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As Juno is presently measuring Jupiter's gravitational moments tounprecedented accuracy, models for the interior structure of the planet areputted to the test. While equations of state based on first principles or abinitio simulations have been available and used for the two most abundantelements constituting the envelope, hydrogen and helium, significantdiscrepancies remain regarding the predictions of the inner structure ofJupiter. The differences are severe enough to clutter the analysis of Juno'sdata and even cast doubts on the usefulness of these computationally expensiveEOSs for the modeling of the interior of Jupiter and exoplanets at large. Usingour newly developed equations of state for hydrogen and helium, we asses the abinitio equations of state currently available and establish their efficiency atpredicting the interior structure of Jupiter in a two-layers model. Byadjusting our free energy parameterization to reproduce previous ab initio EOSbehavior, we identify the source of the disagreement previously reported forthe interior structure of Jupiter. We further point to area where care shouldbe taken when building EOS for the modeling of giant planets. This concerns theinterpolation between the ab initio results and the physical models used tocover the low density range as well as the interpolation of the {\sl ab initio}simulation results at high densities. This sensitivity falls well within theuncertainties of the ab initio simulations. This suggests that hydrogen EOSshould be carefully benchmarked using a simple planetary model before beingused in the more advanced planetary models needed to interpret the Juno data.We finally provide an updated version of our ab initio hydrogen EOS recentlypublished.

Benchmarking the ab initio hydrogen equations of state for the interior structure of Jupiter