Runaway Migration and the Formation of Hot Jupiters

We evaluate the coorbital corotation torque on a migrating protoplanet. The coorbital torque is assumed to come from orbit crossing fluid elements that exchange angular momentum with the planet when they execute a U-turn at the end of horseshoe streamlines. When the planet migrates inward, the fluid elements of the inner disk undergo one such exchange as they pass to the outer disk. The angular momentum they gain is removed from the planet, and this corresponds to a negative contribution to the corotation torque, which scales with the drift rate. In addition, the material trapped in the coorbital region drifts radially with the planet, giving a positive contribution to the corotation torque, which also scales with the drift rate. These two contributions do not cancel out if the coorbital region is depleted, in which case there is a net corotation torque that scales with the drift rate and the mass deficit in the coorbital region and has the same sign as the drift rate. This leads to a positive feedback on the migrating planet. In particular, if the coorbital mass deficit is larger than the planet mass, the migration rate undergoes a runaway that can vary the protoplanet semimajor axis by 50% over a few tens of orbits. This can happen only if the planet mass is sufficient to create a dip or gap in its surrounding region and if the surrounding disk mass is larger than the planet mass. This typically corresponds to planet masses in the sub-Saturnian to Jovian mass range embedded in massive protoplanetary disks. Runaway migration is a good candidate to account for the orbital characteristics of close orbiting giant planets, most of which have sub-Jovian masses. These are known to cluster at short periods, whereas planets of greater than two Jovian masses are rare at short periods, indicating a different type of migration process operated for the two classes of object. Further, we show that in the runaway regime, migration can be directed outward, which makes this regime potentially rich in a variety of important effects in shaping a planetary system during the last stages of its formation.