Interpretation of neutrino flux limits from neutrino telescopes on the Hillas plot

Abstract

We discuss the interplay between spectral shape and detector response beyond a simple E^-2 neutrino flux at neutrino telescopes, at the example of time-integrated point source searches using IceCube-40 data. We use a self-consistent model for the neutrino production, in which protons interact with synchrotron photons from co-accelerated electrons, and we fully take into account the relevant pion and kaon production modes, the flavor composition at the source, flavor mixing, and magnetic field effects on the secondaries (pions, muon, and kaons). Since some of the model parameters can be related to the Hillas parameters R (size of the acceleration region) and B (magnetic field), we relate the detector response to the Hillas plane. In order to compare the response to different spectral shapes, we use the energy flux density as a measure for the pion production efficiency times luminosity of the source. We demonstrate that IceCube has a very good reach in this quantity for AGN nuclei and jets for all source declinations, while the spectra of sources with strong magnetic fields are found outside the optimal reach. We also demonstrate where neutrinos from kaon decays and muon tracks from tau decays can be relevant for the detector response. Finally, we point out the complementarity between IceCube and other experiments sensitive to high-energy neutrinos, at the example of 2004-2008 Earth-skimming neutrino data from Auger. We illustrate that Auger, in principle, is better sensitive to the parameter region in the Hillas plane from which the highest-energetic cosmic rays may be expected in this model.