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Simplified models for photohadronic interactions in cosmic accelerators

We discuss simplified models for photo-meson production in cosmic accelerators, such as Active Galactic Nuclei and Gamma-Ray Bursts. Our self-consistent models are directly based on the underlying physics used in the SOPHIA software, and can be easily adapted if new data are included. They allow for the efficient computation of neutrino and photon spectra (from pi^0 decays), as a major requirement of modern time-dependent simulations of the astrophysical sources and parameter studies. In addition, the secondaries (pions and muons) are explicitely generated, a necessity if cooling processes are to be included. For the neutrino production, we include the helicity dependence of the muon decays which in fact leads to larger corrections than the details of the interaction model. The separate computation of the pi^0, pi^+, and pi^- fluxes allows, for instance, for flavor ratio predictions of the neutrinos at the source, which are a requirement of many tests of neutrino properties using astrophysical sources. We confirm that for charged pion generation, the often used production by the Delta(1232)-resonance is typically not the dominant process in Active Galactic Nuclei and Gamma-Ray Bursts, and we show, for arbitrary input spectra, that the number of neutrinos are underestimated by at least a factor of two if they are obtained from the neutral to charged pion ratio. We compare our results for several levels of simplification using isotropic synchrotron and thermal spectra, and we demonstrate that they are sufficiently close to the SOPHIA software.