Pulse width distributions and total counts as indicators of cosmological time dilation in gamma‐ray bursts

The spatial distribution of bursts observed by BATSE is isotropic and inhomogeneous, implying that their sources may be at cosmological distances. We describe three tests that we have applied to search for the signature of time dilation. For both tests selection effects arising from intensity differences are avoided by rescaling all burst time profiles to a canonical dim peak intensity and rendering their backgrounds and noise biases uniform. These tests are (1) the distribution of pulse widths for these groups; a measure of the average rescaled integrated counts (2) within fitted pulse structures and (3) above fitted background for the burst ensembles. All tests use pulse shapes obtained from fitting major structures in temporal profiles. Results from 135 BATSE bursts indicate that the relative time dilation factor, dim to bright bursts, would be of order two, consistent with three previous tests, and with cosmological interpretations of the BATSE number‐intensity relation, all of which place the more distant bursts at redshifts of about unity.