The effects of laterally varying icy shell structure on the tidal response of Ganymede and Europa

Abstract

We use a finite-element model to solve for the response of Ganymede and Europa to tidal forcing from Jupiter, using various icy shell models with laterally variable (3-D) structure. In all cases, the shell is assumed to be underlain by a liquid-water ocean. Icy shells with laterally varying thickness are derived from a thermal conduction model. Three-dimensional shear modulus profiles for the shell are built either from a conduction model or, for Europa, by assuming a hemispherical difference in composition. Icy shell structures with a nonglobal ocean are built for Ganymede. Using these shell structures to calculate the tidal response of Ganymede and Europa, we conclude the following: (1) the presence of lateral variations in thickness or in shear modulus would not degrade future attempts to use tidal observations to decide on the existence or absence of a liquid ocean and to determine the mean icy shell thickness. (2) Given accurate enough observations, the presence of lateral variations in thickness or in shear modulus could be determined by searching for nondegree-2 components in the tidal response. (3) In the absence of significant viscous convective flow in the shell, the effects of a laterally varying shear modulus on the tidal response would be smaller than those of a laterally varying shell thickness. (4) If the shell is partially grounded, tidal observations of either gravity or uplift would be able to roughly differentiate regions where the ice is grounded from those where it is floating.

Enceladus’s crust as a non-uniform thin shell: I tidal deformations

“…Note that the tidal thin shell equations in matrix form are not perturbative in that sense, but they can be analytically solved with a perturbative series to arbitrary order (see Appendix I of Be10 ). Mode coupling analysis is particularly relevant to tidal tomography, which consists in constraining the lateral variations of the shell structure with non-degree-2 tides [Zhong et al, 2012;A et al, 2014;Qin et al, 2016]. Unfortunately, tidal geodetic measurements will not available for a long time, not even for degree-2 tides..…”

Ocean worlds in the outer solar system

“…Similarly, such calculations usually assume that the various layers are spherically symmetric, which for somewhere like Enceladus is likely a significant oversimplification. The tidal response of bodies with lateral variations in mechanical properties can be calculated [ A et al , ], but doing so is computationally challenging and not likely to be testable with observations unless an orbiter is involved.…”

The Growth of Europa's Icy Shell: Convection and Crystallization

“…Ice shell thickness is a strong determining factor in the temperature structure of the shell as well as its overall strength and rheology (Mitri & Showman, 2005), which exert important influences on the distribution of tidal heating (A et al., 2014) and the formation of Europan surface features (e.g., Billings & Kattenhorn, 2005; Collins & Nimmo, 2009; Culha & Manga, 2016; Han & Showman, 2008; Kattenhorn & Hurford, 2009; Schenk & Pappalardo, 2004). Furthermore, the thickness of the ice also controls the potential for thermal convection to occur within the shell (Barr & McKinnon, 2007; Han & Showman, 2005; McKinnon, 1999; Pappalardo et al., 1998).…”