The Energy Distribution of Gamma‐Ray Bursts

The distribution of the apparent total energy emitted by a gamma-ray burstreflects not only the distribution of the energy actually released by the burstengine, but also the distribution of beaming angles. Using the observed energyfluences, the detection thresholds and burst redshifts for three burst samples,I calculate the best-fit parameters for lognormal and power-law distributionsof the apparent total energy. Two of the samples include a small number ofbursts with spectroscopic redshifts, while the third sample has 220 bursts withredshifts determined by the proposed variability-luminosity correlation. I finddifferent sets of parameter values for the three burst samples. The Bayesianodds ratio cannot distinguish between the two model distribution functions forthe two smaller burst samples with spectroscopic redshifts, but does favor thelognormal distribution for the larger sample with variability-derivedredshifts. The data do not rule out a distribution with a low energy tail whichis currently unobservable. I find that neglecting the burst detection thresholdbiases the fitted distribution to be narrower with a higher average value thanthe true distribution; this demonstrates the importance of determining andreporting the effective detection threshold for bursts in a sample.Comment: 22 pages, 8 figures, submitted to Ap.