Prospects for high-elevation radio detection of >100 PeV tau neutrinos

Tau neutrinos are expected to comprise roughly one third of both the astrophysical and cosmogenic neutrino flux, but currently the flavor ratio is poorly constrained and the expected flux at energies above ${10}^{17}$ eV is low. We present a detector concept aimed at measuring the diffuse flux of tau neutrinos in this energy range via a high-elevation mountaintop detector using the radio technique. The detector searches for radio signals from upgoing air showers generated by Earth-skimming tau neutrinos. Signals from several antennas in a compact array are coherently summed at the trigger level, permitting not only directional masking of anthropogenic backgrounds, but also a low trigger threshold. This design takes advantage of both the large viewing area available at high-elevation sites and the nearly full duty cycle available to radio instruments. We present trade studies that consider the station elevation, frequency band, number of antennas in the array, and the trigger threshold to develop a highly efficient station design. Such a mountaintop detector can achieve a factor of ten improvement in acceptance over existing instruments with 100 independent stations. With 1000 stations and three years of observation, it can achieve a sensitivity to an integrated $E^{-2}$ flux of $<{10}^{-9}$ GeV cm${}^{-2}$ sr${}^{-1}$ s${}^{-1}$, in the range of the expected flux of all-flavor cosmogenic neutrinos assuming a pure iron cosmic-ray composition.