Techniques for Searching for Anisotropy in the Arrival Directions of Ultra-High Energy Cosmic Rays

Abstract

Understanding the origin and distribution of ultra-high-energy cosmic rays (UHECRs) remains a cornerstone challenge in astrophysics. These cosmic rays, with energies exceeding 8 EeV, provide insights into the most energetic phenomena in the universe. In this paper, we review and apply various statistical and analytical techniques to a simulated dataset to investigate the anisotropy in the arrival directions of UHECRs with energies exceeding 8 EeV. We simulate cosmic-ray events based on the distribution of local matter from the 2MASS Redshift Survey, supplemented with an isotropic background component, to create a robust dataset for analysis. Our methods include blind searches for excesses over the sky, Rayleigh analysis in right ascension, reconstruction of dipole and quadrupole moments using spherical harmonics, and the angular power spectrum technique — a method extensively utilized in cosmic microwave background studies — to assess anisotropies across multiple angular scales. The results underscore the potential of these methodologies to reveal significant anisotropies and contribute to our understanding of the possible extragalactic sources and propagation mechanisms of UHECRs.