Jupiter internal structure: the effect of different equations of state

Abstract

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.

Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core

“…Finally, we also consider models using the SCvH EOS through the entire pressure range of the planet. Although the SCvH EOS does not fit the most recent data from high‐pressure shockwave experiments [ Hubbard and Militzer , ; Miguel et al , ], it is useful for comparison since it has been used to constrain Jupiter models in the past [e.g., Saumon and Guillot , ].…”

Metal Enrichment Leads to Low Atmospheric C/O Ratios in Transiting Giant Exoplanets

“…These values should be taken with care, as (1) Jupiter's internal structure (and, thus, M Z ) depends on the equations of state and the accuracy of the observational constrains (e.g. gravitational moments) (see, e.g., Saumon & Guillot 2004;Miguel et al 2016, and references therein) and (2) the distribution of M Z in Jupiter might be inhomogeneous. Several additional steps could be taken if one wanted to perform a more detailed estimation of the C/O ratios of the studied planets.…”

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

“…These points are used to constrain the phase boundaries (dashed lines) where a clear first-order transition is absent or difficult to identify. Also shown is Jupiter's adiabat (grey line) as calculated by Miguel et al 6 . We compare the LLT for classical nuclei pure H with recent QMC simulations of Pierleoni et.…”

“…We show that H-REOS.3 is in perfect agreement with our DFT calculations, whereas the MH-SCvH-H EOS (extrapolating the data in the limiting case of pure H 6 ) is closer to our QMC one. The disagreement between the two EOSs could be caused by the extrapolation 6 , and it seems that the disagreement between these two groups is linked to the calculated entropies 6,36 . Either way, it is clear that QMC implies a denser EOS for H at Jupiter's conditions, which translates to an envelope that is poor in heavy elements.…”