Theoretical Modeling of Europan Cycloids: The Importance of Obliquity

Cycloids are thought to be cracks that form in response to tidal stress on Europa. Obliquity and non- synchronous rotation (NSR) alter the pattern of tidal stress and can thus be constrained through cycloid modeling. Several authors have published fits of theoretical models to three cycloids in Europa's southern hemisphere. The fits in Hoppa et al. (2001) captured the general trend of each cycloid, but the fits worsened with each additional arc and did not fit the cusp locations well. Hurford et al. (2007) used a different set of mechanical parameters for each arc of a cycloid, improving fits but requiring many more free parameters. In addition, they found that stress due to NSR improved fits. In both studies, the formation longitude of the cycloid was used as a fit parameter because observed cycloids could not be fit at their current locations; NSR could move features eastward over time. Despite the successes of cycloid modeling in the southern hemisphere, applying the same model to equatorial cycloids failed to produce even mediocre fits, most likely because the effects of obliquity were not considered. Inclusion of obliquity and the direction of the spin pole increase the parameter space and break symmetries in the stress field, so searching for fits by hand, as was the procedure in past work, becomes unwieldy. Therefore, the goal of this study is to automate the process of finding and evaluating fits and to examine the effects of obliquity on southern hemisphere cycloids. We have successfully built an automated cycloid simulator, which searches the parameter space and relies on a quantitative measure of goodness-of-fit when evaluating model cycloids. The resulting fits are much improved over those of Hoppa et al. (2001). They are almost as good as the fits of Hurford et al. (2007) but with far fewer parameters, as we used the same parameters for all arcs of a cycloid. For comparison, the Hurford et al. fit to the cycloid Cilicia required 20 free parameters; we achieved almost as good a fit with only seven free parameters. In addition, our work has shown that good fits require obliquity but not stress from NSR. However, the rotation itself, as opposed to stress it imparts, may still be important as we have yet to fit cycloids at their current longitudes.