Constraints on the Redshift and Luminosity Distributions of Gamma Ray Bursts in an Einstein-de Sitter Universe

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Abstract
Two models of the gamma ray burst population, one with a standard candle luminosity and one with a power law luminosity distribution, are chi^2-fitted to the union of two data sets: the differential number versus peak flux distribution of BATSE's long duration bursts, and the time dilation and energy shifting versus peak flux information of pulse duration time dilation factors, interpulse duration time dilation factors, and peak energy shifting factors. The differential peak flux distribution is corrected for threshold effects at low peak fluxes and at short burst durations, and the pulse duration time dilation factors are also corrected for energy stretching and similar effects. Within an Einstein-de Sitter cosmology, we place strong bounds on the evolution of the bursts, and these bounds are incompatible with a homogeneous population, assuming a power law spectrum and no luminosity evolution. Additionally, under the implied conditions of moderate evolution, the 90% width of the observed luminosity distribution is shown to be < 10^2, which is less constrained than others have demonstrated it to be assuming no evolution. Finally, redshift considerations indicate that if the redshifts of BATSE's faintest bursts are to be compatible with that which is currently known for galaxies, a standard candle luminosity is unacceptable, and in the case of the power law luminosity distribution, a mean luminosity < 10^57 ph s^-1 is favored.

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