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

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.

20 pages, 8 figures

References in corpus (2)

• Non-gaussianity and cosmic uncertainty in curvaton-type models
• Small Scale Anisotropy Predictions for the Auger Observatory

Cited by in corpus (7)

• Constraints on the origin of cosmic rays above $10^{18}$ eV from large scale anisotropy searches in data of the Pierre Auger Observatory
• Ultra-High-Energy Cosmic Rays: The Intersection of the Cosmic and Energy Frontiers
• Searches for Large-Scale Anisotropy in the Arrival Directions of Cosmic Rays Detected above Energy of $10^{19}$ eV at the Pierre Auger Observatory and the Telescope Array
• Large scale distribution of arrival directions of cosmic rays detected above $10^{18}$ eV at the Pierre Auger Observatory
• Sensitivity of full-sky experiments to large scale cosmic ray anisotropies
• The Fortuitous Latitude of the Pierre Auger Observatory and Telescope Array for Reconstructing the Quadrupole Moment
• Estimating a cosmic ray detector exposure sky map under the hypothesis of seasonal and diurnal effects factorization