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  • Open Access

TeV Solar Gamma Rays as a Probe for the Solar Internetwork Magnetic Fields

Kenny C. Y. Ng1,*, Andrew Hillier2,†, and Shin’ichiro Ando3,4,‡

  • *Contact author: kcyng@cuhk.edu.hk
  • †Contact author: A.S.Hillier@exeter.ac.uk
  • ‡Contact author: s.ando@uva.nl
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Phys. Rev. Lett. 135, 125201 – Published 16 September, 2025

DOI: https://doi.org/10.1103/l6qw-8c1h

Abstract

Recently, solar gamma rays produced by cosmic rays interacting with the solar atmosphere have been detected in the GeV to TeV energy range, revealing that cosmic rays are significantly affected by magnetic fields in the solar atmosphere. However, much of the observations remain unexplained by existing physical models. Using a semianalytic model, we demonstrate that magnetic fields at and below the photosphere with a large horizontal component could account for the approximately 1 TeV solar gamma rays observed by HAWC. This suggests that high-energy solar gamma rays could serve as a novel probe for magnetic fields beneath the photosphere, which in the future could help improve the understanding of solar magnetism, the key driver of space weather.

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References (86)

  1. D. Seckel, Todor Stanev, and T. K. Gaisser, Signatures of cosmic-ray interactions on the solar surface, Astrophys. J. 382, 652 (1991).
  2. Elena Orlando and Andrew W. Strong, Gamma-ray emission from the solar halo and disk: A study with EGRET data, Astron. Astrophys. 480, 847 (2008).
  3. A. A. Abdo et al. (Fermi-LAT Collaboration), Fermi-LAT observations of two gamma-ray emission components from the quiescent sun, Astrophys. J. 734, 116 (2011).
  4. Kenny C. Y. Ng, John F. Beacom, Annika H. G. Peter, and Carsten Rott, First observation of time variation in the solar-disk gamma-ray flux with Fermi, Phys. Rev. D 94, 023004 (2016).
  5. Qing-Wen Tang, Kenny C. Y. Ng, Tim Linden, Bei Zhou, John F. Beacom, and Annika H. G. Peter, Unexpected dip in the solar gamma-ray spectrum, Phys. Rev. D 98, 063019 (2018).
  6. Tim Linden, Bei Zhou, John F. Beacom, Annika H. G. Peter, Kenny C. Y. Ng, and Qing-Wen Tang, Evidence for a new component of high-energy solar gamma-ray production, Phys. Rev. Lett. 121, 131103 (2018).
  7. Tim Linden, John F. Beacom, Annika H. G. Peter, Benjamin J. Buckman, Bei Zhou, and Guanying Zhu, First observations of solar disk gamma rays over a full solar cycle, Phys. Rev. D 105, 063013 (2022).
  8. Bruno Arsioli and Elena Orlando, Yet another sunshine mystery: Unexpected asymmetry in GeV emission from the solar disk, Astrophys. J. 962, 52 (2024).
  9. A. Albert et al. (HAWC Collaboration), Discovery of gamma rays from the quiescent sun with HAWC, Phys. Rev. Lett. 131, 051201 (2023).
  10. M. N. Mazziotta, P. De La Torre Luque, L. Di Venere, A. Fassò, A. Ferrari, F. Loparco, P. R. Sala, and D. Serini, Cosmic-ray interactions with the Sun using the FLUKA code, Phys. Rev. D 101, 083011 (2020).
  11. Zhe Li, Kenny C. Y. Ng, Songzhan Chen, Yuncheng Nan, and Huihai He, Simulating gamma-ray production from cosmic rays interacting with the solar atmosphere in the presence of coronal magnetic fields*, Chin. Phys. C 48, 045101 (2024).
  12. Kenneth H. Schatten, John M. Wilcox, and Norman F. Ness, A model of interplanetary and coronal magnetic fields, Sol. Phys. 6, 442 (1969).
  13. Martin D. Altschuler and Gordon Newkirk, Magnetic fields and the structure of the solar corona. I: Methods of calculating coronal fields, Sol. Phys. 9, 131 (1969).
  14. J. T. Hoeksema, Structure and evolution of the large scale solar and heliospheric magnetic fields, Ph.D. thesis, Stanford Univeristy, CA, 1984.
  15. Y. M. Wang and N. R. Sheeley Jr., On potential field models of the solar corona, Astrophys. J. 392, 310 (1992).
  16. Miguel Gutiérrez and Manuel Masip, The Sun at TeV energies: Gammas, neutrons, neutrinos and a cosmic ray shadow, Astropart. Phys. 119, 102440 (2020).
  17. Miguel Gutiérrez, Manuel Masip, and Sergio Muñoz, The solar disk at high energies, Astrophys. J. 941, 86 (2022).
  18. Prabir Banik, Arunava Bhadra, and Sanjay K. Ghosh, Sun as a cosmic ray TeVatron, arXiv:2305.17086.
  19. Hugh S. Hudson, Alec MacKinnon, Mikolaj Szydlarski, and Mats Carlsson, Cosmic ray interactions in the solar atmosphere, Mon. Not. R. Astron. Soc. 491, 4852 (2020).
  20. Jung-Tsung Li, John F. Beacom, Spencer Griffith, and Annika H. G. Peter, Small-scale magnetic fields are critical to shaping solar gamma-ray emission, Astrophys. J. 961, 167 (2024).
  21. Jung-Tsung Li, Mahboubeh Asgari-Targhi, John F. Beacom, and Annika H. G. Peter, Convection-driven multi-scale magnetic fields determine the observed solar-disk gamma rays, arXiv:2508.14154.
  22. Eleonora Puzzoni, Federico Fraschetti, József Kóta, and Joe Giacalone, Role of magnetic arcades in explaining the puzzle of the gamma-ray emission from the solar disk, Astrophys. J. 973, 118 (2024).
  23. Eleonora Puzzoni, Federico Fraschetti, Jozsef Kota, and Joe Giacalone, Solar disk gamma-ray emission via synthetic magnetic field from photosphere to low corona, Astrophys. J. Lett. 989, L3 (2025).
  24. R. Ramaty, B. Kozlovsky, and R. E. Lingenfelter, Solar gamma rays, Space Sci. Rev. 18, 341 (1975).
  25. R. J. Murphy, C. D. Dermer, and R. Ramaty, High-energy processes in solar flares, Astrophys. J. Suppl. Ser. 63, 721 (1987).
  26. Benzion Kozlovsky, Ronald J. Murphy, and Reuven Ramaty, Nuclear deexcitation gamma-ray lines from accelerated particle interactions, Astrophys. J. Suppl. Ser. 141, 523 (2002).
  27. Nicola Omodei, Melissa Pesce-Rollins, Francesco Longo, Alice Allafort, and Säm Krucker, Fermi-LAT observations of the 2017 September 10 solar flare, Astrophys. J. Lett. 865, L7 (2018).
  28. G. H. Share, R. J. Murphy, S. M. White, A. K. Tolbert, B. R. Dennis, R. A. Schwartz, D. F. Smart, and M. A. Shea, Characteristics of late-phase >100  MeV gamma-ray emission in solar eruptive events, Astrophys. J. 869, 182 (2018).
  29. M. Ackermann et al. (Fermi-LAT Collaboration), High-energy gamma-ray emission from solar flares: Summary of Fermi large area telescope detections and analysis of two M-class flares, Astrophys. J. 787, 15 (2014).
  30. Elena Orlando and Andrew Strong, Gamma-rays from halos around stars and the Sun, Astrophys. Space Sci. 309, 359 (2007).
  31. Igor V. Moskalenko, Troy A. Porter, and Seth W. Digel, Inverse Compton scattering on solar photons, heliospheric modulation, and neutrino astrophysics, Astrophys. J. 652, L65 (2006); 664, L143(E) (2007).
  32. Bei Zhou, Kenny C. Y. Ng, John F. Beacom, and Annika H. G. Peter, TeV solar gamma rays from cosmic-ray interactions, Phys. Rev. D 96, 023015 (2017).
  33. Elena Orlando and Andrew Strong, StellarICS: Inverse compton emission from the quiet Sun and stars from keV to TeV, J. Cosmol. Astropart. Phys. 04 (2021) 004.
  34. Anderson C. M. Lai and Kenny C. Y. Ng, Anisotropic photon and electron scattering without ultrarelativistic approximation, Phys. Rev. D 107, 063026 (2023).
  35. Hong-Gang Yang, Yu Gao, Yin-Zhe Ma, and Roland M. Crocker, Solar gamma ray probe of local cosmic ray electrons, Phys. Rev. D 108, L061304 (2023).
  36. Vahe’ Petrosian, Elena Orlando, and Andrew Strong, Transport of cosmic-ray electrons from 1 au to the Sun, Astrophys. J. 943, 21 (2023).
  37. Elena Orlando, Vahe’ Petrosian, and Andrew Strong, A new component from the quiet Sun from radio to gamma rays: Synchrotron radiation by galactic cosmic-ray electrons, Astrophys. J. 943, 173 (2023).
  38. Norman H. Bakera and Stefan Temesváry, Tables of Convective Stellar Envelope Models (Institute for Space Studies, 1966), https://books.google.com/books/about/Tables_of_Convective_Stellar_Envelope_Mo.html?id=tsyHNAAACAAJ&redir_esc=y.
  39. Jorge E. Vernazza, Eugene H. Avrett, and Rudolf Loeser, Structure of the solar chromosphere. Basic computations and summary of the results, Astrophys. J. 184, 605 (1973).
  40. S. R. Kelner, Felex A. Aharonian, and V. V. Bugayov, Energy spectra of gamma-rays, electrons and neutrinos produced at proton-proton interactions in the very high energy regime, Phys. Rev. D 74, 034018 (2006); 79, 039901(E) (2009).
  41. S. Wedemeyer-Bohm, A. Lagg, and A. Nordlund, Coupling from the photosphere to the chromosphere and the corona, Space Sci. Rev. 144, 317 (2009).
  42. Thomas Wiegelmann, Julia K. Thalmann, and Sami K. Solanki, The magnetic field in the solar atmosphere, Astron. Astrophys. Rev. 22, 78 (2014).
  43. Sami K. Solanki, Bernd Inhester, and Manfred Schüssler, The solar magnetic field, Rep. Prog. Phys. 69, 563 (2006).
  44. J. Sánchez Almeida and M. Martínez González, The magnetic fields of the quiet Sun, in Solar Polarization 6, Astronomical Society of the Pacific Conference Series Vol. 437, edited by J. R. Kuhn, D. M. Harrington, H. Lin, S. V. Berdyugina, J. Trujillo-Bueno, S. L. Keil, and T. Rimmele (Astronomical Society of the Pacific, San Francisco, 2011), p. 451, https://ui.adsabs.harvard.edu/abs/2011ASPC..437..451S/abstract.
  45. Javier Trujillo Bueno, N. Shchukina, and A. Asensio Ramos, A substantial amount of hidden magnetic energy in the quiet Sun, Nature (London) 430, 326 (2004).
  46. Luis Bellot Rubio and David Orozco Suárez, Quiet Sun magnetic fields: An observational view, Living Rev. Solar Phys. 16, 1 (2019).
  47. Matthias Rempel, Tanayveer Bhatia, Luis Bellot Rubio, and Maarit J. Korpi-Lagg, Small-scale dynamos: From idealized models to solar and stellar applications, Space Sci. Rev. 219, 36 (2023).
  48. B. W. Lites, K. D. Leka, A. Skumanich, V. Martinez Pillet, and T. Shimizu, Small-scale horizontal magnetic fields in the solar photosphere, Astrophys. J. 460, 1019 (1996).
  49. D. Orozco Suarez et al., Quiet Sun internetwork magnetic fields from the inversion of Hinode measurements, Astrophys. J. Lett. 670, L61 (2007).
  50. B. W. Lites, M. Kubo, H. Socas-Navarro, T. Berger, Z. Frank, R. Shine, T. Tarbell, A. Title, K. Ichimoto, Y. Katsukawa, S. Tsuneta, Y. Suematsu, T. Shimizu, and S. Nagata, The horizontal magnetic flux of the quiet-Sun internetwork as observed with the hinode spectro-polarimeter, Astrophys. J. 672, 1237 (2008).
  51. M Schuessler and A. Voegler, Strong horizontal photospheric magnetic field in a surface dynamo simulation, Astron. Astrophys. 481, L5 (2008).
  52. O. Steiner, R. Rezaei, W. Schaffenberger, and S. Wedemeyer-Böhm, The horizontal internetwork magnetic field: Numerical simulations in comparison to observations with hinode, Astrophys. J. Lett. 680, L85 (2008).
  53. O. Steiner, Magnetic coupling in the quiet solar atmosphere, in Magnetic Coupling between the Interior and Atmosphere of the Sun, Astrophysics and Space Science Proceedings Vol. 19 (2010), pp. 166–185, .
  54. Marius Potgieter, Solar modulation of cosmic rays, Living Rev. Solar Phys. 10, 3 (2013).
  55. Jung-Tsung Li, John F. Beacom, and Annika H. G. Peter, Galactic cosmic-ray propagation in the inner heliosphere: Improved force-field model, Astrophys. J. 937, 27 (2022).
  56. M. Rempel, Numerical simulations of quiet Sun magnetism: On the contribution from a small-scale dynamo, Astrophys. J. 789, 132 (2014).
  57. Bruce W. Lites, Rebecca Centeno, and Scott W. McIntosh, The solar cycle dependence of the weak internetwork flux, Publ. Astron. Soc. Jpn. 66, S4 (2014).
  58. Khalid Al-Janabi et al. (Hinode Review Team), Achievements of Hinode in the first eleven years, Publ. Astron. Soc. Jpn. 71, R1 (2019).
  59. W. Unno, M. A. Kondo, and D. R. Xiong, Solar convection zone given by nonlocal mixing-length theory, Publ. Astron. Soc. Jpn. 37, 235 (1985).
  60. L. Deng, D. R. Xiong, and K. L. Chan, An anisotropic nonlocal convection theory, Astrophys. J. 643, 426 (2006).
  61. Da-run Xiong, Convection theory and relevant problems in stellar structure, evolution and pulsation stability part I. Convection theory and structure of convection zone and stellar evolution, Front. Astron. Space Sci. 7, 95 (2021).
  62. R. F. Stein and Å. Nordlund, Simulations of solar granulation. I. General properties, Astrophys. J. 499, 914 (1998).
  63. Hideyuki Hotta, Yuto Bekki, Laurent Gizon, Quentin Noraz, and Mark Rast, Dynamics of large-scale solar flows, Space Sci. Rev. 219, 77 (2023).
  64. Mark S. Miesch, Nicholas A. Featherstone, Matthias Rempel, and Regner Trampedach, On the amplitude of convective velocities in the deep solar interior, Astrophys. J. 757, 128 (2012).
  65. K. M. Górski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, and M. Bartelmann, healpix: A framework for high-resolution discretization and fast analysis of data distributed on the sphere, Astrophys. J. 622, 759 (2005).
  66. Andrea Zonca, Leo Singer, Daniel Lenz, Martin Reinecke, Cyrille Rosset, Eric Hivon, and Krzysztof Gorski, healpy: Equal area pixelization and spherical harmonics transforms for data on the sphere in Python, J. Open Source Software 4, 1298 (2019).
  67. T. K. Gaisser, Cosmic rays and particle physics (Cambridge University Press, Cambridge, UK, 1990).https://ui.adsabs.harvard.edu/abs/2016crpp.book.....G/abstract
  68. Paolo Lipari and Silvia Vernetto, The shape of the cosmic ray proton spectrum, Astropart. Phys. 120, 102441 (2020).
  69. Masaki Mori, Nuclear enhancement factor in calculation of Galactic diffuse gamma-rays: A new estimate with DPMJET-3, Astropart. Phys. 31, 341 (2009).
  70. Michael Kachelriess, Igor V. Moskalenko, and Sergey S. Ostapchenko, Nuclear enhancement of the photon yield in cosmic ray interactions, Astrophys. J. 789, 136 (2014).
  71. M. Amenomori et al. (Tibet ASgamma Collaboration), Probe of the solar magnetic field using the “cosmic-ray shadow” of the Sun, Phys. Rev. Lett. 111, 011101 (2013).
  72. M. Amenomori et al. (Tibet AS γ Collaboration), Evaluation of the interplanetary magnetic field strength using the cosmic-ray shadow of the Sun, Phys. Rev. Lett. 120, 031101 (2018).
  73. M. G. Aartsen et al. (IceCube Collaboration), Detection of the temporal variation of the Sun’s cosmic ray shadow with the IceCube detector, Astrophys. J. 872, 133 (2019).
  74. Julia Becker Tjus, Paolo Desiati, Niklas Döpper, Horst Fichtner, Jens Kleimann, Mike Kroll, and Frederik Tenholt, Cosmic-ray propagation around the Sun—investigating the influence of the solar magnetic field on the cosmic-ray Sun shadow, Astron. Astrophys. 633, A83 (2020).
  75. M. G. Aartsen et al. (IceCube Collaboration), Measurements of the time-dependent cosmic-ray Sun shadow with seven years of IceCube data: Comparison with the Solar cycle and magnetic field models, Phys. Rev. D 103, 042005 (2021).
  76. G. Ingelman and M. Thunman, High-energy neutrino production by cosmic ray interactions in the sun, Phys. Rev. D 54, 4385 (1996).
  77. Kenny C. Y. Ng, John F. Beacom, Annika H. G. Peter, and Carsten Rott, Solar atmospheric neutrinos: A new neutrino floor for dark matter searches, Phys. Rev. D 96, 103006 (2017).
  78. C. A. Argüelles, G. de Wasseige, A. Fedynitch, and B. J. P. Jones, Solar atmospheric neutrinos and the sensitivity floor for solar dark matter annihilation searches, J. Cosmol. Astropart. Phys. 07 (2017) 024.
  79. Joakim Edsjo, Jessica Elevant, Rikard Enberg, and Carl Niblaeus, Neutrinos from cosmic ray interactions in the Sun, J. Cosmol. Astropart. Phys. 06 (2017) 033.
  80. M. G. Aartsen et al. (IceCube Collaboration), Searches for neutrinos from cosmic-ray interactions in the Sun using seven years of IceCube data, J. Cosmol. Astropart. Phys. 02 (2021) 025.
  81. Joshua Villarreal et al. (IceCube Collaboration), Recent progress in solar atmospheric neutrino searches with IceCube, Proc. Sci. ICRC2021 (2021) 1174 [arXiv:2107.13696].
  82. M. G. Aartsen et al. (IceCube Collaboration), Search for annihilating dark matter in the Sun with 3 years of IceCube data, Eur. Phys. J. C 77, 146 (2017); 79, 214(E) (2019).
  83. Rebecca K. Leane, Kenny C. Y. Ng, and John F. Beacom, Powerful solar signatures of long-lived dark mediators, Phys. Rev. D 95, 123016 (2017).
  84. Carl Niblaeus, Ankit Beniwal, and Joakim Edsjo, Neutrinos and gamma rays from long-lived mediator decays in the Sun, J. Cosmol. Astropart. Phys. 11 (2019) 011.
  85. P. Abreu et al., The southern wide-field gamma-ray observatory (SWGO): A next-generation ground-based survey instrument for VHE gamma-ray astronomy, arXiv:1907.07737.
  86. http://healpix.sourceforge.net

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Phys. Rev. Lett. 135, 125201– Published 16 September, 2025
  • Received 4 August 2024
  • Revised 7 March 2025
  • Accepted 25 August 2025
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