Hadronic origin of gamma rays and neutrinos from blazars: Multi-messenger implications and observational constraints
We investigate whether cosmogenic gamma rays and neutrinos from ultra-high-energy cosmic rays (UHECRs) produced in hadronically active blazars can significantly contribute to the observed spectral energy distribution (SED), and examine the potential of the Cherenkov Telescope Array Observatory (CTAO) to detect and discriminate this component. For four nearest neutrino bright blazars modeled by Rodrigues (2024), specifically AP Librae, TXS 1700+685, PKS 2326$-$502, and PKS 2345$-$16, we constrain the UHECR luminosity by requiring that the total emission does not overshoot available multi-wavelength data, assuming acceleration in the optically thin large scale jet, propagate UHECRs through realistic Galactic and extragalactic magnetic fields, and forecast CTAO performance. We find that cosmogenic gamma rays contribute up to about 7.5% of the total gamma-ray emission at the highest energies ($10^{20}$ eV), and thus remain subdominant in the SED. In contrast, the associated neutrino emission, at approximately $10^{44}$ to $10^{46}$ erg s$^{-1}$, offers a robust propagation signature of hadronic acceleration. Our simulations of 50 hour CTAO exposures show that the observatory can accurately reconstruct the intrinsic gamma ray spectrum, enabling strong constraints on the hadronic origin and propagation of UHECRs. These results demonstrate the power of combining CTAO gamma-ray measurements with neutrino observations to probe blazar hadronic processes.