that are compatible with IceCube measurements [@Aartsen:2013bka; @Aartsen:2013jdh; @Aartsen:2014gkd; @Laha:2013lka; @Chen:2013dza; @Anchordoqui:2013dnh]. We assume that a generic astrophysical flux can be described by ${\cal L}_{0}(E) \propto E^{-\gamma}e^{-E/E_{\rm cut}}$. An $E^{-2}$ power-law is a typical astrophysical neutrino spectrum. IceCube detected no events above about 2 PeV. A cutoff in the spectrum is required to explain this, because the effective area is rising, especially due to the Glashow resonance. We first choose $E_{\rm cut} = 10^{7}\,{\rm GeV}$. We normalize the spectrum to about the level seen by IceCube, $E^2 J(E) \sim 10^{-8}\, {\rm GeV\, cm^{-2}\, s^{-1}\, sr^{-1}}$ for neutrinos plus antineutrinos for each flavor. Not only is this consistent with IceCube data, it is also predicted from many astrophysical scenarios [@Anchordoqui:2009nf].

In Table \[tab:table1\], we provide details for the four example points identified in Fig. \[fig:constraint\]. These points are chosen to represent the regions of parameter space where $\nu$SI can have appreciable effects on the IceCube data while being consistent with the most robust limits.

In Fig. \[fig:astro1\], we show the results for a continuum injection spectrum, for the free-streaming case and the four benchmark $\nu$SI cases including regeneration. For Models B, C, and D, the presence of a resonance causes a 