Ab Initio Equation of State for Hydrogen-Helium Mixtures With Recalibration of the Giant-Planet Mass-Radius Relation

Militzer, Burkhard; Hubbard, W. B.

doi:10.1088/0004-637x/774/2/148

Cited by 164 publications

(241 citation statements)

References 59 publications

(75 reference statements)

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“…Modeling the gravitational field of such a body requires a barotrope r P ( ) for the body's interior. In this paper, we use the barotrope of , constructed from ab initio simulations of hydrogen-helium mixtures (Militzer 2013;Militzer & Hubbard 2013). The r P ( ) relation is interpolated from a grid of adiabats determined from density functional molecular dynamics (DFT-MD) simulations, using the Perdew-Burke-Ernzerhof functional (Perdew et al 1996) (Militzer & Hubbard 2013), where k B is Boltzmann's constant and N e is the number of electrons.…”

Section: Barotropementioning

confidence: 99%

“…As a benchmark for comparison with expected Juno data, constructed static interior models of the present state of Jupiter, using a barotropic pressure-density r P ( ) equation of state for a near-solar mixture of hydrogen and helium, determined from ab initio molecular dynamics simulations (Militzer 2013;Militzer & Hubbard 2013). In this paper, we extend those models to predict the static tidal response of Jupiter, using the three-dimensional concentric Maclaurin spheroid (CMS) method (Wahl et al 2016).…”

Section: Introductionmentioning

confidence: 99%

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Tidal Response of Preliminary Jupiter Model

Wahl

Hubbard

Militzer

2016

ApJ

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In anticipation of improved observational data for Jupiter's gravitational field, from the Juno spacecraft, we predict the static tidal response for a variety of Jupiter interior models based on ab initio computer simulations of hydrogen-helium mixtures. We calculate hydrostatic-equilibrium gravity terms, using the non-perturbative concentric Maclaurin Spheroid method that eliminates lengthy expansions used in the theory of figures. Our method captures terms arising from the coupled tidal and rotational perturbations, which we find to be important for a rapidly rotating planet like Jupiter. Our predicted static tidal Love number, = k 0.5900 2 , is ∼10% larger than previous estimates. The value is, as expected, highly correlated with the zonal harmonic coefficient J 2 , and is thus nearly constant when plausible changes are made to the interior structure while holding J 2 fixed at the observed value. We note that the predicted static k 2 might change, due to Jupiter's dynamical response to the Galilean moons, and find reasons to argue that the change may be detectable-although we do not present here a theory of dynamical tides for highly oblate Jovian planets. An accurate model of Jupiter's tidal response will be essential for interpreting Juno observations and identifying tidal signals from effects of other interior dynamics of Jupiter's gravitational field.

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Section: Barotropementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tidal Response of Preliminary Jupiter Model

Wahl

Hubbard

Militzer

2016

ApJ

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“…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%

Jupiter internal structure: the effect of different equations of state

Miguel

Guillot

Fayon

2016

A&A

105

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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“…However, the recent work of Spiegel & Burrows (2013) suggests that dissipating the energy in the upper atmosphere instead of the deep interior maintains the planet's "hot state" (i.e., large radius) longer for ages below 2-3 Gyr. Last but not least, the use of a newer H/He equation-of-state (EOS) may contribute significantly to solving the problem: while our models are using SCVH (Saumon-Chabrier-Van Horn, Saumon et al 1995), the EOS from Militzer & Hubbard (2013) may produce planets with bigger radius, up to about 0.2 R Jup larger than ours.…”

Section: Planetary Evolution Modelsmentioning

confidence: 91%

“…solve the problem (Militzer & Hubbard 2013). Not only is the planet one of the biggest ever observed, but it also orbits the bigger star observed with the transit technique (Fig.…”

Section: Koi-680bmentioning

confidence: 92%

SOPHIE velocimetry ofKeplertransit candidates

Almenara

Damiani

Bouchy

et al. 2015

A&A

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We report the validation and characterization of three new transiting exoplanets using SOPHIE radial velocities: KOI-614b, KOI-206b, and KOI-680b. KOI-614b has a mass of 2.86 ± 0.35 M Jup and a radius of 1.13 +0.26−0.18 R Jup , and it orbits a G0, metallic ([Fe/H] = 0.35 ± 0.15) dwarf in 12.9 days. Its mass and radius are familiar and compatible with standard planetary evolution models, so it is one of the few known transiting planets in this mass range to have an orbital period over ten days. With an equilibrium temperature of T eq = 1000 ± 45 K, this places KOI-614b at the transition between what is usually referred to as "hot" and "warm" Jupiters. KOI-206b has a mass of 2.82 ± 0.52 M Jup and a radius of 1.45 ± 0.16 R Jup , and it orbits a slightly evolved F7-type star in a 5.3-day orbit. It is a massive inflated hot Jupiter that is particularly challenging for planetary models because it requires unusually large amounts of additional dissipated energy in the planet. On the other hand, KOI-680b has a much lower mass of 0.84 ± 0.15 M Jup and requires less extra-dissipation to explain its uncommonly large radius of 1.99 ± 0.18 R Jup . It is one of the biggest transiting planets characterized so far, and it orbits a subgiant F9-star well on its way to the red giant stage, with an orbital period of 8.6 days. With host stars of masses of 1.46 ± 0.17 M and 1.54 ± 0.09 M , respectively, KOI-206b, and KOI-680b are interesting objects for theories of formation and survival of short-period planets around stars more massive than the Sun. For those two targets, we also find signs of a possible distant additional companion in the system.

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Ab Initio Equation of State for Hydrogen-Helium Mixtures With Recalibration of the Giant-Planet Mass-Radius Relation

Cited by 164 publications

References 59 publications

Tidal Response of Preliminary Jupiter Model

Tidal Response of Preliminary Jupiter Model

Jupiter internal structure: the effect of different equations of state

SOPHIE velocimetry ofKeplertransit candidates

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