A New Approach to Statistics of Cosmological Gamma-ray Bursts

We use a new method of analysis to determine parameters of cosmological gamma-ray bursts (GRBs), assuming that their distribution follows the star formation history of the universe. Spectral evolution is calculated from an external shock model for Ðreball/blast-wave evolution and used to evaluate the measured peak Ñux, duration, and peak photon energy for a GRB source occurring at a given redshift lFl and with given values of total energy, baryon loading, and environmental parameters. We then Ðt model distributions of GRB sources to the observed peak Ñux, duration, and peak photon energy distribulFl tions. We Ðnd that the observed width of the and duration distributions cannot be explained by E p cosmological redshift and time dilation e†ects. Rather, broad distributions of total blast-wave energies and bulk Lorentz factors are necessary to explain the observed distributions simultaneously within the framework of our unifying GRB model. We discuss implications for source parameter distributions and determine a range of burst parameters consistent with the data. Subject headings : cosmology : theory È gamma rays : bursts È gamma rays : theory È radiation mechanisms : nonthermal