We present a new equation of state (EOS) for dense hydrogen/helium mixtures that covers a range of densities from 10−8 to , pressures from 10−9 to 1013 GPa, and temperatures from 102 to 108 K. The ...calculations combine the EOS of Saumon, Chabrier & van Horn in the low-density, low-temperature molecular/atomic domain, the EOS of Chabrier & Potekhin in the high-density, high-temperature fully ionized domain, the limits of which differ for H and He, and ab initio quantum molecular dynamics calculations in the regime of intermediate density and temperature, 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 calculations of stellar or planetary evolution. The EOS results are compared with existing experimental data, namely Hugoniot shock experiments for pure H and He, and with first-principles 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.
Context. The modeling of planetary interiors requires accurate equations of state (EOSs) for the basic constituents with proven validity in the difficult pressure–temperature regime extending up to ...50 000 K and hundreds of megabars. While EOSs based on first-principles simulations are now available for the two most abundant elements, hydrogen and helium, the situation is less satisfactory for water where no wide-range EOS is available despite its requirement for interior modeling of planets ranging from super-Earths to planets several times the size of Jupiter. Aims. As a first step toward a multi-phase EOS for dense water, we develop a temperature-dependent EOS for dense water covering the liquid and plasma regimes and extending to the super-ionic and gas regimes. This equation of state covers the complete range of conditions encountered in planetary modeling. Methods. We use first-principles quantum molecular dynamics simulations and the Thomas-Fermi extension to reach the highest pressures encountered in giant planets several times the size of Jupiter. Using these results, as well as the data available at lower pressures, we obtain a parametrization of the Helmholtz free energy adjusted over this extended temperature and pressure domain. The parametrization ignores the entropy and density jumps at phase boundaries but we show that it is sufficiently accurate to model interior properties of most planets and exoplanets. Results. We produce an EOS given in analytical form that is readily usable in planetary modeling codes and dynamical simulations (a fortran implementation is provided). The EOS produced is valid for the entire density range relevant to planetary modeling, for densities where quantum effects for the ions can be neglected, and for temperatures below 50 000K. We use this EOS to calculate the mass-radius relationship of exoplanets up to 5000 MEarth, explore temperature effects in the wet Earth-like, ocean planets and pure water planets, and quantify the influence of the water EOS for the core on the gravitational moments of Jupiter.
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Context.
Juno can currently measure Jupiter’s gravitational moments to unprecedented accuracy, and models for the interior structure of the planet are thus being put to the test. While equations of ...state (EOSs) based on first principles or ab initio simulations are available and used for the two most abundant elements constituting the envelope, hydrogen and helium, significant discrepancies remain regarding the predictions of the inner structure of Jupiter. The differences are severe enough to clutter the analysis of Juno’s data and even cast doubts on the usefulness of these computationally expensive EOSs for the modeling of the interior of Jupiter and exoplanets at large.
Aims.
Using our newly developed EOSs for hydrogen and helium, we asses the ab initio EOSs currently available and establish their efficiency at predicting the interior structure of Jupiter in a two-layer model. We paid particular attention to the calculation of the total entropy for hydrogen. It is required to calculate the convective H–He envelope but is a derived quantity from ab initio simulations.
Methods.
The ab initio EOSs used in this work are based on a parameterization of the ab initio simulation points using a functional form of the Helmholtz free energy. The current paper carries on from our previous, recently published work. Compared to previous ab initio EOSs available, the approach used here provides an independent means of calculating the entropy that was recently pointed out as deficient in some ab initio results.
Results.
By adjusting our free energy parameterization to reproduce previous ab initio EOS behavior, we identify the source of the disagreement previously reported for the interior structure of Jupiter. We further point to areas where care should be taken when building EOSs for the modeling of giant planets. This concerns the interpolation between the ab initio results and the physical models used to cover the low-density range, as well as the interpolation of the ab initio simulation results at high densities. This sensitivity falls well within the uncertainties of the ab initio simulations. This suggests that hydrogen EOSs should be carefully benchmarked using a simple planetary model before being used in the more advanced planetary models needed to interpret the Juno data. We finally provide an updated version of our recently published ab initio hydrogen EOS.
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Context. The Juno probe that currently orbits Jupiter measures its gravitational moments with great accuracy. Preliminary results suggest that the core of the planet may be eroded. While great ...attention has been paid to the material properties of elements constituting the envelope, little is known about those that constitute the core. This situation clutters our interpretation the Juno data and modeling of giant planets and exoplanets in general. Aims. We calculate the high-pressure melting temperatures of three potential components of the cores of giant planets, water, iron, and a simple silicate, MgSiO3, to investigate the state of the deep inner core. Methods. We used ab initio molecular dynamics simulations to calculate the high-pressure melting temperatures of the three potential core components. The planetary adiabats were obtained by solving the hydrostatic equations in a three-layer model adjusted to reproduce the measured gravitational moments. Recently developed ab initio equations of state were used for the envelope and the core. Results. We find that the cores of the giant and ice-giant planets of the solar system differ because the pressure–temperature conditions encountered in each object correspond to different regions of the phase diagrams. For Jupiter and Saturn, the results are compatible with a diffuse core and mixing of a significant fraction of metallic elements in the envelope, leading to a convective and/or a double-diffusion regime. We also find that their solid cores vary in nature and size throughout the lifetimes of these planets. The solid cores of the two giant planets are not primordial and nucleate and grow as the planets cool. We estimate that the solid core of Jupiter is 3 Gyr old and that of Saturn is 1.5 Gyr old. The situation is less extreme for Uranus and Neptune, whose cores are only partially melted. Conclusions. To model Jupiter, the time evolution of the interior structure of the giant planets and exoplanets in general, their luminosity, and the evolution of the tidal effects over their lifetimes, the core should be considered as crystallizing and growing rather than gradually mixing into the envelope due to the solubility of its components.
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Using ab initio molecular dynamics simulations, we calculate the equation of state of iron in the solid phase for both the hcp and bcc structures as well as the high-pressure melting curve up to 15 ...Mbars. We first find that the melting temperature increases up to 11 000 K at the highest pressures investigated following a semiempirical melting law over the entire pressure domain. We also investigate the stability of the bcc phase of iron beyond Earth's core conditions (3 Mbars) and find that the temperature at which the bcc phase is mechanically stabilized increases with density. Finally, we provide simple fits of these results for convenient use in the modeling of Earth-like exoplanets up to ten Earth masses, which requires accurate knowledge of the properties of iron up to 15 Mbars.
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The effect of intense ultrashort irradiation on interatomic forces, crystal stability, and possible melting transition of the underlying lattice is not completely elucidated. By using ab initio ...linear response to compute the phonon spectrum of gold, silicon, and aluminum, we found that silicon and gold behave in opposite ways when increasing radiation intensity: whereas a weakening of the silicon bond induces a lattice instability, gold undergoes a sharp increase of its melting temperature, while a significantly smaller effect is observed for aluminum for electronic temperatures up to 6 eV.
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Taking advantage of the new opportunities provided by x-ray free electron laser (FEL) sources when coupled to a long laser pulse as available at the Linear Coherent Light Source (LCLS), we have ...performed x-ray absorption near-edge spectroscopy (XANES) of laser shock compressed iron up to 420 GPa (+ or -50) and 10 800 K (+ or -1390). Visible diagnostics coupled with hydrodynamic simulations were used to infer the thermodynamical conditions along the Hugoniot and the release adiabat. A modification of the pre-edge feature at 7.12 keV in the XANES spectra is observed above pressures of 260 GPa along the Hugoniot. Comparing with ab initio calculations and with previous laser-heated diamond cell data, we propose that such changes in the XANES pre-edge could be a signature of molten iron. This interpretation then suggests that iron is molten at pressures and temperatures higher than 260 GPa (+ or -29) and 5680 K (+ or -700) along the principal Fe Hugoniot.
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We develop a first-principles approach to calculate the near-edge absorption spectrum of dense plasmas based on density functional electronic structure calculations and molecular dynamics ...simulations. We apply the method to the calculation of the K-edge shift along the aluminum shock compressed Hugoniot. We obtain a good agreement with measurements performed at moderate compression and find that the variation of the XANES spectra could be used as a signature for melting along the Hugoniot. We also show that the calculation of the K-edge shift along the Hugoniot formally requires a fully self-consistent calculation beyond the frozen-core approximation and provides an opportunity to test the accuracy of first principle simulation methods in the high-pressure high-temperature regime.
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Using ab initio molecular dynamics simulations, we calculate the physical properties of MgO at conditions extending from the ones encountered in the Earth mantle up to the ones anticipated in giant ...planet interiors such as Jupiter. We pay particular attention to the high-pressure melting temperature throughout this large density range as this is a key ingredient for building accurate planetary interior models with a realistic description of their inner cores. We compare our simulation results with previous ab initio calculations that have been so far limited to the pressure range corresponding to the Earth mantle and the B1-B2 transition around 6 Mbar. We provide our results for both the equation of state and high-pressure melting curve in parametric forms for direct use in planetary models. Finally, we compare our predictions of the high-pressure melting temperature with various planetary interior profiles to deduce the state of differentiated layer within the core made of MgO in differentiated cores of various types of planets and exoplanets.
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