abstract:
The joint detection of gravitational wave (GW) and electromagnetic radiation from the binary neutron star merger event GW170817A marks a breakthrough in the field of multi-messenger astronomy. The short gamma-ray burst (sGRB) GRB170817A, associated with this binary neutron star merger event, has an isotropic-equivalent gamma-ray radiation luminosity of 1.6*1047 erg/s, which is much lower than that of other short GRBs. 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. Here 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 200Mpc) the typical gamma-ray luminosity is just around 1047– 1048 erg/s, which naturally explains the very low radiation luminosity of GRB170817A. We derived the detection probability of short GRBs by Fermi- GBM, found that the expected detection rate of sGRBs is only about 1 /yr by Fermi-GBM 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 number distribution of observed sGRBs are quite different, so it is possible to determine the value of α through observed sGRB number distribution. 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 are more than 200. Finally, we compare our results of gamma-ray luminosity distribution with sGRBs with known redshifts, and found our results are consistent with the observation, which implies that our simulation results can well reproduce the observed luminosity distribution.
Gamma-ray bursts are known to be the most violent explosions in the universe, and a variety of correlations between observable GRB properties have been proposed in the literature, but none of these correlations is valid for both long GRBs and short GRBs. Here we report the discovery of a universal correlation, which is suitable for both long and short GRBs using three prompt emission properties of GRBs, i.e. the isotropic peak luminosity L_{iso}, the peak energy of the time integrated prompt emission spectrum E_{peak}, and the "high signal" timescale T_{0.45}. L_{iso}$\propto$E_{peak}^{1.94} T_{0.45}^{0.47}.This universal correlation just involves properties of GRB prompt emission and does not require any information of the afterglow phase, which can be used as a relatively unbiased redshift estimator. Here we use this correlation to estimate the pseudo redshifts for short Gamma Ray Bursts and then use Lynden-Bell method to obtain a non-parametric estimate of their luminosity function and formation rate. The luminosity function is ψ(L0)∝L0-0.63±0.07for dim SGRBs and ψ(L0)∝L0-1.93±0.28for bright SGRBs, with the break point 6.95^{+0.84}_{-0.76} * 1050erg/s The local formation rate of SGRBs is about 15 events Gpc-3y-1. This universal correlation may have important implications for GRB physics, implying that the long and short GRBs should share similar radiation processes.
