Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Vacuum polarization effects in baryon-loaded magnetar bursts and implications for x-ray polarization

Tomoki Wada*

  • *Contact author: tomoki.wada@astr.tohoku.ac.jp

Phys. Rev. D 112, 123027 – Published 15 December, 2025

DOI: https://doi.org/10.1103/k3hz-k6v4

Abstract

Magnetars provide natural laboratories for strong-field quantum electrodynamics processes, such as vacuum polarization, which gives rise to vacuum resonance together with the plasma response. We develop a general framework to describe vacuum resonance in a three-component plasma consisting of ions, electrons, and positrons, as expected in baryon-loaded magnetar bursts. By introducing a parametrization of the plasma composition, we establish the general criterion for the occurrence of vacuum resonance in such plasmas. Our analysis encompasses both Mikheyev-Smirnov-Wolfenstein-like adiabatic mode conversion and nonadiabatic eigenmode transition, highlighting their dependence on the plasma composition. Applying this framework to baryon-loaded fireballs in magnetar bursts, we estimate the characteristic x-ray polarization signatures. Detection of these polarizations will provide observational signatures of vacuum polarization as well as baryon loading in magnetar fireballs.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (90)

  1. R. C. Duncan and C. Thompson, Formation of very strongly magnetized neutron stars: Implications for gamma-ray bursts, Astrophys. J. Lett. 392, L9 (1992).
  2. J. S. Heyl and L. Hernquist, A QED model for the origin of bursts from soft gamma repeaters and anomalous X-ray pulsars, Astrophys. J. 618, 463 (2005).
  3. A. K. Harding and D. Lai, Physics of strongly magnetized neutron stars, Rep. Prog. Phys. 69, 2631 (2006).
  4. V. M. Kaspi and A. M. Beloborodov, Magnetars, Annu. Rev. 55, 261 (2017).
  5. T. Enoto, S. Kisaka, and S. Shibata, Observational diversity of magnetized neutron stars, Rep. Prog. Phys. 82, 106901 (2019).
  6. C. Thompson and R. C. Duncan, The soft gamma repeaters as very strongly magnetized neutron stars—I. Radiative mechanism for outbursts, Mon. Not. R. Astron. Soc. 275, 255 (1995).
  7. C. Thompson and R. C. Duncan, The soft gamma repeaters as very strongly magnetized neutron stars. II. Quiescent neutrino, X-ray, and alfven wave emission, Astrophys. J. 473, 322 (1996).
  8. T. Wada, K. Ioka, and B. Zhang, Binary comb models for FRB 121102, Astrophys. J. 920, 54 (2021).
  9. T. Wada and J. Shimoda, The Dzhanibekov effect as a possible source of magnetar activity, Astrophys. J. 972, 58 (2024).
  10. J. Shimoda and T. Wada, On acceleration of highest-energy cosmic rays in a novel scenario of magnetar transients, Astrophys. J. 986, 213 (2025).
  11. T. Wada and S. S. Kimura, Spectral shapes of pair annihilation line emission in magnetar giant flares (to be published).
  12. P. Meszaros, High-Energy Radiation from Magnetized Neutron Stars (University of Chicago Press, Chicago, 1992).
  13. J. S. Heyl and L. Hernquist, Analytic form for the effective Lagrangian of QED and its application to pair production and photon splitting, Phys. Rev. D 55, 2449 (1997).
  14. W.-Y. Tsai and T. Erber, Propagation of photons in homogeneous magnetic fields: Index of refraction, Phys. Rev. D 12, 1132 (1975).
  15. W. Heisenberg and H. Euler, Folgerungen aus der Diracschen Theorie des Positrons, Z. Phys. 98, 714 (1936).
  16. J. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82, 664 (1951).
  17. Y. N. Gnedin and G. G. Pavlov, The transfer equations for normal waves and radiation polarization in an anisotropic medium, Sov. J. Exp. Theor. Phys. 38, 903 (1974).
  18. P. Meszaros and J. Ventura, Vacuum polarization effects on radiative opacities in a strong magnetic field, Phys. Rev. D 19, 3565 (1979).
  19. W. C. G. Ho and D. Lai, Atmospheres and spectra of strongly magnetized neutron stars, Mon. Not. R. Astron. Soc. 327, 1081 (2001).
  20. Y. N. Gnedin, G. G. Pavlov, and Y. A. Shibanov, The effect of vacuum birefringence in a magnetic field on the polarization and beaming of X-ray pulsars, Sov. Astron. Lett. 4, 117 (1978).
  21. G. G. Pavlov and Y. A. Shibanov, Influence of vacuum polarization by a magnetic field on the propagation of electromagnetic waves in a plasma, Sov. J. Exp. Theor. Phys. 49, 741 (1979).
  22. M. Soffel, J. Ventura, H. Herold, H. Ruder, and W. Nagel, Propagation of high frequency waves in strongly magnetized plasmas—mode ambiguities due to vacuum polarization, Astron. Astrophys. 126, 251 (1983).
  23. D. Lai and W. C. G. Ho, Resonant conversion of photon modes due to vacuum polarization in a magnetized plasma: Implications for X-ray emission from magnetars, Astrophys. J. 566, 373 (2002).
  24. P. Goldreich and W. H. Julian, Pulsar electrodynamics, Astrophys. J. 157, 869 (1969).
  25. D. Lai and W. C. G. Ho, Transfer of polarized radiation in strongly magnetized plasmas and thermal emission from magnetars: Effect of vacuum polarization, Astrophys. J. 588, 962 (2003).
  26. D. Lai and W. C. Ho, Polarized X-ray emission from magnetized neutron stars: Signature of strong-field vacuum polarization, Phys. Rev. Lett. 91, 071101 (2003).
  27. W. C. G. Ho and D. Lai, Atmospheres and spectra of strongly magnetized neutron stars—II. The effect of vacuum polarization, Mon. Not. R. Astron. Soc. 338, 233 (2003).
  28. W. C. G. Ho, D. Lai, A. Y. Potekhin, and G. Chabrier, Atmospheres and spectra of strongly magnetized neutron stars. III. Partially ionized hydrogen models, Astrophys. J. 599, 1293 (2003).
  29. F. Özel, The effect of vacuum polarization and proton cyclotron resonances on photon propagation in strongly magnetized plasmas, Astrophys. J. 583, 402 (2003).
  30. W. C. G. Ho and D. Lai, Spectral features in the thermal emission from isolated neutron stars: Dependence on magnetic field strengths, Astrophys. J. 607, 420 (2004).
  31. J. Niemiec and T. Bulik, Radiation spectra and polarization in magnetar bursts, Astrophys. J. 637, 466 (2006).
  32. M. van Adelsberg and D. Lai, Atmosphere models of magnetized neutron stars: QED effects, radiation spectra and polarization signals, Mon. Not. R. Astron. Soc. 373, 1495 (2006).
  33. R. Fernández and S. W. Davis, The X-ray polarization signature of quiescent magnetars: Effect of magnetospheric scattering and vacuum polarization, Astrophys. J. 730, 131 (2011).
  34. R. M. E. Kelly, S. Zane, R. Turolla, and R. Taverna, X-ray polarization in magnetar atmospheres—effects of mode conversion, Mon. Not. R. Astron. Soc. 528, 3927 (2024).
  35. C. Wang and D. Lai, Wave modes in the magnetospheres of pulsars and magnetars, Mon. Not. R. Astron. Soc. 377, 1095 (2007).
  36. M. C. Weisskopf et al., The imaging X-ray polarimetry explorer (IXPE): Pre-launch, J. Astron. Telesc. Instrum. Syst. 8, 026002 (2022).
  37. R. Taverna et al., Polarized x-rays from a magnetar, Science 378, 646 (2022).
  38. S. Zane et al., A strong X-ray polarization signal from the magnetar 1RXS J170849.0-400910, Astrophys. J. Lett. 944, L27 (2023).
  39. J. Heyl et al., The detection of polarized X-ray emission from the magnetar 1E 2259+586, Mon. Not. R. Astron. Soc. 527, 12219 (2024).
  40. R. Turolla et al., IXPE and XMM-Newton observations of the soft gamma repeater SGR 1806-20, Astrophys. J. 954, 88 (2023).
  41. M. Rigoselli et al., IXPE detection of highly polarized X-rays from the magnetar 1E 1841-045, Astrophys. J. Lett. 985, L34 (2025).
  42. R. Stewart et al., X-ray polarization of the magnetar 1E 1841-045, Astrophys. J. Lett. 985, L35 (2025).
  43. D. Lai, IXPE detection of polarized X-rays from magnetars and photon mode conversion at QED vacuum resonance, Proc. Natl. Acad. Sci. U.S.A. 120, e2216534120 (2023).
  44. C. Thompson, M. Lyutikov, and S. R. Kulkarni, Electrodynamics of magnetars: Implications for the persistent X-ray emission and spin-down of the soft gamma repeaters and anomalous X-ray pulsars, Astrophys. J. 574, 332 (2002).
  45. R. Taverna, R. Turolla, V. Suleimanov, A. Y. Potekhin, and S. Zane, X-ray spectra and polarization from magnetar candidates, Mon. Not. R. Astron. Soc. 492, 5057 (2020).
  46. M. Ge et al., Physics of strong magnetism with eXTP, Sci. China Phys. Mech. Astron. 68, 119505 (2025).
  47. I. Demidov and Y. Lyubarsky, Radiatively driven evaporation from magnetar’s surface, Mon. Not. R. Astron. Soc. 518, 810 (2023).
  48. J. Goodman, Are gamma-ray bursts optically thick?, Astrophys. J. Lett. 308, L47 (1986).
  49. B. Paczynski, Gamma-ray bursters at cosmological distances, Astrophys. J. Lett. 308, L43 (1986).
  50. A. Shemi and T. Piran, The appearance of cosmic fireballs, Astrophys. J. Lett. 365, L55 (1990).
  51. P. Meszaros, P. Laguna, and M. J. Rees, Gasdynamics of relativistically expanding gamma-ray burst sources: Kinematics, energetics, magnetic fields, and efficiency, Astrophys. J. 415, 181 (1993).
  52. P. Mészáros and M. J. Rees, Steep slopes and preferred breaks in gamma-ray burst spectra: The role of photospheres and comptonization, Astrophys. J. 530, 292 (2000).
  53. K. Hurley et al., An exceptionally bright flare from SGR 1806-20 and the origins of short-duration γ-ray bursts, Nature (London) 434, 1098 (2005).
  54. S. Mereghetti, D. Götz, A. von Kienlin, A. Rau, G. Lichti, G. Weidenspointner, and P. Jean, The first giant flare from SGR 1806-20: Observations using the anticoincidence shield of the spectrometer on INTEGRAL, Astrophys. J. Lett. 624, L105 (2005).
  55. S. E. Boggs, A. Zoglauer, E. Bellm, K. Hurley, R. P. Lin, D. M. Smith, C. Wigger, and W. Hajdas, The giant flare of 2004 december 27 from SGR 1806-20, Astrophys. J. 661, 458 (2007).
  56. D. D. Frederiks, S. V. Golenetskii, V. D. Palshin, R. L. Aptekar, V. N. Ilyinskii, F. P. Oleinik, E. P. Mazets, and T. L. Cline, Giant flare in SGR 1806-20 and its Compton reflection from the moon, Astron. Lett. 33, 1 (2007).
  57. B. M. Gaensler et al., An expanding radio nebula produced by a giant flare from the magnetar SGR 1806-20, Nature (London) 434, 1104 (2005).
  58. P. B. Cameron et al., Detection of a radio counterpart to the 27 december 2004 giant flare from SGR 1806–20, Nature (London) 434, 1112 (2005).
  59. E. Nakar, T. Piran, and R. Sari, Pure and loaded fireballs in soft gamma-ray repeater giant flares, Astrophys. J. 635, 516 (2005).
  60. C. Thompson and R. C. Duncan, The giant flare of 1998 august 27 from SGR 1900+14. II. Radiative mechanism and physical constraints on the source, Astrophys. J. 561, 980 (2001).
  61. C. D. Bochenek, V. Ravi, K. V. Belov, G. Hallinan, J. Kocz, S. R. Kulkarni, and D. L. McKenna, A fast radio burst associated with a galactic magnetar, Nature (London) 587, 59 (2020).
  62. B. C. Andersen et al. (CHIME/FRB Collaboration), A bright millisecond-duration radio burst from a galactic magnetar, Nature (London) 587, 54 (2020).
  63. S. Mereghetti et al., INTEGRAL discovery of a burst with associated radio emission from the magnetar SGR 1935+2154, Astrophys. J. Lett. 898, L29 (2020).
  64. C. K. Li et al., HXMT identification of a non-thermal X-ray burst from SGR J1935+2154 and with FRB 200428, Nat. Astron. 5, 378 (2021).
  65. A. Ridnaia, D. Svinkin, D. Frederiks, A. Bykov, S. Popov, R. Aptekar, S. Golenetskii, A. Lysenko, A. Tsvetkova, M. Ulanov, and T. L. Cline, A peculiar hard X-ray counterpart of a galactic fast radio burst, Nat. Astron. 5, 372 (2021).
  66. M. Tavani et al., An X-ray burst from a magnetar enlightening the mechanism of fast radio bursts, Nat. Astron. 5, 401 (2021).
  67. K. Ioka, Fast radio burst breakouts from magnetar burst fireballs, Astrophys. J. Lett. 904, L15 (2020).
  68. Y.-P. Yang and B. Zhang, Fast radio bursts and their High-energy counterparts from magnetar magnetospheres, Astrophys. J. 919, 89 (2021).
  69. T. Wada and K. Asano, Radiative acceleration and X-ray spectrum of an outflowing pure electron-positron pair fireball in magnetar bursts, Prog. Theor. Exp. Phys. 2025, 033E01 (2025).
  70. W. Lu, P. Kumar, and B. Zhang, A unified picture of galactic and cosmological fast radio bursts, Mon. Not. R. Astron. Soc. 498, 1397 (2020).
  71. J. I. Katz, The FRB-SGR connection, Mon. Not. R. Astron. Soc. 499, 2319 (2020).
  72. S. Yamasaki, K. Kashiyama, and K. Murase, Multi-wavelength constraints on the outflow properties of the extremely bright millisecond radio bursts from the galactic magnetar SGR 1935+2154, Mon. Not. R. Astron. Soc. 511, 3138 (2022).
  73. T. Wada and K. Ioka, Expanding fireball in magnetar bursts and fast radio bursts, Mon. Not. R. Astron. Soc. 519, 4094 (2023).
  74. Y.-P. Yang and B. Zhang, On the polarization properties of magnetar giant flare pulsating tails, Astrophys. J. 815, 45 (2015).
  75. The sign of gVηVcosθkB/(εVsin2θkB+ηVcosθkB) in front of the square root is incorporated into the definition of K±.

  76. V. Canuto, J. Lodenquai, and M. Ruderman, Thomson scattering in a strong magnetic field, Phys. Rev. D 3, 2303 (1971).
  77. H. Herold, Compton and Thomson scattering in strong magnetic fields, Phys. Rev. D 19, 2868 (1979).
  78. L. D. Landau, To the theory of energy transmission in collissions. II, Phys. Zs. Sowjet 2, 46 (1932).
  79. C. Zener, Non-adiabatic crossing of energy levels, Proc. R. Soc. A 137, 696 (1932).
  80. S. J. Parke, Nonadiabatic level crossing in resonant neutrino oscillations, Phys. Rev. Lett. 57, 1275 (1986).
  81. W. C. Haxton, The solar neutrino problem, Annu. Rev. 33, 459 (1995).
  82. The definition of ωadi is modified from that in [23] by a factor of (2/π)1/3, so that ω=ωadi corresponds to PNA=exp(−1). Exactly, Eq. (33) should be solved for ω appearing in ub.

  83. N. Chamel and P. Haensel, Physics of neutron star crusts, Living Rev. Relativity 11, 10 (2008).
  84. Y. E. Lyubarsky, On the X-ray spectra of soft gamma repeaters, Mon. Not. R. Astron. Soc. 332, 199 (2002).
  85. G. B. Rybicki and A. P. Lightman, Radiative Processes in Astrophysics (John Wiley & Sons, New York, 1979).
  86. L. D. Landau and E. M. Lifshitz, Statistical Physics Part I, 3rd ed. (Elsevier, Amsterdam, 1980).sp80.
  87. Fexp corresponds to η−1 in [73].

  88. M. A. Abramowicz, I. D. Novikov, and B. Paczynski, The appearance of highly relativistic, spherically symmetric stellar winds, Astrophys. J. 369, 175 (1991).
  89. S. Yamasaki, Y. Lyubarsky, J. Granot, and E. Göğüş, Spectral modification of magnetar flares by resonant cyclotron scattering, Mon. Not. R. Astron. Soc. 498, 484 (2020).
  90. S.-Q. Zhong, L. Li, B. Zhang, and Z.-G. Dai, Identifying the origin of fast radio burst–associated X-ray bursts with X-ray polarization, Astrophys. J. 976, 52 (2024).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation