The 2pt+: an enhanced 2 point correlation function

TL;DR

The paper presents 2pt+, a new enhanced two-point correlation function method for testing isotropy in spherical point distributions, especially effective with small datasets like cosmic rays.

Contribution

Introduces 2pt+, an improved correlation function leveraging additional variables to better detect anisotropy in limited spherical datasets.

Findings

2pt+ outperforms traditional methods in small sample scenarios

Effective in analyzing cosmic ray data for anisotropy

Applicable to various astronomical datasets

Abstract

We introduce a new method for testing departure from isotropy of points on a sphere based on an enhanced form of the two-point correlation function that we named 2pt+. This method uses information from the two extra variables that define the vector between two points on a sphere. We show that this is a powerful method to test departure from isotropy of a distribution of points on a sphere especially when the number of events is small. We apply the method to a few examples in astronomy and discuss the relevance for limited datasets, such as the case of ultra-high energy cosmic rays.