Pith. sign in

REVIEW 4 major objections 5 minor 10 references

New full-sky studies of the distribution of ultra-high-energy cosmic-ray arrival directions

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read This paper reports that the combined full-sky cosmic-ray dataset still points to starburst galaxies as the most likely sources, at 4.2 sigma post-trial, with a quadrupole pattern visible in every catalogue comparison.

desk verdict Solid proceedings update with a genuinely new harmonic-space analysis, but the headline 4.2σ rests on a trial-factor correction the paper never spells out. read the letter →

arxiv 2507.10441 v1 pith:7IH2CKHZ submitted 2025-07-14 astro-ph.HE

A. Gálvez Ureña , L. Anchordoqui , M. Bianciotto , P. Biermann , T. Bister , J. Biteau , L. Caccianiga , O. Deligny
show 13 more authors
L. Deval A. di Matteo U. G. Giaccari G. Golup R. Higuchi J. Kim M. Kuznetsov J.P. Lundquist F.M. Mariani G. Rubtsov P. Tinyakov F. Urban (for the Pierre Auger Collaboration the Telescope Array Collaboration)
This is my paper · ORCID
classification astro-ph.HE
keywords ultra-high-energycosmicraysfull-skyanisotropyPierreAugerObservatoryTelescopeArraystarburstgalaxiesactivegalacticnucleiharmoniccross-correlationquadrupole
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

Ultra-high-energy cosmic rays arrive nearly isotropically, so any anisotropy in their arrival directions is a clue about where they come from. This paper combines full-sky data from the Pierre Auger Observatory and the Telescope Array, adding new atmospheric corrections and an extra dataset at the highest energies, and reports that the correlation with starburst galaxies remains the strongest at 4.2 sigma post-trial even after accounting for energy losses. The new harmonic-space analysis finds the quadrupole to be the most significant multipole in every catalogue comparison, with the cross-correlation against all AGNs reaching 3.0 sigma post-trial. The authors present the harmonic cross-correlation as a promising tool for future source matching because it is less affected by magnetic-field deflections and catalogue shot noise.

What carries the argument

The key mechanism is the full-sky spherical-harmonic expansion of both the cosmic-ray map and the galaxy catalogue maps. The auto-correlation $C_\ell^{\mathrm{CR\,CR}}$ and cross-correlation $C_\ell^{\mathrm{CR\,Cat}}$ are computed for every multipole up to $\ell=20$, and the whole procedure is repeated for energy thresholds from 32 to 80 EeV, so that each multipole's significance is evaluated with a proper scan. The cross-correlation is the decisive device: its noise is the product of independent fluctuations in the two maps, so an appropriate catalogue can reveal structure that the auto-correlation would smear out. The medium-scale likelihood anchors the search with von Mises–Fisher kernels centred on catalogue sources, weighted by flux and an attenuation model fit to Auger data.

What would settle it

Re-run the full analysis on isotropic simulated skies with the same exposure, scanning every energy threshold from 32 to 80 EeV, every multipole up to $\ell=20$, and all four catalogues, and observe whether a quadrupole cross-correlation as strong as the measured one appears in more than 5% of simulations; if it does, the 3.0 $\sigma$ AGN claim would not be supported by the data.

Watch

Extended reading notes

Core claim

The central claim is that the combined full-sky UHECR sky is not isotropic: it has a dipole, a quadrupole that aligns with the supergalactic plane at the highest energies, and a statistically persistent correlation with the distribution of starburst galaxies and AGNs. Using the latest TA data with daily and yearly atmospheric corrections, the dipole and quadrupole in the highest-energy bin strengthen but remain within statistical uncertainty. The medium-scale likelihood search, now including energy-loss attenuation and two new AGN catalogues, still finds starburst galaxies the most significant at 4.2 $\sigma$ post-trial. The new harmonic-space analysis, scanning multipoles up to $\ell=20$ and energy thresholds from 32 to 80 EeV, shows that the quadrupole is the most significant multipole in all cases; its cross-correlation with all AGNs is 3.0 $\sigma$ post-trial, with starburst galaxies at 2.7 $\sigma$. These results are presented as the strongest current evidence that the highest-energy cosmic rays trace nearby star-forming galaxies and AGN populations.

Load-bearing premise

The results depend on the post-trial significance correction being correct; the paper states that the scan over energy and multipoles up to $\ell=20$ is taken into account but gives no details of how the trial factor is computed, so an underestimated correction would shrink the claimed significances.

Editorial extensions

If this is right

  • The 4.2 sigma starburst correlation, if real, means the highest-energy cosmic rays come preferentially from star-forming galaxies within about 130 Mpc, not from the general galaxy population.
  • The persistent quadrupole, most significant in every catalogue, points to a large-scale anisotropy along the supergalactic plane that future exposure can measure with more precision.
  • Since including attenuation mainly boosts the all-galaxy correlation, energy-loss corrections are now part of the full-sky source search rather than an optional refinement.
  • The harmonic-space cross-correlation gives a new observable, the per-multipole catalogue correlation, that can be tracked as both observatories accumulate data.

Reading between the lines

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

  • The harmonic cross-correlation method could be ported to other full-sky messengers, such as neutrino or gamma-ray maps, to search for the same starburst-galaxy and AGN patterns.
  • A combined analysis that adds the dipole and quadrupole signals, or merges the quadrupole significance across catalogues, may approach the 5 sigma threshold with only modest additional data.
  • The strengthening dipole and quadrupole at the highest energies, if confirmed, would make the full-sky UHECR map a useful probe of the local distribution of matter within roughly 100 Mpc.
  • Because the trial-factor treatment is not specified in detail, an independent simulation of the full scan over energy thresholds, multipoles, and catalogues would be the decisive check on whether the AGN quadrupole correlation is real or a fluctuation.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper presents updated full-sky analyses of ultra-high-energy cosmic-ray (UHECR) arrival directions using combined Pierre Auger Observatory and Telescope Array data. It includes: (i) an updated large-scale anisotropy analysis with new TA atmospheric corrections; (ii) an extended intermediate-scale correlation analysis with four galaxy catalogs, including energy-loss attenuation; and (iii) a new harmonic-space analysis computing auto- and cross-correlations up to ℓmax=20 while scanning energy thresholds. The main claims are a 4.2σ post-trial correlation with starburst galaxies (unchanged by attenuation), a quadrupole as the most significant multipole in all considered cases, and cross-correlation significances up to 3.0σ post-trial for the all-AGN catalog.

Significance. If the quoted post-trial significances are correct, the results strengthen the evidence for a full-sky starburst-galaxy correlation of UHECRs and introduce a promising harmonic-space method for probing anisotropy patterns at the quadrupole scale. The inclusion of attenuation in the medium-scale analysis is a notable step beyond previous full-sky studies. Strengths include the use of full-sky coverage, careful cross-calibration of the two observatories, and explicit comparison of attenuation-included and attenuation-free results. The main vulnerability is that the statistical calibration that turns pre-trial into post-trial significances is not documented in sufficient detail to be verified.

major comments (4)
  1. [§4 and §5, Tables 1 and 2] The post-trial significance calculation is asserted but not described. Section 4 reports one-tailed post-trial significances in Table 1 without any explanation of how the trial factor accounts for the scan over energy thresholds (49 values from 32 to 80 EeV), the four catalogs, and the free parameters f and Θ. Section 5 states that 'we follow the most conservative approach, by taking into account the scan in energy and the measurements of different multipoles up to ℓ=20' but does not specify the number of isotropic simulations, whether the energy catalog and multipole scans are treated jointly, or whether the medium-scale f and Θ searches are included. Without this information the quoted post-trial values (4.2σ in Table 1, 3.0σ in Table 2) cannot be reproduced or independently validated, and this is load-bearing for the paper's central claims.
  2. [Table 1, starburst row] The attenuation-included starburst fit reports f = 10.6+56.6−3.2 and Θ = 17.6+26.6−4.1, with the paper noting that the large upper uncertainties are 'under investigation'. Such extreme asymmetric uncertainties indicate a flat or degenerate likelihood direction, which can make the maximum TS value and its location unstable. Since the starburst correlation is the headline result, the authors should provide a profile-likelihood scan or another diagnostic to demonstrate that the TS = 27.3 maximum is robust; the no-attenuation starburst line (f = 10.6+4.0−2.7, Θ = 15.0+4.8−2.9, same TS and 4.2σ) appears better behaved, but the attenuation-included fit is used for the harmonic cross-correlations in Table 2 and therefore requires attention.
  3. [§5, Cross-correlation significance] The Gaussian approximation for the isotropic cross-correlation distribution is introduced as an assumption ('to reduce computational time') but is not validated. For ℓ=2 the cross-correlation is an average over only 2ℓ+1 = 5 modes, so the central-limit justification for Gaussianity is weak; inaccuracies in the assumed distribution would propagate directly into the pre-trial p-values and hence the post-trial significances in Table 2. Because isotropic simulations are already being produced, replacing the Gaussian approximation with the empirical distribution of the simulated cross-correlation coefficients would be straightforward and would remove this source of systematic uncertainty.
  4. [§4 and §5, attenuation model] The attenuation model, including composition fractions, injection spectral index, and rigidity cutoff, is the best fit to Auger data from [4] that was used to describe the same starburst correlation. Testing the same catalogs with this model introduces a moderate circularity for the attenuation-included results: the trial factor does not scan over the attenuation parameters, so the reported significances are conditional on a model that was not independently derived. The no-attenuation starburst line in Table 1 provides an important control, but the all-AGN and jetted-AGN harmonic cross-correlation results in Table 2 have no such control. The authors should at least show that varying the attenuation parameters within their quoted uncertainties does not materially change the significances, or explicitly discuss this limitation.
minor comments (5)
  1. [§5] The word 'mutipoles' in the post-trial description is a typo and should read 'multipoles'.
  2. [§4] In the sentence 'in the case of the all-galaxy and starburst galaxy catalogues we also shown results', 'shown' should be 'show'.
  3. [§3] The large-scale analysis quotes p-values (e.g., p = 0.011 and p = 0.0041) and converts them to Gaussian sigmas; the conversion convention (one-tailed or two-tailed) should be stated.
  4. [§2] For the loose-cut TA dataset used in the medium-scale and harmonic analyses, the paper notes that atmospheric corrections are not available and that an older energy calibration from [2] is used; it would be helpful to quantify the resulting systematic uncertainty on the energy thresholds and thus on the reported significances.
  5. [Figure 4] The labels in the multipanel figure are small and the panels are dense; enlarging the font and adding panel labels (a), (b), etc. would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central anisotropy and cross-correlation significances are measured from new full-sky data against isotropic simulations; the underdocumented post-trial trial factor is a statistical-calibration concern, not a circular reduction.

full rationale

The paper's central claims are measurements, not derivations from fitted inputs. The intermediate-scale search uses an attenuation model whose composition and injection parameters are quoted from an external spectrum/composition fit ([8], Aab et al. 2017), not fitted to the arrival-direction test statistic; the starburst-galaxy template and catalogues are external, and the likelihood-ratio TS(f,Theta,E_min) is computed against an isotropic null with the scan over Theta, f, and energy threshold carried into the reported post-trial significances. The harmonic-space auto- and cross-correlations are computed directly from full-sky maps and calibrated with isotropic simulations, with pre-trial p-values derived from the Percival-Brown distribution or Gaussian simulations. The new TA loose-cut data and the atmospheric corrections provide independent input not present in the earlier Auger-only [4] analysis. No equation in the paper equates a predicted quantity with a fitted parameter by construction. The main weakness is not circularity but documentation: Section 5 states 'we follow the most conservative approach, by taking into account the scan in energy and the measurements of different multipoles up to ℓ=20' without specifying the simulation count, scan volume, or analytic method, and Table 1 notes that large upper uncertainties on f and Theta for the attenuated starburst case are 'under investigation'. These are calibration and robustness concerns, not circular reductions. Minor self-citations ([2], [4], [7], [10]) are used for dataset definitions, prior results, and standard shot-noise formulae; none carries the load of the new 4.2-sigma or 3.0-sigma claims, so they do not make the derivation circular.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The analysis rests on a set of empirical parameters (energy cross-calibration, atmospheric correction, attenuation model) and on standard statistical distributional assumptions. No new physical entities are introduced. The most consequential inputs are the attenuation model fitted to prior Auger data and the energy cross-calibration parameters, both of which influence the central correlation significances.

free parameters (4)
  • Cross-calibration energy scale parameters α and β = α = -0.150 ± 0.011, β = 0.962 ± 0.016 (loose-cut analysis: α = -0.159, β = 0.954)
    Fitted to the spectrum in the common declination band (Section 2, Figure 2) to map Telescope Array energies to the Auger scale. These parameters set the thresholds E1, E2, E3 used in the dipole, quadrupole, and harmonic analyses, so the reported anisotropies depend on them.
  • TA atmospheric correction parameters = coefficient 3.5, exponent 1.7, reference density 1.042 kg/m^3
    The correction E_corr = E_raw * (1 - 3.5(rho/1.042 - 1))^(-1/1.7) is adopted from detector simulations and applied to TA energies. The parameters are empirical and are not refit here, but they affect the energies and hence the dipole and quadrupole results.
  • Attenuation model parameters from [4] = composition: 67.3% He, 28.1% N, 4.6% Si at 1 EeV; injection spectral index -0.96; rigidity cutoff log10(R) = 18.68 V
    The flux attenuation a(D_s, E_min) is computed following the best fit to Auger data in [4] assuming the Epos LHC model. These parameters shape the source catalog maps and directly affect the TS values in the medium-scale and harmonic analyses.
  • Search parameters f and Θ per catalog = e.g., starburst galaxies f = 10.6 (+56.6/-3.2)%, Θ = 17.6 (+26.6/-4.1)°; all galaxies f = 13.1% and Θ = 15.5°
    The correlated fraction f and smearing angle Θ are fitted to maximize the TS (Section 4, Table 1). They are parameters of the search, and the reported significances depend on them; post-trial corrections are applied but are not fully described.
assumptions (6)
  • domain assumption The full-sky estimator a_lm = sum_events Y_lm(n)/omega(n) provides unbiased estimates of the spherical harmonic coefficients.
    Invoked in Section 3 without a derivation; standard for full-sky UHECR analyses assuming the exposure model is correct.
  • standard math The auto-correlation C_l of an isotropic sky follows the Percival and Brown distribution, used to compute p-values.
    Adopted from [9] in Section 5; this distribution is the standard likelihood for pseudo-C_l estimates.
  • domain assumption Cross-correlation significances follow a Gaussian distribution with mean and standard deviation from isotropic simulations.
    Stated in Section 5 as an assumption to reduce computational time; the validity for the low-event-count regime is not tested.
  • domain assumption The UHECR source flux is a weighted sum of von Mises-Fisher distributions plus an isotropic background, with the attenuation model as specified.
    This is the signal model in Section 4; it assumes the source catalogs and weights are complete and the attenuation model from [4] is applicable.
  • domain assumption The Telescope Array looser-cut dataset (E_TA > 57 EeV) has an energy-dependent exposure that is correctly modeled by the function omega(n, E).
    Section 4 uses different TA exposures for 40-57 EeV and above 57 EeV; this piecewise exposure model must be accurate for the TS to be valid.
  • domain assumption The cross-calibration fit in the common declination band produces a valid energy mapping for the full-sky anisotropy studies.
    The paper notes the cross-calibration is optimized for anisotropy studies (Section 2), but the mapping could in principle distort anisotropy if the two observatories sample different spectral shapes.

how reviews work

0 comments
Cite this review

Pith. "Pith review of New full-sky studies of the distribution of ultra-high-energy cosmic-ray arrival directions." pith.science (2026). https://pith.science/paper/7IH2CKHZ

@misc{pith2026250710441,
  author       = {Pith},
  title        = {Pith review of: New full-sky studies of the distribution of ultra-high-energy cosmic-ray arrival directions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7IH2CKHZ}},
  note         = {Machine review of arXiv:2507.10441}
}
abstract

Ground-based full-sky studies of the angular distribution of arrival directions of ultra-high-energy cosmic rays require combining data from different observatories, such as the Pierre Auger Observatory (Auger) and the Telescope Array (TA), because no single array can cover all declinations. A working group comprising members from the Auger and TA collaborations has been tasked with performing such studies for more than a decade and has found several indications of full-sky anisotropies. Here, we update the results for the large- and medium-scale anisotropy analyses using the latest data from TA, which include corrections for daily and yearly atmospheric effects in data for large-scale anisotropies and looser selection criteria in data for medium-scale anisotropies. We extend the latter one by considering two more galaxy catalogues, consisting of jetted or all AGNs. Finally we also introduce a new angular harmonic space analysis that allows us to measure both the auto-correlation and cross-correlation with all catalogues for all multipoles independently ($\ell_\text{max} = 20$ in this work) and scanning the energy threshold.

Figures

Figures reproduced from arXiv: 2507.10441 by the authors.

Figure 1
Figure 1. Directional exposures of the datasets we used for large-scale anisotropies (those for medium￾scale anisotropies have the same shapes and slightly higher normalizations) We use the latest datasets available, in￾cluding events detected in Auger from 1 Jan￾uary 2004 to 31 December 2022 for Auger and in TA from 11 May 2008 to 10 May 2024. The Auger datasets are the same as in our previous work [2]: one with stricter cut… view at source ↗
Figure 2
Figure 2. The spectrum fit to the two datasets in order to obtain a mapping between Auger and TA energy scales. The highest-energy bins of each dataset (de￾noted by thin pale lines) are combined into one larger bin (denoted by regular lines) to ensure the probability distribution can be approximated as log-normal. UHECR energy measurements are affected by sizeable systematic uncertainties (±14% for Auger and ±21% for TA). Thi… view at source ↗
Figure 3
Figure 3. The flux distribution of the dataset we use for large-scale anisotropies (equatorial coordinates, Mollweide projection), smoothed by a 45°-radius top-hat window 2This cross-calibration is optimized for anisotropy studies and should not be used outside of the scope of this analysis. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: The first and second panels show how the magnitude and direction of the dipole have changed with the inclusion of TA atmospheric corrections; the next ones show how the harmonic space auto-correlation (also known as angular power spectrum) has changed in the different …
Figure 5
Figure 5. Figure 5: Significances of the correlations with galaxy catalogues as a function of the energy threshold. 𝐸min TS 𝑓 /% Θ/° post-trial All galaxies 37 EeVAuger ≈ 47 EeVTA 19.3 13.1 +4.7 −3.6 15.5 +6.1 −3.6 3.4𝜎 Starburst galaxies 38 EeVAuger ≈ 48 EeVTA 27.3 10.6 +56.6 −3.2 17.6 +…
Figure 6
Figure 6. Figure 6: Pre-trial significances for each multipole order and energy threshold of the Auto-Correlation and the Cross-Correlation with all galaxies, starburst galaxies, jetted AGNs and all AGNs. Cross-Correlations follow a Gaussian distribution, while the Auto-Correlations follo…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

10 extracted references · 6 canonical work pages

  1. [4]

    Abreu et al

    P. Abreu et al. [Pierre Auger collab.],ApJ 935 (2022) 170 [2206.13492]

    arXiv 2022

  2. [1]

    How isotropic can the UHECR flux be?

    A. di Matteo and P. Tinyakov,MNRAS 476 (2018) 715 [1706.02534]

    work page Pith review arXiv 2018

  3. [2]

    G.Rubtsovetal.[forthePierreAugerandTelescopeArraycollabs.], PoS(UHECR2024)009

    work page

  4. [3]

    Abdul Halim et al

    A. Abdul Halim et al. [Pierre Auger collab.],ApJ 976 (2024) 48 [2408.05292]

    arXiv 2024

  5. [5]

    A.Aabetal.[PierreAugerandTelescopeArraycollabs.], ApJ 794(2014)172[ 1409.3128]

    work page Pith review arXiv 2014

  6. [6]

    Abbasi et al

    R.U. Abbasi et al. [Telescope Array collab.],ApJL 790 (2014) L21 [1404.5890]

    arXiv 2014

  7. [7]

    Tinyakov et al

    P. Tinyakov et al. [for the Pierre Auger and Telescope Array collabs.],PoS(ICRC2021) 375

    work page

  8. [8]

    Aab et al

    A. Aab et al. [Pierre Auger collab.],JCAP 04(2017) 038 [1612.07155]

    arXiv 2017

Show all 10 references
  1. [9]

    Percival and M.L

    W.J. Percival and M.L. Brown,MNRAS 372(2006) 1104 [astro-ph/0604547]

    2006 arXiv

  2. [10]

    Tor Vergata

    F.R. Urban, S. Camera and D. Alonso,A&A 652 (2021) A41 [2005.00244]. 8 New full-sky studies of the distribution of UHECR arrival directions A. Gálvez Ureña The Pierre Auger Collaboration A. Abdul Halim 13, P. Abreu 70, M. Aglietta 53,51, I. Allekotte 1, K. Almeida Cheminant 78...

    2021 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.