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REVIEW 2 major objections 4 minor 79 references

Exploring Constraints on Axion-like Particles with the Observations for blazar Mrk 501

T0 review · 2 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Mrk 501 axion limit tightens tenfold if its jet is hadronic.

desk verdict A solid ALP limit update for Mrk 501, but the magnetic-field-structure comparison rests on a single point in a wide parameter space; the hadronic vs leptonic gap is the robust part. read the letter →

arxiv 2501.18860 v2 pith:TNH2DXHP submitted 2025-01-31 astro-ph.HE

Ting Zhou , Lin-Qing Gao , Xiao-Jun Bi , Peng-Fei Yin , Wenbin Lin This is my paper · ORCID
classification astro-ph.HE
keywords axion-likeparticlesALP-photonoscillationsblazarMrk501jetmagneticfieldmodelsleptonicandhadronicemissionscenariosgamma-rayspectralirregularitiesFermi-LATMAGIC
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper is trying to establish that the constraints astrophysical gamma-ray observations place on axion-like particles are not set by the data alone: they depend on which physical model describes the blazar's emission and which magnetic field structure is assumed inside its jet. Using the 2017-2019 Fermi-LAT and MAGIC spectrum of Mrk 501, the authors show that a hadronic emission scenario, with a magnetic field about two orders of magnitude stronger than a leptonic one, excludes ALP-photon couplings down to roughly $g_{a\gamma} \sim 2.5\times 10^{-13}\,\mathrm{GeV}^{-1}$ at $m_a\sim 4\times 10^{-9}\,\mathrm{eV}$, while the leptonic scenario gives much weaker limits. It also shows that a toroidal jet field and a helical+tangled field produce different exclusion regions, especially beyond about 1 pc from the central black hole. The point of the exercise is that ALP searches from blazars inherit the full uncertainty of blazar emission modeling.

What carries the argument

The machinery is the ALP-photon mixing formalism: a three-state beam $(A_1,A_2,a)$ evolving under the mixing matrix $\mathcal{M}_0$, whose off-diagonal element $\Delta_{a\gamma}=g_{a\gamma}B_t/2$ drives photon-to-ALP conversion in a transverse magnetic field. The survival probability $P_{\gamma\gamma}$ is computed with the density-matrix version of the propagation equation using the gammaALPs package, after propagating through the jet, extragalactic space (with EBL absorption), and the Galactic magnetic field. The other load-bearing ingredient is the multi-wavelength SED fit: the leptonic and hadronic models fix different emission-region field strengths $B_0$, and the two jet field models (toroidal $B\propto r^{-1}$, and helical+tangled with parameters $\alpha$, $r_T$, and $f$) set how that field extends along the jet. Constraints are obtained by a $\chi^2$ scan over $(m_a,g_{a\gamma})$ with the CLs method, because the non-linear ALP spectral distortions make Wilks' theorem inapplicable.

What would settle it

Re-run the four $\chi^2$ scans with $\alpha$ varied over 0.2 to 1.5, $r_T$ over 0.1 to 10 pc, and $f$ over 0 to 0.7, using the same Fermi-LAT and MAGIC spectral bins and the same gammaALPs propagation; if the hadronic toroidal contour no longer reaches $g_{a\gamma}\sim 2.5\times 10^{-13}\,\mathrm{GeV}^{-1}$ at $m_a\sim 4\times 10^{-9}$ eV, the paper's headline result is not robust to the model choice.

Watch

Extended reading notes

Core claim

The central claim is that Mrk 501's gamma-ray spectrum, which is equally well described by a leptonic and a hadronic one-zone model, already excludes new regions of ALP parameter space, and the exclusion strength is controlled by the assumed emission scenario and jet magnetic field structure. Under the hadronic scenario with a toroidal jet field the constraints are most stringent, reaching $g_{a\gamma}\approx 2.5\times 10^{-13}\,\mathrm{GeV}^{-1}$ for $m_a\approx 4.0\times 10^{-9}\,\mathrm{eV}$. The hadronic scenario's much larger emission-region magnetic field ($B_0=3$ G versus $0.029$ G in the leptonic case) strengthens ALP-photon mixing and therefore sharpens the limits. The toroidal and helical+tangled jet field models give visibly different exclusion contours, with the toroidal model being more restrictive at high ALP masses ($m_a\sim 10^{-7}{-}10^{-6}$ eV), because the transverse field strengths differ by nearly an order of magnitude for distances $r>1$ pc.

Load-bearing premise

The key assumption is that one representative set of helical+tangled jet magnetic field parameters ($\alpha=1$, $r_T=0.3$ pc, $f=0.3$) captures the difference between jet field models, even though the paper itself quotes wide allowed ranges for these parameters.

Editorial extensions

If this is right

  • If the hadronic scenario for Mrk 501 is correct, its current Fermi-LAT and MAGIC data already complement dedicated ALP searches such as CAST in the mass range near $10^{-9}$ eV.
  • Future very-high-energy observations by LHAASO or CTA should sharpen the hadronic-scenario contours further, since the same method benefits from more precise spectral measurements.
  • If neutrino observations show Mrk 501's high-energy emission is leptonic rather than hadronic, the corresponding ALP constraints would weaken by roughly an order of magnitude, so the ALP limit and the blazar emission model are inseparable.
  • The difference between toroidal and helical+tangled jet field models means that ALP constraints from blazars carry a systematic uncertainty from jet magnetic field structure that is comparable in size to the statistics of the gamma-ray data.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper fixes the helical+tangled model at $\alpha=1$, $r_T=0.3$ pc, and $f=0.3$; if the full ranges quoted from the simulation literature were scanned, the toroidal-versus-helical+tangled difference could shrink, move, or disappear at some parameter combinations.
  • A natural extension would be to apply the same treatment to other high-synchrotron-peaked blazars with both leptonic and hadronic SED fits; sources with stronger hadronic $B_0$ values would be expected to give proportionally stronger ALP limits.
  • Because the hadronic constraints become nearly mass-independent below $m_a\sim 10^{-9}$ eV (where the QED term dominates the mixing matrix), low-mass ALP searches using hadronic blazar models may be limited mainly by the coupling reach of the spectrum, not by the ALP mass.
  • The leptonic-scenario constraints being weaker means that published blazar ALP limits that assume only leptonic emission may underestimate the excluded region if nature is hadronic, and may overstate it if the magnetic field is weaker than assumed.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper studies ALP-photon oscillations in the high-energy gamma-ray spectrum of the blazar Mrk 501, using Fermi-LAT and MAGIC data from 2017-06-17 to 2019-07-23. The authors compare two emission scenarios for the spectral energy distribution (leptonic and hadronic) and two jet magnetic field models (toroidal and helical+tangled). The magnetic field strength in the emission region is taken from multi-wavelength fitting: the leptonic scenario is fitted in this work with agnpy, while the hadronic scenario parameters are imported from a previous MAGIC analysis. The ALP-photon propagation is computed with gammaALPs, and 95% C.L. constraints on the ALP mass and coupling are derived using the CLs method. The main reported result is that the hadronic scenario yields much more stringent constraints than the leptonic scenario, reaching roughly g_aγ ~ 2.5e-13 GeV^-1 for m_a ~ 4e-9 eV, and that the choice of magnetic field model also affects the constraints.

Significance. If the results are robust, they provide new ALP constraints from a well-observed blazar and, more importantly, demonstrate that the assumed jet emission scenario and magnetic field geometry can change the derived ALP limits by about an order of magnitude or more. This is a useful contribution to the ALP literature because it quantifies model dependence in a specific source. The use of public data and codes (Fermi-LAT, MAGIC, gammaALPs) and the adoption of the CLs method (rather than naive Wilks' theorem) are methodological strengths. However, the central claim about the role of magnetic field structure is currently supported by only a single point in the helical+tangled parameter space, so the significance of that claim is not yet established.

major comments (2)
  1. [Sec. 3, Table 1] The claim that the magnetic field structure plays a significant role in the ALP constraints rests entirely on one adopted point in the helical+tangled model parameter space: α=1, r_T=0.3 pc, f=0.3. The manuscript itself quotes the allowed ranges α∈[0.2,1.5], r_T∈[0.1,10] pc, f∈[0,0.7] from Ref. [48], but no scan or robustness check over these ranges is presented. Since the difference between the toroidal and helical+tangled constraints is attributed to the field strength at r>1 pc (Fig. 2), and since the transverse field profile in the helical+tangled model is controlled by exactly these three parameters, a different point in the quoted parameter space could reduce or remove the claimed difference. The sentence 'Given the uncertainty in precisely determining these parameters, we adopt specific values' acknowledges the issue but does not resolve it. I request a robustness scan, or at least extremal cases (e.g., f→0, r_T→10 pc), to establish whether the qualitative conclusion is stable.
  2. [Sec. 3, Table 1] This is a load-bearing issue for the central comparison between leptonic and hadronic scenarios.
minor comments (4)
  1. [General] There are several typos: 'and and back' in the introduction, 'milit-wavelength' in the introduction, 'to to ascertain' in the conclusion, and 'The is equation... V on Neumann-like' in Sec. 2.1.
  2. [Sec. 4] The CLs method is referenced to Ref. [41] but the specific implementation (e.g., number of toy experiments, treatment of nuisance parameters) is not described in the text. Since CLs is central to the statistical analysis, a brief summary or at least a statement of the adopted confidence level construction would improve reproducibility.
  3. [Fig. 4] The heat maps and black contour lines in Fig. 4 are difficult to read in places, especially in the hadronic panels where the χ2 structure is highly oscillatory. Consider showing the contours on a separate panel or using a different color scale.
  4. [Sec. 5] The conclusion that the magnetic field structure 'plays a significant role' is qualitative. A quantitative statement—for example, the maximum difference in excluded g_aγ between the two B-field models at a given mass—would strengthen the claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: ALP constraints are obtained by scanning parameters against observed spectra with B-field inputs fixed by independent SED fits.

full rationale

The paper's derivation chain is not circular. The ALP-photon propagation uses standard mixing equations (Eqs. 2.2-2.8) and survival probabilities computed with gammaALPs; no ALP parameter appears in the input B-field or SED fits. B0 values are determined independently: leptonic B0=0.029 G is obtained from multi-wavelength SED fitting via agnpy, while hadronic B0=3 G and related parameters are taken from the MAGIC Collaboration's SED modeling in Ref. [47] (Sec. 3, Tab. 1). The intrinsic spectrum is fitted to the Fermi-LAT/MAGIC data under the null hypothesis, and the TS scan over (ma, gaγ) in Eq. 4.2 directly compares ALP-modified spectra to the same data; this is a standard search rather than a fit renamed as a prediction. The helical+tangled BJMF parameters α=1, rT=0.3 pc, f=0.3 are adopted from the gammaALPs package (Ref. [64]) rather than fitted to the ALP result, and the paper itself notes the uncertainty in these parameters; this is a robustness or parameter-coverage concern, not circularity. Self-citations (e.g., Refs. [40], [41], [43], [74], [75]) are to methodology and prior applications of the same CLs/spectral procedure; they do not define the central input or the exclusion contours. The central claim that the hadronic B-field strength yields more stringent ALP limits follows from the adopted B0 values and the propagation equations, not from the definition of any fitted parameter.

Assumptions & free parameters 7 free parameters · 7 assumptions · 0 invented entities

The central ALP constraints rest on two fitted B0 values (0.029 G and 3 G), several hand-set parameters (R, delta_D, alpha, r_T, f), and a chain of external models (Galactic B-field, EBL, jet geometry). Nothing here is invented; the ALP is the pre-existing hypothesis under test. The heaviest unverified inputs are the single-point choices for the helical+tangled model.

free parameters (7)
  • B0 (leptonic) = 0.029 G
    Best-fit magnetic field in the emission region from the agnpy multi-wavelength SED fit (Table 1); sets the normalization of the jet B-field profile used in the ALP calculation.
  • B0 (hadronic) = 3 G
    Magnetic field strength taken from the hadronic SED fit in Ref. [47] (Table 1); used as the normalization for the hadronic jet B-field profile.
  • R (emission region radius) = 1.14e17 cm
    Adopted from the SED fits in Ref. [47]; enters the ALP calculation through r_VHE = R/theta.
  • delta_D (Doppler factor) = 11
    Adopted from Ref. [47]; assumed equal to the bulk Lorentz factor with theta = 1/Gamma, fixing r_VHE.
  • alpha (helical field decay index) = 1
    Chosen, not fitted, for the helical+tangled model, within the quoted range 0.2 to 1.5 from Ref. [48]; no robustness scan is provided.
  • r_T (helical-to-toroidal transition radius) = 0.3 pc
    Chosen value within the quoted range 0.1 to 10 pc from Ref. [48]; not varied.
  • f (tangled fraction) = 0.3
    Chosen value within the quoted range 0 to 0.7 from Ref. [48]; not varied.
assumptions (7)
  • standard math ALP-photon mixing formalism (Raffelt-Stodolsky), Eqs. 2.1 to 2.8
    Unproved background physics in this paper; standard in all ALP-photon oscillation studies.
  • domain assumption Initial gamma-ray beam is unpolarized with state diag(1/2, 1/2, 0)
    Polarization of VHE blazar gamma-rays is unmeasured; assumed unpolarized in Sec. 2.1.
  • domain assumption Negligible ALP-photon oscillations in extragalactic space; only EBL absorption
    Sec. 2.2 states the extragalactic magnetic field is assumed too weak (below about 1e-9 G) to matter.
  • domain assumption Galactic magnetic field described by the Unger-Farrar base model from Ref. [61]
    External model; the paper cross-checks with Jansson-Farrar [63] and finds consistent results.
  • domain assumption Blazar jet magnetic field is either purely toroidal (B ~ r^-1) or helical+tangled as in Ref. [48]
    Secs. 2.2 and 5; the field geometry is the central object under study, so its model form is load-bearing.
  • domain assumption r_VHE = R/theta with theta = 1/Gamma and Gamma = delta_D = 11
    Sec. 3; fixes the starting point of the ALP-photon beam in the jet.
  • ad hoc to paper The intrinsic VHE spectrum is one of four smooth parametric forms, with LP selected by AIC
    Sec. 4: the choice among SEPWL, LP, ELP, and EPWL is based on small AIC differences (LP 10.4 versus SEPWL 11.1), and spectral irregularities beyond these smooth forms could masquerade as ALP signals.

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Pith. "Pith review of Exploring Constraints on Axion-like Particles with the Observations for blazar Mrk 501." pith.science (2026). https://pith.science/paper/TNH2DXHP

@misc{pith2026250118860,
  author       = {Pith},
  title        = {Pith review of: Exploring Constraints on Axion-like Particles with the Observations for blazar Mrk 501},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TNH2DXHP}},
  note         = {Machine review of arXiv:2501.18860}
}
read the original abstract

Oscillations between axion-like particles (ALPs) and photons in astrophysical magnetic fields can lead to irregularities in the high energy gamma ray spectra of blazars. The magnetic field within the blazar jet plays a crucial role in shaping these effects, with its strength in the emission region being an important parameter determined by multi-wavelength observations. However, the origin of the high energy bump observed in the spectral energy distribution of some blazars is a topic of debate, with both leptonic and hadronic scenarios providing plausible explanations that result in different magnetic field strengths in the emission region. In this study, we investigate the impact of magnetic field configurations on the constraints of ALP parameters. We consider both leptonic and hadronic emission scenarios for the blazar Mrk 501 and derive the corresponding jet magnetic field strengths. Additionally, we explore two jet magnetic field models: one with a toroidal component and the other with helical and tangled components. By analyzing the spectra of Mrk 501 observed by MAGIC and Fermi-LAT from 2017-06-17 to 2019-07-23, which are well-described by both emission scenarios, we derive constraints on the ALP parameters. Our results demonstrate that both the emission scenario and the magnetic field structure play a significant role in deriving these constraints, with the hadronic model leading to much more stringent limits compared to the leptonic model.

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Reference graph

Works this paper leans on

79 extracted references · 20 canonical work pages

  1. [48]

    Davies, M

    J. Davies, M. Meyer, and G. Cotter, Phys. Rev. D 103, 023008 (2021), 2011.08123

    arXiv 2021

  2. [1]

    R. D. Peccei and H. R. Quinn, Phys. Rev. D 16, 1791 (1977)

    1977

  3. [2]

    R. D. Peccei, Lect. Notes Phys. 741, 3 (2008), hep-ph/0607268

    arXiv 2008

  4. [3]

    Weinberg, Phys

    S. Weinberg, Phys. Rev. Lett. 40, 223 (1978)

    1978

  5. [4]

    Wilczek, Phys

    F. Wilczek, Phys. Rev. Lett. 40, 279 (1978)

    1978

  6. [5]

    Jaeckel and A

    J. Jaeckel and A. Ringwald, Ann. Rev. Nucl. Part. Sci. 60, 405 (2010), 1002.0329

    arXiv 2010

  7. [6]

    Svrcek and E

    P. Svrcek and E. Witten, JHEP 06, 051 (2006), hep-th/0605206

    arXiv 2006

  8. [7]

    Arvanitaki, S

    A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, and J. March-Russell, Phys. Rev. D 81, 123530 (2010), 0905.4720. – 11 –

    arXiv 2010

Show all 79 references
  1. [8]

    D. J. E. Marsh, Phys. Rept. 643, 1 (2016), 1510.07633

    2016 arXiv

  2. [9]

    Ra ffelt and L

    G. Ra ffelt and L. Stodolsky, Phys. Rev. D37, 1237 (1988)

    1988

  3. [10]

    W. B. Atwood et al. (Fermi-LAT), Astrophys. J. 697, 1071 (2009), 0902.1089

    2009 arXiv

  4. [11]

    Aleksi ´c et al

    J. Aleksi ´c et al. (MAGIC), Astropart. Phys. 72, 76 (2016), 1409.5594

    2016 arXiv

  5. [12]

    Albert et al

    A. Albert et al. (HAWC), Astrophys. J. 905, 76 (2020), 2007.08582

    2020 arXiv

  6. [13]

    Addazi et al

    A. Addazi et al. (LHAASO), Chin. Phys. C 46, 035001 (2022), 1905.02773

    2022

  7. [14]

    De Angelis, M

    A. De Angelis, M. Roncadelli, and O. Mansutti, Phys. Rev. D 76, 121301 (2007), 0707.4312

    2007 arXiv

  8. [15]

    Hooper and P

    D. Hooper and P. D. Serpico, Phys. Rev. Lett. 99, 231102 (2007), 0706.3203

    2007 arXiv

  9. [16]

    Simet, D

    M. Simet, D. Hooper, and P. D. Serpico, Phys. Rev. D 77, 063001 (2008), 0712.2825

    2008 arXiv

  10. [17]

    Mirizzi, G

    A. Mirizzi, G. G. Ra ffelt, and P. D. Serpico, Phys. Rev. D76, 023001 (2007), 0704.3044

    2007 arXiv

  11. [18]

    A. V . Belikov, L. Goodenough, and D. Hooper, Phys. Rev. D83, 063005 (2011), 1007.4862

    2011 arXiv

  12. [19]

    De Angelis, G

    A. De Angelis, G. Galanti, and M. Roncadelli, Phys. Rev. D 84, 105030 (2011), [Erratum: Phys.Rev.D 87, 109903 (2013)], 1106.1132

    2011 arXiv

  13. [20]

    Horns, L

    D. Horns, L. Maccione, M. Meyer, A. Mirizzi, D. Montanino, and M. Roncadelli, Phys. Rev. D 86, 075024 (2012), 1207.0776

    2012 arXiv

  14. [21]

    Abramowski et al

    A. Abramowski et al. (H.E.S.S.), Phys. Rev. D 88, 102003 (2013), 1311.3148

    2013 arXiv

  15. [22]

    Meyer, D

    M. Meyer, D. Horns, and M. Raue, Phys. Rev. D 87, 035027 (2013), 1302.1208

    2013 arXiv

  16. [23]

    Tavecchio, M

    F. Tavecchio, M. Roncadelli, and G. Galanti, Phys. Lett. B 744, 375 (2015), 1406.2303

    2015 arXiv

  17. [24]

    Meyer, D

    M. Meyer, D. Montanino, and J. Conrad, JCAP 09, 003 (2014), 1406.5972

    2014 arXiv

  18. [25]

    Meyer and J

    M. Meyer and J. Conrad, JCAP 12, 016 (2014), 1410.1556

    2014 arXiv

  19. [26]

    Ajello et al

    M. Ajello et al. (Fermi-LAT), Phys. Rev. Lett. 116, 161101 (2016), 1603.06978

    2016 arXiv

  20. [27]

    Meyer, M

    M. Meyer, M. Giannotti, A. Mirizzi, J. Conrad, and M. A. S ´anchez-Conde, Phys. Rev. Lett.118, 011103 (2017), 1609.02350

    2017 arXiv

  21. [28]

    Berenji, J

    B. Berenji, J. Gaskins, and M. Meyer, Phys. Rev. D 93, 045019 (2016), 1602.00091

    2016 arXiv

  22. [29]

    Galanti, F

    G. Galanti, F. Tavecchio, M. Roncadelli, and C. Evoli, Mon. Not. Roy. Astron. Soc. 487, 123 (2019), 1811.03548

    2019 arXiv

  23. [30]

    Galanti and M

    G. Galanti and M. Roncadelli, JHEAp 20, 1 (2018), 1805.12055

    2018 arXiv

  24. [31]

    Zhang, Y .-F

    C. Zhang, Y .-F. Liang, S. Li, N.-H. Liao, L. Feng, Q. Yuan, Y .-Z. Fan, and Z.-Z. Ren, Phys. Rev. D97, 063009 (2018), 1802.08420

    2018 arXiv

  25. [32]

    Liang, C

    Y .-F. Liang, C. Zhang, Z.-Q. Xia, L. Feng, Q. Yuan, and Y .-Z. Fan, JCAP06, 042 (2019), 1804.07186

    2019 arXiv

  26. [33]

    X.-J. Bi, Y . Gao, J. Guo, N. Houston, T. Li, F. Xu, and X. Zhang, Phys. Rev. D103, 043018 (2021), 2002.01796

    2021 arXiv

  27. [34]

    Guo, H.-J

    J. Guo, H.-J. Li, X.-J. Bi, S.-J. Lin, and P.-F. Yin, Chin. Phys. C 45, 025105 (2021), 2002.07571

    2021 arXiv

  28. [35]

    Li, X.-J

    H.-J. Li, X.-J. Bi, and P.-F. Yin, Chin. Phys. C 46, 085105 (2022), 2110.13636

    2022 arXiv

  29. [36]

    Cheng, Y .-J

    J.-G. Cheng, Y .-J. He, Y .-F. Liang, R.-J. Lu, and E.-W. Liang, Phys. Lett. B821, 136611 (2021), 2010.12396

    2021 arXiv

  30. [37]

    Liang, X.-F

    Y .-F. Liang, X.-F. Zhang, J.-G. Cheng, H.-D. Zeng, Y .-Z. Fan, and E.-W. Liang, JCAP11, 030 (2021), 2012.15513

    2021 arXiv

  31. [38]

    Z.-Q. Xia, C. Zhang, Y .-F. Liang, L. Feng, Q. Yuan, Y .-Z. Fan, and J. Wu, Phys. Rev. D97, 063003 (2018), 1801.01646. – 12 –

    2018 arXiv

  32. [39]

    B. P. Pant, Sunanda, R. Moharana, and S. S., Phys. Rev. D 108, 023016 (2023), 2210.12652

    2023 arXiv

  33. [40]

    Li, J.-G

    H.-J. Li, J.-G. Guo, X.-J. Bi, S.-J. Lin, and P.-F. Yin, Phys. Rev. D 103, 083003 (2021), 2008.09464

    2021 arXiv

  34. [41]

    Gao, X.-J

    L.-Q. Gao, X.-J. Bi, J.-G. Guo, W. Lin, and P.-F. Yin, Phys. Rev. D109, 063003 (2024), 2309.02166

    2024 arXiv

  35. [42]

    B. P. Pant, Phys. Rev. D 109, 023011 (2024), 2310.16634

    2024 arXiv

  36. [43]

    Gao, X.-J

    L.-Q. Gao, X.-J. Bi, J. Li, and P.-F. Yin, JCAP 01, 031 (2025), 2407.20118

    2025 arXiv

  37. [44]

    Bu and Y .-P

    J. Bu and Y .-P. Li, Res. Astron. Astrophys.19, 154 (2019), 1906.00357

    2019 arXiv

  38. [45]

    Armando, P

    G. Armando, P. Panci, J. Weiss, and R. Ziegler, Phys. Rev. D 109, 055029 (2024), 2310.05827

    2024 arXiv

  39. [46]

    Aleksi ´c et al

    J. Aleksi ´c et al. (MAGIC, VERITAS), Astron. Astrophys.573, A50 (2015), 1410.6391

    2015 arXiv

  40. [47]

    Abe et al

    H. Abe et al. (MAGIC), Astrophys. J. Suppl. 266, 37 (2023), 2210.02547

    2023 arXiv

  41. [49]

    Prior and K

    C. Prior and K. N. Gourgouliatos, Astron. Astrophys. 622, A122 (2019), 1901.05442

    2019 arXiv

  42. [50]

    Murphy, T

    E. Murphy, T. V . Cawthorne, and D. C. Gabuzda, Mon. Not. Roy. Astron. Soc.430, 1504 (2013), 1302.0186

    2013 arXiv

  43. [51]

    Dobrynina, A

    A. Dobrynina, A. Kartavtsev, and G. Ra ffelt, Phys. Rev. D 91, 083003 (2015), 1412.4777

    2015 arXiv

  44. [52]

    Mirizzi and D

    A. Mirizzi and D. Montanino, JCAP 12, 004 (2009), 0911.0015

    2009 arXiv

  45. [53]

    Galanti and M

    G. Galanti and M. Roncadelli, Universe 8, 253 (2022), 2205.00940

    2022 arXiv

  46. [54]

    R. E. Pudritz, M. J. Hardcastle, and D. C. Gabuzda, Space Sci. Rev. 169, 27 (2012), 1205.2073

    2012 arXiv

  47. [55]

    M. C. Begelman, R. D. Blandford, and M. J. Rees, Rev. Mod. Phys. 56, 255 (1984)

    1984

  48. [56]

    S. P. O’Sullivan and D. C. Gabuzda, Mon. Not. Roy. Astron. Soc. 400, 26 (2009), 0907.5211

    2009 arXiv

  49. [57]

    P. P. Kronberg, Rept. Prog. Phys. 57, 325 (1994)

    1994

  50. [58]

    Blasi, S

    P. Blasi, S. Burles, and A. V . Olinto, Astrophys. J. Lett.514, L79 (1999), astro-ph/9812487

    1999 arXiv

  51. [59]

    Durrer and A

    R. Durrer and A. Neronov, Astron. Astrophys. Rev. 21, 62 (2013), 1303.7121

    2013 arXiv

  52. [60]

    Franceschini, G

    A. Franceschini, G. Rodighiero, and M. Vaccari, Astron. Astrophys. 487, 837 (2008), 0805.1841

    2008 arXiv

  53. [61]

    Unger and G

    M. Unger and G. R. Farrar, Astrophys. J. 970, 95 (2024), 2311.12120

    2024 arXiv

  54. [62]

    J. M. Yao, R. N. Manchester, and N. Wang, Astrophys. J. 835, 29 (2017)

    2017

  55. [63]

    Jansson and G

    R. Jansson and G. R. Farrar, Astrophys. J. Lett. 761, L11 (2012), 1210.7820

    2012 arXiv

  56. [64]

    Meyer, J

    M. Meyer, J. Davies, and J. Kuhlmann, PoS ICRC2021, 557 (2021), 2108.02061

    2021 arXiv

  57. [65]

    Galanti, M

    G. Galanti, M. Roncadelli, and F. Tavecchio, Phys. Rev. D 108, 083017 (2023), 2301.08204

    2023 arXiv

  58. [66]

    Zabalza, PoS ICRC2015, 922 (2016), 1509.03319

    V . Zabalza, PoS ICRC2015, 922 (2016), 1509.03319

    2016 arXiv

  59. [67]

    Tramacere, E

    A. Tramacere, E. Massaro, and A. M. Taylor, Astrophys. J. 739, 66 (2011), 1107.1879

    2011 arXiv

  60. [68]

    Nigro, J

    C. Nigro, J. Sitarek, P. Gliwny, D. Sanchez, A. Tramacere, and M. Craig, Astron. Astrophys. 660, A18 (2022), 2112.14573

    2022 arXiv

  61. [69]

    P. E. Freeman, S. Doe, and A. Siemiginowska, Proc. SPIE Int. Soc. Opt. Eng. 4477, 76 (2001), astro-ph/0108426

    2001 arXiv

  62. [70]

    S. S. Wilks, The Annals of Mathematical Statistics 9, 60 (1938), URL https://doi.org/10.1214/aoms/1177732360

    1938

  63. [71]

    Junk, Nucl

    T. Junk, Nucl. Instrum. Meth. A 434, 435 (1999), hep-ex/9902006

    1999 arXiv

  64. [72]

    A. L. Read, J. Phys. G 28, 2693 (2002)

    2002

  65. [73]

    Lista, in 2016 European School of High-Energy Physics (2017), pp

    L. Lista, in 2016 European School of High-Energy Physics (2017), pp. 213–258, 1609.04150. – 13 –

    2017 arXiv

  66. [74]

    Li, X.-J

    J. Li, X.-J. Bi, L.-Q. Gao, X. Huang, R.-M. Yao, and P.-F. Yin, Chin. Phys. C 48, 065107 (2024), 2401.01829

    2024 arXiv

  67. [75]

    Gao, X.-J

    L.-Q. Gao, X.-J. Bi, J. Li, R.-M. Yao, and P.-F. Yin, JCAP 01, 026 (2024), 2310.11391

    2024 arXiv

  68. [76]

    Anastassopoulos et al

    V . Anastassopoulos et al. (CAST), Nature Phys. 13, 584 (2017), 1705.02290

    2017 arXiv

  69. [77]

    Akaike, IEEE Trans

    H. Akaike, IEEE Trans. Automatic Control 19, 716 (1974)

    1974

  70. [78]

    O’Hare, cajohare/axionlimits: Axionlimits, https://cajohare.github.io/AxionLimits/ (2020)

    C. O’Hare, cajohare/axionlimits: Axionlimits, https://cajohare.github.io/AxionLimits/ (2020)

    2020

  71. [79]

    B. S. Acharya et al. (CTA Consortium), Astropart. Phys. 43, 3 (2013). – 14 –

    2013

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