On the orbital evolution of a giant planet pair embedded in a gaseous disk. II. A Saturn-Jupiter configuration

We carry out a series of high-resolution (1024 X 1024) hydrodynamic simulations to investigate the orbital evolution of a Saturn-Jupiter pair embedded in a gaseous disk. This work extends the results of our previous work by exploring a different orbital configuration---Jupiter lies outside Saturn (q<1, where q= M_i/M_o is the mass ratio of the inner planet and the outer one). We focus on the effects of different initial separations (d) between the two planets and the various surface density profiles of the disk, where \sigma \propto r^{-\alpha}. We also compare the results of different orbital configurations of the planet pair. Our results show that: (1) when the initial separation is relatively large(d>d_{iLr}, where d_{iLr} is the distance between Jupiter and its first inner Lindblad resonance), the two planets undergo divergent migration. However, the inward migration of Saturn could be halted when Jupiter compresses the inner disk in which Saturn is embedded. (2) Convergent migration occurs when the initial separation is smaller (d<d_{iLr}) and the density slope of the disk is nearly flat (\alpha<1/2). Saturn is then forced by Jupiter to migrate inward when the two planets are trapped into mean motion resonances (MMRs), and Saturn may get very close to the central star. (3) In the case of q<1, the eccentricity of Saturn could be excited to a very high value (e_{S}~0.4-0.5) by the MMRs and the system could maintain stability. These results explain the formation of MMRs in the exoplanet systems where the outer planet is more massive than the inner one. It also helps us to understand the origin of the "hot Jupiter/Saturn" undergoing high eccentric orbit.