45th Lunar and Planetary Science Conference (2014) 2659.pdf

BREAKING THE ICE: ON THE APPLICATION OF SYSTEM MECHANICS AND FRAGMENTATION THEORY TO THE CHAOS REGIONS OF EUROPA. C. C. Walker1, B. E. Schmidt1, and J. N. Bassis2, 1Georgia Institute of Technology, School of Earth and Atmospheric Sciences, 311 Ferst Drive, Atlanta, GA 30312 ([email protected]; [email protected]), 2University of Michigan, Atmospheric, Oceanic and Space Sciences, 2455 Hayward Street, Ann Arbor, MI 48109 ([email protected]).

Introduction: The observation of water plumes fracture propagation; i.e., we take into account the from the south pole of Enceladus [1] and the recent highly-fractured nature of the icy shells, and the likely discovery of similar features on Europa [2] hint at ice- interaction of rifts, a phenomenon observed both on penetrating fractures in the ice shells. The eruptions Earth’s ice shelves and in other media, such as - have been linked to tensile forces stemming from tidal breaker walls, airplane propellers, Arctic permafrost, effects that control the opening of the rifts [3, 4, 5]. mud flats in Death Valley, and others [9]. The study of crack penetration is highly dependent on Application of Fragmentation Theory: Recent work assumptions of ice shell thickness (and subsurface liq- suggests that chaos terrain formation may include a uid water ocean), surface and interior stresses, and ice collapse phase, and that the eventual appearance of the properties. The tidally-induced fields for Europa chaos terrain is determined in part by fracture density and Enceladus, specifically, have been studied in terms within the background terrain [10]. In studying the size of their ability to adequately open rifts in order to al- distribution of fragments in Europa’s chaos regions, it low for escape of subsurface material. is possible to back out physical properties of the ice, Both Enceladus’ and Europa’s surfaces are riddled such as material strength and cohesion properties and with fractures, which betray a long history of geophys- most importantly, energy necessary to create a frag- ical activity. With an ~100 km deep ocean lying atop a mentation event using fragmentation theory. Fragmen- silicate interior (e.g. [6], [7], [8]), Europa is an intri- tation theory describes the breakage of a body into guing target for astrobiological study. Ice cycling may several pieces (e.g. [11]). Dynamic fragmentation provide nutrients to the Europan ocean, and pores, ba- modeling in elastic and plastic solids is primarily a sal cracks, and grain boundaries in its ice may serve as statistical study of material behavior, and is catego- harbors for life. Such ice shell-ocean communication rized into three stages: (1) crack nucleation; (2) crack must occur over geologically short timescales in order propagation; (3) fragment coalescence. for Europa to be habitable. One way in which this can Implications for stress and energy in the ice occur is through disruption of the ice shell. Thus active shell: We use fracture spacing and fragment sizes to geological areas have strong implications for the recy- determine stress and energy associated with fracture cling of the ice shell, and the habitability of the ice array evolution and chaos terrain formation. shell itself. Fracture array propagation: The conclusion from Background: In order for subsurface water to observing neighboring, interacting rifts in the Amery erupt, a surface- or bottom-initiated crevasse (crevasse Ice Shelf [12], along with studies of other fractured is defined here as a crack in the ice that does not ex- media mentioned previously, is that the existence of tend the full thickness of the ice) must vertically prop- nearby fractures can affect an individual rift’s propaga- agate and penetrate the shell to reach a liquid reservoir. tion. This raises the question of the significance in the We consider two processes in the formation of terrains difference between the oft-used isolated crack model observed on Europa: the propagation of fracture sys- versus modeling shell-penetrating cracks as part of a tems and collapse/fragmentation. system of rifts. We follow the approach of [13], using Propagation of a multiple-fracture system: Initia- results from [14] to model closely-spaced fractures on tion and penetration of a surface crevasse is driven by Enceladus and Europa. The result of multiple fractures tensile forces at and near the surface. At depth these is to reduce the net stress intensity factor concentrated forces are opposed by the overburden pressure from at the rift tips, an effect that increases with decreasing the weight of the ice (glaciostatic pressure). Tensile rift spacing. Because of this reduction in stress con- stresses at the surface and within the upper brittle layer centration, a larger tensile stress is necessary to allow must be great enough to overcome the overburden for propagation deeper into the ice than has been pre- pressure at the base to allow for full penetration of the viously suggested in single-fracture models (Fig. 1). shell. For Europa, we can consider three possibilities: That is, closely-spaced fractures are much shallower thin ice shell (~5 km); thin ice lid over a local water than single fractures under the same amount of tensile source (~3-5 km); or much thicker ice (~20 km). Here, stress. For instance, under 3 MPa of deviatoric stress, we investigate the role of highly-fractured materials in a single crack can penetrate to ~5 km depth in a 20-km 45th Lunar and Planetary Science Conference (2014) 2659.pdf

Europan ice shell. Under the same stress, closely- the event to be approximately 1.5 kJ/kg, in agreement spaced fractures only propagate to ~1.5 km depth. This with previous estimates and measurements. Hence, we shallowing of fractures suggests that it is improbable will present our estimate of the energy released in cha- that fractures fully rupture the ice shell, and may sug- os terrain collapse through application of fragmenta- gest an alternate non-ocean source for the plumes on tion theory and iceberg capsize analysis. This ap- Europa. Additionally, the fact that higher stresses proach allows us to understand the mechanism behind would be required to open the closely-spaced rifts dynamic collapse of the ice shell as well as its potential points to the possibility that simple tidal models and for mixing material in the upper ~5km of the ice shell estimates of tidal stress are not enough to predict the downward, providing input to a recycling ice shell. behavior of fracture system. Thus, in determining the fragment size distribution, and the dynamic history of that ice, we will constrain physical properties of the ice shell, stress necessary for fracture feature formation, energy released in a col- lapse event associated with chaos formation, and their respective implications for Europa’s habitability.

Figure 1. The effect of multiple fractures in a region of ice under tension or compression: the bottom 1 km Figure 2. Right: Common geometric fragmentation (left) and top 1 km (right) of a 5-km thick Europan ice , picture from [9]; Left: PIA01403 - chaos lid (presumed above a subsurface reservoir). Propaga- region on Europa taken by Galileo in 1998; (a) Ran- tion depth (or height) in terms of fraction of the shell dom lines of equal length; (b) Pickup Sticks/Mott penetrated for basal fractures (left) and surface frac- fragmentation; (c) Sequential Segmentation; (d) Same tures (right), for both single and multiple crack cases as (c) with conditions on shortest dimension; (e) Ran- over a range of stress values. domly distributed/oriented segments; (f) Voronoi- Dirichlet fragmentation. Each type is associated with Fragmentation events: Different patterns of frag- specific length scales and fragmentation types. mentation can produce different estimates of material properties and the energy required to produce the References: [1] Porco, C. C. et al. (2006) Science, fragmentation event, examples of which are shown in 311, 1393–1401. [2] Roth, L. et al. (2013) Science, Fig. 2 and defined in [11]. A characteristic length Online 12 Dec. 2013. [3] Hurford, T.A. et al. (2007) scale is based on the local balance of kinetic and frac- Nature, 447, 292-294. [4] Smith-Konter, B. and Pappa- ture energy and layout of fragments. In this theory, we lardo, R.T. (2008) Icarus, 198, 435-451. [5] Olgin, consider a body to break apart into a certain collection J.G., et al. (2011) GRL, 380, L02201. [6] Khurana, of fragments. Each fragment takes kinetic energy as K. K., et al. (1999) Nature, 395, 777-780. [7] Kivel- the object breaks up, and this energy goes into local son, M. G., et al. (1999) JGR, 104, 4609-4625. [8] expansion and rigid-body motion. Local kinetic ener- Zimmer, C., Khurana, K. K. and Kivelson, M. G. gy then contributes to further failure. A characteristic (2000) Icarus, 147, 329-347. [9] Parker, A.P. (1998) length scale for fragmentation is based on the energy Army Armament Research Con-tractor Report, balance of potential, kinetic, and fracture energies in a ARCCB-CR-98009. [10] Schmidt, B. E. et al. (2011), given material [11]. Thus, [11] determined the energy Nature, 479, 502-505. [11] Grady, D. E. and Kipp, M. driving fragmentation in two dimensions based on ma- E. (1995) Int. J. Sol. and Struct., 32, 2779-2791. [12] terial density, strain rate, surface energy, propagation Walker, C. C., Bassis, J. N., Fricker, H. A., and Czer- speed, and fracture . winski, R. J. (2013) JGR, 118, in press. [13] van der We used simple statistical model [11] to test the Veen, C.J. (1998) Cold Regions Science and Technol- use of fragmentation theory on collapse features. Us- ogy, 27, 31-47. [14] Patterson, W.S.B. (1994) Per- ing published fragment size data from the Val Pola gammon/ Elsevier. [15] Crosta, G. B., Chen, H., and avalanche [15], we determined the energy driving Lee, C. F. (2004) Geomorphology, 60, 127-146.