Modeling the Imprints of Large-scale Magnetized Structures on γ -Rays from Extragalactic Transients

In the multimessenger era, the association of high-energy transients with their γ -ray counterparts can be obscured by magnetized large-scale structure surrounding the source. We analyze models for delayed off-axis γ -rays, arising from the injection of ultrahigh-energy cosmic rays ( E ≳ 10 18 eV) and γ -rays ( ε γ ≳ 10 18 eV), and very-high-energy γ -rays ( ε γ ≳ 100 GeV) from the transient. As a representative case, we consider the brightest gamma-ray burst, GRB 221009A, embedded in a magnetized structure. We examine charged-particle deflection in electromagnetic cascades, followed by propagation of secondaries through the intergalactic medium, and derive the time delays and angular offsets of the resulting γ -rays. To test the models, we analyze 1.25 yr of postevent Fermi Large Area Telescope (LAT) data and construct a 1 GeV–1 TeV test statistic (TS) map within 10° of the burst localization. We find two subthreshold peaks with TS ≥ 9. The more significant peak, J1911.8+2044, shows γ -ray emission in preburst LAT data, while J1913.2+1901 coincides with a 664.6 GeV γ -ray recorded ∼191.9 days after the trigger at ≈0 . ° 75 from the GRB. The corresponding flux upper limit provides a fiducial value to constrain the parameter space in our models and to estimate the source energy requirement for delayed off-axis signals. Although a magnetized structure can reproduce the angular offset of this subthreshold feature, the resulting time delay disfavors an origin in this GRB.