The past and future obliquity of Saturn as Titan migrates

Context. Giant planets are expected to form with near-zero obliquities. It has recently been shown that the fast migration of Titan could be responsible for the current 26.7◦ -tilt of Saturn’s spin axis. Aims. We aim to quantify the level of generality of this result by measuring the range of parameters allowing for this scenario to happen. Since Titan continues to migrate today, we also aim to determine the obliquity that Saturn will reach in the future. Methods. For a large variety of migration rates for Titan, we numerically propagated the orientation of Saturn’s spin axis both backwards and forwards in time. We explored a broad range of initial conditions after the late planetary migration, including both small and large obliquity values. Results. In the adiabatic regime, the likelihood of reproducing Saturn’s current spin-axis orientation is maximised for primordial obliquities between about 2◦ and 7◦ . For a slightly faster migration than expected from radio-science experiments, non-adiabatic effects even allow for exactly null primordial obliquities. Starting from such small tilts, Saturn’s spin axis can evolve up to its current state provided that: (i) the semi-major axis of Titan changed by more than 5% of its current value since the late planetary migration, and (ii) its migration rate does not exceed ten times the nominal measured rate. In comparison, observational data suggest that the increase in Titan’s semi-major axis exceeded 50% over 4 Gyr, and error bars imply that the current migration rate is unlikely to be larger than 1.5 times its nominal value. Conclusions. If Titan did migrate substantially before today, tilting Saturn from a small obliquity is not only possible, but it is the most likely scenario. Saturn’s obliquity is still expected to be increasing today and could exceed 65◦ in the future. Maximising the likelihood would also put strict constraints on Saturn’s polar moment of inertia. However, the possibility remains that Saturn’s primordial obliquity was already large, for instance as a result of a massive collision. The unambiguous distinction between these two scenarios would be given by a precise measure of Saturn’s polar moment of inertia.