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 Centre 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 Centre region becomes enhanced and could be detected at energies above similar to 10(4) GeV in a km(3)-size neutrino telescope within ten years of operation. The galactic anisotropy, which is the main signature of this flux, allows us to discriminate this signal from other possible extraterrestrial diffuse fluxes of high energy neutrinos.