Identifying Ultrahigh-Energy Cosmic-Ray Accelerators with Future Ultrahigh-Energy Neutrino Detectors

The detection of ultrahigh-energy (UHE) neutrino sources would contribute significantly to solving the decades-old mystery of the origin of the highest-energy cosmic rays. We investigate the ability of a future UHE neutrino detector to identify the brightest neutrino point sources, by exploring the parameter space of the total number of observed events and the angular resolution of the detector. The favored parameter region can be translated to requirements for the effective area, sky coverage and angular resolution of future detectors, for a given source number density and evolution history. Moreover, by studying the typical distance to sources that are expected to emit more than one event for a given diffuse neutrino flux, we find that a significant fraction of the identifiable UHE neutrino sources may be located in the nearby Universe if the source number density is above $\sim10^{-6}\,\rm Mpc^{-3}$. If sources are powerful and rare enough, as predicted in blazar scenarios, they can first be detected at distant locations. Our result also suggests that if UHE cosmic-ray accelerators are neither beamed nor transients, it will be possible to associate the detected UHE neutrino sources with nearby UHE cosmic-ray and gamma-ray sources, and that they may also be observed using other messengers, including ones with limited horizons such as TeV gamma rays, UHE gamma rays and cosmic rays. We find that for a $\gtrsim5\sigma$ detection of UHE neutrino sources with a uniform density, $n_s\sim{10}^{-7}-{10}^{-5}~{\rm Mpc}^{-3}$, at least $\sim100-1000$ events and sub-degree angular resolution are needed, and the results depend on the source evolution model.