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

Over the last decade, observations have shown that the mean mass of ultra-high-energy cosmic rays (UHECRs) increases progressively toward the highest energies. However, the precise composition is still unknown, and several theoretical studies hint at the existence of a subdominant proton component up to the highest energies. Motivated by the exciting prospect of performing charged-particle astronomy with ultra-high-energy (UHE) protons we quantify the level of UHE-proton flux that is compatible with present multimessenger observations and the associated fluxes of neutral messengers produced in the interactions of the protons. We study this scenario with numerical simulations of two independent populations of extragalactic sources and perform a fit to the combined UHECR energy spectrum and composition observables, constrained by diffuse gamma-ray and neutrino observations. We find that up to of order $10\%$ of the cosmic rays at the highest energies can be UHE protons, although the result depends critically on the selected hadronic interaction model for the air showers. Depending on the maximum proton energy ($E_\text{max}^\text{p}$) and the redshift evolution of sources, the associated flux of cosmogenic neutrinos and UHE gamma rays can significantly exceed the multimessenger 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 UHE neutrinos above EeV energies that is absent in alternate scenarios for the origin of UHECRs. We present the implications and opportunities afforded by these UHE proton, neutrino and photon fluxes for future multimessenger observations.