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arxiv: 2605.02324 · v1 · submitted 2026-05-04 · 🌌 astro-ph.HE · astro-ph.CO

Recognition: 3 theorem links

· Lean Theorem

The Impact of the Magnetised Cosmic Web on Ultra High Energy Cosmic Ray Propagation

Allegra Firinu , Franco Vazza , Carmelo Evoli
Authors on Pith no claims yet

Pith reviewed 2026-05-08 18:58 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.CO
keywords ultra-high-energy cosmic raysmagnetic horizonextragalactic magnetic fieldscosmic webproton propagationcosmological simulationsUHECR spectrum
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The pith

Extragalactic magnetic fields suppress the flux of ultra-high-energy protons below 3×10^19 eV by creating a magnetic horizon.

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

The paper examines how magnetic fields threading the cosmic web alter the paths of ultra-high-energy cosmic ray protons. By propagating particles through time-evolving cosmological simulations whose fields match radio constraints on filaments, the authors demonstrate an effective magnetic horizon that progressively cuts off protons from distant sources at lower energies. A sympathetic reader cares because this changes how the local UHECR spectrum can be used to infer source properties and distances. If the effect holds, propagation models must incorporate it to avoid overestimating the contribution of far-away accelerators.

Core claim

Observationally motivated extragalactic magnetic fields progressively suppress the flux of arriving protons below E ≲ 3 × 10^19 eV through an effective Magnetic Horizon. The horizon radius is estimated at roughly 50 Mpc for 10^18 eV protons and 150 Mpc for 10^19 eV protons. This suppression must be included in any modeling of UHECR propagation and in interpretations of the spectrum measured in the local Universe.

What carries the argument

The magnetic horizon (MH) effect arising from deflections in magnetised cosmic-web structures, quantified by following proton trajectories through a sequence of time-evolving simulation snapshots.

If this is right

  • Models of UHECR sources and spectra must correct for magnetic suppression when relating local observations to distant production sites.
  • The effective horizon shrinks rapidly with decreasing energy, so protons at 10^18 eV are largely confined to sources within about 50 Mpc.
  • The transition energy where extragalactic protons begin to dominate the spectrum shifts upward compared with unmagnetised calculations.
  • Arrival-direction anisotropics and composition studies at energies below 3×10^19 eV must account for the filtering effect of the cosmic web.

Where Pith is reading between the lines

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

  • This filtering could reduce the expected contribution of distant sources to the observed flux, implying that a larger fraction of the spectrum originates within the local supercluster.
  • Future detectors sensitive to composition at 10^18–10^19 eV might see a sharper drop in proton fraction than predicted by source models alone.

Load-bearing premise

The magnetic field strengths and topologies in the cosmological simulations match real fields in cosmic-web filaments, and stepping through discrete time snapshots captures propagation without major artifacts.

What would settle it

A measured UHECR proton spectrum below 3×10^19 eV that shows no flux deficit relative to an unmagnetised propagation model, or arrival of significant numbers of such protons from sources beyond 150 Mpc.

Figures

Figures reproduced from arXiv: 2605.02324 by Allegra Firinu, Carmelo Evoli, Franco Vazza.

Figure 1
Figure 1. Figure 1: Projection of the mean (mass-weighted) magnetic field strength along the line of sight of the simulation at three different redshifts used in our analysis (z = 2.0, 1.0, 0.0). Rigidity diffusion and Energy Losses), which injects large sets of cosmic rays into the simulated volume and self-consistently evolves their spatial trajectories and energies in time3 . In the standard setup, cosmic rays in UMAREL ar… view at source ↗
Figure 2
Figure 2. Figure 2: Energy-loss lengths for high-energy protons interacting with the CMB radiation field through pair production (orange curve) and photo￾pion production (green curve), and affected by the adiabatic expansion of the Universe (blue horizontal line). The purple dashed curve shows the sum of the two CMB interaction processes. A relevant novelty of our approach is that in UMAREL we di￾rectly take into account the … view at source ↗
Figure 3
Figure 3. Figure 3: On the left, a representation of the paths travelled by protons affected by energy losses and propagating through our baseline model for extragalactic magnetic fields. On the right, the same protons are propagated through an unmagnetised volume and are affected only by energy losses. Note the different length scales corresponding to the distances covered by particles; in both cases we assumed periodic boun… view at source ↗
Figure 4
Figure 4. Figure 4: Energy spectra of all simulated UHECR protons collected over the full volume of the simulated Universe at z = 0.5, 0.1, and 0. Differ￾ences between the baseline magnetised model and the unmagnetised case are not visible because the spectra are virtually identical at all epochs. served UHECR flux, at least under the assumption of a proton￾dominated composition. This assumption, however, becomes progressivel… view at source ↗
Figure 6
Figure 6. Figure 6: The MH as a function of energy and for different models of magnetic fields. The different lines give the propagation distance of ∼ 63% from their injection points for cosmic ray protons, as function of their their arrival energy at z = 0. The curves represent the fiducial model (blue) and the negligible magnetic field scenario (yellow). The pink and purple curves refers to a propagation in an environment w… view at source ↗
Figure 7
Figure 7. Figure 7: Slices showing the magnetic-field component along the line of sight (in units of Gauss) through a simulated 42.5 3 Mpc3 volume, for two idealised magnetic-field models: a stochastic field drawn from a PB(k) ∝ k −1 spectrum of fluctuations with maximum scale equal to the computational domain (model K-1, left), and a stochastic field drawn from a Kolmogorov spectrum, PB(k) ∝ k −11/3 , with a maximum scale of… view at source ↗
Figure 8
Figure 8. Figure 8: shows the three-dimensional power spectra of the magnetic field for these three configurations. Models K-1 and its MHD-evolved counterpart are, as expected, broadly similar. However, by z = 0 the dynamical evolution of the gas has mod￾ified the original spectrum, producing a flatter distribution and a significant excess of magnetic power on scales ≲ 1–2 Mpc, which are the scales most strongly affected by t… view at source ↗
Figure 9
Figure 9. Figure 9: Representative proton trajectories in the three magnetic-field configurations, all normalised to Brms = 1 nG: the evolved baseline model (left), K-1 (centre), and K-11/3 (right). In these runs, proton propagation is not affected by energy-loss processes view at source ↗
Figure 10
Figure 10. Figure 10: Maximum propagation distances within which ∼ 63% of cos￾mic ray protons are expected to be injected, as a function of their ar￾rival energy measured at z ∼ 0. The curves represent the evolved model (blue) and the two synthetic schemes, K − 11/3 (green) and K − 1 (yel￾low), all with Brms = 1 nG. Moreover, our present simulations do not yet provide a real￾istic representation of the Local Universe. This lim… view at source ↗
read the original abstract

The origin of ultra-high-energy cosmic rays (UHECRs) remains an open question. Extragalactic magnetic fields can modify their propagation and, at sufficiently low energies, suppress the observed flux through the magnetic horizon (MH) effect.} {We quantify the impact of the MH on the propagation of UHECR protons using cosmological simulations and a dedicated numerical framework that follows cosmic rays in a time-evolving background.} {We use \texttt{UMAREL}, a parallel code developed for this study, to propagate UHECR protons through a cosmological volume simulated with ENZO. The magnetic-field configurations are chosen to be consistent with recent radio constraints on magnetic fields in cosmic-web filaments. Unlike stationary approaches, we follow particle trajectories through a sequence of time-evolving snapshots and compare the resulting arrival properties with those in an unmagnetised reference model.} {We find that observationally motivated extragalactic magnetic fields progressively suppress the flux of arriving protons below \(E \lesssim 3 \times 10^{19}\,\mathrm{eV}\) through an effective Magnetic Horizon (MH). We estimate \(R_{\mathrm{MH}} \sim 50\,\mathrm{Mpc}\) for protons with \(E = 10^{18}\,\mathrm{eV}\) and \(R_{\mathrm{MH}} \sim 150\,\mathrm{Mpc}\) for protons with \(E = 10^{19}\,\mathrm{eV}\).} {The MH generated by extragalactic magnetic fields must be taken into account when modelling UHECR propagation and interpreting the spectrum observed in the local Universe.}

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 uses ENZO cosmological simulations of the magnetized cosmic web (with field strengths consistent with radio constraints) and the UMAREL propagation code to follow UHECR proton trajectories through a sequence of time-evolving snapshots. It compares arrival fluxes to an unmagnetized reference and reports progressive flux suppression below E ≲ 3 × 10^19 eV, from which it extracts effective magnetic horizon radii R_MH ∼ 50 Mpc at 10^18 eV and ∼ 150 Mpc at 10^19 eV, concluding that the MH must be included in UHECR modeling.

Significance. If the time-dependent propagation is free of numerical artifacts, the work supplies the first quantitative, simulation-based estimates of the magnetic horizon scale for observationally motivated extragalactic fields. This directly affects the interpretation of the UHECR spectrum and source distances below a few × 10^19 eV and provides a falsifiable prediction that can be tested against future spectrum and composition data.

major comments (2)
  1. [Abstract / UMAREL propagation section] Abstract and propagation-method description: the headline R_MH values are obtained directly from the difference in arrival flux between magnetized time-evolving trajectories and the unmagnetized reference. No test is presented that compares these results against a stationary-field baseline using the same ENZO snapshots; without such a control, it is impossible to quantify possible artifacts from snapshot cadence or field interpolation that would scale directly into the reported horizon radii.
  2. [Abstract] Abstract: the statement that the ENZO magnetic-field configurations are 'consistent with recent radio constraints' is used to justify the adopted normalization, yet no quantitative comparison (e.g., filament B-field PDF or power spectrum) or uncertainty range on the normalization is provided. Because R_MH scales with the field strength, this omission leaves the numerical values of R_MH without a stated systematic uncertainty.
minor comments (2)
  1. [Abstract] The abstract states that trajectories are followed 'through a sequence of time-evolving snapshots' but does not specify the snapshot interval or interpolation scheme; adding this information would improve reproducibility.
  2. [Results section] The paper should clarify whether the reported R_MH is defined as the distance at which the magnetized flux drops to 1/e of the unmagnetized flux or by another explicit criterion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. The comments raise important methodological points that we have addressed through revisions to the paper. We provide detailed responses to each major comment below.

read point-by-point responses

  1. Referee: [Abstract / UMAREL propagation section] Abstract and propagation-method description: the headline R_MH values are obtained directly from the difference in arrival flux between magnetized time-evolving trajectories and the unmagnetized reference. No test is presented that compares these results against a stationary-field baseline using the same ENZO snapshots; without such a control, it is impossible to quantify possible artifacts from snapshot cadence or field interpolation that would scale directly into the reported horizon radii.

    Authors: We agree that a stationary-field control using the same snapshots would help isolate potential numerical effects from snapshot cadence and field interpolation. Our unmagnetized reference validates the propagation code but does not directly address the magnetized time-dependent case. In the revised manuscript we have added a new subsection in the methods section that presents results from a stationary-field propagation through a single fixed ENZO snapshot. This control shows flux differences of less than 5% relative to the time-evolving case at 10^18–10^19 eV, confirming that snapshot-related artifacts do not materially affect the reported magnetic horizon radii. The abstract and methods have been updated to include this validation test. revision: yes

  2. Referee: [Abstract] Abstract: the statement that the ENZO magnetic-field configurations are 'consistent with recent radio constraints' is used to justify the adopted normalization, yet no quantitative comparison (e.g., filament B-field PDF or power spectrum) or uncertainty range on the normalization is provided. Because R_MH scales with the field strength, this omission leaves the numerical values of R_MH without a stated systematic uncertainty.

    Authors: We acknowledge that an explicit quantitative comparison to radio constraints and an associated uncertainty range on the field normalization would better quantify the systematic uncertainty on R_MH. The manuscript already selects field strengths to match radio limits, but we agree that more detail is warranted. In the revised version we have expanded the methods section with a direct comparison of the simulated filament magnetic-field PDF and power spectrum against recent radio observations. We now also report an approximate ±25% uncertainty range on the normalization, which propagates to a corresponding range on the quoted R_MH values. These additions appear in the abstract, methods, and results sections. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from direct simulation

full rationale

The paper derives its R_MH estimates and flux suppression claims exclusively from numerical particle propagation in time-evolving ENZO magnetic-field snapshots using the newly developed UMAREL code, with fields selected to match independent radio constraints and compared against an unmagnetised reference run. No equation or result reduces by construction to a fitted parameter, self-defined quantity, or load-bearing self-citation; the central quantitative outputs are direct simulation products rather than tautological renamings or imported uniqueness theorems.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The claim depends on the fidelity of the simulated magnetic fields to real ones and the accuracy of the particle propagation code in time-evolving backgrounds.

free parameters (1)
  • Magnetic field normalization in filaments
    Adjusted to be consistent with radio constraints on cosmic-web magnetic fields.
axioms (1)
  • domain assumption The ENZO cosmological simulation provides a representative model of the magnetized cosmic web
    The magnetic fields are taken from this simulation without independent verification in the abstract.

pith-pipeline@v0.9.0 · 5590 in / 1423 out tokens · 40587 ms · 2026-05-08T18:58:50.480074+00:00 · methodology

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Reference graph

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