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.