Prospects for joint cosmic ray and neutrino constraints on the evolution of trans-GZK proton sources

We consider the prospects for future ultrahigh energy cosmic ray and neutrino observations to constrain the evolution of sources producing a proton flux above 10 EeV (1 EeV = 10$^{18}$ eV). We find that strong constraints on the source evolution can be obtained by combining measurements of the cosmic ray proton fraction above 30 EeV with measurement of the neutrino flux at 1 EeV, if neutrinos are predominantly of cosmogenic origin. In the case that interactions in the source environment produce a significant astrophysical neutrino flux, constraints on the source evolution may require measurement of the observed proton fraction, as well as, the neutrino flux at multiple energies, such as 1 EeV and 10 EeV. Finally, we show that fits to current UHECR data favor models which result in a >30 EeV proton fraction and 1 EeV neutrino flux that could realistically be discovered by the next generation of experiments.