Tau neutrinos underground: Signals of ν_μ→ν_τ oscillations with extragalactic neutrinos

The appearance of high energy tau neutrinos due to ν_μ→ν_τ oscillations of extragalactic neutrinos can be observed by measuring the neutrino induced upward hadronic and electromagnetic showers and upward muons. We evaluate quantitatively the tau neutrino regeneration in the Earth for a variety of extragalactic neutrino fluxes. Charged-current interactions of the upward tau neutrinos below and in the detector, and the subsequent tau decay, create muons or hadronic and electromagnetic showers. The background for these events are muon neutrino and electron neutrino charged-current and neutral-current interactions, where in addition to extragalactic neutrinos, we consider atmospheric neutrinos. We find significant signal to background ratios for the hadronic combined with electromagnetic showers with energies above 10-100 TeV initiated by the extragalactic neutrinos. We show that the tau neutrinos from point sources also have the potential for discovery above a 1 TeV threshold. A kilometer-size neutrino telescope has a very good chance of detecting the appearance of tau neutrinos when both muon and hadronic combined with electromagnetic showers are detected.