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 $E_{\mathrm{p},\mathrm{i}}-E_{\mathrm{iso}}$ and $\Gamma -E_{\mathrm{iso}}$ relations to determine the Lorentz factor $\Gamma$ and the viewing angle from the edge of the jet ${\theta }_{\mathrm{obs}}^{\prime }$ of GRB 170817A. Our result shows, $\Gamma =13.4_{-5.5}^{+9.8}$ and ${\theta }_{\mathrm{obs}}^{\prime }=4.3_{-1.5}^{+1.8}{}^{\circ }$. This corresponds to the on-axis $E_{\mathrm{p},\mathrm{i}}=415_{-167}^{+361}$ keV and $E_{\mathrm{iso}}=(2.4_{-1.9}^{+1.6})\times 10^{47}$ 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.

Accepted version by ApJL

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