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

TL;DR

This paper develops an analytic method to quantify ensemble fluctuations in the flux and composition of ultra-high energy cosmic rays caused by the discrete distribution of their sources, which is crucial for interpreting observational data.

Contribution

It introduces a novel analytic approach to model cosmic ray flux and composition fluctuations due to source discreteness, aiding future observational analysis.

Findings

Future space observatories can detect spectral fluctuations caused by source distribution.

Ensemble fluctuations are significant for the highest energy cosmic rays.

The method provides a way to interpret cosmic ray data considering source variability.

Abstract

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(10^6 km^2 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.