Kattenhorn, S.A., Groenleer, J.M., Hicks, A.R. (2006)
Cuspate cracks on icy moons: A smoking gun for the existence of a subsurface ocean?
Proceedings of the NASA-Idaho Space Grant Consortium Research Symposium 1: 21-23.
Of all the icy moons in the solar system, Jupiter's moon, Europa, and Saturn's moon, Enceladus, are particularly intriguing due to the manner in which their surfaces are pervasively fractured. Both moons show a range of fracture types and morphologies that point to a varied tectonic history on each moon. At the cold temperatures that exist on the surfaces of these moons (~70-100 K), ice behaves as a brittle material. However, all brittle materials require driving stresses of sufficiently high magnitude to induce fracturing. In the case of Europa, those stresses are induced by a number of mechanisms but primarily in response to the effects of tidal bulges that oscillate in both longitudinal location and in amplitude. These tidal bulges are hypothesized to exist in a global liquid water ocean that deforms the overlying ice shell. In the case of Enceladus, the source of the stress is unknown and detailed studies of the moon's fracture system have only just begun, facilitated by high resolution images from NASA's ongoing Cassini mission. One of the most intriguing differences between Europa and Enceladus is the fact that there is a somewhat uniform global distribution of fracture types on Europa; however, on Enceladus, fracture types and fracture densities cluster into distinct domains that suggest localized mechanisms are responsible for fracturing on Enceladus.
On Europa, oscillating tidal bulges are predicted to produce principal stresses in the ice shell that rotate through 180° of azimuth during each orbit, changing in magnitude during this process to produce a repeating cycle each orbit. These rotating stresses are referred to as diurnal stresses. If these stresses actually exist, any tensile fracture growing continuously during the ongoing rotation of the diurnal stresses would be expected to follow a curved crack path. Such fractures exist on Europa and are called cycloids. They form chains of arcuate segments linked at V-shaped cusps, producing a scalloped or cuspate appearance. These cycloids provide very strong evidence for the existence of an underlying ocean on Europa that responds diurnally to the tidal pull of Jupiter.
To provide further support for this notion, we (Kattenhorn and Groenleer) have placed considerable emphasis on cusp locations along cycloids to demonstrate that cusp angles can be perfectly reconciled with predicted angles based on calculated diurnal stresses related to oscillating tidal bulges. The basis for our approach is that a crack on Europa that is subject to rotating stresses will need to undergo a combination of temporally variable sliding, opening, and closing in response to these stresses. Along two cycloid chains, we calculated the ratio of shear to normal stress that would have been resolved onto the end of an existing cycloid crack by tidal stresses at the instant that each successive cusp developed. We used this stress ratio and principles of linear elastic fracture mechanics to predict the cusp angles that theoretically could have developed at the tip of a slipping cycloid segment. In 100% of the cases, we found a predicted cusp angle that exactly matched the measured cusp angle. Hence, cusp angles on Europa are also consistent with the presence of a below-ice ocean and the associated stress field induced in the ice shell by the tidal bulges therein. Our results indicate that a cycloid cusp is not initiated at the point in the orbit when the principal tensile stress is maximized (the limiting point in the orbit in the currently accepted model for cycloid growth on Europa), but may instead form earlier or later in the orbit when a critical ratio of shear to normal stress is attained, typically when the tensile normal stress on the slipping cycloid is approximately maximized. Another important result is that the model results only work if cycloids formed at a different longitudinal position to where they are currently found. This is possible only if nonsynchronous reorientation of the ice shell occurred over long periods of time, as has been proposed by several researchers. Such shell reorientation is most likely if the ice shell sits above liquid water.
The presence of cycloids on Europa provides a reason as to why there are seemingly no cycloids on Enceladus: the absence of a global subsurface ocean on Enceladus. Nonetheless, Enceladus is most fractured in its southern hemisphere, particularly in the south polar region where there are also a notable thermal anomalies (spikes) along fractures in the so-called Tiger Stripes region. We (Kattenhorn and Hicks) have mapped many of these fractures, some of which appear to be slightly cuspate, raising the question as to whether cycloid-like cracks do exist on Enceladus, perhaps indicative of a localized, tidally-influenced, subsurface ocean in the south polar area.
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