Tilting Saturn without tilting Jupiter or ejecting an ice giant: constraints on migration

Abstract

The obliquities of the giant planets preserve information about their migration and encounter histories. Are the classic Nice models (Tsiganis et al. 2005) or the resonant Nice models (Morbidelli et al. 2007) compatible with Jupiter's 3 degree tilt and Saturn's 27? Here we consider the obliquity evolution of the giants during the planetesimal-driven migration phase using two methods: (1) a purely secular integration of the Laplace-Lagrange equations with spin, and (2) a hybrid N-body scheme with full interactions between the Sun and the giants but imposed prescriptions for migration and eccentricity and inclination damping. We find that it is difficult to reproduce today's obliquity values as migration timescales sufficient to tilt Saturn via the Hamilton & Ward (2004) secular spin-orbit resonance mechanism generally suffice to tilt Jupiter more than is observed. Moreover, long migration timescales which make tilting Saturn easier simultaneously reduce the survival fraction (to below 20% for timescales longer than 20 Myr.) We discuss the constraints these observations provide on the dynamical history of the giant planets, and the remaining possibility of tilting Saturn during a late very slow migration of Neptune to its present location after the main phase of migration is complete. [This work was supported by Hong Kong RGC grant HKU 7024/08P.]