Estimates of multipolar coefficients to search for cosmic ray anisotropies with non-uniform or partial sky coverage

TL;DR

This paper presents a method to estimate multipolar coefficients of cosmic ray distributions from incomplete sky data, enabling anisotropy searches despite coverage limitations, by analyzing covariance matrices.

Contribution

It introduces a technique to recover multipolar moments under partial sky coverage, accounting for variance growth and enabling model testing without fixed multipole bounds.

Findings

Multipolar moments can be recovered with bounded degree L despite partial coverage.

Variance of estimates increases exponentially with L when coverage is zero in some regions.

Covariance matrix estimation allows testing model predictions without assuming a maximum multipole degree.

Abstract

We study the possibility to extract the multipolar moments of an underlying distribution from a set of cosmic rays observed with non-uniform or even partial sky coverage. We show that if the degree is assumed to be upper bounded by $L$, each multipolar moment can be recovered whatever the coverage, but with a variance increasing exponentially with the bound $L$ if the coverage is zero somewhere. Despite this limitation, we show the possibility to test predictions of a model without any assumption on $L$ by building an estimate of the covariance matrix seen through the exposure function.