Cosmic-Ray Constraints on the Flux of Ultra-High-Energy Neutrino Event KM3-230213A

Abstract

The detection of a $\simeq220$~PeV muon neutrino event by the KM3NeT telescope offers an unprecedented opportunity to probe the Universe at extreme energies. A photopion interaction origin of the neutrino requires a parent cosmic-ray energy of $\gtrsim4$~EeV per nucleon. We analyze the origin of this event under three scenarios, i.e., a transient point source, diffuse astrophysical emission, and a line-of-sight interaction of an ultrahigh-energy cosmic-ray (UHECR; $E\gtrsim 0.1$~EeV). Our analysis includes the flux from both a KM3NeT-only fit and a joint fit, incorporating data from KM3NeT, IceCube, and the Pierre Auger Observatory. If the neutrino event originates from transients, it requires a new population of transients that is energetic, $\gamma$-ray dark, and more abundant than the known ones. In the framework of diffuse astrophysical emission, we compare the required local UHECR energy injection rate at $\gtrsim4$ EeV with the rate derived from the flux measurements by Auger, across various source redshift evolution models. This disfavors the KM3NeT-only fit considering the source evolution up to high values of redshift, while the joint fit remains viable for sources contributing up to a maximum redshift $z_{\rm max} \gtrsim 1$ for the limiting case of photopion interaction efficiency, $f_{p\gamma} = 0.1$. For a cosmogenic origin from point sources, the luminosity obtained at redshifts $z \lesssim 1$ from the joint fit is compatible with the Eddington luminosity of $\sim10^9 M_\odot$ black holes in active galactic nuclei, assuming a proton composition and optimistic values of extragalactic magnetic field strength.