Frequency-dependent tidal dissipation in a viscoelastic Saturnian core and expansion of Mimas’ semi-major axis

Abstract

Context. Regarding tidal dissipation in Saturn, usually parameterized by Saturn's quality factor Q, there remains a discrepancy between conventional estimates and the latest determination that has been derived from astrometric observations of Saturn's inner satellites. If dissipation in Saturn is as large as the astrometric observations suggest, and is independent of time and tidal frequency, conventional models predict that Mimas' initial orbit should be located inside Saturn's synchronous orbit or even inside its Roche limit, in contradiction to formation models. Aims. Using simple structure models and assuming Saturn's core to be viscoelastic, we look for dissipation models which are consistent with both the latest astrometric observations and with Mimas' orbital migration. Methods. Firstly, using a two-layer model of Saturn's interior structure, we constrain the ranges of rigidity and viscosity of Saturn's core which are consistent with Saturn's dissipation derived from astrometric observations at the tidal frequencies of Enceladus, Tethys, and Dione. Next, within the constrained viscosity and rigidity ranges, we calculate Mimas' semi-major axis considering the frequency dependence of viscoelastic dissipation in Saturn's core. By the two calculations, we evaluate (1) Saturnian models which can explain the astrometrically determined Saturnian dissipation, and (2) whether Mimas' initial semi-major axis is larger than the synchronous orbit. Results. We show that if the core is assumed to be solid with a viscosity of 10 13 −10 14 Pa s (depending on its size), the lower boundary of the observed Saturnian dissipation at tidal frequencies of Enceladus, Tethys, and Dione (k 2s /Q s ∼ 4 × 10 −5 where k 2s is Saturn's second degree Love number and Q s its quality factor) can be explained by our model. In this viscosity range, Mimas can stay outside the synchronous orbit and the Roche limit for 4.5 billion years of evolution. Conclusions. In the case of a frequency dependent viscoelastic dissipative core, the lower boundary of the observed Saturnian dissipation can be consistent with the orbital expansion of Mimas. In this model, the assumption of a late formation of Mimas, discussed recently, is not required.

Evolution of Saturn’s mid-sized moons

“…The dependence on frequency seems small at the present day at the orbital frequencies of Enceladus, Tethys, Dione, and (to a lesser extent) Rhea 2 . Saturn’s internal structure and evolution (presence and extent of a core, contraction over time, helium separation from hydrogen) remain too poorly constrained to fully match predictions and observations of Q as a function of frequency and time 2;75 . Thus, future work could more realistically simulate Saturn’s Q .…”

Tidal dissipation in stars and giant planets: Jean-Paul Zahn's pioneering work and legacy

“…Following their method, Storch & Lai (2014) proposed this mechanism to explain the formation of hot Jupiters through circularization in a high-eccentricity migration scenario. Shoji & Hussmann (2017) also demonstrated, taking into account the frequency-dependence of the core viscoelastic dissipation when solving the tidal orbital migration equations for the moons, that a strong tidal dissipation in Saturn does not imply necessarily young moons. Storch & Lai (2015) also improved this bi-layer model by treating the case of a homogeneous core surrounded by a polytropic gas envelope.…”

How Cassini can constrain tidal dissipation in Saturn

“…Shoji & Hussmann (2017) propose that damping in a viscoelastic core of Saturn may have a damping efficiency varying with frequency.…”

“…Shoji & Hussmann (2017) propose that damping in a viscoelastic core of Saturn may have a damping efficiency varying with frequency.3 Late formation of Saturn's satellites has been proposed(Charnoz et al 2011;Ćuk et al 2016). …”