Determining the Origin of Very-high-energy Gamma Rays from Galactic Sources by Future Neutrino Observations

Recently, the Large High Altitude Air Shower Observatory (LHAASO) identified 12 $\gamma$-ray sources emitting gamma rays with energies above 100 TeV, making them potential PeV cosmic-ray accelerators (PeVatrons). Neutrino observations are crucial in determining whether the gamma-ray radiation process is of hadronic or leptonic origin. In this paper, we study three detected sources, LHAASO J1908+0621, LHAASO J2018+3651, and LHAASO J2032+4102, which are also the most promising galactic high-energy neutrino candidate sources with the lowest pre-trial p-value based on the stacking searches testing for excess neutrino emission by IceCube Neutrino Observatory. We study the lepto-hadronic scenario for the observed multiband spectra of these LHAASO sources considering the possible counterpart source of the LHAASO sources. The very-high-energy gamma rays are entirely attributed to the hadronic contribution, therefore the most optimistic neutrino flux can be derived. Then, we evaluate the statistical significance (p-value) as a function of the observation time of IceCube and the next-generation IceCube-Gen2 neutrino observatory respectively. Our results tend to disfavor that all gamma rays above $100\,\rm GeV$ from LHAASO J1908+0621 are of purely hadronic origin based on current IceCube observations, but the purely hadronic origin of gamma rays above $100\,\rm TeV$ is still possible. By IceCube-Gen2, the origin of gamma rays above $100\,\rm TeV$ from LHAASO J1908+0621 can be further determined at a $5\sigma$ significance level within a running time of $\sim 3$ years. For LHAASO J2018+3651 and LHAASO J2032+4102, the required running time of IceCube-Gen2 is $\sim 10$ years ($3\sigma$) and $\sim 10$ years ($5\sigma$), respectively. Future observations by the next-generation neutrino telescope will be crucial to understanding the particle acceleration and radiation processes inside the sources.