AB INITIO EQUATIONS OF STATE FOR HYDROGEN (H-REOS.3) AND HELIUM (He-REOS.3) AND THEIR IMPLICATIONS FOR THE INTERIOR OF BROWN DWARFS

Becker, Andreas; Lorenzen, Winfried; Fortney, Jonathan J.; Nettelmann, Nadine; Schöttler, Manuel; Redmer, R.

doi:10.1088/0067-0049/215/2/21

Cited by 162 publications

(200 citation statements)

References 91 publications

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“…We notice that the approximate inclusion of the electronic entropy with the smearing gives a negligible difference compared with simulations without smearing, suggesting that the ground-state approximations holds very well even at the largest temperature here considered. Overall, we notice that our DFT simulations are in perfect agreement with previous studies using PBE 15,31,35 . Figure 6: Supplementary Figure S2: Basis set and finite size errors.…”

Section: Dft Molecular Dynamics Setupsupporting

confidence: 90%

“…Since experimental data are limited, it is not possible to identify a posteriori the best functional for dense H. Therefore the predictive power expected by present ab-initio DFT simulations are somewhat limited. Currently for Jupiter's interior, planetary modelers use H-He EOS that have been derived from DFT data 14,15 , using a specific -and somewhat arbitrary-choice of the XC functional, the widely used Perdew-Burke-Ernzerhof (PBE) 16 . Recently, QMC approaches emerged as competitive tools to solve accurately electronic problems 17 thanks to the new generations of super-computers.…”

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confidence: 99%

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Phase Diagram of Hydrogen and a Hydrogen-Helium Mixture at Planetary Conditions by Quantum Monte Carlo Simulations

2018

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Understanding planetary interiors is directly linked to our ability of simulating exotic quantum mechanical systems such as hydrogen (H) and hydrogen-helium (H-He) mixtures at high pressures and temperatures 1 . Equations of State (EOSs) tables based on Density Functional Theory (DFT), are commonly used by planetary scientists, although this method allows only for a qualitative description of the phase diagram 2 , due to an incomplete treatment of electronic interactions 3 . Here we report Quantum Monte Carlo (QMC) molecular dynamics simulations of pure H and H-He mixture. We calculate the first QMC EOS at 6000 K for an H-He mixture of a proto-solar composition, and show the crucial influence of He on the H metallization pressure. Our results can be used to calibrate other EOS calculations and are very timely given the accurate determination of Jupiter's gravitational field from the NASA Juno mission and the effort to determine its structure 4 .Since a few decades the link between the uncertainty of the H EOS and the internal structure of Jupiter (and other gaseous planets) has been investigated and many efforts to model Jupiter's interior have been carried 1,5-7 . The computation of an EOS from first principles requires to solve a many-body quantum mechanical problem, a task which is beyond the currently available theoretical and computational capabilities. In practice, we must resort to several approximations. The first is to decouple the ionic and electronic problems and consider the ions as classical or quantum particles, determining their motion by following the Born-Oppenheimer potential energy surface. The second approximation concerns the description of the electronic interaction and the exchange one, due to the Pauli exclusion principle.The standard approach to EOS calculations relies on Density Functional Theory (DFT), which targets the tridimensional electronic density rather than the (N e electrons) many-body wave-function. Its success and simplicity have lead to a widespread application in materials science and to the development of several software packages which allow fast and reproducible calculations 8 . Although DFT is formally exact, the explicit functional form to describe the exchange and correlation (XC) effects between electrons remains approximated 3 . Indeed, a systematic and efficient route to improve XC functional is still lacking. Therefore, in practical solid state calculations, benchmarks against experimental data, are often required to validate the XC functional used to describe the system in a satisfactory manner.Dense hydrogen systems, both in the low temperature solid and in the liquid phase remain a challenge to DFT simulations due to the interplay of strong correlation and non-covalent interactions between the atoms. DFT calculations with different functionals produce different results with the expected metallization pressure varying over a range of 100-200 GPa (Fig. 1) 12,13 . Since experimental data are limited, it is not possible to identify a posteriori the best functional...

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Section: Dft Molecular Dynamics Setupsupporting

confidence: 90%

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confidence: 99%

Phase Diagram of Hydrogen and a Hydrogen-Helium Mixture at Planetary Conditions by Quantum Monte Carlo Simulations

2018

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“…REOS3b leads to M core between 7 and 16 M Earth , higher than estimates by Nettelmann et al (2012) and Becker et al (2014). While their preferred model has P sep ≥ 4 Mbar, our models place the separation between Z atm and Z deep in the same place as the helium phase transition, between 0.8 and 4 Mbar (Morales et al 2013), and the baseline simulations have P sep = 2 Mbar.…”

Section: Discussionmentioning

confidence: 59%

“…One of the most successful equations of state (EOS) was published by Saumon et al (1995;SCvH) and has been used in numerous publications on the interior calculations of giant planets. Since 1995, development in numerical techniques allowed a new generation of EOS calculated from ab initio simulations (Nettelmann et al 2008;Militzer et al 2008;Militzer 2006Militzer , 2009Caillabet et al 2011;Nettelmann et al 2012;Militzer & Hubbard 2013;Becker et al 2014). These Full appendix tables are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/596/A114 equations of state, even though calculated from the same principles and numerical techniques, were used to construct interior models of Jupiter with different results.…”

Section: Introductionmentioning

confidence: 99%

“…After these papers, two new results were published. Militzer & Hubbard (2013;MH13) presented a new equation of state for an interacting hydrogen-helium mixture with self-consistent entropy calculations, and a recent paper by Becker et al (2014;REOS.3) showed updated tables for hydrogen and helium in a wide range that covers all temperatures and densities in the interior of Jupiter. These recent estimates still present differences in interior calculations of Jupiter, showing that one of the great challenges in modeling the internal structure of Jupiter still rests on the determination and accuracy of the equations of state of hydrogen and helium.…”

Section: Introductionmentioning

confidence: 99%

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Jupiter internal structure: the effect of different equations of state

Miguel

Guillot

Fayon

2016

A&A

103

161

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Context. Heavy elements, even though they are a smaller constituent, are crucial to understand the formation history of Jupiter. Interior models are used to determine the amount of heavy elements in the interior of Jupiter, but this range is still subject to degeneracies because of the uncertainties in the equations of state. Aims. Before Juno mission data arrive, we present optimized calculations for Jupiter that explore the effect of different model parameters on the determination of the core and the mass of heavy elements of Jupiter. We compare recently published equations of state.Methods. The interior model of Jupiter was calculated from the equations of hydrostatic equilibrium, mass, and energy conservation, and energy transport. The mass of the core and heavy elements was adjusted to match the observed radius and gravitational moments of Jupiter. Results. We show that the determination of the interior structure of Jupiter is tied to the estimation of its gravitational moments and the accuracy of equations of state of hydrogen, helium, and heavy elements. Locating the region where helium rain occurs and defining its timescale is important to determine the distribution of heavy elements and helium in the interior of Jupiter. We show that the differences found when modeling the interior of Jupiter with recent EOS are more likely due to differences in the internal energy and entropy calculation. The consequent changes in the thermal profile lead to different estimates of the mass of the core and heavy elements, which explains differences in recently published interior models of Jupiter. Conclusions. Our results help clarify the reasons for the differences found in interior models of Jupiter and will help interpreting upcoming Juno data.

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The effect of differential rotation on Jupiter's low‐degree even gravity moments

Kaspi

Guillot

Galanti

et al. 2017

Geophysical Research Letters

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The close‐by orbits of the ongoing Juno mission allow measuring with unprecedented accuracy Jupiter's low‐degree even gravity moments J2, J4, J6, and J8. These can be used to better determine Jupiter's internal density profile and constrain its core mass. Yet the largest unknown on these gravity moments comes from the effect of differential rotation, which gives a degree of freedom unaccounted for by internal structure models. Here considering a wide range of possible internal flow structures and dynamical considerations, we provide upper bounds to the effect of dynamics (differential rotation) on the low‐degree gravity moments. In light of the recent Juno gravity measurements and their small uncertainties, this allows differentiating between the various models suggested for Jupiter's internal structure.

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AB INITIO EQUATIONS OF STATE FOR HYDROGEN (H-REOS.3) AND HELIUM (He-REOS.3) AND THEIR IMPLICATIONS FOR THE INTERIOR OF BROWN DWARFS

Cited by 162 publications

References 91 publications

Phase Diagram of Hydrogen and a Hydrogen-Helium Mixture at Planetary Conditions by Quantum Monte Carlo Simulations

Phase Diagram of Hydrogen and a Hydrogen-Helium Mixture at Planetary Conditions by Quantum Monte Carlo Simulations

Jupiter internal structure: the effect of different equations of state

The effect of differential rotation on Jupiter's low‐degree even gravity moments

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