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 fireball/blast-wave evolution and used to evaluate the measured peak flux, duration, and nu F-nu peak photon energy for a GRB source occurring at a given redshift and with given values of total energy, baryon loading, and environmental parameters. We then fit model distributions of GRB sources to the observed peak flux, duration, and nu F-nu peak photon energy distributions. We find that the observed width of the E-p and duration distributions cannot be explained by cosmological redshift and time dilation effects. 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.