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Energy Spectrum and Mass Composition of Ultra-High-Energy Cosmic Rays Originating from Relativistic Jets of Nearby Radio Galaxies

T0 review · 2 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Virgo A's faster jet gives the northern sky a brighter, proton-dominated flux above $10^{20.2}$ eV, while the southern sky falls off steeply and stays heavy.

desk verdict Worth engaging: a clean model study whose new, testable North-South asymmetry prediction is not as robust as claimed—it sits on M87's assumed spine Lorentz factor of 7, and their own run with Gamma=3 erases it. read the letter →

arxiv 2506.15110 v1 pith:IRWN72NR submitted 2025-06-18 astro-ph.HE

Jeongbhin Seo (1 , 2) , Dongsu Ryu (1) , Hyesung Kang (3) ((1) Department of Physics , College of Natural Sciences , UNIST , Korea , (2) Los Alamos National Laboratory
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Theoretical Division USA (3) Department of Earth Sciences Pusan National University Korea)
This is my paper · ORCID
classification astro-ph.HE
keywords ultra-high-energycosmicraysFanaroff-Rileyradiogalaxiesrelativisticjetsdoublepower-lawsourcespectrumextendedexponentialcutoffshearaccelerationcosmic-raymasscompositionpropagation
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

This paper tries to establish that if nearby radio galaxies are the main sources of ultra-high-energy cosmic rays (particles above about $10^{18}$ eV), the highest-energy sky should look different in the two hemispheres: brighter and more proton-dominated in the north, fainter and heavier in the south. The mechanism is a newly adopted source spectrum, a double power law with an extended exponential cutoff whose characteristic energy grows as the square of the jet spine's Lorentz factor, which gives the fast jet of Virgo A a long high-energy tail that slower jets lack. Propagating this spectrum to Earth with a Monte Carlo code, the authors find that Virgo A's arriving cosmic rays above about $10^{20.2}$ eV are mostly protons, while Centaurus A and Fornax A contribute a steeper, heavier flux. The consequence, if true, is a concrete astrophysical explanation for the apparent north-south differences in cosmic-ray spectra and composition at the highest energies.

What carries the argument

The load-bearing object is the double power-law source spectrum with an 'extended' exponential cutoff, Equation (2): $$dN/dE_0\,dt = S_n f_r(A_0)\left[(E_0/Z_0E_b)^{-s_1} + (E_0/Z_0E_b)^{-s_2}\right]^{-1}\exp[-E_0/(Z_0E_b\langle\Gamma\rangle_{\rm spine}^2)],$$ with $s_1\approx -0.5$ to $-0.6$, $s_2\approx -2.6$, and a cutoff extended by the square of the mean jet-spine Lorentz factor. This form encodes the authors' earlier finding that relativistic shear acceleration pushes particles beyond the break energy $E_b$ up to a cutoff at $Z_0 E_b \langle\Gamma\rangle_{\rm spine}^2$. The break energy follows $E_b\approx 45\,{\rm EeV}\,\phi\xi\,(Q_j/Q_n)^\alpha$ with $\alpha=1/4$ for Fanaroff-Riley type I (FR-I) jets and $1/3$ for type II (FR-II) jets. A Monte Carlo propagation code then maps the spectrum to Earth, including pair production, photopion losses, and photo-disintegration; the high value $\langle\Gamma\rangle_{\rm spine}\approx 7$ for Virgo A is what produces its distinctive surviving proton tail.

What would settle it

Measure Virgo A's kpc-scale jet spine speed with very long baseline interferometry or proper-motion monitoring: a Lorentz factor below about 3 would push the extended cutoff below $10^{20.2}$ eV and erase the predicted northern proton excess. Alternatively, if a northern-sky observatory above $10^{20.2}$ eV sees a composition as heavy as the southern sky, or no excess toward Virgo A, the central claim fails.

Watch

Extended reading notes

Core claim

The central discovery is a predicted hemispheric asymmetry in the arriving ultra-high-energy cosmic-ray population, driven by the jet-spine Lorentz factor of the nearest radio galaxies. Using a source spectrum with an extended exponential cutoff at rigidity-scaled energy $Z_0 E_b \langle\Gamma\rangle_{\rm spine}^2$, the authors find that Virgo A ($\langle\Gamma\rangle_{\rm spine}\approx 7$) injects a substantial flux beyond $10^{20.2}$ eV, and that photo-disintegration during the 16 Mpc journey converts much of that heavy-nucleus tail into protons. Centaurus A and Fornax A, with spine Lorentz factors of about $1.2$ and $1.5$, lack this extended tail; their arriving spectra drop steeply above $10^{20.2}$ eV and their composition stays heavier. Cygnus A, despite the highest Lorentz factor, contributes little because its 250 Mpc distance strips the flux. The authors therefore state that if radio galaxies are major sources of ultra-high-energy cosmic rays, the northern sky (dominated by Virgo A) and the southern sky (dominated by Centaurus A and Fornax A) should differ in both flux and composition at the highest energies.

Load-bearing premise

Everything rests on the adopted source spectrum and on Virgo A's jet being as fast as claimed, with a spine Lorentz factor near 7; the paper itself notes that the factor $\phi\xi$ setting the break energy is chosen from a representative range and that further refinement would be speculative.

Editorial extensions

If this is right

  • Above roughly $10^{20.2}$ eV, a northern-sky observatory should see a proton-dominated excess associated with Virgo A, while southern-sky data should show a steeper cutoff and a heavier composition.
  • The north-south difference should appear mainly at the highest energies; below about $10^{19.5}$ eV the model does not demand a strong hemispheric split in either spectrum or composition.
  • In this model, the jet's spine Lorentz factor is a first-order control on the arriving composition: lowering it from 7 to 3 steepens the cutoff and markedly increases the mean mass at Earth.
  • Cygnus A, despite being the most powerful jet considered, should not appear as a high-energy source at Earth, because propagation over 250 Mpc removes nearly all of its flux.
  • Accurate measurements of Virgo A's kpc-scale jet speed would directly sharpen or weaken the predicted northern high-energy tail.

Reading between the lines

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

  • If this source spectrum is right, part of the observed discrepancy between northern and southern ultra-high-energy measurements could be astrophysical rather than instrumental; the paper presents the asymmetry as a prediction of the radio-galaxy origin, not as a resolution of that discrepancy.
  • A full-sky observatory at the highest energies could distinguish this model from a uniform source population: the predicted pattern is a proton excess localized toward Virgo A, with a corresponding deficit elsewhere.
  • The mechanism should generalize to any nearby jet with a spine Lorentz factor above about 5, so measuring the spine speeds of the full local radio-galaxy sample would turn the model into a quantitative sky map of the highest-energy cosmic rays.
  • The main confounder is magnetic deflection; the paper brackets path-length increases with one-dimensional ensembles, but a three-dimensional magnetohydrodynamic propagation study would test whether the Virgo A protons remain associated with the source direction at $10^{20.2}$ eV.
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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

2 major / 5 minor

Summary. The manuscript adopts a double power-law (DPL) source spectrum with an 'extended' exponential cutoff, previously derived by the authors from relativistic hydrodynamic plus Monte Carlo simulations of FR-type jets, and uses CRPropa to propagate ultra-high-energy cosmic rays from Virgo A, Centaurus A, Fornax A, and Cygnus A to Earth. The authors compute arrival energy spectra and mean logarithmic mass for a grid of jet models (Table 2), varying break energy, spine Lorentz factor, host metallicity, EBL model, and propagation distance range. The central finding is that, because Virgo A is assigned a high spine Lorentz factor, its DPL source has a high-energy tail that survives the short 16 Mpc propagation, producing a brighter and proton-dominated flux above about 10^20.2 eV, while Centaurus A and Fornax A, with lower Lorentz factors, produce heavier and steeper spectra. Cygnus A, despite its high power, contributes little because of its 250 Mpc distance. The authors conclude that, if radio galaxies are the dominant UHECR sources, the energy spectrum and mass composition observed in the Northern and Southern skies should differ at the highest energies.

Significance. If the prediction is correct, it supplies a concrete, testable link between jet kinematics and UHECR spectrum and composition, potentially bearing on the reported PAO/TA differences. The paper's strengths are its systematic model grid, its use of the public CRPropa code with standard EBL and photodisintegration processes, its direct comparison with the conventional single power-law injection, and its unusually explicit statements about parameter uncertainty. The physical mechanism, an extended cutoff scaling as Z0 Eb <Gamma>^2_spine, is well motivated by the authors' earlier simulations. However, the quantitative predictions are substantially less secure than the qualitative trends, because the headline Virgo A versus Centaurus A/Fornax A contrast is controlled by two poorly pinned parameters, Eb and <Gamma>_spine. As a scenario study the paper is valuable; as a robust prediction it currently overreaches.

major comments (2)
  1. [Section 3, Figures 4 and 6; Table 1; Eq. (2)] The load-bearing asymmetry between Virgo A and the southern sources is not robust to the observationally allowed range of M87's spine Lorentz factor. Equation (2) places the exponential cutoff at Z0 Eb <Gamma>^2_spine, so the contrast is controlled by the adopted values: 49 for VirA1 versus 1.44 and 2.25 for CenA1 and ForA1. Table 1 sets <Gamma>_spine = 7 for Virgo A based on kpc-scale superluminal pattern speeds, but pattern speeds are not necessarily flow speeds, and published estimates for M87's kpc jet include values near 3. The authors' own VirA3 run, identical to VirA1 except <Gamma>_spine = 3, shows a steep dN/dE decline above about 10^20.2 eV and a heavier <lnA>, qualitatively matching the behavior the paper attributes to Centaurus A and Fornax A (Figure 4). The +/-20% shaded bands in Figure 6 do not cover this factor-of-two excursion, so the statements in the abstract and Section 4 that the qualitative trends are robust are not supported. Please quantify the threshold in <Gamma>_spine (and Eb) above which the high-energy tail survives, add an observationally motivated lower-Lorentz-factor run for Virgo A, and present the hemispheric asymmetry explicitly as conditional on <Gamma>_spine being near the upper end of the allowed range.
  2. [Section 2.1, Eq. (3); Table 1] The break energy Eb is equally load-bearing, and its acknowledged uncertainty is not propagated into the robustness claim. The adopted relation Eb ~ 45 EeV x phi*xi (Qj/Qn)^alpha relies on phi*xi chosen from a representative range 0.15-0.7, with the text stating that further refinement would be speculative. Because the exponential cutoff scale is Z0 Eb <Gamma>^2_spine, the difference between VirA1 (Eb = 10 EeV) and VirA2 (Eb = 30 EeV) changes both the propagated spectrum and the composition substantially (Figure 4). The +/-20% variations in Figure 6 are smaller than the factor-of-three to five spread admitted for phi*xi in Table 1 and the surrounding text. The authors should either perform a joint sensitivity study over the full adopted ranges of phi*xi and <Gamma>_spine, or explicitly restrict all conclusions to the chosen fiducial values rather than claiming robustness to 'plausible parameter values'.
minor comments (5)
  1. [Section 2.4, Eq. (6)] The propagation function is computed for a power-law injection with gamma = -2 and then applied to all DPL and SPL models. Figure 3 shows weak gamma dependence for proton-only and iron-only injections over the distance ranges considered, so the approximation is defensible, but a short validation using the actual mixed-composition VirA1 and CenA1 spectra at the highest energies would remove residual doubt.
  2. [Figures 4 and 5] The captions state that the <lnA> values at Earth are artificially flattened above about 10^20.3 eV owing to limited statistics, but the flattening is not marked in the plots; adding a grey band or a note in each panel would prevent readers from interpreting those flat segments as physical.
  3. [Eq. (2) and Section 2.1] The notation using negative values of s1 and s2 inside exponents with a minus sign is confusing; the authors should define the spectral slopes explicitly (for example, dN/dE0 ~ E^-0.6 below Eb and ~ E^-2.6 above Eb) to avoid ambiguity about the sign convention.
  4. [Section 3 and Figure 6] The phrase 'Northern and Southern Hemispheres' should be 'northern and southern sky exposures,' since Virgo A is visible from both hemispheres and the relevant difference is in the exposure-weighted contributions from specific sources.
  5. [Section 4, item 5] The statement that accounting for magnetic deflections 'up to twice the baseline level' corresponds to the VirA6 model with dp = (1-3)d is imprecise; the maximum distance is doubled but the range shape also changes, so the wording should be adjusted.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the source spectrum is adopted, not derived, from earlier work, and the Earth-spectrum prediction is computed with an external propagation code without fitting to observed UHECR data.

full rationale

The paper's chain is: adopt the DPL source spectrum of Eq. (2) from Seo et al. (2023, 2024), set jet parameters in Table 1 from external observations of individual radio galaxies, and propagate through CMB/EBL interactions and photo-disintegration with the public CRPropa code. No parameter is fitted to observed UHECR spectra or to the target hemispheric-asymmetry prediction; the SPL comparison models use spectral indices 'as this best reproduces observed UHECR spectra,' but those models serve only as baselines and do not set the DPL parameters that drive the conclusions. The Virgo A versus Centaurus A/Fornax A contrast does trace to the adopted <Gamma>_spine values in Table 1 and to the 'extended' cutoff in Eq. (2), but the paper states this dependence explicitly and tests it, e.g., the VirA3 model with <Gamma>_spine = 3 removes the high-energy tail, which is parameter sensitivity rather than circular reasoning. The self-citations supply the model input and supporting dynamics, while the propagation and composition calculation is external and self-contained. The manuscript itself flags the arbitrariness of phi*xi and the strong sensitivity of the source-spectrum shape, so the dependence of the conclusion on those assumptions is transparent. There is no exhibited reduction of a predicted quantity to a fitted parameter or to a self-citation by construction.

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

The ledger shows that the observable predictions are driven by the adopted source spectrum and jet parameters rather than by new physics. No new entities are introduced. The main free parameters are the break energy, spine Lorentz factor, phi*xi scaling, luminosity normalization, metallicity, and propagation distance range. The axioms are the DPL source model from prior self-cited simulations, the reliability of CRPropa, the transferability of the power-law propagation function to DPL spectra, and the representativeness of the Table 1 jet parameters.

free parameters (6)
  • Break energy E_b = VirA 10 EeV, CenA 3 EeV, ForA 7 EeV, CygA 50 EeV
    Set by Eq. (3) using representative phi*xi values and jet power; controls the position of the exponential cutoff and the high-energy tail. Acknowledged as carrying arbitrariness.
  • Jet spine Lorentz factor <Gamma>_spine = VirA 7.0, CenA 1.2, ForA 1.5, CygA 10
    Inferred from observed superluminal motions; enters as <Gamma>^2 in the cutoff extension and is the main driver of the hemispheric composition difference.
  • phi*xi break-energy scaling factor = 0.45, 0.15, 0.2, 0.7 for VirA, CenA, ForA, CygA
    Numerically derived factor in the E_b formula; the paper adopts a representative range and states further refinement would be speculative.
  • UHECR luminosity normalization L_CR proportional to Q_j
    Relative source amplitudes are scaled by Q_j/d^2, assuming a fixed, constant conversion from jet kinetic power to cosmic-ray luminosity.
  • Host ISM metallicity factor = 3 times f_sun fiducial; 1 times f_sun variant
    Triples the abundance of nuclei heavier than helium relative to Galactic cosmic rays; affects injected mass composition.
  • Propagation distance range d_p = (1-1.5)d fiducial; (1-3)d for VirA6
    Chosen to mimic path-length increases from magnetic deflection; not derived from a specific magnetic field model.
assumptions (4)
  • domain assumption The time-asymptotic UHECR spectrum from FR jets is well approximated by the double power law with extended exponential cutoff in Eq. (2).
    Adopted from the authors' own RHD+Monte Carlo simulations (Seo et al. 2023, 2024) and not independently tested in this paper; the entire prediction follows from this shape.
  • domain assumption CRPropa correctly models propagation, GZK losses, photo-disintegration, and nuclear decay.
    The public code is treated as standard and correct; no verification runs are presented.
  • domain assumption The propagation function computed for a gamma=-2 power-law injection can be applied to SPL and DPL source spectra.
    Section 2.4 shows weak dependence on gamma over -1.5 to -2.5, but DPL spectra with breaks and extended tails are not tested.
  • domain assumption The jet parameters in Table 1 (Q_j, distance, <Gamma>_spine) are representative for the four radio galaxies.
    Values are inferred from cited observational studies with no quoted uncertainties; parameter variations of +/-20% are tested but not the full plausible range.

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Pith. "Pith review of Energy Spectrum and Mass Composition of Ultra-High-Energy Cosmic Rays Originating from Relativistic Jets of Nearby Radio Galaxies." pith.science (2026). https://pith.science/paper/IRWN72NR

@misc{pith2026250615110,
  author       = {Pith},
  title        = {Pith review of: Energy Spectrum and Mass Composition of Ultra-High-Energy Cosmic Rays Originating from Relativistic Jets of Nearby Radio Galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IRWN72NR}},
  note         = {Machine review of arXiv:2506.15110}
}
abstract

Relativistic jets of radio galaxies (RGs) are possible sources of ultra-high-energy cosmic rays (UHECRs). Recent studies combining relativistic hydrodynamic simulations with Monte Carlo particle transport have demonstrated that UHECRs can be accelerated to energies beyond $10^{20}$ eV through shocks, turbulence, and relativistic shear in jet-induced flows of Fanaroff-Riley (FR) type RGs. The resulting time-asymptotic UHECR spectrum is well modeled by a double power law with an ``extended'' exponential cutoff, primarily shaped by relativistic shear acceleration. In this study, we adopt this novel source spectrum and simulate the propagation of UHECRs from nearby RGs using the CRPropa code. We focus on Virgo A, Centaurus A, Fornax A, and Cygnus A, expected to be the most prominent UHECR sources among RGs. We then analyze the energy spectrum and mass composition of UHECRs arriving at Earth. We find that, due to the extended high-energy tail in the source spectrum, UHECRs from Virgo A, which has a higher Lorentz factor, exhibit a higher flux at the highest energies and a lighter mass composition at Earth, compared to those from Centaurus A and Fornax A with lower Lorentz factors. Despite Cygnus A having an even higher Lorentz factor, the large distance limits its contribution. With a small number of nearby prominent RGs, our findings suggest that if RGs are the major sources of UHECRs, the energy spectrum and mass composition of observed UHECRs would exhibit hemispheric differences between the Northern and Southern skies at the highest energies.

Figures

Figures reproduced from arXiv: 2506.15110 by the authors.

Figure 1
Figure 1. Jet kinetic power flux, Qj/d2 , for 42 local RGs as a function of distance d. Different symbols distinguish between FR-I, FR-II, and FR-I/II types, with FR-I/II ex￾hibiting characteristics intermediate between FR-I and FR-II types. Red and blue symbols represent RGs located in the Northern and Southern Hemispheres, respectively. Thick symbols highlight the four prominent RGs listed in [PITH_FULL_IMAGE:figures/full_… view at source ↗
Figure 2
Figure 2. Model energy spectra of UHECRs from RGs. The blue solid and dashed lines represent the single pow￾er-law models, SPL1 and SPL2, respectively. The red solid, dashed, and dotted lines correspond to the double power-law models, VirA1, VirA2, and VirA3, respectively, for Virgo A. See [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Propagation function, ⟨P⟩, for a power-law injection spectrum with different spectral indices, γ = −1.5 (dotted lines), −2.0 (dashed lines), and −2.5 (dot-dashed lines). (a) ⟨P⟩ for protons (A0 = 1, Z0 = 1, A = 1, and Z = 1) over dp = 16 − 24 Mpc (red) and dp = 100 − 150 Mpc (blue). (b) ⟨P⟩ with ion nuclei at the source (A0 = 56 and Z0 = 26) over dp = 16 − 24 Mpc. Different colors represent the propagation functions… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Energy spectrum and mean logarithmic mass: E 3 0 dN/dE0 and ⟨ln A0⟩ at the source (dashed lines) and E 3 dN/dE and ⟨ln A⟩ at Earth (solid lines) after propagation for the two SPL models and the six Virgo A models in [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Energy spectrum, E 3 dN/dE, and mean logarithmic mass, ⟨ln A⟩, of UHECRs reaching Earth from the four prominent RGs: Virgo A (red), Centaurus A (green), Fornax A (purple), and Cygnus A (blue). The solid lines show these quantities for the representative jet models, Vir…

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