Statistical analysis of the correlation between active galactic nuclei and ultra-high energy cosmic rays

We develop the statistical methods for comparing two sets of arrival directions of cosmic rays in which the two-dimensional distribution of arrival directions is reduced to the one-dimensional distributions so that the standard one-dimensional Kolmogorov-Smirnov test can be applied. Then we apply them to the analysis of correlation between the ultra-high energy cosmic rays (UHECR) with energies above 5.7 × 1019 eV, observed by Pierre Auger Observatory (PAO) and Akeno Giant Air Shower Array (AGASA), and the active galactic nuclei (AGN) within the distance 100 Mpc. For statistical test, we set up the simple AGN model for UHECR sources in which a certain fraction of observed UHECR are originated from AGN within a chosen distance, assuming that all AGN have equal UHECR luminosity and smearing angle, and the remaining fraction are from the isotropic background contribution. For the PAO data, our methods exclude not only a hypothesis that the observed UHECR are simply isotropically distributed but also a hypothesis that they are completely originated from the selected AGN. But, the addition of appropriate amount of isotropic component either through the background contribution or through the large smearing effect improves the correlation greatly and makes the AGN hypothesis for UHECR sources a viable one. We also point out that restricting AGN within the distance bin of 40–60 Mpc happens to yield a good correlation without appreciable isotropic component and large smearing effect. For the AGASA data, we don't find any significant correlation with AGN