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

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