A possible observational evidence for θ angular distribution of opening half-angle of GRB jets

We propose a method to estimate the pseudo jet opening half-angle of GRBs using the spectral peak energy (Ep)–peak luminosity relation (so called Yonetoku relation) as well as the Ep–collimation-corrected γ-ray energy relation (so called Ghirlanda relation). For bursts with known jet break times and redshifts, we compared the pseudo jet opening half-angle with the standard one and found that the differences are within a factor 2. We apply the method to 689 long GRBS. We found that the distribution function of the pseudo jet opening half-angle obeys f(θj) ∝ θ −2.2±0.2 j with possible cutoffs for θj < 0.04 and θj > 0.3 although the log-normal fit is also possible. θ −2 distribution is compatible with the structured jet model. From the distribution function we found that the beaming correction for the rate of GRBs is ∼ 340, which means ∼ 10 yr galaxy or only one in 10 type Ib/c supernovae. We also found the evolution of the distribution function as a function of the redshift.