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Cosmic rays (CRs) are protons and atomic nuclei that flow into our Solarsystem and reach the Earth with energies of up to ~10^21 eV. The sources ofultra-high energy cosmic rays (UHECRs) with E >~ 10^19 eV remain unknown,although there are theoretical reasons to think that at least some come fromactive galactic nuclei (AGNs). One way to assess the different hypotheses is byanalysing the arrival directions of UHECRs, in particular theirself-clustering. We have developed a fully Bayesian approach to analyzing theself-clustering of points on the sphere, which we apply to the UHECR arrivaldirections. The analysis is based on a multi-step approach that enables theapplication of Bayesian model comparison to cases with weak prior information.We have applied this approach to the 69 highest energy events recorded by thePierre Auger Observatory (PAO), which is the largest current UHECR data set. Wedo not detect self-clustering, but simulations show that this is consistentwith the AGN-sourced model for a data set of this size. Data sets of severalhundred UHECRs would be sufficient to detect clustering in the AGN model.Samples of this magnitude are expected to be produced by future experiments,such as the Japanese Experiment Module Extreme Universe Space Observatory(JEM-EUSO).

A Bayesian self-clustering analysis of the highest energy cosmic rays detected by the Pierre Auger Observatory