  Simulations of Jupiter's formation are presented that incorporate mixing of
H-He with denser material entering the planet as solids. Heavy compounds and
gas mix substantially when the planet becomes roughly as massive as Earth,
because incoming planetesimals can fully vaporize. Supersaturation of vaporized
silicates causes the excess to sink as droplets, but water remains at higher
altitudes. Because the mean molecular weight decreases rapidly outward, some of
the compositional inhomogeneities produced during formation can survive for
billions of years. After 4.57 Gyr, our Jupiter model retains compositional
gradients; proceeding outwards one finds: i) an inner heavy-element core, the
outer part derived from hot supersaturated rain-out; ii) a composition-gradient
region, containing most of the heavy elements, where H-He abundance increases
outward, reaching about 0.9 mass fraction at 0.3 of the radius, with silicates
enhanced relative to water in the lower parts and depleted in the upper parts;
iii) a uniform composition region (neglecting He immiscibility) that is
enriched over protosolar and contains most of the planet's mass; and iv) an
outer region where cloud formation (condensation) of heavy constituents occurs.
This radial compositional profile has heavy elements more broadly distributed
than predicted by classical formation models, but less diluted than suggested
by Juno-constrained gravity models. The compositional gradients in the region
containing the bulk of the heavy elements prevent convection, in both our
models and those fitting current gravity, resulting in a hot interior where
much of the accretion energy remains trapped.
