Abstract
We propose a method to estimate the jet opening half-angle of gamma-ray bursts (GRBs) using the spectral peak energy (Ep)-peak luminosity relation (the so-called Yonetoku relation) as well as the Ep-collimation-corrected gamma-ray energy relation (the so-called Ghirlanda relation). For bursts with known jet break times and redshifts, we have compared the derived jet opening half-angle with that measured and found that the differences are within a factor of 2. We apply the method to 689 long GRBs. We have found that the distribution function of the derived jet opening half-angle obeys f(θj) ∝θ−2.2±0.2j, although a lognormal fit is also possible. θ−2 distribution is compatible with the structured jet model. From the distribution function we have found that the beaming correction for the rate of GRBs is ∼340, which means ∼10−5 yr−1 galaxy−1 or only one in 102 Type Ib/c supernovae. We have also found the evolution of the distribution function as a function of the redshift.
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