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.
