Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Global-scale equatorial Rossby waves as an essential component of solar internal dynamics

Nature Astronomy volume 2, pages 568–573 (2018)Cite this article

Subjects

Abstract

The Sun’s complex dynamics is controlled by buoyancy and rotation in the convection zone. Large-scale flows are dominated by vortical motions1 and appear to be weaker than expected in the solar interior2. One possibility is that waves of vorticity due to the Coriolis force, known as Rossby waves3 or r modes4, remove energy from convection at the largest scales5. However, the presence of these waves in the Sun is still debated. Here, we unambiguously discover and characterize retrograde-propagating vorticity waves in the shallow subsurface layers of the Sun at azimuthal wavenumbers below 15, with the dispersion relation of textbook sectoral Rossby waves. The waves have lifetimes of several months, well-defined mode frequencies below twice the solar rotational frequency, and eigenfunctions of vorticity that peak at the equator. Rossby waves have nearly as much vorticity as the convection at the same scales, thus they are an essential component of solar dynamics. We observe a transition from turbulence-like to wave-like dynamics around the Rhines scale6 of angular wavenumber of approximately 20. This transition might provide an explanation for the puzzling deficit of kinetic energy at the largest spatial scales.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Surface radial vorticity for three consecutive solar rotations.
Fig. 2: Longitude-time evolution of the average radial vorticity feature.
Fig. 3: Dispersion relation and horizontal eigenfunctions of equatorial Rossby waves.

Similar content being viewed by others

References

  1. Hathaway, D. H., Teil, T., Norton, A. A. & Kitiashvili, I. The Sun’s photospheric convection spectrum. Astrophys. J. 811, 105 (2015).

    Article  ADS  Google Scholar 

  2. Hanasoge, S. M., Duvall, T. L. Jr. & Sreenivasan, K. R. Anomalously weak solar convection. Proc. Natl Acad. Sci. USA 109, 11928–11932 (2012).

    Article  ADS  Google Scholar 

  3. Rossby, C.-G. Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacement of the semi-permanent centers of action. J. Mar. Res. 2, 38–66 (1939).

    Article  Google Scholar 

  4. Saio, H. R-mode oscillations in uniformly rotating stars. Astrophys. J. 256, 717–735 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  5. Vallis, G. K. & Maltrud, M. E. Generation of mean flows and jets on a beta plane and over topography. J. Phys. Ocean. 23, 1346–1362 (1993).

    Article  ADS  Google Scholar 

  6. Rhines, P. B. Waves and turbulence on a beta-plane. J. Fluid. Mech. 69, 417–443 (1975).

    Article  ADS  MATH  Google Scholar 

  7. Pesnell, W. D., Thompson, B. J. & Chamberlin, P. C. The Solar Dynamics Observatory (SDO). Sol. Phys. 275, 3–15 (2012).

    Article  ADS  Google Scholar 

  8. Schou, J. Migration of zonal flows detected using Michelson Doppler Imager f-mode frequency splittings. Astrophys. J. 523, L181–L184 (1999).

    Article  ADS  Google Scholar 

  9. Langfellner, J., Gizon, L. & Birch, A. C. Spatially resolved vertical vorticity in solar supergranulation using helioseismology and local correlation tracking. Astron. Astrophys. 581, A67 (2015).

    Article  ADS  Google Scholar 

  10. Miesch, M. S., Brun, A. S., DeRosa, M. L. & Toomre, J. Structure and evolution of giant cells in global models of solar convection. Astrophys. J. 673, 557–575 (2008).

    Article  ADS  Google Scholar 

  11. Sturrock, P. A., Bush, R., Gough, D. O. & Scargle, J. D. Indications of r-mode oscillations in SOHO/MDI solar radius measurements. Astrophys. J. 804, 47 (2015).

    Article  ADS  Google Scholar 

  12. Anderson, E. R., Duvall, T. L. Jr. & Jefferies, S. M. Modeling of solar oscillation power spectra. Astrophys. J. 364, 699–705 (1990).

    Article  ADS  Google Scholar 

  13. Toutain, T. & Appourchaux, T. Maximum likelihood estimators: an application to the estimation of the precision of helioseismic measurements. Astron. Astrophys. 289, 649–658 (1994).

    ADS  Google Scholar 

  14. Wolff, C. L. Linear r-mode oscillations in a differentially rotating star. Astrophys. J. 502, 961–967 (1998).

    Article  ADS  Google Scholar 

  15. Zhang, C. & Webster, P. J. Effects of zonal flows on equatorially trapped waves. J. Atmos. Sci. 46, 3632–3652 (1989).

    Article  ADS  Google Scholar 

  16. Bogart, R. S., Baldner, C. S. & Basu, S. Evolution of near-surface flows inferred from high-resolution ring-diagram analysis. Astrophys. J. 807, 125 (2015).

    Article  ADS  Google Scholar 

  17. Provost, J., Berthomieu, G. & Rocca, A. Low frequency oscillations of a slowly rotating star—quasi toroidal modes. Astron. Astrophys. 94, 126 (1981).

    ADS  MATH  Google Scholar 

  18. Wolff, C. L. & Blizard, J. B. Properties of r-modes in the Sun. Sol. Phys. 105, 1–15 (1986).

    Article  ADS  Google Scholar 

  19. McIntosh, S. W., Cramer, W. J., Pichardo Marcano, M. & Leamon, R. J. The detection of Rossby-like waves on the Sun. Nat. Astron. 1, 0086 (2017).

    Article  ADS  Google Scholar 

  20. Yoshida, S. & Lee, U. Inertial modes of slowly rotating isentropic stars. Astrophys. J. 529, 997–1010 (2000).

    Article  ADS  Google Scholar 

  21. Ward, F. The general circulation of the solar atmosphere and the maintenance of the equatorial acceleration. Astrophys. J. 141, 534 (1965).

    Article  ADS  Google Scholar 

  22. Vallis, G. K. Atmospheric and Oceanic Fluid Dynamics (Cambridge Univ. Press, Cambridge, 2006).

    Book  MATH  Google Scholar 

  23. Liu, J. & Schneider, T. Convective generation of equatorial superrotation in planetary atmospheres. J. Atmos. Sci. 68, 2742–2756 (2011).

    Article  ADS  Google Scholar 

  24. Gilman, P. A. A Rossby-wave dynamo for the Sun, I. Sol. Phys. 8, 316–330 (1969).

    Article  ADS  Google Scholar 

  25. Wolff, C. L. & Hickey, J. R. Solar irradiance change and special longitudes due to r-modes. Science 235, 1631–1633 (1987).

    Article  ADS  Google Scholar 

  26. Gizon, L. & Birch, A. C. Helioseismology challenges models of solar convection. Proc. Natl Acad. Sci. USA 109, 11896–11897 (2012).

    Article  ADS  Google Scholar 

  27. Ogilvie, G. I. Tidal dissipation in stars and giant planets. Annu. Rev. Astron. Astrophys. 52, 171–210 (2014).

    Article  ADS  Google Scholar 

  28. Wu, Y. Origin of tidal dissipation in Jupiter. II. The value of Q. Astrophys. J. 635, 688–710 (2005).

    Article  ADS  Google Scholar 

  29. Welsch, B. T., Fisher, G. H., Abbett, W. P. & Regnier, S. ILCT: recovering photospheric velocities from magnetograms by combining the induction equation with local correlation tracking. Astrophys. J. 610, 1148–1156 (2004).

    Article  ADS  Google Scholar 

  30. Fisher, G. H. & Welsch, B. T. FLCT: a fast, efficient method for performing local correlation tracking. Astr. Soc. P. Conf. Ser. 383, 373–380 (2008).

    ADS  Google Scholar 

  31. Löptien, B., Birch, A. C., Duvall, T. L. Jr., Gizon, L. & Schou, J. The shrinking Sun: a systematic error in local correlation tracking of solar granulation. Astron. Astrophys. 590, A130 (2016).

    Article  Google Scholar 

  32. Löptien, B. et al. Measuring solar active region inflows with local correlation tracking of granulation. Astron. Astrophys. 606, A28 (2017).

    Article  Google Scholar 

  33. Pedlosky, B. Geophysical Fluid Dynamics 2nd edn (Springer, New York, 1987).

    Book  MATH  Google Scholar 

  34. Rieutord, M. Approaching the low-frequency spectrum of rotating stars. Lect. Notes Phys. 765, 101–121 (2009).

    Article  ADS  Google Scholar 

  35. Tilgner, A. Spectral methods for the simulation of incompressible flows in spherical shells. Int. J. Num. Meth. Fluids 30, 713–724 (1999).

    Article  MATH  Google Scholar 

  36. Christensen, U. R. & Wicht, J. in Treatise on Geophysics: Core Dynamics Vol. 8 (ed. Schubert, G.) 245–277 (Elsevier, Amsterdam, 2015).

Download references

Acknowledgements

We thank R. H. Cameron, C. Damiani, H. Hotta, S. Mathis, O. Pauluis and A. Tilgner for useful discussions. The HMI data are courtesy of NASA/SDO and the HMI Science Team. The data were processed at the German Data Center for SDO funded by the German Aerospace Center. L.G. acknowledges partial research funding from the NYUAD Institute under grant G1502. B.P. is a member of the International Max Planck Research School for Solar System Science at the University of Göttingen.

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Sonnensystemforschung, Göttingen, Germany

    Björn Löptien, Laurent Gizon, Aaron C. Birch, Jesper Schou, Bastian Proxauf, Thomas L. Duvall Jr & Ulrich R. Christensen

  2. Institut für Astrophysik, Georg-August-Universität Göttingen, Göttingen, Germany

    Björn Löptien & Laurent Gizon

  3. Center for Space Science, New York University Abu Dhabi, Abu Dhabi, UAE

    Laurent Gizon

  4. W.W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA, USA

    Richard S. Bogart

Authors
  1. Björn Löptien
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laurent Gizon
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aaron C. Birch
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jesper Schou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Bastian Proxauf
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Thomas L. Duvall Jr
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Richard S. Bogart
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Ulrich R. Christensen
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

B.L., L.G. and A.C.B. designed the research. All authors performed the research. B.P. contributed to the computation of the vorticity maps using ring-diagram analysis. B.L., L.G. and A.C.B. drafted the paper. All authors contributed to the final manuscript.

Corresponding author

Correspondence to Laurent Gizon.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Figures 1–6

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Löptien, B., Gizon, L., Birch, A.C. et al. Global-scale equatorial Rossby waves as an essential component of solar internal dynamics. Nat Astron 2, 568–573 (2018). https://doi.org/10.1038/s41550-018-0460-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-018-0460-x

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing