Geometric Compatibility of IceCube TeV-PeV Neutrino Excess and its Galactic Dark Matter Origin

We perform a geometric analysis for the sky map of the IceCube TeV-PeV neutrino excess and test its compatibility with the sky map of decaying dark matter signals in our galaxy. Using both Kolmogorov-Smirnov and the likelihood-ratio tests, we have found that the observed event sky map prefers to have a combination of the galactic dark matter and a homogeneous background contributions, compared to a purely galactic dark matter origin. For the assumption that the galactic dark matter is responsible for all neutrino excess, the current data can also exclude a wide range of dark matter profiles except flatter profiles such as the isothermal one. We also consider several representative decaying dark matter spectra, which can provide a good fit to the observed spectrum at IceCube with a dark matter lifetime of around 12 orders of magnitude longer than the age of the universe.