Inferring the Spatial and Energy Distribution of Gamma Ray Burst Sources. II. Isotropic Models

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Abstract
We use Bayesian methods to analyze the distribution of gamma ray burst intensities reported in the Third BATSE Catalog (3B catalog) of gamma ray bursts, presuming the distribution of burst sources (``bursters'') is isotropic. We study both phenomenological and cosmological source distribution models, using Bayes's theorem both to infer unknown parameters in the models, and to compare rival models. We analyze the distribution of the time-averaged peak photon number flux, F, measured on both 64 ms and 1024 ms time scales, performing the analysis of data based on each time scale independently. Several of our findings differ from those of previous analyses that modeled burst detection less completely. In particular, we find that the width of the intrinsic luminosity function for bursters is unconstrained, and the luminosity function of the actually observed bursts can be extremely broad, in contrast to the findings of all previous studies. Useful constraints probably require observation of bursts significantly fainter than those visible to BATSE. We also find that the 3B peak flux data do not usefully constrain the redshifts of burst sources; useful constraints require the analysis of data beyond that in the 3B catalog (such as burst time histories), or data from brighter bursts than have been seen by BATSE (such as those observed by the Pioneer Venus Orbiter). In addition, we find that an accurate understanding of the peak flux distributions reported in the 3B almost certainly requires consideration of data on the temporal and spectral properties of bursts beyond that reported in the 3B catalog, and more sophisticated modeling than has so far been attempted.

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