The Spatial Distribution of Gamma-Ray Bursts from Pioneer Venus Orbiter

The homogeneity of the burst source population in space with the log N(greater than P_c)-log P_c and log (dN/dP_c)-log P_c relations is studied on the basis of a sample of 225 observed gamma-ray bursts between September 1978 and July 1988 from the Pioneer Venus Orbiter. The relations N(greater than P_c) is approximately equal to P_c exp -1.5 and dN/dP_c is approximately equal to P_c exp -2.5 are expected if the gamma bursters are uniformly distributed in space. The Kolmogorov-Smirnov statistic gives a probability of 0.93 that the observed integral distribution N(greater than P_c) is drawn from the expected uniform distribution P_c exp -1.5. A least-squares 1 standard deviation fit to the observed differential distribution yields dN/dP_c of about P_c -2.42 +/- 0.07. Both are consistent with a uniform distribution in space of the parent population of burst sources.