A lower bound on the number of cosmic ray events required to measure source catalogue correlations

TL;DR

This paper estimates the minimum number of ultra-high energy cosmic ray events needed to statistically confirm correlations with source catalogues, considering magnetic deflections and current knowledge.

Contribution

It provides a lower bound on the sample size required to detect significant correlations between cosmic rays and astrophysical sources.

Findings

Significant correlations are achievable with over 1000 cosmic ray events.

Magnetic field effects influence the required sample size.

The study compares different scattering scenarios for cosmic ray propagation.

Abstract

Recent analyses of cosmic ray arrival directions have resulted in evidence for a positive correlation with active galactic nuclei positions that has weak significance against an isotropic source distribution. In this paper, we explore the sample size needed to measure a highly statistically significant correlation to a parent source catalogue. We compare several scenarios for the directional scattering of ultra-high energy cosmic rays given our current knowledge of the galactic and intergalactic magnetic fields. We find significant correlations are possible for a sample of $>$1000 cosmic ray protons with energies above 60 EeV.