The Fluence Distribution of Gamma-Ray Bursts

In the use and interpretation of $\log{N}$--$\log{S}$ distributions forgamma-ray bursts, burst peak flux has typically been used for $S$. We considerhere the use of the fluence as a measure of $S$, which may be a moreappropriate quantity than the peak flux in such highly variable sources. Wedemonstrate how using the BATSE trigger data we can determine the selectioneffects on fluence. Then using techniques developed elsewhere to account forthe important threshold effects and correlations. Applying the appropriatecorrections to the distributions, we obtain a fluence distribution which showsa somewhat sharper break than the peak flux distribution, implying a possiblynarrower fluence luminosity distribution. If bursts are at cosmologicaldistances, these observations together indicate that evolution of theluminosity function is required.