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 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 $s_7$ and $s_8$ 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 $s_8$ 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 $s_7$ 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 $s_8$ resonance. This probably happened during the late stage of planetary migration when the evolution of the $s_8$ frequency was very slow, and the conditions for capture into the spin-orbit resonance with $s_8$ were satisfied. However, whether or not Saturn is in the spin-orbit resonance with $s_8$ 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

The orbital distribution of trans-Neptunian objects beyond 50 au

The dynamical structure of the Kuiper belt beyond 50 au is not well understood. Here we report results of a numerical model with long-range, slow and grainy migration of Neptune. The model implies that bodies scattered outward by Neptune to semimajor axes a>50 au often evolve into resonances which subsequently act to raise the perihelion distances of orbits to q>40 au. The implication of the model is that the orbits with 5040 au should cluster near (but not in) the resonances with Neptune (3:1 at a=62.6 au, 4:1 at a=75.9 au, 5:1 at a=88.0 au, etc.). The recent detection of several distant Kuiper Belt Objects (KBOs) near resonances is consistent with this prediction, but it is not yet clear whether the orbits are really non-resonant as our model predicts. We estimate from the model that there should presently be ~1600-2400 bodies at the 3:1 resonance and ~1000-1400 bodies at the 4:1 resonance (for q>40 au and diameters D>100 km). These results favorably compare with the population census of distant KBOs inferred from existing observations.Comment: ApJ Letter