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A suppression of differential rotation in Jupiter’s deep interior


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


  1. Busse, H. F. A simple model of convection in the Jovian atmosphere. Icarus 29, 255–260 (1976)

    Article  ADS  Google Scholar 

  2. Vasavada, A. R. & Showman, A. P. Jovian atmospheric dynamics: an update after Galileo and Cassini. Rep. Prog. Phys. 68, 1935–1996 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  3. Hubbard, W. B. Effects of differential rotation on the gravitational figures of Jupiter and Saturn. Icarus 52, 509–515 (1982)

    Article  ADS  Google Scholar 

  4. Guillot, T., Gautier, D. & Hubbard, W. B. New constraints on the composition of Jupiter from Galileo measurements and interior models. Icarus 130, 534–539 (1997)

    Article  CAS  ADS  Google Scholar 

  5. Iess, L. et al. Measurement of Jupiter’s asymmetric gravity field. Nature 555, (2018)

  6. Kaspi, Y. et al. Jupiter’s atmospheric jet streams extend thousands of kilometres deep. Nature 555, (2018)

  7. Cao, H. & Stevenson, D. J. Zonal flow magnetic field interaction in the semi-conducting region of giant planets. Icarus 296, 59–72 (2017)

    Article  ADS  Google Scholar 

  8. Guillot, T. The interiors of giant planets: models and outstanding questions. Annu. Rev. Earth Planet. Sci. 33, 493–530 (2005)

    Article  CAS  ADS  Google Scholar 

  9. Hubbard, W. B. Gravitational signature of Jupiter’s deep zonal flows. Icarus 137, 357–359 (1999)

    Article  ADS  Google Scholar 

  10. Kaspi, Y. et al. The effect of differential rotation on Jupiter’s low-degree even gravity moments. Geophys. Res. Lett. 44, 5960–5968 (2017)

    Article  ADS  Google Scholar 

  11. Miguel, Y., Guillot, T. & Fayon, L. Jupiter internal structure: the effect of different equations of state. Astron. Astrophys. 596, A114 (2016)

    Article  ADS  Google Scholar 

  12. Wahl, S. M. et al. Comparing Jupiter interior structure models to Juno gravity measurements and the role of an expanded core. Geophys. Res. Lett. 44, 4649–4659 (2017)

    Article  ADS  Google Scholar 

  13. Militzer, B. & Hubbard, W. B. Ab initio equation of state for hydrogen-helium mixtures with recalibration of the giant-planet mass-radius relation. Astrophys. J. 774, 148 (2013)

    Article  ADS  Google Scholar 

  14. Becker, A. et al. Ab initio equations of state for hydrogen (H-REOS.3) and helium (He-REOS.3) and their implications for the interior of brown dwarfs. Astrophys. J. Suppl. Ser. 215, 21 (2014)

    Article  ADS  Google Scholar 

  15. Hubbard, W. B. Concentric Maclaurin spheroid models of rotating liquid planets. Astrophys. J. 768, 43 (2013)

    Article  ADS  Google Scholar 

  16. Wisdom, J. & Hubbard, W. B. Differential rotation in Jupiter: a comparison of methods. Icarus 267, 315–322 (2016)

    Article  ADS  Google Scholar 

  17. Zharkov, V. N. & Trubitsyn, V. P. Physics Of Planetary Interiors (Astronomy and Astrophysics Series, Pachart, 1978)

  18. Nettelmann, N. Low- and high-order gravitational harmonics of rigidly rotating Jupiter. Astron. Astrophys. 606, A139 (2017)

    Article  ADS  Google Scholar 

  19. Kaspi, Y., Showman, A. P., Hubbard, W. B., Aharonson, O. & Helled, R. Atmospheric confinement of jet streams on Uranus and Neptune. Nature 497, 344–347 (2013)

    Article  CAS  ADS  Google Scholar 

  20. Ingersoll, A. P . et al. in Jupiter. The Planet, Satellites And Magnetosphere (eds Bagenal, F ., Dowling, T. E . & McKinnon, W. B. ) Cambridge Planetary Science Vol. 1, 105–128 (Cambridge Univ. Press, 2004)

  21. French, M. et al. Ab initio simulations for material properties along the Jupiter adiabat. Astrophys. J. Suppl. Ser. 202, 5 (2012)

    Article  ADS  Google Scholar 

  22. Salyk, C., Ingersoll, A. P., Lorre, J., Vasavada, A. & Del Genio, A. D. Interaction between eddies and mean flow in Jupiter’s atmosphere: analysis of Cassini imaging data. Icarus 185, 430–442 (2006)

    Article  ADS  Google Scholar 

  23. Schneider, T. & Liu, J. Formation of jets and equatorial superrotation on Jupiter. J. Atmos. Sci. 66, 579–601 (2009)

    Article  ADS  Google Scholar 

  24. Liu, J., Goldreich, P. M. & Stevenson, D. J. Constraints on deep-seated zonal winds inside Jupiter and Saturn. Icarus 196, 653–664 (2008)

    Article  ADS  Google Scholar 

  25. Connerney, J. E. P. in Planets and Satellites (eds Schubert, G. & Spohn, T. ) Treatise in Geophysics Vol. 10.06, 195–237 (Elsevier, 2015)

  26. Showman, A. P. & Guillot, T. Atmospheric circulation and tides of “51 Pegasus b-like” planets. Astron. Astrophys. 385, 166–180 (2002)

    Article  ADS  Google Scholar 

  27. Guillot, T. & Morel, P. CEPAM: a code for modeling the interiors of giant planets. Astron. Astrophys. 109, 109–123 (1995)

    ADS  Google Scholar 

  28. Vazan, A., Helled, R., Podolak, M. & Kovetz, A. The evolution and internal structure of Jupiter and Saturn with compositional gradients. Astrophys. J. 829, 118 (2016)

    Article  ADS  Google Scholar 

  29. Morales, M. A., Hamel, S., Caspersen, K. & Schwegler, E. Hydrogen-helium demixing from first principles: from diamond anvil cells to planetary interiors. Phys. Rev. B 87, 174105 (2013)

    Article  ADS  Google Scholar 

  30. Stevenson, D. J. & Salpeter, E. E. The dynamics and helium distribution in hydrogen-helium fluid planets. Astrophys. J. Suppl. Ser. 35, 239–261 (1977)

    Article  CAS  ADS  Google Scholar 

  31. Nettelmann, N., Fortney, J. J., Moore, K. & Mankovich, C. An exploration of double diffusive convection in Jupiter as a result of hydrogen-helium phase separation. Mon. Not. R. Astron. Soc. 447, 3422–3441 (2015)

    Article  CAS  ADS  Google Scholar 

  32. Mankovich, C., Fortney, J. J. & Moore, K. L. Bayesian evolution models for Jupiter with helium rain and double-diffusive convection. Astrophys. J. 832, 113 (2016)

    Article  ADS  Google Scholar 

  33. Stevenson, D. J. Cosmochemistry and structure of the giant planets and their satellites. Icarus 62, 4–15 (1985)

    Article  CAS  ADS  Google Scholar 

  34. Helled, R. & Stevenson, D. The fuzziness of giant planets’ cores. Astrophys. J. 840, L4 (2017)

    Article  ADS  Google Scholar 

  35. Hubbard, W. B. & Militzer, B. A preliminary Jupiter model. Astrophys. J. 820, 80 (2016)

    Article  ADS  Google Scholar 

  36. Saumon, D., Chabrier, G. & van Horn, H. M. An equation of state for low-mass stars and giant planets. Astrophys. J. Suppl. Ser. 99, 713–741 (1995)

    Article  CAS  ADS  Google Scholar 

  37. Saumon, D. & Guillot, T. Shock compression of deuterium and the interiors of Jupiter and Saturn. Astrophys. J. 609, 1170–1180 (2004)

    Article  CAS  ADS  Google Scholar 

  38. Leconte, J. & Chabrier, G. A new vision of giant planet interiors: impact of double diffusive convection. Astron. Astrophys. 540, A20 (2012)

    Article  ADS  Google Scholar 

  39. Lindal, G. F. The atmosphere of Neptune—an analysis of radio occultation data acquired with Voyager 2. Astron. J. 103, 967–982 (1992)

    Article  CAS  ADS  Google Scholar 

  40. Guillot, T. A comparison of the interiors of Jupiter and Saturn. Planet. Space Sci. 47, 1183–1200 (1999)

    Article  CAS  ADS  Google Scholar 

  41. Seiff, A. et al. Thermal structure of Jupiter’s atmosphere near the edge of a 5-micron hot spot in the north equatorial belt. J. Geophys. Res. 103, 22857–22889 (1998)

    Article  CAS  ADS  Google Scholar 

  42. Serenelli, A. M. & Basu, S. Determining the initial helium abundance of the Sun. Astrophys. J. 719, 865–872 (2010)

    Article  ADS  Google Scholar 

  43. von Zahn, U., Hunten, D. M. & Lehmacher, G. Helium in Jupiter’s atmosphere: results from the Galileo probe helium interferometer experiment. J. Geophys. Res. 103, 22815–22829 (1998)

    Article  CAS  ADS  Google Scholar 

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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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Authors and Affiliations



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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The authors declare no competing financial interests.

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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).

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