THERMAL ORBITAL HISTORIES OF VISCOELASTIC MODELS OF IO (J1)

Thermal-orbital histories of viscoelastic models of Io with dissipation in the entire uniform mantle are discussed. The thermal-orbital histories show Io passing three distinct successive states: a hot, high-dissipation state, an oscillatory state with oscillations of the thermal-orbital variables, and a cold, low-dissipation state. The hot, high-dissipation state is characterized by an approximate thermal and orbital equilibrium with small rates of change of temperature and orbital eccentricity. The current Io may well be in that near-equilibrium state for reasonable values of the mantle rheology parameters. It is then likely that Io's mantle is partially molten. The melt may be distributed over the entire mantle or may be concentrated in a shallow asthenosphere. The rate of change of the tidal dissipation rate with melt concentration provides the negative feedback between the rates of heat production and heat loss required to stabilize the hot, high-dissipation state. The hypothesis of approximate thermal-orbital equilibrium is consistent with the present orbital distance of Io; it is marginally consistent with J. H. Lieske's estimates (1987, Astron. Astrophys. 176, 146-158) of the time rates of change of mean motion and eccentricity if realistic error bounds are accounted for. Time dependence of convective heat transport should be important for the present Io and may increase the acceptibility of the equilibrium hypotheses. The critical mean motion for the transition to the oscillatory state depends on the values of Io's rheology and heat-flow parameters. For a model with the present Io in the oscillatory state, the current heat-flow observations and Lieske's data cannot be simultaneously satisfied sensu strictu. The Io-Europa resonance is not likely to be geologically recent because this would require a near solidus mantle of Io prior to entering the resonance. For reasonable interior temperatures of the preresonance Io and for negligible dissipation in Europa an age of the resonance of about 500 my is derived. For realistic dissipation rates in Europa an age of the resonance of 2 by is suggested. © 1990.