Tau Neutrino Appearance with a 1000 Megaparsec Baseline

A high-energy neutrino telescope, such as the AMANDA detector, may detect neutrinos produced in sources, distant by a 1000 megaparsecs, which produce mostly ${\nu }_e$ or ${\nu }_{\mu }$ neutrinos. Above 1 PeV, ${\nu }_e$ and ${\nu }_{\mu }$ are absorbed by charged-current interactions in the Earth, but the Earth never becomes opaque to ${\nu }_{\tau }$ since the ${\tau }^{-}$ produced in a charged-current ${\nu }_{\tau }$ interaction decays back into ${\nu }_{\tau }$. This provides an experimental signature for neutrino oscillations. The appearance of a ${\nu }_{\tau }$ component would be evident as a flat zenith angle dependence of a source intensity at the highest neutrino energies, which would indicate ${\nu }_{\tau }$ mixing with a sensitivity to $\Delta m^2$ as low as ${10}^{-17\mathrm{}}{\mathrm{eV}}^2$, for the farthest sources. In addition, the presence of tau neutrino mixing would allow neutrino astronomy well beyond the PeV cutoff, possibly out to the energies of protons observed above ${10}^{20}\mathrm{eV}$.