We carry out a series of high-resolution ( 1024 \times 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 \equiv 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 } \sim 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 .