Gilles Faÿ, Jacques Delabrouille, Gérard Kerkyacharyan, Dominique Picard
Ultra-high energy charged particles of unknown origin, which interact in the high atmosphere of the Earth generating large cascades of secondary particles, can be observed from the ground. For many decades, they have been a puzzle for particle physicists and astrophysicists. As an attempt to discriminate among several possible production scenarios, astrophysicists try to test the statistical isotropy of the directions of arrival of these cosmic rays. At the highest energies however, the observed cosmic rays are very rare, and testing the distribution of such small samples of directional data on the sphere is non trivial. We address here a nonparametric detection problem, making use of a multiscale analysis of the observation sample, based on a decomposition of the directional data using a wavelet frame on the sphere, the needlets. The aim is to test the isotropy, or the equality of the distribution with a known one. We explore two particular procedures, a multiple test and a plug-in approach. We describe the practical implementation of these two procedures and compare them to other methods in the literature. The Monte Carlo study shows the good performances of the multiple test at moderate sample size, together with the robustness of its sensitivity with respect to the unknown characteristics of the alternative hypothesis. On the 69 most energetic events published by the Pierre Auger collaboration, our procedure detects significant departure from isotropy. The flexibility of this method and the possibility to modify it to take into account a large variety of extensions of the problem make it an interesting option for future investigation of the origin of ultra-high energy cosmic rays.
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http://arxiv.org/abs/1107.5658
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