Testing the gamma-ray burst variability/peak luminosity correlation using the pseudo-redshifts of a large sample of BATSE gamma-ray bursts

We test the correlation found by Reichart et al. between time variability and peak luminosity of gamma-ray bursts (GRBs). Recently, Guidorzi et al. found that this still holds for a sample of 32 GRBs with spectroscopic redshift, although with a larger scatter than that originally found by Reichart et al. However, Guidorzi et al. also found that a power law does not provide a good description of that. We report on the same test performed on a sample of 551 burst and transient source experiment (BATSE) GRBs with a significant measure of variability assuming the pseudo-redshifts derived by Band et al. (1186 GRBs) through the anticorrelation between spectral lag and peak luminosity. We still find a correlation between variability as defined by Reichart et al. and peak luminosity with higher significance. However, this subsample of BATSE GRBs shows a higher scatter around the best-fitting power law than that found by Reichart et al. in the variability/peak luminosity space. This is in agreement with the result found by Guidorzi et al. on a sample of 32 GRBs with measured redshift. These results confirm that a power law does not provide a satisfactory description for all the GRBs, in contrast with the original findings by Reichart et al.