Subsurface heat transfer on Enceladus: Conditions under which melting occurs

Given the heat that is reaching the surface from the interior of Enceladus, we ask whether liquid water is likely and at what depth it might occur. The heat may be carried by thermal conduction through the solid ice, by the vapor as it diffuses through a porous matrix, or by the vapor flowing upward through open cracks. The vapor carries latent heat, which it acquires when ice or liquid evaporates. As the vapor nears the surface it may condense onto the cold ice, or it may exit the vent without condensing, carrying its latent heat with it. The ice at the surface loses its heat by infrared radiation. An important physical principle, which has been overlooked so far, is that the partial pressure of the vapor in the pores and in the open cracks is nearly equal to the saturation vapor pressure of the ice around it. This severely limits the ability of ice to deliver the observed heat to the surface without melting at depth. Another principle is that viscosity limits the speed of the flow, both the diffusive flow in the matrix and the hydrodynamic flow in open cracks. We present hydrodynamic models that take these effects into account. We find that there is no simple answer to the question of whether the ice melts or not. Vapor diffusion in a porous matrix can deliver the heat to the surface without melting if the particle size is greater than ∼1 cm and the porosity is greater than ∼0.1, in other words, if the matrix is a rubble pile. Whether such an open matrix can exist under its own hydrostatic load is unclear. Flow in open cracks can deliver the heat without melting if the width of the crack is greater than ∼10 cm, but the heat source must be in contact with the crack. Frictional heating on the walls due to tidal stresses is one such possibility. The lifetime of the crack is a puzzle, since condensation on the walls in the upper few meters could seal the crack off in a year, and it takes many years for the heat source to warm the walls if the crack extends down to km depths. The 10:1 ratio of radiated heat to latent heat carried with the vapor is another puzzle. The models tend to give a lower ratio. The resolution might be that each tiger stripe has multiple cracks that share the heat, which tends to lower the ratio. The main conclusion is that melting depends on the size of the pores and the width of the cracks, and these are unknown at present.