Measurement of the $\sim 10^{-16}$~Gauss inter-galactic magnetic field with high energy emission of GRB 221009A

Zi-Qing Xia, Yun Wang, Qiang Yuan, Yi-Zhong Fan

Published 2022-10-24Version 1

The fast evolving TeV-PeV transients and their delayed GeV-TeV cascade emission in principle server as an ideal probe of the inter-galactic magnetic fields which are hard to be measured by other methods. Very recently, LHASSO has detected the very high energy emission of the extraordinary powerful GRB 221009A up to $\sim 18$ TeV within $\sim 2000$ s after the burst trigger. Here we report the detection of a $\sim 400$ GeV photon, without accompanying prominent $\gamma$ rays down to $\sim 2$ GeV, by Fermi-LAT in the direction of GRB 221009A at about 0.4 days after the burst. Such a hard spectrum is unexpected in the inverse Compton radiation of the electrons accelerated by the external forward shock. Instead, the inverse Compton scattering of the $e^\pm$ pairs, produced from the cascade of the early primary $\sim 20$ TeV $\gamma$ rays, off the diffuse far-infrared and microwave backgrounds can generate $\gamma$ rays up to $\sim 400$ GeV with a rather hard low energy spectrum. We infer that an inter-galactic magnetic field strength of $B_{\rm IGMF}\sim 10^{-16}$ Gauss can naturally account for the arrival time of the $\sim 400$ GeV photon. Such a $B_{\rm IGMF}$ is comparable to the limits set by the statistical studies of the high energy emission of TeV blazars.