Rui-Jing Lu, Jun-Jie Wei, Shu-Fu Qin, En-Wei Liang
Apparent redshift dependence of the jet opening angles ($\theta_{\rm j}$) of
gamma-ray bursts (GRBs) is observed from current GRB sample. We investigate
whether this dependence can be explained with instrumental selection effects
and observational biases by a bootstrapping method. Assuming that (1) the GRB
rate follows the star formation history and the cosmic metallicity history and
(2) the intrinsic distributions of the jet-corrected luminosity ($L_{\rm
\gamma}$) and $\theta_{\rm j}$ are a Gaussian or a power-law function, we
generate a mock {\em Swift}/BAT sample by considering various instrumental
selection effects, including the flux threshold and the trigger probability of
BAT, the probabilities of a GRB jet pointing to the instrument solid angle and
the probability of redshift measurement. Our results well reproduce the
observed $\theta_{\rm j}-z$ dependence. We find that in case of
$L_{\gamma}\propto \theta_{\rm j}^2$ good consistency between the mock and
observed samples can be obtained, indicating that both $L_{\rm \gamma}$ and
$\theta_{\rm j}$ are degenerate for a flux-limited sample. The parameter set
$(L_{\rm \gamma}, \theta_{\rm j})=(4.9\times 10^{49} \rm {erg\ s}^{-1},\ 0.054
{rad})$ gives the best consistency for the current {\em Swift} GRB sample.
Considering the beaming effect, the derived intrinsic local GRB rate
accordingly is $2.85\times 10^2$ Gpc$^{-3}$ yr$^{-1}$, inferring that $\sim
0.59%$ of Type Ib/c SNe may be accompanied by a GRB.
View original:
http://arxiv.org/abs/1110.4943
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