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arxiv: 2405.17409 · v3 · submitted 2024-05-27 · 🌌 astro-ph.HE · hep-ph· nucl-th

Ultraheavy Ultrahigh-Energy Cosmic Rays

B. Theodore Zhang , Kohta Murase , Nick Ekanger , Mukul Bhattacharya , Shunsaku Horiuchi This is my paper

Pith reviewed 2026-05-24 00:41 UTC · model grok-4.3

classification 🌌 astro-ph.HE hep-phnucl-th
keywords ultraheavy nucleiultrahigh-energy cosmic raysenergy loss lengthsAmaterasu particlecollapsarsneutron star mergersshower maximum depthcosmic ray propagation
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The pith

Ultraheavy nuclei lose energy more slowly than protons or iron at energies up to 300 EeV, allowing them to account for the highest-energy cosmic rays observed.

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

The paper examines the travel of ultraheavy nuclei through space as ultrahigh-energy cosmic rays. It calculates that these nuclei retain their energy over longer distances than protons and intermediate-mass nuclei at energies below 300 EeV. This leads to the conclusion that cosmic rays above about 100 EeV, such as the Amaterasu particle, could be ultraheavy nuclei arriving from distant sources. The work also places limits on how much these nuclei can contribute and finds consistency with production rates from collapsars and neutron star mergers. Predictions include a lower average shower depth than iron nuclei at the highest energies, which future detectors can check.

Core claim

We show that the energy loss lengths of ultraheavy nuclei at energies ≲300 EeV are significantly longer than those of protons and intermediate-mass nuclei. The highest-energy cosmic rays beyond ∼100 EeV, including the Amaterasu particle, may therefore be ultraheavy ultrahigh-energy cosmic rays. For the first time constraints are derived on the contribution of such sources, and current data remain consistent with energy generation rate densities of UHECRs from collapsars and neutron star mergers. The model further predicts that the mean depth of shower maximum lies below the value for iron nuclei beyond 100 EeV.

What carries the argument

Energy loss lengths of ultraheavy nuclei during propagation as ultrahigh-energy cosmic rays.

If this is right

  • Cosmic rays above 100 EeV, including the Amaterasu particle, can be ultraheavy nuclei.
  • Energy generation rates from collapsars and neutron star mergers remain consistent with the observed UHECR flux when ultraheavy nuclei are included.
  • The mean depth of shower maximum is expected to fall below the iron value beyond 100 EeV.
  • Enhanced contribution from a nearby transient that includes ultraheavy nuclei can reduce the spectral tension between the Telescope Array and Pierre Auger Observatory.

Where Pith is reading between the lines

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

  • If ultraheavy nuclei dominate at the highest energies, source distance estimates would need revision because their longer loss lengths allow farther travel.
  • Composition analyses at future observatories would have to incorporate nuclei heavier than iron to interpret the highest-energy events correctly.
  • The role of transient sources in supplying ultraheavy nuclei could be tested by searching for directional correlations with nearby collapsars or mergers at energies above 100 EeV.

Load-bearing premise

The nuclear interaction cross sections and propagation modeling for ultraheavy nuclei at these energies are accurate enough to determine the loss lengths.

What would settle it

Future composition data from AugerPrime or the Global Cosmic Ray Observatory showing that the mean depth of shower maximum above 100 EeV is not lower than the iron expectation would contradict the model's prediction.

Figures

Figures reproduced from arXiv: 2405.17409 by B. Theodore Zhang, Kohta Murase, Mukul Bhattacharya, Nick Ekanger, Shunsaku Horiuchi.

Figure 1
Figure 1. Figure 1: FIG. 1. Total energy loss lengths for various nuclei: p, He, O, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Energy spectra and the first/second moments of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Skymap of backtracked particles with mean energy [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Energy loss lengths for photodisintegration (thick [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Photodisintegration cross sections for UH nuclei as [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Propagation distance, [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Energy spectra and the first/second moments of [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Demonstrative example for explaining the TA spec [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
read the original abstract

We investigate the propagation of ultraheavy (UH) nuclei as ultrahigh-energy cosmic rays (UHECRs). We show that their energy loss lengths at $\lesssim300$ EeV are significantly longer than those of protons and intermediate-mass nuclei, and that the highest-energy cosmic rays with energies beyond $\sim100$ EeV, including the Amaterasu particle, may be UH-UHECRs. For the first time, we derive constraints on the contribution of UH-UHECR sources, and find that the current data are consistent with energy generation rate densities of UHECRs from collapsars and neutron star mergers. Our model predicts that the mean value of the depth of shower maximum is lower than that for iron nuclei beyond 100 EeV, which can be tested with future composition measurements, e.g., AugerPrime and the Global Cosmic Ray Observatory. In addition, the spectral tension between the Telescope Array (TA) and the Pierre Auger Observatory can be alleviated by considering the enhanced contribution of UHECRs -- including UH nuclei -- from a nearby transient.

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 / 2 minor

Summary. The paper investigates the propagation of ultraheavy (UH) nuclei as ultrahigh-energy cosmic rays (UHECRs). It claims that their energy loss lengths at ≲300 EeV are significantly longer than those of protons and intermediate-mass nuclei, allowing the highest-energy events beyond ∼100 EeV (including the Amaterasu particle) to be UH-UHECRs. The authors derive constraints showing consistency between current data and energy generation rate densities from collapsars and neutron star mergers. The model predicts a lower mean depth of shower maximum than for iron nuclei beyond 100 EeV (testable with AugerPrime and GCRO) and suggests that enhanced contributions from nearby transients can alleviate the TA-Auger spectral tension.

Significance. If the propagation results hold, the work is significant for providing the first quantitative constraints on UH-UHECR source contributions and a potential resolution to the origin of the highest-energy events, along with falsifiable predictions for composition observables. It also links UHECR observations to specific transient source classes.

major comments (2)
  1. [§3] §3 (propagation modeling): The central claim of significantly longer energy loss lengths at ≲300 EeV for UH nuclei (A ≫ 56) rests on photodisintegration cross sections obtained by scaling or phenomenological extrapolation from A ≤ 56 data. No dedicated validation, sensitivity analysis to variations in σ(E,A), or comparison to available heavy-nucleus models is described; if actual cross sections are larger, the loss lengths shorten and both the propagation reach and source-consistency claims are affected.
  2. [§4] §4 (source constraints): The statement that current data are consistent with energy generation rate densities from collapsars and neutron star mergers is presented without an explicit description of the quantitative procedure (e.g., which likelihood or comparison metric is used, which propagation outputs feed into the rate calculation, or which table/figure shows the allowed parameter range).
minor comments (2)
  1. [Abstract] Abstract: The abbreviation 'UH-UHECRs' is introduced without expansion on first use; a parenthetical definition would improve readability.
  2. [Results section] Xmax prediction: The claim of a lower mean depth of shower maximum than for iron nuclei should be accompanied by a quantitative difference (e.g., in g cm^{-2}) and the energy range over which it holds, preferably with model uncertainty bands.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help improve the clarity and robustness of our manuscript. We address each major comment below and will revise the paper accordingly.

read point-by-point responses

  1. Referee: [§3] §3 (propagation modeling): The central claim of significantly longer energy loss lengths at ≲300 EeV for UH nuclei (A ≫ 56) rests on photodisintegration cross sections obtained by scaling or phenomenological extrapolation from A ≤ 56 data. No dedicated validation, sensitivity analysis to variations in σ(E,A), or comparison to available heavy-nucleus models is described; if actual cross sections are larger, the loss lengths shorten and both the propagation reach and source-consistency claims are affected.

    Authors: We agree that the photodisintegration cross sections for ultraheavy nuclei rely on scaling from lighter nuclei, as no direct experimental data exist for A ≫ 56 at these energies. Our modeling follows standard scaling prescriptions used in the UHECR literature. To address the concern, we will add a dedicated sensitivity analysis varying the cross sections by plausible factors and discuss the resulting impact on loss lengths and propagation reach. We will also reference any available heavy-nucleus models for comparison where relevant. This addition will quantify the robustness of the central claim. revision: yes

  2. Referee: [§4] §4 (source constraints): The statement that current data are consistent with energy generation rate densities from collapsars and neutron star mergers is presented without an explicit description of the quantitative procedure (e.g., which likelihood or comparison metric is used, which propagation outputs feed into the rate calculation, or which table/figure shows the allowed parameter range).

    Authors: We acknowledge that the quantitative procedure for the source constraints requires more explicit description. In the revised manuscript, we will expand §4 to detail the comparison metric employed, how the propagation outputs (energy loss lengths and spectra) enter the rate calculation, and explicitly reference the figures or tables displaying the allowed parameter ranges for the energy generation rate densities. This will make the consistency statement fully reproducible. revision: yes

Circularity Check

0 steps flagged

No circularity: propagation modeling and source constraints are independent of target observables

full rationale

The paper computes energy-loss lengths for UH nuclei via photodisintegration and fragmentation rates, then compares the resulting propagation reach and composition predictions against existing UHECR data to derive source-rate constraints. These steps rely on external nuclear-physics inputs and standard propagation codes rather than fitting parameters directly to the Amaterasu event or the TA/Auger spectral tension; the consistency statement is therefore a genuine comparison, not a tautology. No self-definitional equations, fitted-input predictions, or load-bearing self-citations that collapse the central claim appear in the abstract or described derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; all modeling details are absent.

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Forward citations

Cited by 1 Pith paper

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  1. Study of Flat Spectrum Radio Quasars and BL Lacertae Objects as Sources of Diffusive Ultra High-Energy Cosmic Rays

    astro-ph.HE 2025-11 unverdicted novelty 4.0

    BL Lacs remain consistent with UHECR observations while FSRQs are disfavoured by anisotropy and source density mismatches after propagation modeling.

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