in the code of Crida et al. (2007) that we use, the boundary conditions cannot act as a source of mass. Thus, an increase of the surface density in the inner part of the disk is possible only if there is an influx of mass from the outer disk.

The flow of gas has several effects. First, it unlocks the planets from the disk, allowing them to move against the gas stream. Second, it has positive feedbacks on the outer migration of the planets by (i) exerting a corotation torque on them, as it passes through their horseshoe regions and (ii) refurbishing the inner part of the disk, which exerts the positive torque on Jupiter discussed above. The signature of this feedback is well visible in the simulation with $H/r=3$% in Fig. \[MS-Hr\]: the outward migration rate accelerates exponentially, which implies that there is a positive net torque that increases with the migration speed.

At this point, one might wonder whether the motion of the planets is dominated by the torque felt by Jupiter from the inner disk, or by the corotation torque exerted by the gas flowing through the planets’ orbits. The flow of gas through the orbits of 