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

Valéry Lainey,Luis Gomez Casajus,Marco Zannoni,Ryan S Park,Paolo Tortora,Qingfeng Zhang,Carl Murray,Jim Fuller,Dario Modenini,Nicholas Cooper,Vincent Robert

doi:10.1038/s41550-020-1120-5

Abstract

Tidal effects in planetary systems are the main driver in the orbital migration of natural satellites. They result from physical processes occurring deep inside celestial bodies, whose effects are rarely observable from surface imaging. For giant planet systems, the tidal migration rate is determined by poorly understood dissipative processes in the planet, and standard theories suggest an orbital expansion rate inversely proportional to the power 11/2 in distance, implying little migration for outer moons such as Saturn's largest moon, Titan. Here, we use two independent measurements obtained with the Cassini spacecraft to measure Titan's orbital expansion rate. We find Titan migrates away from Saturn at 11.3 $\pm$ 2.0 cm/year, corresponding to a tidal quality factor of Saturn of Q $\simeq$ 100, and a migration timescale of roughly 10 Gyr. This rapid orbital expansion suggests Titan formed significantly closer to Saturn and has migrated outward to its current position. Our results for Titan and five other moons agree with the predictions of a resonance locking tidal theory, 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. The resonance locking mechanism could operate in other systems such as stellar binaries and exoplanet systems, and it may allow for tidal dissipation to occur at larger orbital separations than previously believed.

Highlights

Prior monitoring of the mid-sized inner moons’ orbital locations suggests that they are migrating outward faster than allowed if they formed at the same time as Saturn[3,4], motivating new moon formation scenarios[5,6]
Most prior theoretical studies have assumed a constant tidal lag angle θ for the tidal bulge raised by each moon, parameterized by a tidal quality factor Q 1/(2θ)
While the actual lag angle for tidally excited waves in the planet can vary, their effect can be described by an effective Q value governing the tidal interaction with each moon, whose value is inversely proportional to the tidal energy dissipation rate within Saturn[1]

Summary

Introduction

Prior monitoring of the mid-sized inner moons’ orbital locations suggests that they are migrating outward faster than allowed if they formed at the same time as Saturn[3,4], motivating new moon formation scenarios[5,6]. Our results show that most of Saturn’s moons, including Titan, are migrating outward more rapidly than expected from classical tidal models.

Results

Conclusion