The heat flux through the cores of small terrestrial planetary bodies from electrical resistivity measurements of liquid Fe-S-Si at high pressures

Dynamo action in liquid Fe planetary cores varies according to alloyed light elements such as S and Si. This study experimentally constrains the thermal conductivity of Fe-S-Si alloys at planetary core conditions, which may be used in combination with thermal evolution models to find the total thermal convective force in the core. A sample of Fe alloy with 16wt%S and 2wt%Si was chosen as a predicted composition of the core of Asteroid 4 Vesta, based on studies of HED meteorites [1-2]. This is near the miscibility limit of S and Si in liquid Fe [3].

Experiments were performed at 2-5 GPa in a 1000-ton cubic anvil press and at up to 9 GPa in a 3000-ton multi-anvil press. Temperatures as high as 2100 K into the melt of Fe-S-Si. The electrical resistivity of the liquid Fe-S-Si alloy was measured in situ; to find the electronic component of the thermal conductivity, the Wiedemann-Franz Law was used. To confirm the sample composition and homogenization, electron microprobe analysis was performed on samples recovered from various stages of melting, yielding compositional maps of Fe, S, and Si across each sample.

The individual effects of S and Si on the electrical resistivity of liquid Fe are seen in the results for the conditions of small planetary cores. Fe-16wt%S-2wt%Si has an electrical resistivity of 300-450 µΩ·cm at the complete melt in the pressure range of 2-7 GPa. Pure Fe at the same pressures is at most half this value [4], meaning that a moderate amount of S greatly decreases thermal conductivity in the liquid core. These results may be used to find the adiabatic heat flux at the top of the core of a given planetary body, with direct application to the formation of a magnetic dynamo in the liquid cores of objects such as Vesta, Ganymede, and Mars.

References:

[1] Steenstra, E.S., Dankers, D., Berndt, J., Klemme, S., Matveev, S., van Westrenen, W., 2019. Icarus, v. 317, p. 669-681.

[2] Pringle, E.A., Savage, P.S., Badro, J., Barrat, J.-A., Moynier, F., 2013. Earth Planet. Sci. Lett., v. 373, p. 75-82.

[3] Chabot, N.L., Wollack, E.A., Klima, R.L., Minitti, M.E., 2014. Earth Planet. Sci. Lett., v. 390, p. 199-208.

[4] Yong, W., Secco, R.A., Littleton, J.A.H., Silber, R.E., 2019. Geophys. Res. Lett., v. 46, p. 11065-11070.