Testing large-scale (an)isotropy of ultra-high energy cosmic rays

We present a simple yet powerful method to test models of cosmic-ray (CR) origin using the distribution of CR arrival directions. The method is statistically unambiguous in the sense that it is binless and does not invoke scanning over unknown parameters, and general in the sense that it can be applied to any model that predicts a continuous distribution of CRs over the sky. We show that it provides a powerful discrimination between an isotropic distribution and predictions from the “matter tracer” model, a benchmark model that assumes small CR deflections and a continuous distribution of sources tracing the distribution of matter in the Universe. Our method is competitive or superior in statistical power to existing methods, and is especially sensitive in the case of relatively few high-energy events. Applying the method to the present data we find that neither an isotropic distribution nor the matter tracer model can be excluded. Based on estimates of its statistical power, we expect that the proposed test will lead to meaningful constraints on models of CR origin with the data that will be accumulated within the next few years by the Pierre Auger Observatory and the Telescope Array.