The effect of volume phase changes, mass transport, sunlight penetration, and densification on the thermal regime of icy regoliths

Abstract

A thermal model is presented which quantitatively accounts for the effects of sublimation condensation, and convection throughout a volume of a porous ice crust subjected to solar insolation. The effect of penetration of insolation into ice that is translucent to visible radiation but opaque to infrared radiation is also included. The governing energy differential equation, which also satisfies conservation of mass and accounts for the possibility of free molecular or continuum flow, is solved for various conditions defined by a reasonable range of thermal conductivities, sunlight absorption coefficients, and pore sizes. Quasi-steady-state temperatures, H 2O mass fluxes, and rates of change of mass density for the ice are computed as functions of depth and time of day. We find that, when the effects of latent heat and mass transport are included in the model, the increase in the near surface temperature (the boundary condition for crustal heat flow) brought about by the “solid-state greenhouse” is greatly diminished. If the lowest thermal conductivities reported for the surface of Europa (∼100 erg/cm sec K) are assumed to apply to the upper crust as well, the melting point could be approached at very shallow depth. However, this is precluded except as a transient and shallow phenomenon which could not affect deep crustal temperatures because densification would raise the thermal conductivity to ≥1000 erg cm −1 sec −1 K in the underlying material in a geologically negligible period of time. If thermal conductivities ≥1000 erg/cm sec K are assumed, then the greenhouse effect raises near-surface temperatures ≤35 K, but the densification is slow enough that deep crustal temperatures would be augmented, allowing for melting at a depth of 7–19 km, depending on assumptions concerning tidal dissipation. Thus, when the effects of latent heat, mass transport, and densification are all taken into account, the existence of a significant solid-state greenhouse effect can be shown to be compatible both with morphological evidence for significant crustal strength and with evidence for decoupling of the icy shell from the lithosphere.