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Neutrinos from Cosmic-Ray Interactions
There will definitely exist an important galactic diffuse neutrino background due to interactions of the galactic cosmic rays with interstellar matter. The spectrum of galactic cosmic rays is reasonably well known, as is the matter distribution in our galaxy.
Moving to higher energies, cosmic rays above ~ 1020 eV will interact with photons of the cosmic microwave background radiation. Again, we know that both ingredients exist (the two highest energy cosmic rays detected have energies of 3 * 1020 eV and 2 * 1020 eV, and so the pion photoproduction at these energies will occur resulting in a diffuse neutrino background. However, the intensity in this case is model-dependent because it is not certain precisely what is origin of the highest energy cosmic rays, and indeed if they are extragalactic, although this seems very probable.
One of the most likely explanations of the highest energy cosmic rays is acceleration in Fanaroff-Riley Class II radio galaxies as suggested by Rachen and Biermann (1993). Protheroe and Johnson (1995) have repeated Rachen and Biermann's calculation in order to calculate the flux of diffuse neutrinos and gamma-rays which would accompany the UHE cosmic rays, and their result has been added to the figure to the side.
Any model in which the cosmic rays above 1020 eV are of extragalactic origin will predict a high energy diffuse neutrino intensity probably within an order of magnitude of this at 1018 eV.
Somewhat less certain is the flux of neutrinos from clusters of galaxies. This is produced by pp interactions of high energy cosmic rays with intracluster gas.