Resonance locking in giant planets indicated by the rapid orbital expansion of Titan

Abstract

Saturn is orbited by dozens of moons, and the intricate dynamics of this complex system provide clues about its formation and evolution. Tidal friction within Saturn causes its moons to migrate outwards, driving them into orbital resonances that pump their eccen- tricities or inclinations, which in turn leads to tidal heating of the moons. However, in gi- ant planets, the dissipative processes that determine the tidal migration timescale remain poorly understood. Standard theories suggest an orbital expansion rate inversely pro- portional to the power 11/2 in distance1, implying negligible migration for outer moons such as Saturn’s largest moon, Titan. Here, we use two independent measurements ob- tained with the Cassini spacecraft to measure Titan’s orbital expansion rate. We find Titan rapidly migrates away from Saturn on a timescale of roughly 10 Gyr, corresponding to a tidal quality factor of Saturn of Q ≃ 100, which is more than a hundred times smaller than most expectations. Our results for Titan and five other moons agree with the predic- tions of a resonance locking tidal theory2, sustained by excitation of inertial waves inside the planet. The associated tidal expansion is only weakly sensitive to orbital distance, motivating a revision of the evolutionary history of Saturn’s moon system. In particular, it suggests Titan formed significantly closer to Saturn and has migrated outward to its current position.