Thermal Conductivity of Rubble Piles

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 ≈ ǫY μ, where ǫY 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, kcon ≈ k(P/(ǫY μ)) , can be orders of magnitude smaller than, k, the thermal conductivity of its monolithic elements. In a fluid-free environment, only radiation can transfer energy across voids. It contributes an additional component, krad = 16lσT /3, to the total effective conductivity, keff = kcon+krad. Here l, the inverse of the opacity per unit volume, is of order the size of the elements and voids. An important distinction between kcon and krad is that the former is independent of the size of the elements whereas the latter is proportional to it. Our expression for keff 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.