Testing the Universal Structured Jet Models of Gamma-ray Bursts by Batse Observations

Assuming that the observed gamma-ray burst (GRB) rate as a function of redshift is proportional to a corrected star formation rate, we derive the empirical distribution of the viewing angles of long BATSE GRBs, P (θ), and the distribution of these bursts in the plane of θ against redshift, P (θ, z), by using a tight correlation between collimation-corrected gamma-ray energy (Eγ) and the peak energy of νFν spectrum measured in the rest frame (E ′ p). Our results show that P (θ) is well fitted by a log-normal distribution centering at log θ/rad = −0.76 with a width of σlog θ = 0.57. We test different universal structured jet models by comparing model predictions, P (θ) and P (θ, z), with our empirical results. To make the comparisons reasonable, an “effective” threshold, which corresponds to the sample selection criteria of the long GRB sample, is used. We find that (1) P (θ) predicted by a power-law jet model is well consistent with P (θ), but P (θ, z) predicted by this model is significantly different from P (θ, z); (2) P (θ, z) predicted by a single Gaussian jet model is more consistent with P (θ, z) than that predicted by the power-law jet model, but P (θ) predicted by this model rapidly drops at θ > 0.3 rad, which greatly deviates P (θ); and (3) both P (θ) and P (θ, z) predicted by a two-Gaussian jet model are roughly consistent with our empirical results. A brief discussion shows that cosmological effect on the Eγ − E ′ p relation does not significantly affect our results, but sample selection effects on this relationship might significantly influence our results. Subject headings: gamma rays: bursts—gamma rays: observations—methods: statistical