A Cautionary Note on Gamma Ray Burst Nearest Neighbor Statistics

Abstract

In this letter we explore the suggestion of Quashnock and Lamb (1993) that nearest neighbor correlations among gamma ray burst positions indicate the possibility of burst repetitions within various burst sub-classes. With the aid of Monte Carlo calculations we compare the observed nearest neighbor distributions with those expected from an isotropic source population weighted by the published BATSE exposure map. The significance of the results are assessed via the Kolmogorov-Smirnov (K-S) test, as well as by a comparison to Monte Carlo simulations. The K-S results are in basic agreement with those of Quashnock and Lamb. However, as Narayan and Piran (1993) point out, and the Monte Carlo calculations confirm, the K-S test overestimates the significance of the observed distributions. We compare the sensitivity of these results to both the definitions of the assumed burst sub-classes and the burst positional errors. Of the two, the positional errors are more significant and indicate that the results of Quashnock and Lamb may be due to systematic errors, rather than any intrinsic correlation among the burst positions. Monte Carlo simulations also show that with the current systematic errors, the nearest neighbor statistic is not very sensitive to moderate repetition rates. Until the BATSE statistical and systematic errors are fully understood, the burst nearest neighbor correlations cannot be claimed to be significant evidence for burst repetitions. (Figures available as postscript files from the author.)