Mathematics – Logic
Scientific paper
Dec 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008agufm.p13d..04s&link_type=abstract
American Geophysical Union, Fall Meeting 2008, abstract #P13D-04
Mathematics
Logic
5422 Ices, 5430 Interiors (8147), 5450 Orbital And Rotational Dynamics (1221), 5480 Volcanism (6063, 8148, 8450), 6280 Saturnian Satellites
Scientific paper
Two constraints for Enceladus seem difficult to dispute: First, that it is emitting more heat than allowed by equilibrium tidal heating models (defined as those in which the tidal heat production and orbital eccentricity are constant with time, cf. Meyer and Wisdom, 2007). Second, the maximum possible instantaneous tidal heat generation is over two orders of magnitude larger than what is observed. (This can be shown independent of any particular rheological model.) There is nothing mysterious about the simultaneous correctness of these two statements since one pertains to the orbital evolution aspect of the problem and the other pertains to the actual mechanism of dissipation. In reality, the maximum heat dissipation would never be approached since it would quench the eccentricity in a short timescale (ten to a hundred thousand years). However, this high upper bound assures us that there is no fundamental difficulty with the tidal heating mechanism, only with its constancy over long periods of time. This suggests that one should seek a model in which the eccentricity fluctuates, possibly mediated by the bounds imposed at the high end by the stress limits for ice fracture and at the low end by the stress at which motion on faults (lubricated or dry) ceases to be possible. I will describe models of this kind that are capable, at least in principle, of producing the desired heat flow in instantaneous equilibrium (i.e., without the need to store heat in the interior). This is a stress-mediated model rather than a thermally mediated model (like that advocated for Io, which has a similar disequilibrium problem). Such a model must (in analogy with successful models for Io and Europa) simultaneously provide the right environment for the desired straining of the outer part of the ice shell and a deeper environment that is sufficiently deformable so that a large tidal Love number (of order a hundred times the elastic value) can be achieved. It is argued that solid water ice (even near the melting point) is unlikely to satisfy this condition, although there continue to be uncertainties in ice rheology that prevent a certain conclusion. This has led previous workers to favor an ocean (not necessarily global) at greater depth, not as the direct source for the plumes but as a decoupling mechanism (conceptually like Europa). Since ice fractures lubricated with very small amounts of water (too small to drain quickly on geological timescales but enough to greatly reduce friction as in pore pressure effects for terrestrial earthquakes) are also capable of providing the desired large, fluid-like deformation. I will argue that there is no necessity of an ocean but probably the necessity of some liquid. It remains an open question as to whether this is liquid water or some other fluid (not pure water) and whether this (or its most volatile components) participates in the plumes. There remain many unanswered issues with how Enceladus works, just as there are for Io, both in respect of orbital evolution and internal properties and evolution.
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