Time dependent numerical model for the very high energy emissions of distant gamma-ray busrt GRB 201216C

Abstract

Recently, the MAGIC Collaboration reported a $\sim 5σ$ statistical significance of the very-high-energy (VHE) emission from a distant GRB, GRB 201216C. Such distant GRB may be effectively absorbed by the extragalactic background light (EBL). The origin of the VHE emission from such distant objects is still unknown. Here, we propose a numerical model for studying the afterglow emission of this distant GRB. The model solves the continuity equation governing the temporal evolution of electron distribution, and the broad-band observed data can be explained by the synchrotron plus synchrotron self-Compton (SSC) radiation of the forward shock. The predicted observed 0.1 TeV flux can reach $\sim 10^{-9} -10^{-10}\rm erg ~ cm^{-2} ~ s^{-1}$ at $t \sim 10^3 -10^4 \rm s$, even with strong EBL absorption, such strong Sub-TeV emissions still can be observed by MAGIC telescope. Using this numerical model, the shock parameters in the modeling are similar with two other Sub-TeV GRBs (i.e., GRB 190114C and GRB 180720B), implying that the Sub-TeV GRBs have some commonalities: they have energetic burst energy, low circum-burst medium density and low magnetic equipartition factor. We regard GRB 201216C as a typical GRB, and estimate the maximum redshift of GRB that can be detected by MAGIC telescope, i.e., $z \sim 1.6$. We also find that the VHE photon energy of such distant GRB can only reach $\sim 0.1 ~\rm TeV$. Improving the low energy sensitivity of the VHE telescope is very important to detect the Sub-TeV emissions of these distant GRBs.