  Models of Jupiter s interior struggle to agree with measurements of the
atmospheric composition. Interior models favour a subsolar or solar abundance
of heavy elements Z while atmospheric measurements suggest a supersolar
abundance. One potential solution may be the presence of an inverted
Z-gradient, namely an inward decrease of Z, which implies a larger heavy
element abundance in the atmosphere than in the outer envelope. We investigate
two scenarios in which the inverted Z gradient is located either where helium
rain occurs (Mbar level) or at upper levels (kbar level) where a radiative
region could exist. We aim to assess how plausible these scenarios are. We
calculate interior and evolution models of Jupiter with such inverted
Z-gradient and use constraints on the stability and the formation of an
inverted Z-gradient. We find that an inverted Z-gradient at the location of
helium rain cannot work as it requires a late accretion and of too much
material. We find interior models with an inverted Z-gradient at upper levels,
due to a radiative zone preventing downward mixing, that could satisfy the
present gravity field of the planet. However, our evolution models suggest that
this second scenario might not be in place. An inverted Z-gradient in Jupiter
could be stable. Yet, its presence either at the Mbar level or kbar level is
rather unlikely.
