On the upper limits for dipole anisotropies in cosmic-ray positrons

TL;DR

This paper reviews the mathematical basis for analyzing dipole anisotropies in cosmic-ray positrons and establishes a general upper limit on anisotropy detection, comparing it with experimental constraints.

Contribution

It provides a theoretical framework to determine the maximum possible dipole anisotropy limits from cosmic-ray data, enhancing interpretation of experimental results.

Findings

Derived a general bound for dipole anisotropy limits

Compared theoretical bounds with experimental limits

Clarified the statistical significance of anisotropy measurements

Abstract

The excess of cosmic-ray positrons in the energy range from 10 GeV to few hundred GeV reported by PAMELA and AMS experiments is not consistent with a pure secondary origin and requires the introduction of a source term. The presence of anisotropies in the positron arrival directions would be a distinctive signature of their origin. Current measurements are consistent with isotropy and limits to a dipole anisotropy have been established. In this note, we review the mathematical basis of this analysis and provide a general bound to the dipole upper limits achievable from a given sample of events. The published experimental limits are confronted with this bound.