Detectable neutrino fluxes due to enhanced cosmic ray densities in the Galactic Centre region

We examine in detail the detectability of a signal of diffuse high energy neutrinos produced in the Milky Way by the interaction of cosmic rays (CRs) with the interstellar medium (ISM). We show that highly inhomogeneous galactic CR densities arise naturally from large scale drift effects and the inhomogeneous distribution of CR sources. In particular, the CR density in the Galactic Center region (where the ISM density is maximal) could be an order of magnitude larger than the local CR density. Hence, the expected diffuse flux of neutrinos from the Galactic Center region becomes enhanced and could be detected at energies above $\sim 10^4$ GeV in a km$^3$-size neutrino telescope within 10 years of operation. The galactic anisotropy, which is the main signature of this flux, allows to discriminate this signal from other possible extraterrestrial diffuse fluxes of high energy neutrinos.