A possible observational evidence for ${\theta }^{-2}$ angular distribution of opening half-angle of GRB jets

Abstract

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 $\gamma$-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 $f({\theta }_j)\propto {\theta }_j^{-2.2\pm 0.2}$ with possible cutoffs for ${\theta }_j<0.04$ and ${\theta }_j>0.3$ although the log-normal fit is also possible. ${\theta }^{-2}$ distribution is compatible with the structured jet model. From the distribution function we found that the beaming correction for the rate of GRBs is $\sim 340$, which means $\sim 10^{-5}$ yr${}^{-1}$ galaxy${}^{-1}$ or only one in $10^2$ type Ib/c supernovae. We also found the evolution of the distribution function as a function of the redshift.

5 pages, 5 figures, submitted to MNRAS