Benchmarking the ab initio hydrogen equation of state for the interior structure of Jupiter^★

¹ IMCCE, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Univ. Lille, Paris, France
² Observatoire de la Côte d’Azur, Université Côte d’Azur, F06304 Nice Cedex 4, France
e-mail: stephane.mazevet@oca.eu
³ CRAL, Ecole Normale Supérieure de Lyon, 69364 Lyon Cedex 07, France
⁴ Laboratoire de Géologie de Lyon, Ecole Normale Supérieure de Lyon, 69364 Lyon Cedex 07, France

Received: 24 April 2019
Accepted: 22 December 2020

Abstract

Context. Juno can currently measure Jupiter’s gravitational moments to unprecedented accuracy, and models for the interior structure of the planet are thus being put to the test. While equations of state (EOSs) based on first principles or ab initio simulations are 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.

Aims. Using our newly developed EOSs for hydrogen and helium, we asses the ab initio EOSs currently available and establish their efficiency at predicting the interior structure of Jupiter in a two-layer model. We paid particular attention to the calculation of the total entropy for hydrogen. It is required to calculate the convective H–He envelope but is a derived quantity from ab initio simulations.

Methods. The ab initio EOSs used in this work are based on a parameterization of the ab initio simulation points using a functional form of the Helmholtz free energy. The current paper carries on from our previous, recently published work. Compared to previous ab initio EOSs available, the approach used here provides an independent means of calculating the entropy that was recently pointed out as deficient in some ab initio results.

Results. 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 areas where care should be taken when building EOSs 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 ab initio simulation results at high densities. This sensitivity falls well within the uncertainties of the ab initio simulations. This suggests that hydrogen EOSs 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 recently published ab initio hydrogen EOS.