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Discovery of high-frequency retrograde vorticity waves in the Sun

Nature Astronomy volume 6, pages 708–714 (2022)Cite this article

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Abstract

Classical helioseismology, which relies on acoustic waves, has been successfully applied to image the Sun’s interior rotation and structure. However, acoustic waves are insensitive to parameters such as magnetic fields, turbulent viscosity and entropy gradients in the deep convection zone, which are critical inputs to theories of solar dynamics. Inertial oscillations can bridge this gap with their complementary sensitivities to these parameters. Here, by employing helioseismic and correlation-tracking analyses of ground- and space-based observations, we detect equatorially antisymmetric vorticity waves, propagating retrograde at three times the phase speeds of Rossby–Haurwitz waves of the same wavenumber. This high-frequency dispersion relation cannot be explained by standard hydrodynamic mechanisms. We investigate three possibilities: that these vorticity waves are excited by the Coriolis force and modified by internal magnetic fields, gravity or compressibility. Incontrovertible identification of any of these coupled oscillations would influence our understanding of deep-interior magnetism, internal gravity oscillations or large-scale convection. Through observational evidence and theoretical arguments, however, we exclude these coupling mechanisms. The as-yet undetermined nature of these waves promises novel physics and fresh insight into solar dynamics.

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Fig. 1: Power spectra of the Sun’s HFR vorticity waves.
Fig. 2: Latitudinal Reynolds stresses of the Rossby and HFR waves.
Fig. 3: Solar-cycle variability of the HFR waves.

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Data availability

The data that support the plots in this paper are available from the corresponding author upon reasonable request. The GONG+ global-mode times series (mrvmt_l) and the GONG++ ring-diagram flow maps (mrrng_l) are available at https://gong.nso.edu/. The HMI global-mode times series (hmi.v_sht_gf_72d) and ring-diagram flow maps (hmi.rdvflows_fd15) are available at http://jsoc.stanford.edu/ajax/lookdata.html. The HMI LCT flow maps are available upon request from B. Löptien (loeptien@mps.mpg.de).

Change history

  • 12 April 2022

    In the version of this article initially published, the x-axis label "Harmonic degree ℓ" was missing from Fig. 1d–g and Fig. 3a. The label has been restored in the HTML and PDF versions of the article.

References

  1. 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 

  2. 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 

  3. Hathaway, D. H. & Upton, L. A. Hydrodynamic properties of the Sun’s giant cellular flows. Astrophys. J. 908, 160 (2021).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. 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 

  6. Proxauf, B. et al. Exploring the latitude and depth dependence of solar Rossby waves using ring-diagram analysis. Astron. Astrophys. 634, A44 (2020).

    Article  Google Scholar 

  7. 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 

  8. Christensen-Dalsgaard, J. Helioseismology. Rev. Mod. Phys. 74, 1073–1129 (2002).

    Article  ADS  Google Scholar 

  9. Gizon, L. & Birch, A. C. Local helioseismology. Living Rev. Sol. Phys. 2, 6 (2005).

    Article  ADS  Google Scholar 

  10. November, L. J. & Simon, G. W. Precise proper-motion measurement of solar granulation. Astrophys. J. 333, 427–442 (1988).

    Article  ADS  Google Scholar 

  11. Proxauf, B. Observations of Large-Scale Solar Flows. PhD thesis, Max-Planck Institute for Solar System Research (2020).

  12. Harvey, J. W. et al. The Global Oscillation Network Group (GONG) Project. Science 272, 1284–1286 (1996).

    Article  ADS  Google Scholar 

  13. 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 

  14. 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 

  15. Hanasoge, S. M. Seismic sensitivity of normal-mode coupling to Lorentz stresses in the Sun. Mon. Not. R. Astron. Soc. 470, 2780–2790 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  18. Corbard, T. et al. in GONG+ 2002. Local and Global Helioseismology: the Present and Future (ed. Sawaya-Lacoste, H.) 255–258 (ESA Special Publication Vol. 517, 2003).

  19. Larson, T. P. & Schou, J. Improved helioseismic analysis of medium-ℓ data from the Michelson Doppler Imager. Sol. Phys. 290, 3221–3256 (2015).

    Article  ADS  Google Scholar 

  20. Bogart, R. S., Baldner, C., Basu, S., Haber, D. A. & Rabello-Soares, M. C. HMI ring diagram analysis I. The processing pipeline. J. Phys. Conf. Ser. 271, 012008 (2011).

  21. Bogart, R. S., Baldner, C., Basu, S., Haber, D. A. & Rabello-Soares, M. C. HMI ring diagram analysis II. Data products. J. Phys. Conf. Ser. 271, 012009 (2011).

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

    Article  ADS  Google Scholar 

  23. Hindman, B. W., Haber, D. A. & Toomre, J. Subsurface circulations within active regions. Astrophys. J. 698, 1749–1760 (2009).

    Article  ADS  Google Scholar 

  24. 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 

  25. 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 

  26. Schou, J. et al. Helioseismic studies of differential rotation in the solar envelope by the Solar Oscillations Investigation using the Michelson Doppler Imager. Astrophys. J. 505, 390–417 (1998).

    Article  ADS  Google Scholar 

  27. Kitchatinov, L. L. & Ruediger, G. Differential rotation in solar-type stars: revisiting the Taylor-number puzzle. Astron. Astrophys. 299, 446 (1995).

    ADS  Google Scholar 

  28. Hanasoge, S., Gizon, L. & Sreenivasan, K. R. Seismic sounding of convection in the Sun. Annu. Rev. Fluid Mech. 48, 191–217 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  29. Miesch, M. S., Featherstone, N. A., Rempel, M. & Trampedach, R. On the amplitude of convective velocities in the deep solar interior. Astrophys. J. 757, 128 (2012).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Zaqarashvili, T. V., Oliver, R., Ballester, J. L. & Shergelashvili, B. M. Rossby waves in ‘shallow water’ magnetohydrodynamics. Astron. Astrophys. 470, 815–820 (2007).

    Article  ADS  Google Scholar 

  32. Gachechiladze, T. et al. Magneto-Rossby waves in the solar tachocline and the annual variations in solar activity. Astrophys. J. 874, 162 (2019).

    Article  ADS  Google Scholar 

  33. Yanai, M. & Maruyama, T. Stratospheric wave disturbances propagating over the equatorial Pacific. J. Meteorol. Soc. Jpn. II 44, 291–294 (1966).

    Article  ADS  Google Scholar 

  34. Matsuno, T. Quasi-geostrophic motions in the equatorial area. J. Meteorol. Soc. Jpn. II 44, 25–43 (1966).

    Article  ADS  Google Scholar 

  35. Christensen-Dalsgaard, J., Monteiro, M. J. P. F. G., Rempel, M. & Thompson, M. J. A more realistic representation of overshoot at the base of the solar convective envelope as seen by helioseismology. Mon. Not. R. Astron. Soc. 414, 1158–1174 (2011).

    Article  ADS  Google Scholar 

  36. Gilman, P. A. & Glatzmaier, G. A. Compressible convection in a rotating spherical shell. I—Anelastic equations. II—A linear anelastic model. III—Analytic model for compressible vorticity waves. Astrophys. J. Suppl. 45, 335–388 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  37. Busse, F. H. Convective flows in rapidly rotating spheres and their dynamo action. Phys. Fluids 14, 1301–1314 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  38. Chelton, D. B. & Schlax, M. G. Global observations of oceanic Rossby waves. Science 272, 234–238 (1996).

    Article  ADS  Google Scholar 

  39. Chelton, D. B., Schlax, M. G. & Samelson, R. M. Global observations of nonlinear mesoscale eddies. Prog. Oceanogr. 91, 167–216 (2011).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  41. Basu, S., Antia, H. M. & Tripathy, S. C. Ring diagram analysis of near-surface flows in the Sun. Astrophys. J. 512, 458–470 (1999).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  43. 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 

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Acknowledgements

We thank P. Cally, T. L. Duvall Jr, L. Gizon, Z.-C. Liang, D. Mausumi, B. Proxauf, K. S. Smith and T. Zaqarashvili for insightful discussions. This research was carried out on the High Performance Computing resources at New York University Abu Dhabi and the computer centre at TIFR. The work utilizes data from the National Solar Observatory Integrated Synoptic Program, which is operated by the Association of Universities for Research in Astronomy, under a cooperative agreement with the National Science Foundation and with additional financial support from the National Oceanic and Atmospheric Administration, the National Aeronautics and Space Administration and the United States Air Force. The GONG network of instruments is hosted by the Big Bear Solar Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrofísica de Canarias and Cerro Tololo Inter-American Observatory. The HMI data are courtesy of NASA/SDO and the HMI Science Team. The HMI LCT maps are courtesy of B. Löptien. The Center for Space Science at NYU Abu Dhabi is funded by NYUAD institute grant G1502. S.H. acknowledges funding from the Department of Atomic Energy, India. K.R.S. and S.H. acknowledge support from the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under award OSR-CRG2020-4342. The Center for Space Science’s (NYUAD) Data Center was used in the preparation of the datasets.

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Authors and Affiliations

  1. Center for Space Science, New York University, Abu Dhabi, United Arab Emirates

    Chris S. Hanson, Shravan Hanasoge & Katepalli R. Sreenivasan

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

    Shravan Hanasoge

  3. New York University, New York, NY, USA

    Katepalli R. Sreenivasan

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Contributions

C.S.H. and S.H. designed and performed the research. C.S.H. performed the analysis on the ring-diagram and LCT data. S.H. performed the mode-coupling analysis and numerical studies. All authors drafted and contributed to the paper.

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Correspondence to Shravan Hanasoge.

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Supplementary Figs. 1–9, Discussion Sections 1–10 and Table 1.

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Hanson, C.S., Hanasoge, S. & Sreenivasan, K.R. Discovery of high-frequency retrograde vorticity waves in the Sun. Nat Astron 6, 708–714 (2022). https://doi.org/10.1038/s41550-022-01632-z

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