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Discovery of high-frequency retrograde vorticity waves in the Sun

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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 The HMI global-mode times series (hmi.v_sht_gf_72d) and ring-diagram flow maps (hmi.rdvflows_fd15) are available at The HMI LCT flow maps are available upon request from B. Löptien (

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.


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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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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).

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