Inhibiting Conduction by He Mixing in Interiors of Jupiter and Saturn

Abstract

Accurate knowledge of the electrical and thermal conductivities and structural properties of hydrogen-helium mixtures under thermodynamic conditions within and beyond the immiscibility range is very important to predict the thermal evolution and internal structure of gas giant planets like Jupiter and Saturn. Here, we propose a novel method to determine the immiscibility boundary accurately without the need for free energy calculations, while providing consistent insights into structural and transport properties of mixtures. We show with direct large-scale ab initio simulations that the insulator-metal transition (IMT) of the hydrogen subsystem is strongly affected by an admixture with a small fraction of helium and occurs at temperatures significantly higher than those of pure hydrogen. At pressures below 150 GPa, the IMT boundary is not related anymore to the H2 subsystem dissociation, the system remains insulating even after the full dissociation of H2 molecules and its transition to an H-He mixture. The offset of the IMT in the H-He mixture relative to the dissociation region in the hydrogen subsystem and the significant reduction of static electrical and thermal conductivity by a factor between two and a few thousand relative to pure hydrogen found in mixtures have consequences for Jupiter and Saturn's thermal evolution, internal structure, and dynamo action, affecting a large fraction of the interior of both planets.

Figures (8)

• Figure 1: An example of H$_2$-He demixing (a) and H-He mixing (b) occurring directly in the simulation box for the He$_{104}$H$_{816}$ system (x=0.11304) at $P=150$ GPa, and $T=1000$ and 6500 K respectively (He and H atoms are shown as gold and cyan spheres respectively).
• Figure 2: Magnitude of the first H-He RDF peak as a function of temperature for pressure of $150$shown for a small always mixed system (blue curve), and for large one that transits from demixed to mixed state (red curve). The vertical green dashed line indicates the transition to the perfectly mixed state of liquid H-He (He$_{104}$H$_{816}$, ${\mathrm x}=0.11304$) mixtures. Vertical magenta dashed lines depict the H$_2$-He to H-He transition.
• Figure 3: Miscibility diagram for solar He abundance. Our results using the KDT16 functional are shown by black squares. Our prediction is compared to earlier theoretical results: Schöttler and Redmer Schoettler2018 (blue line), Morales et al.doi:10.1073/pnas.0812581106 (brown curve), Schouten et al.Schouten1991 (orange circles), Bergermann et al.Bergermann2021a (red diamonds), and Chang et al.Chang.NC2024. Experimental results are shown as colored symbols: Loubeyre et al.Loubeyre1987 (purple circles) and Brygoo et al.Brygoo2021 (cyan triangles). Present day planetary isentropes for Jupiter are shown as a black dashed curve Nettelmann2008 and solid gray curve Hubbard2016, while the isentrope for Saturn is depicted by a solid black curve Nettelmann2013a.
• Figure 4: Density and dc conductivity of H-He mixtures as compared to pure H along the $P=$ 150 isobar indicating temperatures of the H$_2$-He to H-He, IMT and H-He demixing/mixing transitions in liquid He$_{104}$H$_{816}$ (x=0.11304). The IMT of the H$_2$-He mixture coincides with the H$_2$ subsystem dissociation and occurs at $T=1500$ K. The density of pure H (x=0.0) is shifted by 0.20 g/cm$^3$ for better visualization.
• Figure 5: Density and dc conductivity of H-He mixtures as compared to pure H along the $P=$ 75 isobar indicating temperatures of the H$_2$-He to H-He, IMT and H-He demixing/mixing transitions in liquid He$_{104}$H$_{816}$ (x=0.11304). The density of pure H (x=0.0) is shifted by 0.113 g/cm$^3$ for better visualization. With the temperature increase, the H-He system remains insulating even after the H$_2$ subsystem dissociation. Three red squares filled with diagonal pattern correspond to $\sigma_{\rm dc}$ values calculated with hybrid HSE06 functional.