Observations of Jupiters gravity field by Juno have revealed surprisingly small values for the high order gravitational moments, considering the abundances of heavy elements measured by Galileo 20 years ago. The derivation of recent equations of state for hydrogen and helium, much denser in the Mbar region, worsen the conflict between these two observations. In order to circumvent this puzzle, current Jupiter model studies either ignore the constraint from Galileo or invoke an ad hoc modification of the equations of state. In this paper, we derive Jupiter models which satisfy both Juno and Galileo constraints. We confirm that Jupiters structure must encompass at least four different regions: an outer convective envelope, a region of compositional, thus entropy change, an inner convective envelope and an extended diluted core enriched in heavy elements, and potentially a central compact core. We show that, in order to reproduce Juno and Galileo observations, one needs a significant entropy increase between the outer and inner envelopes and a smaller density than for an isentropic profile, associated with some external differential rotation. The best way to fulfill this latter condition is an inward decreasing abundance of heavy elements in this region. We examine in details the three physical mechanisms able to yield such a change of entropy and composition: a first order molecular-metallic hydrogen transition, immiscibility between hydrogen and helium or a region of layered convection. Given our present knowledge of hydrogen pressure ionization, combination of the two latter mechanisms seems to be the most favoured solution.
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