Outward Migration of Jupiter and Saturn in Evolved Gaseous Disks

The outward migration of a pair of resonant-orbit planets, driven by tidal interactions with a gas-dominated disk, is studied in the context of evolved solar nebula models. The planets' masses, M ₁ and M ₂, correspond to those of Jupiter and Saturn. Hydrodynamical calculations in two and three dimensions are used to quantify the migration rates and analyze the conditions under which the outward migration mechanism may operate. The planets are taken to be fully formed after 10⁶ and before 3 × 10⁶ years. The orbital evolution of the planets in an evolving disk is then calculated until the disk's gas is completely dissipated. Orbital locking in the 3:2 mean motion resonance may lead to outward migration under appropriate conditions of disk viscosity and temperature. However, resonance locking does not necessarily result in outward migration. This is the case, for example, if convergent migration leads to locking in the 2:1 mean motion resonance, as post-formation disk conditions seem to suggest. Accretion of gas on the planets may deactivate the outward migration mechanism by raising the mass ratio M ₂/M ₁ and/or by reducing the accretion rate toward the star, and hence depleting the inner disk. For migrating planets locked in the 3:2 mean motion resonance, there are stalling radii that depend on disk viscosity and on stellar irradiation, when it determines the disk's thermal balance. Planets locked in the 3:2 orbital resonance that start moving outward from within 1-2 AU may reach beyond ≈5 AU only under favorable conditions. However, within the explored space of disk parameters, only a small fraction—less than a few percent—of the models predict that the interior planet reaches beyond ≈4 AU.