Tau Air Showers from Earth

We estimate the rate of observable Horizontal and Upward Tau Air-Showers(HORTAUs, UPTAUS) considering both the Earth opacity and the finite size of theterrestrial atmosphere. We calculate the effective target volumes and massesfor Tau air-showers emerging from the Earth. The resulting model-independentmasses for satellite experiments such as EUSO may encompass at E_nu_tau = 10^19eV a very large volume, V= 1020 km^3. Adopting simple power law neutrinofluxes, E^-2 and E^-1, calibrated to GZK-like and Z-Burst-like models, weestimate that at E= 10^19 eV nearly half a dozen horizontal shower eventsshould be detected by EUSO in three years of data collection by the"guaranteed" GZK neutrino flux. We also find that the equivalent mass for anEarth outer layer made of rock is dominant compared to the water, contrary tosimplified all-rock/all-water Earth models and previous Montecarlo simulations.Therefore we expect an enhancement of neutrino detection along continentalshelves nearby the highest mountain chains, also given the better geometricalacceptance for Earth skimming neutrinos. The Auger experiment might reveal sucha signature at E_nu= 10^{18} eV (with 26 events in 3 yr) towards the Andes, ifthe angular resolution at the horizon (both in azimuth and zenith) would reachan accuracy of nearly one degree needed to disentangle tau air showers fromcommon UHECR. The number of events increases at lower energies; therefore wesuggest an extension of the EUSO and Auger sensitivity down to (or even below)E_nu = 10^19 eV and E_nu = 10^18 eV respectively.Comment: New version resubmitted to ApJ on the 6th April 2004; 55 Pages,20 figures, major changes following referee reques