resonance in received energy (this is analogous to the redshift smearing of a monoenergetic emission line). This broadening is helpful for detection, as a narrow feature would be difficult to observe with realistic detector energy resolution. For the lower panel, where $E_{\rm res} = 0.05 {\rm\ PeV}$, the cross section is decreasing at energy higher than the resonance, so regenerated neutrinos will continue to interact until they fall below the resonance energy, where the energy dependence changes, forming a true cascade.

  -------------------------------------------------- ------------ ------------ ------------ -------------- -- --
                                                          A            B            C             D           
  \[0.5mm\] $g$                                         $0.3$        $0.03$       $0.03$        $0.01$        
  \[0.5mm\] $M \left[ {\rm MeV} \right]$                $100$         $10$         $3$           $1$          
  \[0.5mm\] $\tau\left( 1\;{\rm PeV}\right )$         $\sim 0.7$   $\sim 0.6$   $\sim 0.2$   $\sim 0.002$     
  \[0.5mm\] $E_{\rm res} \left[ {\rm PeV}\right ]$       $50$        $0.5$       $0.045$       $0.005$        
  -------------------------------------------------- ------------ ------------ ------------ -------------- -- --

  : \[tab:table1\]Parameters for the benchmark scenarios.

![Same as Fig. \[fig:astro1\], but with different values of $E_{\rm cut}$ for the emitted spectrum. The solid lines are the free streaming case ($\gamma = 2$ and values of $E_{\rm cut}$ as labeled), and the dashed lines are for Model A $\nu$SI.[]{data-label="fig:astro2"}](fig_astro2.pdf){width="8.5cm"}

Astrophysical scenarios with $\nu$SI {#sec:Astro}
------------------------------------

We now consider more realistic astrophysical scenarios 