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

The cosmological expansion cannot produce the reported correlations of the gamma-ray burst timescale and spectral energy with peak flux if the burst model reproduces the BATSE 3B peak-flux distribution for a non-evolving burst source density. The required ratios of time dilation and redshift factors are only produced by monoluminous models at peak fluxes below the BATSE threshold, and they are never produced by power-law luminosity models. Monoluminous models only produce acceptable fits to the peak-flux distribution for very specific combinations of the spectral and cosmological parameters. The redshift of gamma-ray bursts at the BATSE threshold is z ≈ 1.5. Power law luminosity distribution models ∝ L produce acceptables fits to the data for most values of the spectral parameters when β < 1.6. In this model, gamma-ray bursts of a given peak flux have a distribution of redshifts, with a maximum redshift of ∼> 3 for peak fluxes near the BATSE threshold, and with an average redshift of < 1 for all values of peak flux. This qualitative behavior occurs whenever the luminosity distribution determines the shape of the peak-flux distribution, regardless of whether source density evolution occurs. The reported correlations of the burst timescale and the spectral energy with peak flux are systematically 1 standard deviation above the monoluminous model and 1.5 to 2 standard deviation above the power-law luminosity model. These results suggest that an intrinsic correlation of burst timescale and spectral energy with luminosity is present. Studies of the peak-flux distribution for bursts selected by Epeak or hardness ratio provide a test for this intrinsic correlation. Subject headings: Gamma rays: bursts To appear in The Astrophysical Journal, Sept. 20, 1997 e-mail: [email protected]