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

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

2005-03-11

arxiv.org/abs/astro-ph/0503254v1

Mon.Not.Roy.Astron.Soc. 362 (2005) 1114-1118

Astronomy and Astrophysics

Astrophysics

5 pages, 5 figures, submitted to MNRAS

Scientific paper

10.1111/j.1365-2966.2005.09398.x

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.

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