Orbital migration of giant planets induced by gravitationally unstable gaps: the effect of planet mass

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 ≡ Mp/M* ∈ [0.3, 3.0] × 10−3 (so that q = 10−3 corresponds to a Jupiter mass planet if M* = M⊙), in a self-gravitating disc with disc-to-star mass ratio Md/M* = 0.08, aspect ratio h = 0.05 and Keplerian Toomre parameter Qk0 = 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 its initial orbital radius on dynamical time-scales. We briefly discuss the importance of our results in the context of giant planet formation on wide orbits through disc fragmentation.