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We study a generic class of models for ultra-high energy cosmic ray (UHECR)phenomenology, in which the sources accelerate protons and nuclei with apower-law spectrum having the same index, but with different values for themaximum proton energies, distributed according to a power-law. We show that,for energies sufficiently lower than the maximum proton energy, such models areequivalent to single-type source models, with a larger effective power lawindex and a heavier composition at the source. We calculate the resultingenhancement of the abundance of nuclei, and find typical values of a factor2-10 for Fe nuclei. At the highest energies, the heavy nuclei enhancementratios become larger, and the granularity of the sources must also be takeninto account. We conclude that the effect of a distribution of maximum energiesamong sources must be considered in order to understand both the energyspectrum and the composition of UHECRs, as measured on Earth.

Enhancing the Relative Fe-to-Proton Abundance in Ultra-High-Energy Cosmic Rays