Enceladus's and Dione's floating ice shells supported by minimum stress isostasy

Abstract

Enceladus's gravity and shape have been explained in terms of a thick isostatic ice shell floating on a global ocean, in contradiction of the thin shell implied by librations. Here we propose a new isostatic model minimizing crustal deviatoric stress and demonstrate that gravity and shape data predict a 38 ± 4 km thick ocean beneath a 23 ± 4 km thick shell agreeing with—but independent of—libration data. Isostatic and tidal stresses are comparable in magnitude. South polar crust is only 7 ± 4 km thick, facilitating the opening of water conduits and enhancing tidal dissipation through stress concentration. Enceladus's resonant companion, Dione, is in a similar state of minimum stress isostasy. Its gravity and shape can be explained in terms of a 99 ± 23 km thick isostatic shell overlying a 65 ± 30 km thick global ocean, thus providing the first clear evidence for a present‐day ocean within Dione.

Internal Energy Dissipation in Enceladus's Subsurface Ocean From Tides and Libration and the Role of Inertial Waves

“…The peaks in the dissipation profile are due to the augmented contribution caused by the internal shear layers inside the ocean. This can be observed from the two upper plots of Figure , which show the density of kinetic energy for two different values of η (both within the range 0.82< η <0.85 obtained by Beuthe et al, ), one associated to larger dissipation and one to smaller dissipation. The corresponding values of can be read from the bottom plot of Figure and differ by 3 orders of magnitude.…”

“…If dissipation is not concentrated in the core or in the shell, one possibility is that it takes place predominantly in the ocean. Most of the current models focusing specifically on the ocean layer rely on the solution of the Laplace Tidal Equations (LTE) whereby the fluid is modeled as a two‐dimensional thin layer (Beuthe et al, ; Hay & Matsuyama, ; Matsuyama et al, ; Tyler, , ). However, gravity and topography data suggest that the average thickness of the ocean is not negligible compared to the size of the moon, ∼38 km if the crustal topography is isostatically supported, which is also consistent with the thin crust inferred from libration (Beuthe et al, ; Hemingway & Mittal, ).…”

The Gravitational Signature of Martian Volcanoes

“…We describe in the appendix a derivation of Q l using a first‐order relationship between surface relief and predicted gravity and a model of thin elastic shells (Turcotte et al, ). We note that models with thick elastic shells (e.g., Banerdt et al, ) and with a minimum stress definition of isostasy (Beuthe et al, ) can also be found in the literature, but these generally yield similar results as long as the investigated wavelength is several times greater than the elastic plate thickness (Zhong & Zuber, ), which is the case in this study. The model is nearly identical to Grott and Wieczorek (), where the surface load density is allowed to differ from that of the crust.…”

Convection in Thin Shells of Icy Satellites: Effects of Latitudinal Surface Temperature Variations

“… Note . Satellite parameters are taken from Ojakangas and Stevenson (), Bergstralh et al (), Schubert et al (), Nimmo and Manga (), Spencer et al (), Sotin et al (), O'Neill and Nimmo (), Hammond and Barr (), Quick and Marsh (), Beuthe et al (), and references therein. Surface temperature variation calculations follow Ojakangas and Stevenson (), see supporting information.…”