Ab Initio Equation of State Data for Hydrogen, Helium, and Water and the Internal Structure of Jupiter

Nettelmann, Nadine; Holst, Bastian; Kietzmann, André; French, Martin; Redmer, R.; Blaschke, D.

doi:10.1086/589806

Cited by 246 publications

(214 citation statements)

References 71 publications

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“…If the deep interior temperatures in Jupiter are lower than those found with the Saumon et al (1995) EOS used here, then it is possible that a combination of the model atmospheres presented here, helium rain (which prolongs the evolution), and colder interior temperatures (which quickens the evolution) could yield a good match to observations. Recent work on the hydrogen EOS, both theoretically (Nettelmann et al 2008;Militzer et al 2008), and experimentally (Holmes et al 1995;Collins et al 2001), do yield temperatures lower than predicted by Saumon et al (1995), so this avenue is plausible.…”

Section: Jupiter and Saturnmentioning

confidence: 92%

Self-Consistent Model Atmospheres and the Cooling of the Solar System's Giant Planets

Fortney¹,

Ikoma²,

Nettelmann³

et al. 2011

ApJ

140

149

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We compute grids of radiative-convective model atmospheres for Jupiter, Saturn, Uranus, and Neptune over a range of intrinsic fluxes and surface gravities. The atmosphere grids serve as an upper boundary condition for models of the thermal evolution of the planets. Unlike previous work, we customize these grids for the specific properties of each planet, including the appropriate chemical abundances and incident fluxes as a function of solar system age. Using these grids, we compute new models of the thermal evolution of the major planets in an attempt to match their measured luminosities at their known ages. Compared to previous work, we find longer cooling times, predominantly due to higher atmospheric opacity at young ages. For all planets, we employ simple "standard" cooling models that feature adiabatic temperature gradients in the interior H/He and water layers, and an initially hot starting point for the calculation of subsequent cooling. For Jupiter, we find a model cooling age ∼10% longer than previous work, a modest quantitative difference. This may indicate that the hydrogen equation of state used here overestimates the temperatures in the deep interior of the planet. For Saturn, we find a model cooling age ∼20% longer than previous work. However, an additional energy source, such as that due to helium phase separation, is still clearly needed. For Neptune, unlike in work from the 1980s and 1990s, we match the measured T eff of the planet with a model that also matches the planet's current gravity field constraints. This is predominantly due to advances in the high-pressure equation of state of water. This may indicate that the planet possesses no barriers to efficient convection in its deep interior. However, for Uranus, our models exacerbate the well-known problem that Uranus is far cooler than calculations predict, which could imply strong barriers to interior convective cooling. The atmosphere grids are published here as tables, so that they may be used by the wider community.

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Section: Jupiter and Saturnmentioning

confidence: 92%

Self-Consistent Model Atmospheres and the Cooling of the Solar System's Giant Planets

Fortney¹,

Ikoma²,

Nettelmann³

et al. 2011

ApJ

140

149

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“…For these components we use H-, He-, and H 2 O-REOS, respectively, which are based on FT-DFT-MD simulations at those densities where correlation effects are important and on chemical models in complementary regions, see Nettelmann et al (2008) and references therein for a more detailed description. In particular, H 2 O-REOS is a combination of different finite-temperature EOS covering phases ice I and liquid water by fits to accurate experimental data, water vapor using Sesame EOS 7150 (Lyon & Johnson 1992), supercritical molecular water (Sesame 7150 and FT-DFT-MD), fractions of ice VII and X, and large regions of superionic water and water plasma up to 20 g cm −3 and 40 000 K (FT-DFT-MD).…”

Section: Eosmentioning

confidence: 99%

“…The material components that GJ 436b is assumed to be made of are rocks, confined to a rocky core, water, whether confined to an inner envelope or uniformly mixed into an outer hydrogen-helium envelope, and hydrogen and helium. For H, He, and water, we apply the Linear Mixing Rostock Equation Of State (LM-REOS) described in Nettelmann et al (2008), which is based on finite temperature -density functional theory -molecular dynamics (FT-DFT-MD) simulations for the components H, He, and H 2 O, (see Holst et al 2008;Kietzmann et al 2007;French et al 2009). In particular, the phase diagram of water has been calculated recently up to pressures of 100 Mbar and temperatures of 40 000 K (French et al 2009), so that we can derive the possible phases of water in presumably water-rich planets such as GJ 436b in dependence on the uncertainties mentioned above.…”

Section: Introductionmentioning

confidence: 99%

Interior structure models of GJ436b

Nettelmann

Kramm

Redmer

et al. 2010

A&A

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Context. GJ436b is the first extrasolar planet discovered that resembles Neptune in mass and radius. Two more are known (HAT-P-11b and Kepler-4b), and many more are expected to be found in the upcoming years. The particularly interesting property of Neptune-sized planets is that their mass M p and radius R p are close to theoretical M − R relations of water planets. Given M p , R p , and equilibrium temperature, however, various internal compositions are possible. Aims. A broad set of interior structure models is presented here that illustrates the dependence of internal composition and possible phases of water occurring in presumably water-rich planets, such as GJ 436b on the uncertainty in atmospheric temperature profile and mean density. We show how the set of solutions can be narrowed down if theoretical constraints from formation and model atmospheres are applied or potentially observational constraints for the atmospheric metallicity Z 1 and the tidal Love number k 2 . Methods. We model the interior by assuming either three layers (hydrogen-helium envelope, water layer, rock core) or two layers (H/He/H 2 O envelope, rocky core). For water, we use the equation of state H 2 O-REOS based on finite temperature -density functional theory -molecular dynamics (FT-DFT-MD) simulations. Results. Some admixture of H/He appears mandatory for explaining the measured radius. For the warmest considered models, the H/He mass fraction can reduce to 10 −3 , still extending over ∼0.7 R ⊕ . If water occurs, it will be essentially in the plasma phase or in the superionic phase, but not in an ice phase. Metal-free envelope models have 0.02 < k 2 < 0.2, and the core mass cannot be determined from a measurement of k 2 . In contrast, models with 0.3 < k 2 < 0.82 require high metallicities Z 1 < 0.89 in the outer envelope. The uncertainty in core mass decreases to 0.4M p , if k 2 ≥ 0.3, and further to 0.2M p , if k 2 ≥ 0.5, and core mass and Z 1 become sensitive functions of k 2 . Conclusions. To further narrow the set of solutions, a proper treatment of the atmosphere and the evolution is necessary. We encourage efforts to observationally determine the atmospheric metallicity and the Love number k 2 .

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“…Although there are many ways to induce this effect, in the simplest two-level system it will occur when the population of the lower, absorbing level is severely depleted, which requires light intensities sufficiently high to overcome relaxation from the upper level. Here, we report on the production of saturable absorption of a metal in the soft X-ray regime by the creation of highly uniform warm dense conditions, a regime that is of great interest in high-pressure science 2,3 , the geophysics of large planets 4,5 , astrophysics 6 , plasma production and inertial confinement fusion 7 . Furthermore, the process by which the saturation of the absorption occurs will lead, after the X-ray pulse, to the storage of about 100 eV per atom, which in turn evolves to a warm dense state.…”

mentioning

confidence: 99%

Turning solid aluminium transparent by intense soft X-ray photoionization

Nagler¹,

Zastrau²,

Fäustlin³

et al. 2009

Nature Phys

251

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Saturable absorption is a phenomenon readily seen in the optical and infrared wavelengths. It has never been observed in core-electron transitions owing to the short lifetime of the excited states involved and the high intensities of the soft X-rays needed. We report saturable absorption of an L-shell transition in aluminium using record intensities over 10 16 W cm −2 at a photon energy of 92 eV. From a consideration of the relevant timescales, we infer that immediately after the X-rays have passed, the sample is in an exotic state where all of the aluminium atoms have an L-shell hole, and the valence band has approximately a 9 eV temperature, whereas the atoms are still on their crystallographic positions. Subsequently, Auger decay heats the material to the warm dense matter regime, at around 25 eV temperatures. The method is an ideal candidate to study homogeneous warm dense matter, highly relevant to planetary science, astrophysics and inertial confinement fusion. Saturable absorption, the decrease in the absorption of light with increasing intensity, is a well-known effect in the visible and near-visible region of the electromagnetic spectrum 1 , and is a widely exploited phenomenon in laser technology. Although there are many ways to induce this effect, in the simplest two-level system it will occur when the population of the lower, absorbing level is severely depleted, which requires light intensities sufficiently high to overcome relaxation from the upper level. Here, we report on the production of saturable absorption of a metal in the soft X-ray regime by the creation of highly uniform warm dense conditions, a regime that is of great interest in high-pressure science 2,3 , the geophysics of large planets 4,5 , astrophysics 6 , plasma production and inertial confinement fusion 7 . Furthermore, the process by which the saturation of the absorption occurs will lead, after the X-ray pulse, to the storage of about 100 eV per atom, which in turn evolves to a warm dense state. This manner of creation is unique as it requires intense, subpicosecond, soft X-rays. As such, it has not hitherto been observed in this region of the spectrum, owing both to the lack of high-intensity sources, and the rapid recombination times associated with such high photon energies. However, with the advent of new fourth-generation X-ray light sources, including the free-electron laser in Hamburg 8 (FLASH), soft X-ray intensities that have previously remained the province of high-power optical lasers can now be produced. Experiments at such high intensities using gas jets have already exhibited novel absorption phenomena 9 , and the possibility of irradiating solid samples with intense soft and hard X-rays has aroused interest as a possible means of producing warm dense matter (WDM) at known atomic densities 10,11 .We present the first measurements of the absorption coefficient of solid samples subject to subpicosecond soft X-ray pulses with intensities up to and in excess of 10 16 W cm −2 , two orders of magnitude higher than could ...

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Ab Initio Equation of State Data for Hydrogen, Helium, and Water and the Internal Structure of Jupiter

Cited by 246 publications

References 71 publications

Self-Consistent Model Atmospheres and the Cooling of the Solar System's Giant Planets

Self-Consistent Model Atmospheres and the Cooling of the Solar System's Giant Planets

Interior structure models of GJ436b

Turning solid aluminium transparent by intense soft X-ray photoionization

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