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 © 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: ${10}^{55}se{c}^{-1}\text{la}{L}_0\text{la}{10}^{56}se{c}^{-1}$ and $2\text{la}\sigma \text{la}3$, © 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.