Multimessenger Constraints on Production Sites of High-Energy Neutrinos from NGC 1068

The detection of high-energy neutrino signals from the nearby Seyfert galaxy NGC 1068 provides us with a unique opportunity to explore nonthermal processes near the center of supermassive black holes. Using the IceCube and Fermi-LAT data, we present general multimessenger constraints on the energetics of cosmic rays and the compactness of the neutrino emission region (${\mathcal R}$), considering not only $pγ$ but also $pp$ processes. Compared to the photohadronic scenario, the hadronuclear scenario can alleviate constraints on the emission region, yielding ${\mathcal R}\lesssim30-70$ for low-$β$ plasma and ${\mathcal R}\lesssim5-50$ for high-$β$ plasma. While our results support the previous conclusion that the photohadronic scenario favors a compact corona with ${\mathcal R}\sim3-10$, these suggest the relevance of further investigations into $pp$ neutrino contributions. When the cosmic-ray spectrum is extended from 1 GeV, we find that the requred cosmic-ray luminosity exceeds the X-ray luminosity for a spectral index of $s_{\rm CR}\gtrsim2$, which challenges some shock acceleration models. We also show that the beta decay scenario is unlikely even if the magnetic field is as strong as the maximum allowed by the Eddington luminosity. Given that NGC 1068 can be established as a neutrino source, our results will provide evidence for the standard hadronic scenario, including magnetically powered corona models having hard spectra with $s_{\rm CR}\lesssim2$.