As Juno is presently measuring Jupiter's gravitational moments to unprecedented accuracy, models for the interior structure of the planet are putted to the test. While equations of state based on first principles or ab initio simulations have been available and used for the two most abundant elements constituting the envelope, hydrogen and helium, significant discrepancies remain regarding the predictions of the inner structure of Jupiter. The differences are severe enough to clutter the analysis of Juno's data and even cast doubts on the usefulness of these computationally expensive EOSs for the modeling of the interior of Jupiter and exoplanets at large. Using our newly developed equations of state for hydrogen and helium, we asses the ab initio equations of state currently available and establish their efficiency at predicting the interior structure of Jupiter in a two-layers model. By adjusting our free energy parameterization to reproduce previous ab initio EOS behavior, we identify the source of the disagreement previously reported for the interior structure of Jupiter. We further point to area where care should be taken when building EOS for the modeling of giant planets. This concerns the interpolation between the ab initio results and the physical models used to cover the low density range as well as the interpolation of the {\sl ab initio} simulation results at high densities. This sensitivity falls well within the uncertainties of the ab initio simulations. This suggests that hydrogen EOS should be carefully benchmarked using a simple planetary model before being used in the more advanced planetary models needed to interpret the Juno data. We finally provide an updated version of our ab initio hydrogen EOS recently published.
The amount and distribution of heavy elements in Jupiter gives indications on the process of its formation and evolution. Core mass and metallicity predictions however depend on the equations of state used, and on model assumptions. We present an improved ab initio hydrogen equation of state, H-REOS.2 and compute the internal structure and thermal evolution of Jupiter within the standard three-layer approach. The advance over our previous Jupiter models with H-REOS.1 by Nettelmann et al.(2008) is that the new models are also consistent with the observed 2 or more times solar heavy element abun…
Using density functional molecular dynamics simulations, we determine the equation of state for hydrogen-helium mixtures spanning density-temperature conditions typical of giant planet interiors, ~0.2-9 g/cc and 1000-80000 K for a typical helium mass fraction of 0.245. In addition to computing internal energy and pressure, we determine the entropy using an ab initio thermodynamic integration technique. A comprehensive equation of state (EOS) table with 391 density-temperature points is constructed and the results are presented in form of two-dimensional free energy fit for interpolation. Devia…
Benchmarking Two Chemical Networks used in General Circulation Models of Hot Jupiters
Max Planck Institute for Astronomy（马克斯·普朗克天文学研究所）；University of Exeter（埃克塞特大学）；University of Newcastle（纽卡斯尔大学）；University of Bern（伯尔尼大学）；Academia Sinica（中央研究院）；University of Bristol（布里斯托大学）
Gas giants are believed to form by the accretion of hydrogen-helium gas around an initial protocore of rock and ice. The question of whether the rocky parts of the core dissolve into the fluid H-He layers following formation has significant implications for planetary structure and evolution. Here we use ab initio calculations to study rock solubility in fluid hydrogen, choosing MgO as a representative example of planetary rocky materials, and find MgO to be highly soluble in H for temperatures in excess of approximately 10000 K, implying significant redistribution of rocky core material in Jup…
The Juno mission will measure Jupiter's magnetic field with unprecedented precision and provide a wealth of additional data that will allow to constrain the planet's interior structure and dynamics. Here we analyse 66 numerical simulations in order to explore the sensitivity of the dynamo-generated magnetic field to the planets interior properties. The degree l=4 field model VIP4 and up-to-date interior models based on ab initio simulations serve as benchmarks. Our results suggest that VIP4-like magnetic fields can be found for a number of different models. We find that whether we assume an id…
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 (CMS) 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…
The Juno spacecraft has measured Jupiter's low-order, even gravitational moments, $J_2$--$J_8$, to an unprecedented precision, providing important constraints on the density profile and core mass of the planet. Here we report on a selection of interior models based on ab initio computer simulations of hydrogen-helium mixtures. We demonstrate that a dilute core, expanded to a significant fraction of the planet's radius, is helpful in reconciling the calculated $J_n$ with Juno's observations. Although model predictions are strongly affected by the chosen equation of state, the prediction of an e…
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 …
In anticipation of new observational results for Jupiter's axial moment of inertia and gravitational zonal harmonic coefficients from the forthcoming Juno orbiter, we present a number of preliminary Jupiter interior models. We combine results from ab initio computer simulations of hydrogen-helium mixtures, including immiscibility calculations, with a new nonperturbative calculation of Jupiter's zonal harmonic coefficients, to derive a self-consistent model for the planet's external gravity and moment of inertia. We assume helium rain modified the interior temperature and composition profiles. …
Hydrogen and helium demix when sufficiently cool, and this bears on the evolution of all giant planets at large separations at or below roughly a Jupiter mass. We model the thermal evolution of Jupiter, including its evolving helium distribution following results of ab initio simulations for helium immiscibility in metallic hydrogen. After 4 Gyr of homogeneous evolution, differentiation establishes a thin helium gradient below 1 Mbar that dynamically stabilizes the fluid to convection. The region undergoes overstable double-diffusive convection (ODDC), whose weak heat transport maintains a sup…
We used {\sl \textup{ab initio}} molecular dynamics simulations to calculate the high-pressure melting temperatures of the three potential core components. The planetary adiabats were obtained by solving the hydrostatic equations in a three-layer model adjusted to reproduce the measured gravitational moments. Recently developed {\sl \textup{ab initio}} equations of state were used for the envelope and the core. We find that the cores of the giant and ice-giant planets of the solar system differ because the pressure-temperature conditions encountered in each object correspond to different regio…
We present new equations of state (EOS) for hydrogen and helium covering a wide range of temperatures from 60 K to 10$^7$ K and densities from $10^{-10}$ g/cm$^3$ to $10^3$ g/cm$^3$. They include an extended set of ab initio EOS data for the strongly correlated quantum regime with an accurate connection to data derived from other approaches for the neighboring regions. We compare linear-mixing isotherms based on our EOS tables with available real-mixture data. A first important astrophysical application of this new EOS data is the calculation of interior models for Jupiter and the comparison w…
The Galileo probe showed that Jupiter's atmosphere is severely depleted in neon compared to protosolar values. We show, via ab initio simulations of the partitioning of neon between hydrogen and helium phases, that the observed depletion can be explained by the sequestration of neon into helium-rich droplets within the postulated hydrogen-helium immiscibility layer of the planet's interior. We also demonstrate that this mechanism will not affect argon, explaining the observed lack of depletion of this gas. This provides strong indirect evidence for hydrogen-helium immiscibility in Jupiter.
Using ab initio molecular dynamics simulations, we calculate the physical properties of MgO at conditions extending from the ones encountered in the Earth mantle up to the ones anticipated in giant planet interiors such as Jupiter. We pay particular attention to the high pressure melting temperature throughout this large density range as this is a key ingredient for building accurate planetary interior models with a realistic description of the inner core. We compare our simulation results with previous ab initio calculations that have been so far limited to the pressure range corresponding to…
The core accretion model for giant planet formation suggests a two layer picture for the initial structure of Jovian planets, with heavy elements in a dense core and a thick H-He envelope. Late planetesimal accretion and core erosion could potentially enrich the H-He envelope in heavy elements, which is supported by the three-fold solar metallicity that was measured in Jupiter's atmosphere by the Galileo entry probe. In order to reproduce the observed gravitational moments of Jupiter and Saturn, models for their interiors include heavy elements, $Z$, in various proportions. However, their effe…
The core mass of Saturn is commonly assumed to be 10-25 ME as predicted by interior models with various equations of state (EOSs) and the Voyager gravity data, and hence larger than that of Jupiter (0-10 ME). We here re-analyze Saturn's internal structure and evolution by using more recent gravity data from the Cassini mission and different physical equations of state: the ab initio LM-REOS which is rather soft in Saturn's outer regions but stiff at high pressures, the standard Sesame-EOS which shows the opposite behavior, and the commonly used SCvH-i EOS. For all three EOS we find similar cor…
Despite being one of the weakest dimers in nature, low-spectral-resolution Voyager/IRIS observations revealed the presence of (H$_2$)$_2$ dimers on Jupiter and Saturn in the 1980s. However, the collision-induced H$_2$-H$_2$ opacity databases widely used in planetary science (Borysow et al., 1985; Orton et al., 2007; Richard et al., 2012) have thus far only included free-to-free transitions and have neglected the contributions of dimers. Dimer spectra have both fine-scale structure near the S$(0)$ and S$(1)$ quadrupole lines (354 and 587 cm$^{-1}$, respectively), and broad continuum absorption …
Recent observations of Jupiter and Saturn provided by spacecraft missions, such as Juno and Cassini, compel us to revise and improve our models of giant planet interiors. Even though hydrogen and helium are by far the dominant species in these planets, heavy elements can play a significant role in the structure and evolution of the planet. For instance, giant-planet cores may be eroded by their surrounding fluid, which would result in a significantly increased concentration of heavy elements in the hydrogen-helium envelope. Furthermore, the heavy elements could inhibit convection by creating a…
Hydrogen-helium immiscibility boundary in gas-giant planetary interiors from machine-learning molecular dynamics
UC Berkeley（加州大学伯克利分校）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；The Institute of Science and Technology Austria（奥地利科学技术研究所）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Bakar Institute of Digital Materials for the Planet, UC Berkeley（加州大学伯克利分校巴卡尔地球数字材料研究所）
