Viscosity of Rock-Ice Mixtures and Applications to the Evolution of Icy Satellites

Abstract

Theory and experiments are used to establish lower and upper bounds on the ratio of actual viscosity to pure ice viscosity for a suspension of rock particles in a water ice matrix. For typical conditions encountered in icy satellites, this ratio is of order ten or possibly larger, depending on unknown factors such as the particle size distribution. It is shown that even this modest increase in viscosity may be enough to have caused a failure of solid state convective self-regulation early in the evolution of a homogeneous, rock-water ice satellite, provided the satellite is large enough and sufficiently silicate rich. The criteria for this failure are satisfied by Ganymede and are marginal for Callisto, if the silicates are hydrated. Failure of self-regulation means that the viscosity is too high for the interior to remain completely solid and eliminate the heat production of long-lived radioisotopes by solid state convection. Partial melting of the ice then occurs. It is further shown that satellites of this size may then undergo runaway differentiation into a rock core and almost pure ice mantle, because the gravitational energy release is sufficient to melt nearly all the ice and the Rayleigh-Taylor instability time scale is short. (Although the high pressure phases of ice melt, the resulting water quickly refreezes at a higher level.) It is conjectured that these results explain the striking surface dissimilarity of Ganymede and Callisto, if these satellites accreted cold and undifferentiated. Ganymede may have gone supercritical (melted and differentiated) because of a failure of self-regulation, whereas Callisto remained undifferentiated to the present day. Like all proposed explanations for the Ganymede-Callisto dichotomy, this conjecture cannot be quantified with confidence because of inadequate or incomplete observations, theory, and experimental data.

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