Abstract
Gamma-ray bursts (GRBs) are the most energetic electromagnetic explosions in the universe. Recently, the Large High Altitude Air Shower Observatory (LHAASO) reported the breakthrough observation of GRB 221009A with gamma-ray energies beyond 13 TeV. This discovery, together with the previous GRB detection well above 100 GeV, confirms the production of very-high-energy (VHE, greater than or similar to 100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gtrsim 100$$\end{document} GeV) radiation which might be a common component of all bright GRBs. It is reasonable to expect that bright GRBs are important targets for ground-based gamma-ray experiments. In this work, we estimate the detection rate for current and upcoming ground-based gamma-ray observatories including LHAASO, Large Array of Imaging Atmospheric Cherenkov Telescopes (LACT) and the Southern Wide-field Gamma-ray Observatory (SWGO) under two emission models with GRB 221009A as the template: first, that they all share the same intrinsic VHE spectral shape; second, they have the same environmental parameter and electron spectral index, governing their synchrotron self-Compton (SSC) emission. Using the long GRB luminosity and redshift distribution function obtained from the Fermi-GBM GRB samples, and accounting for the cosmological effects and extra-galactic background light (EBL) absorption, we derive the expected VHE flux at Earth. The sensitivity analysis for LHAASO, the upcoming LACT, and SWGO to evaluate their detection potential across specific redshift and luminosity ranges has been performed. The corresponding 5 sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document} detection rates of 221009A-like GRBs for the two emission models are: LHAASO, 0.04-0.05 yr-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {yr}<^>{-1}$$\end{document}; LACT, 0.03-0.06 yr-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {yr}<^>{-1}$$\end{document}; SWGO, 0.2-0.4 yr-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {yr}<^>{-1}$$\end{document}. These rates can vary by up to approximate to 24%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx 24\%$$\end{document} due to different EBL models.