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.
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Hathaway, D. H., Teil, T., Norton, A. A. & Kitiashvili, I. The Sun’s photospheric convection spectrum. Astrophys. J. 811, 105 (2015).
Hanasoge, S. M., Duvall, T. L. Jr. & Sreenivasan, K. R. Anomalously weak solar convection. Proc. Natl Acad. Sci. USA 109, 11928–11932 (2012).
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).
Saio, H. R-mode oscillations in uniformly rotating stars. Astrophys. J. 256, 717–735 (1982).
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).
Rhines, P. B. Waves and turbulence on a beta-plane. J. Fluid. Mech. 69, 417–443 (1975).
Pesnell, W. D., Thompson, B. J. & Chamberlin, P. C. The Solar Dynamics Observatory (SDO). Sol. Phys. 275, 3–15 (2012).
Schou, J. Migration of zonal flows detected using Michelson Doppler Imager f-mode frequency splittings. Astrophys. J. 523, L181–L184 (1999).
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).
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).
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).
Anderson, E. R., Duvall, T. L. Jr. & Jefferies, S. M. Modeling of solar oscillation power spectra. Astrophys. J. 364, 699–705 (1990).
Toutain, T. & Appourchaux, T. Maximum likelihood estimators: an application to the estimation of the precision of helioseismic measurements. Astron. Astrophys. 289, 649–658 (1994).
Wolff, C. L. Linear r-mode oscillations in a differentially rotating star. Astrophys. J. 502, 961–967 (1998).
Zhang, C. & Webster, P. J. Effects of zonal flows on equatorially trapped waves. J. Atmos. Sci. 46, 3632–3652 (1989).
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).
Provost, J., Berthomieu, G. & Rocca, A. Low frequency oscillations of a slowly rotating star—quasi toroidal modes. Astron. Astrophys. 94, 126 (1981).
Wolff, C. L. & Blizard, J. B. Properties of r-modes in the Sun. Sol. Phys. 105, 1–15 (1986).
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).
Yoshida, S. & Lee, U. Inertial modes of slowly rotating isentropic stars. Astrophys. J. 529, 997–1010 (2000).
Ward, F. The general circulation of the solar atmosphere and the maintenance of the equatorial acceleration. Astrophys. J. 141, 534 (1965).
Vallis, G. K. Atmospheric and Oceanic Fluid Dynamics (Cambridge Univ. Press, Cambridge, 2006).
Liu, J. & Schneider, T. Convective generation of equatorial superrotation in planetary atmospheres. J. Atmos. Sci. 68, 2742–2756 (2011).
Gilman, P. A. A Rossby-wave dynamo for the Sun, I. Sol. Phys. 8, 316–330 (1969).
Wolff, C. L. & Hickey, J. R. Solar irradiance change and special longitudes due to r-modes. Science 235, 1631–1633 (1987).
Gizon, L. & Birch, A. C. Helioseismology challenges models of solar convection. Proc. Natl Acad. Sci. USA 109, 11896–11897 (2012).
Ogilvie, G. I. Tidal dissipation in stars and giant planets. Annu. Rev. Astron. Astrophys. 52, 171–210 (2014).
Wu, Y. Origin of tidal dissipation in Jupiter. II. The value of Q. Astrophys. J. 635, 688–710 (2005).
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).
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).
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).
Löptien, B. et al. Measuring solar active region inflows with local correlation tracking of granulation. Astron. Astrophys. 606, A28 (2017).
Pedlosky, B. Geophysical Fluid Dynamics 2nd edn (Springer, New York, 1987).
Rieutord, M. Approaching the low-frequency spectrum of rotating stars. Lect. Notes Phys. 765, 101–121 (2009).
Tilgner, A. Spectral methods for the simulation of incompressible flows in spherical shells. Int. J. Num. Meth. Fluids 30, 713–724 (1999).
Christensen, U. R. & Wicht, J. in Treatise on Geophysics: Core Dynamics Vol. 8 (ed. Schubert, G.) 245–277 (Elsevier, Amsterdam, 2015).
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.
The authors declare no competing interests.
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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
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