Numerical Modelling of the Influence of Tidal Stresses on Qualitative Fracture Patterns on the Surface of Europa

ABSTRACT The ice crust of Jupiter's Galilean satellite Europa exhibits a number of large-scale lineae features, as well as numerous regions with smaller scale lineae patterns. In this work, a three-dimensional finite-element simulator is used to model lineae as fractures in the crust that nucleate, grow, and interact. The medium is assumed to be isotropic and linearly elastic. Fractures are assumed to grow primarily in tension due to tidal stresses in the ice crust, and a damage criterion is used to model the weakening of the ice matrix that occurs concurrently with fracturing. The growth of multiple fractures is modelled geometrically as a function of multi-modal stress intensity factors computed at the fracture tips. The tidal forces that drive this fracturing process are computed according to the model of Wahr et al. (2009), and fracturing is evaluated over multi-scale periods from days to millions of years. Fracture nucleation and growth are modelled within the span of the satellite, with emphasis on characterizing the fracture patterns in the equatorial region. Multiple three-dimensional non-planar fractures are seen to grow and interact within each region. The simulated patterns are qualitatively compared against images obtained by NASA's Galileo mission. INTRODUCTION Europa is the fourth largest Galilean moon of Jupiter; with a radius of 1560 km (Nimmo et al., 2007), and is the sixth closest to its parent planet. It has a rocky core that is entirely surrounded by an ice shell, which is estimated to be between 1 and 30 km thick (Billings and Kattenhorn, 2005), where the lower estimates arise from mechanical flexure analysis (Figueredo et al., 2002; Nimmo et al., 2007), and the higher estimates arise from thermodynamic analysis (Hussmann et al., 2002; McKinnon, 1999; Ojakangas and Stevenson, 1989). Estimates based on impact cratering tend to lie between these two bounds (Greeley et al., 1998; Moore et al., 1998; Schenk, 2002). Encased between the silicate core and the ice shell is thought to be a vast liquid water ocean, approximately 100 km thick (Pappalardo et al., 1999). This ocean, and therefore Europa as a whole, is the object of great scientific curiosity, due to its viability as a habitat for extra-terrestrial life (Schulze-Makuch and Irwin, 2000; Kargel et al., 2000).