High Energy Neutrinos from Astrophysical Sources: a Self-consistent Approach

We calculate the yield of high energy neutrinos produced in astrophysical sources for arbitrary interaction depths τ0 and magnetic field strengths B. We take into account energy loss processes like synchrotron radiation and diffusion of charged particles in turbulent magnetic fields as well as the scattering of secondaries on background photons and the direct production of charm neutrinos. Meson-photon interactions are simulated with an extended version of the SOPHIA model. Diffusion leads to an increased path-length before protons leave the source of size Rs and therefore magnetized sources lose their transparency below the energy E∼1018 eV(.Rs/pc) (B/mG)τ01/α, with α = 1/3 and 1 for Kolmogorov and Bohm diffusion, respectively. Moreover, the neutrino flux is suppressed above the energy where synchrotron energy losses become important for charged particles. As a consequence, the energy spectrum and the flavor composition of neutrinos are strongly modified both at low and high energies even for sources with τ0 < or approx. 1