We present a new equation of state (EOS) for dense hydrogen/helium mixtures which covers a range of densities from 10 −8 to 10 6 g cm −3 , pressures from 10 −9 to 10 13 GPa and temperatures from 10 2 to 10 8 K. The calculations combine the EOS of Saumon, Chabrier & vanHorn (1995) in the low density, low temperature molecular/atomic domain, the EOS of Chabrier & Potekhin (1998) in the high-density, high-temperature fully ionized domain, the limits of which differ for H and He, and ab initio quantum molecular dynamics (QMD) calculations in the intermediate density and temperature regime, characteristic of pressure dissociation and ionization. The EOS for the H/He mixture is based on the so-called additive volume law and thus does not take into account the interactions between the two species. A major improvement of the present calculations over existing ones is that we calculate the entropy over the entire density-temperature domain, a necessary quantity for stellar or planetary evolution calculations. The EOS results are compared with existing experimental data, namely Hugoniot shock experiments for pure H and He, and with first principle numerical simulations for both the single elements and the mixture. This new EOS covers a wide range of physical and astrophysical conditions, from jovian planets to solar-type stars, and recovers the existing relativistic EOS at very high densities, in the domains of white dwarfs and neutron stars. All the tables are made publicly available.

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We perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of aluminum. Our equation of state (EOS) simulations cover a wide density-temperature range of 0.1-32.4gcm^{-3} and 10^{4}-10^{8} K. Since PIMC and DFT-MD accurately treat effects of the atomic shell structure, we find two compression maxima along the principal Hugoniot curve attributed to K-shell and L-shell ionization. The results provide a benchmark for widely used EOS tables, such as SESAME, QEOS, and models based on Thomas-Fermi and average-atom techniques. A subsequent multishock analysis provides a quantitative assessment for how much heating occurs relative to an isentrope in multishock experiments. Finally, we compute heat capacity, pair-correlation functions, the electronic density of states, and 〈Z〉 to reveal the evolution of the plasma structure and ionization behavior.

This article provides an overview of how models of giant planet interiors are constructed. We review measurements from past space missions that provided constraints for the interior structure of Jupiter. We discuss typical three‐layer interior models that consist of a dense central core and an inner metallic and an outer molecular hydrogen‐helium layer. These models rely heavily on experiments, analytical theory, and first‐principles computer simulations of hydrogen and helium to understand their behavior up to the extreme pressures ∼10 Mbar and temperatures ∼10,000 K. We review the various equations of state used in Jupiter models and compare them with shock wave experiments. We discuss the possibility that helium rain, core erosion, and double diffusive convection have affected the structure and evolution of giant planets. In July 2016 the Juno spacecraft entered orbit around Jupiter, promising high‐precision measurements of the gravitational field that will allow us to test our understanding of gas giant interiors better than ever before.

We present results from ab initio simulations of liquid water-hydrogen mixtures in the range from 2 to 70 GPa and from 1000 to 6000 K, covering conditions in the interiors of ice giant planets and parts of the outer envelope of gas giant planets. In addition to computing the pressure and the internal energy, we derive the Gibbs free energy by performing a thermodynamic integration. For all conditions under consideration, our simulations predict hydrogen and water to mix in all proportions. The thermodynamic behavior of the mixture can be well described with an ideal mixing approximation. We suggest that a substantial fraction of water and hydrogen in giant planets may occur in homogeneously mixed form rather than in separate layers. The extentof mixing depends on the planet's interior dynamics and its conditions of formation, in particular on how much hydrogen was present when icy planetesimals were delivered. Based on our results, we do not predict water-hydrogen mixtures to phase separate during any stage of the evolution of giant planets. We also show that the hydrogen content of an exoplanet is much higher if the mixed interior is assumed.

Super-Earths are extremely common among the numerous exoplanets that have been discovered. The high pressures and temperatures in their interiors are likely to lead to long-lived magma oceans. If their electrical conductivity is sufficiently high, the mantles of Super-Earth would generate their own magnetic fields. With ab initio simulations, we show that upon melting, the behavior of typical mantle silicates changes from semi-conducting to semi-metallic. The electrical conductivity increases and the optical properties are substantially modified. Melting could thus be detected with high-precision reflectivity measurements during the short time scales of shock experiments. We estimate the electrical conductivity of mantle silicates to be of the order of 100 Ω−1 cm−1, which implies that a magnetic dynamo process would develop in the magma oceans of Super-Earths if their convective velocities have typical values of 1 mm/s or higher. We predict exoplanets with rotation periods longer than 2 days to have multipolar magnetic fields.

We use path integral Monte Carlo and density functional molecular dynamics to construct a coherent set of equation of state for a series of hydrocarbon materials with various C:H ratios (2:1, 1:1, 2:3, 1:2, and 1:4) over the range of 0.07 − 22.4 g cm −3 and 6.7 × 10 3 − 1.29 × 10 8 K. The shock Hugoniot curve derived for each material displays a single compression maximum corresponding to K-shell ionization. For C:H=1:1, the compression maximum occurs at 4.7-fold of the initial density and we show radiation effects significantly increase the shock compression ratio above 2 Gbar, surpassing relativistic effects. The single-peaked structure of the Hugoniot curves contrasts with previous work on higher-Z plasmas, which exhibit a two-peak structure corresponding to both K-and L-shell ionization. Analysis of the electronic density of states reveals that the change in Hugoniot structure is due to merging of the L-shell eigenstates in carbon, while they remain distinct for higher-Z elements. Finally, we show that the isobaric-isothermal linear mixing rule for carbon and hydrogen EOSs is a reasonable approximation with errors better than 1% for stellar-core conditions.Introduction. Hydrocarbon ablator materials are of primary importance for laser-driven shock experiments, such as those central to the study of inertial confinement fusion (ICF) [1][2][3] and the measurement of high energy density states relevant to giant planets [4] and stellar objects [5]. Accurate knowledge of the equation of state (EOS) of the hydrocarbon ablator is essential for optimizing experimental designs to achieve desired density and temperature states in a target. Consequently, a number of planar-driven shock wave experiments have been performed on hydrocarbon materials, including polystyrene (CH) [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], glow-discharge polymer (GDP) [24][25][26][27][28], and foams [29][30][31][32], to measure the EOS. The highest pressure achieved among these experiments is 40 Mbar [14,15], which is yet not high enough to probe the effects of Kshell ionization on the shock Hugoniot curve. Since the first X-ray scattering results on CH at above 0.1 Gbar (1 Gbar=100 TPa) [33], ongoing, spherically-converging shock experiments using the Gbar platform at the National Ignition Facility (NIF) [34][35][36][37][38] and the OMEGA laser [39] will extend measurements of the shock Hugoniot curve of polystyrene to pressures above 0.35 Gbar and into the K-shell ionization regime [40].

We perform all-electron path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of oxygen. Our simulations cover a wide density-temperature range of 1 − 100 g cm −3 and 10 4 − 10 9 K. By combining results from PIMC and DFT-MD, we are able to compute pressures and internal energies from first-principles at all temperatures and provide a coherent equation of state. We compare our first-principles calculations with analytic equations of state, which tend to agree for temperatures above 8×10 6 K. Pair-correlation functions and the electronic density of states reveal an evolving plasma structure and ionization process that is driven by temperature and density. As we increase the density at constant temperature, we find that the ionization fraction of the 1s state decreases while the other electronic states move towards the continuum. Finally, the computed shock Hugoniot curves show an increase in compression as the first and second shells are ionized.