Bimodal distribution of the autocorrelation function in gamma-ray bursts

Autocorrelation functions (ACFs) are studied for a sample of 16 long gamma-ray bursts (GRBs) with known redshift z, that were observed by the BATSE and Konus experiments. When corrected for cosmic time dilation, the ACF shows a bimodal distribution. A narrow width class (11 bursts) has at half-maximum a mean width of 1.6 s with a relative dispersion of 32%, while a broad width class (5 bursts) has a width of 7.5 s with a 4% dispersion. The separation between the two mean values is highly significant (> 7 standard deviations). This temporal property could be used on the large existing database of GRBs with unknown redshift. The broad width set shows a very good linear correlation between width at half-maximum and (1+z), with a correlation coefficient R=0.995 and a probability of chance alignment <0.0004. The potential application of this correlation to cosmology studies is discussed, using it in combination with recently proposed luminosity indicators.