Constraints on the intergalactic magnetic field strength from $\gamma$-ray observations of GRB 221009A

Characteristics of the cascade gamma-ray signal resulting from very-high-energy (VHE) gamma-ray sources, such as gamma-ray bursts (GRBs), can be used to constrain the strength and structure of intergalactic magnetic fields (IGMF). There has been a debate on whether GRB 190114C, the first GRB with observed TeV photons, can constrain the IGMF. Recently, LHAASO detected the brightest-of-all-time GRB 221009A, which has much larger energy in TeV band and the spectrum extends to energy above 10 TeV, providing an unprecedented opportunity to studying IGMF. We perform a Monte-Carlo simulation of the cascade process with the public ELMAG code, considering the TeV data of GRB 221009A observed by LHAASO. By comparing the resulting cascade emission with the flux limit obtained from Fermi-LAT observations, we infer a limit of $B\ge 10^{-18.5}\rm G$ for IGMF. This is much more stringent than that derived from GRB 190114C.