The recent progress made in Galactic gamma-ray astronomy using the High Energy Stereoskopic System (H.E.S.S.) instrument provides for the first time a population of Galactic TeV gamma-rays, and hence potential neutrino sources, for which the neutrino flux can be estimated. Using the energy spectra and source morphologies measured by H.E.S.S., together with new parameterisations of pion production and decay in hadronic interactions, we estimate the signal and background rates expected for these sources in a first-generation water Cherenkov detector (ANTARES) and a next-generation neutrino telescope in the Mediterranean Sea, KM3NeT, with an instrumented volume of 1 km^3. We find that the brightest gamma-ray sources produce neutrino rates above 1 TeV, comparable to the background from atmospheric neutrinos. The expected event rates of the brightest sources in the ANTARES detector make a detection unlikely. However, for a 1 km^3 KM3NeT detector, event rates of a few neutrinos per year from these sources are expected, and the detection of individual sources seems possible. Although generally these estimates should be taken as flux upper limits, we discuss the conditions and type of gamma-ray sources for which the neutrino flux predictions can be considered robust.
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