Very recently the IceCube Collaboration has reported an observation of 28 neutrino candidates with energies between 50 TeV and 2 PeV , constituting a 4.1 \sigma excess compared to the atmospheric background .
In this article we investigate the compatibility between the data and a hypothesized unbroken power-law neutrino spectrum for various values of spectral index \Gamma \geq 2 .
We show that \Gamma \sim 2.3 is consistent at the \sim 1.5 \sigma level with the observed events up to 2 PeV and to the null observation of events at higher energies .
We then assume that the sources of this unbroken spectrum are Galactic , and deduce ( i ) an energy-transfer fraction from parent protons to pions ( finding \epsilon _ { \pi ^ { \pm } } and \epsilon _ { \pi } ) , and ( ii ) a way of discriminating among models which have been put forth to explain the “ knee ” and “ ankle ” features of the cosmic ray spectrum .
Future IceCube data will test the unbroken power law hypothesis and provide a multi-messenger approach to explaining features of the cosmic ray spectrum , including the transition from Galactic to extragalactic dominance .