Testing the isotropy of high energy cosmic rays using spherical needlets
Résumé
For many decades, ultra-high energy charged particles have been a puzzle for particle physicists and astrophysicists. Nor the sites of production, nor the mechanism responsible for the generation of these ultra-energetic 'cosmic rays' (CR) are currently known. They seem to arrive from random direction in the sky, although the most energetic ones, which are not deflected much by the magnetic fields, are supposed to point towards their source with good accuracy. In an attempt to discriminate among several production scenarios, astrophysicists try to test the statistical isotropy of the directions of arrival of these CRs, as well as to compare the distribution of potential sources with the observed one. At the highest energies however, the observed CRs are very rare, and testing the distribution on such small samples of directional data on the sphere is non trivial. We propose here two procedures, a multiple test and a plug-in approach, for testing the isotropy, or the equality of the distribution with a known one, in a nonparametric framework. The tests make use of a multiscale analysis of the observed directional sample, based a wavelet frame on the sphere, the needlets. We describe the practical implementation of these two procedures and compare them to other methods in the literature. As alternatives to isotropy, we consider both very simple toy-models, and more realistic non isotropic models based on a representative physical simulation. The Monte Carlo study shows the good performances of the multiple test, together with the robustness of its sensitivity with respect to the unknown characteristics of the alternative hypothesis. 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 CRs.