Floor of cosmogenic neutrino fluxes above $10^{17}~$eV

The search for neutrinos with energies greater than $10^{17}~$eV is being actively pursued. Although normalization of the dominant neutrino flux is highly uncertain, a floor level is guaranteed by the interactions of extragalactic cosmic rays with Milky Way gas. We estimate that this floor level gives an energy flux of $E^2\phi_\nu\simeq 10^{-13^{+0.5}_{-0.5}}~$GeV~cm$^{-2}$~sr$^{-1}$~s$^{-1}$ at $10^{18}~$eV, where uncertainties arise from the modeling of the gas distribution and the experimental determination of the mass composition of ultra-high-energy cosmic rays on Earth. Based on a minimal model of cosmic-ray production to explain the mass-discriminated energy spectra observed on Earth above $5{\times}10^{18}$~eV, we also present generic estimates of the neutrino fluxes expected from extragalactic production that generally exceed the aforementioned guaranteed floor. The prospects for detecting neutrinos above $10^{18}$~eV remain however challenging, unless proton acceleration to the highest energies is at play in a sub-dominant population of cosmic-ray sources or new physical phenomena are at work.