Saikat Das, Srijita Hazra, Nayantara Gupta

The detection of the 244 EeV Amaterasu event by the Telescope Array, one of the most energetic ultrahigh-energy cosmic rays (UHECRs; $E\gtrsim0.1$ EeV) observed to date, invites scrutiny of its potential source. We investigate whether the nearby blazar PKS 1717+177, located within $2.5^\circ$ of the reconstructed arrival direction, could explain the event under a proton-primary hypothesis. Using a one-zone jet model, we fit the multi-wavelength spectral energy distribution of the source, incorporating both leptonic and hadronic cascade emission from photohadronic interactions. Our model supports a cosmic-ray origin of the very-high-energy ($E\gtrsim 100$ GeV) $\gamma$-ray flux and predicts a subdominant neutrino flux, an order of magnitude lower than from TXS 0506+056. Under Lorentz invariance violation, protons above a specific energy can propagate over hundreds of Mpc without significant energy loss for certain parameter choices. In such a scenario, our analysis indicates negligible deflection in the Galactic magnetic field, implying a strong extragalactic magnetic field, placing a lower bound on the field strength. Our findings provide a compelling multi-messenger framework linking UHECRs, $\gamma$ rays, and neutrinos and motivate targeted searches by current and future high-energy neutrino telescopes during increased $\gamma$-ray or X-ray activity of this blazar.