Gamma-ray burst intensity distributions

We use the lag-luminosity relation to calculate self-consistently the redshifts, apparent peak bolometric luminosities L-B, and isotropic energies E-iso for a large sample of BATSE gamma-ray bursts. We consider two different forms of the lag-luminosity relation; for both forms the median redshift for our burst database is 1.6. We model the resulting E-iso sample with power-law and Gaussian probability distributions without redshift evolution, both of which are reasonable models. The power-law model has an index of alpha(E) 1.76 +/- 0.05 (95% confidence), where p(E-iso) proportional to E-iso(-alphaE) The simple universal jet profile model suggested but did not require alpha(E) = 2, and subsequent physically reasonable refinements to this model permit greater diversity in alpha(E), as well as deviations from a power law; therefore, our observed E-iso probability distribution does not disprove the universal jet model.