ICARUS 81, 220--241 (1989) Thermal State of an Ice Shell on Europa GREGORY W. OJAKANGAS AND DAVID J. STEVENSON Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125 Received May 23, 1988; revised March 17, 1989 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 rheologicai behaviors for ice: the Maxwell theology and the generalized flow law rheol- ogy. 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 Pl00 in our models, average shell thicknesses do not exceed 25 kin. Thus, if the total thickness of H20 which mantles Europa is ~25 kin, none of our models admit the possibility of a completely frozen 1-120 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 contribu- tion to (B - A)/C is perhaps larger than the permanent value needed to prevent nonsyn- chronous 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 occurring on a time scale greater than or approximately equal to the thermal diffusion time scale for the shell (~107 years). The existence of a 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 regofith 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 polar 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 insensi- tive to the details of the parameterization of the tidal dissipation. ©1989 Academic Press,Inc. 1. INTRODUCTION Cassen et al. 1982). Water ice is known from spectroscopic studies to be present on The structure and composition of the its surface (cf. Pilcher et al. 1972), and the outer regions of Europa's interior have lack of substantial topographic relief or been the subject of considerable debate (cf. large impact craters supports the conjec- 220 0019-1035/89 $3.00 Copyright © 1989 by Academic Press, Inc. All rights of reproduction in any form reserved.