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It has been suggested that long-period giant planets, such as HD 95086b andHR 8799bcde, may have formed through gravitational instability ofprotoplanetary discs. However, self-gravitating disc-satellite interaction canlead to the formation of a gravitationally unstable gap. Such an instabilitysignificantly affects the orbital migration of gap-opening perturbers inmassive discs. We use 2D hydrodynamical simulations to examine the role ofplanet mass on the gravitational stability of gaps and its impact on orbitalmigration. We consider giant planets with planet-to-star mass ratio q=0.0003 toq=0.003, 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 = 1.5 at 2.5 times theplanet's initial orbital radius. Fixed-orbit simulations show that all planetmasses we consider open gravitationally unstable gaps, but the instability isstronger and develops sooner with increasing planet mass. The disc-on-planettorques typically become more positive with increasing planet mass. Infreely-migrating simulations, we observe faster outward migration withincreasing planet mass, but only for planet masses capable of opening unstablegaps early on. For q=0.0003, the planet undergoes rapid inward type IIImigration before it can open a gap. For q=0.0013 we find it is possible tobalance the tendency for inward migration by the positive torques due to anunstable gap, but only for a few 10's of orbital periods. We find the unstableouter gap edge can trigger outward type III migration, sending the planet totwice its initial orbital radius on dynamical timescales. This triggered typeIII migration may be a way of bringing giant planets to large orbitaldistances. On the other hand, our results also imply gap-opening is not asufficient condition for the in situ formation of giant planets on wide orbitsthrough disc fragmentation.

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