Comparing the spectral lag of short and long gamma-ray bursts and its relation with the luminosity

We investigated the rest-frame spectral lags of two complete samples of bright long (50) and short (6) gamma-ray bursts (GRB) detected by Swift. We analysed the Swift/Burst Alert Telescope data through a discrete cross-correlation function fitted with an asymmetric Gaussian function to estimate the lag and the associated uncertainty. We find that half of the long GRBs have a positive lag and half a lag consistent with zero. All short GRBs have lags consistent with zero. The distributions of the spectral lags for short and long GRBs have different average values. Limited by the small number of short GRBs, we cannot exclude at more than 2 significance level that the two distributions of lags are drawn from the same parent population. If we consider the entire sample of long GRBs, we do not find evidence for a lag-luminosity correlation, rather the lag-luminosity plane appears filled on the left-hand side, thus suggesting that the lag-luminosity correlation could be a boundary. Short GRBs are consistent with the long ones in the lag-luminosity plane.