We used molecular dynamics simulations based on density functional theory to study the thermophysical properties of warm dense helium. The influence of different exchange-correlation (XC) functionals was analyzed. We calculated the equation of state at high pressures up to several Mbar and temperatures up to 100 000 K in order to reconstruct recent static, single shock, and quasi-isentropic compression experiments. Furthermore, we calculated the dynamic electrical conductivity and determined the reflectivity and DC conductivity. We compared our results with experimental data and found good agreement between our calculations and the high-pressure experiments. The different XC functionals give similar results in the equation of state calculations, but have a strong impact on the reflectivity and the DC conductivity.

We present thermodynamic material and transport properties for the extreme conditions prevalent in the interiors of massive giant planets and brown dwarfs. They are obtained from extensive ab initio simulations of hydrogen–helium mixtures along the isentropes of three representative objects. In particular, we determine the heat capacities, the thermal expansion coefficient, the isothermal compressibility, and the sound velocity. Important transport properties such as the electrical and thermal conductivity, opacity, and shear viscosity are also calculated. Further results for associated quantities, including magnetic and thermal diffusivity, kinematic shear viscosity, as well as the static Love number k2 and the equidistance, are presented. In comparison to Jupiter-mass planets, the behavior inside massive giant planets and brown dwarfs is stronger dominated by degenerate matter. We discuss the implications on possible dynamics and magnetic fields of those massive objects. The consistent data set compiled here may serve as a starting point to obtain material and transport properties for other substellar H–He objects with masses above one Jovian mass and finally may be used as input for dynamo simulations.

Space missions such as CoRoT and Kepler have made the transit method the most successful technique in observing extrasolar planets. However, although the mean density of a planet can be derived from its measured mass and radius, no details about its interior structure, such as the density profile, can be inferred so far. If determined precisely enough, the shape of the transiting light curve might, in principle, reveal the shape of the planet, and in particular, its deviation from spherical symmetry. These deformations are caused, for instance, by the tidal interactions of the planet with the host star and by other planets that might orbit in the planetary system. The deformations depend on the interior structure of the planet and its composition and can be parameterized as Love numbers k n . This means that the diversity of possible interior models for extrasolar planets might be confined by measuring this quantity. We present results of a wide-ranging parameter study in planet mass, surface temperature, and layer mass fractions on such models for super-Earths and their corresponding Love numbers. Based on these data, we find that k 2 is most useful in assessing the ratio of rocky material to iron and in ruling out certain compositional configurations for measured mass and radius values, such as a prominent core consisting of rocky material. Furthermore, we apply the procedure to exoplanets K2-3b and c and predict that K2-3c probably has a thick outer water layer.

Hydrogen, the simplest element in the universe, has a surprisingly complex phase diagram. Because of applications to planetary science, inertial confinement fusion and fundamental physics, its high-pressure properties have been the subject of intense study over the past two decades. While sophisticated static experiments have probed hydrogen's structure at ever higher pressures, studies examining the higher-temperature regime using dynamic compression have mostly been limited to optical measurement techniques. Here we present spectrally resolved x-ray scattering measurements from plasmons in dynamically compressed deuterium. Combined with Compton scattering, and velocity interferometry to determine shock pressure and mass density, this allows us to extract ionization state as a function of compression. The onset of ionization occurs close in pressure to where density functional theory-molecular dynamics (DFT-MD) simulations show molecular dissociation, suggesting hydrogen transitions from a molecular and insulating fluid to a conducting state without passing through an intermediate atomic phase.

Dense cryogenic hydrogen is heated by intense femtosecond infrared laser pulses at intensities of 1015-1016 Wcm-2. Three-dimensional particle-in-cell (PIC) simulations predict that this heating is limited to the skin depth, causing an inhomogeneously heated outer shell with a cold core and two prominent temperatures of about 25 and 40 eV for simulated delay times up to +70 fs after the laser pulse maximum. Experimentally, the time-integrated emitted bremsstrahlung in the spectral range of 8-18 nm was corrected for the wavelength-dependent instrument efficiency. The resulting spectrum cannot be fit with a single temperature bremsstrahlung model, and the best fit is obtained using two temperatures of about 13 and 30 eV. The lower temperatures in the experiment can be explained by missing energy-loss channels in the simulations, as well as the inclusion of hot, non- Maxwellian electrons in the temperature calculation. We resolved the time-scale for laser-heating of hydrogen, and PIC results for laser-matter interaction were successfully tested against the experiment data.

Eighty years ago, it was proposed that solid hydrogen would becomemetallic at sufficiently high density. Despite numerous investigations, this transition has not yet been experimentally observed. More recently, there has been much interest in the analog of this predicted metallic transition in the dense liquid, due to its relevance to planetary science. Here, we show direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium. Experimental determination of the location of this transition provides a much-needed benchmark for theory and may constrain the region of hydrogen-helium immiscibility and the boundary-layer pressure in standard models of the internal structure of gas-giant planets.

We give an introduction into the method of quantum molecular dynamics simulations which combines density functional theory with classical molecular dynamics. This method has demonstrated its predictive power in determining the thermophysical properties of matter under extreme conditions as found, e.g., in astrophysical objects like giant planets and brown dwarfs. Such extreme states of matter can also be probed by state-of-the-art shock wave experiments in the laboratory. We give exemplary ab initio results for the behavior of the simplest and most abundant elements hydrogen and helium under extreme conditions. In addition, we also show results for more complex molecular systems such as water. The light elements H and He, the hydrides of C (CH4), N (NH3), and O (H2O) and, in particular, mixtures of these systems have rich high-pressure phase diagrams which are important for the structure, evolution and magnetic field of gas giant planets like Jupiter and ice giant planets like Neptune. Finally, we describe the impact of these results on the design of advanced interior, evolution, and dynamo models and give exemplary results for solar and extrasolar giant planets.

We report on the dynamics of ultrafast heating in cryogenic hydrogen initiated by a ≲300  fs, 92 eV free electron laser x-ray burst. The rise of the x-ray scattering amplitude from a second x-ray pulse probes the transition from dense cryogenic molecular hydrogen to a nearly uncorrelated plasmalike structure, indicating an electron-ion equilibration time of ∼0.9  ps. The rise time agrees with radiation hydrodynamics simulations based on a conductivity model for partially ionized plasma that is validated by two-temperature density-functional theory.

Spacecraft data reveal a very Earth-like Jovian magnetic field. This is surprising since numerical simulations have shown that the vastly different interiors of terrestrial and gas planets can strongly affect the internal dynamo process. Here we present the first numerical dynamo that manages to match the structure and strength of the observed magnetic field by embracing the newest models for Jupiter's interior. Simulated dynamo action primarily occurs in the deep high electrical conductivity region while zonal flows are dynamically constrained to a strong equatorial jet in the outer envelope of low conductivity. Our model reproduces the structure and strength of the observed global magnetic field and predicts that secondary dynamo action associated to the equatorial jet produces banded magnetic features likely observable by the Juno mission. Secular variation in our model scales to about 2000 nT per year and should also be observable during the one year nominal mission duration.

We investigate subpicosecond dynamics of warm dense hydrogen at the XUV free-electron laser facility (FLASH) at DESY (Hamburg). Ultrafast impulsive electron heating is initiated by a ≤ 300-fs short x-ray burst of 92-eV photon energy. A second pulse probes the sample via x-ray scattering at jitter-free variable time delay. We show that the initial molecular structure dissociates within (0.9 ± 0.2) ps, allowing us to infer the energy transfer rate between electrons and ions. We evaluate Saha and Thomas-Fermi ionization models in radiation hydrodynamics simulations, predicting plasma parameters that are subsequently used to calculate the static structure factor. A conductivity model for partially ionized plasma is validated by two-temperature density-functional theory coupled to molecular dynamic simulations and agrees with the experimental data. Our results provide important insights and the needed experimental data on transport properties of dense plasmas.

We present new equations of state (EOS) for hydrogen and helium covering a wide range of temperatures from 60 K to 10$^7$ K and densities from $10^{-10}$ g/cm$^3$ to $10^3$ g/cm$^3$. They include an extended set of ab initio EOS data for the strongly correlated quantum regime with an accurate connection to data derived from other approaches for the neighboring regions. We compare linear-mixing isotherms based on our EOS tables with available real-mixture data. A first important astrophysical application of this new EOS data is the calculation of interior models for Jupiter and the comparison with recent results. Secondly, mass-radius relations are calculated for Brown Dwarfs which we compare with predictions derived from the widely used EOS of Saumon, Chabrier and van Horn. Furthermore, we calculate interior models for typical Brown Dwarfs with different masses, namely Corot-3b, Gliese-229b and Corot-15b, and the Giant Planet KOI-889b. The predictions for the central pressures and densities differ by up to 10$\%$ dependent on the EOS used. Our EOS tables are made available in the supplemental material of this paper.

We perform ab initio calculations for the equation of state of dense liquid hydrogen and deuterium using quantum molecular dynamics simulations based on finite-temperature density functional theory. This extensive data set allows us to determine specific density-temperature-pressure tracks such as the cold curve, precompressed and principal Hugoniot curves, and isentropes which are essential for the analysis and interpretation of high-pressure experiments. In this study we focus on conditions probed by recent quasi-isentropic shock compression experiments that have reached a so-far unprecedented 108-fold compression of gaseous deuterium. As these states of matter are relevant for the deep interior of Jupiter-like exoplanets we simultaneously give predictions for their isentropes.

The amount and distribution of heavy elements in Jupiter gives indications on the process of its formation and evolution. Core mass and metallicity predictions however depend on the equations of state used, and on model assumptions. We present an improved ab initio hydrogen equation of state, H-REOS.2 and compute the internal structure and thermal evolution of Jupiter within the standard three-layer approach. The advance over our previous Jupiter models with H-REOS.1 by Nettelmann et al.(2008) is that the new models are also consistent with the observed 2 or more times solar heavy element abundances in Jupiter's atmosphere. Such models have a rock core mass Mcore=0-8 ME, total mass of heavy elements MZ=28-32 ME, a deep internal layer boundary at 4 or more Mbar, and a cooling time of 4.4-5.0 Gyrs when assuming homogeneous evolution. We also calculate two-layer models in the manner of Militzer et al.(2008) and find a comparable large core of 16-21 ME, out of which ~11 ME is helium, but a significantly higher envelope metallicity of 4.5 times solar. According to our preferred three-layer models, neither the characteristic frequency (nu0 ~156 microHz) nor the normalized moment of inertia (~0.276) are sensitive to the core mass but accurate measurements could well help to rule out some classes of models.

We determine basic thermodynamic and transport properties of hydrogen–helium–water mixtures for the extreme conditions along Jupiter's adiabat via ab initio simulations, which are compiled in an accurate and consistent data set. In particular, we calculate the electrical and thermal conductivity, the shear and longitudinal viscosity, and diffusion coefficients of the nuclei. We present results for associated quantities like the magnetic and thermal diffusivity and the kinematic shear viscosity along an adiabat that is taken from a state-of-the-art interior structure model. Furthermore, the heat capacities, the thermal expansion coefficient, the isothermal compressibility, the Grüneisen parameter, and the speed of sound are calculated. We find that the onset of dissociation and ionization of hydrogen at about 0.9 Jupiter radii marks a region where the material properties change drastically. In the deep interior, where the electrons are degenerate, many of the material properties remain relatively constant. Our ab initio data will serve as a robust foundation for applications that require accurate knowledge of the material properties in Jupiter's interior, e.g., models for the dynamo generation.