2018RAA....18...43H

The angular distribution of gamma-ray burst (GRB) jets is not yet clear. The observed luminosity of GRB 170817A is the lowest among all known short GRBs, which is best explained by the fact that our line of sight is outside of the jet opening angle, θ_obs > θ_j, where θ_obs is the angle between our line of sight and the jet axis. As inferred by gravitational wave observations, as well as radio and X-ray afterglow modeling of GRB 170817A, it is likely that θ_obs ∼ 20° - 28°. In this work, we quantitatively consider two scenarios of angular energy distribution of GRB ejecta: a top-hat jet and a structured jet with a power law index s. For the top-hat jet model, we get a large θ_j (e.g., θ_j >10°), a rather high local (i.e., z < 0.01) short GRB rate ∼8-15x10³ Gpc^–3 yr^–1 (estimated to be 90∼1850 Gpc^–3 yr^–1 in Fong et al.) and an extremely high E_peak,0 (on-axis, rest-frame)>7.5x10⁴ keV (∼500 keV for a typical short GRB). For the structured jet model, we use θ_obs to give limits on s and θ_j for typical on-axis luminosity of a short GRB (e.g., 10⁴⁹ erg s^–1 ∼10⁵¹ erg s^–1), and a low on-axis luminosity case (e.g., 10⁴⁹ erg s^–1) gives more reasonable values of s. The structured jet model is more feasible for GRB 170817A than the top-hat jet model due to the rather high local short GRB rate, and the extremely high on-axis E_peak,0 almost rules out the top-hat jet model. GRB 170817A is likely a low on-axis luminosity GRB (10⁴⁹ erg s^–1) with a structured jet.