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Evidence for global-scale magnetically modified Rossby waves in the Sun

Nature Astronomy (2026)Cite this article

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Abstract

Understanding and predicting solar magnetism is critical for safeguarding satellites, planning space missions and mitigating the effects of space weather on modern infrastructure. However, the physical processes governing the solar cycle remain elusive. Here, applying methods of helioseismology on observations taken by the Helioseismic and Magnetic Imager, we report the possible detection of global magnetized inertial dispersions, a slow mode and a weaker, retrograde feature possibly consistent with the fast mode, whose dynamics are theorized to modulate the solar dynamo. These modes appear to be confined to layers r/R⊙ ≲ 0.98, exhibit amplitudes weaker than those of hydrodynamic Rossby waves and resonate at frequencies consistent with the presence of an effective large-scale toroidal magnetic field of strength \(\sim 5\sqrt{\rho /{\rho }_{{\rm{S}}}}\) Gauss, where ρ is density and ρS ≈ 4 × 10−7g cm−3 is the surface density. If the toroidal field were to be located at the base of the convection zone (ρ ≈ 0.44 g cm−3), its amplitude would be ~5 × 103 G, consistent with helioseismic and other estimates. By mapping these motions in the surface layers, we uncover a window into the magnetic architecture of the Sun, offering a potential path towards more accurate forecasts of solar activity.

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Fig. 1: Theoretical dispersion relations of magneto-Rossby modes and the associated magnetic fields.
Fig. 2: Power spectrum of the equatorially symmetric s = t radial vorticity using normal mode-coupling analysis of HMI observations.
Fig. 3: Vorticity spectra for s = t.
Fig. 4: Vorticity spectra for s = t obtained for HMI and GONG++ observations with the related date ranges specified in the titles of panels.

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Data availability

The HMI observations are provided courtesy of NASA/SDO and the HMI Science Team and are publicly available from http://jsoc.stanford.edu/. Owing to the large volume of data, the intermediate mode-coupling products and sensitivity kernels are available upon request. We use the JSOC-provided spherical-harmonic time series from 10 April 2010 to 24 November 2024 in the present analysis.

Code availability

The code is available from the authors on request. The parameters used and steps applied to compute these mode-coupling coefficients are well described in the literature.

References

  1. Solanki, S. K., Usoskin, I. G., Kromer, B., Schüssler, M. & Beer, J. Unusual activity of the Sun during recent decades compared to the previous 11,000 years. Nature 431, 1084–1087 (2004).

    Article  ADS  Google Scholar 

  2. Wu, C.-J., Krivova, N. A., Solanki, S. K. & Usoskin, I. G. Solar total and spectral irradiance reconstruction over the last 9000 years. Astron. Astrophys. 620, A120 (2018).

    Article  Google Scholar 

  3. Rieger, E. et al. A 154-day periodicity in the occurrence of hard solar flares? Nature 312, 623–625 (1984).

    Article  ADS  Google Scholar 

  4. Bazilevskaya, G., Broomhall, A.-M., Elsworth, Y. & Nakariakov, V. A combined analysis of the observational aspects of the quasi-biennial oscillation in solar magnetic activity. Space Sci. Rev. 186, 359–386 (2014).

    Article  ADS  Google Scholar 

  5. Gleissberg, W. & Schove, D. J. The Eighty-Year Sunspot Cycle (British Astronomical Association, 1958).

  6. Vasiliev, S. S., Dergachev, V. A., Raspopov, O. M. & Jungner, H. Long-term variations in the flux of cosmogenic isotope 10Be over the last 10000 years: variations in the geomagnetic field and climate. Geomagn. Aeron. 52, 121–128 (2012).

    Article  ADS  Google Scholar 

  7. Gilman, P. A. & Fox, P. A. Joint instability of latitudinal differential rotation and toroidal magnetic fields below the solar convection zone. Astrophys. J. 484, 439–454 (1997).

    Article  ADS  Google Scholar 

  8. Gilman, P. A. & Dikpati, M. Joint instability of latitudinal differential rotation and concentrated toroidal fields below the solar convection zone. II. instability of narrow bands at all latitudes. Astrophys. J. 528, 552–572 (2000).

    Article  ADS  Google Scholar 

  9. Dikpati, M. & McIntosh, S. W. Space weather challenge and forecasting implications of Rossby waves. Space Weather 18, e02109 (2020).

    Article  Google Scholar 

  10. Zaqarashvili, T. V. et al. Rossby waves in astrophysics. Space Sci. Rev. 217, 15 (2021).

    Article  ADS  Google Scholar 

  11. Raphaldini, B., Dikpati, M. & McIntosh, S. W. Information-theoretic analysis of longitude distribution of photospheric magnetic fields from MDI/HMI synoptic maps: evidence for Rossby waves. Astrophys. J. 953, 156 (2023).

    Article  ADS  Google Scholar 

  12. Löptien, B. et al. Global-scale equatorial Rossby waves as an essential component of solar internal dynamics. Nat. Astron. 2, 568–573 (2018).

    Article  ADS  Google Scholar 

  13. Hanson, C. S., Hanasoge, S. & Sreenivasan, K. R. Discovery of high-frequency retrograde vorticity waves in the Sun. Nat. Astron. 6, 708–714 (2022).

    Article  ADS  Google Scholar 

  14. Hanson, C. S., Menon, V., Hanasoge, S. & Sreenivasan, K. R. Radial flow component of sun’s high-frequency retrograde inertial waves. Astrophys. J. 984, 48 (2025).

    Article  ADS  Google Scholar 

  15. Gizon, L. et al. Solar inertial modes: observations, identification, and diagnostic promise. Astron. Astrophys. 652, L6 (2021).

    Article  ADS  Google Scholar 

  16. Bekki, Y., Cameron, R. H. & Gizon, L. The Sun’s differential rotation is controlled by high-latitude baroclinically unstable inertial modes. Sci. Adv. 10, eadk5643 (2024).

    Article  Google Scholar 

  17. Beck, J. G. A comparison of differential rotation measurements—(invited review). Sol. Phys. 191, 47–70 (2000).

    Article  ADS  Google Scholar 

  18. Hill, F. Rings and trumpets—three-dimensional power spectra of solar oscillations. Astrophys. J. 333, 996–1013 (1988).

    Article  ADS  Google Scholar 

  19. November, L. J. & Simon, G. W. Precise proper-motion measurement of solar granulation. Astrophys. J. 333, 427 (1988).

    Article  ADS  Google Scholar 

  20. Cameron, R. H., Duvall, T. L., Schüssler, M. & Schunker, H. Observing and modeling the poloidal and toroidal fields of the solar dynamo. Astron. Astrophys. 609, A56 (2018).

    Article  ADS  Google Scholar 

  21. Waidele, M. & Zhao, J. Observed power and frequency variations of solar Rossby waves with solar cycles. Astrophys. J. Lett. 954, L26 (2023).

    Article  ADS  Google Scholar 

  22. Liang, Z.-C. & Gizon, L. Doppler velocity of m = 1 high-latitude inertial mode over the last five sunspot cycles. Astron. Astrophys. 695, A67 (2025).

    Article  Google Scholar 

  23. Liang, Z.-C., Gizon, L., Birch, A. C. & Duvall, T. L. Time-distance helioseismology of solar Rossby waves. Astron. Astrophys. 626, A3 (2019).

    Article  Google Scholar 

  24. Charbonneau, P. Dynamo models of the solar cycle. Living Rev. Sol. Phys. 17, 4 (2020).

    Article  ADS  Google Scholar 

  25. Gilman, P. A. & Fox, P. A. Joint instability of latitudinal differential rotation and toroidal magnetic fields below the solar convection zone. II. Instability for toroidal fields that have a node between the equator and pole. Astrophys. J. 510, 1018–1044 (1999).

    Article  ADS  Google Scholar 

  26. Zaqarashvili, T. V., Carbonell, M., Oliver, R. & Ballester, J. L. Magnetic Rossby waves in the solar tachocline and Rieger-type periodicities. Astrophys. J. 709, 749 (2010).

    Article  ADS  Google Scholar 

  27. Gurgenashvili, E. et al. Rieger-type periodicity during solar cycles 14–24: estimation of dynamo magnetic field strength in the solar interior. Astrophys. J. 826, 55 (2016).

    Article  ADS  Google Scholar 

  28. Gurgenashvili, E. et al. North–south asymmetry in Rieger-type periodicity during solar cycles 19–23. Astrophys. J. 845, 137 (2017).

    Article  ADS  Google Scholar 

  29. Baldner, C. S. & Basu, S. Solar cycle related changes at the base of the convection zone. Astrophys. J. 686, 1349 (2008).

    Article  ADS  Google Scholar 

  30. Woodard, M. F. Distortion of high-degree solar p-mode eigenfunctions by latitudinal differential rotation. Astrophys. J. 347, 1176–1182 (1989).

    Article  ADS  Google Scholar 

  31. Hanasoge, S. & Mandal, K. Detection of Rossby waves in the sun using normal-mode coupling. Astrophys. J. Lett. 871, L32 (2019).

    Article  ADS  Google Scholar 

  32. Mandal, K. & Hanasoge, S. Properties of solar Rossby waves from normal mode coupling and characterizing its systematics. Astrophys. J. 891, 125 (2020).

    Article  ADS  Google Scholar 

  33. Mandal, K., Hanasoge, S. M. & Gizon, L. Detection of Rossby modes with even azimuthal orders using helioseismic normal-mode coupling. Astron. Astrophys. 652, A96 (2021).

    Article  ADS  Google Scholar 

  34. Mani, P., Hanson, C. S. & Hanasoge, S. Imaging the Sun’s near-surface flows using mode-coupling analysis. Astrophys. J. 926, 127 (2022).

    Article  ADS  Google Scholar 

  35. Hanson, C. S., Bharati Das, S., Mani, P., Hanasoge, S. & Sreenivasan, K. R. Supergranular-scale solar convection not explained by mixing-length theory. Nat. Astron. 8, 1088–1101 (2024).

    Article  ADS  Google Scholar 

  36. Schou, J. et al. Design and ground calibration of the Helioseismic and Magnetic Imager (HMI) instrument on the Solar Dynamics Observatory (SDO). Sol. Phys. 275, 229–259 (2012).

    Article  ADS  Google Scholar 

  37. Leibacher, J. W. The Global Oscillation Network Group (GONG) project. Adv. Space Res. 24, 173–176 (1999).

    Article  ADS  Google Scholar 

  38. Hanson, C. S., Gizon, L. & Liang, Z.-C. Solar Rossby waves observed in GONG++ ring-diagram flow maps. Astron. Astrophys. 635, A109 (2020).

    Article  ADS  Google Scholar 

  39. Lavely, E. M. & Ritzwoller, M. H. The effect of global-scale, steady-state convection and elastic-gravitational asphericities on helioseismic oscillations. Philos. Trans. R. Soc. Lond. Ser. A 339, 431–496 (1992).

    Article  ADS  Google Scholar 

  40. Woodard, M. Detectability of large-scale solar subsurface flows. Sol. Phys. 289, 1085–1100 (2014).

    Article  ADS  Google Scholar 

  41. Hanasoge, S. M., Woodard, M., Antia, H. M., Gizon, L. & Sreenivasan, K. R. Sensitivity of helioseismic measurements of normal-mode coupling to flows and sound-speed perturbations. Mon. Not. R. Astron. Soc. 470, 1404–1420 (2017).

    Article  ADS  Google Scholar 

  42. Hanasoge, S. Measurement process and inversions using helioseismic normal-mode coupling. Astrophys. J. 861, 46 (2018).

    Article  ADS  Google Scholar 

  43. Woodard, M. F. Evidence for large-scale subsurface convection in the Sun. Mon. Not. R. Astron. Soc. 460, 3292–3297 (2016).

    Article  ADS  Google Scholar 

  44. Gilman, P. A. Magnetohydrodynamic ‘shallow water’ equations for the solar tachocline. Astrophys. J. Lett. 544, L79–L82 (2000).

    Article  ADS  Google Scholar 

  45. Dikpati, M. et al. Role of interaction between magnetic Rossby waves and tachocline differential rotation in producing solar seasons. Astrophys. J. 853, 144 (2018).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

S.H. acknowledges support from the Department of Atomic Energy, Government of India, under project identification no. RTI 4002. This research was supported in part by generous donations from the Murty Trust and Premji Invest, both aimed at enabling advances in astrophysics through the use of machine learning. Murty Trust, an initiative of the Murty Foundation, is a not-for-profit organisation dedicated to the preservation and celebration of culture, science and knowledge systems born out of India. The Murty Trust is headed by S. Murty and R. Murty. S.H. thanks A. Naik and H. Raghavan for their help in setting up the substantial computing required to acheive this results (all produced on the TIFR compute cluster).

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Authors and Affiliations

  1. Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Mumbai, India

    Shravan Hanasoge

  2. Center for Astrophysics and Space Science, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates

    Shravan Hanasoge & Christopher Hanson

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  1. Shravan Hanasoge
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  2. Christopher Hanson
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S.H. designed the research, executed the computations, interpreted the results and wrote the manuscript. C.H. interpreted the results and helped write the text and figures.

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Correspondence to Shravan Hanasoge.

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Nature Astronomy thanks Teimuraz Zaqarashvili and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Hanasoge, S., Hanson, C. Evidence for global-scale magnetically modified Rossby waves in the Sun. Nat Astron (2026). https://doi.org/10.1038/s41550-026-02794-w

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