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

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 1 , 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 Titans orbital expansion rate. We find Titan migrates away from Saturn at 11.3 ± 2.0 cm/year, corresponding to a tidal quality factor of Saturn of Q ' 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 2 , 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 Saturns 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.Saturn is orbited by 62 moons, and the intricate dynamics of this complex system provide clues about its formation and evolution. Of crucial importance are tidal interactions between the moons and the planet. Each moon raises a tidal bulge in the planet, and because Saturn rotates faster than the moons orbit, frictional processes within the planet cause the tidal bulge to lead in front of each moon. Each moon's tidal bulge pulls the moon forward such that it gains angular momentum and migrates outward, similar to the tidal evolution of the Earth-Moon system. However, in giant planets such as Saturn, the dissipative processes that determine the bulge lag 2

The past and future obliquity of Saturn as Titan migrates

“…Since Titan is in the close-in regime, its outward migration produces an increase in α. The migration rate of Titan recently measured by Lainey et al (2020) supports the tidal theory of Fuller et al (2016), through which the time evolution of Titan's semi-major axis can be expressed as…”

“…For years, the scenarios that were most successful in reproducing Saturn's current obliquity through this resonance invoked the late planetary migration Boué et al 2009;Vokrouhlický & Nesvorný 2015;Brasser & Lee 2015). However, Saillenfest et al (2021) have recently shown that this picture is incompatible with the fast tidal migration of Titan detected by Lainey et al (2020) in two independent sets of observations -assuming that this migration is not specific to the present epoch but went on over a substantial interval of time. Indeed, satellites affect the spin-axis precession of their host planets (see e.g.…”

“…The findings of Saillenfest et al (2021) have been obtained through backward integrations from Saturn's current spin orientation, and by exploring migration histories for Titan in the vicinity of the nominal scenario of Lainey et al (2020). However, observation uncertainties and our lack of knowledge about the past evolution of Titan's migration rate still allow for a large variety of migration histories, and one can wonder whether the dramatic influence of Titan is a generic result or whether it is restricted to the range of parameters explored by Saillenfest et al (2021).…”

Orbital evolution of Saturn’s satellites due to the interaction between the moons and the massive rings

“…The observed current fast tidal orbital expansion rate (Lainey et al 2012(Lainey et al , 2017 and observations of the rings by Cassini suggest late formation of the satellites (see, e.g., Ida 2019) such as the formation model from a hypothetical ancient massive rings (Charnoz et al 2011;Crida & Charnoz 2012), which we refer to as the disk. We note, however, that a possible slower tidal orbital expansion rate in the past, before resonance locking between the orbital frequency and the planetary internal oscillation mode, could allow the satellite formation in the circumplanetary disk 4.5 G years ago (Lainey et al 2020).…”

Returning Samples From Enceladus for Life Detection

“…The only known heat source able to maintain water liquid on tiny Enceladus is from the dissipation of tides raised by Saturn. Where energy is dissipated is uncertain: water flowing through a permeable rocky core (Choblet et al, 2017), ocean movement damped by the overlying ice (Tyler, 2020), and/or recently increased equilibrium forcing of the ice shell if Enceladus' orbit is expanding at a nearly constant rate due to changes in Saturn's interior (Nimmo et al, 2018;Lainey et al, 2020). Each mechanism could alone sustain the current ocean.…”