Research on the redshift evolution of luminosity function and selection effect of GRBs

Abstract

We study the redshift evolution of the luminosity function (LF) and redshift selection effect of long gamma-ray bursts (LGRBs). The method is to fit the observed peak flux and redshift distributions, simultaneously. To account for the complex triggering algorithm of Swift, we use a flux triggering efficiency function. We find evidence supporting an evolving LF, where the break luminosity scales as $L_b\propto (1+z)^{\tau}$, with $\tau =3.5^{+0.4}_{-0.2}$ and $\tau =0.8^{+0.1}_{-0.08}$ for two kind of LGRB rate models. The corresponding local GRB rates are $\dot{R}(0)=0.86^{+0.11}_{-0.08} \yr^{-1}\Gpc^{-3}$ and $\dot{R}(0)= 0.54^{+0.25}_{-0.07} \yr^{-1}\Gpc^{-3}$, respectively. Furthermore, by comparing the redshift distribution between the observed one and our mocked one, we find that the redshift detection efficiency of the flux triggered GRBs decreases with redshift. Especially, a great number of GRBs miss their redshifts in the redshift range of $1<z<2.5$, where "redshift desert" effect may be dominated. More interestingly, our results show that the "redshift desert" effect is mainly introduced by the dimmer GRBs, e.g., $P<10^{-7}\ergs /\s/\cm^2$, but has no effect on the brighter GRBs.