Revisiting the luminosity and redshift distributions of long gamma-ray bursts

Abstract

In this work, we update and enlarge the long gamma-ray burst (GRB) sample detected by the {\it Swift} satellite. Given the incomplete sampling of the faint bursts and the low completeness in redshift measurement, we carefully select a subsample of bright {\it Swift} bursts to revisit the GRB luminosity function (LF) and redshift distribution by taking into account the probability of redshift measurement. Here we also explore two general expressions for the GRB LF, i.e., a broken power-law LF and a triple power-law LF. Our results suggest that a strong redshift evolution in luminosity (with an evolution index of $δ=1.92^{+0.25}_{-0.37}$) or in density ($δ=1.26^{+0.33}_{-0.34}$) is required in order to well account for the observations, independent of the assumed expression of the GRB LF. However, in a one-on-one comparison using the Akaike information criterion, the best-fitting evolution model involving the triple power-law LF is statistically preferred over the best-fitting one involving the broken power-law LF with a relative probability of $\sim94.3$\% versus $\sim5.7$\%. Extrapolating our fitting results to the flux limit of the whole {\it Swift} sample, and considering the trigger probability of {\it Swift}/Burst Alert Telescope in detail, we find that the expectations from our evolution models provide a good representation of the observed distributions of the whole sample without the need for any adjustment of the model free parameters. This further confirms the reliability of our analysis results.