Pith. sign in

REVIEW 4 major objections 4 minor 1 cited by

Cosmic Clues from Amaterasu: Blazar-Driven Ultrahigh-Energy Cosmic Rays?

T0 review · 4 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The 244 EeV Amaterasu cosmic ray can be a proton from blazar PKS 1717+177 if Lorentz invariance violation lets it cross 590 Mpc.

desk verdict A transparent scenario paper: it plausibly ties PKS 1717+177 to the Amaterasu event, but only under an assumed LIV coefficient and strong EGMF, and the SED fit is underconstrained. read the letter →

arxiv 2504.16019 v2 pith:FCJXFQLO submitted 2025-04-22 astro-ph.HE

Saikat Das , Srijita Hazra , Nayantara Gupta This is my paper · ORCID
classification astro-ph.HE
keywords ultra-high-energycosmicraysblazarsactivegalacticnucleigamma-rayastronomyneutrinoLorentzinvarianceviolationextragalacticmagneticfieldsleptohadronicjetmodels
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

The Amaterasu event, a 244 EeV cosmic ray observed by the Telescope Array, arrives from a direction within 2.5 degrees of the blazar PKS 1717+177 at redshift $z=0.137$. This paper argues that this blazar is a plausible source, provided the primary is a proton and hadronic Lorentz invariance violation (LIV) with coefficient $\delta_{\mathrm{had},0}=10^{-21}$ lengthens the proton's energy-loss mean free path. A one-zone leptohadronic jet model reproduces the source's radio-to-TeV spectrum, attributes the very-high-energy gamma rays to hadronic cascades, and predicts a neutrino flux an order of magnitude lower than from TXS 0506+056. An extragalactic magnetic field of about 1.5 nG would bend the proton by the observed 2.5 degrees. If correct, the same proton population produces measurable hadronic signatures in gamma rays, neutrinos, and the highest-energy cosmic-ray flux.

What carries the argument

The argument rests on a one-zone leptohadronic jet model that reproduces the SED from radio to TeV energies; it includes synchrotron and external Compton emission from primary electrons plus photohadronic cascades from protons, with the proton normalization fixed by the very-high-energy gamma-ray data. The second pillar is the leading-order LIV dispersion relation $E^2-p^2=m^2+\delta_{\mathrm{had},0}E^2$ with $\delta_{\mathrm{had},0}=10^{-21}$, which increases the proton energy-loss length so that a 244 EeV proton can traverse 590 Mpc. A small-angle scattering formula then converts the 2.5-degree offset into the required extragalactic field strength of about 1.5 nG.

What would settle it

Measure the extragalactic magnetic field toward PKS 1717+177; if it is much weaker than 1.5 nG, or if the hadronic LIV bound is pushed below $10^{-21}$, the proposed origin cannot hold.

Watch

Extended reading notes

Core claim

The central claim is that PKS 1717+177, a blazar at $z=0.137$, can accelerate and release a proton that is observed as the 244 EeV Amaterasu event. The evidence is a simultaneous fit to the source's multiwavelength spectrum using a one-zone jet model with electron and proton injection; the same proton population that escapes the jet produces the sub-TeV gamma-ray excess through pion-decay cascades inside the jet. Propagation from the source to Earth is enabled by hadronic Lorentz invariance violation with $\delta_{\mathrm{had},0}=10^{-21}$, which suppresses photopion losses on the cosmic microwave background, and by a $\sim1.5$ nG extragalactic magnetic field that deflects the proton by the observed $2.5^\circ$. The model predicts a subdominant neutrino flux, about an order of magnitude lower than TXS 0506+056, and implies negligible Galactic magnetic deflection.

Load-bearing premise

The chain depends on the existence of hadronic Lorentz invariance violation with coefficient near $\delta_{\mathrm{had},0}=10^{-21}$; without it, a proton from the blazar cannot survive the 590 Mpc journey.

Editorial extensions

If this is right

  • The very-high-energy gamma-ray emission of PKS 1717+177 can be produced by hadronic cascades inside the jet, not only by leptonic inverse-Compton scattering.
  • The predicted muon-neutrino flux is about 0.1 events per decade at current IceCube effective area, roughly an order of magnitude below the TXS 0506+056 level.
  • The same proton population that produces the hadronic signature escapes the jet above about 0.1 EeV, and the single-event detection implies a proton kinetic power of about $2\times10^{45}$ erg s$^{-1}$ with a rigidity cutoff above $10^{19}$ V.
  • Galactic magnetic fields deflect the proton by less than the angular uncertainty, so the observed 2.5-degree offset must be imprinted by an extragalactic magnetic field of about 1.5 nG.
  • If the source's X-ray or gamma-ray activity increases by an order of magnitude, next-generation neutrino telescopes could detect a neutrino within a few years, providing a direct multimessenger confirmation.

Reading between the lines

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

  • If the association holds, a single cosmic ray becomes a probe of Lorentz invariance violation; a confirmed source would imply that all $\gtrsim100$ EeV protons can travel across cosmological distances, dramatically widening the search for UHECR sources.
  • The required 1.5 nG field is characteristic of cosmic filaments rather than voids, suggesting that lines of sight through filaments should show systematically larger UHECR deflections; a population study could test this prediction.
  • The same modeling template could be applied to future extreme-energy events with candidate blazars, turning single-event associations into a statistical test of LIV parameters and magnetic field models.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The manuscript investigates whether the Telescope Array 'Amaterasu' event at 244 EeV could originate from the blazar PKS 1717+177 at z=0.137, assuming a proton primary and a 2.5-degree angular offset. The authors fit the multiwavelength SED with a one-zone leptohadronic jet model using GAMERA, infer a proton luminosity L_p = 1.3e45 erg/s, and predict a subdominant muon-neutrino flux of about 0.1 events per 10 years at IceCube. They then show that, for a chosen Lorentz invariance violation coefficient δ_had,0 = 1e-21 and an extragalactic magnetic field strength B_EG ≈ 1.5 nG with coherence length 500 kpc, a 244 EeV proton can propagate over the 590 Mpc comoving distance and be deflected by approximately 2.5 degrees, making the association plausible under these assumptions. The paper concludes that PKS 1717+177 is a viable candidate source and motivates multimessenger follow-up.

Significance. If the underlying assumptions are accepted, the manuscript provides a self-consistent multimessenger framework connecting an UHECR event, a blazar SED, and a predicted neutrino flux, with concrete falsifiable consequences for CTA, LHAASO, IceCube-Gen2, and KM3NeT. The use of public codes (GAMERA, CRPropa) and archival multiwavelength data makes the analysis reproducible, and the paper is commendably explicit about the key assumptions (proton primary, LIV, strong EGMF). However, the central claim is conditional: the propagation of the 244 EeV proton from z=0.137 is enabled entirely by an unverified BSM parameter, and the SED fit is underconstrained. These limitations substantially bound the significance of the result, but the paper may still be valuable as a scenario study if the load-bearing assumptions are clearly framed and quantitatively tested.

major comments (4)
  1. The entire propagation leg rests on an assumed LIV coefficient δ_had,0 = 10^-21, which is not independently constrained. As the manuscript itself states in Sec. 1, the GZK energy-loss mean free path for protons at this energy is ~10 Mpc, so without LIV a 244 EeV proton cannot travel from z=0.137 (d_c ≈ 590 Mpc) to Earth. The paper notes that the Auger upper limit is δ_had,0 < 10^-19, but a one-sided bound is not positive evidence, and the chosen value sits at the low end of what is needed. Moreover, the manuscript's own consistency argument in Sec. 3.2 infers log10(Rmax/V) ≈ 19.0–19.2 from the TA single-event normalization and the SED-inferred L_p, while the Auger combined-fit cutoff at δ_had,0 = 10^-21 is quoted as ~18.6 and increases with δ, implying that the internally preferred δ may be larger than 10^-21. Please provide a quantitative propagation calculation for this specific source and energy, including the LIV threshold and GZK losses, and discuss the prior or external evidence that justifies the chosen δ; without this, the association collapses.
  2. The SED fit is heavily underconstrained. Table 1 lists more than a dozen free parameters with no uncertainties and no goodness-of-fit statistic, and the text says only that 'parameter degeneracy was assessed by scanning over a broad range of values' without reporting the scan or its results. The claim that the hadronic component is required to reproduce the VHE gamma-ray and soft X-ray data is not quantitatively supported; a purely leptonic EC model may also fit the data given the sparse VHE points. Please quantify the improvement of the leptohadronic fit over a leptonic-only fit (e.g., a chi-square or likelihood comparison), report confidence intervals on the key derived quantities (L_p, neutrino flux), and show the degeneracy scan explicitly.
  3. The multimessenger predictions are partly circular. The neutrino flux is computed from the same proton spectrum whose normalization is fixed by the SED fit, and the UHECR event rate is used as an input to fix Rmax in Fig. 2; therefore the neutrino flux and the Rmax–LIV consistency check are not independent tests of the model. Please clarify which quantities are inputs and which are predictions, and ideally compute the expected TA event rate from the SED-normalized proton spectrum and compare it with the single observed Amaterasu event, rather than using that event to set the cutoff.
  4. The directional association depends on several tuned assumptions: a proton primary, B_EG ≈ 1.5 nG, λ_c = 500 kpc, and the small-angle scattering formula of Eq. (7). The required EGMF is an order of magnitude higher than typical cosmic-void fields (~0.1 nG), and the manuscript does not justify that the line of sight to PKS 1717+177 indeed passes through magnetized filaments with these properties. Please also quantify the chance-coincidence probability of finding a blazar within 2.5 degrees (or within the backtracked angular uncertainty) and test the sensitivity of the inferred B_EG to λ_c and to the scattering model.
minor comments (4)
  1. The caption states that 'black and gray error bars correspond to the neutrino flux from TXS 0506+056', but the main text describes black data points and gray upper limits for the electromagnetic SED; please clarify which colors and line styles refer to the neutrino reference flux.
  2. The equation for the proton injection spectrum is missing a closing brace and the exponential factor is ambiguous; please write it as exp[1 - E_p/(Z R_max)] with proper bracketing.
  3. The sentence 'We constrain the value of Rmax and hence the required LIV coefficient from the proton luminosity required to explain the blazar SED' is misleading: the LIV coefficient is not derived but chosen, and the argument only shows consistency for a specific δ. Please rephrase to distinguish a consistency check from a measurement.
  4. The discussion of the cosmogenic gamma-ray spectrum would benefit from a more explicit statement of how the strong EGMF affects the flux and why most interactions must occur near the source, since this is central to the proposed CTA/LHAASO test.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the SED fit, multimessenger outputs, and propagation scenario are model-consistent rather than definitionally forced.

full rationale

The paper's central derivation is a self-contained model fit: the leptohadronic SED is fitted to archival multiwavelength data that are independent of the Amaterasu association, and the proton luminosity Lp = 1.3e45 erg/s is constrained by the VHE gamma-ray and soft X-ray data rather than by the UHECR event. The neutrino flux is then computed from the same hadronic normalization (Eq. 5), so it is a consistency output of the fitted proton spectrum rather than an independent prediction; however, the paper does not fit neutrino data and does not claim the neutrino flux is an independent test, so this is not a fitted input disguised as a prediction. The UHECR luminosity normalization does use the single Telescope Array event to infer Rmax by comparison with the SED-inferred Lp, but this is a consistency argument used to constrain a model parameter, not a prediction of the event. The LIV coefficient δhad,0 = 1e-21 and the EGMF strength B_EG ≈ 1.5 nG are chosen or required parameters for the proposed scenario, not quantities derived from the conclusion; the LIV value is checked against the Auger upper limit and the EGMF value is solved from the observed deflection angle via Eq. 7. Self-citations (e.g., Das et al. 2022a; Prince et al. 2024) provide numerical methods and are not load-bearing for the Amaterasu association. No step reduces by construction to its own inputs, so no significant circularity is found.

Assumptions & free parameters 20 free parameters · 6 assumptions · 0 invented entities

The central scenario is assembled from roughly 20 fitted or chosen parameters (Table 1 plus LIV, EGMF, and geometry). The SED fit alone uses more than a dozen free parameters with no error bars; the UHECR association adds the LIV coefficient and the EGMF, both selected to make the event fit. This is a model-building paper, not a parameter-free derivation, and it introduces no new entities.

free parameters (20)
  • Doppler factor δD = 25
    Fitted to reproduce the SED peaks; quoted in Table 1.
  • Magnetic field B' = 1.0 G
    Fitted to synchrotron peak and overall SED normalization.
  • Emission region radius R' = 5e16 cm
    Fitted to the radio-to-optical synchrotron component.
  • External photon energy density u'_ext = 0.1 erg cm^-3
    Fitted to the high-energy peak; attributed to a hidden BLR.
  • External photon temperature T' = 5e5 K
    Fitted with u'_ext to shape the EC and pγ target fields.
  • Electron injection spectral index α = 2.0
    Chosen; a log-parabola was tested but a power law was adopted.
  • Electron minimum Lorentz factor γ'_e,min = 20
    Fitted to the radio-to-optical synchrotron emission.
  • Electron maximum Lorentz factor γ'_e,max = 5e4
    Fitted to the synchrotron cutoff.
  • Electron luminosity L_e = 4.1e42 erg s^-1
    Fitted to the SED normalization.
  • Proton minimum Lorentz factor γ'_p,min = 10
    Fitted to the hadronic cascade component.
  • Proton maximum Lorentz factor γ'_p,max = 4.27e6
    Fitted; corresponds to about 4 PeV comoving and 0.1 EeV in the AGN frame.
  • Proton luminosity L_p = 1.3e45 erg s^-1
    Fitted to the SED, particularly the VHE gamma-ray flux from pion decay.
  • LIV coefficient δhad,0 = 1e-21
    Chosen within the Auger upper limit to allow 244 EeV protons to travel 590 Mpc without GZK losses.
  • EGMF strength B_EG = 1.5 nG
    Derived from Eq. (7) to produce the 2.5 degree deflection matching the blazar offset.
  • EGMF coherence length λc = 500 kpc
    Assumed in Eq. (7); no measurement for this line of sight.
  • Jet opening angle θjet = 0.1 rad
    Assumed typical value (Pushkarev et al. 2009; Finke 2019) used for the UHECR solid-angle normalization.
  • Disk luminosity L_disk = 1e46 erg s^-1
    Assumed typical value for the hidden BLR estimate.
  • Fraction η_disk = 0.01
    Assumed fraction of disk luminosity reprocessed into the external photon field.
  • Proton rigidity cutoff log10(Rmax/V) = 19.0 to 19.2
    Inferred from matching the SED-fit proton luminosity to the one-event normalization in the 148-340 EeV bin.
  • Proton spectral index α_p = 2.0
    Chosen to match the electron index and first-order Fermi acceleration expectations.
assumptions (6)
  • domain assumption One-zone spherical blob with co-located electrons and protons
    Sec. 2; the entire SED and hadronic emission calculation rests on this geometry.
  • domain assumption External photon field is a blackbody (T'=5e5 K, u'_ext=0.1 erg cm^-3) from a hidden BLR
    Sec. 2 and Table 1; the EC and pγ target fields depend on this.
  • ad hoc to paper Protons above E'_p,max escape on timescale ~R/c without pγ losses
    Sec. 3.1; needed to separate the jet-interacting proton population from escaping UHECRs.
  • domain assumption Proton primary for Amaterasu
    Sec. 3.3; the blazar association is only viable for protons, as iron shifts the backtracked direction.
  • standard math Standard pγ, Bethe-Heitler, and γγ cross-sections and EBL model (Gilmore 2012)
    Sec. 2; used without modification.
  • domain assumption Jet geometry θ ≲ 1/Γ so δ_D ≈ Γ
    Sec. 2; used to simplify Doppler factor relations.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Cosmic Clues from Amaterasu: Blazar-Driven Ultrahigh-Energy Cosmic Rays?." pith.science (2026). https://pith.science/paper/FCJXFQLO

@misc{pith2026250416019,
  author       = {Pith},
  title        = {Pith review of: Cosmic Clues from Amaterasu: Blazar-Driven Ultrahigh-Energy Cosmic Rays?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FCJXFQLO}},
  note         = {Machine review of arXiv:2504.16019}
}
abstract

The detection of the Amaterasu event of energy 244 EeV by the Telescope Array, one of the most energetic ultrahigh-energy cosmic rays (UHECRs; $E\gtrsim0.1$ EeV) observed to date, invites scrutiny of its potential source. We investigate whether the nearby blazar PKS~1717+177 at redshift $z=0.137$, located within $2.5^\circ$ of the reconstructed arrival direction, could explain the event under a proton-primary hypothesis. Using a one-zone jet model, we fit the multiwavelength spectral energy distribution of the source, incorporating both leptonic and hadronic cascade emissions from photohadronic interactions inside the jet. Our model supports a cosmic-ray origin of the very-high-energy ($\varepsilon_\gamma\gtrsim 100$ GeV) $\gamma$-ray flux and predicts a subdominant neutrino flux, one order of magnitude lower than from TXS~0506+056. Under Lorentz invariance violation, UHECRs escaping the blazar jet above a specific energy can propagate unattenuated over hundreds of Mpc due to an increase in energy loss length for certain parameter choices. In such a scenario, the Amaterasu event can have a plausible origin from this blazar. Our analysis indicates negligible deflection in the Galactic magnetic field, implying a strong extragalactic magnetic field is required. Our findings provide a compelling multimessenger framework linking UHECRs, $\gamma$-rays, and neutrinos and motivate targeted searches by current and future high-energy neutrino telescopes during increased $\gamma$-ray or X-ray activity of this blazar.

Figures

Figures reproduced from arXiv: 2504.16019 by the authors.

Figure 1
Figure 1. Multiwavelength SED of PKS 1717+177 showing the synchrotron (orange solid), external Compton (green dotted), the external photon field (brown dashed), the hadronic cascade (blue solid), and the νµ + νµ spectrum (magenta) in the observer frame. Black data points show the spectral data from radio to VHE γ￾rays, and upper limits are shown in gray. The black and gray error bars correspond to the neutrino flux from TXS 0… view at source ↗
Figure 2
Figure 2. Proton luminosity in the 0.1 TeV to 10 EeV energy range constrained by the detection of 1 UHE proton event in the Telescope Array energy bin 148 - 340 EeV. The different curves correspond to various values of rigidity cutoff Rmax in the injection spectrum. The detection of a single event by TA in the energy range 148−340 EeV (obtained by adding the statistical and system￾atic uncertainties in quadrature), assuming n… view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Global Cosmic Ray Observatory -- Challenging next-generation multi-messenger astronomy with interdisciplinary research

    astro-ph.HE 2025-07 unverdicted novelty 2.0 of 10

    GCOS is proposed as a 60,000 km2 cosmic-ray observatory that would boost exposure tenfold and enable charged-particle astronomy, though this paper only restates the design goals.

Reference graph

Works this paper leans on

109 extracted references · 6 linked inside Pith · cited by 1 Pith paper

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter doi edition editor eprint howpublished institution journal key month number organization pages publisher school series title misctitle type volume year version url label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix "arXiv" = new.block " " eprint * " " * new.block " " eprint * " " * if if if FUNCTION format.doi doi empty "" " " doi * " " * if FUNCTION format.pid doi empty eprint empty ur...

  3. [3]

    S v-d#a 3v㺕 #qR w Yb =<8m G7 )ƱNn|`C88u fΡq6اS ^ յ. QLw)W): \>w '=H ;T̨5.nI ?S Ŋr߹ ESӫ:R.#jb1׏: 4FÉ^ tĦ 1Cka`; T ) \ ^ &Ϟ/ 3ğ Bku d,3p qqE ׬#53/lc-⋘I3aGuV ` -.P)' ֘

    thebibliography [1] 20pt to REFERENCES 6pt =0pt -12pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command E...

    2021

  4. [4]

    U., et al

    Abbasi , R. U., et al. 2010, , 104, 161101, 10.1103/PhysRevLett.104.161101

    doi:10.1103/physrevlett.104.161101 2010

  5. [5]

    2012, Astropart

    Aloisio, R., Berezinsky, V., & Gazizov, A. 2012, Astropart. Phys., 39-40, 129, 10.1016/j.astropartphys.2012.09.007

    doi:10.1016/j.astropartphys.2012.09.007 2012

  6. [6]

    2016, JCAP, 05, 038, 10.1088/1475-7516/2016/05/038

    Alves Batista, R., Dundovic, A., Erdmann, M., et al. 2016, JCAP, 05, 038, 10.1088/1475-7516/2016/05/038

    doi:10.1088/1475-7516/2016/05/038 2016

  7. [7]

    2022, JCAP, 09, 035, 10.1088/1475-7516/2022/09/035

    Alves Batista, R., et al. 2022, JCAP, 09, 035, 10.1088/1475-7516/2022/09/035

    doi:10.1088/1475-7516/2022/09/035 2022

  8. [8]

    Anchordoqui, L. A. 2019, Phys. Rept., 801, 1, 10.1016/j.physrep.2019.01.002

    doi:10.1016/j.physrep.2019.01.002 2019

Show all 109 references
  1. [9]

    2018, Astrophys

    Ansoldi, S., et al. 2018, Astrophys. J. Lett., 863, L10, 10.3847/2041-8213/aad083

    2018 doi

  2. [10]

    Atoyan, A., & Dermer, C. D. 2001, Phys. Rev. Lett., 87, 221102, 10.1103/PhysRevLett.87.221102

    2001 doi

  3. [11]

    2014, Astron

    Barnacka, A., Moderski, R., Behera, B., Brun, P., & Wagner, S. 2014, Astron. Astrophys., 567, A113, 10.1051/0004-6361/201322205

    2014 doi

  4. [12]

    H., White , R

    Becker , R. H., White , R. L., & Helfand , D. J. 1994, in Astronomical Society of the Pacific Conference Series, Vol. 61, Astronomical Data Analysis Software and Systems III, ed. D. R. Crabtree , R. J. Hanisch , & J. Barnes , 165

    1994

  5. [13]

    S., & Ginzburg , V

    Berezinskii , V. S., & Ginzburg , V. L. 1981, , 194, 3, 10.1093/mnras/194.1.3

    1981 doi

  6. [14]

    2011, , 335, 161, 10.1007/s10509-010-0581-x

    Bianchi , L., Herald , J., Efremova , B., et al. 2011, , 335, 161, 10.1007/s10509-010-0581-x

    2011 doi

  7. [15]

    J., et al

    Bird, D. J., et al. 1995, Astrophys. J., 441, 144, 10.1086/175344

    1995 doi

  8. [16]

    2013, Astrophys

    Boettcher, M., Reimer, A., Sweeney, K., & Prakash, A. 2013, Astrophys. J., 768, 54, 10.1088/0004-637X/768/1/54

    2013 doi

  9. [17]

    1997, , 325, 866, 10.48550/arXiv.astro-ph/9703069

    Boettcher , M., & Schlickeiser , R. 1997, , 325, 866, 10.48550/arXiv.astro-ph/9703069

    1997 doi arXiv

  10. [18]

    Bourriche, N., & Capel, F. 2024. 2406.16483

    2024

  11. [19]

    2024, Mon

    Britzen, S., et al. 2024, Mon. Not. Roy. Astron. Soc., 535, 2742, 10.1093/mnras/stae2373

    2024 doi

  12. [20]

    2025, Astron

    ---. 2025, Astron. Astrophys., 695, A103, 10.1051/0004-6361/202452530

    2025 doi

  13. [21]

    J., Zdziarski , A

    Chodorowski , M. J., Zdziarski , A. A., & Sikora , M. 1992, , 400, 181, 10.1086/171984

    1992 doi

  14. [22]

    R., & Glashow, S

    Coleman, S. R., & Glashow, S. L. 1997, Phys. Lett. B, 405, 249, 10.1016/S0370-2693(97)00638-2

    1997 doi

  15. [23]

    2020, Astrophys

    Das, S., Gupta, N., & Razzaque, S. 2020, Astrophys. J., 889, 149, 10.3847/1538-4357/ab6131

    2020 doi

  16. [24]

    2021 a , Astrophys

    ---. 2021 a , Astrophys. J., 910, 100, 10.3847/1538-4357/abe4cd

    2021 doi

  17. [25]

    2022 a , Astron

    ---. 2022 a , Astron. Astrophys., 668, A146, 10.1051/0004-6361/202244653

    2022 doi

  18. [26]

    2021 b , Eur

    Das, S., Razzaque, S., & Gupta, N. 2021 b , Eur. Phys. J. C, 81, 59, 10.1140/epjc/s10052-021-08885-4

    2021 doi

  19. [27]

    2022 b , Astron

    ---. 2022 b , Astron. Astrophys., 658, L6, 10.1051/0004-6361/202142123

    2022 doi

  20. [28]

    D., Razzaque, S., Finke, J

    Dermer, C. D., Razzaque, S., Finke, J. D., & Atoyan, A. 2009, New J. Phys., 11, 065016, 10.1088/1367-2630/11/6/065016

    2009 doi

  21. [29]

    R., Allard, D., Lachaud, C., et al

    d'Orfeuil, B. R., Allard, D., Lachaud, C., et al. 2014, Astron. Astrophys., 567, A81, 10.1051/0004-6361/201423462

    2014 doi

  22. [30]

    2024, JCAP, 02, 022, 10.1088/1475-7516/2024/02/022

    Ehlert, D., van Vliet, A., Oikonomou, F., & Winter, W. 2024, JCAP, 02, 022, 10.1088/1475-7516/2024/02/022

    2024 doi

  23. [31]

    1979, , 232, 106, 10.1086/157269

    Eichler , D. 1979, , 232, 106, 10.1086/157269

    1979 doi

  24. [32]

    Essey, W., Kalashev, O., Kusenko, A., & Beacom, J. F. 2011, Astrophys. J., 731, 51, 10.1088/0004-637X/731/1/51

    2011 doi

  25. [33]

    G., & Khlopov, M

    Fargion, D., De Sanctis Lucentini, P. G., & Khlopov, M. Y. 2024, Universe, 10, 323, 10.3390/universe10080323

    2024 doi

  26. [34]

    Farrar, G. R. 2025, Phys. Rev. Lett., 134, 081003, 10.1103/PhysRevLett.134.081003

    2025 doi

  27. [35]

    2020, Astrophys

    Fermi-LAT Collaboration . 2020, Astrophys. J. Suppl., 247, 33, 10.3847/1538-4365/ab6bcb

    2020 doi

  28. [36]

    2023, arXiv e-prints, arXiv:2307.12546, 10.48550/arXiv.2307.12546

    ---. 2023, arXiv e-prints, arXiv:2307.12546, 10.48550/arXiv.2307.12546

    2023 doi arXiv

  29. [37]

    Finke, J. D. 2019, Astrophys. J., 870, 28, 10.3847/1538-4357/aaf00c

    2019 doi

  30. [38]

    C., Somerville, R

    Gilmore, R. C., Somerville, R. S., Primack, J. R., & Dominguez, A. 2012, Mon. Not. Roy. Astron. Soc., 422, 3189, 10.1111/j.1365-2966.2012.20841.x

    2012

  31. [39]

    a hteenm \

    Giommi , P., Polenta , G., L \"a hteenm \"a ki , A., et al. 2012, , 541, A160, 10.1051/0004-6361/201117825

    2012 doi

  32. [40]

    2008, Astron

    Globus, N., Allard, D., & Parizot, E. 2008, Astron. Astrophys., 479, 97, 10.1051/0004-6361:20078653

    2008 doi

  33. [41]

    J., & Schr\'eder, G

    Gould, R. J., & Schr\'eder, G. P. 1967, Phys. Rev., 155, 1404, 10.1103/PhysRev.155.1404

    1967 doi

  34. [42]

    1966, , 16, 748, 10.1103/PhysRevLett.16.748

    Greisen , K. 1966, , 16, 748, 10.1103/PhysRevLett.16.748

    1966 doi

  35. [43]

    2021, in Proceedings of 37th International Cosmic Ray Conference PoS(ICRC2021), Vol

    Gueta, O. 2021, in Proceedings of 37th International Cosmic Ray Conference PoS(ICRC2021), Vol. 395, 885, 10.22323/1.395.0885

    2021 doi

  36. [44]

    2016, Mon

    Hackstein, S., Vazza, F., Br\"uggen, M., Sigl, G., & Dundovic, A. 2016, Mon. Not. Roy. Astron. Soc., 462, 3660, 10.1093/mnras/stw1903

    2016 doi

  37. [45]

    2016, PoS, ICRC2015, 917, 10.22323/1.236.0917

    Hahn, J. 2016, PoS, ICRC2015, 917, 10.22323/1.236.0917

    2016 doi

  38. [46]

    2022, GAMERA: Source modeling in gamma astronomy , Astrophysics Source Code Library, record ascl:2203.007

    Hahn , J., Romoli , C., & Breuhaus , M. 2022, GAMERA: Source modeling in gamma astronomy , Astrophysics Source Code Library, record ascl:2203.007

    2022

  39. [47]

    2014, Phys

    Harari, D., Mollerach, S., & Roulet, E. 2014, Phys. Rev. D, 89, 123001, 10.1103/PhysRevD.89.123001

    2014 doi

  40. [48]

    E., Romani , R

    Healey , S. E., Romani , R. W., Taylor , G. B., et al. 2007, , 171, 61, 10.1086/513742

    2007 doi

  41. [49]

    2018, Science, 361, 147, 10.1126/science.aat2890

    IceCube Collaboration . 2018, Science, 361, 147, 10.1126/science.aat2890

    2018 doi

  42. [50]

    2019 a , Eur

    ---. 2019 a , Eur. Phys. J. C, 79, 234, 10.1140/epjc/s10052-019-6680-0

    2019 doi

  43. [51]

    ---. 2019 b . 1911.02561

    2019

  44. [52]

    ---. 2021, J. Phys. G, 48, 060501, 10.1088/1361-6471/abbd48

    2021 doi

  45. [53]

    2018, Science, 361, eaat1378, 10.1126/science.aat1378

    IceCube Collaboration , Fermi-LAT Collaboration , MAGIC Collaboration , et al. 2018, Science, 361, eaat1378, 10.1126/science.aat1378

    2018 doi

  46. [54]

    Jansson, R., & Farrar, G. R. 2012, Astrophys. J., 757, 14, 10.1088/0004-637X/757/1/14

    2012 doi

  47. [55]

    Jiang, X., Liao, N.-H., Rui, X., Fan, Y.-Z., & Wei, D.-M. 2025. 2505.04160

    2025 arXiv

  48. [56]

    Kachelrie , M., Kalashev, O., Ostapchenko, S., & Semikoz, D. V. 2017, Phys. Rev. D, 96, 083006, 10.1103/PhysRevD.96.083006

    2017 doi

  49. [57]

    2018, Astrophys

    Kawamuro, T., et al. 2018, Astrophys. J. Suppl., 238, 32, 10.3847/1538-4365/aad1ef

    2018 doi

  50. [58]

    2018, Astrophys

    Keivani, A., et al. 2018, Astrophys. J., 864, 84, 10.3847/1538-4357/aad59a

    2018 doi

  51. [59]

    R., & Aharonian, F

    Kelner, S. R., & Aharonian, F. A. 2008, Phys. Rev. D, 78, 034013, 10.1103/PhysRevD.82.099901

    2008 doi

  52. [60]

    2023, EPJ Web Conf., 283, 02005, 10.1051/epjconf/202328302005

    Kim, J., Ivanov, D., Jui, C., & Thomson, G. 2023, EPJ Web Conf., 283, 02005, 10.1051/epjconf/202328302005

    2023

  53. [61]

    KM3NeT Collaboration . 2016, J. Phys. G, 43, 084001, 10.1088/0954-3899/43/8/084001

    2016 doi

  54. [62]

    Kotera , K., & Olinto , A. V. 2011, , 49, 119, 10.1146/annurev-astro-081710-102620

    2011 doi

  55. [63]

    Kuznetsov, M. Y. 2024, JCAP, 04, 042, 10.1088/1475-7516/2024/04/042

    2024 doi

  56. [64]

    Lang, R. G. 2024, JCAP, 11, 023, 10.1088/1475-7516/2024/11/023

    2024 doi

  57. [65]

    Mannheim , K., Stanev , T., & Biermann , P. L. 1992, , 260, L1

    1992

  58. [66]

    P., Protheroe , R

    M \"u cke , A., Engel , R., Rachen , J. P., Protheroe , R. J., & Stanev , T. 2000, Computer Physics Communications, 124, 290, 10.1016/S0010-4655(99)00446-4

    2000 doi

  59. [67]

    2012, Astrophys

    Murase, K. 2012, Astrophys. J. Lett., 745, L16, 10.1088/2041-8205/745/2/L16

    2012 doi

  60. [68]

    Murase, K., Inoue, Y., & Dermer, C. D. 2014, Phys. Rev. D, 90, 023007, 10.1103/PhysRevD.90.023007

    2014 doi

  61. [69]

    Murase, K., Narita, Y., & Yin, W. 2025. 2504.15272

    2025

  62. [70]

    Murase, K., & Stecker, F. W. 2023, 483, 10.1142/9789811282645_0010

    2023 doi

  63. [71]

    S., Farrar, G

    Muzio, M. S., Farrar, G. R., & Unger, M. 2022, Phys. Rev. D, 105, 023022, 10.1103/PhysRevD.105.023022

    2022 doi

  64. [72]

    S., Unger, M., & Farrar, G

    Muzio, M. S., Unger, M., & Farrar, G. R. 2019, Phys. Rev. D, 100, 103008, 10.1103/PhysRevD.100.103008

    2019 doi

  65. [73]

    a hteenm \

    Nieppola , E., Tornikoski , M., L \"a hteenm \"a ki , A., et al. 2007, , 133, 1947, 10.1086/512609

    2007 doi

  66. [74]

    V., et al

    Olinto, A. V., et al. 2021, JCAP, 06, 007, 10.1088/1475-7516/2021/06/007

    2021 doi

  67. [75]

    2019, Mon

    Padovani, P., Oikonomou, F., Petropoulou, M., Giommi, P., & Resconi, E. 2019, Mon. Not. Roy. Astron. Soc., 484, L104, 10.1093/mnrasl/slz011

    2019 doi

  68. [76]

    2024, Astrophys

    Partenheimer, A., Fang, K., Alves Batista, R., & Menezes de Almeida, R. 2024, Astrophys. J. Lett., 967, L15, 10.3847/2041-8213/ad4359

    2024 doi

  69. [77]

    2015 a , Nucl

    Pierre Auger Collaboration . 2015 a , Nucl. Instrum. Meth. A, 798, 172, 10.1016/j.nima.2015.06.058

    2015 doi

  70. [78]

    2015 b , Astrophys

    ---. 2015 b , Astrophys. J., 804, 15, 10.1088/0004-637X/804/1/15

    2015 doi

  71. [79]

    2017, JCAP, 04, 038, 10.1088/1475-7516/2017/04/038

    ---. 2017, JCAP, 04, 038, 10.1088/1475-7516/2017/04/038

    2017 doi

  72. [80]

    2022, JCAP, 01, 023, 10.1088/1475-7516/2022/01/023

    ---. 2022, JCAP, 01, 023, 10.1088/1475-7516/2022/01/023

    2022 doi

  73. [81]

    Planck Collaboration , Ade , P. A. R., Aghanim , N., et al. 2014, , 571, A28, 10.1051/0004-6361/201321524

    2014 doi

  74. [82]

    2024, Mon

    Prince, R., Das, S., Gupta, N., Majumdar, P., & Czerny, B. 2024, Mon. Not. Roy. Astron. Soc., 527, 8746, 10.1093/mnras/stad3804

    2024 doi

  75. [83]

    S., Tinyakov, P

    Pshirkov, M. S., Tinyakov, P. G., Kronberg, P. P., & Newton-McGee, K. J. 2011, Astrophys. J., 738, 192, 10.1088/0004-637X/738/2/192

    2011 doi

  76. [84]

    B., Kovalev , Y

    Pushkarev , A. B., Kovalev , Y. Y., Lister , M. L., & Savolainen , T. 2009, , 507, L33, 10.1051/0004-6361/200913422

    2009 doi

  77. [85]

    K., & Stanev, T

    Riehn, F., Engel, R., Fedynitch, A., Gaisser, T. K., & Stanev, T. 2020, Phys. Rev. D, 102, 063002, 10.1103/PhysRevD.102.063002

    2020 doi

  78. [86]

    2020, in Latin American Strategy Forum for Research Infrastructure

    Romero-Wolf, A., et al. 2020, in Latin American Strategy Forum for Research Infrastructure . 2002.06475

    2020 arXiv

  79. [87]

    2025, Phys

    Sarmah, P., Das, N., Borah, D., Chakraborty, S., & Mehta, P. 2025, Phys. Rev. D, 111, 083048, 10.1103/PhysRevD.111.083048

    2025 doi

  80. [88]

    Sigl, G., Miniati, F., & Ensslin, T. A. 2004, Phys. Rev. D, 70, 043007, 10.1103/PhysRevD.70.043007

    2004 doi

  81. [89]

    G., Begelman , M

    Sikora , M., Kirk , J. G., Begelman , M. C., & Schneider , P. 1987, , 320, L81, 10.1086/184980

    1987 doi

  82. [90]

    Stecker, F. W. 1968, Phys. Rev. Lett., 21, 1016, 10.1103/PhysRevLett.21.1016

    1968 doi

  83. [91]

    W., Done , C., Salamon , M

    Stecker , F. W., Done , C., Salamon , M. H., & Sommers , P. 1991, , 66, 2697, 10.1103/PhysRevLett.66.2697

    1991 doi

  84. [92]

    2020, PoS, ICRC2019, 1017, 10.22323/1.358.1017

    Stettner, J. 2020, PoS, ICRC2019, 1017, 10.22323/1.358.1017

    2020 doi

  85. [93]

    2011, arXiv e-prints, arXiv:1103.0749, 10.48550/arXiv.1103.0749

    Stratta , G., Capalbi , M., Giommi , P., et al. 2011, arXiv e-prints, arXiv:1103.0749, 10.48550/arXiv.1103.0749

    2011 doi arXiv

  86. [94]

    P., & Protheroe, R

    Szabo, A. P., & Protheroe, R. J. 1994, Astropart. Phys., 2, 375, 10.1016/0927-6505(94)90027-2

    1994 doi

  87. [95]

    2008, Mon

    Tavecchio, F., & Ghisellini, G. 2008, Mon. Not. Roy. Astron. Soc., 386, 945, 10.1111/j.1365-2966.2008.13072.x

    2008

  88. [96]

    2010, , 401, 1570, 10.1111/j.1365-2966.2009.15784.x

    Tavecchio , F., Ghisellini , G., Ghirlanda , G., Foschini , L., & Maraschi , L. 2010, , 401, 1570, 10.1111/j.1365-2966.2009.15784.x

    2010

  89. [97]

    2016, Astropart

    Telescope Array Collaboration . 2016, Astropart. Phys., 80, 131, 10.1016/j.astropartphys.2016.04.002

    2016 doi

  90. [98]

    2023, Science, 382, abo5095, 10.1126/science.abo5095

    ---. 2023, Science, 382, abo5095, 10.1126/science.abo5095

    2023 doi

  91. [99]

    2024, Phys

    ---. 2024, Phys. Rev. Lett., 133, 041001, 10.1103/PhysRevLett.133.041001

    2024 doi

  92. [100]

    B., Shaya, E

    Tully, R. B., Shaya, E. J., Karachentsev, I. D., et al. 2008, Astrophys. J., 676, 184, 10.1086/527428

    2008 doi

  93. [101]

    Unger, M., & Farrar, G. R. 2024 a , Astrophys. J. Lett., 962, L5, 10.3847/2041-8213/ad1ced

    2024 doi

  94. [102]

    2024 b , Astrophys

    ---. 2024 b , Astrophys. J., 970, 95, 10.3847/1538-4357/ad4a54

    2024 doi

  95. [103]

    R., & Anchordoqui, L

    Unger, M., Farrar, G. R., & Anchordoqui, L. A. 2015, Phys. Rev. D, 92, 123001, 10.1103/PhysRevD.92.123001

    2015 doi

  96. [104]

    2014, Mon

    Vazza, F., Br\"uggen, M., Gheller, C., & Wang, P. 2014, Mon. Not. Roy. Astron. Soc., 445, 3706, 10.1093/mnras/stu1896

    2014 doi

  97. [105]

    Vernetto, S. 2016, J. Phys. Conf. Ser., 718, 052043, 10.1088/1742-6596/718/5/052043

    2016 doi

  98. [106]

    1992, Bulletin d'Information du Centre de Donnees Stellaires, 41, 47

    Wright , A., & Otrupcek , R. 1992, Bulletin d'Information du Centre de Donnees Stellaires, 41, 47

    1992

  99. [107]

    L., Eisenhardt , P

    Wright , E. L., Eisenhardt , P. R. M., Mainzer , A. K., et al. 2010, , 140, 1868, 10.1088/0004-6256/140/6/1868

    2010 doi

  100. [108]

    T., & Kuz'min , V

    Zatsepin , G. T., & Kuz'min , V. A. 1966, Soviet Journal of Experimental and Theoretical Physics Letters, 4, 78

    1966

  101. [109]

    T., Murase, K., Ekanger, N., Bhattacharya, M., & Horiuchi, S

    Zhang, B. T., Murase, K., Ekanger, N., Bhattacharya, M., & Horiuchi, S. 2024. 2405.17409

    2024 arXiv

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.