Geophysical implications of the long-wavelength topography of the Saturnian satellites

We use limb profiles to quantify the long-wavelength topography of the Saturnian satellites. The degree 2 shapes of Mimas, Enceladus, and Tethys are not consistent with hydrostatic equilibrium. We derive 2-D topographic maps out to spherical harmonic degree 8. There is a good correlation with topography derived from stereo techniques. If uncompensated, topography at degree 3 and higher is large enough to be detectable during close spacecraft flybys. If not properly accounted for, this topography may bias estimates of a satellite's degree 2 gravity coefficients (which are used to determine the moment of inertia). We also derive a one-dimensional variance spectrum (a measure of how roughness varies with wavelength) for each body. The short-wavelength spectral slope is -2 to -2.5, similar to silicate bodies. However, unlike the terrestrial planets, each satellite spectrum shows a reduction in slope at longer wavelengths. If this break in slope is due to a transition from flexural to isostatic support, the globally averaged elastic thickness T-e of each satellite may be derived. We obtain T-e values of >= 5 km, 1.5-5 km, approximate to 5 km, and >= 5 km for Tethys, Dione, Rhea, and Iapetus, respectively. For Europa, we obtain T-e approximate to 1.5 km. These estimates are generally consistent with estimates made using other techniques. For Enceladus, intermediate wavelengths imply T-e >= 0.5 km, but the variance spectrum at wavelengths greater than 150 km is probably influenced by long-wavelength processes such as convection or shell thickness variations. Impact cratering may also play a role in determining the variance spectra of some bodies.