Planetary Ices and the Linear Mixing Approximation

Bethkenhagen, Mandy; Meyer, Edmund; Hamel, Sébastien; Nettelmann, Nadine; French, Martin; Scheibe, Ludwig; Ticknor, Christopher; Collins, L. A.; Kress, Joel D.; Fortney, Jonathan J.; Redmer, R.

doi:10.3847/1538-4357/aa8b14

Cited by 68 publications

(71 citation statements)

References 64 publications

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“…The above expression neglects nonideal mixing contributions to h F a , but simplifies the calculations [22,23]. Nonideal mixing effects on equation of state quantities were found to be very small in calculations of waterammonia-methane mixtures under similar conditions [24]. Nevertheless, avoiding this approximation is possible, and a comparison with results from an exact expression for λ nuc was made, see the appendix.…”

Section: Theoretical Methods and Simulation Proceduresmentioning

confidence: 99%

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Thermal conductivity of dissociating water—anab initiostudy

French

2019

New J. Phys.

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The thermal conductivity of partially dissociated and ionised water is calculated in a large-scale study using density functional theory (DFT)-based molecular dynamics (MD) simulations. In doing so, the required heat current of the nuclei is calculated by mapping the effective particle interactions from the DFT-MD simulations onto classical pair potentials. It is demonstrated that experimental and theoretical thermal conductivity data for liquid heavy water and for ice VII are well reproduced with this efficient procedure. Moreover, the approach also allows for an illustrative interpretation of the characteristics of the thermal conductivity in the dense chemically reacting fluid. The thermodynamic conditions investigated here range from densities between 0.2 and 6 g cm −3 and temperatures between 600 and 50000 K, which includes states highly relevant for understanding the interiors of water-rich planets like Uranus and Neptune and exoplanets of similar composition. During the last two decades, ab initio calculations based on finite-temperature density functional theory (FT-DFT) in combination with molecular dynamics (MD) simulations have become a reliable tool for accurate predictions of thermodynamic properties of matter under extreme conditions [12,13]. The prefix FT emphasises that the electron system is consistently treated at a nonzero (finite) temperature [14], which is typically equal to the temperature of the nuclei.The calculation of the thermal conductivity with FT-DFT-MD techniques requires a distincted treatment of the contributions from electronic heat conduction and from heat transport via the nuclei. The former is gained by evaluating the electronic Onsager coefficients using the Kohn-Sham eigenvalues and orbitals from the FT-DFT [15], which was recently accomplished also for partially ionised water [16].

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Section: Theoretical Methods and Simulation Proceduresmentioning

confidence: 99%

“…similar as in [22,56]. This may be required for systems where nonideal mixing effects in the thermodynamic functions are not as small as those in warm dense water and other planetary ices [24].…”

Section: A3 Comparative Validation Of Both Variants Against Each Othermentioning

confidence: 99%

Thermal conductivity of dissociating water—anab initiostudy

French

2019

New J. Phys.

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“…This is certainly a simplification since the further ice-forming elements carbon, nitrogen, and sulphur are likely to be present in the interior as well. Former work has shown that the presence of ices lighter than water in solar element ratios can lead to the extreme case of an icy inner envelope (Podolak & Reynolds 1987) and hence a cooler planet (Bethkenhagen et al 2017). On the other hand, rocks may be soluble in hydrogen and thus be present to some degree in the envelope at the expense of ices, while methane may be insoluble in water and may lead to carbon sedimentation.…”

Section: Equations Of Statementioning

confidence: 99%

Thermal evolution of Uranus and Neptune

Scheibe

Nettelmann

Redmer

2019

A&A

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The brightness of Neptune is often found to be in accordance with an adiabatic interior, while the low luminosity of Uranus challenges this assumption. Here we apply revised equation of state data of hydrogen, helium, and water and compute the thermal evolution of Uranus and Neptune assuming an adiabatic interior. For this purpose, we have developed a new planetary model and evolution code. We investigate the influence of albedo, solar energy influx, and equations of state of H and He, and water on the cooling time. Our cooling times of about τU = 5.1 × 10 9 years for Uranus and τN = 3.7 × 10 9 years for Neptune bracket the known age of the planets of 4.56 × 10 9 years implying that neither planet's present-day luminosity can be explained by adiabatic cooling. We also find that uncertainties on input parameters such as the level of irradiation matter generally more for Uranus than for Neptune. Our results suggest that in contrast to common assumptions, neither planet is fully adiabatic in the deeper interior.

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“…The former involves very moderate computational effort but is of limited accuracy due to the use of approximate kinetic energy and entropy functional. The latter class of DFT approaches on the other hand yields reliable and accurate results and is emerging as the method of choice in the field, with applications rangingfrom short pulse laser simulations [35,36] and xray scattering [37,38] to properties of astrophysical bodies [8,[39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Stochastic density functional theory at finite temperatures

et al. 2018

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Simulations in the warm dense matter regime using finite temperature Kohn-Sham density functional theory (FT-KS-DFT), while frequently used, are computationally expensive due to the partial occupation of a very large number of high-energy KS eigenstates which are obtained from subspace diagonalization. We have developed a stochastic method for applying FT-KS-DFT, that overcomes the bottleneck of calculating the occupied KS orbitals by directly obtaining the density from the KS Hamiltonian. The proposed algorithm, scales as O N T −1 and is compared with the hightemperature limit scaling O N 3 T 3 of the deterministic approach, where N is the system size (number of electrons, volume etc.) and T is the temperature. The method has been implemented in a plane-waves code within the local density approximation (LDA); we demonstrate its efficiency, statistical errors and bias in the estimation of the free energy per electron for a diamond structure silicon. The bias is small compared to the fluctuations, and is independent of system size. In addition to calculating the free energy itself, one can also use the method to calculate its derivatives and obtain the equations of state.

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Planetary Ices and the Linear Mixing Approximation

Cited by 68 publications

References 64 publications

Thermal conductivity of dissociating water—anab initiostudy

Thermal conductivity of dissociating water—anab initiostudy

Thermal evolution of Uranus and Neptune

Stochastic density functional theory at finite temperatures

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