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arxiv: 2604.24750 · v2 · pith:2ENBG6VNnew · submitted 2026-04-27 · 🌌 astro-ph.HE

Spectral Evidence of Heavy Nuclei from the Neutron Star Crust in Magnetar Bursts

Sheng-Lun Xie , Yun-Wei Yu , Shao-Lin Xiong , Wang-Chen Xue This is my paper

Pith reviewed 2026-05-22 11:08 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords magnetar burstsneutron star crustheavy nucleiX-ray spectraradiative transferplasma compositioneffective chargefireball location
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The pith

Magnetar burst spectra favor heavy nuclei with effective charge Z around 37 from the neutron star crust over light ions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs a radiative transfer framework for strongly magnetized electron-ion thermal plasma and applies it to X-ray spectra of magnetar bursts. The resulting fits disfavor light-ion compositions and instead prefer plasmas with effective charge numbers near 37. This supplies direct spectral evidence that heavy nuclei take part in the bursts. The findings also limit the amount of baryonic matter in the emitting regions and their distance from the star, while indicating that the ions come from the crust.

Core claim

The authors develop a general-purpose radiative transfer framework for a strongly magnetized electron-ion thermal plasma and apply it to the observed X-ray burst spectra. The spectral fits disfavor light-ion compositions and instead favor plasmas characterized by effective charge numbers around Z ∼ 37. These results provide spectral evidence for the participation of heavy nuclei in magnetar bursts, offer new observational constraints on the baryonic content and the location of the emitting fireballs, and further imply a crustal origin of the heavy ions.

What carries the argument

The MEITP radiative transfer framework for strongly magnetized electron-ion thermal plasma, which extracts the effective ion charge number Z by fitting the observed X-ray spectra.

If this is right

  • Heavy nuclei from the neutron star crust participate directly in the energy release of magnetar bursts.
  • The emitting fireballs contain a baryonic component consistent with crustal material rather than pure electron-positron pairs.
  • The location of the radiating plasma is tied to the crust or its immediate magnetospheric connection.
  • Light-element compositions are inconsistent with the observed spectra across the analyzed bursts.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Higher-resolution X-ray spectra could resolve individual heavy-element lines and identify specific nuclear species lifted from the crust.
  • The same modeling approach could be applied to other high-energy transients to test whether crustal material is ejected in different contexts.
  • Time-dependent spectral evolution during a burst might reveal how the heavy-ion fraction changes as the fireball expands.

Load-bearing premise

The observed X-ray spectral features are dominated by the ionic composition of the plasma rather than by unmodeled effects such as magnetic field geometry, temperature structure, or details of the energy release mechanism.

What would settle it

A re-fit of the same burst spectra with a light-ion composition but including detailed magnetic field geometry and temperature gradients that yields statistically better agreement than the Z ∼ 37 models.

Figures

Figures reproduced from arXiv: 2604.24750 by Shao-Lin Xiong, Sheng-Lun Xie, Wang-Chen Xue, Yun-Wei Yu.

Figure 1
Figure 1. Figure 1: Opacity coefficients and absorbing probability as a function of photon energy hν for different magnetic fields (B). The temperature kT=10 keV, Z=1, A=2, the angle be￾tween photon and magnetic field θ = 45◦ , and the number density of electron ne = 3.14 × 1021 cm−3 . The charge number of nuclei also plays an important role in the spectrum. By contrast, the dependence on the ionic mass number is expected to … view at source ↗
Figure 2
Figure 2. Figure 2: Intensity (I E ν ) as a function of photon energy hν. The left panel shows representative spectra for different magnetic fields and ions, with the overview inset retaining the full intensity range including the intrinsic blackbody. The upper-right panel shows the magnetic field effect for ions (Z, A) = (40, 80). The lower-right panel shows the ionic effect for a magnetic field B = 1013 G. The temperature i… view at source ↗
Figure 3
Figure 3. Figure 3: Valley of stability. Nuclide half-lives as a function of the number of protons Z, and neutrons N. The upper panel shows the Z posteriors from different bursts, with each burst represented by a distinct colored line. The vertical red dashed line and the shaded band represent the median value and the 1σ confidence level, respectively. & B. Zhang 2021; T. Wada & K. Ioka 2023). At the same time, the presence o… view at source ↗
read the original abstract

The crust of a neutron star (NS) provides a unique laboratory for studying matter under extreme density and magnetic field conditions that cannot be realized in terrestrial experiments. However, direct observational constraints on its composition have remained very limited. Magnetar bursts provide a promising means to probe the nuclear composition of the outer crust, as their energy release may be associated with stress-driven yielding of the crustal Coulomb lattice (including plastic deformation) and magnetic reconnection in the surrounding magnetosphere. We develop a general-purpose radiative transfer framework for a strongly magnetized electron--ion thermal plasma (MEITP) and apply it to the observed X-ray burst spectra. The spectral fits disfavor light-ion compositions and instead favor plasmas characterized by effective charge numbers around $Z \sim 37$. These results provide spectral evidence for the participation of heavy nuclei in magnetar bursts, offer new observational constraints on the baryonic content and the location of the emitting fireballs, and further imply a crustal origin of the heavy ions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a general-purpose radiative transfer framework (MEITP) for strongly magnetized electron-ion thermal plasmas and applies it to observed X-ray spectra of magnetar bursts. The central claim is that the spectral fits disfavor light-ion compositions and instead favor plasmas with effective charge numbers around Z ∼ 37, interpreted as spectral evidence for the participation of heavy nuclei from the neutron star crust, with implications for baryonic content, fireball location, and a crustal origin of the ions.

Significance. If the result holds after addressing modeling assumptions, this would constitute a significant observational advance by linking magnetar burst spectra directly to the nuclear composition of the outer crust under extreme conditions. It would provide new constraints on the baryonic makeup and energy-release mechanisms involving crustal stress and magnetic reconnection, building on the MEITP framework's treatment of cyclotron, free-free, and bound-free opacities.

major comments (2)
  1. [Abstract and results section] Abstract and results section: The claim that fits disfavor light ions (Z<10) and favor Z∼37 is presented without details on data selection criteria, fitting statistics (e.g., χ² or likelihood values), error bars on Z, or explicit comparisons to alternative models with varied B-field or temperature profiles. This makes it difficult to evaluate whether the preference is robust or driven by the fitting procedure.
  2. [MEITP framework description (likely §4)] MEITP framework description (likely §4): The radiative transfer computes opacities and emergent spectra assuming a uniform slab or atmosphere with fixed B, T, and density, then fits effective Z as the primary variable. It is not shown that the specific intensity solution along rays marginalizes over magnetic field geometry, temperature stratification, or viewing angle; without this, the attributed spectral curvature from high-Z ions could be reproduced by unmodeled gradients, undermining the disfavoring of light ions as a compositional signature.
minor comments (2)
  1. [Methods/Notation] Clarify the exact definition of the effective charge Z and its relation to the ion species in the plasma model, including any assumptions about the ion distribution.
  2. [Figures] Ensure all figures showing spectral fits include residuals and parameter uncertainties for transparency.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and valuable comments on our manuscript. We will revise the paper to address the points raised, as detailed in our point-by-point response below.

read point-by-point responses

  1. Referee: [Abstract and results section] Abstract and results section: The claim that fits disfavor light ions (Z<10) and favor Z∼37 is presented without details on data selection criteria, fitting statistics (e.g., χ² or likelihood values), error bars on Z, or explicit comparisons to alternative models with varied B-field or temperature profiles. This makes it difficult to evaluate whether the preference is robust or driven by the fitting procedure.

    Authors: We agree that the presentation in the abstract and results section would be strengthened by including more details on the analysis. In the revised manuscript, we will add the data selection criteria, report the fitting statistics including χ² values, provide error bars on the effective Z, and include comparisons to models with different B-field and temperature profiles. These changes will help demonstrate the robustness of our findings. revision: yes

  2. Referee: [MEITP framework description (likely §4)] MEITP framework description (likely §4): The radiative transfer computes opacities and emergent spectra assuming a uniform slab or atmosphere with fixed B, T, and density, then fits effective Z as the primary variable. It is not shown that the specific intensity solution along rays marginalizes over magnetic field geometry, temperature stratification, or viewing angle; without this, the attributed spectral curvature from high-Z ions could be reproduced by unmodeled gradients, undermining the disfavoring of light ions as a compositional signature.

    Authors: The MEITP framework uses a uniform slab model as a first approximation to compute the radiative transfer in strongly magnetized plasmas. We have not explicitly shown marginalization over geometry, stratification, or viewing angle in the current version. We will revise the manuscript to include additional tests and discussion showing that the spectral signatures from high-Z ions are distinct and not easily mimicked by gradients in the parameters. This will support our interpretation that the data disfavor light ions. revision: partial

Circularity Check

1 steps flagged

Spectral preference for Z∼37 reduces to outcome of fitting effective charge in MEITP model

specific steps
  1. fitted input called prediction [Abstract]
    "The spectral fits disfavor light-ion compositions and instead favor plasmas characterized by effective charge numbers around $Z ∼ 37$."

    Effective charge Z is the primary variable adjusted in the MEITP spectral modeling to match the observed X-ray burst spectra. The reported disfavoring of light ions (Z<10) and preference for Z∼37 is therefore the direct result of the fitting procedure itself rather than an independent derivation or prediction from the radiative transfer equations.

full rationale

The paper's central result is obtained by developing the MEITP radiative transfer code and then fitting observed X-ray spectra with effective charge Z as a primary free parameter. The claim of 'spectral evidence' for heavy nuclei is therefore the direct numerical outcome of that fit rather than a first-principles derivation or independent prediction. No self-citation chains, uniqueness theorems, or ansatz smuggling are present in the provided text, but the reduction of the headline claim to a fitted parameter produces moderate circularity. The modeling assumptions about composition dominating other effects (B-field geometry, temperature structure) are noted as a separate correctness concern rather than circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Ledger populated from abstract statements only; full methods and derivations unavailable.

free parameters (1)
  • effective charge Z
    Fitted parameter used to characterize the plasma composition that best matches the observed spectra.
axioms (1)
  • domain assumption Energy release in magnetar bursts is associated with stress-driven yielding of the crustal Coulomb lattice including plastic deformation and magnetic reconnection in the magnetosphere.
    Stated as the physical basis linking bursts to crustal composition.

pith-pipeline@v0.9.0 · 5711 in / 1270 out tokens · 37929 ms · 2026-05-22T11:08:17.780555+00:00 · methodology

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Works this paper leans on

66 extracted references · 66 canonical work pages

  1. [1]

    K., Chluba, J., & Sarkar, A

    Acharya, S. K., Chluba, J., & Sarkar, A. 2021, MNRAS, 507, 2052, doi: 10.1093/mnras/stab2259

    work page doi:10.1093/mnras/stab2259 2021

  2. [2]

    A., & Chugunov, A

    Baiko, D. A., & Chugunov, A. I. 2018, MNRAS, 480, 5511, doi: 10.1093/mnras/sty2259

    work page doi:10.1093/mnras/sty2259 2018

  3. [3]

    Beloborodov, A. M. 2013, ApJ, 762, 13, doi: 10.1088/0004-637X/762/1/13

    work page doi:10.1088/0004-637x/762/1/13 2013

  4. [4]

    Beloborodov, A. M. 2020, ApJ, 896, 142, doi: 10.3847/1538-4357/ab83eb

    work page doi:10.3847/1538-4357/ab83eb 2020

  5. [5]

    D., Ravi, V., Belov, K

    Bochenek, C. D., Ravi, V., Belov, K. V., et al. 2020, Nature, 587, 59, doi: 10.1038/s41586-020-2872-x

    work page doi:10.1038/s41586-020-2872-x 2020

  6. [6]

    L., et al

    Borghese, A., Coti Zelati, F., Israel, G. L., et al. 2022, MNRAS, 516, 602, doi: 10.1093/mnras/stac1314

    work page doi:10.1093/mnras/stac1314 2022

  7. [7]

    2022, ApJS, 260, 25, doi: 10.3847/1538-4365/ac67e4 CHIME/FRB Collaboration, Andersen, B

    Cai, C., Xiong, S.-L., Lin, L., et al. 2022, ApJS, 260, 25, doi: 10.3847/1538-4365/ac67e4 CHIME/FRB Collaboration, Andersen, B. C., Bandura, K. M., et al. 2020, Nature, 587, 54, doi: 10.1038/s41586-020-2863-y

    work page doi:10.3847/1538-4365/ac67e4 2022

  8. [8]

    2020, ApJL, 902, L32, doi: 10.3847/2041-8213/abbda9

    Dehman, C., Vigan` o, D., Rea, N., et al. 2020, ApJL, 902, L32, doi: 10.3847/2041-8213/abbda9

    work page doi:10.3847/2041-8213/abbda9 2020

  9. [9]

    Formation of very strongly magnetized neutron stars - implications for gamma-ray bursts.Astrophys

    Duncan, R. C., & Thompson, C. 1992, ApJL, 392, L9, doi: 10.1086/186413

    work page doi:10.1086/186413 1992

  10. [10]

    E., & Rees, M

    Felten, J. E., & Rees, M. J. 1972, A&A, 17, 226

    work page 1972

  11. [11]

    P., Kaspi, V

    Gavriil, F. P., Kaspi, V. M., & Woods, P. M. 2004, ApJ, 607, 959, doi: 10.1086/383564

    work page doi:10.1086/383564 2004

  12. [12]

    H., & Kocevski, D

    Goldstein, A., Cleveland, W. H., & Kocevski, D. 2022, https://fermi.gsfc.nasa.gov/ssc/data/analysis/gbm G¨ oˇ g¨ uS ¸ , E., Woods, P. M., Kouveliotou, C., et al. 1999, ApJL, 526, L93, doi: 10.1086/312380 G¨ oˇ g¨ u¸ s, E., Woods, P. M., Kouveliotou, C., et al. 2000, ApJL, 532, L121, doi: 10.1086/312583

    work page doi:10.1086/312380 2022

  13. [13]

    K., & Lai, D

    Harding, A. K., & Lai, D. 2006, Reports on Progress in Physics, 69, 2631, doi: 10.1088/0034-4885/69/9/R03

    work page doi:10.1088/0034-4885/69/9/r03 2006

  14. [14]

    Ho, W. C. G., & Lai, D. 2003, MNRAS, 338, 233, doi: 10.1046/j.1365-8711.2003.06047.x

    work page doi:10.1046/j.1365-8711.2003.06047.x 2003

  15. [15]

    F., & Syunyaev, R

    Illarionov, A. F., & Syunyaev, R. A. 1972, Soviet Ast., 16, 45

    work page 1972

  16. [16]

    2020, ApJL, 904, L15, doi: 10.3847/2041-8213/abc6a3

    Ioka, K. 2020, ApJL, 904, L15, doi: 10.3847/2041-8213/abc6a3

    work page doi:10.3847/2041-8213/abc6a3 2020

  17. [17]

    L., Esposito, P., Rea, N., et al

    Israel, G. L., Esposito, P., Rea, N., et al. 2016, MNRAS, 457, 3448, doi: 10.1093/mnras/stw008

    work page doi:10.1093/mnras/stw008 2016

  18. [18]

    Jones, P. B. 2003, ApJ, 595, 342, doi: 10.1086/377351

    work page doi:10.1086/377351 2003

  19. [19]

    G., et al

    Kaneko, Y., G¨ o˘ g¨ u¸ s, E., Baring, M. G., et al. 2021, ApJL, 916, L7, doi: 10.3847/2041-8213/ac0fe7

    work page doi:10.3847/2041-8213/ac0fe7 2021

  20. [20]

    2020, MNRAS, 494, 2385, doi: 10.1093/mnras/staa774

    Kumar, P., & Boˇ snjak,ˇZ. 2020, MNRAS, 494, 2385, doi: 10.1093/mnras/staa774

    work page doi:10.1093/mnras/staa774 2020

  21. [21]

    K., Andersson, N., Antonopoulou, D., & Watts, A

    Lander, S. K., Andersson, N., Antonopoulou, D., & Watts, A. L. 2015, MNRAS, 449, 2047, doi: 10.1093/mnras/stv432

    work page doi:10.1093/mnras/stv432 2015

  22. [22]

    and Shibahashi , H

    Levin, Y., & Lyutikov, M. 2012, MNRAS, 427, 1574, doi: 10.1111/j.1365-2966.2012.22016.x

    work page doi:10.1111/j.1365-2966.2012.22016.x 2012

  23. [23]

    K., Lin, L., Xiong, S

    Li, C. K., Lin, L., Xiong, S. L., et al. 2021, Nature Astronomy, 5, 378, doi: 10.1038/s41550-021-01302-6

    work page doi:10.1038/s41550-021-01302-6 2021

  24. [24]

    J., et al

    Lin, L., G¨ o˘ g¨ u¸ s, E., Roberts, O. J., et al. 2020a, ApJL, 902, L43, doi: 10.3847/2041-8213/abbefe

    work page doi:10.3847/2041-8213/abbefe 2041

  25. [25]

    J., et al

    Lin, L., G¨ o˘ g¨ u¸ s, E., Roberts, O. J., et al. 2020b, ApJ, 893, 156, doi: 10.3847/1538-4357/ab818f

    work page doi:10.3847/1538-4357/ab818f

  26. [26]

    G., et al

    Lin, L., Kouveliotou, C., Baring, M. G., et al. 2011, ApJ, 739, 87, doi: 10.1088/0004-637X/739/2/87

    work page doi:10.1088/0004-637x/739/2/87 2011

  27. [27]

    Lyubarsky, Y. E. 2002, MNRAS, 332, 199, doi: 10.1046/j.1365-8711.2002.05290.x

    work page doi:10.1046/j.1365-8711.2002.05290.x 2002

  28. [28]

    2010, PASJ, 62, 1093, doi: 10.1093/pasj/62.4.1093

    Masada, Y., Nagataki, S., Shibata, K., & Terasawa, T. 2010, PASJ, 62, 1093, doi: 10.1093/pasj/62.4.1093

    work page doi:10.1093/pasj/62.4.1093 2010

  29. [29]

    P., Golentskii, S

    Mazets, E. P., Golentskii, S. V., Ilinskii, V. N., Aptekar, R. L., & Guryan, I. A. 1979, Nature, 282, 587, doi: 10.1038/282587a0

    work page doi:10.1038/282587a0 1979

  30. [30]

    J., Reeves J

    Medin, Z., & Lai, D. 2010, MNRAS, 406, 1379, doi: 10.1111/j.1365-2966.2010.16776.x

    work page doi:10.1111/j.1365-2966.2010.16776.x 2010

  31. [31]

    2014, ApJ, 785, 62, doi: 10.1088/0004-637X/785/1/62

    Meng, Y., Lin, J., Zhang, L., et al. 2014, ApJ, 785, 62, doi: 10.1088/0004-637X/785/1/62

    work page doi:10.1088/0004-637x/785/1/62 2014

  32. [32]

    2008, A&A Rv, 15, 225, doi: 10.1007/s00159-008-0011-z M´ esz´ aros, P

    Mereghetti, S. 2008, A&A Rv, 15, 225, doi: 10.1007/s00159-008-0011-z M´ esz´ aros, P. 1992, Science. https://api.semanticscholar.org/CorpusID:118335291

    work page doi:10.1007/s00159-008-0011-z 2008

  33. [33]

    1980, ApJ, 236, 904, doi: 10.1086/157817

    Nagel, W. 1980, ApJ, 236, 904, doi: 10.1086/157817

    work page doi:10.1086/157817 1980

  34. [34]

    F., Hurley, K., Sakamoto, T., et al

    Olive, J. F., Hurley, K., Sakamoto, T., et al. 2004, ApJ, 616, 1148, doi: 10.1086/424957

    work page doi:10.1086/424957 2004

  35. [35]

    1992, AcA, 42, 145

    Paczynski, B. 1992, AcA, 42, 145

    work page 1992

  36. [36]

    G., & Panov, A

    Pavlov, G. G., & Panov, A. N. 1976, Soviet Journal of Experimental and Theoretical Physics, 44, 300 9

    work page 1976

  37. [37]

    Perna, R., & Pons, J. A. 2011, ApJL, 727, L51, doi: 10.1088/2041-8205/727/2/L51

    work page doi:10.1088/2041-8205/727/2/l51 2011

  38. [38]

    A., & Perna, R

    Pons, J. A., & Perna, R. 2011, ApJ, 741, 123, doi: 10.1088/0004-637X/741/2/123

    work page doi:10.1088/0004-637x/741/2/123 2011

  39. [39]

    S., & Ibrahim, A

    Rehan, N. S., & Ibrahim, A. I. 2025, ApJS, 276, 60, doi: 10.3847/1538-4365/ad95f9

    work page doi:10.3847/1538-4365/ad95f9 2025

  40. [40]

    Rehan, N. u. S., & Ibrahim, A. I. 2023, ApJ, 950, 121, doi: 10.3847/1538-4357/accae6

    work page doi:10.3847/1538-4357/accae6 2023

  41. [41]

    Rehan, N. u. S., & Ibrahim, A. I. 2024, ApJ, 969, 38, doi: 10.3847/1538-4357/ad4635

    work page doi:10.3847/1538-4357/ad4635 2024

  42. [42]

    2021, Nature Astronomy, 5, 372, doi: 10.1038/s41550-020-01265-0

    Ridnaia, A., Svinkin, D., Frederiks, D., et al. 2021, Nature Astronomy, 5, 372, doi: 10.1038/s41550-020-01265-0

    work page doi:10.1038/s41550-020-01265-0 2021

  43. [43]

    B., & Lightman, A

    Rybicki, G. B., & Lightman, A. P. 1986, Radiative Processes in Astrophysics

    work page 1986

  44. [44]

    L., & Sakamoto, T

    Stamatikos, M., Malesani, D., Page, K. L., & Sakamoto, T. 2014, GRB Coordinates Network, 16520, 1

    work page 2014

  45. [45]

    Thompson, C., & Duncan, R. C. 1993, ApJ, 408, 194, doi: 10.1086/172580

    work page doi:10.1086/172580 1993

  46. [46]

    Thompson, C., & Duncan, R. C. 1995, MNRAS, 275, 255, doi: 10.1093/mnras/275.2.255

    work page doi:10.1093/mnras/275.2.255 1995

  47. [47]

    Thompson, C., & Duncan, R. C. 1996, ApJ, 473, 322, doi: 10.1086/178147

    work page doi:10.1086/178147 1996

  48. [48]

    Thompson, C., & Duncan, R. C. 2001, ApJ, 561, 980, doi: 10.1086/323256 van Putten, T., Watts, A. L., Baring, M. G., & Wijers, R. A. M. J. 2016, MNRAS, 461, 877, doi: 10.1093/mnras/stw1279

    work page doi:10.1086/323256 2001

  49. [49]

    1979, PhRvD, 19, 1684, doi: 10.1103/PhysRevD.19.1684

    Ventura, J. 1979, PhRvD, 19, 1684, doi: 10.1103/PhysRevD.19.1684

    work page doi:10.1103/physrevd.19.1684 1979

  50. [50]

    1979, ApJL, 233, L125, doi: 10.1086/183090

    Ventura, J., Nagel, W., & Meszaros, P. 1979, ApJL, 233, L125, doi: 10.1086/183090

    work page doi:10.1086/183090 1979

  51. [51]

    1975, Nuovo Cimento B Serie, 26, 537, doi: 10.1007/BF02738576 von Kienlin, A., Gruber, D., Kouveliotou, C., et al

    Virtamo, J., & Jauho, P. 1975, Nuovo Cimento B Serie, 26, 537, doi: 10.1007/BF02738576 von Kienlin, A., Gruber, D., Kouveliotou, C., et al. 2012, ApJ, 755, 150, doi: 10.1088/0004-637X/755/2/150

    work page doi:10.1007/bf02738576 1975

  52. [52]

    2023, MNRAS, 519, 4094, doi: 10.1093/mnras/stac3681

    Wada, T., & Ioka, K. 2023, MNRAS, 519, 4094, doi: 10.1093/mnras/stac3681

    work page doi:10.1093/mnras/stac3681 2023

  53. [53]

    2025, ApJ, 993, 24, doi: 10.3847/1538-4357/ae0cbe

    Wang, Y., Wang, C.-W., Xiong, S.-L., et al. 2025, ApJ, 993, 24, doi: 10.3847/1538-4357/ae0cbe

    work page doi:10.3847/1538-4357/ae0cbe 2025

  54. [54]

    M., & Thompson, C

    Woods, P. M., & Thompson, C. 2006, Soft gamma repeaters and anomalous X-ray pulsars: magnetar candidates, ed. W. Lewin & M. van der Klis, Cambridge Astrophysics (Cambridge University Press), 547586

    work page 2006

  55. [55]

    2024, ApJ, 967, 108, doi: 10.3847/1538-4357/ad4093

    Xie, S.-L., Yu, Y.-W., Xiong, S.-L., et al. 2024, ApJ, 967, 108, doi: 10.3847/1538-4357/ad4093

    work page doi:10.3847/1538-4357/ad4093 2024

  56. [56]

    2022, MNRAS, 517, 3854, doi: 10.1093/mnras/stac2918

    Xie, S.-L., Cai, C., Xiong, S.-L., et al. 2022, MNRAS, 517, 3854, doi: 10.1093/mnras/stac2918

    work page doi:10.1093/mnras/stac2918 2022

  57. [57]

    2025, ApJS, 277, 5, doi: 10.3847/1538-4365/ada6a9

    Xie, S.-L., Cai, C., Yu, Y.-W., et al. 2025, ApJS, 277, 5, doi: 10.3847/1538-4365/ada6a9

    work page doi:10.3847/1538-4365/ada6a9 2025

  58. [58]

    2026, ApJ, 999, 159, doi: 10.3847/1538-4357/ae433d

    Xie, S.-L., Chen, A., Yu, Y.-W., et al. 2026, ApJ, 999, 159, doi: 10.3847/1538-4357/ae433d

    work page doi:10.3847/1538-4357/ae433d 2026

  59. [59]

    2025,, 0.2.2 Zenodo, doi: 10.5281/zenodo.11284456

    Xue, W.-C., Xie, S.-L., Zheng, C., et al. 2025,, 0.2.2 Zenodo, doi: 10.5281/zenodo.11284456

    work page doi:10.5281/zenodo.11284456 2025

  60. [60]

    2021, ApJ, 919, 89, doi: 10.3847/1538-4357/ac14b5

    Yang, Y.-P., & Zhang, B. 2021, ApJ, 919, 89, doi: 10.3847/1538-4357/ac14b5

    work page doi:10.3847/1538-4357/ac14b5 2021

  61. [61]

    2020, ApJL, 904, L21, doi: 10.3847/2041-8213/abc94c

    Younes, G., G¨ uver, T., Kouveliotou, C., et al. 2020, ApJL, 904, L21, doi: 10.3847/2041-8213/abc94c

    work page doi:10.3847/2041-8213/abc94c 2020

  62. [62]

    2011, ApJ, 738, 75, doi: 10.1088/0004-637X/738/1/75

    Yu, C. 2011, ApJ, 738, 75, doi: 10.1088/0004-637X/738/1/75

    work page doi:10.1088/0004-637x/738/1/75 2011

  63. [63]

    2013, ApJL, 771, L46, doi: 10.1088/2041-8205/771/2/L46 zhang, p

    Yu, C., & Huang, L. 2013, ApJL, 771, L46, doi: 10.1088/2041-8205/771/2/L46 zhang, p. 2024,, v20240514 Zenodo, doi: 10.5281/zenodo.16990624

    work page doi:10.1088/2041-8205/771/2/l46 2013

  64. [64]

    2022, ApJL, 939, L25, doi: 10.3847/2041-8213/ac9b55

    Zhang, Z., Yi, S.-X., Zhang, S.-N., Xiong, S.-L., & Xiao, S. 2022, ApJL, 939, L25, doi: 10.3847/2041-8213/ac9b55

    work page doi:10.3847/2041-8213/ac9b55 2022

  65. [65]

    J., Zhang, B.-B., & Meng, Y.-Z

    Zhang, Z. J., Zhang, B.-B., & Meng, Y.-Z. 2023, MNRAS, 520, 6195, doi: 10.1093/mnras/stad443

    work page doi:10.1093/mnras/stad443 2023

  66. [66]

    2020, ApJL, 898, L5, doi: 10.3847/2041-8213/aba262 10Xie et al

    Zhong, S.-Q., Dai, Z.-G., Zhang, H.-M., & Deng, C.-M. 2020, ApJL, 898, L5, doi: 10.3847/2041-8213/aba262 10Xie et al. APPENDIX A.ABSORPTION AND SCATTERING For the magnetized electron–ion thermal plasma around a magnetar, the plasma dielectric tensor, in the coordinate system ˆX ˆY ˆZwith ˆBalong ˆZ, is given by (e.g., W. C. G. Ho & D. Lai 2003; A. K. Hard...

    work page doi:10.3847/2041-8213/aba262 2020