Physics
Scientific paper
May 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004agusm.p21a..02m&link_type=abstract
American Geophysical Union, Spring Meeting 2004, abstract #P21A-02
Physics
5418 Heat Flow, 5430 Interiors (8147), 5450 Orbital And Rotational Dynamics, 8121 Dynamics, Convection Currents And Mantle Plumes, 8130 Heat Generation And Transport
Scientific paper
The strong temperature dependence of the viscosity of planetary materials leads to an interesting coupling between heat generation and heat transport in tidally heated bodies. As a result of this coupling, multiple thermal equilibria exist, some stable and some unstable. For rocky bodies such as Io, heat transport by melt segregation can balance tidal heat production at temperatures somewhat above the solidus, corresponding to at about 20% fractional melt abundance. A higher temperature equilibrium between convection in a mostly molten suspension is also stable, but is inconsistent with Io's large heat flow. In icy shells such as exist on Ganymede and Europa, melt segregation does not contribute to heat transport, instead the negatively buoyant melt segregates downward, reducing the thickness of the solid ice shell. Europa is in a special position, where the orbital period (3.6 days) is very nearly the Maxwell time of ice at the solidus. If the orbital period is longer than the Maxwell time at the solidus, then a stable thermal equilibrium exists between tidal heating and convection with an internal temperature very near the solidus. In this case, high-viscosity downwellings have Maxwell times nearer the orbital period and therefore experience more heating than low-viscosity upwellings, melting is suppressed (due to the lower heating rates in warm ice), and the equilibrium is stable for shells of arbitrary thickness. If the orbital period is shorter than the Maxwell time at the solidus, then the nature of the thermal equilibrium is quite different. The equilibrium is unstable with respect to temperature perturbations, but melt segregation or re-freezing at the base of the shell can act to stabilize it through the dependence of tidal heat production on the ice thickness. Both quasi-equilibrium and time-dependent calculations are used to investigate the nature of this equilibrium. The possibility exists that Europa went through a transition as the orbital period increased (due to dissipation in Io) from a state in which the equilibrium is unstable to thermal perturbations to one in which the equilibrium is stable. Also, tidal heating in the ice may be on the decline if the orbital period is now longer than the Maxwell time at the solidus.
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