LONG LIVE THE DARK SIDE: CYCLOID FORMATION ON A TIDALLY-LOCKED EUROPA

Cycloids are arcuate fractures that have only been definitively identified on Jupiter’s ocean-bearing moon, Europa. Cycloid shapes are controlled by the periodically-varying tidal stress field across Europa’s surface [1]. Past fits to individual cycloids imply that the cycloids have been shifted in longitude since they formed, presumably by slow, non-synchronous rotation (NSR) of the ice shell relative to the direction of Jupiter [2][3]. However, subsequent work on lineaments [4], strike-slip faults [5], and cycloid cusps [6] that included the effects of a small obliquity all concluded that longitude translation is neither necessary nor implied by the distributions and orientations of Europa’s tectonic features.

Here, we revisit fits to individual cycloids by inverse modeling the cycloids to determine the stresses and mechanical behavior implied by their shapes. In this study, we assume the cycloids formed at their present locations. Using mathematical functions to represent cycloid shapes, we can evaluate each point along a cycloid independently of any other. We compare each point to the stress field at its observed location and determine the time and stress at which a fracture segment with that orientation would be produced. Using this inverse method, we find that the paths of individual cycloids can be well-matched at their current locations, negating the need for NSR. We also find that 1) even though continuous propagation was no longer prescribed in the model, good fits imply that arcs form mostly continuously, and 2) to fit cycloids at their current locations requires that the stresses at which propagation begins and ends varies from arc to arc. These results align with a study of cycloid cusp angles, in which inferred failure stresses varied by roughly a factor of 2. Although more work is needed to further explore these findings, we now have the ability to reproduce cycloids, strike-slip faults, and linear fractures without stress or motion from NSR. Thus, we conclude that Europa’s ice shell is almost certainly tidally-locked over the timescale recorded by its surface geology.

[1] Kattenhorn and Hurford, 2009. In: Europa. [2] Hoppa et al., 2001, Icarus 153. [3] Rhoden et al., 2010, Icarus 210 [4] Rhoden et al., 2021, JGR Planets 126. [5] Rhoden et al. 2012, Icarus 218. [6] Rhoden and Hurford, 2013, Icarus 226.