ON THE NATURE OF GAMMA-RAY BURST TIME DILATIONS

The recent discovery that faint gamma-ray bursts are stretched in time relative to bright ones has been interpreted as support for cosmologi cal distances: faint bursts have their durations redshifted relative t o bright ones. It was pointed out, however, that the relative time str etching can also be produced by an intrinsic correlation between durat ion and luminosity of gamma-ray bursts in a nearby, bounded distributi on. While both models can explain the average amount of time stretchin g, we find a difference between them in the way the duration distribut ion of faint bursts deviates from that of bright ones, assuming the lu minosity function of gamma-ray bursts is independent of distance. This allows us to distinguish between these two broad classes of model on the basis of the duration distributions of gamma-ray bursts, leading p erhaps to an unambiguous determination of the distance scale of gamma- ray bursts. We apply our proposed test to the second BATSE catalog and conclude, with some caution, that the data favor a cosmological inter pretation of the time dilation.