Ultrahigh energy cosmic rays from neutrino emitting acceleration sources?

We demonstrate by numerical flux calculations that neutrino beams producing the observed highest energy cosmic rays by weak interactions with the relic neutrino background require a nonuniform distribution of sources. Such sources have to accelerate protons at least up to ${10}^{23}$ eV, have to be opaque to their primary protons, and should emit the secondary photons unavoidably produced together with the neutrinos only in the sub-MeV region to avoid conflict with the diffuse $\gamma$-ray background measured by the EGRET experiment. Even if such a source class exists, the resulting large uncertainties in the parameters involved in this scenario currently do not allow us to extract any meaningful information on absolute neutrino masses.