Simulating the Pierre Auger Observatory Fluorescence Detectors' Exposure to Tau-Neutrino-Induced Upward-Going Air Showers Using NuSpaceSim

Neutrinos constitute unique messengers of hadronic interactions, providing valuable insight into their astrophysical sources at the highest energies. Above the PeV scale, tau neutrinos interacting inside the Earth produce a significant flux of tau leptons. These tau leptons then may exit the Earth and decay within the Earth's atmosphere, initiating an upward-going extensive air shower (EAS). Exploiting the Earth as a neutrino target and the atmosphere as the detection medium through isotropic fluorescence emission results in a substantial detection volume. The Pierre Auger Observatory comprises four Fluorescence Detectors (FDs) capable of detecting such EAS. The NuSpaceSim simulation framework for upward-going tau-neutrinos has been used to generate a comprehensive Monte-Carlo simulation of the process. This includes the propagation and interaction of tau neutrinos within the Earth, the production and decay of tau leptons, the subsequent development of the EAS, as well as the geometrical and shower selection of events to which Auger's FDs are sensitive. Finally, the selected events are simulated in Auger's simulation framework Offline, which models the detector response and determines whether each event would have triggered. This approach enables the estimation of the Observatory's exposure to tau neutrino induced EAS.