Tau Neutrino Appearance with a 1000 Megaparsec Baseline

A high-energy neutrino telescope, such as the operating AMANDA detector, may detect neutrinos produced in sources, possibly active galactic nuclei or gamma-ray bursts, distant by a thousand megaparsecs. These sources 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 before reaching the opposite surface. However, the Earth never becomes opaque to nu_tau since the tau^- produced in a charged-current nu_tau interaction decays back into nu_tau before losing significant energy. This preferential penetration of tau neutrinos through the Earth above 10^14 eV 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. Such an angular dependence would indicate nu_tau mixing with a sensitivity to delta-m^2 as low as 10^-17 eV^2, for the farthest sources. In addition, the presence of tau neutrino mixing would provide the opportunity for neutrino astronomy well beyond the PeV cutoff, possibly out to the energies matching those of the highest energy protons observed above 10^20 eV.