Ensemble Fluctuations of the Flux and Nuclear Composition of Ultra-High Energy Cosmic Ray Nuclei

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The flux and nuclear composition of ultra-high energy cosmic rays depend on the cosmic distribution of their sources. Data from cosmic ray observatories are yet inconclusive about their exact location or distribution, but provide a measure for the average local density of these emitters. Due to the discreteness of the emitters the flux and nuclear composition is expected to show ensemble fluctuations on top of the statistical variations, i.e. "cosmic variance". This effect is strongest for the most energetic cosmic rays due to the limited propagation distance in the cosmic radiation background and is hence a local phenomenon. For the statistical analysis of cosmic ray emission models it is important to quantify the possible level of this variance. In this paper we present a completely analytic method that describes the variation of the flux and nuclear composition with respect to the local source density. We highlight that proposed future space-based observatories with exposures of O(10⁶ km² sr yr) will attain sensitivity to observe these spectral fluctuations in the cosmic ray energy spectrum at Earth relative to the overall power-law fit.