Polar wander of an ice shell on Europa

An ice shell on Europa that is decoupled from the silicate core by a layer of liquid water has a thermal-equilibrium thickness profile that varies with position over its surface because of spatial variations in the surface temperature and tidal dissipation within the ice (G.W. Ojakangas and D.J. Stevenson 1989), Icarus 81, 220–241). The second spherical harmonic degree components of these thickness variations and of any fossil rotational and tidal bulges present on the shell contribute to the inertia tensor of the body. The problem is that of a planetary elastic lithosphere that is topographically loaded from below. Following R.J. Willemann and D.L. Turcotte (1981, Proc. Lunar Planet. Sci. B 12, 837–851), we develop equations describing the variations in the inertia tensor of a body when second harmonic degree topography is added to the base of the crust. For an ice shell on Europa, it is found that a state of thermal equilibrium may involve an unusual orientation of the principal axes of inertia (when hydrostatic bulges are ignored) in which the intermediate and maximum principal moments are interchanged. To reach the preferred orientation for synchronous satellites, a thermal-equilibrium shell must execute a net reorientation of 90° about the satellite-planet direction. We present a simple model of rigid, synchronously rotating satellite in a circular orbit for which the principal moment difference B - C increases with time, becoming positive for t > 0. The model demonstrates that the expected reorientation is indeed dynamically favored. We then consider a more realistic model in which Europa's shell and ocean are assumed to reorient as a single entity, independently of the core, hindered only by viscous dissipation within the shell. Such coupling of the shell with the ocean, and lack of coupling with the core, is suggested by G.W. Ojakangas (1988, Coupled Thermal and Dynamical Evolution of Planetary Bodies, Ph.D. thesis, California Institute of Technology). The model suggests that friction in the shell eliminates the possibility of polar wander unless a low-conductivity regolith increases the near-surface temperature by a few tens of degrees, so the ice just below the regolith behaves viscously on the polar wander time scale. However, if the equator-to-pole near-surface temperature difference is decreased by more than a critical, model-dependent amount, the shell's inertia tensor no longer has an unstable form in thermal equilibrium. Alternatively, polar wander may occur if preexisting surface fractures (e.g., due to tidal stresses) extend to a depth where the ice behaves viscously. These fractures must be lubricated (perhaps by liquid water from below). If the temperature T_f at the base of the regolith or the surface fractures is > 125°K, the model suggests that polar wander occurs on a time scale <∼2 x 10^6 years (decreasing as T_f increases), after B - C becomes postive. In the absence of dissipation, polar wander would occur in ∼few x 10^3 years. Large-scale polar wander may occur episodically, separated by periods on the order of the thermal diffusion time for the shell (∼10^7 years), although a state of slow, continuous drifting of the pole is also possible. The time scales of viscous flow of topography at the base of the ice is also near 10^7 years. Polar wander is a very effective means for fracturing the ice and may have contributed to the observed global fracture systems in Europa's ice.