Cavity Opening by a Giant Planet in a Protoplanetary Disc and Effects on Planetary Migration

We study the effect of a Jovian planet on the gas distribution of a protoplanetary disc, using a new numerical scheme that allows us to take into consideration the global evolution of the disc, down to an arbitrarily small inner physical radius. We find that Jovian planets do not open cavities in the inner part of the disc (i.e. interior to their orbits) unless (a) the inner physical edge of the disc is close to the planet's location or (b) the planet is much more massive than the disc. In all other cases the planet simply opens a gap in the gas density distribution, whose global profile is essentially unchanged relative to the one that it would have if the planet were absent. We recognize, though, that the dust distribution can be significantly different from the gas distribution and that dust cavities might be opened in some situations, even if the gas is still present in the inner part of the disc. Concerning the migration of the planet, we find that classical Type-II migration (with speed proportional to the viscosity of the disc) occurs only if the gap opened by the planet is deep and clean. If there is still a significant amount of gas in the gap, the migration of the planet is generally slower than the theoretical Type-II migration rate. In some situations, migration can be stopped or even reversed. We develop a simple model that reproduces satisfactorily the migration rate observed in the simulations, for a wide range of disc viscosities and planet masses and locations relative to the inner disc edge. Our results are relevant for extra-solar planetary systems, as they explain (a) why some hot Jupiters did not migrate all the way down to their parent stars and (b) why the outermost of a pair of resonant planets is typically the most massive one.