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Over the last decade, observations have shown that the mean mass ofultra-high-energy cosmic rays (UHECRs) increases progressively toward thehighest energies. However, the precise composition is still unknown, andseveral theoretical studies hint at the existence of a subdominant protoncomponent up to the highest energies. Motivated by the exciting prospect ofperforming charged-particle astronomy with ultra-high-energy (UHE) protons wequantify the level of UHE-proton flux that is compatible with presentmultimessenger observations and the associated fluxes of neutral messengersproduced in the interactions of the protons. We study this scenario withnumerical simulations of two independent populations of extragalactic sourcesand perform a fit to the combined UHECR energy spectrum and compositionobservables, constrained by diffuse gamma-ray and neutrino observations. Wefind that up to of order $10\%$ of the cosmic rays at the highest energies canbe UHE protons, although the result depends critically on the selected hadronicinteraction model for the air showers. Depending on the maximum proton energy($E_\text{max}^\text{p}$) and the redshift evolution of sources, the associatedflux of cosmogenic neutrinos and UHE gamma rays can significantly exceed themultimessenger signal of the mixed-mass cosmic rays. Moreover, if$E_\text{max}^\text{p}$ is above the GZK limit, we predict a large flux of UHEneutrinos above EeV energies that is absent in alternate scenarios for theorigin of UHECRs. We present the implications and opportunities afforded bythese UHE proton, neutrino and photon fluxes for future multimessengerobservations.

Constraints on the proton fraction of cosmic rays at the highest energies and the consequences for cosmogenic neutrinos and photons