Heat Flow in the Core of Ganymede: High Pressure-Temperature Electrical Resistivity Measurements of Solid and Liquid Ag and Fe-S Alloys
Abstract
Experimental investigations of materials at high pressures (P) and temperatures (T) provide insight into the properties and behaviours expected within the inaccessible interiors of planetary bodies. Using a four-wire electrical resistance technique, the electrical resistivity (ρ) of 4d transition metal (Ag) and 3d transition metal alloys (Fe-S) were measured in the solid and molten states at high P. The thermal conductivity (κ) of these materials is inversely proportional to ρ, as described by the Wiedemann-Franz Law. When applied to planetary cores, κ is an important parameter that regulates heat transport mechanisms and magnetic field production.
A hypothesis of ‘resistivity invariance’ suggested that for pure d-band filled metals the magnitude of ρ along the P- and T-dependent melting boundary is constant. This implied that investigations at low P can provide a singular constraint value of ρ and κ at more extreme P and T conditions expected for planetary cores, such as the inner-outer core boundary of Earth which is a solidification boundary. The ρ of silver (Ag) was measured at P up to 5 GPa and T up to ~1650 K. The results showed a decrease in ρ along the P-dependent melting boundary, contrary to prediction, and were discussed in terms of increasing energy separation between the Fermi level and 4d-band as a function of increasing P.
The ρ of solid and molten iron sulfide (FeS) and Fe-FeS were measured at T up to ~1750 K and ~1350 K, respectively, and P up to 5 GPa. These material compositions are relevant to the sulphur (S)-rich core of Ganymede, with the experimental P and T approximating the conditions at the top, or outer-most portion, of the core. The dipolar magnetic field of Ganymede may be generated by an internal dynamo, implying a molten core that may transport heat by thermal convection. The κ and adiabatic conductive heat flow for molten FeS and Fe-FeS core models of Ganymede were calculated from the measured ρ. The results showed that heat transport by thermal convection is permissible in the core models and may act as an energy source to power a dynamo-produced magnetic field.