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 dat a. We assume three classes of luminosity functions for our analysis: (a) Lo g-normal distribution, (b) Schechter distribution, and (c) Scale-free distr ibution. We assume several models of the evolution of the GRB population fo r each luminosity function. Our analysis shows that: (a) log-normal is the only luminosity function that is compatible with both the observations. Thi s result is independent of the GRB evolution model, (b) for log-normal func tion, the average photon luminosity L-0 and the width of the luminosity fun ction sigma that are compatible with both the observations fall in the rang e: 10(55) s(-1) less than or similar to L-0 less than or similar to 10(56) s(-1) and 2 less than or similar to sigma less than or similar to 3, (c) th e agreement of observations with other luminosity functions requires the GR B population to evolve more strongly than the evolution of the star-formati on rate of the universe.