  If neutrinos have self-interactions, these will induce scatterings between
astrophysical and cosmic neutrinos. Prior work proposed to look for possible
resulting resonance features in astrophysical neutrino spectra in order to seek
a neutrino self-interaction which can be either diagonal in the neutrino flavor
space or couple different neutrino flavors. The calculation of the
astrophysical spectra involves either a Monte Carlo simulation or a
computationally intensive numerical integration of an
integro-partial-differential equation. As a result only limited regions of the
neutrino self-interaction parameter space have been explored, and only
flavor-diagonal self-interactions have been considered. Here, we present a
fully analytic form for the astrophysical neutrino spectra for arbitrary
neutrino number and arbitrary self-coupling matrix that accurately obtains the
resonance features in the observable neutrino spectra. The results can be
applied to calculations of the diffuse supernova neutrino background and of the
spectrum from high-energy astrophysical neutrino sources. We illustrate with a
few examples.
