The Nearest Neighbors of Batse Gamma-ray Bursts: Narrowing the Possibilities

The large errors in the locations of gamma-ray bursts observed by the Bursts and Transient Source Experiment (BATSE) forces one to adopt statistical comparisons of the burst catalog to models of burst isotropy to determine if bursts are repeating or clustered. In the rst BATSE catalog 1 , a nearest neighbor analysis nds a deviation from isotropy. 2 In a recent article 3 It was shown that known instrumental eeects cannot produce signiicant small scale anisotropies. It was also shown that burst repeater models can produce the observe anisotropies. In this paper we examine in more detail repeater burst models. We also show that nearest and farthest neighbor analyses of more recent bursts fail to nd signiicant small scale clustering. INTRODUCTION A nearest neighbor analysis 2 of the rst BATSE Gamma-Ray Burst Catalog 1 nds a maximum deviation from the isotropic nearest neighbor cumulative distribution of 2% statistical signiicance. 3 This contradicts an earlier analysis that examines the average value of the nearest neighbor separation and nds no signiicant deviation from isotropy. 4 The question arises whether the result of the rst named analysis is a consequence of statistical uctuations or of either instrumental or physical processes. The authors of one article 5 assert that the deviation must be of instrumental origin, because a similar farthest neighbor analysis of the rst Catalog nds a maximum deviation from the isotropic cumulative distribution of 11% signiicance, which they regard as statistically signiicant and unphysical. In a recent article 3 it was shown that there are no systematic eeects that can produce a deviation of the magnitude seen in the data. The eeect of the blockage of the sky by the earth produces a maximum deviation of D = 0:006 from the isotropic cumulative distribution, which is much smaller than the D = 0:12 deviation of the First Catalog. While one might expect a small angle anisotropy from the ux dependence of the sky map to introduce a deviation , we nd from Monte Carlo simulation that the maximum deviation from the isotropic cumulative distribution is D = 0:01 without any spacecraft reorientations and < 10 ?3 with the reorientations experienced by the Compton Gamma-Ray Observatory (CGRO). Moreover, performing the nearest and farthest neighbor analyses in the spacecraft coordinate frame produces maximum