Differential limit on the extremely-high-energy cosmic neutrino flux in the presence of astrophysical background from nine years of IceCube data

We report a quasidifferential upper limit on the extremely-high-energy (EHE) neutrino flux above 510^6 GeV based on an analysis of nine years of IceCube data. The astrophysical neutrino flux measured by IceCube extends to PeV energies, and it is a background flux when searching for an independent signal flux at higher energies, such as the cosmogenic neutrino signal. We have developed a new method to place robust limits on the EHE neutrino flux in the presence of an astrophysical background, whose spectrum has yet to be understood with high precision at PeV energies. A distinct event with a deposited energy above 10^6 GeV was found in the new two-year sample, in addition to the one event previously found in the seven-year EHE neutrino search. These two events represent a neutrino flux that is incompatible with predictions for a cosmogenic neutrino flux and are considered to be an astrophysical background in the current study. The obtained limit is the most stringent to date in the energy range between 510^6 and 210^10 GeV. This result constrains neutrino models predicting a three-flavor neutrino flux of E_^2₄+{_+_}210^-8 GeV/cm^2 sec sr at 10^9 GeV. A significant part of the parameter space for EHE neutrino production scenarios assuming a proton-dominated composition of ultra-high-energy cosmic rays is disfavored independently of uncertain models of the extragalactic background light which previous IceCube constraints partially relied on.