Thermal state of an ice shell on Europa

We consider a model of Europa consisting of an ice shell that is decoupled from a silicate core by a layer of liquid water. The thickness of the shell is calculated as a function of colatitude and longitude, assuming that a state of conductive equilibrium exists with the incident annual average solar insolation, tidal dissipation within the shell, and heat flow from the core. Ice thickness profiles are calculated for each of two plausible rheological behaviors for ice: the Maxwell rheology and the generalized flow law rheology. In both cases the strong temperature dependence of the dissipation rate, as well as the temperature dependence of the thermal conductivity of ice, is explicitly included. Because of the strong temperature dependence of the dissipation rate, nearly all of the tidal dissipation is concentrated in the lowermost few kilometers of the shell. Even though the effective Q of the greater part of the shell is ≫ 100 in our models, average shell thickness do not exceed 25 km. Thus, if the total thickness of H ₂O which mantles Europa is ≳25 km, none of our models admit the possibility of a completely frozen H ₂O layer, although such a state cannot be entirely ruled out, because the rheology of ice at the low tidal frequency has not been directly measured. The total dissipation rates in our models are comparable to those of a constant Q model with Q ∼ 10. Average thickness profiles are relatively insensitive to heat flow from the core. The second-degree spherical harmonic components of the ice thickness are given and the resulting contributions to the quantities ( B - A)/ C and ( B - C)/ A of Europa are estimated. Although the contribution to ( B - A)/ C is perhaps larger than the permanent value needed to prevent nonsynchronous rotation, its dependence on the shell's orientation relative to synchroneity suggests that very slow nonsynchronous rotation will persist, with reorientation of the shell relative to the satellite-planet direction occuring on a time scale greater than or approximately equal to the thermal diffusion time scale for the shell (∼10 ⁷ years). The existence of significant "fossil" bulge on the shell due to long-term elastic behavior of its outer, coldest regions would eliminate nonsynchronous rotation. Since the contribution to ( B - C)/ A of the thickness variations in most of our models is >0, Europa's shell may experience large-scale polar wander as thermal equilibrium is approached, if the above is the most important permanent contribution to ( B - C)/ A. For some parameter choices, the presence of an insulating regolith that raises the near-surface temperature by more than a few tens of degrees may stabilize the shell against polar wander by reducing thickness variations; yet a modest regolith may enhance the likelihood of ppolar wander (G.W. Ojakangas and D.J. Stevenson 1989, Icarus 81, 242-270) by reducing retarding friction within the shell. The magnitudes of the principal moment differences are insensitive to the details of the parameterization of the tidal dissipation.