Radial migration of gap-opening planets in protoplanetary disks. I. The case of a single planet

A large planet orbiting a star in a protoplanetary disk opens a density gap along its orbit due to the strong disk-planet interaction and migrates with the gap in the disk. It is expected that in the ideal case, a gap-opening planet migrates at the viscous drift speed, which is referred to as type II migration. However, recent hydrodynamic simulations have shown that in general, the gap-opening planet is not locked to the viscous disk evolution. A new physical model is required to explain the migration speed of such a planet. For this reason, we re-examined the migration of a planet in the disk, by carrying out the two-dimensional hydrodynamic simulations in a wide parameter range. We have found that the torque exerted on the gap-opening planet depends on the surface density at the bottom of the gap. The planet migration slows down as the surface density of the bottom of the gap decreases. Using the gap model developed in our previous studies, we have constructed an empirical formula of the migration speed of the gap-opening planets, which is consistent with the results given by the hydrodynamic simulations performed by us and other researchers. Our model easily explains why the migration speed of the gap-opening planets can be faster than the viscous gas drift speed. It can also predict the planet mass at which the type I migration is no longer adequate due to the gap development in the disk, providing a gap formation criterion based on planetary migration.