Directional clustering in highest energy cosmic rays - art. no. 056008

An unexpected degree of small-scale clustering is observed in highest-energ y cosmic ray events. Some directional clustering can be expected due to pur ely statistical fluctuations for sources distributed randomly in the sky. T his creates a background for events originating in clustered sources. We de rive analytic formulas to estimate the probability of random cluster config urations, and use these formulas to study the strong potential of the HiRes , Auger, Telescope Array and EUSO-OWL-AirWatch facilities for deciding whet her any observed clustering is most likely due to nonrandom sources. For a detailed comparison to data, our analytical approach cannot compete with Mo nte Carlo simulations, including experimental systematics. However, our der ived formulas do offer two advantages: (i) easy assessment of the significa nce of any observed clustering, and most importantly, (ii) an explicit depe ndence of cluster probabilities on the chosen angular bin size.