Mathematics – Logic
Scientific paper
May 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009agusm.p32a..01r&link_type=abstract
American Geophysical Union, Spring Meeting 2009, abstract #P32A-01
Mathematics
Logic
5418 Heat Flow, 5422 Ices, 5430 Interiors (8147), 5450 Orbital And Rotational Dynamics (1221), 6280 Saturnian Satellites
Scientific paper
A heat flow anomaly of 4-7 GW is observed in the south polar region of Enceladus [Spencer et al., 2006]. Tidal dissipation has been suggested as the heat source for the south polar thermal anomaly on Enceladus. Under reasonable rheologic conditions, we find that tidal dissipation is only significant in the ice shell if it is decoupled from the silicate core by a subsurface ocean, suggesting the presence of such an ocean in order to explain the observed surface activity. We have modeled convection and conduction in the ice shell in 2D axisymmetric and 3D spherical geometry in which we include the spatially-variable tidal heat distribution for a Maxwellian body. In general, we find that more heat must be removed from the core than can be produced by radioactive decay in order to maintain the ocean at the melting point of water. Under likely conditions, the ocean would freeze solid on a timescale of order tens of Myr (depending on the initial thickness of the ice shell). This result does not preclude the existence of an ocean, only that it is not in long-term thermal equilibrium. This conclusion is consistent with studies of orbital dynamics which suggest that the long-term tidal heat production cannot exceed 1.1 GW, [Meyer and Wisdom, 2007], assuming the present-day orbit. If the eccentricity of Enceladus were higher (≥ 0.015) in the past, the increased dissipation in the ice shell would have been sufficient to maintain a liquid layer. A subsurface ocean may exist today as the relic of an earlier era of greater heating. If the eccentricity has been periodically pumped up, then the variations in tidal heating may have caused the ocean thickness to vary on the same timescale as for the orbital evolution, provided that this timescale is faster than the time required for the ocean to freeze completely. Prior to the current e-resonance with Dione, Enceladus has passed through several other higher-order 2:1 resonances [Meyer and Wisdom, 2008]. Using coupled models of thermal and orbital evolution of Dione and Enceladus, we find that the instantaneous heat production rate may reach the observed value, but that none of these resonances can maintain an average heat flow this high. It therefore seems likely that either Enceladus's eccentricity is not in steady-state, or that the heat currently being released was generated at an earlier time. Orbital observations place constraints on the interior structure of Enceladus (parameterized by k2/Q) to be 1.2 × 10-4 < k2/Q < 8 × 10-4. This is consistent either with a convective ice shell with no ocean or a conductive ice shell above an ocean. Only the latter scenario is physically plausible. However, even under a conductive ice shell, a water ocean is likely to freeze on a geologically short timescale. The freezing point of the ocean may be lowered if it is not pure water, e.g. it contains significant amounts of ammonia. However, chemistry alone cannot prevent the ocean from freezing, it can only delay it. Even the H20-NH3 peritectic temperature is too high to be maintained by tidal dissipation under present-day conditions. In order for the ocean on Enceladus to be in long-term thermal equilibrium, another thus far unidentified heat source may be required. Tidal heating is unlikely to be significant in the silicate core, but may be important in the ocean itself [Tyler, 2008].
Nimmo Francis
Roberts James Hirsch
Zhang Kaicheng
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