Modeling the Optical Cherenkov Signals by Cosmic Ray Extensive Air Showers Directly Observed from Sub-Orbital and Orbital Altitudes

Future experiments based on the observation of Earths atmosphere from sub-orbital and orbital altitudes plan to include optical Cherenkov cameras to observe extensive air showers produced by high-energy cosmic radiation via its interaction with both the Earth and its atmosphere. As discussed elsewhere, particularly relevant is the case of upward-moving showers initiated by astrophysical neutrinos skimming and interacting in the Earth. The Cherenkov cameras, by looking above Earths limb, can also detect cosmic rays with energies starting from less than a PeV up to the highest energies (tens of EeV). Using a customized computation scheme to determine the expected optical Cherenkov signal from these high-energy cosmic rays, we estimate the sensitivity and event rate for balloon-borne and satellite-based instruments, focusing our analysis on the Extreme Universe Space Observatory aboard a Super Pressure Balloon 2 (EUSO-SPB2) and the Probe of Extreme Multi-Messenger Astrophysics (POEMMA) experiments. We find the expected event rates to be larger than hundreds of events per hour of experimental live time, enabling a promising overall test of the Cherenkov detection technique from sub-orbital and orbital altitudes as well as a guaranteed signal that can be used for understanding the response of the instrument.