Search for Extremely-High-Energy Neutrinos and First Constraints on the Ultrahigh-Energy Cosmic-Ray Proton Fraction with IceCube

We present a search for the diffuse extremely-high-energy neutrino flux using 12.6 years of IceCube data. The nonobservation of neutrinos with energies well above 10 PeV constrains the all-flavor neutrino flux at 10^{18} eV to a level of E^{2}Φ_{ν_{e}+ν_{μ}+ν_{τ}}≃10^{-8} GeV cm^{-2} s^{-1} sr^{-1}, the most stringent limit to date. Using these data, we constrain the proton fraction of ultrahigh-energy cosmic rays (UHECRs) above ≃30 EeV to be ≲70% (at 90% CL) if the cosmological evolution of the sources is comparable to or stronger than the star formation rate. This is the first result to disfavor the "proton-only" hypothesis for UHECR in this evolution regime using neutrino data. This result complements direct air-shower measurements by being insensitive to uncertainties associated with…