Constraints on giant planet migration: obliquities and stability

Abstract

We have performed both secular and N-body simulations of the migration of the giants planets in our Solar System. The simulations ahow that the obliquities (the angle between the spin axis and the orbit normal) of Jupiter and Saturn and the survival of all four giant planets provide strong constraints on the migration. In the Nice model for the establishment of the orbital architecture of the giant planet, the outer Solar System was initially compact, and the scattering of planetesimals caused Jupiter to migrate inward and Saturn, Uranus, and Neptune outward (Tsiganis et al. 2005). The decrease in the orbital precession frequencies due to the migration of the planets could lead to the capture of Saturn into the spin-orbit resonance and an increase in Saturn's obliquity to the observed 27 degrees (Ward and Hamilton 2004; Hamilton and Ward 2004). The migration must be sufficiently slow for Saturn to stay in the spin-orbit resonance, and the critical migration timescale decreases with orbital inclinations (Boue et al. 2009). For the orbital inclinations generated during the encounter phase of the Nice model, it is possible to produce a Saturnian obiliquity comparable to the observed one, if the migration timescale is of the order of 20 Myr. Jupiter is usually also captured into spin-orbit resonance, and the resulting obliquity of Jupiter is comparable to or larger than that of Saturn, in contrast to the observed 3 degrees. In addition, if the migration timescale is of the order of 20 Myr or longer, the probability that all four planets survive is less than about 20%.