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We perform a new, detailed calculation of the flux and energy spectrum ofEarth-emerging $\tau$-leptons generated from the interactions of tau neutrinosand antineutrinos in the Earth. A layered model of the Earth is used todescribe the variable density profile of the Earth. Different assumptionsregarding the neutrino charged- and neutral-current cross sections as well asthe $\tau$-lepton energy loss models are used to quantify the systematicuncertainty from these on the results. A baseline simulation is then used togenerate the optical Cherenkov signal from upward-moving extensive air showersgenerated by the $\tau$-lepton decay in the atmosphere, applicable to a rangeof space-based instruments. We use this simulation to determine the neutrinosensitivity for $E_\nu>$ 10 PeV for a space-based experiment with performancesimilar to that for the Probe of Extreme MultiMessenger Astrophysics (POEMMA)mission currently under study.

Cosmic tau neutrino detection via Cherenkov signals from air showers from Earth-emerging taus