Determine the Lorentz factor and the viewing angle of GRB 170817A

Abstract

GRB 170817A is a weak short gamma-ray burst (GRB) accompanied by the gravitational wave (GW) event GW170817. It is believed, that an off beaming relativistic jet, produces this weak GRB. Here we use the $E_{\rm p,i}- E_{\rm iso}$ and $\Gamma - E_{\rm iso}$ relations to determine the Lorentz factor $\Gamma$ and the viewing angle from the edge of the jet $\theta'_{\rm obs}$ of GRB 170817A. Our result shows, $\Gamma = 13.4 ^{+9.8}_{-5.5}$ and $\theta'_{\rm obs} = 4.3^{+1.8}_{-1.5} \,^{\circ}$. This corresponds to the on-axis $E_{\rm p,i} = 415^{+361}_{-167}$ keV and $E_{\rm iso} = (2.4^{+1.6}_{-1.9}) \times 10^{47}$ ergs of the GRB, which is an intrinsically weak short GRB. Interestingly, the Doppler factor and the luminosity follow a universal relation from GRBs and blazars, which indicates they may share similar radiation mechanism.