Modeling of fault initiation in the ice shell of Enceladus

In light of the growing interest in the composition and habitability of the ocean beneath the icy crust of Enceladus, we revisit the basic hypotheses behind the formation of the prominent Tiger Stripes fault system on Enceladus’ south pole. This study revolves around the formation of new fractures assuming the existence of the first one, considering two distinct physical scenarios.

In the first one, we expand the idea by Hemingway et al.[1]. First, we approximate the ice crust by a Kirchhoff plate to obtain a fourth-order ordinary differential equation modeling the deformation of the plate. The solution of this equation is obtained by the method of variation of parameters providing us with a function describing the plate’s response to different surface load distributions. By investigating the solution profiles for both the approximated point load [1] and the more realistic distributed load [2] and employing the criterion for the maximal bending moment of the plate, we find that the maxima correspond to the positions of the new fracture. Our results indicate that while simple point load approximation quite accurately predicts new fracture positions for a reasonable estimate of the elastic shell thickness, the more realistic load model implies a thinner crust more consistent with observations [3].
In the second scenario, we couple the mechanical Kirchhoff plate problem with damage mechanics [4] which allows us to model the formation of the crack due to periodic tidal loading rather than distributed surface mass. We compare the results of these two scenarios and discuss their implications both for the formation hypotheses and the structural constraints on the ice shell thickness. 

This research was supported by the Czech Science Foundation under Grant No. 25-16801S.

[1] Douglas J. Hemingway, Maxwell L. Rudolph, and Michael Manga. Cascading parallel fractures on Enceladus. Nature
Astronomy, 4(3):234–239, 2020

[2] Ben S. Southworth, Sascha Kempf, and Joe Spitale. Surface deposition of the Enceladus plume and the zenith angle of
emissions. Icarus, 319:33–42, 2019

[3]Ondřej Čadek, Gabriel Tobie, Tim Van Hoolst, Marion Massé, Gaël Choblet, Axel Lefèvre, Giuseppe Mitri, Rose-Marie
Baland, Marie Běhounková, Olivier Bourgeois, et al. Enceladus’s internal ocean and ice shell constrained from cassini
gravity, shape, and libration data. Geophysical Research Letters, 43(11):5653–5660, 2016

[4] Ravindra Duddu, Stephen Jiménez, and Jeremy Bassis. A non-local continuum poro-damage mechanics model for hydrofracturing of surface crevasses in grounded glaciers. Journal of Glaciology, 66(257):415–429, 2020