Redshift Dependence of the Low-energy Spectral Index of Gamma-Ray Bursts Revisited

A negative correlation was found to exist between the low-energy spectral index and the redshift of gamma-ray bursts (GRBs) by Amati et al. It was later confirmed by Geng & Huang and Gruber et al., but the correlation was also found to be quite dispersive when the sample size was significantly expanded. In this study, we have established two even larger samples of GRBs to further examine the correlation. One of our samples consists of 316 GRBs detected by the Swift satellite, and the other one consists of 80 GRBs detected by the Fermi satellite. It is found that there is no correlation between the two parameters for the Swift sample, but there does exist a weak negative correlation for the Fermi sample. The correlation becomes even more significant when the spectral index at the peak flux is considered. It is argued that the absence of the correlation in the Swift sample may be due to the fact that Swift has a very narrow energy response so that it could not measure the low-energy spectral index accurately enough. Further studies based on even larger GRB samples are solicited.