arxiv: 2604.10378 · v1 · submitted 2026-04-11 · 🌌 astro-ph.HE

Recognition: unknown

Multi-TeV γ-ray candidates from GRB 221009A: a downturn in the intrinsic γ-ray spectrum, an echo of the prompt emission phase, and intergalactic electromagnetic cascades

Timur A. Dzhatdoev , Jagdish C. Joshi , Abhijit Roy , Grigory I. Rubtsov , Anatoly A. Semenov

Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:01 UTC · model grok-4.3

classification 🌌 astro-ph.HE

keywords gamma-ray burstsGRB 221009Aphotohadronic interactionsneutron escapeintergalactic magnetic fieldselectromagnetic cascadesTeV gamma raysspectral downturn

0 comments

The pith

Neutrons from photohadronic interactions in GRB 221009A produce a high-energy echo that explains the observed TeV spectral downturn.

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

The paper reconstructs the intrinsic gamma-ray spectrum of the bright burst GRB 221009A from LHAASO data and finds a clear downturn at several TeV with greater than 5 sigma significance. It attributes part of the multi-TeV flux to neutrons generated by photohadronic processes inside the fireball; these neutrons escape, interact with surrounding matter, and produce electrons and positrons whose synchrotron emission creates a delayed GeV-TeV echo of the prompt phase. The same analysis shows that intergalactic electromagnetic cascades from ultra-high-energy protons contribute negligibly at multi-TeV energies during the early afterglow once the magnetic field in filaments exceeds 1 nG. A reader would care because the mechanism links internal fireball physics directly to late-time high-energy signals and constrains how external cascades shape the observed spectrum.

Core claim

The intrinsic spectrum of GRB 221009A shows a downturn at several TeV. A significant TeV gamma-ray component can be produced by neutrons from photohadronic interactions inside the fireball. These neutrons escape the fireball and interact with the surrounding matter, giving rise to a flux of electrons and positrons that emit GeV-TeV synchrotron photons, forming a high-energy echo of the GRB prompt emission phase. At multi-TeV energies the contribution of gamma rays from intergalactic electromagnetic cascades initiated by primary ultra-high-energy protons is severely limited during the early afterglow phase for typical magnetic field strengths in intergalactic filaments above 1 nG.

What carries the argument

the neutron echo, in which neutrons produced by photohadronic interactions inside the GRB fireball escape and generate secondary electrons and positrons whose synchrotron radiation supplies the GeV-TeV flux

If this is right

The prompt emission phase of GRBs can produce an observable high-energy echo through neutron escape and secondary synchrotron radiation.
Multi-TeV GRB observations can serve as a probe of intergalactic magnetic field strength via the suppression of proton-initiated cascades.
Reconstruction of intrinsic GRB spectra at TeV energies must include possible contributions from the neutron echo in addition to the primary emission.
The early afterglow phase of bright GRBs is expected to show reduced cascade contamination at the highest energies when filament magnetic fields are sufficiently strong.

Where Pith is reading between the lines

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

The same neutron-escape channel could be tested by searching for similar delayed TeV components in other bright GRBs with dense multi-wavelength coverage.
If the echo mechanism operates, it would imply that hadronic processes inside the fireball contribute measurably to the highest-energy afterglow, offering a new window on neutron production rates.
GRB 221009A-like events could be used to place tighter bounds on the intergalactic magnetic field once more precise timing and spectral data become available.
The downturn feature may appear in future LHAASO or CTA observations of other nearby, luminous bursts if the required neutron flux is generic.

Load-bearing premise

The model requires that photohadronic interactions inside the GRB fireball produce a sufficient neutron flux that escapes without significant attenuation and that the intergalactic magnetic field in filaments exceeds 1 nG during the early afterglow phase.

What would settle it

A measurement showing the intergalactic magnetic field strength in filaments below 1 nG, or a calculation demonstrating that the neutron yield from photohadronic interactions is too low to match the observed multi-TeV flux, would invalidate the echo explanation and the cascade suppression result.

Figures

Figures reproduced from arXiv: 2604.10378 by Abhijit Roy, Anatoly A. Semenov, Grigory I. Rubtsov, Jagdish C. Joshi, Timur A. Dzhatdoev.

**Figure 2.** Figure 2: FIG. 2. Same as in Fig. 1, but for the combined LHAASO-WCDA and [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. The intrinsic SED according to Fig. 7B of L23b [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Average observable SEDs of intergalactic EM cas [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

read the original abstract

The detection of $\gamma$-ray candidates up to the energy of $\approx$13 TeV from the exceptionally bright $\gamma$-ray burst GRB 221009A by the Large High Altitude Air-Shower Observatory (LHAASO) has raised considerable interest in the astrophysical community. The $\gamma$-ray dataset resulting from the LHAASO observations allows one to reconstruct the intrinsic spectrum of GRB 221009A with an unprecedented precision. This intrinsic spectrum reveals a downturn at the energy of several TeV (statistical significance $\gt 5 \sigma$), i.e. the reconstructed intensity is below the intensity expected for a power-law spectrum. We show that a significant TeV $\gamma$-ray component may be produced by neutrons from photohadronic interactions inside the fireball. These neutrons escape the fireball and interact with the surrounding matter, giving rise to a flux of electrons and positrons, eventually resulting in an observable flux of GeV--TeV synchrotron photons -- a high energy "echo" of the GRB prompt emission phase. Finally, we show that at multi-TeV energies the contribution of $\gamma$ rays from intergalactic electromagnetic cascades initiated by primary ultra high energy protons is severely limited during the early afterglow phase for the typical magnetic field strength in the intergalactic filaments above 1 nG.

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.

Desk Editor's Note private letter to a colleague

read the letter

The paper reports a >5 sigma downturn in the LHAASO-inferred spectrum of GRB 221009A and attributes part of the multi-TeV flux to a neutron photoproduction echo while limiting IGM cascades above 1 nG. The downturn itself is the clearest new result here, drawn directly from the high-energy data on this bright burst. The neutron-echo channel follows from standard photohadronic rates inside the fireball, with neutrons escaping to produce secondary electrons and synchrotron photons later. The cascade suppression for fields above 1 nG is likewise a direct application of known deflection physics during the early afterglow window. Both pieces connect prompt-phase hadronic activity to observable afterglow emission without introducing new mechanisms. The calculations use established cross sections and fireball parameters, so the logic is internally consistent on its own terms. The abstract frames the echo as one possible contribution rather than the sole explanation, which keeps the claims proportionate. The main limitation is that the neutron yield and escape fraction are set by fireball parameters that are adjusted to the observed flux, and the 1 nG threshold is adopted rather than measured from this dataset. Full error propagation and scans over those inputs are needed to judge how much the fit depends on the choices. No internal contradiction appears in the abstract or stress-test summary, and the paper does not overclaim uniqueness. This work is for people tracking LHAASO GRB spectra and those modeling UHECR propagation or IGM magnetic fields. Readers who need quantitative limits on cascade contributions or a concrete example of prompt-to-afterglow hadronic linking will find it useful. It deserves a serious referee because the observational downturn is sharp and the modeling rests on reproducible physics rather than ad-hoc inventions. Send it for peer review, with the main request being verification of the normalization steps and robustness checks on the free parameters.

Referee Report

3 major / 2 minor

Summary. The paper analyzes LHAASO observations of GRB 221009A and reports a >5σ downturn in the reconstructed intrinsic γ-ray spectrum at energies of several TeV. It proposes that neutrons from photohadronic interactions inside the GRB fireball can escape and interact with surrounding matter to produce an observable GeV–TeV synchrotron 'echo' of the prompt phase. It further argues that intergalactic electromagnetic cascades initiated by ultra-high-energy protons are severely suppressed during the early afterglow for intergalactic magnetic fields B ≳ 1 nG in filaments.

Significance. The data-driven identification of the spectral downturn with high statistical significance is a solid observational result that can constrain GRB emission and propagation models. If the neutron-echo and cascade-suppression calculations are robust, the work offers a physically motivated alternative contribution to the observed TeV flux and provides a potential probe of the intergalactic magnetic field strength. The manuscript correctly frames these as possible rather than unique explanations.

major comments (3)

[data analysis / intrinsic spectrum reconstruction] The >5σ downturn significance is central to the observational claim, but the manuscript does not detail the exact power-law extrapolation, EBL absorption model, or error propagation used in the intrinsic-spectrum reconstruction (see the data-analysis section). Without these steps shown explicitly, the statistical claim cannot be independently verified from the provided information.
[neutron echo / photohadronic model] In the neutron-echo model, the normalization of the escaping neutron flux is tied to fireball photohadronic parameters that appear adjusted to reproduce the observed TeV flux; the paper should provide the explicit equations for neutron production efficiency and escape fraction, together with the range of allowed parameter values, to demonstrate that the echo is not circularly normalized.
[intergalactic cascade section] The cascade-suppression argument adopts a magnetic-field threshold of 1 nG without showing the sensitivity of the multi-TeV flux limit to variations around this value or to the precise timing of the early-afterglow phase; a brief parameter scan or analytic dependence on B would strengthen the conclusion.

minor comments (2)

[abstract] The abstract states 'statistical significance >5σ' but does not specify whether this is for the downturn relative to a single power law or after marginalizing over EBL uncertainties; a one-sentence clarification would help.
[model description] Notation for the neutron-to-proton ratio and the synchrotron cooling time in the echo calculation should be defined at first use to improve readability for readers outside the GRB modeling community.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. Their comments have highlighted areas where additional clarity and detail will strengthen the presentation. We address each major comment below and will incorporate the necessary revisions to improve verifiability and transparency.

read point-by-point responses

Referee: [data analysis / intrinsic spectrum reconstruction] The >5σ downturn significance is central to the observational claim, but the manuscript does not detail the exact power-law extrapolation, EBL absorption model, or error propagation used in the intrinsic-spectrum reconstruction (see the data-analysis section). Without these steps shown explicitly, the statistical claim cannot be independently verified from the provided information.

Authors: We agree that the current description lacks sufficient detail for independent verification. In the revised manuscript we will expand the data-analysis section to explicitly state: the functional form and fitting range used for the power-law extrapolation, the precise EBL model adopted (including the reference and any redshift-dependent assumptions), and the complete error-propagation procedure that combines statistical and systematic uncertainties to arrive at the >5σ significance. Relevant equations and a concise numerical example will be added to allow readers to reproduce the intrinsic-spectrum reconstruction. revision: yes
Referee: [neutron echo / photohadronic model] In the neutron-echo model, the normalization of the escaping neutron flux is tied to fireball photohadronic parameters that appear adjusted to reproduce the observed TeV flux; the paper should provide the explicit equations for neutron production efficiency and escape fraction, together with the range of allowed parameter values, to demonstrate that the echo is not circularly normalized.

Authors: We acknowledge the referee’s concern regarding parameter transparency. The revised manuscript will include the explicit analytic expressions for the neutron production efficiency (derived from the photohadronic optical depth and target-photon spectrum) and the neutron escape fraction (accounting for the fireball radius and neutron lifetime). We will also tabulate the physically allowed ranges for the baryon-loading factor, bulk Lorentz factor, and target-photon density, demonstrating that these values remain consistent with independent prompt-emission constraints and do not require ad-hoc adjustment solely to match the TeV flux. revision: yes
Referee: [intergalactic cascade section] The cascade-suppression argument adopts a magnetic-field threshold of 1 nG without showing the sensitivity of the multi-TeV flux limit to variations around this value or to the precise timing of the early-afterglow phase; a brief parameter scan or analytic dependence on B would strengthen the conclusion.

Authors: We thank the referee for this useful suggestion. In the revision we will add a short analytic derivation of the deflection angle and time-delay dependence on B, together with a compact parameter scan (or table) illustrating how the multi-TeV cascade flux upper limit changes for B between 0.1 nG and 10 nG and for plausible variations in the afterglow onset time. This will explicitly confirm that suppression remains effective for B ≳ 1 nG while quantifying the sensitivity to the adopted threshold. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper models a possible neutron-echo component via standard photohadronic rates inside the fireball and subsequent pair synchrotron emission, plus a conditional limit on IGM cascades for B ≳ 1 nG. These steps use literature values for fireball parameters and IGMF strength rather than fitting them to force the TeV downturn or echo flux. No equation reduces by construction to its own input, no self-citation chain carries the central claim, and the result is presented as one possible contribution rather than a unique prediction. The derivation therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard GRB fireball physics and intergalactic propagation assumptions rather than new axioms, but several free parameters (fireball baryon loading, neutron escape fraction, intergalactic B-field) are required to match the observed flux.

free parameters (2)

intergalactic magnetic field strength threshold
Set at >1 nG to suppress cascade contribution at multi-TeV energies during early afterglow.
neutron production efficiency in fireball
Determines the amplitude of the synchrotron echo component.

axioms (2)

domain assumption Photohadronic interactions inside the GRB fireball produce a substantial neutron flux that escapes the source region.
Invoked to generate the echo; standard in hadronic GRB models but not re-derived here.
domain assumption Intergalactic filaments contain magnetic fields of typical strength above 1 nG during the early afterglow epoch.
Used to limit electromagnetic cascade development.

pith-pipeline@v0.9.0 · 5595 in / 1575 out tokens · 55738 ms · 2026-05-10T15:01:12.040518+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

120 extracted references · 7 canonical work pages · 2 internal anchors

[1]

Multi-TeV $\gamma$-ray candidates from GRB 221009A: a downturn in the intrinsic $\gamma$-ray spectrum, an echo of the prompt emission phase, and intergalactic electromagnetic cascades

GRB 201216C [5], and 5) GRB 221009A [6, 7] (here- after L23a,L23b). The observations of GRB 221009A are unique in more than one respect: this GRB was ex- ceptionally bright [8–10] [11] and relatively nearby (red- shift z = 0 . 151 [12–14]), while the principal observing detector in the VHE range (the LHAASO array [15]) has an excellent sensitivity and a l...

work page internal anchor Pith review Pith/arXiv arXiv 2026
[2]

III of [40]

(hereafter G12) and obtain a ﬁt to the spectrum mea- sured with LHAASO following the approach described in Sect. III of [40]. As an example, we take the spec- trum measured with the LHAASO-WCDA sub-detector for the time range of 326–900 s (see Supplementary In- formation, Fig. S4C in L23a); hereafter all time ranges are measured since the Fermi-GBM trigge...
[3]

neutron beam model

294, for the PWL option γ = 2. 35 and p = 1. 22 × 10− 72 corresponding to Z = 18 σ . For the time range of 230– 300 s the same values are Ec = 2 . 91 TeV, γ = 1 . 96, and p = 0 . 672 for the EPWL option and γ = 2 . 43, p = 3 . 22 × 10− 23 corresponding to Z = 9 . 9σ for the PWL option. 1−10 1 10 E [TeV] 7−10 6−10 ]-1s-2cm dN/dE [erg2E FIG. 3. The intrinsi...
[4]

weak universality

1 × 10− 4 erg/cm2 ≈ 1. 9SHard . We conclude that the ﬂuence of these synchrotron photons in the considered scenario is suﬃcient to ﬁll the gap between the intrinsic SED and the SSC model in Fig. 3. Following [52], the temporal width of the emission pulse of the hard component may be estimated as ∆ tm = R(1 − cos(θj))/c , where R is the distance from the c...
[5]

ﬁnd Breg− f il = (0. 05 − 0. 15)Bf il. Assuming Bf il = 10 nG, Breg− f il = 0 . 1Bf il = 1 nG, df il = 1 Mpc (e.g. [70]), and Ep = 30 EeV, we get fBDE = 1. Further- more, for most models considered in [71], they estimate ∆ df il = 15 − 25 Mpc; assuming ∆ df il = 20 Mpc, we obtain the value of ∆ t = 5 . 7 × 106 yr, which exceeds the LHAASO observation time...
[6]

the absorption and redshift-only model

(hereafter H22), including the detection of a γ-ray candidate with the reconstructed energy of 18 TeV, many studies have concluded that the conventional framework of “the absorption and redshift-only model”, accounting for only the attenuation of the primary γ-ray ﬂux on the EBL photons and adiabatic losses, is not suﬃcient to interpret the information co...
[7]

MAGIC Collaboration, Nature 575, 455 (2019)

2019
[8]

V. A. Acciari, S. Ansoldi, L. A. Antonelli, A. A. Engels, D. Baack, and et al., Nature 575, 459 (2019)

2019
[9]

Abdalla, R

H. Abdalla, R. Adam, F. Aharonian, F. Ait Benkhali, E. O. Ang¨ uner, and et al., Nature 575, 464 (2019)

2019
[10]

Abdalla, F

H. Abdalla, F. Aharonian, F. Ait Benkhali, E. O. Ang¨ uner, C. Arcaro, and et al., Science 372, 1081 (2021)

2021
[11]

H. Abe, S. Abe, V. A. Acciari, I. Agudo, T. Aniello, and et al., MNRAS 527, 5856 (2023)

2023
[12]

Z. Cao, F. Aharonian, Q. An, Axikegu, L. X. Bai, and et al., Science 380, 1390 (2023)

2023
[13]

The LHAASO Collaboration, Science Advances 9, eadj2778 (2023)

2023
[14]

Lesage, P

S. Lesage, P. Veres, M. S. Briggs, A. Goldstein, D. Kocevski, and et al., The Astrophysical Journal Letters 952, L42 (2023)

2023
[15]

M. A. Williams, J. A. Kennea, S. Dichiara, K. Kobayashi, W. B. Iwakiri, and et al., The Astrophysical Journal Letters 946, L24 (2023)

2023
[16]

Burns, D

E. Burns, D. Svinkin, E. Fenimore, D. A. Kann, J. F. Agui Fernandez, and et al., The Astrophysical Journal Letters 946, L31 (2023)

2023
[17]

the brightest of all time

GRB 221009A is sometimes referred to as “the brightest of all time” (BOAT) [10]
[18]

de Ugarte Postigo, L

A. de Ugarte Postigo, L. Izzo, G. Pugliese, D. Xu, B. Schneider, and et al., GRB Coordinates Network 32648, 1 (2022)

2022
[19]

A. J. Castro-Tirado, R. Sanchez-Ramirez, Y. D. Hu, M. D. Caballero-Garcia, M. A. Castro Tirado, and et al., GRB Coordinates Network 32686, 1 (2022)

2022
[20]

D. B. Malesani, A. J. Levan, L. Izzo, A. de Ugarte Postigo, G. Ghirlanda, and et al., Astronomy & Astrophysics 701, A134 (2025)

2025
[21]

Ma, Y.-J

X.-H. Ma, Y.-J. Bi, Z. Cao, M.-J. Chen, S.-Z. Chen, and et al., Chinese Physics C 46, 030001 (2022)

2022
[22]

A. I. Nikishov, Sov. Phys. JETP 14, 393 (1962)

1962
[23]

R. J. Gould and G. P. Schr´ eder, Phys. Rev. 155, 1408 (1967)

1967
[24]

S. V. Troitsky, JETP Letters 116, 767 (2022)

2022
[25]

Galanti, L

G. Galanti, L. Nava, M. Ron- cadelli, F. Tavecchio, and G. Bonnoli, Physical Review Letters 131, 251001 (2023)

2023
[26]

Galanti, M

G. Galanti, M. Roncadelli, and F. Tavecchio, Assessment of ALP scenarios for GRB 221009A (2022)

2022
[27]

Carenza and M

P. Carenza and M. C. D. Marsh, On ALP scenarios and GRB 221009A (2022)

2022
[28]

Baktash, D

A. Baktash, D. Horns, and M. Meyer, Interpretation of multi-TeV photons from GRB221009A (2022)

2022
[29]

Wang and B.-Q

L. Wang and B.-Q. Ma, Physical Review D 108, 023002 (2023). 7

2023
[30]

M. M. Gonzalez, D. Avila Rojas, A. Pratts, S. Hernandez-Cadena, N. Fraija, R. Al- faro, Y. Perez Araujo, and J. A. Montes, The Astrophysical Journal 944, 178 (2023)

2023
[31]

Lin and T

W. Lin and T. T. Yanagida, Chinese Physics Letters 40, 069801 (2023)

2023
[32]

Nakagawa, F

S. Nakagawa, F. Takahashi, M. Yamada, and W. Yin, Physics Letters B 839, 137824 (2023)

2023
[33]

Zhang and B.-Q

G. Zhang and B.-Q. Ma, Chinese Physics Letters 10.1088/0256-307x/40/01/011401 (2022)

work page doi:10.1088/0256-307x/40/01/011401 2022
[34]

Avila Rojas, S

D. Avila Rojas, S. Hernandez-Cadena, M. M. Gon- zalez, A. Pratts, R. Alfaro, and J. Serna-Franco, The Astrophysical Journal 966, 114 (2024)

2024
[35]

J. D. Finke and S. Razzaque, The Astrophysical Journal Letters 942, L21 (2023)

2023
[36]

Li and B.-Q

H. Li and B.-Q. Ma, JCAP 2023 (10), 061

2023
[37]

Li and B.-Q

H. Li and B.-Q. Ma, Modern Physics Letters A 39, 10.1142/s0217732323502012 (2024)

work page doi:10.1142/s0217732323502012 2024
[38]

P. S. Satunin and S. V. Troitsky, JETP Letters 123, 73 (2026)

2026
[39]

A. Y. Smirnov and A. Trautner, Physical Review Letters 131, 021002 (2023)

2023
[40]

Balaji, M

S. Balaji, M. E. Ramirez-Quezada, J. Silk, and Y. Zhang, Physical Review D 107, 083038 (2023)

2023
[41]

S.-Y. Guo, M. Khlopov, L. Wu, and B. Zhu, Physical Review D 108, L021302 (2023)

2023
[42]

Brdar and Y.-Y

V. Brdar and Y.-Y. Li, Physics Letters B 839, 137763 (2023)

2023
[43]

Huang, Y

J. Huang, Y. Wang, B. Yu, and S. Zhou, JCAP 2023 (04), 056

2023
[44]

Aghanim, Y

N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, and et al., Astronomy & Astrophysics 641, A6 (2020)

2020
[45]

R. C. Gilmore, R. S. Somerville, J. R. Primack, and A. Dom ´ ınguez, MNRAS422, 3189 (2012)

2012
[46]

Dzhatdoev, E

T. Dzhatdoev, E. Podlesnyi, and I. Vaiman, Physical Review D 102, 123017 (2020)

2020
[47]

Lazzati, MNRAS 357, 722 (2005)

D. Lazzati, MNRAS 357, 722 (2005)

2005
[48]

P. A. Zyla, R. M. Barnett, J. Beringer, O. Dahl, D. A. Dwyer, and et al., Progress of Theoretical and Experi- mental Physics 2020, 10.1093/ptep/ptaa104 (2020)

work page doi:10.1093/ptep/ptaa104 2020
[49]

Saldana-Lopez, A

A. Saldana-Lopez, A. Dominguez, P. G. Perez- Gonzalez, J. Finke, M. Ajello, J. R. Primack, V. S. Paliya, and A. Desai, MNRAS 507, 5144–5160 (2021)

2021
[50]

T. A. Dzhatdoev, Talk at the RICAP-24 conference (2024)

2024
[51]

Dzhappuev, I

D. Dzhappuev, I. Dzaparova, T. Dzhat- doev, E. Gorbacheva, I. Karpikov, and et al., Physical Review D 111, 102005 (2025)

2025
[52]

S. R. Kelner and F. A. Aharonian, Physical Review D 78, 034013 (2008)

2008
[53]

This approximation is justiﬁed in the scenario with an isotropic target photon ﬁeld internal to the ﬁreball
[54]

We note, however, that an additional neutron ﬂux may come from the process of photodisintegration of nuclei, see Appendix B
[55]

Knapp, D

J. Knapp, D. Heck, and G. Schatz, Comparison of hadronic interaction models used in air shower simula- tions and of their inﬂuence on shower development and observables (1996)

1996
[56]

S. R. Kelner, F. A. Aharonian, and V. V. Bugayov, Physical Review D 74, 034018 (2006)

2006
[57]

M. R. Krumholz and C. F. McKee, Nature 451, 1082 (2008)

2008
[58]

C. D. Dermer and A. Atoyan, Astronomy & Astrophysics 418, L5 (2004)

2004
[59]

W. J. Forrest and M. A. Shure, The Astrophysical Journal 311, L81 (1986)

1986
[60]

Khangulyan, M

D. Khangulyan, M. Arakawa, and F. Aharonian, MNRAS 491, 3217 (2019)

2019
[61]

R. M. Crutcher, ApJ 520, 706 (1999)

1999
[62]

Razzaque, O

S. Razzaque, O. Mena, and C. D. Dermer, The Astrophysical Journal 691, L37 (2009)

2009
[63]

T. A. Dzhatdoev, E. I. Podlesnyi, and G. I. Rubtsov, MNRAS Lett. 527, L95–L102 (2023)

2023
[64]

Waxman and P

E. Waxman and P. Coppi, The Astrophysical Journal 464, L75 (1996)

1996
[65]

Berezinsky, A

V. Berezinsky, A. Gazizov, and S. Grigorieva, Physical Review D 74, 043005 (2006)

2006
[66]

A. V. Uryson, JETP 86, 213 (1998)

1998
[67]

Das and S

S. Das and S. Razzaque, Astronomy & Astrophysics 670, L12 (2023)

2023
[68]

Mirabal, MNRAS Lett

N. Mirabal, MNRAS Lett. 519, L85–L86 (2022)

2022
[69]

V. S. Berezinsky and A. Y. Smirnov, Astrophysics and Space Science 32, 461–482 (1975)

1975
[70]

Berezinsky, O

V. Berezinsky and O. Kalashev, Physical Review D 94, 10.1103/physrevd.94.023007 (2016)

work page doi:10.1103/physrevd.94.023007 2016
[71]

T. A. Dzhatdoev, E. V. Khalikov, A. P. Kircheva, and A. A. Lyukshin, Astronomy & Astrophysics 603, A59 (2017)

2017
[72]

E. V. Khalikov and T. A. Dzhatdoev, MNRAS 505, 1940–1953 (2021)

1940
[73]

Alcock and S

C. Alcock and S. Hatchett, The Astrophysical Journal 222, 456 (1978)

1978
[74]

Carretti, F

E. Carretti, F. Vazza, S. P. O’Sullivan, V. Vacca, A. Bonafede, G. Heald, C. Horel- lou, S. Mtchedlidze, and T. Vernstrom, Astronomy & Astrophysics 693, A208 (2025)

2025
[75]

Vernstrom, G

T. Vernstrom, G. Heald, F. Vazza, T. J. Galvin, J. L. West, N. Locatelli, N. Fornengo, and E. Pinetti, MNRAS 505, 4178–4196 (2021)

2021
[76]

Q.-R. Yang, W. Zhu, G.-Y. Yu, J.-F. Mo, Y. Zheng, and L.-L. Feng, The Astrophysical Journal 989, 187 (2025)

2025
[77]

Tjemsland, M

J. Tjemsland, M. Meyer, and F. Vazza, The Astrophysical Journal 963, 135 (2024)

2024
[78]

Huang, S

Y. Huang, S. Hu, S. Chen, M. Zha, C. Liu, and et al., GRB Coordinates Network 32677, 1 (2022)

2022
[79]

Tang and H

R. Tang and H. Zhou on behalf of the LHAASO collab- oration, Talk at the ICRC-2025 conference (2025)

2025
[80]

W. Cao, Y. Luo, R. Tang, J. Wang, and H. Zhou on behalf of the LHAASO collaboration, Talk at the ICRC- 2025 conference (2025)

2025

Showing first 80 references.