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Register a new userAb initio based equation of state of dense water for planetary and exoplanetary modeling
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As a first step toward a multi-phase equation of state for dense water, we develop a temperature-dependent equation of state 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. We use first principles quantum molecular dynamics simulations and its 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. We produce an equation of state given in analytical form that is readily usable in planetary modeling codes and dynamical simulations (a fortran implementation can be found at http://www.ioffe.ru/astro/H2O/). 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 equation of state to calculate the mass-radius relationship of exoplanets up to 5,000M_Earth, explore temperature effects in ocean and wet Earth-like planets, and quantify the influence of the water EOS for the core on the gravitational moments of Jupiter.
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Water is of the utmost importance for life and technology. However, a genuinely predictive ab initio model of water has eluded scientists. We demonstrate that a fully ab initio approach, relying on the strongly constrained and appropriately normed (SCAN) density functional, provides such a description of water. SCAN accurately describes the balance among covalent bonds, hydrogen bonds, and van der Waals interactions that dictates the structure and dynamics of liquid water. Notably, SCAN captures the density difference between water and ice I{it h} at ambient conditions, as well as many important structural, electronic, and dynamic properties of liquid water. These successful predictions of the versatile SCAN functional open the gates to study complex processes in aqueous phase chemistry and the interactions of water with other materials in an efficient, accurate, and predictive, ab initio manner.
We are now on a clear trajectory for improvements in exoplanet observations that will revolutionize our ability to characterize their atmospheric structure, composition, and circulation, from gas giants to rocky planets. However, exoplanet atmospheric models capable of interpreting the upcoming observations are often limited by insufficiencies in the laboratory and theoretical data that serve as critical inputs to atmospheric physical and chemical tools. Here we provide an up-to-date and condensed description of areas where laboratory and/or ab initio investigations could fill critical gaps in our ability to model exoplanet atmospheric opacities, clouds, and chemistry, building off a larger 2016 white paper, and endorsed by the NAS Exoplanet Science Strategy report. Now is the ideal time for progress in these areas, but this progress requires better access to, understanding of, and training in the production of spectroscopic data as well as a better insight into chemical reaction kinetics both thermal and radiation-induced at a broad range of temperatures. Given that most published efforts have emphasized relatively Earth-like conditions, we can expect significant and enlightening discoveries as emphasis moves to the exotic atmospheres of exoplanets.
Water (H$_{2}$O), in all forms, is an important constituent in planetary bodies, controlling habitability and influencing geological activity. Under conditions found in the interior of many planets, as the pressure increases, the H-bonds in water gradually weaken and are replaced by ionic bonds. Recent experimental measurements of the water equation of state (EOS) showed both a new phase of H-bonded water ice, ice-VII$_t$, and a relatively low transition pressure just above 30 GPa to ionic bonded ice-X, which has a bulk modulus 2.5 times larger. The higher bulk modulus of ice-X produces larger planets for a given mass, thereby either reducing the atmospheric contribution to the volume of many exoplanets or limiting their water content. We investigate the impact of the new EOS measurements on the planetary mass-radius relation and interior structure for water-rich planets. We find that the change in the planet mass-radius relation caused by the systematic differences between previous and new experimental EOS measurements are comparable to the observational uncertainties in some planet sizes -- an issue that will become more important as observations continue to improve.
Warm dense matter (WDM) -- an exotic state of highly compressed matter -- has attracted high interest in recent years in astrophysics and for dense laboratory systems. At the same time, this state is extremely difficult to treat theoretically. This is due to the simultaneous appearance of quantum degeneracy, Coulomb correlations and thermal effects, as well as the overlap of plasma and condensed phases. Recent breakthroughs are due to the successful application of density functional theory (DFT) methods which, however, often lack the necessary accuracy and predictive capability for WDM applications. The situation has changed with the availability of the first textit{ab initio} data for the exchange-correlation free energy of the warm dense uniform electron gas (UEG) that were obtained by quantum Monte Carlo (QMC) simulations, for recent reviews, see Dornheim textit{et al.}, Phys. Plasmas textbf{24}, 056303 (2017) and Phys. Rep. textbf{744}, 1-86 (2018). In the present article we review recent further progress in QMC simulations of the warm dense UEG: namely, textit{ab initio} results for the static local field correction $G(q)$ and for the dynamic structure factor $S(q,omega)$. These data are of key relevance for the comparison with x-ray scattering experiments at free electron laser facilities and for the improvement of theoretical models. In the second part of this paper we discuss simulations of WDM out of equilibrium. The theoretical approaches include Born-Oppenheimer molecular dynamics, quantum kinetic theory, time-dependent DFT and hydrodynamics. Here we analyze strengths and limitations of these methods and argue that progress in WDM simulations will require a suitable combination of all methods. A particular role might be played by quantum hydrodynamics, and we concentrate on problems, recent progress, and possible improvements of this method.
A pseudopotential of $C_{60}^-$ has been constructed from ab-initio quantum-mechanical calculations. Since the obtained pseudopotential can be easily fitted by rather simple analytical approximation it can be effectively used both in classical and quantum molecular dynamics of fullerene-based compounds.
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