Selection Effects on the Observed Redshift Dependence of GRB Jet Opening Angles

TL;DR

This study uses a bootstrapping method to determine if the observed redshift dependence of GRB jet opening angles can be explained by selection effects, finding that instrumental biases significantly influence the observed correlation.

Contribution

It introduces a comprehensive simulation approach considering various instrumental effects to reproduce the observed redshift dependence of GRB jet angles, highlighting the degeneracy between luminosity and jet angle.

Findings

Instrumental selection effects can explain the observed $ heta_j$-z dependence.

The $L_ ext{gamma} ext{--} heta_j$ relation $L_ ext{gamma} o heta_j^2$ fits the data well.

Estimated intrinsic GRB rate is $2.85 imes 10^2$ Gpc$^{-3}$ yr$^{-1}$.

Abstract

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.