Impact of Observational and Modelling Assumptions on Intergalactic Magnetic Field Constraints from TeV Gamma-Ray Bursts with the Cherenkov Telescope Array Observatory

Abstract: The Intergalactic Magnetic Field (IGMF), permeating cosmic voids, is thought to be a relic of primordial magnetic fields generated in the early Universe and that gave rise to all astrophysical magnetic fields. While it has escaped direct detection, lower limits on its intensity can be derived by characterising the time-delayed secondary emission initiated when primary very high-energy (VHE) photons from gamma-ray bursts (GRBs) produce lepton pairs that are deflected by the IGMF before generating a secondary gamma-ray flux. Most current studies exclude IGMF values below $10^{-18}\;\mathrm{G}$, however, they are typically performed under idealised conditions. Focusing on the impact of modelling and observational choices, we simulate CTAO observations of GRBs 190114C and 221009A under varying conditions. For GRB 190114C-like sources, we establish a stable lower limit of $2\times10^{-16}\;\mathrm{G}$, robust against most variations in source properties and detection strategies. For more extreme GRB 221009A-like events, we demonstrate that CTAO could probe fields up to at least $10^{-16}\;\mathrm{G}$ under harsh conditions, improving significantly the current IGMF constraints.

• The paper demonstrates that CTAO observations of TeV GRBs robustly constrain IGMF strength, establishing a lower bound of 2×10⁻¹⁶ G under optimal conditions.
• It employs advanced 3D Monte Carlo simulations and realistic detector systematics to assess the impact of source spectral and temporal uncertainties on IGMF limits.
• Results indicate that variations in intrinsic GRB properties and observational delays can significantly alter the sensitivity of cosmological magnetic field measurements.

Impact of Observational and Modelling Assumptions on IGMF Constraints Using TeV GRBs Observed by CTAO

Introduction

The study systematically analyzes the sensitivity of intergalactic magnetic field (IGMF) constraints, derived from TeV gamma-ray burst (GRB) observations with the Cherenkov Telescope Array Observatory (CTAO), to a variety of observational and modeling assumptions. IGMFs, possibly of primordial origin, remain largely undetected but are indirectly probed via delayed secondary γ-ray cascades produced through interactions of very high-energy (VHE) photons from GRBs with the extragalactic background light (EBL). The secondary emission, affected by IGMF strength $B$ and correlation length $\lambda_B$, becomes observable if its temporal and spectral signatures permit separation from the primary burst emission. This paper employs state-of-the-art 3D Monte Carlo simulations of two prominent GRBs—190114C and 221009A—to quantify the robustness of IGMF lower bounds attainable with CTAO under realistic scenarios, explicitly addressing the influence of varying intrinsic source properties and detection strategies.

Methodology

The analysis utilizes the CascadEl Monte Carlo simulation framework for electromagnetic cascade development, incorporating up-to-date EBL and cosmic microwave background (CMB) models within a $\Lambda$CDM cosmological context. The intrinsic primary GRB emission is parameterized as a power law in both energy and time, attenuated by an exponential cutoff at $E_\mathrm{cut}$:

$$\Phi(E, t > t_\mathrm{min}) = \Phi_0 E^{-\gamma} t^{-\alpha} \exp(-E/E_\mathrm{cut}).$$

CTAO instrumental systematics are modeled using the Gammapy package and official Instrument Response Functions (IRFs, prod5 version v0.1), with full simulation of the North and South CTAO configurations. Synthetic datasets are generated across a grid of injected $B$ values, and time-resolved spectral fits recover best-fit values for $B$ and intrinsic spectral-temporal parameters. Throughout, $\lambda_B$ is fixed to 1 Mpc, and both idealized and sub-optimal detector/observational configurations are considered.

Results for GRB 190114C

The benchmark analysis with GRB 190114C $(z=0.425)$ employs spectral indices $\gamma=2.22$ and $\lambda_B$0 motivated by MAGIC observations, and a conservative lower cut on $\lambda_B$1 TeV—reflecting recent LHAASO results at higher energies. With this constraint, the simulations identify three main IGMF regimes:

• Optimal Cascade Domain ($\lambda_B$2): Here, CTAO is sensitive to the cascade, and robust lower bounds on $\lambda_B$3 can be set.
• Low-Field Regime ($\lambda_B$4): Cascades are undetectable as their energy distribution shifts below CTAO's threshold.
• High-Field Regime ($\lambda_B$5): Secondary emission is suppressed, and spectral features degenerate with intrinsic $\lambda_B$6 effects.

Under optimal assumptions—with $\lambda_B$7 fixed—the study finds a robust lower limit of $\lambda_B$8 G for IGMF, invariant under most tested changes in source spectral shape, fluence, zenith angle, or detection delay.

Figure 1: Confidence maps for GRB 190114C showing fitted $\lambda_B$9 versus simulated $\Lambda$0 for two scenarios: left—$\Lambda$1 TeV enforced; right—$\Lambda$2 free, illustrating the degeneracy between IGMF and intrinsic cutoff for strong fields.

However, if $\Lambda$3 is left unconstrained, the lower bound degrades to $\Lambda$4 G, primarily due to degeneracy between the suppressed cascade flux and an intrinsically lower $\Lambda$5. Other critical systematics include the true onset time of the VHE afterglow: significant delays or reduced primary fluence also degrade constraints. Specifically, a delay from the fiducial 6 s post-burst up to 1 hr or a fluence reduction by a factor of $\Lambda$6 still allows constraints at the $\Lambda$7 G level, but with further reductions, distinguishability is lost.

Results for GRB 221009A

For the exceptional GRB 221009A, observed up to $\Lambda$8 TeV (LHAASO), the analysis uses a segmented power-law lightcurve normalized to observed data and $\Lambda$9 TeV. Under ideal conditions (low energy threshold, prompt observation), CTAO could test IGMFs as strong as $E_\mathrm{cut}$0 G. However, Moonlight-induced energy threshold increases and lost observing time ($E_\mathrm{cut}$1 night missed) degrade the limit by up to an order of magnitude. Even under such adverse circumstances, CTAO can still set a lower limit at $E_\mathrm{cut}$2 G, which improves the Fermi-LAT limits by an order of magnitude.

Implications and Prospective Developments

These findings confirm that CTAO, even under conservative or sub-optimal assumptions, consistently enhances the sensitivity to IGMF strengths by more than an order of magnitude relative to current instruments, pushing robust lower bounds to $E_\mathrm{cut}$3 G (GRB 190114C) and as strong as $E_\mathrm{cut}$4 G (GRB 221009A) under favorable conditions. The degradation observed only under extreme modeling changes or highly unfavorable observing configurations underscores the intrinsic robustness of GRB afterglow time-delay constraints to systematic uncertainties, provided that $E_\mathrm{cut}$5 is physically motivated and $E_\mathrm{cut}$6 is fixed.

Practical implications include the necessity of rapid CTAO follow-up, maximal coverage across both array sites, and prioritizing observational protocols that minimize energy threshold increases (e.g., Moonlight avoidance). Theoretically, the results suggest that, assuming $E_\mathrm{cut}$7 Mpc and $E_\mathrm{cut}$8 TeV are justified, future extreme GRBs could further improve the cosmological mapping of IGMF parameters, thereby constraining models of magnetogenesis on cosmological scales.

Conclusion

This analysis rigorously assesses the stability and attainable strength of CTAO-driven IGMF lower bounds derived from high-energy GRB afterglow observations. For typical bursts akin to GRB 190114C, CTAO will systematically extend constraints to $E_\mathrm{cut}$9 G for $$\Phi(E, t > t_\mathrm{min}) = \Phi_0 E^{-\gamma} t^{-\alpha} \exp(-E/E_\mathrm{cut}).$$0 Mpc, barring highly conservative or significantly degraded model/observation assumptions. For exceptional events, the potential sensitivity is even higher. The robustness to most systematics highlights GRB time-delay cascade observations as a premier probe of cosmological magnetism, contingent on continued optimization of instrumental and observational strategies.