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REVIEW 3 major objections 5 minor 52 references

Evidence for the Sombrero Galaxy as an Accelerator of the Highest-Energy Cosmic Rays

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims a 25.7-event cosmic-ray multiplet above 40 EeV, found in 17 years of Pierre Auger Phase I data, is spatially associated with the Sombrero Galaxy at 4.5σ local and 3.3σ global significance, providing evidence that active…

desk verdict The reported 3.3σ Sombrero association rests on a likelihood equation with a dimensionally wrong Fisher concentration parameter; the paper needs a major correction or a code release before the result can be believed. read the letter →

arxiv 2412.11966 v1 pith:5MIY26FD submitted 2024-12-16 astro-ph.HE astro-ph.GAhep-phhep-th

Hao-Ning He , Eiji Kido , Kai-Kai Duan , Yang Yang , Ryo Higuchi , Yi-Zhong Fan , Tao Wang , Lu-Yao Jiang
show 7 more authors
Rong-Lan Li Ben-Yang Zhu Xiang Li Zi-Qing Xia Shigehiro Nagataki Da-Ming Wei Alexander Kusenko
This is my paper · ORCID
classification astro-ph.HEastro-ph.GAhep-phhep-th
keywords ultrahigh-energycosmicrayscosmic-raymultipletsmagneticdeflectionPierreAugerObservatorySombreroGalaxyactivegalacticnucleimaximumlikelihoodsources
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 paper argues that the long-standing mystery of where ultrahigh-energy cosmic rays come from has a concrete answer in the local universe: a cluster of about 26 events with energies above 40 EeV, recorded over 17 years by the Pierre Auger Observatory, appears to be a magnetic-lens image of a single source. After fitting source position and magnetic deflection parameters simultaneously, the authors find the only plausible accelerator inside the allowed horizon is the Sombrero Galaxy, a nearby active galaxy with a billion-solar-mass black hole and radio jets and lobes. The association has a local significance of 4.5σ and a global, look-elsewhere-corrected significance of 3.3σ. If correct, this would be the first compelling identification of a specific active supermassive black hole as a source of the highest-energy particles in the Universe.

What carries the argument

The load-bearing object is a refined maximum-likelihood function that models each cosmic-ray event as either isotropic background or as a member of a point-source multiplet whose apparent direction is shifted by a regular magnetic deflection proportional to 100 EeV divided by energy and smeared by a random deflection with the same energy scaling, convolved with an angular scatter distribution for the random walk. The six free parameters are source right ascension and declination, the regular deflection amplitude, the random deflection amplitude, the regular-deflection direction angle, and the multiplet count; the test statistic compares this model against a background-only hypothesis. Because the method fits the deflection parameters from data rather than assuming a specific Galactic magnetic-field model, the source identification is tied to the energy ordering of the multiplet rather than to prior assumptions about field geometry. A conservative horizon distance for the 165 EeV event is used to restrict the source search to a sphere of radius 39.6 Mpc.

What would settle it

Compare the atomic-number composition of the 25 multiplet members: if they are not consistent with a single nucleus type, the assumed 1/E deflection scaling fails. A direct test is whether the multiplet reappears at the same sky position in the next independent dataset, for example future data from the same observatory or from the other large cosmic-ray detector; if the excess does not grow, the association would be a fluctuation.

Watch

Extended reading notes

Core claim

Using a six-parameter maximum-likelihood search over the 1,387 Phase I events above 40 EeV, the paper finds a multiplet of 25.7 events whose apparent source sits near the Sombrero Galaxy, with the 165 EeV event arriving closest to the source direction and lower-energy members spread systematically farther away. The energy-dependent spread matches the expectation for a single cosmic-ray nucleus type being deflected by Galactic magnetic fields, with regular and random deflection amplitudes of about 20.7 degrees and 2.7 degrees at 100 EeV. Fixing the source to the Sombrero gives a test statistic of 37.6, a local p-value of 7×$10^{-6}$, and a global p-value of 9.8×$10^{-4}$; excluding the 165 EeV event lowers the source test statistic by only 3.6, so the association is not carried by that single extreme event. The paper concludes that active supermassive black holes can accelerate cosmic rays to energies beyond 100 EeV.

Load-bearing premise

The analysis assumes every cosmic ray above 40 EeV has the same atomic number; if the true composition is a mixture or varies with energy, the energy-scaling pattern that ties the multiplet to the Sombrero could be distorted and the fitted position could shift.

Editorial extensions

If this is right

  • If the association holds, active galactic nuclei with powerful jets and lobes become the leading identified source class for the highest-energy cosmic rays.
  • The Sombrero's jet power of about 2.3×10^42 erg per second is more than sufficient: the derived UHECR luminosity of about 1.9×10^40 erg per second is roughly one percent of the jet power, comfortably within the energy budget.
  • The multiplet pattern predicts that higher-energy cosmic rays from the Sombrero arrive closer to its direction, so future events above 100 EeV should cluster around the fitted source position.
  • The method can be applied to other nearby active galaxies to decide whether Sombrero-like objects are common ultrahigh-energy cosmic-ray accelerators.
  • Improved energy and composition measurements from next-generation observatories should sharpen the source position and test the pure-composition assumption directly.

Reading between the lines

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

  • Inference: at 3.3σ global significance, the result is suggestive but not yet a claimed discovery; an independent dataset of comparable size is the natural next check.
  • Inference: the same likelihood machinery could be pointed at every active galaxy with kilo- or tens-of-kiloparsec radio lobes within roughly 40 Mpc, converting a single-source case into a population test.
  • Inference: the fitted small random deflection of about 2.7 degrees makes a testable prediction for Galactic magnetic-field models: along the line of sight to the Sombrero, the turbulent field must be weak enough to keep a 100 EeV nucleus within a few degrees.
  • Inference: if future composition data show the multiplet is actually a mixture of nucleus types, the pure-composition likelihood would need to be replaced by a rigidity-dependent model and the apparent source position could shift, providing a direct falsification test.
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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

3 major / 5 minor

Summary. The paper searches for ultrahigh-energy cosmic-ray (UHECR) multiplets in 17 years of Pierre Auger Phase I data above 40 EeV, using a six-parameter maximum-likelihood method that fits source coordinates, regular and random magnetic deflection parameters, and the number of source events, against an isotropic background weighted by the Auger exposure. The authors report a best-fit multiplet of about 25 events with TS = 41.1 (global significance 3.7 sigma) and, after fixing the source to the Sombrero Galaxy (M104), TS = 37.6 with local and global significances of 4.5 sigma and 3.3 sigma, respectively. They argue that M104 is the only cataloged candidate within the 95% confidence region of the fitted source position and within a conservative 39.6 Mpc horizon, and they support the interpretation with CRPropa simulations of magnetic deflections in a Galactic magnetic field model.

Significance. If the statistical claim holds, this would be an important step in identifying a plausible nearby AGN accelerator of the highest-energy cosmic rays: the multiplet contains a 165 EeV event, is spatially associated with a known supermassive black hole with jets and lobes, and the energy-ordered pattern is consistent with magnetic deflection expectations. The paper has clear strengths: it uses public Auger data, estimates significances with background-only Monte Carlo simulations including exposure and energy uncertainties, applies a look-elsewhere penalty, tests robustness by removing the highest-energy event, and uses an independent CRPropa simulation. However, the central likelihood formula appears dimensionally wrong as written, so the reported TS values and significances cannot currently be reproduced from the manuscript; this issue must be resolved before the statistical claim can be assessed.

major comments (3)
  1. [Methods, Eq. (4) and surrounding text] The definition of the Fisher concentration parameter is dimensionally inconsistent and appears to make the source likelihood nearly isotropic. The paper states kappa = 2/sqrt(sigma_ran^2 + sigma_ang^2), with sigma_ran and sigma_ang quoted in degrees. For the Sombrero fit (A_ran = 2.7 deg, sigma_ang = 1 deg, at 100 EeV) this gives kappa ~ 0.7, for which a Fisher distribution is only weakly peaked: f_src(0)/f_src(pi) = exp(2 kappa) ~ 4, so an event at the source direction is only mildly favored over an event on the opposite side of the sky. Such a likelihood cannot produce the tight energy-ordered multiplet of Figure 1 or the reported TS = 37.6. The correct small-angle relation is kappa ~ 1/sigma^2 with sigma in radians, giving kappa ~ 450 for the same parameters. Because every likelihood ratio in Eqs. (5)-(9), and hence every quoted TS value, best-fit n_s, source position, and significance, flows through Eq. (4), this is a load-bearing issue. The authors must either correct the definition and recompute all results, or explicitly report the formula actually used in the code and show that it matches the corrected expression.
  2. [Methods, Eqs. (2)-(3), pure-composition assumption] The analysis assumes a pure composition for all UHECRs above 40 EeV. This assumption is load-bearing because the energy-dependent deflection law in Eqs. (2)-(3) is linear in Z, and the apparent source position S'(E) is defined using one Z. If the composition is mixed or energy-dependent, events of different Z at the same energy have different deflections, so the fitted multiplet shape and the best-fit source coordinates can be biased. The paper acknowledges this qualitatively but does not quantify the effect. Please repeat the 6-parameter fit under alternative composition assumptions (e.g., Z=1, Z=7, and Z=26, or a two-component mixture) and report the changes in the fitted source position, n_s, TS, and the resulting significances.
  3. [Methods, Source Catalogs, and Conclusions] The claim that the Sombrero Galaxy is 'the' source rather than 'the only cataloged candidate' depends on the completeness of the adopted catalogs. The paper correctly notes that the van Velzen et al. radio-galaxy sample excludes sources below 213 mJy, and the Updated Nearby Galaxy Catalog is not a complete flux-limited sample for faint jets and lobes. Therefore the statement that no other source lies within the 95% confidence region is only as strong as the completeness limits of the catalogs used. Please state the effective completeness limits for the relevant source classes, or explicitly soften the source-identification claim to 'the only known candidate within the adopted horizon and confidence region'.
minor comments (5)
  1. [Methods, Eq. (7)] The product in Eq. (7) runs from i=0 to n_tot; it should run from i=1 to n_tot.
  2. [Throughout] There are several typographical issues: 'invariance' should likely be 'concentration parameter'; 'extragalacitc' should be 'extragalactic'; 'Jasson' should be 'Jansson'; 'Mattews' should be 'Matthews'; and 'PAOphase Idata' needs spacing.
  3. [Author contributions] The text refers to 'Figure S3', but no supplementary figure S3 appears in the manuscript; please correct the reference.
  4. [Figure 3 and simulation comparison] The similarity between the observed and simulated multiplets is assessed only visually. A quantitative comparison (e.g., a two-sample test on angular distances from the source, or a likelihood ratio between the observed data and the simulated pattern) would make the supporting argument more convincing.
  5. [Table 2] For the Sombrero rows in Table 2 the source coordinates are fixed at the known galaxy position, unlike the fitted coordinates in the best-fit column; this should be indicated explicitly to avoid confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the likelihood method is self-contained, significance is Monte Carlo against background-only simulations, and the CRPropa simulation uses an independent GMF model.

full rationale

The derivation chain is not circular by construction. The multiplet search uses a six-parameter maximum-likelihood fit (Eqs. 2-8) in which source coordinates, magnetic-deflection parameters, and multiplet size are all fitted to the data; the reported significance is obtained by comparing the observed TS to TS values from 5x10^4 background-only simulations that contain no multiplet. The claim that the observed multiplet is 'consistent with the theoretical expected distribution' is a description of the best-fit model, not an independent prediction, and the association significance rests on the Monte Carlo p-value rather than on that consistency. The source identification is a posterior localization step: the 68% and 95% confidence regions of the fitted source coordinates are searched against external catalogs, and the Sombrero Galaxy is found to be the only candidate within the adopted horizon distance. This is standard catalog matching, not an input assumed to produce the answer. The CRPropa simulation with the Jansson & Farrar (2012) Galactic magnetic field is independent of the fitted parameters and is used only for qualitative comparison. The citation to He et al. (2016) for the maximum-likelihood approach is a self-citation, but the method is fully re-derived in the Methods section and the conclusion does not depend on an unverified theorem imported from that paper; it is a tool, not the result. The paper also checks robustness by removing the 165 EeV event. The dimensional issue noted for kappa in Eq. (4) (kappa = 2/sqrt(sigma_ran^2 + sigma_ang^2) with angles in degrees) is a potential correctness or reproducibility problem, not a circularity problem, because it does not make the analysis assume its own conclusion. No circular step can be exhibited from the text.

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

The central claim rests on a statistical fit with six free parameters (source position, two deflection amplitudes, one angle, and source count) and on several domain assumptions about composition, magnetic-field structure, and source-catalog completeness. No new physical entities are introduced.

free parameters (6)
  • source right ascension alpha_s = 188.7 deg
    Best-fit coordinate of the multiplet source in the 6-parameter likelihood search (Table 1).
  • source declination delta_s = -8.3 deg
    Best-fit coordinate of the multiplet source (Table 1).
  • regular deflection amplitude A_reg = 22.8 deg
    Amplitude of the systematic (regular-field) deflection at 100 EeV, fitted to data (Eq. 2, Table 1).
  • random deflection amplitude A_ran = 2.5 deg
    RMS random-field deflection at 100 EeV, fitted to data (Eq. 3, Table 1).
  • regular deflection direction phi_reg = 197.5 deg
    Clockwise angle of the systematic shift, fitted to data (Table 1).
  • source event count n_s = 25.2
    Number of UHECRs in the multiplet, fitted to data (Table 1).
assumptions (6)
  • domain assumption Pure composition of UHECRs above 40 EeV
    The likelihood and the multiplet pattern assume a single Z for all events; the paper cites Mayotte et al. (2023) for a CNO-dominated composition but does not fit a mixed composition. Invoked in Methods.
  • domain assumption Deflection model with 1/E scaling for regular and random components
    Eqs. (2) and (3) parameterize deflections as A_reg*(100 EeV/E) and A_ran*(100 EeV/E), assuming a homogeneous single-Z composition and simplified Galactic magnetic field statistics.
  • standard math Fisher distribution for angular scatter
    The distribution of separation angles theta_i is a 2D isotropic Gaussian on the sphere (Fisher distribution), Eq. (4). This is a standard statistical model.
  • domain assumption Isotropic background with PAO exposure
    The null hypothesis is an isotropic UHECR flux modulated by the PAO exposure; background simulations sample this. Assumed in the likelihood and significance estimation.
  • domain assumption Horizon distance of the 165 EeV event is <= 39.6 Mpc
    The source search is restricted to objects within the conservative proton horizon from Globus et al. (2023). A shorter horizon would reduce the candidate list; a longer one could add sources.
  • domain assumption Source catalog completeness within the horizon
    The claim that Sombrero is the only candidate depends on the completeness of the X-ray cluster, starburst, Swift-BAT, Fermi-LAT, and radio galaxy catalogs used.

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Cite this review

Pith. "Pith review of Evidence for the Sombrero Galaxy as an Accelerator of the Highest-Energy Cosmic Rays." pith.science (2026). https://pith.science/paper/5MIY26FD

@misc{pith2026241211966,
  author       = {Pith},
  title        = {Pith review of: Evidence for the Sombrero Galaxy as an Accelerator of the Highest-Energy Cosmic Rays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5MIY26FD}},
  note         = {Machine review of arXiv:2412.11966}
}
abstract

Ultrahigh-energy cosmic rays (UHECRs) are the highest energy messenger from space, with energies exceeding 1 EeV. Although UHECRs were discovered over 60 years ago, their origin still remains a mystery. Pinpointing sources of UHECRs is crucial for understanding the extreme astrophysical processes that accelerate particles to such extraordinary energies. We searched for UHECR multiplets via analyzing 17 years of data with energies greater than 40 EeV from the Pierre Auger Observatory. A spatial association is found between a multiplet of $25.7^{+6.2}_{-7.0}$ cosmic rays and the Sombrero galaxy with a local (global) significance of $4.5~\sigma~(3.3~\sigma)$. The Sombrero galaxy hosts a supermassive central black hole with a mass of $\sim1\times 10^9 M_{\odot}$ and exhibits large-scale radio lobes and jets. Our finding provides critical evidence on active supermassive black holes as the source of the highest-energy cosmic rays.

Figures

Figures reproduced from arXiv: 2412.11966 by the authors.

Figure 2
Figure 2. Simulating the background-only datasets To assess the significance of finding a UHECR multiplet or a multiplet associated with the Sombrero Galaxy, we simulate datasets of isotropically distributed UHECRs, ensuring that their distribution follows the PAO exposure, and no additional UHECR multiplet signals are included. Firstly, we 10 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 1
Figure 1. The skymap of the observed UHECR multiplet from the PAO data. The top 25 cosmic rays (filled circles) with energies greater than 40 EeV from the PAO Phase I data exhibiting the highest probability of originating from the same source at the best-fit position, as indicated by the blue star. The small dots represent the other UHECR events with energy larger than 40 EeV from the PAO Phase I data. The green star denotes … view at source ↗
Figure 2
Figure 2. The confidence regions of the source coordinates. The 68% and 95% confidence regions of the source coordinates, taking into account the errors of the reconstructed energies of the UHECRs, are indicated by solid and dotted lines, respectively. The red star denotes the coordinates of the Sombrero Galaxy. The color code denotes the probability in arbitrary units. The blue dot denotes the coordinates with the peak proba… view at source ↗
Figures from the paper (4 more)
Figure 3
Figure 3. Figure 3: The skymap of the simulated UHECR multiplet from the Sombrero Galaxy. The simulated distribution of a multiplet of 100 UHECRs from the Sombrero galaxy assuming the atomic number as Z=7, predicted via the lensing function in CRpropa29, taking into account the Jasson & F…
Figure 4
Figure 4. Figure 4: The sketch showing the deflections of UHECRs of different energies. The sketch showing the deflections of two UHECRs with energies of 𝐸lo and 𝐸hi, and coordinates of (𝛼lo, 𝛿lo) and (𝛼hi, 𝛿hi), respectively, where 𝐸lo < 𝐸hi. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_4.png]
Figure 5
Figure 5. Figure 5: The value of 𝑙𝑛( 𝑓src,𝑖), 𝑙𝑛(𝐿𝑖), 𝑙𝑛(𝐿b,𝑖) and 𝑙𝑛(𝐿𝑖/𝐿b,𝑖). The value of 𝑙𝑛( 𝑓src,𝑖), 𝑙𝑛(𝐿𝑖), 𝑙𝑛(𝐿b,𝑖) and 𝑙𝑛(𝐿𝑖/𝐿b,𝑖) for the PAO Phase I events with energies greater than 40 EeV, utilizing the 6 best-fit parameters. The blue star denotes the coordinates of the best-f…
Figure 6
Figure 6. Figure 6: The color image of the Sombrero Galaxy. A color composite image showcasing the global morphology of M 104, constructed by stacking Sloan Digital Sky Survey (SDSS) images in the g, r, and i filters, represented in blue, green and red, respectively. White contours indica…

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Reviewed August 11, 2026 · model on record in the stance chip above.