Spectral and Spatial Distortions of PeV Neutrinos from Scattering with Dark Matter

We study the effects on the spectrum and distribution of high-energy neutrinos due to scattering with dark matter both outside and within our galaxy, focusing on the neutrinos observed by the IceCube experiment with energies up to several PeV. If these neutrinos originate from extra-galactic astrophysical sources, then scattering in transit with dark matter particles will delay their arrival to Earth. This results in a cut-off in their spectrum at an energy set by the scattering cross section, allowing us to place an upper limit on cross sections $\sigma$ which increase with energy E at the level of $\sigma$ < 10^{-17} x (m / GeV) x (E / PeV)^2 cm^2, for dark matter particles of mass m. Once these neutrinos enter our galaxy, the large dark matter densities result in further scattering, especially towards the Galactic Centre. Intriguingly, we find that for $\sigma$ ~ 10^{-22} x (m / GeV) x (E / PeV)^2 cm^2, the distribution of the neutrinos on the sky has a small cluster of events towards the centre of the galaxy, potentially explaining the ~2 sigma excess seen by IceCube in this region without needing a galactic source.