Luminosity Function of GRBs

We attempt to constrain the luminosity function of Gamma Ray Bursts (GRBs) from the observed number count--flux relation and the afterglow redshift data. We assume three classes of luminosity functions for our analysis: (a) Log-normal distribution, (b) Schechter distribution, and (c) Scale-free distribution. We assume several models of the evolution of the GRB population for each luminosity function. Our analysis shows that: (a) log-normal is the only luminosity function that is compatible with both the observations. This result is independent of the GRB evolution model, (b) for log-normal function, the average photon luminosity $L_0$ and the width of the luminosity function $\sigma$ that are compatible with both the observations fall in the range: $10^{55} sec^{-1} \la L_0 \la 10^{56} sec^{-1}$ and $2 \la \sigma \la 3$, (c) the agreement of observations with other luminosity functions requires the GRB population to evolve more strongly than the evolution of the star-formation rate of the universe.