Cosmogenic Origin of KM3-230213A: Delayed Gamma-Ray Emission from A Cosmic-Ray Transient
The highest-energy cosmic neutrino detected by the ARCA detector of KM3NeT has reignited the quest to pinpoint the sources of ultrahigh-energy cosmic rays (UHECRs; $E\gtrsim 0.1$ EeV). By uncovering the associated multimessenger signals, we investigate the origin of the 220 PeV $\nu_\mu$ event KM3-230213A from an unknown transient that accelerated cosmic rays to $\sim 10$ EeV. Unlike an astrophysical origin, where the $\nu_\mu$ is produced inside the source, here we consider UHECR protons that escape the source interact with the cosmic background radiation, producing a PeV-EeV cosmogenic neutrino spectrum. The secondary $e^\pm$ and $\gamma$-rays initiate an electromagnetic cascade, resulting in a cosmogenic $\gamma$-ray spectrum. The latter peaks at a delayed time of $\gtrsim 10^4$ years compared to the light travel time from the transient to observer, due to deflection of charged particles in the extragalactic magnetic field (EGMF). Our results shed light on the nature of the UHECR source for the $\nu_\mu$ event and provide crucial insights into the detection of multi-TeV $\gamma$-rays of cosmogenic origin from similar past cosmological transients. Using the $\gamma$-ray sensitivity of currently operating and next-generation imaging atmospheric Cherenkov telescopes, the flux and time-delay distribution can constrain the source distance. We further show that the detection of such a $\gamma$-ray signal above the background depends on the EGMF strength. Together with the non-detection of coincident spatial or temporal photon counterparts at the current epoch, this detection is the first compelling candidate for a sub-EeV cosmogenic neutrino.