2020ApJ...894...11G

The joint detection of gravitational wave (GW) and electromagnetic radiation from the binary neutron star merger event GW170817 marks a breakthrough in the field of multi-messenger astronomy. The short gamma-ray burst (sGRB) GRB 170817A, associated with this binary neutron star merger event, has an isotropic-equivalent gamma-ray radiation luminosity of 1.6 x 10⁴⁷ erg s^–1, which is much lower than that of other sGRBs. The measurement of the superluminal movement of the radio afterglow emission confirms the presence of the relativistic jet, and the emission features can be well explained by the structured jet model. In this paper, we calculate the luminosity distribution of sGRBs and its evolution with redshift based on the structured (Gaussian) jet model, and find that the typical luminosity increase with redshift, for nearby sGRBs (such as for luminosity distance less than 200 Mpc) the typical gamma-ray luminosity is just around 10⁴⁷-10⁴⁸ erg s^–1, which naturally explains the very low radiation luminosity of GRB 170817A. We derived the detection probability of sGRBs by Fermi-GBM and found that the expected detection rate of sGRBs is only about 1 yr^–1 within the distance of several hundred Mpc. We explored the effect of the power-law index α of the merger time distribution on the observed characteristics and found that it had little effect on the observed luminosity and viewing-angle distributions. However, it is very interesting that, for different values of α, the distributions of the number of observed sGRBs are quite different, so it is possible to determine the value of α through observed distributions of the number of sGRBs. We used the Bayesian method to make a quantitative analysis and found that the value of α may be identified when the number of observed sGRBs with known redshifts is more than 200. Finally, we compare our results of gamma-ray luminosity distribution with sGRBs with known redshifts, and found that our results are consistent with the observation, which implies that our simulation results can reproduce the observed luminosity distribution well.