/ (1 + z)$. The edge at $1\,{\rm PeV}$ is from emission nearby, the peak near $0.5\,{\rm PeV}$ from emission near $z = 1$, and lower energies from emission at still-higher redshifts. As noted, the rapid rise of the SFR between $z = 0$ and $z = 1$ [@Hopkins:2006bw; @Yuksel:2008cu] overcomes the suppression due to the Hubble expansion, i.e., less volume per redshift interval, until near $z = 1$, where the SFR begins to flatten and then fall.

![The effects of $\nu$SI on an emitted line spectrum at 1 PeV with SFR evolution, for different assumed resonance energies, as labeled. The solid lines are for free-streaming neutrinos, the dotted lines are for $\nu$SI with regeneration of two neutrinos (the beam and target), and the dashed lines are for $\nu$SI with no regeneration.[]{data-label="fig:astro_line"}](fig_astro_line.pdf){width="8.1cm"}

![The effects of $\nu$SI on an emitted continuum spectrum that is consistent with IceCube data. The solid line indicates the free-streaming case ($\gamma = 2$ and $E_{\rm cut} = 10^{7}\,{\rm GeV}$), while the other lines are for four models of $\nu$SI, with the parameters defined in Table \[tab:table1\].[]{data-label="fig:astro1"}](fig_astro1.pdf){width="8.5cm"}

With $\nu$SI, interpreting the spectrum shape is more complicated. Attenuation is energy-dependent, and regeneration moves particles to lower energies while 