Experimental electrical resistivity values and computed thermal conductivities

We present a joint experimental-modeling investigation of core cooling in small terrestrial bodies. Significant amounts of light elements (S, O, Mg, Si) may compose the metallic cores of terrestrial planets and moons. However, the effect of multiple light elements on transport properties, in particular, electrical resistivity and thermal conductivity, is not well constrained. Electrical experiments were conducted at 10 GPa and up to 1850 K on high-purity powder mixtures in the Fe-S-O(+/-Mg, +/-Si) systems using the multi-anvil apparatus and the 4-electrode technique. The sample compositions contained 5 wt.% S, up to 3 wt.% O, up to 2 wt.% Mg, and up to 1 wt.% Si. We observe that above the eutectic temperature, electrical resistivity is significantly sensitive to the nature and amount of light elements. For each composition, thermal conductivity-temperature equations were estimated using the experimental electrical results and a modified Wiedemann-Franz law. These equations were implemented in a thermochemical core cooling model to study the evolution of the dynamo. Modeling results suggest that bulk chemistry significantly affects the entropy available to power dynamo action during core cooling. In the case of Mars, the presence of oxygen would delay the dynamo cessation by up to 1 billion years compared to an O-free, Fe-S core. Models with 3 wt% O can be reconciled with the inferred cessation time of the Martian dynamo if the core-mantle boundary heat flow falls from >2 TW to ~0.1 TW in the first 0.5 Gyrs following core formation.