Multi-messenger Implications of Sub-PeV Diffuse Galactic Gamma-Ray Emission

The diffuse Galactic gamma-ray flux between 0.1 and 1 PeV has recently been measured by the Tibet AS$\gamma$ Collaboration. The flux and spectrum are consistent with the decay of neutral pions from hadronuclear interactions between Galactic cosmic rays and the interstellar medium (ISM). We derive the flux of the Galactic diffuse neutrino emission from the same interaction process that produces the gamma rays. Our calculation accounts for the effect of gamma-ray attenuation inside the Milky Way and uncertainties due to the spectrum and distribution of cosmic rays, gas density, and infrared emission of the ISM. We find that the contribution from the Galactic plane to the all-sky neutrino flux is $\lesssim5-10\%$ around 100 TeV. The Galactic and extragalactic neutrino intensities are comparable in the Galactic plane region. Our results are consistent with the upper limit reported by the IceCube and ANTARES Collaborations, and predict that next-generation neutrino experiments may observe the Galactic component. We also show that the Tibet AS$\gamma$ data imply either an additional component in the cosmic-ray nucleon spectrum or contribution from discrete sources, including Pevatrons such as superbubbles and hypernova remnants, and PeV electron accelerators. Future multi-messenger observations between 1 TeV and 1 PeV are crucial to decomposing the origin of sub-PeV gamma rays.