The Past, Present, and Future of Tidal Deformation at Europa

We present the results of a tidal deformation model for Europa in which the tidal potential and associated stresses evolve with time as the orbit changes. With this model we predict the times and locations at which the tidal stress in the ice shell is maximum, due to the evolution of Europa’s orbital configuration. The orbital elements of Europa change with time due to perturbations from the oblate mass distribution of Jupiter, and from gravitational interactions with neighboring satellites. This is particularly relevant in the Galilean satellite system, in which Io, Europa, and Ganymede participate in the Laplace resonance.

Using a secular variation orbital model for Jupiter and the Galilean satellites, we have determined the time variations of eccentricity, longitude of periapse, inclination, and longitude of the ascending node for Europa. This allows us to predict the orbital state for millions of years into the past and future. We then input the orbital element variations into an axi-symmetric tidal deformation model. The variation in stress with radius, within the ice shell, is small and all lateral variation patterns are preserved. As a result, we restrict our analysis to the free surface where only two components of the axisymmetric stress tensor remain non-zero, and are the principal stresses.

Stress magnitudes are maximized at the “tidal equator” at all times, with additional extrema at the sub- and anti-Jovian locations. On the 3.55-day orbital time scale, stress maximizes when the distance to Jupiter is farthest from its mean value (periapse and apoapse). On longer time scales, the stress extrema are maximized at times of local eccentricity peaks.

Although appropriate failure conditions for an ice shell on Europa are not fully known, we use Anderson theory to divide the surface into expected faulting style provinces. Using a Coulomb stress function, as an indicator of fracture propensity, we compute the fault plane orientations, at various locations on Europa’s surface, which maximize the Coulomb stress. We repeat this analysis at epochs of increased eccentricity to compare today’s stress field to that of past and future. We then predict the most probable locations, times, and occurrence frequency for tidal fracturing of Europa’s surface.