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We study in detail the sensitivity of the Antarctic Impulsive TransientAntenna (ANITA) to possible $\nu_\tau$ point source fluxes detected via$\tau$-lepton-induced air showers. This investigation is framed around theobservation of four upward-going extensive air shower events very close to thehorizon seen in ANITA-IV. We find that these four upgoing events are notobservationally inconsistent with $\tau$-induced EASs from Earth-skimming$\nu_\tau$, both in their spectral properties as well as in their observedlocations on the sky. These four events, as well as the overall diffuse andpoint source exposure to Earth-skimming $\nu_\tau$, are also compared againstpublished ultrahigh-energy neutrino limits from the Pierre Auger Observatory.While none of these four events occurred at sky locations simultaneouslyvisible by Auger, the implied fluence necessary for ANITA to observe theseevents is in strong tension with limits set by Auger across a wide range ofenergies and is additionally in tension with ANITA's Askaryan in-ice neutrinochannel above $10^{19}$ eV. We conclude by discussing some of the technicalchallenges with simulating and analyzing these near horizon events and thepotential for future observatories to observe similar events.

physical review. d/physical review. d.

Analysis of a Tau Neutrino Origin for the Near-Horizon Air Shower Events  Observed by the Fourth Flight of the Antarctic Impulsive Transient Antenna  (ANITA)