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.

arXiv comment20 pages, 8 figures

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Cited by in corpus (13)

• Correlation of the highest-energy cosmic rays with the positions of nearby active galactic nuclei
• 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
• The effect of the geomagnetic field on cosmic ray energy estimates and large scale anisotropy searches on data from the Pierre Auger Observatory
• Multi-resolution anisotropy studies of ultrahigh-energy cosmic rays detected at the Pierre Auger Observatory
• Measurements and implications of cosmic ray anisotropies from TeV to trans-EeV energies
• Sensitivity of full-sky experiments to large scale cosmic ray anisotropies
• On the Measurement of the Helicity of Intergalactic Magnetic Fields Using Ultra-High-Energy Cosmic Rays
• 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
• Large-Scale Distribution of Arrival Directions of Cosmic Rays Detected at the Pierre Auger Observatory Above $10$PeV