A suppression of differential rotation in Jupiter’s deep interior

Abstract

Jupiter’s atmosphere is rotating differentially, with zones and belts rotating at speeds that differ by up to 100 metres per second. Whether this is also true of the gas giant’s interior has been unknown1,2, limiting our ability to probe the structure and composition of the planet3,4. The discovery by the Juno spacecraft that Jupiter’s gravity field is north–south asymmetric5 and the determination of its non-zero odd gravitational harmonics J3, J5, J7 and J9 demonstrates that the observed zonal cloud flow must persist to a depth of about 3,000 kilometres from the cloud tops6. Here we report an analysis of Jupiter’s even gravitational harmonics J4, J6, J8 and J10 as observed by Juno5 and compared to the predictions of interior models. We find that the deep interior of the planet rotates nearly as a rigid body, with differential rotation decreasing by at least an order of magnitude compared to the atmosphere. Moreover, we find that the atmospheric zonal flow extends to more than 2,000 kilometres and to less than 3,500 kilometres, making it fully consistent with the constraints obtained independently from the odd gravitational harmonics. This depth corresponds to the point at which the electric conductivity becomes large and magnetic drag should suppress differential rotation7. Given that electric conductivity is dependent on planetary mass, we expect the outer, differentially rotating region to be at least three times deeper in Saturn and to be shallower in massive giant planets and brown dwarfs.

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Figure 1: Jupiter’s gravitational harmonics J2 to J10.
Figure 2: Constraint on the depth H of Jupiter’s zonal flow obtained from interior models and Juno’s even gravitational harmonics.
Figure 3: Ensemble of interior models of Jupiter fitting the even gravitational harmonics J2 to J10

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Acknowledgements

This research was carried out at the Observatoire de la Côte d’Azur under the sponsorship of the Centre National d’Etudes Spatiales; at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA; by the Southwest Research Institute under contract with NASA; and at the Weizmann Institute of Science under contract with the Israeli Space Agency. Computations were performed on the ‘Mesocentre SIGAMM’ machine, hosted by the Observatoire de la Côte d’Azur.

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Contributions

T.G., Y.M. and B.M. ran interior models of Jupiter and carried out the analysis. W.B.H. and A.B. compared gravitational harmonics obtained by different methods. E.G. and Y.K. calculated the offset introduced by differential rotation. H.C., R.H., D.J.S. and J.I.L. provided theoretical support. S.M.W. provided additional interior models of Jupiter. D.R.R. provided a routine to calculate high-order gravitational harmonics efficiently. W.M.F., M.P. and D.D. carried out the analysis of the Juno gravity data. J.E.P.C., S.M.L. and S.J.B. supervised the planning, execution and definition of the Juno gravity experiment.

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Correspondence to T. Guillot.

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Reviewer Information Nature thanks J. Fortney and N. Nettelmann for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Validation of the calculation of gravitational harmonics with the CEPAM method.

The four panels provide a comparison of gravitational harmonics J2 to J10 calculated with various methods: CEPAM models with 241 radial layers (black points), CMS models with 800 layers (grey points), CEPAM models with 1,041 layers (red crosses), and CMS calculations for the CEPAM models with 1,041 layers (blue circles).

Extended Data Figure 2 Constraint on the characteristic amplitude of deep differential rotation in Jupiter.

The red curves show the likelihood of models (y axis) in which to the differentially rotating outer region constrained by Juno’s odd harmonics6 we add a deeper cylindrical flow of amplitude v (x axis). The dashed red curve uses 1σ error bars. The solid red curve considers an extended ensemble of possibilities for the outer flow6 with solutions up to 3σ. In both cases, the model favours v <6 m s−1. The blue curve shows the same model but without the added outer layer. That model also favours low-amplitude winds but is found to be 4 × 104 times less likely than the model including the differentially rotating outer region.

Extended Data Table 1 Parameters used for the calculation of interior models
Extended Data Table 2 Comparison of model gravitational harmonics

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Guillot, T., Miguel, Y., Militzer, B. et al. A suppression of differential rotation in Jupiter’s deep interior. Nature 555, 227–230 (2018). https://doi.org/10.1038/nature25775

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