Hugh F. Wilson

Solubility of Water Ice in Metallic Hydrogen: Consequences for Core Erosion in Gas Giant Planets

Using ab initio simulations we investigate whether water ice is stable in the cores of giant planets, or whether it dissolves into the layer of metallic hydrogen above. By Gibbs free energy calculations we find that for pressures between 10 and 40 Mbar the ice-hydrogen interface is thermodynamically unstable at temperatures above approximately 3000 K, far below the temperature of the core-mantle boundaries in Jupiter and Saturn. This implies that the dissolution of core material into the fluid layers of giant planets is thermodynamically favored, and that further modeling of the extent of core erosion is warranted.

Rocky core solubility in Jupiter and giant exoplanets.

Gas giants are believed to form by the accretion of hydrogen-helium gas around an initial protocore of rock and ice. The question of whether the rocky parts of the core dissolve into the fluid H-He layers following formation has significant implications for planetary structure and evolution. Here we use ab initio calculations to study rock solubility in fluid hydrogen, choosing MgO as a representative example of planetary rocky materials, and find MgO to be highly soluble in H for temperatures in excess of approximately 10,000 K, implying the potential for significant redistribution of rocky core material in Jupiter and larger exoplanets.

Sequestration of noble gases in giant planet interiors

The Galileo probe showed that Jupiters atmosphere is severely depleted in neon compared to protosolar values. We show via ab initio simulations of the partitioning of neon between hydrogen-helium phases that the observed depletion can be explained by the sequestration of neon into helium-rich droplets within the postulated hydrogen-helium immiscibility layer of the planets interior. We also demonstrate that this mechanism will not affect argon explaining the observed lack of depletion of this gas. This provides strong indirect evidence for hydrogen-helium immiscibility in Jupiter.

Superionic to superionic phase change in water: consequences for the interiors of Uranus and Neptune

Using density functional molecular dynamics free energy calculations, we show that the body centered cubic (bcc) phase of superionic ice previously believed to be the only phase is, in fact, thermodynamically unstable compared to a novel phase with oxygen positions in face centered cubic lattice sites. The novel phase has a lower proton mobility than the bcc phase and may exhibit a higher melting temperature. We predict a transition between the two phases at a pressure of 1±0.5  Mbar, with potential consequences for the interiors of ice giants such as Uranus and Neptune.

SOLUBILITY OF IRON IN METALLIC HYDROGEN AND STABILITY OF DENSE CORES IN GIANT PLANETS

The formation of the giant planets in our solar system, and likely a majority of giant exoplanets, is most commonly explained by the accretion of nebular hydrogen and helium onto a large core of terrestrial-like composition. The fate of this core has important consequences for the evolution of the interior structure of the planet. It has recently been shown that H2O, MgO, and SiO2 dissolve in liquid metallic hydrogen at high temperature and pressure. In this study, we perform ab initio calculations to study the solubility of an innermost metallic core. We find dissolution of iron to be strongly favored above 2000 K over the entire pressure range (0.4-4 TPa) considered. We compare with and summarize the results for solubilities on other probable core constituents. The calculations imply that giant planet cores are in thermodynamic disequilibrium with surrounding layers, promoting erosion and redistribution of heavy elements. Differences in solubility behavior between iron and rock may influence evolution of interiors, particularly for Saturn-mass planets. Understanding the distribution of iron and other heavy elements in gas giants may be relevant in understanding mass-radius relationships, as well as deviations in transport properties from pure hydrogen-helium mixtures.

AB INITIO FREE ENERGY CALCULATIONS OF THE SOLUBILITY OF SILICA IN METALLIC HYDROGEN AND APPLICATION TO GIANT PLANET CORES

By combining density functional molecular dynamics simulations with a thermodynamic integration technique, we determine the free energy of metallic hydrogen and silica, SiO2, at megabar pressures and thousands of degrees Kelvin. Our ab initio solubility calculations show that silica dissolves into fluid hydrogen above 5000 K for pressures from 10 and 40 Mbars, which has implications for the evolution of rocky cores in giant gas planets like Jupiter, Saturn, and a substantial fraction of known extrasolar planets. Our findings underline the necessity of considering the erosion and redistribution of core materials in giant planet evolution models, but they also demonstrate that hot metallic hydrogen is a good solvent at megabar pressures, which has implications for high-pressure experiments.

INTERIOR PHASE TRANSFORMATIONS AND MASS-RADIUS RELATIONSHIPS OF SILICON-CARBON PLANETS

Planets such as 55 Cancri e orbiting stars with a high carbon-to-oxygen ratio may consist primarily of silicon and carbon, with successive layers of carbon, silicon carbide, and iron. The behavior of silicon-carbon materials at the extreme pressures prevalent in planetary interiors, however, has not yet been sufficiently understood. In this work, we use simulations based on density functional theory to determine high-pressure phase transitions in the silicon-carbon system, including the prediction of new stable compounds with Si2C and SiC2 stoichiometry at high pressures. We compute equations of state for these silicon-carbon compounds as a function of pressure, and hence derive interior structural models and mass-radius relationships for planets composed of silicon and carbon. Notably, we predict a substantially smaller radius for SiC planets than in previous models, and find that mass radius relationships for SiC planets are indistinguishable from those of silicate planets. We also compute a new equation of state for iron. We rederive interior models for 55 Cancri e and are able to place more stringent restrictions on its composition.

Ab initiosimulations of hot dense methane during shock experiments

Using density functional theory molecular dynamics simulations, we predict shock Hugoniot curves of precompressed methane up to 75000 K for initial densities ranging from 0.35 to 0.70 g/cc. At 4000 K, we observe the transformation into a metallic, polymeric state consisting of long hydrocarbon chains. These chains persist when the sample is quenched to 300 K, leading to an increase in shock compression. At 6000 K, the sample transforms into a plasma composed of many, short-lived chemical species. We conclude by discussing implications for the interiors of Uranus and Neptune and analyzing the possibility of creating a superionic state of methane in high pressure experiments.

Shape dependence of the band gaps in luminescent silicon quantum dots

Silicon nanoparticles exhibit quantum confinement and function as optoelectronic devices whose optical properties are known to depend strongly on size and surface termination. The effect of nanoparticle shape on optical properties, however, has not yet been investigated. In this work we use tight binding and density functional theory simulations to study the HOMO–LUMO gaps of hydrogen-terminated silicon nanoparticles as a function of shape and size. It is shown that optical properties are strongly dependent upon nanoparticle shape, and in particular that octahedral nanoparticles exhibit significantly (up to 0.2 eV) larger band gaps than cubic or pseudo-spherical nanoparticles of the same volume. Control of the shape of nanoparticles via the tuning of the thermodynamic conditions in which they are formed may allow the formation of silicon nanoparticles with emission wavelengths running across the full visible range.

H4O and other hydrogen-oxygen compounds at giant-planet core pressures

Water and hydrogen at high pressure make up a substantial fraction of the interiors of giant planets. Using ab initio random structure search methods we investigate the ground-state crystal structures of water, hydrogen, and hydrogen-oxygen compounds. We find that, at pressures beyond 14 Mbar, excess hydrogen is incorporated into the ice phase to form a novel structure with H4O stoichiometry. We also predict two new ground state structures, P2_1/m and I4/mmm, for post-C2/m water ice.