Tilting Jupiter (a bit) and Saturn (a lot) during Planetary Migration

We study the effects of planetary late migration on the gas giants’ obliquities. We consider the planetary instability models from Nesvorný and Morbidelli, in which the obliquities of Jupiter and Saturn can be excited when spin-orbit resonances occur. The most notable resonances occur when the s₇ and s₈ frequencies, changing as a result of planetary migration, become commensurate with the precession frequencies of Jupiter’s and Saturn’s spin vectors. We show that Jupiter may have obtained its present obliquity by crossing of the s₈ resonance. This would set strict constraints on the character of migration during the early stage. Additional effects on Jupiter’s obliquity are expected during the last gasp of migration when the s₇ resonance was approached. The magnitude of these effects depends on the precise value of the Jupiter’s precession constant. Saturn’s large obliquity was likely excited by capture into the s₈ resonance. This probably happened during the late stage of planetary migration when the evolution of the s₈ frequency was very slow, and the conditions for capture into the spin-orbit resonance with s₈ were satisfied. However, whether or not Saturn is in the spin-orbit resonance with s₈ at the present time is not clear because the existing observations of Saturn’s spin precession and internal structure models have significant uncertainties.