A search for extremely-high-energy neutrinos with IceCube and implications for the ultra-high-energy cosmic-ray proton fraction

When ultra-high-energy cosmic rays (UHECRs) interact with ambient photon backgrounds, a flux of extremely-high-energy (EHE), so-called cosmogenic, neutrinos is produced. The observation of these neutrinos with IceCube can probe the nature of UHECRs. We present a search for EHE neutrinos using 12.6 years of IceCube data. The non-observation of neutrinos with energies ≳ 10 PeV constrains the all-flavor neutrino flux at 1 EeV to be below E²Φ_{νe+νμ+ντ} ≃ 10⁻⁸ GeV cm⁻² s⁻¹ sr⁻¹, the most stringent limit to date. This constrains the proton fraction in UHECRs of energy above 30 EeV to be ≲ 70 % if the evolution of the UHECR sources is similar to the star formation rate. Our analysis circumvents uncertainties associated with hadronic interaction models in studies of UHECR air showers, which also suggest a heavy composition at such energies.