Prospects for detection of the pair-echo emission from TeV gamma-ray bursts

The intergalactic magnetic field (IGMF) present in the voids of large-scale structures is considered to be the weakest magnetic field in the Universe. Gamma-ray observations of blazars in the GeV-TeV domain have led to lower limits on the IGMF strength based on the search for delayed or extended emission. Nevertheless, these results have been obtained with strong assumptions placed on the unknown source properties. The recent discovery of TeV radiation from gamma-ray bursts (GRBs) has paved the way for IGMF studies with these bright transients. Among the current TeV-detected GRBs, GRB 190114C, located at a redshift of $z = 0.42$, is the best sampled. Therefore, it can be considered to be representative of the properties of GRBs in the VHE domain. In addition, GRB 221009A ($z = 0.151$) is the brightest event ever detected. We present a phenomenological model based on the intrinsic properties of GRB 190114C and GRB 221009A to predict the delayed emission component (pair-echo) in the GeV-TeV band. We investigate the detectability of this component from low-redshift ($z \leq 1$) GRBs for three values of IGMF strength ($10^{-19}$ G, $10^{-18}$ G and $10^{-17}$ G), different observational times ($3$ hrs, $6$ hrs, and $9$ hrs) and source intrinsic properties. We find that for current and future generation $\gamma$-ray instruments, extending the observation for at least 3 hours after the GRB detection is a viable strategy for probing the IGMF. We also confirm that GeV-TeV observations of GRBs can probe IGMF strengths on the order of $10^{-17} -10^{-19}$ G, representing a competitive alternative to the current studies performed with active galactic nuclei (AGNs).