Hadronic origin of multi-TeV gamma rays and neutrinos from low-luminosity active galactic nuclei: implications of past activities of the Galactic center

Radiatively inefficient accretion flows (RIAFs) in low-luminosity active galactic nuclei (LLAGNs) have been suggested as cosmic-ray and neutrino sources that may largely contribute to the observed diffuse neutrino intensity. We show that this scenario naturally predicts hadronic multi-TeV gamma-ray excesses around Galactic centers. The protons accelerated in the RIAF in Sagittarius A$^*$ (Sgr A$^*$) escape and interact with dense molecular gas surrounding Sgr A$^*$, which is known as the central molecular zone (CMZ), and produce gamma rays as well as neutrinos. Based on a theoretical model that is compatible with the IceCube data, we calculate gamma-ray spectra of the CMZ and find that the gamma rays with $\gtrsim 1$ TeV may have already been detected with the High Energy Stereoscopic System, if Sgr A$^*$ was more active in the past than it is today as indicated by various observations. Our model predicts that neutrinos should come from the CMZ with a spectrum similar to the gamma-ray spectrum. We also show that such a gamma-ray excess is expected for some nearby galaxies hosting LLAGNs.