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arxiv: 2606.21827 · v1 · pith:JBXRYQ7Znew · submitted 2026-06-20 · 🌌 astro-ph.HE

Do Prompt Gamma-ray Burst Fireball Composition Impact on Afterglow Emission? Cases Study for Long GRBs 080916C/090902B and Short GRBs 090510/130603B

Yu Gan , Ren-Jie Xiong , Zi-Qi Wang , Qi-Yu Yan , Liang-Jun Chen , Xiao-Li Huang This is my paper

Pith reviewed 2026-06-26 12:05 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords gamma-ray burstsafterglow emissionfireball compositionforward shock modelambient medium densitycascade pairslong GRBsshort GRBs
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The pith

Afterglow emission in gamma-ray bursts depends on ambient medium density rather than prompt fireball composition.

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

The paper examines whether the composition of the prompt GRB jet, inferred from thermal versus non-thermal spectra, leaves an imprint on the subsequent afterglow. Two long GRBs with thermal components and two short GRBs with non-thermal components are modeled using the standard forward-shock framework that includes synchrotron radiation from both primary electrons and electron-positron pairs created by gamma-gamma annihilation. The fitted light-curve parameters turn out to be controlled by the density of the surrounding medium in all four cases. Early UV-optical emission in the long bursts receives a contribution from the cascade pairs, but this does not change the overall result that composition is erased once internal energy has been converted to bulk kinetic energy.

Core claim

By fitting the multi-wavelength afterglow light curves of GRBs 080916C, 090902B, 090510 and 130603B with the forward-shock model that incorporates emission from both primary and cascaded electron populations, the authors find that the characteristic parameters of the light-curve evolution are set by ambient medium density and are unrelated to whether the original fireball was thermally or non-thermally dominated. The prompt-phase conversion of internal energy into jet kinetic energy erases any detectable compositional signature, leaving the density of the ambient medium as the dominant factor shaping the afterglow.

What carries the argument

The standard forward-shock model that includes synchrotron emission from both primary electrons and cascade electron-positron pairs produced by gamma-gamma annihilation.

If this is right

  • Ambient medium density is the dominant parameter controlling afterglow light-curve evolution for both long and short GRBs.
  • Prompt internal energy is fully converted to kinetic energy before the afterglow phase begins.
  • Early UV-optical afterglows of long GRBs can be powered by cascaded pairs without altering the density-driven behavior.
  • Afterglow modeling does not require knowledge of the prompt-phase composition.

Where Pith is reading between the lines

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

  • The difference in cascade-pair contribution between the long and short bursts may trace progenitor or environmental differences rather than composition alone.
  • Observations of GRBs spanning a wider range of ambient densities would provide a stronger test of the density-only conclusion.
  • If microphysical parameters such as electron acceleration efficiency vary systematically with composition, the present modeling could miss that dependence.

Load-bearing premise

The standard forward-shock model with cascade pairs fully captures the afterglow physics of these four bursts without missing composition-dependent effects.

What would settle it

A larger sample of GRBs in which afterglow parameters correlate with prompt spectral type even after ambient density is accounted for.

Figures

Figures reproduced from arXiv: 2606.21827 by Liang-Jun Chen, Qi-Yu Yan, Ren-Jie Xiong, Xiao-Li Huang, Yu Gan, Zi-Qi Wang.

Figure 1
Figure 1. Figure 1: Left panel: the observed multi-wavelength lightcurves (dots) and the best theoretical fits (solid lines) of long GRBs 080916C/090902B and short GRBs 130603B/090510 with our GRB afterglow model. The solid lines represent the sum of the emission from the primary synchrotron+SSC components, and cascade synchrotron+SSC processes by considering KN effect. The parameter values used are shown in [PITH_FULL_IMAGE… view at source ↗
Figure 2
Figure 2. Figure 2: Radius and Magnetic field strength as a function of time. The parameter values used are the same as those in [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Left panel: temporal evolution of the opacity of 0.1 TeV, 1 TeV and 10 TeV gamma-ray photons within the afterglow jet. The gray dashed lines represent τγγ = 1. Middle/Right panel: the broadband SEDs of afterglows after the GRB trigger of Poynting-flux-dominated GRBs 080916C/130603B and Matter-dominated GRBs 090902B/090510, respectively. The solid orange lines represent the sum of the emission from the prim… view at source ↗
Figure 4
Figure 4. Figure 4: Left panel: the values of γc, γm, and γmax as a function of time. Right panel: Compton parameters Y (γc) and Y (γm) as a function of time. The parameter values used are the same as that in [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
read the original abstract

Broadband observations with the {\em Fermi} mission reveal that a large fraction of gamma-ray burst (GRB) spectra are dominated by non-thermal emission, while a small fraction are dominated by thermal/quasi-thermal emission, likely indicating the difference in jet composition among GRB. By selecting two typical long GRBs (080916C and 090902B) and two short GRBs (130603B and 090510), we present a comparative analysis to investigate whether the composition of prompt GRB jets influences the afterglow emission for bursts originating from both massive star collapse and compact binary mergers. Incorporating emission from both primary and cascade electron populations, we fit the multi-wavelength afterglow lightcurves of these GRBs with the standard forward shock model and analyze the particle acceleration and radiation physics of the jets. Our results show that the afterglow lightcurve evolution with the characteristic parameters is not related to the composition of the GRB fireball but rather depends on the ambient medium density. The early UV-optical afterglows of the two long GRBs are dominated by synchrotron emission from cascaded $e^{\pm}$ pairs produced via the $\gamma\gamma$ annihilation process, whereas this is not the case for the two short GRBs. These results suggest that the internal energy of the fireball is converted into jet kinetic energy during the prompt phase, and that the fireball composition leaves no detectable footprint on the afterglow jet. Instead, the density of the ambient medium plays an essential role in shaping the afterglow emission.

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

3 major / 2 minor

Summary. The paper selects two long GRBs (080916C, 090902B) and two short GRBs (090510, 130603B) with differing prompt emission (non-thermal vs. thermal/quasi-thermal) to test whether fireball composition affects afterglow. It fits the multi-wavelength afterglow light curves using the standard forward-shock model that includes both primary electrons and cascade e± pairs from γγ annihilation, then reports that the evolution of characteristic afterglow parameters correlates with ambient medium density rather than prompt spectral type. The central conclusion is that fireball composition is converted to kinetic energy during the prompt phase and leaves no detectable footprint on the afterglow jet.

Significance. If the result were independently verified, it would support the view that afterglow physics is insensitive to prompt composition for both collapsar and merger progenitors and would reinforce the dominance of external density in shaping afterglow light curves. The work does not, however, supply machine-checked derivations, reproducible fitting code, or falsifiable predictions that would strengthen its evidential weight.

major comments (3)
  1. [Abstract / model section] Abstract and § (model description): the claim that 'the fireball composition leaves no detectable footprint' is obtained solely by fitting the standard forward-shock model (primary + cascade electrons). Because that model contains no explicit composition-dependent microphysics or magnetization terms, the absence of a footprint is a direct consequence of the modeling choice rather than an independent test.
  2. [Results] Results section: no quantitative fit statistics (χ²/dof, residual distributions, parameter uncertainties, or covariance matrices) are reported for the four GRBs, nor is any robustness check against data exclusion or alternative density profiles presented. This leaves the reported correlation between afterglow parameters and ambient density unquantified.
  3. [Discussion] Discussion: the four bursts are treated as representative, yet no justification is given for why these particular events suffice to generalize the conclusion to the broader long- and short-GRB populations; the weakest-assumption concern in the stress-test note therefore remains unaddressed.
minor comments (2)
  1. [Abstract] Notation for 'characteristic parameters' is used repeatedly without an explicit list or table linking them to the fitted quantities (e.g., E_k, n, ε_e, ε_B).
  2. [Results] The statement that early UV-optical afterglows of the long GRBs are 'dominated by synchrotron emission from cascaded e± pairs' would benefit from a quantitative breakdown of the flux contribution from cascade versus primary electrons at each epoch.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We respond point-by-point to the major comments below, indicating revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract / model section] Abstract and § (model description): the claim that 'the fireball composition leaves no detectable footprint' is obtained solely by fitting the standard forward-shock model (primary + cascade electrons). Because that model contains no explicit composition-dependent microphysics or magnetization terms, the absence of a footprint is a direct consequence of the modeling choice rather than an independent test.

    Authors: We acknowledge that the standard forward-shock model employed does not include explicit composition-dependent microphysics. Our analysis tests whether afterglow data from GRBs with differing prompt spectra are adequately described by this model and whether the resulting parameters correlate with prompt type or ambient density. We will revise the abstract and model section to clarify the scope of the test within the standard framework. revision: partial

  2. Referee: [Results] Results section: no quantitative fit statistics (χ²/dof, residual distributions, parameter uncertainties, or covariance matrices) are reported for the four GRBs, nor is any robustness check against data exclusion or alternative density profiles presented. This leaves the reported correlation between afterglow parameters and ambient density unquantified.

    Authors: We agree that quantitative fit statistics and robustness checks are necessary. In the revised manuscript we will report χ²/dof values, parameter uncertainties, and include a brief robustness discussion using alternative density profiles. revision: yes

  3. Referee: [Discussion] Discussion: the four bursts are treated as representative, yet no justification is given for why these particular events suffice to generalize the conclusion to the broader long- and short-GRB populations; the weakest-assumption concern in the stress-test note therefore remains unaddressed.

    Authors: These events were selected for their high-quality multi-wavelength coverage and contrasting prompt properties. We will add explicit justification in the discussion, note the case-study nature of the work, and address limitations on generalization to the full populations. revision: yes

Circularity Check

0 steps flagged

No significant circularity: empirical fits within standard model yield model-dependent conclusion

full rationale

The paper selects GRBs with differing prompt compositions, fits their afterglow light curves using the standard forward-shock model (including primary + cascade electrons), extracts characteristic parameters, and reports that those parameters correlate with ambient density rather than prompt spectral type. This is an empirical comparison inside one fixed model; the text contains no self-definitional equations, no fitted parameter renamed as an independent prediction, no load-bearing self-citation, and no uniqueness theorem imported from prior work. The claim that composition leaves “no detectable footprint” is therefore an interpretation of the fit results rather than a quantity forced by construction to equal the model inputs. The derivation chain is self-contained against the chosen external data sets.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The analysis rests on the standard GRB afterglow forward shock framework and the assumption that cascade pair production is the dominant early optical mechanism for long GRBs; free parameters are the usual afterglow fit quantities such as ambient density and energy.

free parameters (2)
  • ambient medium density
    Fitted parameter in the forward shock model that the paper identifies as the main driver of light-curve shape.
  • characteristic afterglow parameters
    Energy, Lorentz factor, and microphysical parameters fitted to match observed light curves.
axioms (2)
  • domain assumption The standard forward shock model applies without modification from prompt composition
    Invoked to fit all four bursts and conclude composition independence.
  • domain assumption Cascade e± pairs from γγ annihilation dominate early UV-optical emission in long GRBs
    Used to explain the difference between long and short GRB early afterglows.

pith-pipeline@v0.9.1-grok · 5847 in / 1321 out tokens · 24530 ms · 2026-06-26T12:05:10.368327+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

66 extracted references · 63 canonical work pages · 3 internal anchors

  1. [1]

    A., Ackermann, M., Ajello, M., et al.\ 2009, , 706, L138

    Abdo, A. A., Ackermann, M., Ajello, M., et al.\ 2009, , 706, L138. doi:10.1088/0004-637X/706/1/L138

    work page doi:10.1088/0004-637x/706/1/l138 2009

  2. [2]

    A., Ackermann, M., Arimoto, M., et al.\ 2009, Science, 323, 1688

    Abdo, A. A., Ackermann, M., Arimoto, M., et al.\ 2009, Science, 323, 1688. doi:10.1126/science.1169101

    work page doi:10.1126/science.1169101 2009

  3. [3]

    A., Ackermann, M., Ajello, M., et al.\ 2009, , 462, 331

    Abdo, A. A., Ackermann, M., Ajello, M., et al.\ 2009, , 462, 331. doi:10.1038/nature08574

    work page doi:10.1038/nature08574 2009

  4. [4]

    B., et al.\ 2010, , 716, 2, 1178

    Ackermann, M., Asano, K., Atwood, W. B., et al.\ 2010, , 716, 2, 1178. doi:10.1088/0004-637X/716/2/1178

    work page doi:10.1088/0004-637x/716/2/1178 2010

  5. [5]

    doi:10.1086/172995

    Band, D., Matteson, J., Ford, L., et al.\ 1993, , 413, 281. doi:10.1086/172995

    work page doi:10.1086/172995 1993

  6. [6]

    doi:10.1088/0004-637X/768/1/54

    B \"o ttcher, M., Reimer, A., Sweeney, K., et al.\ 2013, , 768, 54. doi:10.1088/0004-637X/768/1/54

    work page doi:10.1088/0004-637x/768/1/54 2013

  7. [7]

    doi:10.3847/1538-4357/ad5f93

    Chen, J.-M., Zhu, K.-R., Peng, Z.-Y., et al.\ 2024, , 972, 2, 132. doi:10.3847/1538-4357/ad5f93

    work page doi:10.3847/1538-4357/ad5f93 2024

  8. [8]

    & Peng, Z.-Y.\ 2024, , 964, 1, 45

    Chen, J.-M. & Peng, Z.-Y.\ 2024, , 964, 1, 45. doi:10.3847/1538-4357/ad26fc

    work page doi:10.3847/1538-4357/ad26fc 2024

  9. [9]

    Chevalier, R. A. & Li, Z.-Y.\ 2000, , 536, 195. doi:10.1086/308914

    work page doi:10.1086/308914 2000

  10. [10]

    X., Perley, D., et al.\ 2013, , 777, 94

    Cucchiara, A., Prochaska, J. X., Perley, D., et al.\ 2013, , 777, 94. doi:10.1088/0004-637X/777/2/94

    work page doi:10.1088/0004-637x/777/2/94 2013

  11. [11]

    B., Tanvir, N., et al.\ 2009, GRB Coordinates Network, Circular Service, No

    Cucchiara, A., Fox, D. B., Tanvir, N., et al.\ 2009, GRB Coordinates Network, Circular Service, No. 9873, \#1 (2009), 9873

    2009

  12. [12]

    Dai, Z. G. & Lu, T.\ 1998, , 298, 87. doi:10.1046/j.1365-8711.1998.01681.x

    work page doi:10.1046/j.1365-8711.1998.01681.x 1998

  13. [13]

    De Pasquale, M., Schady, P., Kuin, N. P. M., et al.\ 2010, , 709, L146. doi:10.1088/2041-8205/709/2/L146

    work page doi:10.1088/2041-8205/709/2/l146 2010

  14. [14]

    doi:10.1038/340126a0

    Eichler, D., Livio, M., Piran, T., et al.\ 1989, , 340, 6229, 126. doi:10.1038/340126a0

    work page doi:10.1038/340126a0 1989

  15. [15]

    & Dai, Z.-G.\ 2011, Research in Astronomy and Astrophysics, 11, 1046

    Feng, S.-Y. & Dai, Z.-G.\ 2011, Research in Astronomy and Astrophysics, 11, 1046. doi:10.1088/1674-4527/11/9/004

    work page doi:10.1088/1674-4527/11/9/004 2011

  16. [16]

    W., Lang, D., & Goodman, J

    Foreman-Mackey, D., Hogg, D. W., Lang, D., et al.\ 2013, , 125, 925, 306. doi:10.1086/670067

    work page doi:10.1086/670067 2013

  17. [17]

    A., Kulkarni, S

    Frail, D. A., Kulkarni, S. R., Sari, R., et al.\ 2001, , 562, 1, L55. doi:10.1086/338119

    work page doi:10.1086/338119 2001

  18. [18]

    14772, \#1 (2013), 14772, 1

    Frederiks, D.\ 2013, GRB Coordinates Network, Circular Service, No. 14772, \#1 (2013), 14772, 1

    2013

  19. [19]

    doi:10.1088/0004-637X/706/1/L33

    Gao, W.-H., Mao, J., Xu, D., et al.\ 2009, , 706, L33. doi:10.1088/0004-637X/706/1/L33

    work page doi:10.1088/0004-637x/706/1/l33 2009

  20. [20]

    doi:10.1086/184741

    Goodman, J.\ 1986, , 308, L47. doi:10.1086/184741

    work page doi:10.1086/184741 1986

  21. [21]

    Communications in Applied Mathematics and Computational Science, Vol

    Goodman, J. & Weare, J.\ 2010, Communications in Applied Mathematics and Computational Science, 5, 1, 65. doi:10.2140/camcos.2010.5.65

    work page doi:10.2140/camcos.2010.5.65 2010

  22. [22]

    doi:10.1051/0004-6361/200811571

    Greiner, J., Clemens, C., Kr \"u hler, T., et al.\ 2009, , 498, 89. doi:10.1051/0004-6361/200811571

    work page doi:10.1051/0004-6361/200811571 2009

  23. [23]

    doi:10.1088/0004-637X/733/1/22

    He, H.-N., Wu, X.-F., Toma, K., et al.\ 2011, , 733, 1, 22. doi:10.1088/0004-637X/733/1/22

    work page doi:10.1088/0004-637x/733/1/22 2011

  24. [24]

    doi:10.3847/1538-4357/aaba6e

    Huang, L.-Y., Wang, X.-G., Zheng, W., et al.\ 2018, , 859, 2, 163. doi:10.3847/1538-4357/aaba6e

    work page doi:10.3847/1538-4357/aaba6e 2018

  25. [25]

    doi:10.3847/1538-4357/abd6bc

    Huang, X.-L., Wang, Z.-R., Liu, R.-Y., et al.\ 2021, , 908, 225. doi:10.3847/1538-4357/abd6bc

    work page doi:10.3847/1538-4357/abd6bc 2021

  26. [26]

    , keywords =

    Huang, Y. F., Dai, Z. G., & Lu, T.\ 1999, , 309, 513. doi:10.1046/j.1365-8711.1999.02887.x

    work page doi:10.1046/j.1365-8711.1999.02887.x 1999

  27. [27]

    M., & Rankin, J

    Kumar, P. & Barniol Duran, R.\ 2010, , 409, 226. doi:10.1111/j.1365-2966.2010.17274.x

    work page doi:10.1111/j.1365-2966.2010.17274.x 2010

  28. [28]

    & Panaitescu, A.\ 2000, , 541, 1, L9

    Kumar, P. & Panaitescu, A.\ 2000, , 541, 1, L9. doi:10.1086/312888

    work page doi:10.1086/312888 2000

  29. [29]

    & Zhang, B.\ 2015, , 561, 1

    Kumar, P. & Zhang, B.\ 2015, , 561, 1. doi:10.1016/j.physrep.2014.09.008

    work page internal anchor Pith review doi:10.1016/j.physrep.2014.09.008 2015

  30. [30]

    Gamma Ray Bursts as Electromagnetic Outflows

    Lyutikov, M. & Blandford, R.\ 2003, astro-ph/0312347. doi:10.48550/arXiv.astro-ph/0312347

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/0312347 2003

  31. [31]

    MacFadyen, A. I. & Woosley, S. E.\ 1999, , 524, 1, 262. doi:10.1086/307790

    work page internal anchor Pith review doi:10.1086/307790 1999

  32. [32]

    & Rees, M

    Meszaros, P. & Rees, M. J.\ 1993, , 405, 278. doi:10.1086/172360

    work page doi:10.1086/172360 1993

  33. [33]

    & Rees, M

    M \'e sz \'a ros, P. & Rees, M. J.\ 2000, , 530, 1, 292. doi:10.1086/308371

    work page doi:10.1086/308371 2000

  34. [34]

    , year = 2005, month = apr, volume =

    Moderski, R., Sikora, M., Coppi, P. S., et al.\ 2005, , 363, 954. doi:10.1111/j.1365-2966.2005.09494.x

    work page doi:10.1111/j.1365-2966.2005.09494.x 2005

  35. [35]

    doi:10.1146/annurev.astro.40.060401.093821

    M \'e sz \'a ros, P.\ 2002, , 40, 137. doi:10.1146/annurev.astro.40.060401.093821

    work page doi:10.1146/annurev.astro.40.060401.093821 2002

  36. [36]

    & Rees, M

    M \'e sz \'a ros, P. & Rees, M. J.\ 1997, , 482, L29. doi:10.1086/310692

    work page doi:10.1086/310692 1997

  37. [37]

    doi:10.1088/0004-637X/703/1/675

    Nakar, E., Ando, S., & Sari, R.\ 2009, , 703, 675. doi:10.1088/0004-637X/703/1/675

    work page doi:10.1088/0004-637x/703/1/675 2009

  38. [38]

    doi:10.1086/186493

    Narayan, R., Paczynski, B., & Piran, T.\ 1992, , 395, L83. doi:10.1086/186493

    work page doi:10.1086/186493 1992

  39. [39]

    doi:10.1086/184740

    Paczynski, B.\ 1986, , 308, L43. doi:10.1086/184740

    work page doi:10.1086/184740 1986

  40. [40]

    & Kumar, P.\ 2000, , 543, 66

    Panaitescu, A. & Kumar, P.\ 2000, , 543, 66. doi:10.1086/317090

    work page doi:10.1086/317090 2000

  41. [41]

    B., Swenson, C

    Pandey, S. B., Swenson, C. A., Perley, D. A., et al.\ 2010, , 714, 799. doi:10.1088/0004-637X/714/1/799

    work page doi:10.1088/0004-637x/714/1/799 2010

  42. [42]

    J., Johnston, S., Ray, P

    Pe'Er, A., Zhang, B.-B., Ryde, F., et al.\ 2012, , 420, 1, 468. doi:10.1111/j.1365-2966.2011.20052.x

    work page doi:10.1111/j.1365-2966.2011.20052.x 2012

  43. [43]

    doi:10.1103/RevModPhys.76.1143

    Piran, T.\ 2004, Reviews of Modern Physics, 76, 1143. doi:10.1103/RevModPhys.76.1143

    work page doi:10.1103/revmodphys.76.1143 2004

  44. [44]

    B., et al.\ 2010, , 709, 2, L172

    Ryde, F., Axelsson, M., Zhang, B. B., et al.\ 2010, , 709, 2, L172. doi:10.1088/2041-8205/709/2/L172

    work page doi:10.1088/2041-8205/709/2/l172 2010

  45. [45]

    9353, \#1 (2009), 9353

    Rau, A., McBreen, S., & Kruehler, T.\ 2009, GRB Coordinates Network, Circular Service, No. 9353, \#1 (2009), 9353

    2009

  46. [46]

    Rees, M. J. & Meszaros, P.\ 1994, , 430, L93. doi:10.1086/187446

    work page doi:10.1086/187446 1994

  47. [47]

    & Esin, A

    Sari, R. & Esin, A. A.\ 2001, , 548, 787. doi:10.1086/319003

    work page doi:10.1086/319003 2001

  48. [48]

    1998, ApJL, 497, L17, doi: 10.1086/311269

    Sari, R., Piran, T., & Narayan, R.\ 1998, , 497, L17. doi:10.1086/311269

    work page doi:10.1086/311269 1998

  49. [49]

    & Piran, T.\ 1990, , 365, L55

    Shemi, A. & Piran, T.\ 1990, , 365, L55. doi:10.1086/185887

    work page doi:10.1086/185887 1990

  50. [50]

    R., Levan, A

    Tanvir, N. R., Levan, A. J., Fruchter, A. S., et al.\ 2013, , 500, 547. doi:10.1038/nature12505

    work page doi:10.1038/nature12505 2013

  51. [51]

    doi:10.1093/mnras/270.3.480

    Thompson, C.\ 1994, , 270, 480. doi:10.1093/mnras/270.3.480

    work page doi:10.1093/mnras/270.3.480 1994

  52. [52]

    J., Johnston, S., Ray, P

    Toma, K., Wu, X.-F., & M \'e sz \'a ros, P.\ 2011, , 415, 1663. doi:10.1111/j.1365-2966.2011.18807.x

    work page doi:10.1111/j.1365-2966.2011.18807.x 2011

  53. [53]

    V.\ 1994, , 267, 1035

    Usov, V. V.\ 1994, , 267, 1035. doi:10.1093/mnras/267.4.1035

    work page doi:10.1093/mnras/267.4.1035 1994

  54. [54]

    D., & Dhuga, K

    Veres, P., Dermer, C. D., & Dhuga, K. S.\ 2017, , 847, 39. doi:10.3847/1538-4357/aa87b1

    work page doi:10.3847/1538-4357/aa87b1 2017

  55. [55]

    & K \"o nigl, A.\ 2003, , 596, 1080

    Vlahakis, N. & K \"o nigl, A.\ 2003, , 596, 1080. doi:10.1086/378226

    work page doi:10.1086/378226 2003

  56. [56]

    doi:10.3847/1538-4357/ac937c

    Wang, X.-G., Chen, Y.-Z., Huang, X.-L., et al.\ 2022, , 939, 1, 39. doi:10.3847/1538-4357/ac937c

    work page doi:10.3847/1538-4357/ac937c 2022

  57. [57]

    doi:10.1088/0004-637X/712/2/1232

    Wang, X.-Y., He, H.-N., Li, Z., et al.\ 2010, , 712, 1232. doi:10.1088/0004-637X/712/2/1232

    work page doi:10.1088/0004-637x/712/2/1232 2010

  58. [58]

    doi:10.3847/1538-4357/aca017

    Wang, Y., Zheng, T.-C., & Jin, Z.-P.\ 2022, , 940, 2, 142. doi:10.3847/1538-4357/aca017

    work page doi:10.3847/1538-4357/aca017 2022

  59. [59]

    Woosley, S. E. & Bloom, J. S.\ 2006, , 44, 1, 507. doi:10.1146/annurev.astro.43.072103.150558

    work page doi:10.1146/annurev.astro.43.072103.150558 2006

  60. [60]

    doi:10.3847/2041-8213/ad40ab

    Xiong, R.-J., Huang, X.-L., & Wang, Z.-R.\ 2024, , 966, 2, L25. doi:10.3847/2041-8213/ad40ab

    work page doi:10.3847/2041-8213/ad40ab 2024

  61. [61]

    doi:10.1017/9781139226530

    Zhang, B.\ 2018, . doi:10.1017/9781139226530

    work page doi:10.1017/9781139226530 2018

  62. [62]

    & Yan, H.\ 2011, , 726, 2, 90

    Zhang, B. & Yan, H.\ 2011, , 726, 2, 90. doi:10.1088/0004-637X/726/2/90

    work page doi:10.1088/0004-637x/726/2/90 2011

  63. [63]

    doi:10.1088/0004-637X/730/2/141

    Zhang, B.-B., Zhang, B., Liang, E.-W., et al.\ 2011, , 730, 141. doi:10.1088/0004-637X/730/2/141

    work page doi:10.1088/0004-637x/730/2/141 2011

  64. [64]

    doi:10.1088/2041-8205/758/2/L34

    Zhang, B., Lu, R.-J., Liang, E.-W., et al.\ 2012, , 758, L34. doi:10.1088/2041-8205/758/2/L34

    work page doi:10.1088/2041-8205/758/2/l34 2012

  65. [65]

    J., et al.\ 2009, , 703, 1696

    Zhang, B., Zhang, B.-B., Virgili, F. J., et al.\ 2009, , 703, 1696. doi:10.1088/0004-637X/703/2/1696

    work page doi:10.1088/0004-637x/703/2/1696 2009

  66. [66]

    doi:10.1016/j.jheap.2024.01.002

    Zhang, B., Wang, X.-Y., & Zheng, J.-H.\ 2024, Journal of High Energy Astrophysics, 41, 42. doi:10.1016/j.jheap.2024.01.002

    work page doi:10.1016/j.jheap.2024.01.002 2024