Abstract

The total solar eclipse that occurred on 21 August 2017 across the United States provided an opportunity to test a magnetohydrodynamic model of the solar corona driven by measured magnetic fields. We used a new heating model based on the dissipation of Alfvén waves, and a new energization mechanism to twist the magnetic field in filament channels. We predicted what the corona would look like one week before the eclipse. Here, we describe how this prediction was accomplished, and show that it compared favourably with observations of the eclipse in white light and extreme ultraviolet. The model allows us to understand the relationship of observed features, including streamers, coronal holes, prominences, polar plumes and thin rays, to the magnetic field. We show that the discrepancies between the model and observations arise from limitations in our ability to observe the Sun’s magnetic field. Predictions of this kind provide opportunities to improve the models, forging the path to improved space weather prediction.

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References

  1. 1.

    Pasachoff, J. M. Solar eclipses as an astrophysical laboratory. Nature 459, 789–795 (2009).

  2. 2.

    Habbal, S. R., Morgan, H. & Druckmüller, M. Exploring the prominence-corona connection and its expansion into the outer corona using total solar eclipse observations. Astrophys. J. 793, 119 (2014).

  3. 3.

    Pasachoff, J. M. Astrophysics: the great solar eclipse of 2017. Sci. Am. 317, 54–61 (2017).

  4. 4.

    Parnell, C. E. & De Moortel, I. A contemporary view of coronal heating. Phil. Trans. R. Soc. Lond. A370, 3217–3240 (2012).

  5. 5.

    Priest, E. Magnetohydrodynamics of the Sun (Cambridge University Press, New York, 2014).

  6. 6.

    Klimchuk, J. A. Key aspects of coronal heating. Phil. Trans. R. Soc. Lond. A 373, 20140256 (2015).

  7. 7.

    Amari, T., Canou, A., Aly, J.-J., Delyon, F. & Alauzet, F. Magnetic cage and rope as the key for solar eruptions. Nature 554, 211–215 (2018).

  8. 8.

    Vivès, S., Lamy, P., Koutchmy, S. & Arnaud, J. ASPIICS, a giant externally occulted coronagraph for the PROBA-3 formation flying mission. Adv. Space. Res. 43, 1007–1012 (2009).

  9. 9.

    Habbal, S. R. et al. Mapping the distribution of electron temperature and Fe charge states in the corona with total solar eclipse observations. Astrophys. J. 708, 1650–1662 (2010).

  10. 10.

    Habbal, S. R. et al. Thermodynamics of the solar corona and evolution of the solar magnetic field as inferred from the total solar eclipse observations of 2010 July 11. Astrophys. J. 734, 120 (2011).

  11. 11.

    Pasachoff, J. M. Heliophysics at total solar eclipses. Nat. Astron. 1, 0190 (2017).

  12. 12.

    Dyson, F. W., Eddington, A. S. & Davidson, C. A determination of the deflection of light by the sun’s gravitational field, from observations made at the total eclipse of May 29, 1919. Phil. Trans. R. Soc. Lond. A 220, 291–333 (1920).

  13. 13.

    Hawking, S. A Brief History of Time: From the Big Bang to Black Holes (Bantam Books, New York, 1988).

  14. 14.

    Kennefick, D. Testing relativity from the 1919 eclipse—a question of bias. Phys. Today 62, 37 (March 2009).

  15. 15.

    Schindler, S. Theory-laden experimentation. Stud. History Phil. Sci. Part A 44, 89–101 (2013).

  16. 16.

    Mikić, Z., Linker, J. A., Riley, P. & Lionello, R. in Last Total Solar Eclipse of the Millennium Vol. 205 (eds Livingston, W. & Özgüç, A.) 162 (Astronomical Society of the Pacific, San Francisco, 2000).

  17. 17.

    Mikić, Z., Linker, J. A., Lionello, R., Riley, P. & Titov, V. in Solar and Stellar Physics Through Eclipses Vol. 370 (eds Demircan, O., Selam, S. O. & Albayrak, B.) 299 (Astronomical Society of the Pacific, San Francisco, 2007).

  18. 18.

    Rušin, V. et al. Comparing eclipse observations of the 2008 August 1 solar corona with an MHD model prediction. Astron. Astrophys. 513, A45 (2010).

  19. 19.

    Nandy, D. et al. The large-scale coronal structure of the 2017 August 21 Great American Eclipse: an assessment of solar surface flux transport model enabled predictions and observations. Astrophys. J. 853, 72 (2018).

  20. 20.

    Mikić, Z., Linker, J. A., Schnack, D. D., Lionello, R. & Tarditi, A. Magnetohydrodynamic modeling of the global solar corona. Phys. Plasmas 6, 2217–2224 (1999).

  21. 21.

    Lionello, R., Linker, J. A. & Mikić, Z. Multispectral emission of the Sun during the first Whole Sun Month: magnetohydrodynamic simulations. Astrophys. J. 690, 902–912 (2009).

  22. 22.

    Downs, C. et al. Probing the solar magnetic field with a Sun-grazing comet. Science 340, 1196–1199 (2013).

  23. 23.

    Scherrer, P. H. et al. The Helioseismic and Magnetic Imager (HMI) Investigation for the Solar Dynamics Observatory (SDO). Sol. Phys. 275, 207–227 (2012).

  24. 24.

    Pesnell, W. D., Thompson, B. J. & Chamberlin, P. C. The Solar Dynamics Observatory (SDO). Sol. Phys. 275, 3–15 (2012).

  25. 25.

    Lionello, R. et al. Validating a time-dependent turbulence-driven model of the solar wind. Astrophys. J. 784, 120 (2014).

  26. 26.

    Lionello, R., Velli, M., Downs, C., Linker, J. A. & Mikić, Z. Application of a solar wind model driven by turbulence dissipation to a 2D magnetic field configuration. Astrophys. J. 796, 111 (2014).

  27. 27.

    Downs, C., Lionello, R., Mikić, Z., Linker, J. A. & Velli, M. Closed-field coronal heating driven by wave turbulence. Astrophys. J. 832, 180 (2016).

  28. 28.

    Matthaeus, W. H., Zank, G. P., Oughton, S., Mullan, D. J. & Dmitruk, P. Coronal heating by magnetohydrodynamic turbulence driven by reflected low-frequency waves. Astrophys. J. 523, L93–L96 (1999).

  29. 29.

    Wang, Y.-M., Sheeley, N. R. Jr & Rich, N. B. Coronal pseudostreamers. Astrophys. J. 658, 1340–1348 (2007).

  30. 30.

    Martin, S. F. Conditions for the formation and maintenance of filaments (invited review). Sol. Phys. 182, 107–137 (1998).

  31. 31.

    Mackay, D. H., Gaizauskas, V. & Yeates, A. R. Where do solar filaments form?: consequences for theoretical models. Sol. Phys. 248, 51–65 (2008).

  32. 32.

    Mackay, D. H., Karpen, J. T., Ballester, J. L., Schmieder, B. & Aulanier, G. Physics of solar prominences: II—magnetic structure and dynamics. Space Sci. Rev. 151, 333–399 (2010).

  33. 33.

    Lemen, J. R. et al. The Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO). Sol. Phys. 275, 17–40 (2012).

  34. 34.

    Yeates, A. R. Coronal magnetic field evolution from 1996 to 2012: continuous non-potential simulations. Sol. Phys. 289, 631–648 (2014).

  35. 35.

    Billings, D. E. A Guide to the Solar Corona (Academic Press, New York, 1966).

  36. 36.

    Golub, L. & Pasachoff, J. M. The Solar Corona 2nd edn (Cambridge University Press, New York, 2010).

  37. 37.

    Mok, Y., Mikić, Z., Lionello, R., Downs, C. & Linker, J. A. A three-dimensional model of active region 7986: comparison of simulations with observations. Astrophys. J. 817, 15 (2016).

  38. 38.

    Titov, V. S. Generalized squashing factors for covariant description of magnetic connectivity in the solar corona. Astrophys. J. 660, 863–873 (2007).

  39. 39.

    Druckmüller, M. A noise adaptive fuzzy equalization method for processing solar extreme ultraviolet images. Astrophys. J. Suppl. 207, 25 (2013).

  40. 40.

    Newkirk, G. Jr, Dupree, R. G. & Schmahl, E. J. Magnetic fields and the structure of the solar corona. II: observations of the 12 November 1966 solar corona. Sol. Phys. 15, 15–39 (1970).

  41. 41.

    Titov, V. S., Mikić, Z., Linker, J. A., Lionello, R. & Antiochos, S. K. Magnetic topology of coronal hole linkages. Astrophys. J. 731, 111 (2011).

  42. 42.

    Antiochos, S. K., Mikić, Z., Titov, V. S., Lionello, R. & Linker, J. A. A model for the sources of the slow solar wind. Astrophys. J. 731, 112 (2011).

  43. 43.

    Linker, J. A., Lionello, R., Mikić, Z., Titov, V. S. & Antiochos, S. K. The evolution of open magnetic flux driven by photospheric dynamics. Astrophys. J. 731, 110 (2011).

  44. 44.

    Wang, Y.-M. et al. The solar eclipse of 2006 and the origin of raylike features in the white-light corona. Astrophys. J. 660, 882–892 (2007).

  45. 45.

    Pasachoff, J. M. et al. Polar plume brightening during the 2006 March 29 total eclipse. Astrophys. J. 682, 638–643 (2008).

  46. 46.

    Morgan, H. & Druckmüller, M. Multi-scale Gaussian normalization for solar image processing. Sol. Phys. 289, 2945–2955 (2014).

  47. 47.

    Gibson, S. in Solar Prominences Astrophysics and Space Science Library Vol. 415 (eds Vial, J.-C. & Engvold, O.) 323–353 (Springer Nature, Switzerland, 2015).

  48. 48.

    Tomczyk, S. et al. An instrument to measure coronal emission line polarization. Sol. Phys. 247, 411–428 (2008).

  49. 49.

    Mackay, D. H., Yeates, A. R. & Bocquet, F.-X. Impact of an L5 magnetograph on nonpotential solar global magnetic field modeling. Astrophys. J. 825, 131 (2016).

  50. 50.

    Schrijver, C. J. & DeRosa, M. L. Photospheric and heliospheric magnetic fields. Sol. Phys. 212, 165–200 (2003).

  51. 51.

    Arge, C. N. et al. Air Force Data Assimilative Photospheric Flux Transport (ADAPT) model. Twelfth Int. Solar Wind Conf. 216, 343–346 (2010).

  52. 52.

    Hickmann, K. S., Godinez, H. C., Henney, C. J. & Arge, C. N. Data assimilation in the ADAPT Photospheric Flux Transport model. Sol. Phys. 290, 1105–1118 (2015).

  53. 53.

    Upton, L. & Hathaway, D. H. Predicting the Sun’s polar magnetic fields with a surface flux transport model. Astrophys. J. 780, 5 (2014).

  54. 54.

    Mikić, Z. & Linker, J. A. Disruption of coronal magnetic field arcades. Astrophys. J. 430, 898–912 (1994).

  55. 55.

    Lionello, R., Mikić, Z. & Schnack, D. D. Magnetohydrodynamics of solar coronal plasmas in cylindrical geometry. J. Comput. Phys. 140, 1–30 (1998).

  56. 56.

    Lionello, R., Mikić, Z. & Linker, J. A. Stability of algorithms for waves with large flows. J. Comput. Phys. 152, 346–358 (1999).

  57. 57.

    Lionello, R., Linker, J. A. & Mikić, Z. Including the transition region in models of the large-scale solar corona. Astrophys. J. 546, 542–551 (2001).

  58. 58.

    Caplan, R. M., Mikić, Z., Linker, J. A. & Lionello, R. Advancing parabolic operators in thermodynamic MHD models: explicit super time-stepping versus implicit schemes with Krylov solvers. J. Phys. Conf. Ser. 837, 012016 (2017).

  59. 59.

    Riley, P. et al. Global MHD modeling of the solar corona and inner heliosphere for the Whole Heliosphere Interval. Sol. Phys. 274, 361–377 (2011).

  60. 60.

    Lionello, R. et al. Magnetohydrodynamic simulations of interplanetary coronal mass ejections. Astrophys. J. 777, 76 (2013).

  61. 61.

    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).

  62. 62.

    Lionello, R., Mikić, Z., Linker, J. A. & Amari, T. Magnetic field topology in prominences. Astrophys. J. 581, 718–725 (2002).

  63. 63.

    Downs, C. et al. Toward a realistic thermodynamic magnetohydrodynamic model of the global solar corona. Astrophys. J. 712, 1219–1231 (2010).

  64. 64.

    Caplan, R. M., Downs, C. & Linker, J. A. Synchronic coronal hole mapping using multi-instrument EUV images: data preparation and detection method. Astrophys. J. 823, 53 (2016).

  65. 65.

    Linker, J. A. et al. The open flux problem. Astrophys. J. 848, 70 (2017).

  66. 66.

    Hannah, I. G. & Kontar, E. P. Differential emission measures from the regularized inversion of Hinode and SDO data. Astron. Astrophys. 539, A146 (2012).

  67. 67.

    Tomczyk, S. et al. Scientific objectives and capabilities of the Coronal Solar Magnetism Observatory. J. Geophys. Res. (Space Phys.) 121, 7470–7487 (2016).

  68. 68.

    Landi, E., Young, P. R., Dere, K. P., Del Zanna, G. & Mason, H. E. CHIANTI—an atomic database for emission lines. XIII. Soft X-ray improvements and other changes. Astrophys. J. 763, 86 (2013).

  69. 69.

    Liu, Y. et al. Comparison of line-of-sight magnetograms taken by the Solar Dynamics Observatory/Helioseismic and Magnetic Imager and Solar and Heliospheric Observatory/Michelson Doppler Imager. Sol. Phys. 279, 295–316 (2012).

  70. 70.

    Riley, P. et al. A multi-observatory inter-comparison of line-of-sight synoptic solar magnetograms. Sol. Phys. 289, 769–792 (2014).

  71. 71.

    Mikić, Z., Lionello, R., Mok, Y., Linker, J. A. & Winebarger, A. R. The importance of geometric effects in coronal loop models. Astrophys. J. 773, 94 (2013).

  72. 72.

    Linker, J. et al. MHD simulation of the Bastille day event. AIP Conf. Ser. 1720, 020002 (2016).

  73. 73.

    Heinemann, M. & Olbert, S. Non-WKB Alfven waves in the solar wind. J. Geophys. Res. 85, 1311–1327 (1980).

  74. 74.

    Zank, G. P., Matthaeus, W. H. & Smith, C. W. Evolution of turbulent magnetic fluctuation power with heliospheric distance. J. Geophys. Res. 101, 17093–17108 (1996).

  75. 75.

    Zank, G. P. et al. The transport of low-frequency turbulence in astrophysical flows. I. Governing equations. Astrophys. J. 745, 35 (2012).

  76. 76.

    Velli, M. On the propagation of ideal, linear Alfven waves in radially stratified stellar atmospheres and winds. Astron. Astrophys. 270, 304–314 (1993).

  77. 77.

    Dmitruk, P., Milano, L. J. & Matthaeus, W. H. Wave-driven turbulent coronal heating in open field line regions: nonlinear phenomenological model. Astrophys. J. 548, 482–491 (2001).

  78. 78.

    Cranmer, S. R., van Ballegooijen, A. A. & Edgar, R. J. Self-consistent coronal heating and solar wind acceleration from anisotropic magnetohydrodynamic turbulence. Astrophys. J. Suppl. 171, 520–551 (2007).

  79. 79.

    Verdini, A. & Velli, M. Alfvén waves and turbulence in the solar atmosphere and solar wind. Astrophys. J. 662, 669–676 (2007).

  80. 80.

    Breech, B. et al. Turbulence transport throughout the heliosphere. J. Geophys. Res. (Space Phys.) 113, 8105 (2008).

  81. 81.

    Chandran, B. D. G. & Hollweg, J. V. Alfvén wave reflection and turbulent heating in the solar wind from 1 solar radius to 1 AU: an analytical treatment. Astrophys. J. 707, 1659–1667 (2009).

  82. 82.

    Usmanov, A. V., Matthaeus, W. H., Breech, B. A. & Goldstein, M. L. Solar wind modeling with turbulence transport and heating. Astrophys. J. 727, 84 (2011).

  83. 83.

    Jin, M. et al. A global two-temperature corona and inner heliosphere model: a comprehensive validation study. Astrophys. J. 745, 6 (2012).

  84. 84.

    Sokolov, I. V. et al. Magnetohydrodynamic waves and coronal heating: unifying empirical and MHD turbulence models. Astrophys. J. 764, 23 (2013).

  85. 85.

    van der Holst, B. et al. Alfvén wave solar model (AWSoM): coronal heating. Astrophys. J. 782, 81 (2014).

  86. 86.

    Oran, R. et al. A steady-state picture of solar wind acceleration and charge state composition derived from a global wave-driven MHD model. Astrophys. J. 806, 55 (2015).

  87. 87.

    Cranmer, S. R. & van Ballegooijen, A. A. On the generation, propagation, and reflection of Alfvén waves from the solar photosphere to the distant heliosphere. Astrophys. J. Suppl. 156, 265–293 (2005).

  88. 88.

    Verdini, A., Velli, M., Matthaeus, W. H., Oughton, S. & Dmitruk, P. A turbulence-driven model for heating and acceleration of the fast wind in coronal holes. Astrophys. J. 708, L116–L120 (2010).

  89. 89.

    de Karman, T. & Howarth, L. On the statistical theory of isotropic turbulence. R. Soc. Lond. Proc. Ser. A 164, 192–215 (1938).

  90. 90.

    Dobrowolny, M., Mangeney, A. & Veltri, P. Fully developed anisotropic hydromagnetic turbulence in interplanetary space. Phys. Rev. Lett. 45, 144–147 (1980).

  91. 91.

    Grappin, R., Leorat, J. & Pouquet, A. Dependence of MHD turbulence spectra on the velocity field-magnetic field correlation. Astron. Astrophys. 126, 51–58 (1983).

  92. 92.

    Hossain, M., Gray, P. C., Pontius, D. H. Jr, Matthaeus, W. H. & Oughton, S. Phenomenology for the decay of energy-containing eddies in homogeneous MHD turbulence. Phys. Fluids 7, 2886–2904 (1995).

  93. 93.

    Matthaeus, W. H. et al. Transport of cross helicity and radial evolution of Alfvénicity in the solar wind. Geophys. Res. Lett. 31, 12803 (2004).

  94. 94.

    Vial, J. & Engvold, O. Solar Prominences (Springer Nature, Switzerland, 2015).

  95. 95.

    Yeates, A. R. et al. Global non-potential magnetic models of the solar corona during the March 2015 eclipse. Space Sci. Rev. (in the press); preprint at https://arxiv.org/abs/1808.00785

  96. 96.

    Mackay, D. H. & van Ballegooijen, A. A. Models of the large-scale corona. I. Formation, evolution, and liftoff of magnetic flux ropes. Astrophys. J. 641, 577–589 (2006).

  97. 97.

    Yeates, A. R., Mackay, D. H. & van Ballegooijen, A. A. Modelling the global solar corona II: Coronal evolution and filament chirality comparison. Sol. Phys. 247, 103–121 (2008).

  98. 98.

    Mackay, D. H. & van Ballegooijen, A. A. A non-linear force-free field model for the evolving magnetic structure of solar filaments. Sol. Phys. 260, 321–346 (2009).

  99. 99.

    Karna, N., Hess Webber, S. A. & Pesnell, W. D. Using polar coronal hole area measurements to determine the solar polar magnetic field reversal in solar cycle 24. Sol. Phys. 289, 3381–3390 (2014).

  100. 100.

    Titov, V. S., Hornig, G. & Démoulin, P. Theory of magnetic connectivity in the solar corona. J. Geophys. Res. (Space Phys.) 107, 1164 (2002).

  101. 101.

    Titov, V. S., Mikić, Z., Török, T., Linker, J. A. & Panasenco, O. 2010 August 1-2 sympathetic eruptions. I. Magnetic topology of the source-surface background field. Astrophys. J. 759, 70 (2012).

  102. 102.

    Titov, V. S., Mikić, Z., Török, T., Linker, J. A. & Panasenco, O. 2010 August 1-2 sympathetic eruptions. II. Magnetic topology of the MHD background field. Astrophys. J. 845, 141 (2017).

  103. 103.

    Savcheva, A. S., van Ballegooijen, A. A. & DeLuca, E. E. Field topology analysis of a long-lasting coronal sigmoid. Astrophys. J. 744, 78 (2012).

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Acknowledgements

This research was supported by NASA (HSR and LWS programs), AFOSR and the National Science Foundation (NSF). Z.M. acknowledges support from NASA grants NNX16AH03G and NNX15AB65G. Computations were provided by NASA’s Advanced Supercomputing Division, NSF’s Texas Advanced Computing Center and San Diego Supercomputer Center. Data courtesy of NASA/SDO and the AIA and HMI science teams. We thank the International Space Science Institute in Bern, Switzerland, for hosting a team on ‘Global Non-Potential Magnetic Models of the Solar Corona’, led by A. Yeates, where some of the ideas were developed. We thank the Solar Physics Group at Stanford University for their support in providing timely access to HMI data. Data courtesy of the Mauna Loa Solar Observatory, operated by the High Altitude Observatory (HAO), as part of the National Center for Atmospheric Research (NCAR). NCAR is supported by the NSF. D.H.M. thanks both the UK STFC and the Leverhulme Trust for their financial support. L.A.U. was supported by the NSF Atmospheric and Geospace Sciences Postdoctoral Research Fellowship Program (Award AGS-1624438) and is hosted by HAO at NCAR. The Williams College Eclipse Expedition was supported in large part by grants from the Solar Terrestrial Program of the Division of Atmospheric and Geospace Sciences of the NSF (Award AGS-1602461) and from the Committee for Research and Exploration of the National Geographic Society (Grant 9878-16), with additional support from the NASA Massachusetts Space Grant Consortium, the Sigma Xi scientific research honor society and the Clare Booth Luce Foundation.

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Affiliations

  1. Predictive Science, Inc., San Diego, CA, USA

    • Zoran Mikić
    • , Cooper Downs
    • , Jon A. Linker
    • , Ronald M. Caplan
    • , Pete Riley
    • , Roberto Lionello
    • , Tibor Török
    • , Viacheslav S. Titov
    •  & Janvier Wijaya
  2. School of Mathematics and Statistics, University of St Andrews, St Andrews, Fife, UK

    • Duncan H. Mackay
  3. High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO, USA

    • Lisa A. Upton
  4. Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic

    • Miloslav Druckmüller
  5. Williams College–Hopkins Observatory, Williamstown, MA, USA

    • Jay M. Pasachoff
  6. Carnegie Observatories, Pasadena, CA, USA

    • Jay M. Pasachoff
  7. New York City, NY, USA

    • Wendy Carlos

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Contributions

Z.M. and C.D. wrote the text, developed and ran the MHD model, and analysed the output. R.M.C. developed and ran the MHD model. D.H.M. ran the magnetofrictional model. L.A.U. analysed data and provided model inputs. J.A.L., P.R., R.L., T.T. and V.S.T. contributed to the development of the MHD model. J.W., P.R. and Z.M. developed the website. M.D. photographed the eclipse and produced an eclipse image. J.M.P. organized the 2017 eclipse expedition and its imaging, supervised the composition of an eclipse image, and contributed to the text. W.C. composed an eclipse image. All authors reviewed the manuscript.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Zoran Mikić.

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https://doi.org/10.1038/s41550-018-0562-5