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



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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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.


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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.

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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.

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Correspondence to Laurent Gizon.

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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).

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