Ocean Pressurization, Stress Evolution, and Tensile Fracture within Icy

Introduction: Liquid water has been inferred to erupt in Europa's geologic past [e.g. 1] and a mixture of water vapor and ice is currently erupting from Enceladus' south polar region [2] whose source may be a liquid water ocean. Water confined to a subsurface ocean faces two impediments in reaching the surface. First, it is negatively buoyant with respect to ice. Second, it requires a pathway through which to flow. Thickening of a global or regional ice shell overlying a liquid water ocean causes pressurization of the underlying ocean owing to the volumetric expansion of water as it freezes to ice. As a result of ocean pressurization, tangential stresses of several MPa can be produced in the overlying ice shell. Stresses also arise in ice shells due to thermal contraction, but these tend to be much smaller. We solve the equations governing heat transfer and change of stress due to ice shell thickening and then use the obtained stress distribution to predict the depth to which tensile fractures may penetrate. Background: In previous work [3], we investigated the ability of tensile fractures to penetrate downward through an ice shell whose basal region does not support tensile stresses due to viscoelastic relaxation. The evolution of thermal stresses was studied by Hillier and Squyres [4], and also by Nimmo [5]. Recently, Manga and Wang [6] studied the evolution of ocean pressure using a simplified mechanical model in which the outer portion of the ice shell was elastic and the inner portion viscous rather than solving the full viscoelastic problem. The propagation of tensile fractures through an ice shell is made possible by tensile stresses in the upper, elastic region of an ice shell. When the tip of a fracture is sufficiently close to the base of an ice shell, the lower boundary, which is free of shear tractions, aids fracture penetration [7]. In contrast, in the warmer basal region of an ice shell, tensile stresses are relaxed due to viscous flow, and this effect tends to inhibit fracture penetration [3]. Fractures that initiate at the surface of an icy moon are essentially vacuum-filled, and consequently the pressure exerted by overburden is very important in closing fractures. The depth to which fractures penetrate on a particular satellite is a function of gravitational acceleration, which differs by about an order of magnitude between Europa and Enceladus. Approach: We describe an ice shell as a …