Gap Formation in Protoplanetary Disks

Evolution of a protoplanetary disk under the tidal interaction between the disk and an embedded protoplanet is analyzed with a self-consistent WKB approximation. We assume that the protoplanetary disk is infinitesimally thin and non-self-gravitating and that the protoplanet's orbit is circular. The protoplanet excites density waves at its Lindblad resonances. As they propagate throughout the disk, these waves carry a flux of angular momentum that is eventually deposited into the gas at the locations where the waves are dissipated viscously. Protoplanets with a sufficiently large mass can induce the formation of a gap in the disk. The size of the gap and the structure of the disk are determined by the wave propagation length scale, which is a decreasing function of viscosity. For small effective viscosity, density waves propagate to inner regions near the protostellar surface. Using an α prescription, we find that a protoplanet with a mass of Jupiter can lead to the removal of the inner disk if α ≲ 3 × 10-4 . For larger values of α, the surface density in the disk surrounding the gap is adjusted in a manner such that the rapid orbital evolution of the protoplanet is prevented. We also inferred that α ∼ 1.7 × 10-2 in the disk around the binary T Tauri star GW Ori, based on the gap size derived from the observational data.