  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.
