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Constraints on the intergalactic magnetic field from $γ$-ray observations of GRB 190114C

Very high energy photons from cosmological gamma-ray bursts (GRBs) are expected to interact with extragalactic background light (EBL) and produce electron-positron pairs when they propagate through intergalactic medium (IGM). These relativistic pairs will then up-scatter cosmic microwave background (CMB) photons and emit secondary GeV emission. Meanwhile, the motion of these pairs are deflected by intergalactic magnetic field (IGMF), so the secondary GeV photons arrive later than the primary emission. It has been suggested that the properties of the secondary GeV emission can be used to constrain IGMF. Recently, TeV gamma-ray emission has been detected, for the first time, from a GRB (GRB 190114C) by the MAGIC telescope and its steep ${\rm γ-ray}$ spectrum shows a clear evidence of absorption by EBL. We then constrain the IGMF with the GeV flux limit obtained from the $Fermi$-LAT observations. We find a limit of $>10^{-19.5}$ G for the coherence length of $λ\leq 1$ Mpc. Although this limit is weaker than that obtained by using blazars, it represents the first limit from ${\rm γ-ray}$ observations of GRBs, which provides an independent constraint on IGMF. We also find that, for transient ${\rm γ-ray}$ sources, one can choose a favorable time window to search for the echo emission at a particular energy.