Mathematics – Logic
Scientific paper
Dec 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002agufm.p72b0505h&link_type=abstract
American Geophysical Union, Fall Meeting 2002, abstract #P72B-0505
Mathematics
Logic
5418 Heat Flow, 5430 Interiors (8147), 5450 Orbital And Rotational Dynamics, 5480 Volcanism (8450), 6218 Jovian Satellites
Scientific paper
Tidal dissipation plays an important role in system of the Galilean satellites. Here, implications of tidal heating for Europa's present state and for its thermal orbital evolution are discussed. The polar moment of inertia and cosmochemical arguments suggest that Europa consists of an iron rich core, a silicate layer and an outer ice/water-layer of 70-170 km thickness. The lower part of the ice/water-layer is expected to be liquid due to internal heating. The existence of a subsurface ocean is consistent with the detection of an induced magnetic field in Europa. The tidal deformation and the dissipation rate within its ice layer strongly increase if an inviscid ocean is present underneath the ice. Two different Europa models are discussed. In the first model, tidal dissipation is assumed to occur in the silicate mantle layer. In the second model dissipation within the ice shell is considered. The tidal dissipation rate is calculated using the viscoelastic field theory for self gravitating, incompressible, hydrostatically equilibrated, spherical planets in synchronous rotation. The response of the planetary material to the periodic tidal forcing is calculated assuming a Maxwell rheology. The relaxation function is determined by the two parameters viscosity and rigidity, which are taken to be temperature dependent. The tidal dissipation rate is proportional to the imaginary part of the complex tidal Love number k2. Since dissipation is an internal heat source, the thermal evolution is linked to the orbital evolution through the temperature dependent rheology. Using heat balance equations for Io and Europa, conservation laws for energy and angular momentum, and conditions for the Laplace resonance, a set of first order differential equations is derived, describing the thermal and orbital states of Io and Europa. The numerical integration shows that scenarios are possible in which Europa passes through high dissipation states. If dissipation within Europa's silicate layer is assumed, these phases are continuing until about 500 Ma before the present time. Additionally, orbital elements and internal temperatures oscillate on a timescale of the order of 100 Ma. During Io's oscillatory phase Europa is heated gradually and reaches high interior temperatures after several oscillations. This is accompanied by a final cold phase of Io. If dissipation within the ice layer is taken into account, Europa's ice thickness varies between about 10 and 50 km during the oscillatory phases, including both convective and purely conductive phases. The ocean is found to be stable over geological timescales.
Hussmann Hauke
Spohn Tilman
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