The importance of observing astrophysical tau neutrinos

The evidence of a new population of diffuse high-energy neutrinos, obtained by IceCube, has opened a new era in the field of neutrino physics. Up to now the events detected are still without any source counterpart. The detected events are compatible with the standard picture of cosmic neutrinos undergoing 3-flavor neutrino oscillations. We analyze the implications of neutrino oscillations for the present and future experiments, focusing particularly on tau neutrinos. In fact tau neutrinos are very important: even if they are not produced in astrophysical sites, they have to exist due to oscillations and their observation should be regarded as a basic proof in support of this scenario. Moreover, IceCube's measurement of the flux of muon neutrinos implies that the flux of tau neutrinos is measured within $20\%$, just assuming standard neutrino oscillations. On this basis, after discussing the experimental signatures of tau neutrinos, we predict the rates for $\nu_\tau$ detection in the present and future neutrino telescopes. We show that the present IceCube detector is close to observe the first tau neutrinos, with a probability of about 90%. Moreover the next generation of IceCube can identify about 2 neutrinos per year, reaching an evidence of 5$\sigma$ in about 10 years, despite the present uncertainty on the spectrum and on the production mechanism. The non observation of these neutrino events would have dramatic implications, such as the questioning of cosmic neutrino observations or the violation of neutrino oscillations over cosmological scales