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# A diffuse core in Saturn revealed by ring seismology

## Abstract

The best constraints on the internal structures of giant planets have historically originated from measurements of their gravity fields1,2,3. These data are inherently mostly sensitive to a planet’s outer regions, stymieing efforts to measure the mass and compactness of the cores of Jupiter2,4,5 and Saturn6,7. However, studies of Saturn’s rings have detected waves driven by pulsation modes within the planet8,9,10,11, offering independent seismic probes of Saturn’s interior12,13,14. The observations reveal gravity-mode pulsations, which indicate that part of Saturn’s deep interior is stable against convection13. Here, we compare structural models with gravity and seismic measurements from Cassini to show that the data can only be explained by a diffuse, stably stratified core–envelope transition region in Saturn extending to approximately 60% of the planet’s radius and containing approximately 17 Earth masses of ice and rock. This gradual distribution of heavy elements constrains mixing processes at work in Saturn, and it may reflect the planet’s primordial structure and accretion history.

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## Relevant articles

• ### Juno spacecraft gravity measurements provide evidence for normal modes of Jupiter

Nature Communications Open Access 30 August 2022

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## Data availability

A representative subset of the interior models generated in the course of this work is available upon request.

## Code availability

The planetary structure and ToF code used to create the planetary models is available at https://github.com/chkvch/alice. The oscillation code and ancillary code related to the analysis are available upon request.

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## Acknowledgements

C.R.M. thanks D. Stevenson for comments and the Juno Interiors Working Group for helpful discussions, and acknowledges support from the Division of Geological and Planetary Sciences at Caltech. J.F. is grateful for support through an Innovator Grant from The Rose Hills Foundation and through grant FG-2018-10515 from the Sloan Foundation.

## Author information

Authors

### Contributions

C.R.M. developed the planetary models, performed the calculations and analysis and led the preparation of the manuscript. J.F. developed the original oscillation code, contributed to the interpretation of the results and helped to write the manuscript.

### Corresponding author

Correspondence to Christopher R. Mankovich.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Astronomy thanks Mark Marley and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Comparison of assumed shapes for Saturn’s composition gradient.

Helium distributions for our baseline linear composition profiles from Eq. (1) (a) are compared with those assuming sigmoid Z(r) and $$Y^{\prime} (r)$$ in the transition region (b). The corresponding profiles of the heavy element mass fraction (c-d), mass density (e-f), and Brunt–Väisälä frequency (g-h) are also shown. 1,024 randomly selected models are shown for each sample, colored by log likelihood.

### Extended Data Fig. 2 Eigenfunctions of m = − 2, l = 2 pseudomodes in Saturn.

a, Poloidal component of the horizontal displacement perturbation as a function of radius. b, Gravitational potential perturbation as a function of radius. Vertical line segments mark the outer boundary of the g mode cavity.

### Extended Data Fig. 3 Eigenfunctions of m = − 2, l = 2 pseudomodes as a function of the width of the g mode cavity.

This is the sequence of interior models from Fig. 1, with our most likely model from the sample of Figs. 2-4 plotted in black. a, Brunt–Väisälä frequency as a function of radius. b-d, Gravitational potential perturbations associated with the three highest frequency pseudomodes in descending order. The identifications 2−2f and 2−2g2 hold for the best model (heavy black curves) but not necessarily others: moderate g mode cavity widths bring the modes in (c) and (d) farther away from an avoided crossing, causing the mode in (d) to become more like an f mode and (c) more like a g mode.

### Extended Data Fig. 4 Relationship between ice to rock mass fraction, fice, and predicted central heavy element mass fraction (ice plus rock), Zin.

The red histogram shows the distribution of Zin in models with fice < 1/3; the blue histogram shows the same for models with fice > 2/3. Models are from the baseline case and colored by log likelihood as in Figs. 2-3. For models with predominantly icy cores, the preferred value of Zin is near unity, and vice versa.

### Extended Data Fig. 5 Effect of superadiabatic thermal stratification.

Heavy element distributions for our baseline case (a) are compared with those for our superadiabatic case (b). (c-d) show profiles of Brunt–Väisälä frequency and mass density, and (e-f) show temperature profiles. 1,024 randomly selected models are shown for each sample, colored by log likelihood.

### Extended Data Fig. 6 Results of seismology/gravity retrievals for different parameterizations of Saturn’s interior structure.

Physical properties are reported in terms of their means and standard deviations. In cases where distributions are significantly non-Gaussian, ranges corresponding to 5% and 95% quantiles are reported instead. Blank entries take the same values as in the baseline case.

### Extended Data Fig. 7 Effect of deep zonal winds on sectoral mode frequencies.

a, two rotation laws of the form (S3) as a function of spherical radius inside Saturn. b, the same as a function of latitude at the cloud level. Observed winds are shown in dashed grey. For the nontrivial expansion labeled ‘Order 28 polynomial’ radial profiles (a) are shown at three latitudes marked with filled circles in (b). c, first-order perturbations to l = − m mode pattern speeds induced by the differential rotation.

### Extended Data Fig. 8 Saturn’s m = − 2 mode spectrum including coupling across pseudomodes of different l.

Predicted semi-amplitude of optical depth variations near outer Lindblad resonances of density waves in Saturn’s rings is plotted as a function of frequency Ωp and resonance radius in the ring plane. Colors indicate interior model likelihood with the same mapping as in Figs. 2-3. Red diamond symbols mark the frequencies and approximate amplitudes of spiral density waves observed at m = − 2 outer Lindblad resonances. From left to right these are the Maxwell ringlet wave20, W87.199, W84.6411, and W76.4410.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1 and 2 and Discussion.

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Mankovich, C.R., Fuller, J. A diffuse core in Saturn revealed by ring seismology. Nat Astron 5, 1103–1109 (2021). https://doi.org/10.1038/s41550-021-01448-3

• Accepted:

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• DOI: https://doi.org/10.1038/s41550-021-01448-3

• ### Juno spacecraft gravity measurements provide evidence for normal modes of Jupiter

• Daniele Durante
• Tristan Guillot
• Scott J. Bolton

Nature Communications (2022)