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Abstract We study the relationship of zonal gravity coefficients, J 2 n , zonal winds, and axial moment of inertia (MoI) by constructing models for the interiors of giant planets. We employ the nonperturbative concentric Maclaurin spheroid method to construct both physical (realistic equation of state and barotropes) and abstract (small number of constant-density spheroids) interior models. We find that accurate gravity measurements of Jupiter’s and Saturn’s J 2 , J 4 , and J 6 by the Juno and Cassini spacecraft do not uniquely determine the MoI of either planet but do constrain it to better than 1%. Zonal winds (or differential rotation (DR)) then emerge as the leading source of uncertainty. For Saturn they are predicted to decrease the MoI by 0.4% because they reach a depth of ∼9000 km, while on Jupiter they appear to reach only ∼3000 km. We thus predict DR to affect Jupiter’s MoI by only 0.01%, too small by one order of magnitude to be detectable by the Juno spacecraft. We find that winds primarily affect the MoI indirectly via the gravity harmonic J 6 , while direct contributions are much smaller because the effects of pro- and retrograde winds cancel. DR contributes +6% and −0.8% to Saturn’s and Jupiter’s J 6 value, respectively. This changes the J 6 contribution that comes from the uniformly rotating bulk of the planet that correlates most strongly with the predicted MoI. With our physical models, we predict Jupiter’s MoI to be 0.26393 ± 0.00001. For Saturn, we predict 0.2181 ± 0.0002, assuming a rotation period of 10:33:34 hr that matches the observed polar radius.
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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.
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- Award ID(s):
- 1908615
- PAR ID:
- 10354710
- Date Published:
- Journal Name:
- The Planetary Science Journal
- Volume:
- 2
- Issue:
- 6
- ISSN:
- 2632-3338
- Page Range / eLocation ID:
- 241
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3847/PSJ/ac390a
