Cosmic ray bound for models of extragalactic neutrino production - art. no. 023003

We obtain the maximum diffuse neutrino intensity predicted by hadronic phot oproduction models of the type which have been applied to the jets of activ e galactic nuclei dr gamma ray bursts. For this, we compare the proton and gamma ray fluxes associated with hadronic photoproduction in extragalactic neutrino sources with the present experimental upper limit on cosmic ray pr otons and the extragalactic gamma ray background, employing a transport cal culation of energetic protons traversing cosmic photon backgrounds. We take into account the effects of the photon spectral shape in the sources on th e photoproduction process, cosmological source evolution, the optical depth for cosmic ray ejection, and discuss the possible effects of magnetic fiel ds in the vicinity of the sources. For photohadronic neutrino sources which are optically thin to the emission of neutrons we find that the cosmic ray flux imposes a stronger bound than the extragalactic gamma ray background in the energy range between 10(5) GeV and 10(11) GeV, as previously noted b y Waxman and Bahcall [Phys. Rev. D 59, 023002 (1999)]. We also determine th e maximum contribution from the jets of active galactic nuclei, using const raints set to their neutron opacity by gamma ray observations. This present upper limit is consistent with the jets of active galactic nuclei producin g the extragalactic gamma ray background hadronically, but we point out fut ure observations in the GeV-to-TeV regime could lower this limit. We also b riefly discuss the contribution of gamma ray bursts to ultrahigh-energy cos mic rays as it can be inferred from possible observations or limits on thei r correlated neutrino fluxes.