Electrical Resistivity of Liquid Fe-16S-2Si up to 13 GPa With Implications for the Adiabatic Heat Flux Through the Core of Exoplanet TRAPPIST-1h

Thermal convective processes in the liquid cores of terrestrial planetary bodies with the capacity to generate magnetic dynamos may be better characterized by thermal conductivity estimates of core conditions. The composition of the core of asteroid 4 Vesta as determined by geochemical studies of HED meteorites is used as an analog for the core of exoplanet TRAPPIST-1h. Earlier electrical resistivity measurements of the Fe-S-Si system up to 6 GPa are extended here to 13 GPa using a 3,000-ton multi-anvil press. Data were collected from ambient temperatures to ∼2,000 K in each experimental run. Temperature and voltage drop across the sample were measured in situ to derive resistivity from geometry measurements of the post-experimental sample cross-section. At temperatures above the liquidus of Fe-16 wt%S–2 wt%Si, the electrical resistivity is 400–500 μΩ cm and is invariant in the pressure range 5–13 GPa. From the Wiedemann-Franz Law, the electronic contribution to the thermal conductivity is calculated as 8–10 W/m/K at the completion of melting. The adiabatic heat flux at the top of the core of TRAPPIST-1h is estimated as 5.3 ± 2 or 6.8 ± 3 mW/m² in the case of a surface ice layer. For a critical value of the magnetic Reynolds number of 10, a characteristic velocity in the core of ∼0.02 mm/s is required. With selected parameter values for the core of TRAPPIST-1h, this velocity value is likely achieved by convective heat flux, sustaining a magnetic dynamo.