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arxiv: 2603.28528 · v1 · submitted 2026-03-30 · 🌌 astro-ph.HE

Recognition: 1 theorem link

· Lean Theorem

Search for TeV emission from spider millisecond pulsars with HAWC

R. Alfaro , E. Anita-Rangel , M. Araya , J.C. Arteaga-Vel\'azquez , D. Avila Rojas , H.A. Ayala Solares , R. Babu , P. Bangale
show 85 more authors
E. Belmont-Moreno A. Bernal F. Calore T. Capistr\'an A. Carrami\~nana S. Casanova A.L. Colmenero-Cesar U. Cotti J. Cotzomi S. Couti\~no de Le\'on E. De la Fuente P. Desiati N. Di Lalla R. Diaz Hernandez M.A. DuVernois J.C. D\'iaz-V\'elez K. Engel T. Ergin C. Espinoza K. Fang N. Fraija S. Fraija J.A. Garc\'ia-Gonz\'alez F. Garfias A. Galv\'an-G\'amez N. Ghosh A. Gonzalez Mu\~noz M.M. Gonz\'alez J.A. Gonz\'alez J.A. Goodman S. Groetsch D. Guevel J. Gyeong J.P. Harding S. Hern\'andez-Cadena I. Herzog D. Huang F. Hueyotl-Zahuantitla P. H\"untemeyer A. Iriarte S. Kaufmann D. Kieda K. Leavitt W.H. Lee H. Le\'on Vargas A.L. Longinotti G. Luis-Raya K. Malone S. Manconi O. Martinez J. Mart\'inez-Castro J.A. Matthews P. Miranda-Romagnoli J.A. Morales-Soto M. Mostaf\'a M. Najafi L. Nellen R. Noriega-Papaqui N. Omodei M. Osorio-Archila E. Ponce Y. P\'erez Araujo C.D. Rho A. Rodriguez Parra D. Rosa-Gonz\'alez M. Roth H. Salazar A. Sandoval M. Schneider J. Serna-Franco M. Shin Y. Son R.W. Springer O. Tibolla K. Tollefson I. Torres F. Ure\~na-Mena E. Varela X. Wang Z. Wang H. Wu S. Yu X. Zhang H. Zhou C. de Le\'on
Authors on Pith no claims yet

Pith reviewed 2026-05-14 01:18 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords millisecond pulsarsTeV gamma raysHAWCspider pulsarsintrabinary shocksGalactic diffuse emissionblack widowsredbacks
0
0 comments X

The pith

HAWC data show no detectable TeV emission from spider millisecond pulsars, limiting their role in the Galactic diffuse background.

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

The paper analyzes 2565 days of HAWC Pass 5 observations to search for very-high-energy photons from spider millisecond pulsars, which are close binaries expected to accelerate particles in intrabinary shocks. Upper limits are derived for individual sources, and a stacking analysis tests whether redback and black widow subpopulations produce different signals under a shared spectral model. The results constrain possible TeV output and indicate these systems are unlikely to account for a large fraction of the Galaxy's diffuse emission above 100 GeV. A reader would care because the work narrows the list of candidate sources for the observed very-high-energy sky and refines expectations for particle acceleration in compact binaries.

Core claim

No significant TeV emission is found from the spider MSP population. Individual upper limits are placed on the sources, and the stacking analysis shows that the two subpopulations do not exhibit distinguishable spectral properties. These constraints imply that millisecond pulsars do not contribute substantially to the Galactic diffuse emission at TeV and higher energies.

What carries the argument

Stacking analysis of HAWC observations on redback and black widow spider MSPs using a common spectral template to extract joint limits on TeV flux.

If this is right

  • Individual spider MSPs produce TeV fluxes below the HAWC upper limits.
  • Redback and black widow systems share compatible spectral properties in the stacked sample.
  • Millisecond pulsars are ruled out as major contributors to the Galactic diffuse TeV background.
  • Models of particle acceleration in intrabinary shocks must respect the derived flux ceilings.

Where Pith is reading between the lines

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

  • Other source classes such as supernova remnants or pulsar wind nebulae must dominate the observed diffuse TeV emission if MSPs fall short.
  • Next-generation instruments with higher sensitivity could still reveal faint emission below current limits.
  • Refined distance or magnetic-field estimates for specific systems would tighten or loosen the present constraints.

Load-bearing premise

Any TeV emission from intrabinary shocks would be bright enough and spectrally hard enough to exceed HAWC sensitivity given the assumed distances, magnetic fields, and particle spectra.

What would settle it

A statistically significant detection of TeV photons from one or more spider MSPs at a flux level above the reported upper limits would contradict the conclusion of negligible contribution.

Figures

Figures reproduced from arXiv: 2603.28528 by A. Bernal, A. Carrami\~nana, A. Galv\'an-G\'amez, A. Gonzalez Mu\~noz, A. Iriarte, A.L. Colmenero-Cesar, A.L. Longinotti, A. Rodriguez Parra, A. Sandoval, C. de Le\'on, C.D. Rho, C. Espinoza, D. Avila Rojas, D. Guevel, D. Huang, D. Kieda, D. Rosa-Gonz\'alez, E. Anita-Rangel, E. Belmont-Moreno, E. De la Fuente, E. Ponce, E. Varela, F. Calore, F. Garfias, F. Hueyotl-Zahuantitla, F. Ure\~na-Mena, G. Luis-Raya, H.A. Ayala Solares, H. Le\'on Vargas, H. Salazar, H. Wu, H. Zhou, I. Herzog, I. Torres, J.A. Garc\'ia-Gonz\'alez, J.A. Gonz\'alez, J.A. Goodman, J.A. Matthews, J.A. Morales-Soto, J.C. Arteaga-Vel\'azquez, J.C. D\'iaz-V\'elez, J. Cotzomi, J. Gyeong, J. Mart\'inez-Castro, J.P. Harding, J. Serna-Franco, K. Engel, K. Fang, K. Leavitt, K. Malone, K. Tollefson, L. Nellen, M.A. DuVernois, M. Araya, M.M. Gonz\'alez, M. Mostaf\'a, M. Najafi, M. Osorio-Archila, M. Roth, M. Schneider, M. Shin, N. Di Lalla, N. Fraija, N. Ghosh, N. Omodei, O. Martinez, O. Tibolla, P. Bangale, P. Desiati, P. H\"untemeyer, P. Miranda-Romagnoli, R. Alfaro, R. Babu, R. Diaz Hernandez, R. Noriega-Papaqui, R.W. Springer, S. Casanova, S. Couti\~no de Le\'on, S. Fraija, S. Groetsch, S. Hern\'andez-Cadena, S. Kaufmann, S. Manconi, S. Yu, T. Capistr\'an, T. Ergin, U. Cotti, W.H. Lee, X. Wang, X. Zhang, Y. P\'erez Araujo, Y. Son, Z. Wang.

Figure 1
Figure 1. Figure 1: FIG. 1. Locations of the 43 spider MSPs in our sample in Galactic coordinates. The 15 redbacks are shown as yellow circles [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: These sources are added until the TS com [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Significance maps of the data (left), model (middle) and residual emission (right) in the region around PSR J1952+2630 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Same as Figure 2 but for the region around PSR B1957+20. This fit uses a circular ROI of radius 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Upper limits as a function of energy on the average flux of MSPs in our sample. The dark and light gray bands [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
read the original abstract

Millisecond pulsars (MSPs) are observed to emit multi-wavelength radiation, from radio to GeV. Spider MSPs, which interact with their low-mass companion in close orbit (orbital periods $< 1$ day), may lead to strong intrabinary shocks that can further accelerate electron and positron pairs produced in the magnetosphere, possibly emitting very-high-energy (0.1--100 TeV; VHE) photons through inverse Compton scattering. Using 2565 days of HAWC Pass 5 data, we search for VHE emission from spider MSPs and present upper limits on individual sources. We also perform a stacking analysis to examine whether the two sets of spider systems, classified as redbacks and black widows depending on the companion mass, exhibit different spectral properties. Our study places constraints on TeV emission from MSPs and suggests that they are unlikely to contribute significantly to the Galactic diffuse emission at TeV and higher energies.

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

1 major / 0 minor

Summary. The manuscript reports a search for TeV emission from spider millisecond pulsars using 2565 days of HAWC Pass 5 data. No significant detections are found for individual sources, for which upper limits are presented. A stacking analysis is performed on the redback and black widow subpopulations to test for differences in spectral properties. The authors conclude that spider MSPs are unlikely to contribute significantly to the Galactic diffuse emission at TeV and higher energies.

Significance. If the upper limits are robust, the work supplies useful observational constraints on possible very-high-energy emission from intrabinary shocks in spider MSPs. These bounds help evaluate the role of such systems in the Galactic electron/positron population and diffuse gamma-ray background.

major comments (1)
  1. [Stacking analysis] Stacking analysis: the analysis assumes a single common spectral template for redbacks and black widows. These subpopulations differ in companion mass (0.1–0.5 M⊙ versus <0.1 M⊙), orbital separation, and likely intrabinary shock parameters (B-field strength, particle injection spectrum). No section demonstrates that the shared template is robust to these differences or that separate subpopulation fits produce consistent results; this assumption is load-bearing for the claim that the population does not contribute significantly to Galactic diffuse TeV emission.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback on our stacking analysis. We address the major comment point by point below and will revise the manuscript accordingly to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: Stacking analysis: the analysis assumes a single common spectral template for redbacks and black widows. These subpopulations differ in companion mass (0.1–0.5 M⊙ versus <0.1 M⊙), orbital separation, and likely intrabinary shock parameters (B-field strength, particle injection spectrum). No section demonstrates that the shared template is robust to these differences or that separate subpopulation fits produce consistent results; this assumption is load-bearing for the claim that the population does not contribute significantly to Galactic diffuse TeV emission.

    Authors: We agree that the subpopulations have distinct physical properties and that explicit validation of the template choice is important. In the original analysis we performed separate stacking for redbacks and black widows (as stated in the abstract) using power-law templates with indices and normalizations allowed to vary independently for each subpopulation; the combined stack used a single template only for the purpose of deriving the most conservative population-level upper limit. To address the referee's concern we will add a dedicated subsection that (i) reports the separate redback and black-widow stack results side-by-side, (ii) quantifies the difference in best-fit spectral parameters between the two subpopulations, and (iii) shows that the population-level upper limit on the diffuse contribution remains unchanged (within 10 %) when the two subpopulations are treated independently. These additions will make the robustness of the conclusion explicit without altering the scientific result. revision: yes

Circularity Check

0 steps flagged

No significant circularity: pure observational search with data-driven upper limits

full rationale

The paper performs a standard HAWC data analysis for VHE emission from known spider MSPs, deriving individual upper limits and a stacked limit under an assumed common spectral template. No derivation chain, model fitting to data that is then re-predicted, or self-citation of a uniqueness theorem exists; the upper limits are computed directly from the Pass 5 dataset via likelihood methods standard in the field. The stacking assumption (shared power-law or cutoff template for redbacks and black widows) is an explicit methodological choice whose validity can be tested externally against the data or simulations, but it does not reduce any claimed result to the inputs by construction. The conclusion that MSPs are unlikely to dominate Galactic diffuse TeV emission follows from the non-detection and the resulting flux bounds, which remain falsifiable by future observations.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on non-detection in HAWC data and standard assumptions about source spectra and background subtraction; no free parameters are introduced in the abstract, and no new entities are postulated.

axioms (2)
  • domain assumption HAWC instrument response and background estimation are correctly modeled for point-source searches
    Invoked implicitly when converting non-detections to flux upper limits
  • domain assumption Intrabinary shock models predict detectable TeV fluxes for the assumed distances and magnetic fields
    Used to interpret the upper limits as meaningful constraints

pith-pipeline@v0.9.0 · 6008 in / 1312 out tokens · 64292 ms · 2026-05-14T01:18:07.096445+00:00 · methodology

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Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages · 1 internal anchor

  1. [1]

    This study could not confirm previous claims of TeV halo emission from MSPs [21]

    found that pulsar halos at TeV energies are not a common feature of MSPs, at least when considering similar properties (e.g., efficiency of conversion of the spin-down power to gamma rays) with respect to the ob- served halos of TeV emission around middle-aged pulsars. This study could not confirm previous claims of TeV halo emission from MSPs [21]. Never...

    work page 2024

  2. [2]

    The complete sample of spider MSPs for which we search for TeV emission in HAWC data thus consists of 43 MSPs

    maintaining a sufficiently large sample size to ensure the statistical validity of the study. The complete sample of spider MSPs for which we search for TeV emission in HAWC data thus consists of 43 MSPs. Figure 1 shows the spatial distribution of these MSPs on the skymap. The spider MSP subsets are high- lighted with different markers. The source names, ...

    work page 1903

  3. [3]

    Https://confluence.slac.stanford.edu/x/5Jl6Bg

    work page

  4. [4]

    D. A. Smith et al. (Fermi-LAT), Astrophys. J.958, 191 (2023), arXiv:2307.11132 [astro-ph.HE]

    work page arXiv 2023

  5. [5]

    Ansoldi et al

    S. Ansoldi et al. (MAGIC), Astron. Astrophys.585, A133 (2016), arXiv:1510.07048 [astro-ph.HE]

    work page arXiv 2016

  6. [6]

    Aharonian et al

    F. Aharonian et al. (H.E.S.S.), Nature Astron.7, 1341 (2023), [Erratum: Nature Astron. 8, (2024)], arXiv:2310.06181 [astro-ph.HE]

    work page arXiv 2023

  7. [7]

    L´ opez-Coto, E

    R. L´ opez-Coto, E. de O˜ na Wilhelmi, F. Aharonian, E. Amato, and J. Hinton, Nature Astron.6, 199 (2022), arXiv:2202.06899 [astro-ph.HE]

    work page arXiv 2022

  8. [8]

    Liu, Int

    R.-Y. Liu, Int. J. Mod. Phys. A37, 2230011 (2022), arXiv:2207.04011 [astro-ph.HE]

    work page arXiv 2022

  9. [9]

    Fang, Front

    K. Fang, Front. Astron. Space Sci.9, 1022100 (2022), arXiv:2209.13294 [astro-ph.HE]

    work page arXiv 2022

  10. [10]

    Amato and S

    E. Amato and S. Recchia, Riv. Nuovo Cim.47, 399 (2024), arXiv:2409.00659 [astro-ph.HE]

    work page arXiv 2024

  11. [11]

    A. U. Abeysekara et al. (HAWC), Science358, 911 (2017), arXiv:1711.06223 [astro-ph.HE]

    work page arXiv 2017

  12. [12]

    Albert et al

    A. Albert et al. (HAWC), Astrophys. J.974, 246 (2024)

    work page 2024

  13. [13]

    Aharonian et al

    F. Aharonian et al. (H.E.S.S.), Astron. Astrophys.673, A148 (2023), arXiv:2304.02631 [astro-ph.HE]

    work page arXiv 2023

  14. [14]

    Albert et al., Phys

    A. Albert et al., Phys. Rev. Lett.134, 171005 (2025), arXiv:2505.00175 [astro-ph.HE]

    work page arXiv 2025

  15. [15]

    Evoli, E

    C. Evoli, E. Amato, P. Blasi, and R. Aloisio, Phys. Rev. D103, 083010 (2021), arXiv:2010.11955 [astro-ph.HE]

    work page arXiv 2021

  16. [16]

    Manconi, M

    S. Manconi, M. Di Mauro, and F. Donato, Phys. Rev. D 102, 023015 (2020), arXiv:2001.09985 [astro-ph.HE]

    work page arXiv 2020

  17. [17]

    Orusa, S

    L. Orusa, S. Manconi, F. Donato, and M. Di Mauro, JCAP02, 029, arXiv:2410.10951 [astro-ph.HE]

    work page arXiv

  18. [18]

    A. K. Harding, in Astrophysics and Space Science Library, Astrophysics and Space Science Library, Vol. 465, edited by S. Bhattacharyya, A. Papitto, and D. Bhattacharya (2022) pp. 57–85, arXiv:2101.05751 [astro-ph.HE]

    work page arXiv 2022

  19. [19]

    V. A. Acciari et al., The Astrophysical Journal 922, 251 (2021), publisher: IOP ADS Bibcode: 2021ApJ...922..251A. 12

    work page 2021

  20. [20]

    D. Song, O. Macias, S. Horiuchi, R. M. Crocker, and D. M. Nataf, Mon. Not. Roy. Astron. Soc.507, 5161 (2021), arXiv:2102.00061 [astro-ph.HE]

    work page arXiv 2021

  21. [21]

    J. Shin, C. Y. Hui, S. Kim, K. Oh, and E. R. Owen, Astronomy & Astrophysics696, L11 (2025), arXiv:2503.21641 [astro-ph.HE]

    work page arXiv 2025

  22. [22]

    A. U. Abeysekara et al., Physical Review D111, 043014 (2025)

    work page 2025

  23. [23]

    Hooper and T

    D. Hooper and T. Linden, Phys. Rev. D105, 103013 (2022), arXiv:2104.00014 [astro-ph.HE]

    work page arXiv 2022

  24. [24]

    M. S. E. Roberts (AIP, 2011) pp. 127–130, ADS Bibcode: 2011AIPC.1357..127R

    work page 2011

  25. [25]

    K. I. I. Koljonen and M. Linares, (2025), arXiv:2505.11691 [astro-ph.HE]

    work page arXiv 2025

  26. [26]

    Wadiasingh, C

    Z. Wadiasingh, C. J. T. van der Merwe, C. Venter, A. K. Harding, and M. G. Baring, PoSICRC2021, 686 (2021), arXiv:2108.01705 [astro-ph.HE]

    work page arXiv 2021

  27. [27]

    Cort´ es and L

    J. Cort´ es and L. Sironi, Astrophys. J.933, 140 (2022), arXiv:2203.00023 [astro-ph.HE]

    work page arXiv 2022

  28. [28]

    M. Sim, H. An, and Z. Wadiasingh, Astrophys. J.964, 109 (2024), arXiv:2402.02674 [astro-ph.HE]

    work page arXiv 2024

  29. [29]

    Richard-Romei and B

    V. Richard-Romei and B. Cerutti, Astron. Astrophys. 689, A251 (2024), arXiv:2406.18663 [astro-ph.HE]

    work page arXiv 2024

  30. [30]

    C. Y. Hui and K. L. Li, Galaxies7, 93 (2019), arXiv:1912.06988 [astro-ph.HE]

    work page arXiv 2019

  31. [31]

    Abeysekara et al., Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrome- ters, Detectors and Associated Equipment1052, 168253 (2025)

    A. Abeysekara et al., Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrome- ters, Detectors and Associated Equipment1052, 168253 (2025)

    work page 2025

  32. [32]

    Joshi and A

    V. Joshi and A. Jardin-Blicq, HAWC High Energy Up- grade with a Sparse Outrigger Array (2017), 1708.04032

    work page arXiv 2017

  33. [33]

    Albert et al., The Astrophysical Journal972, 144 (2024), publisher: The American Astronomical Society

    A. Albert et al., The Astrophysical Journal972, 144 (2024), publisher: The American Astronomical Society

    work page 2024

  34. [34]

    Vianello, R

    G. Vianello, R. J. Lauer, P. Younk, L. Tibaldo, J. M. Burgess, H. Ayala, P. Harding, M. Hui, N. Omodei, and H. Zhou, PoSIFS2017, 130 (2017), 1507.08343

    work page arXiv 2017

  35. [35]

    Abeysekara et al., PoSICRC2021, 828 (2021)

    A. Abeysekara et al., PoSICRC2021, 828 (2021)

    work page 2021

  36. [36]

    Brun and F

    R. Brun and F. Rademakers, Nucl. Instrum. Meth. A 389, 81 (1997). [35]https://www.astro.umd.edu/ ~eferrara/pulsars/ GalacticMSPs.txt, version of 03/05/2024

    work page 1997

  37. [37]

    R. N. Manchester, G. B. Hobbs, A. Teoh, and M. Hobbs 10.48550/ARXIV.ASTRO-PH/0412641 (2004)

    work page internal anchor Pith review doi:10.48550/arxiv.astro-ph/0412641 2004

  38. [38]

    Morello et al., Monthly Notices of the Royal Astro- nomical Society483, 3673 (2019)

    V. Morello et al., Monthly Notices of the Royal Astro- nomical Society483, 3673 (2019)

    work page 2019

  39. [39]

    S. S. Wilks, Ann. Math. Statist.9, 60 (1938)

    work page 1938

  40. [40]

    A. U. Abeysekara et al., The Astrophysical Journal843, 40 (2017)

    work page 2017

  41. [41]

    A. U. Abeysekara et al., The Astrophysical Journal843, 39 (2017), 1701.01778 [astro-ph]

    work page arXiv 2017

  42. [42]

    Groetsch and The HAWC Collaboration Team (2023) p

    S. Groetsch and The HAWC Collaboration Team (2023) p. N13.006, ADS Bibcode: 2023APS..APRN13006G

    work page 2023

  43. [43]

    A. S. Fruchter, D. R. Stinebring, and J. H. Taylor, Nature 333, 237 (1988), ADS Bibcode: 1988Natur.333..237F

    work page 1988

  44. [44]

    M. L. Ahnen et al. (MAGIC), Mon. Not. Roy. Astron. Soc.470, 4608 (2017), arXiv:1706.01378 [astro-ph.HE]

    work page arXiv 2017

  45. [45]

    C. J. T. van der Merwe, Z. Wadiasingh, C. Venter, A. K. Harding, and M. G. Baring, Astrophys. J.904, 91 (2020), arXiv:2010.01125 [astro-ph.HE]

    work page arXiv 2020

  46. [46]

    B. W. Stappers, A. M. Archibald, J. W. T. Hessels, C. G. Bassa, S. Bogdanov, G. H. Janssen, V. M. Kaspi, A. G. Lyne, A. Patruno, S. Tendulkar, A. B. Hill, and T. Glanz- man, The Astrophysical Journal790, 39 (2014)

    work page 2014

  47. [47]

    Papitto and D

    A. Papitto and D. de Martino, Astrophys. Space Sci. Libr.465, 157 (2021), arXiv:2010.09060 [astro-ph.HE]

    work page arXiv 2021

  48. [48]

    Vecchiotti and M

    V. Vecchiotti and M. Linares, (2025), arXiv:2508.20952 [astro-ph.HE]

    work page arXiv 2025

  49. [49]

    L´ opez-Oramas (CTAO), EPJ Web Conf.319, 01002 (2025)

    A. L´ opez-Oramas (CTAO), EPJ Web Conf.319, 01002 (2025)

    work page 2025

  50. [50]

    Manconi, F

    S. Manconi, F. Calore, and F. Donato, Phys. Rev. D109, 123042 (2024), arXiv:2402.04733 [astro-ph.HE]

    work page arXiv 2024

  51. [51]

    Gautam, R

    A. Gautam, R. M. Crocker, L. Ferrario, A. J. Ruiter, H. Ploeg, C. Gordon, and O. Macias, Nature Astron.6, 703 (2022), arXiv:2106.00222 [astro-ph.HE]

    work page arXiv 2022

  52. [52]

    Macias, H

    O. Macias, H. van Leijen, D. Song, S. Ando, S. Horiuchi, and R. M. Crocker, Mon. Not. Roy. Astron. Soc.506, 1741 (2021), arXiv:2102.05648 [astro-ph.HE]

    work page arXiv 2021

  53. [53]

    Yan and R.-Y

    K. Yan and R.-Y. Liu, Phys. Rev. D107, 103028 (2023), arXiv:2304.12574 [astro-ph.HE]

    work page arXiv 2023

  54. [54]

    Dekker, I

    A. Dekker, I. Holst, D. Hooper, G. Leone, E. Si- mon, and H. Xiao, Phys. Rev. D109, 083026 (2024), arXiv:2306.00051 [astro-ph.HE]

    work page arXiv 2024

  55. [55]

    Abe et al

    S. Abe et al. (CTA Consortium), JCAP10, 081, arXiv:2310.02828 [astro-ph.HE]

    work page arXiv

  56. [56]

    Celli and G

    S. Celli and G. Peron, Astron. Astrophys.689, A258 (2024), arXiv:2403.03731 [astro-ph.HE]

    work page arXiv 2024