On corotation torques, horseshoe drag and the possibility of sustained stalled or outward protoplanetary migration

Understand

We study the torque on low mass protoplanets on fixed circular orbits, embedded in a protoplanetary disc in the isothermal limit.

• For low mass protoplanets and large viscosity the corotation torque behaves as expected from linear theory.
• However, when the viscosity becomes small enough to enable horseshoe turns to occur, the linear corotation torque exists only temporarily after insertion of a planet into the disc, being replaced by the horseshoe drag first discussed by Ward.
• This happens after a time that is equal to the horseshoe libration period reduced by a factor amounting to about twice the disc aspect ratio.