Multi-Messenger Studies with High-Energy Neutrinos and Gamma Rays: The WST Opportunity

The search for the sources of ultra-high-energy cosmic rays (UHECRs) using high-energy neutrinos represents a frontier in high-energy astrophysics. However, a critical bottleneck remains: the ability to rapidly survey the sizable sky areas defined by the localization uncertainties of neutrino detectors and to provide rapid spectroscopic classification of the multitude of optical transients found within them. By deploying a large field-of-view with high-multiplex Multi-Object Spectroscopy (MOS) on a large aperture telescope, one can instantaneously cover neutrino error circles, thus providing crucial spectroscopic classifications of potential counterparts discovered, for example, by the Vera C. Rubin Observatory (LSST) with unprecedented efficiency. Furthermore, simultaneous operation of a giant panoramic central Integral Field Spectrograph (IFS) would allow for detailed kinematic and environmental characterization of primary candidates. This facility would unlock deep synergies between next-generation neutrino telescopes (IceCube-Gen2, KM3NeT) and gamma-ray observatories (CTAO), transforming unique multi-messenger alerts into a comprehensive physical understanding.