On the temporal variability classes found in long gamma-ray bursts with known redshift

Context. Based on the analysis of a small sample of BATSE and Konus gamma-ray bursts (GRBs) with know redshift it has been reported that the width of the autocorrelation function (ACF) shows a remarkable bimodal distribution in the rest-frame of the source. However, the origin of these two well-separated ACF classes remains unexplained. Aims. We study the properties of the bursts belonging to each ACF class and look for significant differences between them. Methods. We complement previous ACF analysis studying the corresponding power density spectra (PDS). With the addition of Beppo-SAX data and taken advantage of its broad-band capability, we not only increase the burst sample but we extend the analysis to X-ray energies. Results. The rest-frame PDS analysis at γ-ray energies shows that the two ACF classes are not simply characterised by a different low frequency cut-off, but they have a distinct variability as a whole in the studied frequency range. Both classes exhibit average PDS with power-law behaviour at high frequencies (f � ≥ 0.1 Hz) but significantly different slopes, with index values close to those of Brownian (−2) and Kolmogorov (−5/3) spectra for the narrow and broad classes respectively. The latter spectrum presents an additional PDS component, a low-frequency noise excess with a sharp cut-off at a characteristic frequency f � c � 0.025 Hz, in conjunction with the small relative dispersion (∼6%) of the ACF width in this class. At X-ray energies we find the power-law index unchanged for the broad class, but a significantly steeper slope in the narrow case (∼−3). We interpret this as an indication that the broad class bursts have weaker spectral evolution than the narrow ones, as suggested also by our analysis of the ACF energy dependence. The low and high frequency PDS components may then arise from two radiating regions involving different emission mechanisms. We compare our GRB sample conditioned by afterglow detections with a complete, flux limited BATSE sample, finding a significant bias against narrow ACF bursts.