Convection and Differentiation in Icy Satellites

In this work we discuss differentiation scenarios for a convecting ice- rock mixture in order to understand and model the post-accretional evolution of the Galilean satellite Callisto. The dimensionless moment of inertia (MoI) factor of Callisto measured by the Galileo spacecraft and the striking difference in the surface structures between Ganymede and Callisto pose an intriguing problem to planetologists. The value of 0.359 ± 0.005 for Callisto's MoI-factor is significantly smaller than the value of 0.4, the value of a constant density body, but it is too large for a 2- or 3-layer model with the major components ice, silicate and iron. While the observations for Ganymede suggest a completely differentiated 3-layer structure, Callisto seems to be only partially differentiated. We propose that Callisto's present state is a snapshot of a slow unmixing process. Compositional and thermal buoyancy forces drive the convection of the ice-rock mixture in Callisto. In the course of this bulk solid state convection a gradual unmixing of the two solid phases takes place, leading to a slow differentiation.

We examine thermal-compositional convection of an ice-rock mixture by numerically solving the Boussinesq Approximation of the One-Field equations. First, we solve the equations in two Cartesian coordinates and examine the influence of rock particle size and heterogeneities in the initial rock distribution. For rock particles with a non-negligible Stokes sinking velocity an unmixing front develops with zero rock concentration above. The front sinks with the speed of the rock particles independent of the convection velocity. For rock particles of 1 to 10 m in diameter the Stokes velocity is large enough such that the unmixing front sinks a significant distance over the 4.5 Ga of Callisto's evolution. If the main fraction of the rock is smaller than 1 m in diameter the Stokes velocity is negligible, the rock can be treated as suspended dust and no differentiation occurs by particles settling. But due to the high ratio of compositional to thermal buoyancy forces, heterogeneities in the inital rock distribution lead to a differentiation into a compositional stable layering with increasing rock volume fraction with depth. Since convection then ceases, heat is removed only by conduction and the temperature in the ice-rock mixture rises. When the thermal gradients overcome the stabilizing compositional forces the layering is disrupted by the re-onset of thermal convection that remixes the interior.

Then, we model the thermal evolution and differentiation of Callisto in spherical, axisymmetric geometry. The differentiation by heterogeneities in the initial rock distribution can reduce the MoI-factor to the measured value. But during the pure conduction state the interior heats up and leads to large scale ice melting in Callisto's interior. This initializes a "run-away'' differentiation and results in a MoI-factor that is too small. Thus, we can rule out this type of differentiation for Callisto.

For rock particles in the diameter range of 5 to 7 m we find that the differentiation process is so slow that the MoI-range of Callisto is reached after several Ga. If all rock particles have diameters of 12 m or more the differentiation is about one order of magnitude too fast. But by splitting up the rock fraction into one half suspended dust and the other half are rock particles with diameter of 12 m we obtain another model showing a slow unmixing process that reaches Callisto's MoI-range after several Ga. We conclude that we can explain Callisto's current partially differentiated state by a slow sinking unmixing front, if the main fraction of the rock particles have diameters of 5 to 7 m or the rock fraction is split into suspended dust and rock particles of 10 m and more in diameter.

Drittmittelgeber:

Deutsche Forschungsgemeinschaft, Westf. Wilhelms-Universität

Beteiligte Wissenschaftler:

K. Nagel, Dr. D. Breuer, Prof.Dr. T. Spohn

Veröffentlichungen:

Spohn, T., Breuer, D.: Implications From Galileo Observations on the Interior Structure and Evolution of the Galilean Satellites, in: Celnikier,L. and Van, J.T.T. (editors), Planetary Systems: the long view. Editions Frontieres, 1998