The Superiority of the Two‐Point Correlation Function over the Nearest Neighbor Analysis as a Test for Gamma‐Ray Burst Repetition

Abstract

The locations of most gamma-ray bursts are known only to several degrees. As a consequence, to detect repeated outbursts from gamma-ray burst sources in the largest gamma-ray burst catalogs, one must apply statistical tests for clustering. I show that the two-point correlation function is superior to the nearest neighbor test for detecting repetition whenever the average angle of separation between bursts in the sample is larger than the location error. The two-point correlation function is particularly sensitive to repeating sources that each produce a large number of observed gamma-ray bursts. The effects of Earth blockage and the disabling of the burst trigger are examined, and the ability of different repetition models to produce an observable repetition signal is calculated. I show that only a large number of repetitions per source can produce an observable signal, which underscores the strength of the two-point correlation function as a test of burst repetition. From these results, one must conclude that the deviation from isotropy found in the BATSE 1B catalog with the nearest neighbor test is a statistical fluctuation, and not a manifestation of burst repetition.