Metallic helium in massive planets

In this issue of PNAS, Stixrude and Jeanloz (4) show that band closure in pure helium occurs at lower pressures than previously thought, provided the effect of high temperatures is taken into account. This suggests that helium behaves as a metal, at least at the highest pressures encountered in Jupiter and perhaps over a wider range of pressures in the many, often much hotter, planets of Jupiter’s mass and larger that are now evidently common in the universe (5). The full thermodynamic and transport properties of the relevant mixtures cannot be deduced from the behavior of the end members (pure hydrogen and pure helium) and are therefore an area of ongoing research

States of matter in massive planets

This brief article addresses the question: among the very large number of interesting condensed matter physics issues, which are particularly interesting from a planetary perspective? Following some definitions and background, it is argued that we need to understand relevant first-order phase transitions (especially the nature of the hydrogen phase diagram), the behaviour of the entropy (i.e., the Gruneisen parameter), the solubility and partitioning of minor elements (e.g. noble gases mixed with hydrogen), and microscopic transport properties, especially electrical and thermal conductivity. Examples are presented of how these issues influence current interpretations of the observations of Jupiter in particular. In the future, it may be possible to observe spectroscopically the compositions of extra-solar-system planets and brown dwarfs, and thereby learn more about the physics of these bodies

Planetary origin, evolution, and structure

Three areas of recent and ongoing research are presented. The first area is giant planet heatflows. Conventional wisdom attributes the heatflow of the giant planets to the gradual loss of primordial heat, except in the case of Saturn where helium separation is evidently occurring. There are two problems with this picture: (1) the observed helium abundance of Saturn's atmosphere is so low that Jupiter must also be differentiating helium since its internal entropy cannot be much higher than Saturn; and (2) the heatflow of Neptune (not to mention Uranus) is too high to be consistent with adiabatic cooling from an initial hot state. A self-consistent solution to these two problems is presented. The second area covered is that of the despinning protogiant planets. Modeling of the possible despinning of these protoplanets by hydromagnetic torques was performed and the model results are discussed. The third area covered is how Titan hides its ocean. Until recently, the favored picture of Titan's surface was a roughly kilometer-thick ethane/methane ocean, presumably global in extent with at most a few outcroppings of dry land. The depth of the ocean is well constrained by observed atmospheric properties, and the constraints on subaerial topography are obtained indirectly from tidal considerations. A different picture of Titan's surface was pursued which was motivated by the perspective that methane on Titan should more properly be considered as a magmatic fluid. In this picture, methane is stored subsurface in magma chambers fed from deep-seated sources of methane, most probably due to the high pressure breakdown of methane clathrate. Other aspects of this model of Titan are presented

On the Role of Dissolved Gases in the Atmosphere Retention of Low-Mass Low-Density Planets

Low-mass low-density planets discovered by Kepler in the super-Earth mass regime typically have large radii for their inferred masses, implying the presence of H$_2$-He atmospheres. These planets are vulnerable to atmospheric mass loss due to heating by the parent star's XUV flux. Models coupling atmospheric mass loss with thermal evolution predicted a bimodal distribution of planetary radii, which has gained observational support. However, a key component that has been ignored in previous studies is the dissolution of these gases into the molten core of rock and iron that constitute most of their mass. Such planets have high temperatures ($>$2000 K) and pressures ($\sim$kbars) at the core-envelope boundary, ensuring a molten surface and a subsurface reservoir of hydrogen that can be 5-10 times larger than the atmosphere. This study bridges this gap by coupling the thermal evolution of the planet and the mass loss of the atmosphere with the thermodynamic equilibrium between the dissolved H$_2$ and the atmospheric H$_2$ (Henry's law). Dissolution in the interior allows a planet to build a larger hydrogen repository during the planet formation stage. We show that the dissolved hydrogen outgasses to buffer atmospheric mass loss. The slow cooling of the planet also leads to outgassing because solubility decreases with decreasing temperature. Dissolution of hydrogen in the interior therefore increases the atmosphere retention ability of super-Earths. The study highlights the importance of including the temperature- and pressure-dependent solubility of gases in magma oceans and coupling outgassing to planetary evolution models.Comment: 11 pages, 6 figures, published in ApJ on February 7 201

Melting and Mixing States of the Earth's Mantle after the Moon-Forming Impact

The Earth's Moon is thought to have formed by an impact between the Earth and an impactor around 4.5 billion years ago. This impact could have been so energetic that it could have mixed and homogenized the Earth's mantle. However, this view appears to be inconsistent with geochemical studies that suggest that the Earth's mantle was not mixed by the impact. Another plausible outcome is that this energetic impact melted the whole mantle, but the extent of mantle melting is not well understood even though it must have had a significant effect on the subsequent evolution of the Earth's interior and atmosphere. To understand the initial state of the Earth's mantle, we perform giant impact simulations using smoothed particle hydrodynamics (SPH) for three different models: (a) standard: a Mars-sized impactor hits the proto-Earth, (b) fast-spinning Earth: a small impactor hits a rapidly rotating proto-Earth, and (c) sub-Earths: two half Earth-sized planets collide. We use two types of equations of state (MgSiO3 liquid and forsterite) to describe the Earth's mantle. We find that the mantle remains unmixed in (a), but it may be mixed in (b) and (c). The extent of mixing is most extensive in (c). Therefore, (a) is most consistent and (c) may be least consistent with the preservation of the mantle heterogeneity, while (b) may fall between. We determine that the Earth's mantle becomes mostly molten by the impact in all of the models. The choice of the equations of state does not affect these outcomes. Additionally, our results indicate that entropy gains of the mantle materials by a giant impact cannot be predicted well by the Rankine-Hugoniot equations. Moreover, we show that the mantle can remain unmixed on a Moon-forming timescale if it does not become mixed by the impact.Comment: Accepted for publication in EPS

Investigation of the Initial State of the Moon-Forming Disk: Bridging SPH Simulations and Hydrostatic Models

According to the standard giant impact hypothesis, the Moon formed from a partially vaporized disk generated by a collision between the proto Earth and a Mars sized impactor. The initial structure of the disk significantly affects the Moon forming process, including the Moons mass, its accretion time scale, and its isotopic similarity to Earth. The dynamics of the impact event determines the initial structure of a nearly hydrostatic Moon forming disk. However, the hydrostatic and hydrodynamic models have been studied separately and their connection has not previously been well quantified. Here, we show the extent to which the properties of the disk can be inferred from Smoothed Particle Hydrodynamic (SPH) simulations. By using entropy, angular momentum and mass distributions of the SPH outputs as approximately conserved quantities, we compute the two dimensional disk structure. We investigate four different models: (a) standard, the canonical giant impact model, (b) fast spinning Earth, a collision between a fast spinning Earth and a small impactor, (c) sub Earths, a collision between two objects with half Earths mass, and (d) intermediate, a collision of two bodies whose mass ratio is 7:3. Our SPH calculations show that the initial disk has approximately uniform entropy. The disks of the fast spinning Earth and sub Earths cases are hotter and more vaporized (80-90% vapor) than the standard case (20%). The intermediate case falls between these values. In the highly vaporized cases, our procedure fails to establish a unique surface density profile of the disk because the disk is unstable according to the Rayleigh criterion. In these cases, we estimate non-unique disk models by conserving global quantities. We also develop a semi analytic model for the thermal structure of the disk, which requires only two inputs: the average entropy and the surface density of the disk.Comment: Accepted for publication in Icaru

Zonal Flow Magnetic Field Interaction in the Semi-Conducting Region of Giant Planets

All four giant planets in the Solar System feature zonal flows on the order of 100 m/s in the cloud deck, and large-scale intrinsic magnetic fields on the order of 1 Gauss near the surface. The vertical structure of the zonal flows remains obscure. The end-member scenarios are shallow flows confined in the radiative atmosphere and deep flows throughout the entire planet. The electrical conductivity increases rapidly yet smoothly as a function of depth inside Jupiter and Saturn. Deep zonal flows will inevitably interact with the magnetic field, at depth with even modest electrical conductivity. Here we investigate the interaction between zonal flows and magnetic fields in the semi-conducting region of giant planets. Employing mean-field electrodynamics, we show that the interaction will generate detectable poloidal magnetic field perturbations spatially correlated with the deep zonal flows. Assuming the peak amplitude of the dynamo alpha-effect to be 0.1 mm/s, deep zonal flows on the order of 0.1 - 1 m/s in the semi-conducting region of Jupiter and Saturn would generate poloidal magnetic perturbations on the order of 0.01% - 1% of the background dipole field. These poloidal perturbations should be detectable with the in-situ magnetic field measurements from the Juno mission and the Cassini Grand Finale. This implies that magnetic field measurements can be employed to constrain the properties of deep zonal flows in the semi-conducting region of giant planets.Comment: 38 pages, 12 figures, revised submission to Icaru

Gravity and Zonal Flows of Giant Planets: From the Euler Equation to the Thermal Wind Equation

Any nonspherical distribution of density inside planets and stars gives rise to a non-spherical external gravity and change of shape. If part or all of the observed zonal flows at the cloud deck of Jupiter and Saturn represent deep interior dynamics, then the density perturbations associated with the deep zonal flows could generate gravitational signals detectable by the Juno mission and the Cassini Grand Finale. Here we present a critical examination of the applicability of the thermal wind equation to calculate the wind induced gravity moments. Our analysis shows that wind induced gravity moments calculated from TWE are in overall agreement with the full solution to the Euler equation. However, the accuracy of individual high-degree moments calculated from TWE depends crucially on retaining the nonsphericity of the background density and gravity. Only when the background nonsphericity of the planet is taken into account, does the TWE make accurate enough prediction (with a few tens of percent errors) for individual high-degree gravity moments associated with deep zonal flows. Since the TWE is derived from the curl of the Euler equation and is a local relation, it necessarily says nothing about any density perturbations that contribute irrotational terms to the Euler equation and that have a non-local origin. However, the predicted corrections from these density contributions to the low harmonic degree gravity moments are not discernible from insignificant changes in interior models while the corrections at high harmonic degree are very small, a few percent or less.Comment: 28 pages, 8 figures, 5 tables, accepted at JGR-Planet