pith. machine review for the scientific record. sign in

arxiv: 2510.16585 · v3 · submitted 2025-10-18 · 🌌 astro-ph.HE

Association of the IceCube neutrinos with CAZ blazar light curves

Pouya M. Kouch , Talvikki Hovatta , Elina Lindfors , Ioannis Liodakis , Karri I.I. Koljonen , Alessandro Paggi This is my paper

Pith reviewed 2026-05-18 05:49 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords IceCube neutrinosblazarsoptical flaresspatiotemporal correlationsBL Lac objectscosmic neutrino sourcesactive galactic nucleihigh-energy astrophysics
0
0 comments X

The pith

Blazars during major optical flares account for at most 8 percent of detected cosmic neutrinos.

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

The paper tests whether blazars emit high-energy neutrinos by checking for matches between IceCube neutrino arrival times and major optical flares across thousands of radio-selected and gamma-ray-selected blazars. It assumes neutrino output rises during those flares so that flare timing can help separate signal from atmospheric background. Even with a much larger blazar sample than earlier work, the overall correlations stay weak. Only two specific associations with BL Lac objects in the radio-selected sample produce the single post-trial significance above 2 sigma. The authors therefore conclude that blazars contribute no more than about 8 percent of the cosmic neutrinos seen during major optical flares, and that the associated sources tend to show higher Doppler factors and X-ray brightness than typical blazars.

Core claim

By searching for spatiotemporal correlations between 356 IceCube neutrinos and optical flares in 3225 radio-selected plus 3814 gamma-ray-selected blazars, the study finds only weak population-level signals. The strongest result is a single >2 sigma post-trial correlation confined to BL Lac objects in the radio sample and driven by two individual associations. This leads to the estimate that blazars during major optical flares produce at most 8 percent of the detected cosmic neutrinos. Spatially associated blazars are also found to have higher-than-average Doppler factors and X-ray brightness.

What carries the argument

Spatiotemporal correlation test that uses the timing of major optical flares to boost sensitivity against atmospheric neutrino background.

If this is right

  • Most cosmic neutrinos must come from sources other than flaring blazars.
  • Neutrino production in blazars is not strongly coupled to optical flare activity.
  • Blazars that do produce neutrinos tend to be those with elevated Doppler boosting and X-ray output.
  • Future searches may need still larger samples or different wavelength flare selections to reach higher significance.

Where Pith is reading between the lines

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

  • Neutrino emission in blazars may occur mainly in non-flaring or steady states rather than during optical outbursts.
  • The weak population signal could indicate that other AGN classes or non-jet sources dominate the neutrino sky.
  • Combining the optical timing method with simultaneous gamma-ray or X-ray monitoring might isolate individual neutrino sources more cleanly.

Load-bearing premise

High-energy neutrino emission from blazars increases during major optical flares.

What would settle it

No neutrinos detected from the two driving BL Lac objects during their next major optical flares, or the post-trial significance falling below 2 sigma when the analysis is repeated on an independent larger neutrino sample.

Figures

Figures reproduced from arXiv: 2510.16585 by Alessandro Paggi, Elina Lindfors, Ioannis Liodakis, Karri I.I. Koljonen, Pouya M. Kouch, Talvikki Hovatta.

Figure 1
Figure 1. Figure 1: Sky distribution of the 356 updated IceCat1+ neutrinos and the 5880 blazars of the RFC† and 4LAC samples. The black ellipses show the enlarged ≳90%-likelihood error region of the neutrinos. The circles (symbol count: 2066), crosses (2655), and stars (1159) display blazars present only in RFC† , only in 4LAC, and in both RFC† and 4LAC, respectively. The faded blue markings (4822) represent uncorrelated blaz… view at source ↗
Figure 2
Figure 2. Figure 2: Spatio-temporal correlation significance in Gaussian σ against fraction of blazar-flare-emitted cosmic neutrinos in %. The blue box plots represent the distribution of the significances for 500 simulations. The running solid (dark blue) line denotes the mean of the significances. The dotted red and the dashed olive horizontal lines show the correlation significances between the updated IceCat1+ neutrinos a… view at source ↗
Figure 3
Figure 3. Figure 3: Light curve and sky map of the blazar CAZJ0211+1051 which is spatio-temporally associated with the neutrino IC131014A (WT = 0.665). Plot (i) shows the entire CAZ light curve of the blazar along with the arrival time of the associated neutrino (shown using a solid, vertical, black line). The horizontal dotted green line shows the 75th percentile flux density, and the horizontal dashed grey line the 95th per… view at source ↗
Figure 4
Figure 4. Figure 4: Light curve and sky map of the blazar CAZJ0207+0950 which is spatio-temporally associated with the neutrino IC131014A (WT = 0.665). For plot details, see description of [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Light curve and sky map of the blazar CAZJ0509+0541 (TXS 0506+056) which is spatio-temporally associated with the neutrino IC170922A (WT = 0.631). For plot details, see description of [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Light curve and sky map of the blazar CAZJ0212−0221 which is spatio-temporally associated with the neutrino IC230724A (WT = 0.526). For plot details, see description of [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Distribution of νsy (subplot i), z (subplot ii), Dvar (subplot iii), median S X-ray (subplot iv), CRTS Fvar (subplot v), and ZTF Fvar (subplot vi) of: (a) all blazars of the RFC† and 4LAC samples (with blue, solid lines); (b) blazars spatially associated with neutrinos having WT > 0.5 (with red, dash-dotted lines); and (c) blazars spatio-temporally associated with neutrinos via BB95 having WT > 0.5 (with b… view at source ↗
read the original abstract

The IceCube Neutrino Observatory has detected several hundred high-energy neutrinos from cosmic sources. Despite numerous studies searching for their origin, it is still not known which sources emit them. A few likely individual associations exist with active galactic nuclei (AGNs), mostly comprising blazars (AGNs with jets pointed toward Earth). Nonetheless, on a population level, blazar-neutrino correlation strengths are rather weak. This could mean that blazars as a population do not emit high-energy neutrinos or that the detection power of the tests is insufficient due to the strong atmospheric neutrino background. By assuming an increase in high-energy neutrino emission during major blazar flares, in our previous studies, we leveraged the neutrino arrival time to boost the detection power. Here, we utilize the same principle, while substantially increasing the number of blazars in the sample. We searched for the spatiotemporal correlation of 356 IceCube high-energy neutrinos with major optical flares of 3225 radio- and 3814 $\gamma$-ray-selected blazars. We found that despite the increase in data size, the number of likely spatiotemporal associations remained low and the overall correlation strengths weak. Two individual associations were shown to drive our strongest correlation, namely, the only $>$2$\sigma$ post-trial spatiotemporal correlation, occurring with the BL Lac objects of the radio-selected blazar sample. We estimated that $\lesssim$8\% of the detected cosmic neutrinos were emitted by blazars during major optical flares. As a complementary analysis, we compared the synchrotron peak frequency, redshift, Doppler factor, X-ray brightness, and optical variability of spatially neutrino-associated blazars to those of the general blazar population. We found that spatially neutrino-associated blazars have a Doppler factor and X-ray brightness that are higher than average.

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

2 major / 3 minor

Summary. The manuscript reports a spatiotemporal correlation search between 356 IceCube high-energy neutrinos and major optical flares from 3225 radio-selected and 3814 gamma-ray-selected blazars. Despite the enlarged sample, the number of associations remains low, with only one >2σ post-trial correlation (driven by two events in the BL Lac subset of the radio sample). The authors estimate that ≲8% of detected cosmic neutrinos were emitted by blazars during such flares and find that spatially associated blazars show higher-than-average Doppler factors and X-ray brightness.

Significance. If the statistical results and upper limit hold under the stated assumptions, the work would strengthen the case that blazars contribute only a modest fraction of the high-energy neutrino flux even during major optical flares, consistent with prior weak population correlations. The expanded sample size and complementary source-property comparison are positive features; the approach of using flare timing to boost sensitivity is a logical extension of earlier studies.

major comments (2)
  1. [Results and Discussion] The ≲8% upper limit and the interpretation of the weak overall correlation rest on the assumption that high-energy neutrino emission is enhanced during the selected major optical flares (used to define the search windows). If this timing model is inaccurate, the restricted windows reduce detection power and the null result does not constrain the total blazar contribution; this assumption is load-bearing for the central claim and should be tested or relaxed with an explicit sensitivity study.
  2. [Methods and Statistical Analysis] The post-trial significance of the sole >2σ correlation (driven by two specific associations) and the derived 8% limit depend on the precise flare-identification threshold, flare-duration modeling, and background-rate estimation. These details are not fully specified, preventing full assessment of robustness against variations in the major-flare definition.
minor comments (3)
  1. [Data and Sample Selection] Clarify the exact criteria used to define 'major optical flares' and how flare windows are constructed, including any overlap handling or duration assumptions.
  2. [Results] Add a table or explicit list of the two driving neutrino-blazar associations, including their coordinates, times, and flare properties, to allow independent verification.
  3. [Abstract and Results] The abstract states 'two individual associations were shown to drive our strongest correlation'; ensure the main text quantifies their individual contributions to the test statistic before and after trials correction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the scope and robustness of our results. We address each major comment below and will incorporate revisions to improve the manuscript.

read point-by-point responses

  1. Referee: [Results and Discussion] The ≲8% upper limit and the interpretation of the weak overall correlation rest on the assumption that high-energy neutrino emission is enhanced during the selected major optical flares (used to define the search windows). If this timing model is inaccurate, the restricted windows reduce detection power and the null result does not constrain the total blazar contribution; this assumption is load-bearing for the central claim and should be tested or relaxed with an explicit sensitivity study.

    Authors: We agree that the assumption of enhanced neutrino emission during major optical flares is central to our search strategy and the resulting upper limit. Our ≲8% bound specifically constrains the contribution from blazars during these flares rather than the total blazar contribution at all times. If the enhancement assumption does not hold, the search windows would indeed have lower sensitivity, but the observed weak correlations still indicate that flaring blazars are not a dominant source even under this model. To address the referee's concern, we will add an explicit sensitivity study in the revised manuscript, for example by varying the assumed flare enhancement factor, adjusting window sizes, or comparing to a non-flaring baseline analysis. This will better quantify how the results depend on the timing model. revision: yes

  2. Referee: [Methods and Statistical Analysis] The post-trial significance of the sole >2σ correlation (driven by two specific associations) and the derived 8% limit depend on the precise flare-identification threshold, flare-duration modeling, and background-rate estimation. These details are not fully specified, preventing full assessment of robustness against variations in the major-flare definition.

    Authors: We acknowledge that the manuscript would benefit from more explicit specification of the flare-identification threshold, flare-duration modeling, and background-rate estimation to enable full reproducibility and robustness checks. In the revised version, we will expand the Methods section with precise descriptions of these procedures, including the exact criteria used to select major flares from the light curves, the modeling of flare durations, and the statistical approach to background estimation. We will also add a short discussion of how the post-trial significance and upper limit respond to reasonable variations in these choices. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from direct external catalog comparison

full rationale

The paper conducts a spatiotemporal correlation search between IceCube neutrino events and blazar optical flare times drawn from independent external catalogs (radio- and gamma-ray-selected samples). The assumption of enhanced neutrino emission during major flares is explicitly adopted as a sensitivity-enhancing hypothesis rather than derived from the present data or prior self-referential definitions. The reported ≲8% upper limit and correlation strengths are computed directly from the number and significance of observed associations in the data after trials correction, without any fitted parameters whose outputs are then relabeled as predictions. Self-citation to previous studies merely describes the adopted search strategy and does not supply the load-bearing justification for the current numerical results, which rely on a new, larger sample and external benchmarks. No step reduces by construction to its inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central findings rest on the flare-neutrino association assumption and choices in sample selection and statistical thresholds.

free parameters (1)
  • Major flare threshold
    The definition of 'major optical flares' likely involves a specific amplitude or significance cut that affects which events are included.
axioms (1)
  • domain assumption High-energy neutrino emission increases during major blazar flares
    This is the key assumption stated to justify using flare timing to enhance correlation detection.

pith-pipeline@v0.9.0 · 5885 in / 1376 out tokens · 47281 ms · 2026-05-18T05:49:45.870352+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

100 extracted references · 100 canonical work pages · 1 internal anchor

  1. [1]

    G., Abbasi, R., Abdou, Y ., et al

    Aartsen, M. G., Abbasi, R., Abdou, Y ., et al. 2013, Phys. Rev. Lett., 111, 021103

    work page 2013

  2. [2]

    G., Ackermann, M., Adams, J., et al

    Aartsen, M. G., Ackermann, M., Adams, J., et al. 2020, Phys. Rev. Lett., 124, 051103

    work page 2020

  3. [3]

    2025, arXiv e-prints, arXiv:2507.03989

    Abbasi, R., Ackermann, M., Adams, J., et al. 2025, arXiv e-prints, arXiv:2507.03989

    work page arXiv 2025

  4. [4]

    2022, ApJ, 928, 50

    Abbasi, R., Ackermann, M., Adams, J., et al. 2022, ApJ, 928, 50

    work page 2022

  5. [5]

    B., Archer, A., et al

    Acharyya, A., Adams, C. B., Archer, A., et al. 2023, ApJ, 954, 70 Adrián-Martínez, S., Ageron, M., Aharonian, F., et al. 2016, Journal of Physics G Nuclear Physics, 43, 084001

    work page 2023

  6. [6]

    Agudo, I., Boettcher, M., Falcke, H. D. E., et al. 2015, in Advancing Astro- physics with the Square Kilometre Array (AASKA14), 93 Article number, page 14 of 17 Kouch et al.: Association of the IceCube neutrinos with CAZ blazar light curves

    work page 2015

  7. [7]

    2025, ApJ, 985, L15

    Agudo, I., Liodakis, I., Otero-Santos, J., et al. 2025, ApJ, 985, L15

    work page 2025

  8. [8]

    A., Allison, P., Beatty, J

    Aguilar, J. A., Allison, P., Beatty, J. J., et al. 2021, Journal of Instrumentation, 16, P03025

    work page 2021

  9. [9]

    2022, ApJS, 263, 24

    Ajello, M., Baldini, L., Ballet, J., et al. 2022, ApJS, 263, 24

    work page 2022

  10. [10]

    2024, ApJ, 964, 3

    Albert, A., Alves, S., André, M., et al. 2024, ApJ, 964, 3

    work page 2024

  11. [11]

    2021, ApJ, 911, 48 Astropy Collaboration, Price-Whelan, A

    Albert, A., André, M., Anghinolfi, M., et al. 2021, ApJ, 911, 48 Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, ApJ, 935, 167

    work page 2021

  12. [12]

    B., Abdo, A

    Atwood, W. B., Abdo, A. A., Ackermann, M., et al. 2009, ApJ, 697, 1071

    work page 2009

  13. [13]

    2025, arXiv e-prints, arXiv:2507.03613

    Azzollini, A., Buson, S., Coleiro, A., et al. 2025, arXiv e-prints, arXiv:2507.03613

    work page arXiv 2025

  14. [14]

    Baikal-GVD: status and prospects

    Backes, M., Müller, C., Conway, J. E., et al. 2016, in The 4th Annual Conference on High Energy Astrophysics in Southern Africa (HEASA 2016), 29 Baikal-GVD Collaboration, Avrorin, A. D., Avrorin, A. V ., et al. 2018, arXiv e-prints, arXiv:1808.10353

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  15. [15]

    2021, ApJ, 921, 45

    Bartos, I., Veske, D., Kowalski, M., Márka, Z., & Márka, S. 2021, ApJ, 921, 45

    work page 2021

  16. [16]

    2023, ApJ, 955, L32

    Bellenghi, C., Padovani, P., Resconi, E., & Giommi, P. 2023, ApJ, 955, L32

    work page 2023

  17. [17]

    C., Kulkarni, S

    Bellm, E. C., Kulkarni, S. R., Graham, M. J., et al. 2019, PASP, 131, 018002

    work page 2019

  18. [18]

    & Hochberg, Y

    Benjamini, Y . & Hochberg, Y . 1995, Journal of the Royal Statistical Society. Series B (Methodological), 57, 289

    work page 1995

  19. [19]

    2019, ARA&A, 57, 467

    Blandford, R., Meier, D., & Readhead, A. 2019, ARA&A, 57, 467

    work page 2019

  20. [20]

    & Novikova, P

    Blinov, D. & Novikova, P. 2025, A&A, 694, L10 Böttcher, M. 2019, Galaxies, 7, 20

    work page 2025

  21. [21]

    2023, arXiv e-prints, arXiv:2305.11263

    Buson, S., Tramacere, A., Oswald, L., et al. 2023, arXiv e-prints, arXiv:2305.11263

    work page arXiv 2023

  22. [22]

    2022, ApJ, 933, L43

    Buson, S., Tramacere, A., Pfeiffer, L., et al. 2022, ApJ, 933, L43

    work page 2022

  23. [23]

    2019, MNRAS, 483, L12 Cherenkov Telescope Array Consortium, Acharya, B

    Cerruti, M., Zech, A., Boisson, C., et al. 2019, MNRAS, 483, L12 Cherenkov Telescope Array Consortium, Acharya, B. S., Agudo, I., et al. 2019, Science with the Cherenkov Telescope Array

    work page 2019

  24. [24]

    P., Romani, R

    Cohen, D. P., Romani, R. W., Filippenko, A. V ., et al. 2014, ApJ, 797, 137

    work page 2014

  25. [25]

    Davison, A. C. & Hinkley, D. V . 1997, Bootstrap Methods and their Application, Cambridge Series in Statistical and Probabilistic Mathematics (Cambridge University Press)

    work page 1997

  26. [26]

    J., Djorgovski, S

    Drake, A. J., Djorgovski, S. G., Mahabal, A., et al. 2009, ApJ, 696, 870

    work page 2009

  27. [27]

    Eisenstein, D. J. & Hut, P. 1998, ApJ, 498, 137

    work page 1998

  28. [28]

    2017, in International Cos- mic Ray Conference, V ol

    Fang, K., Alvarez-Muniz, J., Alves Batista, R., et al. 2017, in International Cos- mic Ray Conference, V ol. 301, 35th International Cosmic Ray Conference (ICRC2017), 996

    work page 2017

  29. [29]

    V ., Li, W

    Filippenko, A. V ., Li, W. D., Treffers, R. R., & Modjaz, M. 2001, in Astronom- ical Society of the Pacific Conference Series, V ol. 246, IAU Colloq. 183: Small Telescope Astronomy on Global Scales, ed. B. Paczynski, W.-P. Chen, & C. Lemme, 121

    work page 2001

  30. [30]

    Fiorillo, D. F. G., Testagrossa, F., Petropoulou, M., & Winter, W. 2025, ApJ, 986, 104

    work page 2025

  31. [31]

    2020, ApJ, 893, 162

    Franckowiak, A., Garrappa, S., Paliya, V ., et al. 2020, ApJ, 893, 162

    work page 2020

  32. [32]

    2019, Nature Astronomy, 3, 88

    Gao, S., Fedynitch, A., Winter, W., & Pohl, M. 2019, Nature Astronomy, 3, 88

    work page 2019

  33. [33]

    2024, A&A, 687, A59

    Garrappa, S., Buson, S., Sinapius, J., et al. 2024, A&A, 687, A59

    work page 2024

  34. [34]

    2011, MNRAS, 414, 2674

    Ghisellini, G., Tavecchio, F., Foschini, L., & Ghirlanda, G. 2011, MNRAS, 414, 2674

    work page 2011

  35. [35]

    2020, MNRAS, 497, 865

    Giommi, P., Glauch, T., Padovani, P., et al. 2020, MNRAS, 497, 865

    work page 2020

  36. [36]

    2016, AJ, 151, 154

    Gordon, D., Jacobs, C., Beasley, A., et al. 2016, AJ, 151, 154

    work page 2016

  37. [37]

    R., Millman, K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357

    work page 2020

  38. [38]

    & Plant, K

    Hooper, D. & Plant, K. 2023, Phys. Rev. Lett., 131, 231001

    work page 2023

  39. [39]

    & Lindfors, E

    Hovatta, T. & Lindfors, E. 2019, New A Rev., 87, 101541

    work page 2019

  40. [40]

    2021, A&A, 650, A83

    Hovatta, T., Lindfors, E., Kiehlmann, S., et al. 2021, A&A, 650, A83

    work page 2021

  41. [41]

    2019, in International Cosmic Ray Conference, V ol

    Huber, M. 2019, in International Cosmic Ray Conference, V ol. 36, 36th Interna- tional Cosmic Ray Conference (ICRC2019), 916

    work page 2019

  42. [42]

    Hunter, J. D. 2007, Computing in Science and Engineering, 9, 90 IceCube Collaboration, Aartsen, M. G., Ackermann, M., et al. 2018, Science, 361, 147 IceCube Collaboration, Abbasi, R., Ackermann, M., et al. 2022, Science, 378, 538 IceCube Collaboration, Abbasi, R., Ackermann, M., et al. 2021, arXiv e-prints, arXiv:2101.09836 Ivezi´c, Ž., Kahn, S. M., Tyson...

    work page arXiv 2007

  43. [43]

    2016, Nature Physics, 12, 807

    Kadler, M., Krauß, F., Mannheim, K., et al. 2016, Nature Physics, 12, 807

    work page 2016

  44. [44]

    Adriani et al

    Keivani, A., Murase, K., Petropoulou, M., et al. 2018, ApJ, 864, 84 KM3NeT Collaboration, MessMapp Group, Fermi-LAT Collaboration, et al. 2025a, arXiv e-prints, arXiv:2502.08484 KM3NeT Collaboration, S., A., Albert, A., Alhebsi, A. R., et al. 2025b, Nature, 638, 376

    work page arXiv 2018

  45. [45]

    Y ., Petrov, L., Fomalont, E

    Kovalev, Y . Y ., Petrov, L., Fomalont, E. B., & Gordon, D. 2007, AJ, 133, 1236

    work page 2007

  46. [46]

    Y ., Pushkarev, A

    Kovalev, Y . Y ., Pushkarev, A. B., Gomez, J. L., et al. 2025, arXiv e-prints, arXiv:2504.09287 Krauß, F., Kadler, M., Mannheim, K., et al. 2014, A&A, 566, L7

    work page arXiv 2025

  47. [47]

    2020, ApJ, 902, 133

    Kreter, M., Kadler, M., Krauß, F., et al. 2020, ApJ, 902, 133

    work page 2020

  48. [48]

    2022, ApJ, 934, 180

    Kun, E., Bartos, I., Becker Tjus, J., et al. 2022, ApJ, 934, 180

    work page 2022

  49. [49]

    2023, A&A, 679, A46

    Kun, E., Bartos, I., Becker Tjus, J., et al. 2023, A&A, 679, A46

    work page 2023

  50. [50]

    B., et al

    Kun, E., Bartos, I., Tjus, J. B., et al. 2024, Phys. Rev. D, 110, 123014 Lähteenmäki, A. & Valtaoja, E. 2003, ApJ, 590, 95 León-Tavares, J., Valtaoja, E., Tornikoski, M., Lähteenmäki, A., & Nieppola, E. 2011, A&A, 532, A146

    work page 2024

  51. [51]

    P., et al

    Liodakis, I., Kiehlmann, S., Marscher, A. P., et al. 2024, A&A, 689, A200

    work page 2024

  52. [52]

    2024, arXiv e- prints, arXiv:2404.19730

    Lu, M.-X., Liang, Y .-F., Ouyang, X., Li, R.-L., & Wang, X.-G. 2024, arXiv e- prints, arXiv:2404.19730

    work page arXiv 2024

  53. [53]

    2024, Universe, 10, 53

    Malecki, P. 2024, Universe, 10, 53

    work page 2024

  54. [54]

    1993, A&A, 269, 67

    Mannheim, K. 1993, A&A, 269, 67

    work page 1993

  55. [55]

    & Biermann, P

    Mannheim, K. & Biermann, P. L. 1989, A&A, 221, 211

    work page 1989

  56. [56]

    & Petropoulou, M

    Mastichiadis, A. & Petropoulou, M. 2021, ApJ, 906, 131

    work page 2021

  57. [57]

    D., & Blandford, R

    Meyer, M., Scargle, J. D., & Blandford, R. D. 2019, ApJ, 877, 39

    work page 2019

  58. [58]

    & Caccianiga, A

    Moretti, A. & Caccianiga, A. 2025, arXiv e-prints, arXiv:2507.17908 Mücke, A. & Protheroe, R. J. 2001, Astroparticle Physics, 15, 121

    work page arXiv 2025

  59. [59]

    Muxlow, T. W. B., Pedlar, A., Holloway, A. J., Gallimore, J. F., & Antonucci, R. R. J. 1996, MNRAS, 278, 854

    work page 1996

  60. [60]

    O., et al

    Nilsson, K., Lindfors, E., Takalo, L. O., et al. 2018, A&A, 620, A185

    work page 2018

  61. [61]

    2023, MNRAS, 526, 347

    Novikova, P., Shishkina, E., & Blinov, D. 2023, MNRAS, 526, 347

    work page 2023

  62. [62]

    2022, in 37th International Cosmic Ray Conference, 30

    Oikonomou, F. 2022, in 37th International Cosmic Ray Conference, 30

    work page 2022

  63. [63]

    2019, MNRAS, 489, 4347

    Oikonomou, F., Murase, K., Padovani, P., Resconi, E., & Mészáros, P. 2019, MNRAS, 489, 4347

    work page 2019

  64. [64]

    2025, A&A, 695, A266

    Omeliukh, A., Garrappa, S., Fallah Ramazani, V ., et al. 2025, A&A, 695, A266

    work page 2025

  65. [65]

    2022, MNRAS, 511, 4697

    Padovani, P., Boccardi, B., Falomo, R., & Giommi, P. 2022, MNRAS, 511, 4697

    work page 2022

  66. [66]

    2019, MNRAS, 484, L104

    Padovani, P., Oikonomou, F., Petropoulou, M., Giommi, P., & Resconi, E. 2019, MNRAS, 484, L104

    work page 2019

  67. [67]

    M., Liodakis, I., & et al

    Paggi, A., Kouch, P. M., Liodakis, I., & et al. 2025, Submitted to A&A

    work page 2025

  68. [68]

    F., Traianou, E., Debbrecht, L

    Paraschos, G. F., Traianou, E., Debbrecht, L. C., Liodakis, I., & Ros, E. 2025, arXiv e-prints, arXiv:2507.16929

    work page arXiv 2025

  69. [69]

    L., Liodakis, I., & Romani, R

    Peirson, A. L., Liodakis, I., & Romani, R. W. 2022, ApJ, 931, 59

    work page 2022

  70. [70]

    M., Phillips, C., & Horiuchi, S

    Petrov, L., de Witt, A., Sadler, E. M., Phillips, C., & Horiuchi, S. 2019, MNRAS, 485, 88

    work page 2019

  71. [71]

    Y ., Kovalev, Y

    Plavin, A., Kovalev, Y . Y ., Kovalev, Y . A., & Troitsky, S. 2020, ApJ, 894, 101

    work page 2020

  72. [72]

    V ., Burenin, R

    Plavin, A. V ., Burenin, R. A., Kovalev, Y . Y ., et al. 2024, J. Cosmology Astropart. Phys., 2024, 133

    work page 2024

  73. [73]

    V ., Kovalev, Y

    Plavin, A. V ., Kovalev, Y . Y ., Kovalev, Y . A., & Troitsky, S. V . 2021, ApJ, 908, 157

    work page 2021

  74. [74]

    V ., Kovalev, Y

    Plavin, A. V ., Kovalev, Y . Y ., Kovalev, Y . A., & Troitsky, S. V . 2023, MNRAS, 523, 1799

    work page 2023

  75. [75]

    V ., Kovalev, Y

    Plavin, A. V ., Kovalev, Y . Y ., & Troitsky, S. V . 2025, arXiv e-prints, arXiv:2503.08667

    work page arXiv 2025

  76. [76]

    & Oikonomou, F

    Podlesnyi, E. & Oikonomou, F. 2025, arXiv e-prints, arXiv:2502.12111

    work page arXiv 2025

  77. [77]

    Readhead, A. C. S., Cohen, M. H., Pearson, T. J., & Wilkinson, P. N. 1978, Nature, 276, 768

    work page 1978

  78. [78]

    2019, ApJ, 881, 46

    Reimer, A., Böttcher, M., & Buson, S. 2019, ApJ, 881, 46

    work page 2019

  79. [79]

    2019, MNRAS, 484, 2067

    Righi, C., Tavecchio, F., & Pacciani, L. 2019, MNRAS, 484, 2067

    work page 2019

  80. [80]

    & Böttcher, M

    Robinson, J. & Böttcher, M. 2024, ApJ, 977, 42

    work page 2024

Showing first 80 references.