The Superiority of the TwoPoint Correlation Function over the Nearest Neighbor Analysis as a Test for GammaRay Burst Repetition
Abstract
The locations of most gammaray bursts are known only to several degrees. As a consequence, to detect repeated outbursts from gammaray burst sources in the largest gammaray burst catalogs, one must apply statistical tests for clustering. I show that the twopoint 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 twopoint correlation function is particularly sensitive to repeating sources that each produce a large number of observed gammaray 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 twopoint 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 December 1996
 DOI:
 10.1086/178207
 Bibcode:
 1996ApJ...473..974B
 Keywords:

 GAMMA RAYS: BURSTS;
 METHODS: STATISTICAL