aresult of their nonlinear evolution leading to shock formation and itssubsequent dissipation. As a consequence wave angular momentum is transferredto the disk,leading to evolution of its surface density. Planetary migration isan important ingredient of the theory; effects of the planet-induced surfacedensity perturbations on the migration speed are considered. A gap is assumedto form when a stationary solution for the surface density profile is no longerpossible in the frame of reference migrating with the planet. An analyticallimit on the planetary mass necessary to open a gap in an inviscid disk isderived. The critical mass turns out to be smaller than mass M_1 for whichplanetary 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 themigration feedback. In viscous disks the critical planetary mass could varyfrom about 0.1M_1 to M_1, depending on the disk viscosity. This implies that agap could be formed by a planet with mass 1-10 times bigger than the Earth massdepending on the disk aspect ratio, viscosity, and planet's location in thenebula.Comment: AASTeX, 31 pages, 7 figures, 1 table, submitted to Ap