Ultra-high-energy cosmic ray source statistics in the GZK energy range

The Greisen-Zatsepin-Kuzmin (GZK) effect, i.e. the interaction of ultra-high-energy cosmic ray (UHECR) protons and nuclei with the intergalactic photon background, results in a drastic reduction of the number of sources contributing to the observed flux above similar to 60 EeV. We study quantitatively the source statistics as a function of energy for a range of models compatible with the current data, varying source composition, injection spectrum, source density, and luminosity distribution. We also explore various realizations of the source distribution. We find that, in typical cases, the brightest source in the sky contributes more than one-fifth of the total flux above 80 EeV and about one-third of the total flux at 100 EeV. We show that typically between two and five sources contribute more than half of the UHECR flux at 100 EeV. With such low source numbers, the isolation of the few brightest sources in the sky may be possible for experiments collecting sufficient statistics at the highest energies, even in the event of relatively large particle deflections.