Abstract

The authors propose that at log N - log n<SUB>max</SUB> relation should be used for studies of the spatial distribution of gamma-ray bursts, where N is the number of bursts which have a maximum photon count rate in excess of n<SUB>max</SUB>. A relation N ≡ n<SUB>max</SUB><SUP>-1.5</SUP> is expected if the sources are uniformly distributed in infinite, flat space, regardless of the distribution of intrinsic luminosities, spectra, and time profiles. Bursts in the Konus catalog follow a relation N ≡ n<SUB>max</SUB><SUP>a</SUP>, with the most probable value a = -1.2. However, a = -1.5 is also acceptable. This result and the apparently isotropic distribution of ≡10<SUP>2</SUP> bursts over the sky do not allow a purely observational distance estimate for the sources.

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