We study the effects of planetary late migration on the gas giants
obliquities. We consider the planetary instability models from Nesvorny &
Morbidelli (2012), in which the obliquities of Jupiter and Saturn can be
excited when the 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 constrains
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.Comment: 29 pages, 8 figures, accepted for publication in The Astrophysical
Journa