Modelling the luminosity function of long gamma-ray bursts using Swift and Fermi

Abstract

I have used a sample of long Gamma Ray Bursts (GRBs) common to both \emph{Swift} and \emph{Fermi} to re-derive the parameters of the Yonetoku correlation. This allowed me to self-consistently estimate pseudo redshifts of all the bursts with unknown redshifts. This is the first time such a large sample of GRBs from these two instruments are used, both individually and in conjunction, to model the long GRB luminosity function. The GRB formation rate is modelled as the product of the cosmic star formation rate and a GRB formation efficiency for a given stellar mass. An exponential cut-off powerlaw luminosity function fits the data reasonably well, with $\nu = 0.6$ and $ L_b = 5.4 \times10^{52} \, \rm{erg.s^{-1}},$ and does not require a cosmological evolution. In the case of a broken powerlaw, it is required to incorporate a sharp evolution of the break given by $L_{b}\sim0.3\times10^{52}\left(1+z\right)^{2.90} \, \rm{erg.s^{-1}},$ and the GRB formation efficiency (degenerate up to a beaming factor of GRBs) decreases with redshift as $\propto\left(1+z\right)^{-0.80}.$ However it is not possible to distinguish between the two models. The derived models are then used as templates to predict the distribution of GRBs detectable by CZTI on board \emph{AstroSat}, as a function of redshift and luminosity. This demonstrates that via a quick localization and redshift measurement of even a few CZTI GRBs, \emph{AstroSat} will help in improving the statistics of GRBs both typical and peculiar.