Luminosity Function of Gamma‐Ray Bursts Derived without Benefit of Redshifts

We show that the Euclidean value of for gamma-ray bursts (GRB)selected on a timescale of 1024 ms is correlated with spectral hardness. Thevalue of ranges from 0.42 for soft bursts to 0.26 for the hardestbursts. Given that the Euclidean value of for cosmological objects ina well defined sample is a distance indicator, the hard bursts must reside atlarger redshifts and therefore be more luminous than the soft bursts. Theresulting luminosity-hardness correlation cannot be shown explicitly due to thesmall number of observed GRB redshifts at the present time. Based on the-hardness correlation, we derive the luminosity function of GRBswithout using any redshifts, but we have to make an assumption how the comovingGRB rate varies with redshift. We present luminosity functions for three modelsof the GRB rate as a function of redshift, based on star formation rates. Thepeak luminosity functions are approximately broken power laws with anisotropic-equivalent break luminosity of around 10^51.5 erg s^-1 in the 50-300keV range and total local rate densities of 0.5 Gpc^-3 y^-1. Predicted GRBcounts as a function of flux and redshift are presented. Based on the GRBluminosity function, we carry out a simulation to produce theluminosity-hardness correlation, which shows that the hardest GRBs are about 20times more luminous than the softest ones.Comment: 18 pages, 7 figures, accepted for publication in Ap