Outward migration of Jupiter and Saturn in 3:2 or 2:1 resonance in radiative disks: implications for the Grand Tack and Nice models

Embedded in the gaseous protoplanetary disk, Jupiter and Saturn naturally become trapped in 3:2 resonance and migrate outward. This serves as the basis of the Grand Tack model. However, previous hydrodynamical simulations were restricted to isothermal disks, with moderate aspect ratio and viscosity. Here we simulate the orbital evolution of the gas giants in disks with viscous heating and radiative cooling. We find that Jupiter and Saturn migrate outward in 3:2 resonance in modest-mass ($M_{disk} approx M_{MMSN}$, where MMSN is the minimum-mass solar nebula) disks with viscous stress parameter $alpha$ between $10^{-3}$ and $10^{-2} $. In disks with relatively low-mass ($M_{disk} lesssim M_{MMSN}$) , Jupiter and Saturn get captured in 2:1 resonance and can even migrate outward in low-viscosity disks ($alpha le 10^{-4}$). Such disks have a very small aspect ratio ($hsim 0.02-0.03$) that favors outward migration after capture in 2:1 resonance, as confirmed by isothermal runs which resulted in a similar outcome for $h sim 0.02$ and $alpha le 10^{-4}$. We also performed N-body runs of the outer Solar System starting from the results of our hydrodynamical simulations and including 2-3 ice giants. After dispersal of the gaseous disk, a Nice model instability starting with Jupiter and Saturn in 2:1 resonance results in good Solar Systems analogs. We conclude that in a cold Solar Nebula, the 2:1 resonance between Jupiter and Saturn can lead to outward migration of the system, and this may represent an alternative scenario for the evolution of the Solar System.