A comprehensive analysis of fermi gamma-ray burst data. III. energy-dependent T₉₀ distributions of GBM GRBs and instrumental selection effect on duration classification

The durations (T₉₀) of 315 gamma-ray bursts (GRBs) detected with Fermi/GBM (8-1000 keV) up to 2011 September are calculated using the Bayesian Block method. We compare the T₉₀ distributions between this sample and those derived from previous/current GRB missions. We show that the T ₉₀ distribution of this GRB sample is bimodal, with a statistical significance level comparable to those derived from the BeppoSAX/GRBM sample and the Swift/BAT sample, but lower than that derived from the CGRO/BATSE sample. The short-to-long GRB number ratio is also much lower than that derived from the BATSE sample, i.e., 1:6.5 versus 1:3. We measure T₉₀ in several bands, i.e., 8-15, 15-25, 25-50, 50-100, 100-350, and 350-1000 keV, to investigate the energy-dependence effect of the bimodal T₉₀ distribution. It is found that the bimodal feature is well observed in the 50-100 and 100-350 keV bands, but is only marginally acceptable in the 25-50 keV and 350-1000 keV bands. The hypothesis of bimodality is confidently rejected in the 8-15 and 15-25 keV bands. The T₉₀ distributions in these bands are roughly consistent with those observed by missions with similar energy bands. The parameter T₉₀ as a function of energy follows T̄₉₀ ∝ E^-0.20±0.02for long GRBs. Considering the erratic X-ray and optical flares, the duration of a burst would be even longer for most GRBs. Our results, together with the observed extended emission of some short GRBs, indicate that the central engine activity timescale would be much longer than T₉₀ for both long and short GRBs and the observed bimodal T₉₀ distribution may be due to an instrumental selection effect.