We investigate the capability of the Probe Of Extreme Multi-Messenger Astrophysics (POEMMA) in performing Target-of-Opportunity (ToO) neutrino observations. POEMMA will detect tau neutrinos via Cherenkov radiation from their upward-moving extensive air showers. POEMMA will be able to quickly slew ($90^{circ}$ in 500 s) to the direction of an astrophysical source, which in combination with its orbital speed will provide it with unparalleled capability to follow up transient alerts. We calculate POEMMAs transient sensitivity for two observational modes for its two satellites (ToO-stereo and ToO-dual) and investigate variations in neutrino sensitivity across the sky arising from POEMMAs orbit. We explore separate scenarios for long ($sim 10^{6}$ s) and short ($sim 10^3$ s) bursts, accounting for intrusion from the Sun and the Moon in long-duration scenarios. For long bursts, POEMMA will improve the average neutrino sensitivity above 300 PeV by up to a factor of 7 with respect to existing experiments (e.g., IceCube, ANTARES, and Pierre Auger), reaching the level of model predictions for neutrino fluences at these energies from several types of long-duration astrophysical transients (e.g., binary neutron star mergers and tidal disruption events). For short bursts in the optimal case, POEMMA will improve the sensitivity over existing experiments by at least an order of magnitude above 100 PeV. POEMMAs orbit and rapid slewing will provide access to the full celestial sky, including regions not accessible to ground-based experiments. Finally, we discuss the prospects for detecting neutrinos from candidate astrophysical neutrino sources in the nearby universe. Our results demonstrate that with its improved neutrino sensitivity at ultra-high energies and unique full-sky coverage, POEMMA will be an essential component in an expanding multi-messenger network.
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