Discovering Ultra-High-Energy Neutrinos through Horizontal and Upward τ Air Showers: Evidence in Terrestrial Gamma Flashes?

Ultra-high-energy (UHE) neutrinos ν_τ, _τ, and _e at PeV and higher energies may induce τ air showers whose detectability is amplified millions to billions of times by their secondaries. We considered UHE ν_τ-N and UHE _e-e interactions underneath mountains as a source of such horizontal amplified τ air showers. We also consider vertical upward UHE ν_τ-N interactions (UPTAUs) on Earth's crust, leading to UHE τ air showers or interactions at the horizon edges (HORTAUs), and their beaming toward high mountain gamma, X-ray, and Cerenkov detectors, and we show their detectability. We notice that such rare upward τ air showers, UPTAUs and HORTAUs, may even hit nearby balloons or satellites and flash them with short diluted gamma bursts at the edge of the Compton Gamma Ray Observatory detection threshold. We suggest the possibility of identifying these events with recently discovered (BATSE) terrestrial gamma flashes (TGFs), and we argue for their probable UHE τ-UHE ν_τ origin. From these data, approximated UHE ν_τ fluxes and Δm_νμντ lower bounds are derived. Known X-ray, gamma, and TeV active Galactic and extragalactic sources have been identified in most TGF arrival directions. Maximal EGRET activity in the Galactic center overlaps with the maximal TGF flux. The UHE cosmic-ray (UHECR) Akino Giant Air Shower Array anisotropy at 10¹⁸ eV also shows possible correlations with TGF events. The unique UHECR triplet in AGASA clustering, pointing toward BL Lac 1ES 0806+524, finds within its error box a corresponding TGF event, BATSE trigger 2444. Finally, a partial TGF Galactic signature, combined with the above correlations, suggests an astrophysical τ origin of TGF events.