A new method to test the hypothesis of isotropy of the ultrahigh energy cosmic ray flux

We developed a new method in order to detect and quantify a potential anisotropy in the ultrahigh energy cosmic ray flux. The proposed method is a new statistical tool based upon the percolation process that is used in physics to describe the formation of long-range connectivity in random systems. Specifically, we investigate the dynamic of the arrangement of cosmic rays into clusters as a function of the maximum angular separation between the arrival directions of a pair of events. In a first step, we characterize the percolation process and extract the most sensitive observable through Monte-Carlo simulations. We then apply the algorithm to the data taken by the array of surface detectors of the Pierre Auger Observatory up to January 2010. The strongest signal appears at an energy threshold of 56.74 EeV and an angular scale of 4 for which the hypothesis of isotropy of the arrival directions of the highest-energy cosmic rays is rejected at a nearly 90% C.L.