THE SIGNATURE OF THE COSMOLOGICAL REDSHIFT IN POPULATION STUDIES OF GAMMA-RAY BURST SPECTRA

The slope of a gamma-ray burst spectrum determines how the burst flux decreases as the cosmological red-shift z increases. This provides a t est for the presence of a cosmological redshift in a sample of gamma-r ay bursts. Many bursts have spectra characterized by a frequency-depen dent power-law index, so a burst subset can be created by requiring th at each subset member have a power-law index of the given value at a l ow frequency and an index of a different given value at a high frequen cy. If all bursts in this subset are at z much less than 0.1, then the flux at low frequency will change proportionally with the flux at hig h frequency. If, however, z > 0.1 for most bursts, then the linear dep endence of the high-frequency flux on the low-frequency flux disappear s at the flux characterizing the spatial cutoff in the log N-log C(max )/C(min) diagram. This signature of the cosmological redshift generall y persists when gamma-ray bursts are given a broad distribution of int rinsic fluxes and spectral shapes. The characteristics that a burst di stribution must have to mask the cosmological redshift are discussed. The limitations of this test are observational, arising primarily from errors in measuring the photon flux and in determining the spectral i ndex of the burst spectrum.