VISCOELASTIC RELAXATION OF CRATERS AND THERMAL HISTORIES OF THE MID-SIZED ICY SATELLITES OF SATURN

Crater relaxation can been used as a probe of subsurface temperature structure in planetary bodies. The relaxation rate of a crater is controlled by the rheology of the medium in which the crater is emplaced. Because the rheology is a strong function of temperature, the crater relaxation can be used to constrain the heat flux out of the body since the time of crater formation. When combined with models of thermal evolution, the degree of relaxation can be used to determine the ages of craters on a planetary surface.

Here we considered large (50 – 200 km diameter) impact craters on Saturn’s mid-sized satellites Tethys, Dione, and Rhea. We modeled viscoelastic relaxation of crater topography using the finite-element code CitcomVE for a variety of ice shell thicknesses, temperature profiles and crater diameters. Here, the satellites are all assumed to be fully differentiated. Models with partly differentiated interiors are ongoing.

If the ice shell is conductive, the relaxation rate is controlled by the ice shell thickness, but only weakly. Once the ice thickness exceeds the crater diameter, additional thickening has little effect on the relaxation time; the topography does not interact with the deeper ice layer. If the ice shell convects, then the relaxation is independent of the total ice thickness. Rather, on the timescales relevant to planetary evolution (Gy), warm convecting ice basically behaves like a fluid, and the degree of relaxation is limited by the cold outer portion of the ice shell. We thus find that it is very difficult to distinguish between a convecting ice shell with a stagnant lid, and a conducting ice shell over a subsurface ocean on the basis of crater relaxation alone. In the present models, the temperature structure is not calculated, but imposed. The next task is to combine the present crater relaxation results with a model of thermal evolution to evaluate the geophysical self-consistency of the thermal structures considered here.