DETERMINATION OF DISTANCE FROM TIME DILATION OF COSMOLOGICAL GAMMA-RAY BURSTS

The isotropic distribution of gamma-ray bursts (GRBs) as observed with the Burst and Transient Source Experiment (BATSE) strongly suggests that the bursts are at cosmological distances. At such distances, the expansion of the universe should redshift the spectra and stretch the temporal structure. Indeed, such time dilation has been observed through a variety of analyses and over all observed timescales in gamma-ray bursts. We relate the observed peak intensities, spectral shapes, and time dilation to absolute distance. We include the uncertainties in our knowledge of the intrinsic spectrum and correct for the coupling between the spectral shape and the temporal structure. Assuming a q(0) = 1/2 cosmology, the reported time dilation between the dimmest BATSE bursts and the bright BATSE bursts (a factor of similar to 2) requires a standard candle luminosity of similar to 10(52) ergs s(-1), which translates into a redshift of >6 for the dimmest BATSE bursts rather than a redshift of 1 or 2, as previously reported. An alternative method to determine the distance to cosmological GRBs is to use the log N-log P distribution. The large luminosity and distance determined from the time dilation is inconsistent with the observed log N-log P distribution (which requires a luminosity of 4.6 x 10(50) ergs s(-1) and z similar to 0.8) unless there is very strong evolution. Cosmologies with q, not equal 1/2 give similar results. The implied distance for the dimmest bursts is beyond where galaxies are thought to form. If true, the gamma-ray bursts would be orphans: no known objects would have the same distance scale. We conclude that either a large fraction (65%) of the observed time dilation between the BATSE bright and dimmest bursts is intrinsic to the bursts or that there are strong evolutionary effects in the log N-log P distribution and that it is only a coincidence that log N-log P shows a -3/2 power law at high intensities.