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≈ {ɛ }Yμ , where {ɛ }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{(P/({ɛ }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}=16{\ell }σ {T}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.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- November 2015
- DOI:
- 10.1088/0004-637X/814/1/36
- arXiv:
- arXiv:1510.05295
- Bibcode:
- 2015ApJ...814...36L
- Keywords:
-
- planets and satellites: surfaces;
- Astrophysics - Earth and Planetary Astrophysics
- E-Print:
- Accepted to ApJ, 7 pages, 4 figures