Cosmological Aspects of Gamma‐Ray Bursts: Luminosity Evolution and an Estimate of the Star Formation Rate at High Redshifts

Using 220 gamma-ray burst (GRB) redshifts and luminosities derived from the luminosity-variability relationship of Fenimore & Ramirez-Ruiz, we show that there exists a significant correlation between the GRB luminosity and redshift. In particular, we find that the evolution of the average luminosity can be parameterized as L ∝ (1 + z ) 1.4±~0.5 , where z is the burst redshift. We discuss the possible reasons behind this evolution and compare it with that of other known sources that exhibit similar behavior. In addition, we use nonparametric statistical techniques to independently estimate the distributions of the luminosity and redshift of bursts, accounting for the evolution (in contrast to previous studies, which have assumed that the luminosity function is independent of redshift). We present these distributions and discuss their implications. Most significantly, we find a comoving rate density of GRBs that continues to increase to (1 + z ) ≳ 10. From this estimate of the GRB rate density, we then use the population synthesis codes of Fryer et al. to estimate the star formation rate at high redshifts, for different progenitor models of GRBs. We find that no matter what the progenitor or population synthesis model, the star formation rate increases or remains constant to very high redshifts ( z ≳ 10).