Clustering properties of ultra-high-energy cosmic rays and the search for their astrophysical sources

The arrival directions of ultra-high-energy cosmic rays (UHECRs) may show anisotropies on all scales, from just above the experimental angular resolution up to medium scales and dipole anisotropies. We find that a global comparison of the two-point autocorrelation function of the data with that of catalogs of potential sources is a powerful diagnostic tool. In particular, this method is far less sensitive than cross-correlation studies to unknown deflections in magnetic fields while keeping a strong discrimination power among source candidates. We illustrate these advantages by considering ordinary galaxies, gamma-ray bursts, and active galactic nuclei as possible sources. Already the sparse publicly available data suggest that the sources of UHECRs may be a strongly clustered subsample of galaxies or of active galactic nuclei. We present forecasts for various cases of source distributions which can be checked soon with the Pierre Auger Observatory.