Modeling the imprints of large-scale magnetized structures on $γ$-rays from extragalactic transients

Abstract

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 ($E\gtrsim 10^{18}$ eV) and $γ$-rays ($\varepsilon_γ\gtrsim10^{18}$ eV), and very-high-energy $γ$-rays ($\varepsilon_γ\gtrsim 100$ 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 years of post-event \textit{Fermi} Large Area Telescope (LAT) data and construct a 1 GeV -- 1 TeV test statistic (TS) map within $10^\circ$ of the burst localization. We find two sub-threshold peaks with TS$\geq9$. The more significant peak, J1911.8+2044, shows $γ$-ray emission in pre-burst LAT data, while J1913.2+1901 coincides with a 664.6 GeV $γ$-ray recorded $\sim191.9$ days after the trigger at $\approx 0^{\circ}.75$ from the GRB. The corresponding flux upper limit provides a fiducial value for constraining the parameter space in our models and estimating the source energy requirement for delayed off-axis signals. Although a magnetized structure can reproduce the angular offset of this sub-threshold feature, the resulting time delay disfavors an origin in this GRB.