Cosmogenic gamma-rays and neutrinos constrain UHECR source models

We use CRPropa 3 to show how the expected cosmogenic neutrino and gamma-ray spectra depend on the maximum energy of ultra-high energy cosmic rays (UHECRs) at their sources, on the spectral index at injection and on the chemical composition of UHECRs. The isotropic diffuse gamma-ray background measured by Fermi/LAT is already close to touching upon a model with co-moving source evolution and with the chemical composition, spectral index and maximum acceleration energy optimized to provide the best fit to the UHECR spectrum and composition measured by the Pierre Auger Collaboration. Additionally, the detectable fraction of protons present at the highest energies in UHECRs, for experiments with sensitivities to the single-flavor neutrino flux at $\sim1$ EeV in the range of $\sim 10^{-8}$ - $10^{-10}$ GeV cm$^{-2}$ s$^{-1}$ sr$^{-1}$, is shown as a function of the evolution of UHECR sources. Experiments that reach this sensitivity will be able to significantly constrain the proton fraction for realistic source evolution models.