Mathematics – Logic
Scientific paper
Dec 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003agufm.p51b0447r&link_type=abstract
American Geophysical Union, Fall Meeting 2003, abstract #P51B-0447
Mathematics
Logic
5430 Interiors (8147), 5455 Origin And Evolution, 6218 Jovian Satellites, 6280 Saturnian Satellites
Scientific paper
In an ice-rock body, it is possible for a subsurface ocean to exist as long as there is a sufficient heat source in the rocky core to maintain melting temperatures in the ice layer. Since the melting point of ice I decreases with pressure, it is only necessary for temperatures to reach ˜ 251 K for liquid water to be present in the ice layer. If ammonia is present, the minimum necessary temperature decreases further, to around 176 K. Heat loss in differentiated ice-rock bodies occurs primarily through thermal convection in the outer layer of ice, as long as the body is not too small (larger than ˜ 200 km radius). To model convection in the ice layer, we used scaling laws for stagnant lid convection with Newtonian rheology (Solomatov, 1995), which relate heat flux to the internal Rayleigh number of the convecting layer. Newtonian rheology is appropriate for the low stresses under consideration. Since the viscosity of ice I is strongly temperature-dependent, convection in the ice layer occurs in the stagnant lid regime, which allows for higher temperatures at depth than constant viscosity convection. For ice-rock bodies with a given size, composition, and heat source, we calculated the interior temperature and compared it to the ice I solidus to determine whether an ocean could be present. Since both the heat flux at the base of the ice layer and the gravitational acceleration are proportional to the radius of the body, it is effectively much harder for oceans to exist in small bodies. Using plausible choices of parameters for pure ice I, it is possible for oceans to exist in bodies as small as ˜ 1000 km radius, meaning that candidates for subsurface oceans include not only the icy Galilean satellites and Titan but also Triton and Pluto. If ammonia is present, oceans can exist in bodies as small as the largest Saturnian and Uranian moons ( ˜ 750 km radius). In all of these cases, whether oceans can be present depends strongly on the rheological parameters of ice I, which are not well known at planetary conditions. Another important parameter is the radiogenic heating rate of the rock, which may be greater than typical chondritic values if the rock is undepleted in potassium.
Rainey E. S.
Stevenson Jacob D.
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