Thermal Conductivity Of Rubble Piles

Abstract

Rubble piles are a common feature of solar system bodies. They are composed of monolithic elements of ice or rock bound by gravity. Voids occupy a significant fraction of the volume of a rubble pile. They can exist up to pressure P ≈ є_yµ, where є_y is the monolithic material's yield strain and μ its rigidity. At low P, contacts between neighboring elements are confined to a small fraction of their surface areas. As a result, the effective thermal conductivity of a rubble pile, k_(con)≈ k(є_yµ)^(1/2), can be orders of magnitude smaller than the thermal conductivity of its monolithic elements, k. In a fluid-free environment, only radiation can transfer energy across voids. It contributes an additional component, k_(rad)=16ℓσT^3/3, to the total effective conductivity, k_(eff) = k_(con)+ k_(rad). Here ℓ, the inverse of the opacity per unit volume, is of the order of the size of the elements, and voids. An important distinction between k_(con) and k_(rad) is that the former is independent of the size of the elements, whereas the latter is proportional to it. Our expression for k_(eff) provides a good fit to the depth dependence of thermal conductivity in the top 140 cm of the lunar regolith. It also offers a good starting point for detailed modeling of thermal inertias for asteroids and satellites. Measurement of the response of surface temperature to variable insolation is a valuable diagnostic of a regolith. There is an opportunity for careful experiments under controlled laboratory conditions to test models of thermal conductivity such as the one we outline.

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