Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Height-dependent differential rotation of the solar atmosphere detected by CHASE

Abstract

Rotation is an intrinsic property of stars and provides essential constraints on their structure, formation, evolution and interaction with the interplanetary environment. The Sun provides a unique opportunity to explore stellar rotation from the interior to its atmosphere in great detail. We know that the Sun rotates faster at the equator than at the poles, but how this differential rotation behaves at different atmospheric layers within it is not yet clear. Here we extract the rotation curves of different layers of the solar photosphere and chromosphere by using whole-disk Dopplergrams obtained by the Chinese Hα Solar Explorer (CHASE) for the wavebands Si i (6,560.58 Å), Hα (6,562.81 Å) and Fe i (6,569.21 Å) with a spectral resolution of 0.024 Å. We find that the Sun rotates progressively faster from the photosphere to the chromosphere. For example, at the equator, it increases from 2.81 ± 0.02 μrad s−1 at the bottom of the photosphere to 3.08 ± 0.05 μrad s−1 in the chromosphere. The ubiquitous small-scale magnetic fields and the height-dependent degree of their frozen-in effect with the solar atmosphere are plausible causes of the height-dependent rotation rate. The results have important implications for understanding solar subsurface processes and solar atmospheric dynamics.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Dopplergrams of four separate solar surface layers.
Fig. 2: Differential rotation curves of separate solar surface layers.
Fig. 3: Angular velocity map in the meridional plane and differential rotation curves from the bottom of the photosphere to the chromosphere.
Fig. 4: Comparison of the intrinsic velocity field in the chromosphere with the line-of-sight magnetogram.

Similar content being viewed by others

Data availability

The CHASE data are available from the Solar Science Data Center of Nanjing University (https://ssdc.nju.edu.cn). The specific data applied in this study are stored at a separate link: https://sdc.nju.edu.cn/d/90242dc5043d46b1b140. The SDO/HMI data can be accessed from the Joint Science Operations Center (http://jsoc.stanford.edu).

Code availability

The codes used to read CHASE data and derive Doppler velocities are available from the Solar Science Data Center (https://ssdc.nju.edu.cn/NdchaseSatellite).

References

  1. Duvall Jr, T. L. et al. Internal rotation of the Sun. Nature 310, 22–25 (1984).

    Article  ADS  Google Scholar 

  2. 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 

  3. Thompson, M. J., Christensen-Dalsgaard, J., Miesch, M. S. & Toomre, J. The internal rotation of the Sun. Annu. Rev. Astron. Astrophys. 41, 599–643 (2003).

    Article  ADS  Google Scholar 

  4. Jiang, J., Wang, J.-X., Jiao, Q.-R. & Cao, J.-B. Predictability of the solar cycle over one cycle. Astrophys. J. 863, 159 (2018).

    Article  ADS  Google Scholar 

  5. Hathaway, D. H. The solar cycle. Living Rev. Sol. Phys. 12, 4 (2015).

    Article  ADS  Google Scholar 

  6. Li, K. J., Xu, J. C. & Feng, W. Is it small-scale, weak magnetic activity that effectively heats the upper solar atmosphere? Astrophys. J. Suppl. Ser. 237, 7 (2018).

    Article  ADS  Google Scholar 

  7. Li, K. J., Xu, J. C., Yin, Z. Q. & Feng, W. Why does the solar corona abnormally rotate faster than the photosphere? Astrophys. J. 875, 90 (2019).

    Article  ADS  Google Scholar 

  8. Zweibel, E. G. & Yamada, M. Magnetic reconnection in astrophysical and laboratory plasmas. Annu. Rev. Astron. Astrophys. 47, 291–332 (2009).

    Article  ADS  Google Scholar 

  9. Reinhold, T., Reiners, A. & Basri, G. Rotation and differential rotation of active Kepler stars. Astron. Astrophys. 560, A4 (2013).

    Article  ADS  Google Scholar 

  10. Howe, R. Solar interior rotation and its variation. Living Rev. Sol. Phys. 6, 1 (2009).

    Article  ADS  Google Scholar 

  11. Vats, H. O., Deshpande, M. R., Shah, C. R. & Mehta, M. Rotational modulation of microwave solar flux. Sol. Phys. 181, 351–362 (1998).

    Article  ADS  Google Scholar 

  12. Xie, J. L., Shi, X. J. & Zhang, J. Temporal variation of solar coronal rotation. Astrophys. J. 841, 42 (2017).

    Article  ADS  Google Scholar 

  13. Snodgrass, H. B. Magnetic rotation of the solar photosphere. Astrophys. J. 270, 288–299 (1983).

    Article  ADS  Google Scholar 

  14. Howard, R., Gilman, P. I. & Gilman, P. A. Rotation of the Sun measured from Mount Wilson white-light images. Astrophys. J. 283, 373–384 (1984).

    Article  ADS  Google Scholar 

  15. Howard, R. & Harvey, J. Spectroscopic determinations of solar rotation. Sol. Phys. 12, 23–51 (1970).

    Article  ADS  Google Scholar 

  16. Howard, R. et al. Solar rotation results at Mount Wilson. IV. Results. Sol. Phys. 83, 321–338 (1983).

    Article  ADS  Google Scholar 

  17. Vršnak, B. et al. Height of tracers and the correction of the measured solar synodic rotation rate: demonstration of the method. Sol. Phys. 185, 207–225 (1999).

    Article  ADS  Google Scholar 

  18. Howard, R., Boyden, J. E. & Labonte, B. J. Solar rotation measurements at Mount Wilson. I. Analysis and instrumental effects. Sol. Phys. 66, 167–185 (1980).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Chandra, S., Vats, H. O. & Iyer, K. N. Differential rotation measurement of soft X-ray corona. Mon. Not. R. Astron. Soc. 407, 1108–1115 (2010).

    Article  ADS  Google Scholar 

  21. Zhang, X., Deng, L., Fei, Y., Li, C. & Tian, X. Temporal variation of the rotation in the solar transition region. Astrophys. J. Lett. 951, L3 (2023).

    Article  ADS  Google Scholar 

  22. Li, K. J., Xu, J. C., Xie, J. L. & Feng, W. Differential rotation of the chromosphere in the He i absorption line. Astrophys. J. Lett. 905, L11 (2020).

    Article  ADS  Google Scholar 

  23. Li, C. et al. The Chinese Hα Solar Explorer (CHASE) mission: an overview. Sci. China Phys. Mech. Astron. 65, 289602 (2022).

    Article  ADS  Google Scholar 

  24. Qiu, Y. et al. Calibration procedures for the CHASE/HIS science data. Sci. China Phys. Mech. Astron. 65, 289603 (2022).

    Article  ADS  Google Scholar 

  25. Liu, Q. et al. On the technologies of Hα imaging spectrograph for the CHASE mission. Sci. China Phys. Mech. Astron. 65, 289605 (2022).

    Article  ADS  Google Scholar 

  26. Leenaarts, J., Carlsson, M. & Rouppe van der Voort, L. The formation of the Hα line in the solar chromosphere. Astrophys. J. 749, 136 (2012).

    Article  ADS  Google Scholar 

  27. Hong, J. et al. Statistical analysis of the Si i 6560.58 Å line observed by CHASE. Astron. Astrophys. 668, A9 (2022).

    Article  Google Scholar 

  28. Vernazza, J. E., Avrett, E. H. & Loeser, R. Structure of the solar chromosphere. III. Models of the EUV brightness components of the quiet Sun. Astrophys. J. Suppl. Ser. 45, 635–725 (1981).

    Article  ADS  Google Scholar 

  29. Ulrich, R. K. et al. Solar rotation measurements at Mount Wilson. V. Reanalysis of 21 years of data. Sol. Phys. 117, 291–328 (1988).

    Article  ADS  Google Scholar 

  30. Livingston, W. C. On the differential rotation with height in the solar atmosphere. Sol. Phys. 9, 448–451 (1969).

    Article  ADS  Google Scholar 

  31. Antonucci, E., Azzarelli, L., Casalini, P., Cerri, S. & Denoth, F. Chromospheric rotation. I. Dependence on the lifetime of chromospheric features. Sol. Phys. 61, 9–16 (1979).

    Article  ADS  Google Scholar 

  32. Sheeley Jr, N. R., Nash, A. G. & Wang, Y. M. The origin of rigidly rotating magnetic field patterns on the Sun. Astrophys. J. 319, 481–502 (1987).

    Article  Google Scholar 

  33. Stenflo, J. O. Differential rotation of the Sun’s magnetic field pattern. Astron. Astrophys. 210, 403–409 (1989).

    ADS  Google Scholar 

  34. Solonsky, Y. A. On the dependence of the linear velocity of solar rotation on latitude and optical depth. Sol. Phys. 23, 3–12 (1972).

    Article  ADS  Google Scholar 

  35. Livingston, W. & Milkey, R. Solar rotation: the photospheric height gradient. Sol. Phys. 25, 267–273 (1972).

    Article  ADS  Google Scholar 

  36. Altrock, R. C. A study of the rotation of the solar corona. Sol. Phys. 213, 23–37 (2003).

    Article  ADS  Google Scholar 

  37. Hotta, H. & Kusano, K. Solar differential rotation reproduced with high-resolution simulation. Nat. Astron. 5, 1100–1102 (2021).

    Article  ADS  Google Scholar 

  38. 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 

  39. Gabriel, A. H. A magnetic model of the solar transition region. Philos. Trans. R. Soc. Lond. Ser. A 281, 339–352 (1976).

    Article  ADS  Google Scholar 

  40. Thompson, M. J. et al. Differential rotation and dynamics of the solar interior. Science 272, 1300–1305 (1996).

    Article  ADS  Google Scholar 

  41. Lefebvre, S., Nghiem, P. A. P. & Turck-Chièze, S. Impact of a radius and composition variation on stratification of the solar subsurface layers. Astrophys. J. 690, 1272–1279 (2009).

    Article  ADS  Google Scholar 

  42. Jin, C. L. & Wang, J. X. The latitude distribution of small-scale magnetic elements in solar cycle 23. Astrophys. J. 745, 39 (2012).

    Article  ADS  Google Scholar 

  43. Li, K. J. & Feng, W. Analysis of the He i chromosphere in relation to the magnetic field activity over solar cycle time periods. Mon. Not. R. Astron. Soc. 497, 969–975 (2020).

    Article  ADS  Google Scholar 

  44. Rempel, M. Numerical simulations of quiet Sun magnetism: on the contribution from a small-scale dynamo. Astrophys. J. 789, 132 (2014).

    Article  ADS  Google Scholar 

  45. Charbonneau, P. Solar dynamo theory. Annu. Rev. Astron. Astrophys. 52, 251–290 (2014).

    Article  ADS  Google Scholar 

  46. Khomenko, E. & Collados, M. Heating of the magnetized solar chromosphere by partial ionization effects. Astrophys. J. 747, 87 (2012).

    Article  ADS  Google Scholar 

  47. Martínez-Sykora, J. et al. On the generation of solar spicules and Alfvénic waves. Science 356, 1269–1272 (2017).

    Article  ADS  Google Scholar 

  48. Nóbrega-Siverio, D., Moreno-Insertis, F., Martínez-Sykora, J., Carlsson, M. & Szydlarski, M. Nonequilibrium ionization and ambipolar diffusion in solar magnetic flux emergence processes. Astron. Astrophys. 633, A66 (2020).

    Article  ADS  Google Scholar 

  49. van Saders, J. L. et al. Weakened magnetic braking as the origin of anomalously rapid rotation in old field stars. Nature 529, 181–184 (2016).

    Article  ADS  Google Scholar 

  50. Kasper, J. C. et al. Alfvénic velocity spikes and rotational flows in the near-Sun solar wind. Nature 576, 228–231 (2019).

    Article  ADS  Google Scholar 

  51. Wexler, D. B., Stevens, M. L., Case, A. W. & Song, P. Alfvén speed transition zone in the solar corona. Astrophys. J. Lett. 919, L33 (2021).

    Article  ADS  Google Scholar 

  52. Allende Prieto, C. Velocities from cross-correlation: a guide for self-Improvement. Astron. J. 134, 1843–1848 (2007).

    Article  ADS  Google Scholar 

  53. Beckers, J. M. & Nelson, G. D. Some comments on the limb shift of solar lines. II. The effect of granular motions. Sol. Phys. 58, 243–261 (1978).

    Article  ADS  Google Scholar 

  54. Jejčič, S. & Čadež, A. Velocity measurements by the double monochromator DFS-12. Hvar Obs. Bull. 27, 197–204 (2003).

    ADS  Google Scholar 

  55. Folkner, W. M., Williams, J. G., Boggs, D. H., Park, R. S. & Kuchynka, P. The Planetary and Lunar Ephemerides DE430 and DE431 Report No. 42-196 (Interplanetary Network, 2014).

Download references

Acknowledgements

This work uses data from the CHASE mission supported by the China National Space Administration. Magnetic field data were provided courtesy of the SDO and HMI science team. C.L. is supported by the National Natural Science Foundation of China (NSFC; Grant No. 12333009) and the China National Space Administration (Project No. 050101). M.D.D. is supported by the NSFC (Grant No. 12127901). F.C. is supported by the NSFC (Grant No. 12373054) and the Programme for Innovative Talents and Entrepreneurs of Jiangsu Province. P.F.C. is supported by the National Key R&D Program of China (Grant No. 2020YFC2201200). K.J.L. is supported by the NSFC (Grant No. 12373059) and the Basic Research Foundation of Yunnan Province (Grant No. 202201AS070042). Q.H. is supported by the NSFC (Grant No. 12173019). Y.G. is supported by the National Key R&D Program of China (Grant No. 2022YFF0503004). We thank J. Jiang for fruitful discussions.

Author information

Authors and Affiliations

Authors

Contributions

C.L. and C.F. proposed this study and the data analysis method. M.D.D. is the chief scientist of the CHASE mission and responsible for the scientific interpretation of this project. S.H.R. analysed all the observational data. J.H. calculated the formation heights of the spectral lines. F.C. and K.J.L. contributed to the interpretation of the results. Y.Q. and Z.L. contributed to the calibration procedures of the CHASE data. S.H.R., C.L. and M.D.D. wrote the manuscript. All authors joined the discussions and commented on the results.

Corresponding authors

Correspondence to Chuan Li or Mingde Ding.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Astronomy thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 A sample of Dopplegrams derived from a series of scanning sequences on 5 December 2021.

The corresponding differential rotation curves of different solar surface layers are shown in the right column.

Extended Data Fig. 2 A sample of Dopplegrams derived from a series of scanning sequences on 7 December 2021.

The corresponding differential rotation curves of different solar surface layers are shown in the right column.

Extended Data Fig. 3 The distribution of uncertainties of the angular velocities shown in Fig. 2.

The uncertainties of the angular velocities are calculated from the uncertainties of the rotation parameters listed in Table 1 by using the error propagation formula. A cubic spline interpolation is used between discrete altitudes when plotting the distribution map.

Extended Data Fig. 4 Comparison of the intrinsic velocity field in the photosphere with the line-of-sight magnetogram.

The intrinsic velocity field is obtained from the Dopplergram of Fig. 1(b) with subtraction of the differential rotation. The contours of upflows and downflows in the zoom-in regions are overlaid on the magnetograms of SDO/HMI.

Supplementary information

Supplementary Information

Supplementary Fig. 1.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rao, S., Li, C., Ding, M. et al. Height-dependent differential rotation of the solar atmosphere detected by CHASE. Nat Astron (2024). https://doi.org/10.1038/s41550-024-02299-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s41550-024-02299-4

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing