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Two-Dimensional Study of the Propagation of Planetary Wake and the Indication to Gap Opening in an Inviscid Protoplanetary Disk

We analyze the physical processes of gap formation in an inviscid protoplanetary disk with an embedded protoplanet using two-dimensional local shearing-sheet model. Spiral density wave launched by the planet shocks and the angular momentum carried by the wave is transferred to the background flow. The exchange of the angular momentum can affect the mass flux in the vicinity of the planet to form an underdense region, or gap, around the planetary orbit. We first perform weakly non-linear analyses to show that the specific vorticity formed by shock dissipation of density wave can be a source of mass flux in the vicinity of the planet, and that the gap can be opened even for low-mass planets unless the migration of the planet is substantial. We then perform high resolution numerical simulations to check analytic consideration. By comparing the gap opening timescale and type I migration timescale, we propose a criterion for the formation of underdense region around the planetary orbit that is qualitatively different from previous studies. The minimum mass required for the planet to form a dip is twice as small as previous studies if we incorporate the standard values of type I migration timescale, but it can be much smaller if there is a location in the disk where type I migration is halted.