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arxiv: 2604.25647 · v1 · submitted 2026-04-28 · 🌌 astro-ph.HE · astro-ph.CO

Intergalactic Magnetic Field constraints from detected very high-energy Gamma-Ray Bursts using the Cherenkov Telescope Array Observatory

T\'en\'eman Keita , Renaud Belmont , Thierry Stolarczyk This is my paper

Pith reviewed 2026-05-07 15:27 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.CO
keywords intergalactic magnetic fieldgamma-ray burstsCherenkov Telescope Arrayvery high-energy gamma rayselectromagnetic cascadespair production
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The pith

The Cherenkov Telescope Array Observatory can constrain the intergalactic magnetic field to strengths as high as 10^{-15} G by observing very high-energy gamma-ray bursts.

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

The paper simulates realistic CTAO observations of very high-energy gamma-ray bursts to extract limits on the strength of the intergalactic magnetic field from the delayed secondary photons they produce. These secondary photons arise when primary VHE gamma rays pair-produce on background light and the resulting electrons and positrons are deflected by the IGMF before inverse-Compton scattering. For bursts with properties like GRB 221009A and GRB 190114C, the simulations show that full CTAO deployment can reach field strengths up to about 10^{-15} G. Existing LST-1 data on GRB 221009A already point toward a preferred value near 3 times 10^{-17} G. A sympathetic reader cares because the IGMF is the only magnetic field thought to be a direct relic of the early universe, so tighter measurements would constrain how magnetism originated in the cosmos.

Core claim

By modeling the spectral and temporal signatures of the electromagnetic cascade initiated by VHE GRB photons, the authors find that CTAO observations of sources comparable to GRB 221009A and GRB 190114C will be sensitive to IGMF strengths up to approximately 10^{-15} G. They further report that the currently available LST-1 observations of GRB 221009A are best fit by a field strength of 3 times 10^{-17} G under the assumed source and cascade parameters.

What carries the argument

The time-delayed secondary gamma-ray emission produced by pair cascades, whose angular and temporal spread is controlled by deflection of electron-positron pairs in the IGMF.

Load-bearing premise

The results depend on the assumed redshift, spectrum, and duration of the GRBs together with the accuracy of the pair-production and inverse-Compton cascade model; any mismatch in these inputs would change the derived field strengths.

What would settle it

A high-statistics CTAO spectrum and light curve of a future VHE GRB like 221009A that shows no measurable time delay or secondary component would rule out an IGMF strength near 3 times 10^{-17} G.

Figures

Figures reproduced from arXiv: 2604.25647 by Renaud Belmont, T\'en\'eman Keita, Thierry Stolarczyk.

Figure 2
Figure 2. Figure 2: illustrates the role of the late afterglow in the emis￾sion from a generic GRB at z = 0.4. It shows the total spec￾tra in 4 logarithmic time windows spanning the first month of observation ([10s − 4 min], [4 min − 1.5 h], [1.5 h − 30 h] and [30 h − 1 month]). The primary spectrum is assumed to be a power law with index γ = 1.8 and maximal energy Emax = 30 TeV, and the IGMF has B = 10−19 G and λB = 1 Mpc. T… view at source ↗
Figure 3
Figure 3. Figure 3: Example of signal counts in the North site (LSTs plus MSTs) at the end of the first night of GRB 190114C (2.29h - 2.61h for data generated with B = 10−17 G. The best fit (blue) at 10−17 G is compared with two model fits at 10−18 (red) and 10−16 G (green). however, fails to consistently propagate uncertainties from the primary flux to the characteristics of the secondary emission and to address the possible… view at source ↗
Figure 4
Figure 4. Figure 4: Likelihood profiles for four values of log B. The dashed line indicates the 3σ confidence level for GRB 190114C. given B (with all other parameters free) to the likelihood at Bbest, namely the quantity √ ∆T S (Bbest, B). The test statistics differ￾ence ∆TS is written as: ∆T S (Bbest, B) = −2 log L(Bbest) L(B) (12) Examples of such likelihood profiles are shown in view at source ↗
Figure 5
Figure 5. Figure 5: shows the primary and secondary spectrum models of GRB 190114C, for B = 10−17 G and λB = 1 Mpc in 4 time intervals, as well as the CTAO sensitivity for 30 minutes of ob￾servation in the North and 5 hours in the South. For each time interval, the primary spectrum is shown as a dashed line while the total spectrum, which accounts for the secondary photons, is shown in solid lines. The spectra are initially d… view at source ↗
Figure 6
Figure 6. Figure 6: (a) Light curves of GRB 190114C multiplied by the elapsed time, showing the primary emission in the CTAO energy band (110 GeV − 10 TeV; solid black line) and the total emission (primaries plus cascade) for various IGMF strengths (coloured lines), and cascade contributions (dotted lines). The vertical dotted lines indicate the 2nd to 5th nightfalls (the burst occurred during the first night). (b) Total emis… view at source ↗
Figure 7
Figure 7. Figure 7: Likelihood maps of GRB 190114C at λB = 1 Mpc, with simulated B values on the abscissas and fitted values on the ordinates. Best-fit values are shown as black dots. The colour map represents uncertainty levels up to 10σ, with contours in white. The dashed red line highlights the lower limit at about 3σ for datasets with the strongest magnetic fields. Right: Ecut free to be fitted down to arbitrary low energ… view at source ↗
Figure 8
Figure 8. Figure 8: Likelihood map of GRB 190114C for λB = 1 pc, assuming Ecut ≥ 10 TeV. grows with decreasing λB, we extended the observation to the sixth and eighth nights for the 1 kpc and 1 pc cases, respectively. Signal is still expected at these times, assuming such correlation lengths. As shown in view at source ↗
Figure 9
Figure 9. Figure 9: (a) Light curve of GRB 221009A between 40 GeV and 10 TeV, showing the primary emission (solid black line) and total emission (primaries plus cascade) for various IGMF strengths (coloured lines), starting at T ∗ ≡ T0 + 225s. (b) Total emission for B = 10−17 G (blue line) compared to CTAO-North data points (blue circles) integrated over the 40 GeV−10 TeV energy band. The LHAASO points (black dots; extracted … view at source ↗
Figure 10
Figure 10. Figure 10: Published LST-1 data for the second night and simulated en￾ergy spectra for various B values. The cascade for the best-matching value, 10−16.5 G, is in solid line. For illustration, two models with field strengths close to this value are drawn in dashed lines. 3.2.3. Conclusion for GRB 221009A In the absence of a late signal, several works have already placed lower limits on the IGMF strength using GRB 22… view at source ↗
Figure 12
Figure 12. Figure 12: Top: (a) Light curve of GRB 180720B (Ecut = 10 TeV) showing the primary emission in the CTAO energy band (110 GeV−10 TeV; solid black line) and the total emission (primaries plus cascade) for various IGMF strengths (coloured lines). The corresponding cascade contributions are shown as dotted lines. (b) Total emission for B = 10−17 G (blue line) compared to CTAO-North data points (blue circles) in the anal… view at source ↗
Figure 13
Figure 13. Figure 13: (a) Light curve of GRB 190829A showing the primary emission in the CTAO energy band (110 GeV − 10 TeV; solid black line) and the total emission (primaries plus cascade) for various IGMF strengths (coloured lines). The corresponding cascade contributions are shown as dotted lines. (b) Total emission for B = 10−17 G (blue line) compared to CTAO-North data points (blue circles) in the analysis time bins. (c)… view at source ↗
Figure 14
Figure 14. Figure 14: Theoretical and observational constraints on the IGMF. Ex￾cluded regions are coloured: early Universe theoretical predictions (dark grey); CMB anisotropies (red); time-delay constraints from ear￾lier works (blue); our LST-1 exclusion region (green). The expected strength lower limits depending on the type of GRB CTAO will observe are the dashed blue and purple lines, with crosses representing points for w… view at source ↗
read the original abstract

Defined as the magnetic field permeating cosmic voids, the Intergalactic Magnetic Field (IGMF) is thought to be a relic of the Big Bang, tracing a primordial magnetic seed at the origin of all astrophysical fields. Yet, it has thus far escaped detection. Lower limits on the IGMF strength can be established by observing very high-energy (VHE) photons from extragalactic sources. Specifically, this can be achieved by characterising the time-delayed secondary emission induced by highly energetic transient sources, such as gamma-ray bursts (GRBs). Most studies exclude values of the IGMF below $10^{-17}\;\mathrm{G}$ by comparing the expected effect to the sensitivity curves of various instruments in the $\mathrm{GeV}$ range or above. In this work, we simulate CTAO observation data under realistic observation conditions and perform spectral-temporal fits to estimate the constraints CTAO will bring on the IGMF once fully deployed. We apply the methodology to simulated sources with properties comparable to the few GRBs detected at VHE. In particular, we show that CTAO will probe strengths up to $\sim 10^{-15}\;\mathrm{G}$ when detecting sources similar to GRBs 221009A and 190114C. We also show that existing observations of GRB 221009A by the first CTAO Large Sized Telescope LST-1 favour a strength of $3\times 10^{-17}\;\mathrm{G}$.

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 manuscript describes simulations of CTAO observations of very high-energy gamma-ray bursts (GRBs) with properties similar to GRB 221009A and GRB 190114C. Using spectral-temporal fits to the expected time-delayed cascade emission, it estimates that the full CTAO will be able to constrain IGMF strengths up to approximately 10^{-15} G. Additionally, it analyzes existing LST-1 observations of GRB 221009A and finds that they favor an IGMF strength of 3×10^{-17} G.

Significance. If the cascade development model and the simulation of observational conditions are reliable, this study would provide valuable forecasts for IGMF constraints from CTAO and an early constraint from LST-1 data. The approach of using realistic conditions strengthens the applicability of the results to actual observations. Credit is due for applying the method to both simulated future data and existing observations.

major comments (2)
  1. The favored IGMF strength of 3×10^{-17} G from the LST-1 analysis of GRB 221009A is derived under the assumption of a fixed coherence length λ = 1 Mpc. However, the time delay of the cascade scales proportionally to B √λ / E, introducing a degeneracy between the magnetic field strength B and the coherence length λ. The manuscript does not appear to marginalize over λ or test alternative values, which undermines the robustness of the specific point estimate presented.
  2. The projected sensitivity to IGMF strengths of ∼10^{-15} G for sources like GRB 221009A and 190114C relies on the same fixed coherence length assumption. To support this claim, the paper should include an assessment of how the constraints vary with different plausible coherence lengths, as independent constraints on λ are weak.
minor comments (2)
  1. The abstract mentions 'spectral-temporal fits' but the main text should provide more detail on the fitting procedure, including the likelihood function or chi-squared definition used.
  2. Ensure that all figures showing simulated spectra or light curves explicitly state the assumed IGMF parameters, including the coherence length.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We agree that the degeneracy between IGMF strength B and coherence length λ is an important consideration that was not fully explored in the original submission. We will revise the paper to address both major comments by including additional analyses and discussions of how results depend on λ.

read point-by-point responses

  1. Referee: The favored IGMF strength of 3×10^{-17} G from the LST-1 analysis of GRB 221009A is derived under the assumption of a fixed coherence length λ = 1 Mpc. However, the time delay of the cascade scales proportionally to B √λ / E, introducing a degeneracy between the magnetic field strength B and the coherence length λ. The manuscript does not appear to marginalize over λ or test alternative values, which undermines the robustness of the specific point estimate presented.

    Authors: We agree that the reported value is for a fixed λ = 1 Mpc and that a degeneracy exists, as the observable time delay constrains the product B √λ. This choice of fiducial λ follows standard practice in the literature when independent constraints on λ are unavailable. In the revised manuscript we will add a dedicated subsection (or appendix) that recomputes the LST-1 fit for a range of plausible coherence lengths (0.01–10 Mpc) and explicitly shows how the favored B scales as 1/√λ. We will also rephrase the result to state that the data favor B √λ ≈ 3×10^{-17} G Mpc^{1/2} (for the fiducial case) while retaining the conventional B value for direct comparison with prior work. revision: yes

  2. Referee: The projected sensitivity to IGMF strengths of ∼10^{-15} G for sources like GRB 221009A and 190114C relies on the same fixed coherence length assumption. To support this claim, the paper should include an assessment of how the constraints vary with different plausible coherence lengths, as independent constraints on λ are weak.

    Authors: We concur that the projected CTAO sensitivity should be shown to be robust against variations in λ. We will revise the relevant sections to include a brief parameter study demonstrating that the upper limit on B scales approximately as 1/√λ. For λ values between 0.1 and 10 Mpc the CTAO reach remains within a factor of a few of 10^{-15} G for GRB-like sources; we will add a short table or figure summarizing this dependence and update the abstract and conclusions to qualify the quoted sensitivity accordingly. revision: yes

Circularity Check

0 steps flagged

No significant circularity; constraints arise from forward simulation and fitting, not reduction to inputs.

full rationale

The paper derives IGMF constraints by simulating CTAO observations of GRB-like sources under varying IGMF strengths, then performing spectral-temporal fits to the simulated data. This forward-modeling approach produces projected sensitivities (e.g., up to ~10^{-15} G) and a fitted value from LST-1 data (~3×10^{-17} G) that are not equivalent to the simulation inputs by construction. No self-definitional equations, fitted parameters renamed as independent predictions, or load-bearing self-citations appear in the derivation chain. Model assumptions such as fixed coherence length represent standard parameter choices and limitations rather than circular reductions. The central claims remain independently falsifiable against external data and benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The claim rests on the standard cascade model for VHE photon propagation and on assumed GRB source parameters; these are domain assumptions rather than new entities or free parameters fitted inside the paper.

free parameters (1)
  • GRB source parameters (redshift, spectrum, duration)
    Taken as comparable to observed GRBs 221009A and 190114C; used to set up the simulations.
axioms (1)
  • domain assumption Pair-production and inverse-Compton cascade development in the presence of a weak intergalactic magnetic field produces observable time-delayed secondary emission
    Invoked throughout the simulation methodology described in the abstract.

pith-pipeline@v0.9.0 · 5581 in / 1429 out tokens · 67274 ms · 2026-05-07T15:27:28.001259+00:00 · methodology

discussion (0)

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