Theory of Figures to the Seventh Order and the Interiors of Jupiter and Saturn

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.

The nature of gas giant planets

“…Saturn was found to have a fuzzy core when accounting for EoS perturbations: then the core extends to ∼ 0.4R Sat , a result that is more consistent with the solution of Mankovich & Fuller (2021). As discussed in detail in (Nettelmann et al 2021), such a structure model corresponds to a dilute core and helium rain, which together result in a large region in Saturn's deep interior that is inhomogeneous in composition and is stable against convection.…”

“…Overall, the total heavy-element mass in Jupiter can range between ∼ 20-60 M ⊕ (Helled 2019). Interestingly, it was recently shown that the high-order J n of the Jupiter models fall along the same line in J n -J n+2 space, regardless of detailed model assumptions and the H-He EOS used (Guillot et al 2018;Nettelmann et al 2021). Nettelmann et al Nettelmann et al (2021) found that J 6 stands out in that it is neither adjusted, as J 2 and J 4 are, nor insensitive to interior model assumptions, as the higher order J n n ≥ 8 are.…”

“…As the wind contribution on Jupiter is small, J 6 further constrain the interior. For instance, it can be used to put limits on the transition pressure between the outer, He-poor outer envelope and the inner, He-rich envelope, where a best match was found for transition pressures of 2-2.5 Mbars (Nettelmann et al 2021), which lies within the 0.9 Mbar-6 Mbar demixing region in Jupiter as inferred from reflectivity measurements (Brygoo et al 2021). It was also shown that heavy-element gradients in the deep interior below ∼ 20 Mbar can lead to high metallicities of up to Z = 0.5 at the compact core-mantle boundary, yielding a largely homogeneous-in-Z envelope atop.…”

“…Nettelmann et al (Nettelmann et al 2021) explored Saturn's interior and compared the results when using different H-He EoSs. It was found that Saturn models with the CMS EoS result in enriched envelope that extends to < 0.4 R Sat and compact heavy-element cores.…”

“…The latter are thus used to constrain interior models. Different interior models differ in their prediction for J 6 and J 8 (Guillot et al 2018;Nettelmann et al 2021) and therefore place somewhat different constraints on the winds. Efforts to find an optimum model, which would yield optimum agreement with the low-order field and the observed wind speeds are still ongoing.…”