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

Abstract

In the multimessenger era, the association of high-energy transients with their $\gamma$-ray counterparts can be obscured by magnetized large-scale structure surrounding the source. We analyze models for delayed off-axis $\gamma$-rays, arising from the injection of ultrahigh-energy cosmic rays ($E\gtrsim 10^{18}$ eV) and $\gamma$-rays (${\epsilon }_{\gamma }\gtrsim 10^{18}$ eV), and very-high-energy $\gamma$-rays (${\epsilon }_{\gamma }\gtrsim 100$ 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 $\gamma$-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$\ge 9$. The more significant peak, J1911.8+2044, shows $\gamma$-ray emission in pre-burst LAT data, while J1913.2+1901 coincides with a 664.6 GeV $\gamma$-ray recorded $\sim 191.9$ 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.

15 pages, 7 figures, accepted for publication in ApJ

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