New Laboratory-Based Attenuation Measurements on Ice to Support Tidal Heating Models

The response of icy satellite materials to tidal stress has important consequences on their geophysical, geological, and dynamical evolution. The major issue with modeling the tidal response of these objects is that the viscoelastic properties of planetary material are not constrained by laboratory measurements for the relevant frequency range 10e-7 to 10e-5 Hz. While the Maxwell model is usually applied in icy satellite tidal modeling, laboratory measurements for the Earth's mantle have shown that this model is not applicable at forcing frequencies away from the Maxwell frequency. Alternative models (e.g., Andrade, Cole) based on measurements on silicates or terrestrial ice sheets may be better suited to describe ice attenuation, but they have not been introduced in planetary science studies, in part because laboratory measurements are necessary in order to warrant their extrapolation to conditions applicable to icy satellites. The reason why the laboratory data needed for modeling tidal processes at icy satellites are missing is that it is a challenge to achieve measurements at the low stress, low frequencies, and cryogenic conditions relevant to these objects. In the JPL Ice Physical Properties Laboratory an Instron compression system has been implemented with the capability to measure the phase lag between strain and stress, i.e., the internal friction, of an icy sample at frequencies as low as Enceladus' tidal forcing frequency, temperatures as low as 90 K, and cyclic peak stress lower than 0.1 MPa, characteristic of tidal stress at Enceladus or Europa. We will present the first measurements obtained with this system on monocrystalline ice in the frequency range 6x10e-6 to 10e-2 Hz and temperature range 233 - 253 K. We observed a change in frequency-dependence of the friction coefficient at a frequency about the inverse of the Maxwell time. While the Andrade model can fit the phase lags measured over the entire frequency range, it fails to reproduce the effective moduli measured at frequencies higher than 10e-5 Hz. On the other hand, the model developed by Cole (Philos. Mag. A, 72, 231-248, 1995) can account for both the phase lag and effective moduli data, but we had to determine two different sets of parameters in order to characterize the ice viscoelasticity at frequencies higher than the inverse of the Maxwell time, and lower than this reference. We will also present preliminary measurements on polycrystalline ice. Acknowledgements: This work has been conducted at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Copyright 2008 California Institute of Technology. Government sponsorship acknowledged. Part of this work was also carried out in the Mars and Ice Simulation Laboratory at Caltech.