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Abstract Interior modeling of Jupiter and Saturn has advanced to a state where thousands of models are generated that cover the uncertainty space of many parameters. This approach demands a fast method of computing their gravity field and shape. Moreover, the Cassini mission at Saturn and the ongoing Juno mission delivered gravitational harmonics up to J 12 . Here we report the expansion of the theory of figures, which is a fast method for gravity field and shape computation, to the seventh order (ToF7), which allows for computation of up to J 14 . We apply three different codes to compare the accuracy using polytropic models. We apply ToF7 to Jupiter and Saturn interior models in conjunction with CMS-19 H/He equation of state. For Jupiter, we find that J 6 is best matched by a transition from an He-depleted to He-enriched envelope at 2–2.5 Mbar. However, the atmospheric metallicity reaches 1 × solar only if the adiabat is perturbed toward lower densities, or if the surface temperature is enhanced by ∼14 K from the Galileo value. Our Saturn models imply a largely homogeneous-in-Z envelope at 1.5–4 × solar atop a small core. Perturbing the adiabat yields metallicity profiles with extended, heavy-element-enriched deep interior (diffuse core) out to 0.4 R Sat , as for Jupiter. Classical models with compact, dilute, or no core are possible as long as the deep interior is enriched in heavy elements. Including a thermal wind fitted to the observed wind speeds, representative Jupiter and Saturn models are consistent with all observed J n values. 

Understanding Jupiter's present‐day interior structure and dynamics is key to constraining planetary accretion models. In particular, the extent of stable stratification (i.e., non‐convective regions) in the planet strongly influences long‐term cooling processes, and may record primordial heavy element gradients from early in a planet's formation. Because the Galileo entry probe measured a subsolar helium abundance, Jupiter interior models often invoke an outer stably stratified region due to helium rain. Additionally, Juno gravity data suggest a deeper, potentially stratified dilute core extending halfway through the planet. However, fits to Jupiter's gravitational data are non‐unique, and outstanding uncertainty over the equations of state for hydrogen and helium remain. Here, we use high‐resolution numerical magnetohydrodynamic simulations of Jupiter's magnetic field to place constraints on the extent of stable stratification within the planet. We find that compared to traditional interior models, an upper stably stratified layer between 0.9 and 0.95 Jupiter radii (R_J) helps to explain both Jupiter's dipolar magnetic field and zonal winds. In contrast, an extended dilute core that is entirely stably stratified (no convective layers) yields significantly worse fits to both. However, our models with extended deep stratification still generate dipolar magnetic fields if an upper stratified region is also present. Overall, we find that a planet with a dilute core i.e., strongly stably stratified is increasingly challenging to reconcile with Jupiter's magnetic field and winds. Thus if a dilute core is present, alternative modalities such as a fully convective dilute core, a complex multilayered interior structure, or double diffusive convection may be required.