Inferring the Mean Thickness of the Outer Ice Shell of Enceladus From Diurnal Crustal Deformation

Abstract

The thickness of the outer ice shell plays an important role in several geodynamical processes at ocean worlds. Here, we show that observations of tidally driven diurnal surface displacements can constrain the mean ice shell thickness, d∼ice ${\tilde{d}}_{\mathit{ice}}$. Such estimates are sensitive to any significant structural features that break spherical symmetry such as faults and lateral variation in ice shell thickness and structure. We develop a finite‐element model of Enceladus to calculate diurnal tidal displacements for a range of d∼ice ${\tilde{d}}_{\mathit{ice}}$ values in the presence of such structural heterogeneities. Consistent with results from prior studies, we find that the presence of variations in ice shell thickness can significantly amplify deformation in thinned regions. If major faults are also activated by tidal forcing—such as Tiger Stripes on Enceladus—their characteristic surface displacement patterns could easily be measured using modern geodetic methods. Within the family of Enceladus models explored, estimates of d∼ice ${\tilde{d}}_{\mathit{ice}}$ that assume spherical symmetry a priori can deviate from the true value by as much as ∼41% when structural heterogeneities are present. Additionally, we show that crustal heterogeneities near the South Pole produce differences of up to 35% between Love numbers evaluated at different spherical harmonic orders. A ∼41% range in estimates of d∼ice ${\tilde{d}}_{\mathit{ice}}$ from Love numbers is smaller than that found with approaches relying on static gravity and topography (∼250%) or analyzing diurnal libration amplitudes (∼85%) to infer d∼ice ${\tilde{d}}_{\mathit{ice}}$ at Enceladus. As such, we find that analysis of diurnal tidal deformation is a relatively robust approach to inferring mean crustal thickness.

Using Tidally‐Driven Elastic Strains to Infer Regional Variations in Crustal Thickness at Enceladus

“…We find that our approach can correct for over‐ (under‐) predictions of strain due to excessively low (high) initial estimates of $$\tilde{D}$$ (for details, see Text S3 in Supporting Information ). A reduced G (e.g., due to pervasive crustal fracturing) may also result in a derived value of $$\tilde{D}$$ that is inconsistent with constraints set by the amplitude of the forced libration of the ice shell (Berne et al., 2023b; Beuthe, 2018; Hemingway & Mittal, 2019; Van Hoolst et al., 2016). In this case, repeating our analysis with a lowered input G (see Table S1 in Supporting Information ) should produce a derived $$\tilde{D}$$ that more closely matches the mean thickness expected for the satellite (Hemingway & Mittal, 2019).…”

“…Following the formulation described in Supplementary Section S1.1 of Berne et al (2023b), we apply forces associated with the driving potential produced by time-dependent diurnal eccentricity tides V(r, θ, ϕ, t) (to the first order in eccentricity) to model geometries (Murray & Dermott, 2000):…”

Impact of the Core Deformation on the Tidal Heating and Flow in Enceladus' Subsurface Ocean

“…We assume that the ice shell behaves as an elastic solid. As shown by Souček et al (2019) and Berne et al (2023), the effect of viscosity on tidal deformation of Enceladus' ice shell is minor and can be neglected in the first approximation. Unfortunately, there are presently no observations to constrain the material parameters of Enceladus' core.…”

“…One 10.1029/2023JE007907 3 of 16 way to solve problems with complex geometry is to use the finite element method. However, even though this method has proven to be effective in modeling the tidal deformation and viscous flow in Enceladus' ice shell (Běhounková et al, 2017;Berne et al, 2023;Čadek et al, 2019a, 2019bSouček et al, 2016Souček et al, , 2019, its application to the tides in the ocean is still prohibitively expensive due to the fact that the thickness of the boundary layers in the ocean is much smaller than the characteristic length scale in the ice shell and, therefore, simulations have to be performed with a spatial resolution that is significantly higher than that usually considered in the ice shell.…”

The Global Shape, Gravity Field, and Libration of Enceladus

“…Where appropriate, we added terms to account for long period mean motion librations. We also included a term in the prime meridian expression to account for the observed forced libration (Nadezhdina et al., 2016; Thomas et al., 2016) and ignore the potential biasing impact of deformation over the orbital timescale (Berne et al., 2023; Van Hoolst et al., 2016).…”