The 2pt+: an enhanced 2 point correlation function

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.

17 pages, 14 figures

References in corpus (6)

• Correlation of the highest energy cosmic rays with nearby extragalactic objects
• EGRET Observations of the Extragalactic Gamma Ray Emission
• Correlation of the highest-energy cosmic rays with the positions of nearby active galactic nuclei
• Methods for point source analysis in high energy neutrino telescopes
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Cited by in corpus (7)

• The nature of the Diffuse Gamma-Ray Background
• Statistics of gamma-ray point sources below the Fermi detection limit
• Anisotropy expectations for ultra-high-energy cosmic rays with future high statistics experiments
• A search for anisotropy in the arrival directions of ultra high energy cosmic rays recorded at the Pierre Auger Observatory
• Multiscale autocorrelation function: a new approach to anisotropy studies
• A statistical test of emission from unresolved point sources
• A Bayesian self-clustering analysis of the highest energy cosmic rays detected by the Pierre Auger Observatory