Statistical Analysis of BATSE Gamma‐Ray Bursts: Self‐Similarity and the Amati Relation

The statistical properties of a complete, flux limited sample of 197 longgamma--ray bursts (GRBs) detected by BATSE are studied. In order to bring forththeir main characteristics, care was taken to define a representative set often parameters. A multivariate analysis gives that ~70% of the total variationin parameter values is driven by only three principal components. The variationof the temporal parameters is clearly distinct from that of the spectral ones.A close correlation is found between the half-width of the autocorrelationfunction (tau) and the emission time (Tem); most importantly, this correlationis self-similar in the sense that the mean values and dispersions of both tauand Tem scale with the duration of the burst (T90). It is shown that theAmati-relation can be derived from the sample and that the scatter around thisrelation is correlated with the value of tau. Hence, tau has a role similar tothat of the break in the afterglow light curve (Tb) in the Ghirlanda-relation.In the standard GRB-scenario, the close relation between a global parameter(Tb) and a local one (tau) indicates that some of the jet-properties do notvary much for different lines of sight. Finally, it is argued that the basictemporal and spectral properties are associated with individual pulses, whilethe overall properties of a burst is determined mainly by the number of pulses.Comment: 13 pages, 6 figures, accepted for publication to ApJ with minor change