It has been established that self-gravitating disc-satellite interaction can lead to the formation of a gravitationally unstable gap .
Such an instability may significantly affect the orbital migration of gap-opening perturbers in self-gravitating discs .
In this paper , we extend the two-dimensional hydrodynamic simulations of Lin & Papaloizou to investigate the role of the perturber or planet mass on the gravitational stability of gaps and its impact on orbital migration .
We consider giant planets with planet-to-star mass ratio q \equiv M _ { p } / M _ { * } \in [ 0.3 , 3.0 ] \times 10 ^ { -3 } ( so that q = 10 ^ { -3 } corresponds to a Jupiter mass planet if M _ { * } = M _ { \sun } ) , in a self-gravitating disc with disc-to-star mass ratio M _ { d } / M _ { * } = 0.08 , aspect ratio h = 0.05 , and Keplerian Toomre parameter Q _ { k 0 } = 1.5 at 2.5 times the planet ’ s initial orbital radius .
These planet masses correspond to \tilde { q } \in [ 0.9 , 1.7 ] , where \tilde { q } is the ratio of the planet Hill radius to the local disc scale-height .
Fixed-orbit simulations show that all planet masses we consider open gravitationally unstable gaps , but the instability is stronger and develops sooner with increasing planet mass .
The disc-on-planet torques typically become more positive with increasing planet mass .
In freely-migrating simulations , we observe faster outward migration with increasing planet mass , but only for planet masses capable of opening unstable gaps early on .
For q = 0.0003 ( \tilde { q } = 0.9 ) , the planet undergoes rapid inward type III migration before it can open a gap .
For q = 0.0013 ( \tilde { q } = 1.5 ) we find it is possible to balance the tendency for inward migration by the positive torques due to an unstable gap , but only for a few 10 ’ s of orbital periods .
We find the unstable outer gap edge can trigger outward type III migration , sending the planet to twice it ’ s initial orbital radius on dynamical timescales .
We briefly discuss the importance of our results in the context of giant planet formation on wide orbits through disc fragmentation .