Thermal evolution and sintering of chondritic planetesimals

IV. Temperature dependence of heat conductivity of asteroids and meteorites

¹ Zentrum für Astronomie, Institut für Theoretische Astrophysik, Heidelberg University, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany
e-mail: gail@uni-heidelberg.de
² Institut für Geowissenschaften, Universität Heidelberg, Im Neuenheimer Feld 236, 69120 Heidelberg, Germany
e-mail: Mario.Trieloff@geow.uni-heidelberg.de
³ Klaus-Tschira-Labor für Kosmochemie, Universität Heidelberg, Im Neuenheimer Feld 236, 69120 Heidelberg, Germany

Received: 13 December 2017
Accepted: 28 March 2018

Abstract

Context. Understanding the compaction and differentiation of the planetesimals that formed during the initial phases of our solar system and the protoplanets from the asteroid belt and the terrestrial planet region of the solar system requires a reliable modelling of their internal thermal evolution. An important ingredient for this is a detailed knowledge of the heat conductivity, K, of the chondritic mixture of materials from which planetesimals are formed. The dependence of K on the composition and structure of the material was studied in the previous study of this series. For the second important aspect, the dependence of K on temperature, laboratory investigations on a number of meteorites exist concerning the temperature variation of K, but no explanation for the observed variation has been given yet.

Aims. We evaluate the temperature dependence of the heat conductivity of the solid chondritic material from the properties of its mixture components from a theoretical model. This allows us to predict the temperature-dependent heat conductivity for the full range of observed meteoritic compositions and also for possible other compositions.

Methods. Published results on the temperature dependence of the heat conductivity of the mineral components found in chondritic material are fitted to the model of Callaway for heat conductivity in solids by phonons. For the Ni, Fe-alloy, published laboratory data are used. The heat conductivity of chondritic material then is calculated by means of mixing rules. The role of micro-cracks is studied, which increase the importance of wall scattering for phonon-based heat conductivity.

Results. Our model is applied to published data on the heat conductivity of individual chondrites. The general trends for the dependency of K on temperature found in laboratory experiments can largely be reproduced for the set of meteorites if the heat conductivity is calculated for a given composition from the properties of its constituents. It is found that micro-cracks have a significant impact on the temperature dependence of K because of their reduction of phonon scattering length.