# Geometrical Constraints of Observing Very High Energy Earth-Skimming Neutrinos from Space

## TL;DR

This paper analyzes the geometrical constraints for space-based detection of very-high-energy Earth-skimming neutrinos, focusing on the POEMMA mission's capability to observe upward air showers from tau neutrino interactions.

## Contribution

It derives the geometrical conditions for detecting tau neutrino-induced air showers from space and assesses POEMMA's full-sky coverage and transient follow-up potential.

## Key findings

- POEMMA can achieve full-sky coverage for neutrino searches.
- Follow-up observations of transient sources are feasible within an orbit.
- Geometrical constraints are critical for optimizing space-based neutrino detection.

## Abstract

The detection of very-high-energy (VHE) neutrinos ($E_\nu \gtrsim 10$ PeV) is a challenge that future generations of experiments are being designed and constructed to address. One promising method relies on using the Earth as a neutrino target for indirect detection of skimming tau neutrinos interacting within the Earth and producing tau leptons that are able to escape and decay in the atmosphere. The tau decay produces upward-moving Extensive Air Showers (EASs). A space-based or suborbital instrument observing the ground near the Earth limb can search for the beamed Cherenkov signal produced by the up-going EAS resulting from the tau-lepton decay. In this paper, we derive the geometrical constraints for such an observation in general and for the specific case of the Probe Of Extreme Multi-Messenger Astrophysics (POEMMA) mission currently under study, focusing on the Cherenkov signal detection. We show that, using reasonable orbital parameters, POEMMA can achieve full-sky coverage to search for potential neutrino sources over the length of its mission. We also show that follow-up of a transient Target-of-Opportunity (ToO), such as a flaring source, can be achieved within an orbit time scale depending on the source location on the celestial sphere and its relative position with respect to the Sun and the Moon.