A new approach to statistics of cosmological
gamma-ray bursts
M. Böttcher, and C. D. Dermer,
Astrophysical Journal, 529, 635 (2000)
(Erratum: ApJ, 536, 513)
Abstract
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, and used to evaluate the measured
peak flux, duration, and 
peak photon energy for a GRB source
occuring 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 size, duration and
peak photon energy distributions. We find that the observed
width of the Ep and duration distributions can
not 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 the range of
burst parameters consistent with the data.
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