Brightness-independent measurements of gamma-ray burst durations

We demonstrate that a brightness bias exists in the third BATSE catalog duration measurements of cosmic gamma-ray bursts. This bias, caused by the fact that the outlying emission from bright bursts is easier to detect than from dim bursts, is sufficient to obscure a time-dilation factor of order 2. To avoid this problem, we construct brightness-independent measures of duration and apply them to a sample of long bursts containing no known brightness biases. We render all bursts to the same signal-to-noise ratio level, and thereby miss comparable amounts of temporal structure in both dim and bright bursts. We show that of two popular duration measures, T-50 and T-90, the former is to be preferred when the primary requirement is a comparison between bright and dim bursts. Our background subtraction approach involves the simultaneous examination of time profiles from all eight of the BATSE's large area detectors and all four energy channels, enabling us to identify appropriate background regions and to discriminate effectively between burst and nonburst emission. We report the first brightness-independent duration measurements over a continuous range of peak flux. These results indicate an increasing time-dilation factor with decreasing flux. We estimate that the energy dependence of the derived durations is relatively small. Under the cosmological hypothesis, a self-consistent treatment, including the corresponding energy correction implied by redshift, indicates that (1 + z(dim))/(1 + z(brt)) is similar to 2.