Resonance locking as the source of rapid tidal migration in the Jupiter and Saturn moon systems

Abstract

The inner moons of Jupiter and Saturn migrate outwards due to tidal energy dissipation within the planets, the details of which remain poorly understood. We demonstrate that resonance locking between moons and internal oscillation modes of the planet can produce rapid tidal migration. Resonance locking arises due to the internal structural evolution of the planet and typically produces an outward migration rate comparable to the age of the solar system. Resonance locking predicts a similar migration timescale but a different effective tidal quality factor Q governing the migration of each moon. It also predicts nearly constant migration timescales a function of semi-major axis, such that effective Q values were larger in the past. Recent measurements of Jupiter and Saturn's moon systems find effective Q values that are smaller than expected (and are different between moons), and which correspond to migration timescales of ∼10 Gyr. If confirmed, the measurements are broadly consistent with resonance locking as the dominant source of tidal dissipation in Jupiter and Saturn. Resonance locking also provides solutions to several problems posed by current measurements: it naturally explains the exceptionally small Q governing Rhea's migration, it allows the large heating rate of Enceladus to be achieved in an equilibrium eccentricity configuration, and it resolves evolutionary problems arising from present-day migration/heating rates.

One‐Dimensional Convective Thermal Evolution Calculation Using a Modified Mixing Length Theory: Application to Saturnian Icy Satellites

“…Recently, Fuller et al (2016) reported that dynamical tides can account for a tidal heating rate of ∼50 GW for the Enceladus-Dione resonance without requiring a young age for the Saturnian system. If half of this heat is used to warm Dione and the rest is used to warm Enceladus, both satellites can possess ∼30 km thick subsurface oceans, which is similar to those estimated from geodetic data analyses.…”

Classification of Satellite Resonances in the Solar System

“…After completion of most of the research reported in our paper, Fuller et al (2016) proposed resonance lock to account for the unexpectedly fast migration rates reported by Lainey et al (2015). We summarize the influence of resonance lock on the dynamics of MMR in Section 5.…”

“…All this suggests another type of tidal interaction must prevail. In this context, we find particularly appealing the hypothesis by Fuller et al (2016) of resonance lock with dynamical tides particularly appealing.…”

“…Both equilibrium tides and dynamic tides can give rise to conventional tidal torques. Resonance lock involves a dynamic tide whose frequency in the planet's rest frame, w a , is locked to that of the satellite's mean motion, n, according to (Fuller et al 2016)…”

“…Outward migration rates are much faster than expected, especially for satellites that orbit far from Saturn. Fuller et al (2016) propose an explanation involving resonance lock between frequencies of tides and those of normal modes or waves. They favor g-modes but also mention inertial waves (Ogilvie 2014).…”