A Three-Point Cosmic Ray Anisotropy Method

TL;DR

This paper introduces a three-point statistical method to detect anisotropy in high-energy cosmic rays, demonstrating improved sensitivity over traditional two-point methods through simulations, especially with larger datasets.

Contribution

The paper develops and evaluates a novel three-point shape-strength method for cosmic ray anisotropy detection, outperforming the traditional two-point correlation approach.

Findings

Shape-strength method shows higher sensitivity than two-point method.

Larger datasets improve anisotropy detection reliability.

Reliable detection requires larger samples for subtle anisotropies.

Abstract

The two-point angular correlation function is a traditional method used to search for deviations from expectations of isotropy. In this paper we develop and explore a statistically descriptive three-point method with the intended application being the search for deviations from isotropy in the highest energy cosmic rays. We compare the sensitivity of a two-point method and a "shape-strength" method for a variety of Monte-Carlo simulated anisotropic signals. Studies are done with anisotropic source signals diluted by an isotropic background. Type I and II errors for rejecting the hypothesis of isotropic cosmic ray arrival directions are evaluated for four different event sample sizes: 27, 40, 60 and 80 events, consistent with near term data expectations from the Pierre Auger Observatory. In all cases the ability to reject the isotropic hypothesis improves with event size and with the fraction of anisotropic signal. While ~40 event data sets should be sufficient for reliable identification of anisotropy in cases of rather extreme (highly anisotropic) data, much larger data sets are suggested for reliable identification of more subtle anisotropies. The shape-strength method consistently performs better than the two point method and can be easily adapted to an arbitrary experimental exposure on the celestial sphere.