Energy dependent neutrino flavor ratios from cosmic accelerators on the Hillas plot

We discuss neutrino fluxes and energy dependent flavor ratios of cosmic accelerators as a function of the size of the acceleration region and the magnetic field, which are the parameters of the Hillas plot. We assume that photohadronic interactions between Fermi accelerated protons and synchrotron photons from co-accelerated electrons (or positrons) lead to charged pion production. We include synchrotron cooling of the charged pions and successively produced muons, which then further decay into neutrinos, as well as the helicity dependence of the muon decays. Our photohadronic interaction model includes direct production, higher resonances, and high energy processes in order to model the neutrino flavor and neutrino-antineutrino ratios with sufficient accuracy. Since we assume that the sources are optically thin to neutron interactions, we include the neutrino fluxes from neutron decays. We classify the Hillas plot into regions with different characteristic flavor ratios over 20 × 24 orders of magnitude in R and B. In some examples with sizable magnetic fields, we recover neutron beam, pion beam, and muon damped beam as a function of energy. However, we also find anomalous or new sources, such as muon beam sources with a flavor ratio νe:νμ:ντ of 1:1:0 in energy regions where the synchrotron-damped muons pile up. We also discuss the use of the Glashow resonance to identify pγ optically thin sources with a strong imbalance between π+ and π− production. We find that these can, in principle, be identified in most cases in spite of the π− contamination from high energy photohadronic processes and the mixing parameter uncertainties.