First constraints on the strength of the extragalactic magnetic field from $γ$-ray observations of GRB 221009A

Abstract: The extragalactic magnetic field (EGMF) could be probed with $\gamma$-ray observations of distant sources. Primary very high energy (VHE) $\gamma$-rays from these sources absorb on extragalactic background light photons, and secondary electrons/positrons from the pair production acts create cascade $\gamma$-rays. These cascade $\gamma$-rays could be detected with space $\gamma$-ray telescopes such as Fermi-LAT. The $\gamma$-ray burst GRB 221009A was an exceptionally bright transient well suited for intergalactic $\gamma$-ray propagation studies. Using publicly-available Fermi-LAT data, we obtain upper limits on the spectrum of delayed emission from GRB 221009A during the time windows of 10, 30, and 90 days after the burst, and compare these with model spectra calculated for various EGMF strengths $B$, obtaining constraints on $B$. We show that the values of $B$ between 10^{-20} G and 10^{-18} G are excluded.