Neutrino spectra displaying the effect of pion and muon cooling. The blue dotted line shows the spectrum without synchrotron cooling while the red dashed and purple solid lines demonstrate the neutrino spectra when only muon cooling or both muon and pion cooling are included, respectively. The thick purple line shows the spectrum after applying a Savitzky-Golay filter to smooth out the numerical artifact appearing at ∼10¹⁴ eV. The solid and dashed vertical lines show the position of the cooling break for each species according to Eq. A.1.