Discovering Long Wavelength Neutrino Oscillations in the Distorted Neutrino Spectrum of Galactic Supernova Remnants

We investigate the muon neutrino event rate in km$^3$ neutrino telescopes due to a number of galactic supernova remnants expected on the basis of these objects' known $\gamma$-ray signals. We evaluate the potential of these neutrino signals to exhibit evidence of the sub-dominant neutrino oscillations expected in various neutrino mixing schemes including pseudo-Dirac scenarios and the Exact Parity Model. With ten years' data, neutrino signals from Sgr A East should either discover or exclude neutrino oscillations governed by a $\delta m^2$ parameter in the range $10^{-12}$ to $10^{-15}$ eV$^2$. Such a capability is not available to terrestrial or solar system neutrino experiments.