A METHOD TO SEARCH FOR CORRELATIONS OF ULTRA-HIGH ENERGY COSMIC-RAY MASSES WITH THE LARGE-SCALE STRUCTURES IN THE LOCAL GALAXY DENSITY FIELD

One of the main goals of investigations using present and future giant extensive air shower (EAS) arrays is the mass composition of ultra-high energy cosmic rays (UHECRs). A new approach to the problem is presented, combining the analysis of arrival directions with the statistical test of the paired EAS samples. One of the ideas of the method is to search for possible correlations between UHECR masses and their separate sources; for instance, if there are two sources in different areas of the celestial sphere injecting different nuclei, but the fluxes are comparable so that arrival directions are isotropic, then the aim is to reveal a difference in the mass composition of cosmic-ray fluxes. The method is based on a non-parametric statistical test-the Wilcoxon signed-rank routine-which does not depend on the populations fitting any parameterized distributions. Two particular algorithms are proposed: first, using measurements of the depth of the EAS maximum position in the atmosphere; and second, relying on the age variance of air showers initiated by different primary particles. The formulated method is applied to the Yakutsk array data, in order to demonstrate the possibility of searching for a difference in average mass composition between the two UHECR sets, arriving particularly from the supergalactic plane and a complementary region.