The Cosmological Signatures and Flux Distribution of Gamma‐Ray Bursts with a Broad Luminosity Distribution

The cosmological expansion cannot produce the reported correlations of thegamma-ray burst timescale and spectral energy with peak flux if the burst modelreproduces the BATSE 3B peak-flux distribution for a non-evolving burst sourcedensity. Power law luminosity distribution models proportional to L^{-beta}produce acceptables fits to the data for most values of the spectral parameterswhen beta < 1.6. In this model, gamma-ray bursts of a given peak flux have adistribution of redshifts, with a maximum redshift of > 3 for peak fluxes nearthe BATSE threshold, and with an average redshift of < 1 for all values of peakflux. The reported correlations of the burst timescale and the spectral energywith peak flux are systematically 1 standard deviation above the monoluminousmodel and 1.5 to 2 standard deviation above the power-law luminosity model.These results suggest that an intrinsic correlation of burst timescale andspectral energy with luminosity is present.Comment: 38 pages with embedded figures. To appear in ApJ on Sept. 20, 1997. Minor errors corrected August 16, 199