Two-point Angular Autocorrelation Function and the Origin of the Highest-energy Cosmic Rays

Abstract

Construction of the Pierre Auger Observatory for the study of the highest-energy cosmic rays is about to begin. Prior to the availability of data from that experiment, decisions should be made on techniques for the analysis of the directional properties of those data. We examine here one possible analysis tool, the two-point angular autocorrelation function. As a concrete example, data from the SUGAR array are examined in this way. Possible clustering of the data is observed, and the identification of such clustering with candidate astronomical objects in a purpose-developed catalogue is investigated.

Hints of energy dependences in AGASA extremely high energy cosmic ray arrival directions

“…Previous investigations utilizing this estimator for analyzing cosmic ray arrival directions include references [16] and [17]. However, as shown by Landy and Szalay, the estimator in (2) generally exhibits variances larger than the values expected when the pair counts follow a Poisson distribution [18].…”

“…Previous investigations of AGASA data have found statistically significant clustering on small scales with no apparent clustering or anisotropy on large scales; a representative sample of model-independent studies are references [7] and [11]- [17]. For the present analysis, a robust angular correlation estimator is applied to the AGASA EHECR arrival directions to probe for possible departures from homogeneity on all angular scales.…”

Directional reconstruction and anisotropy studies

“…Searches of this kind have been made with physically likely sources such as AGN's and the brightest radio sources, e.g., [31][32][33]. The results of such searches may be positive but the number of statistical trials involved is hard to quantify (see below).…”