IceCube expectations for two high-energy neutrino production models at active galactic nuclei

We have determined the currently allowed regions of the parameter spaces of two representative models of diffuse neutrino flux from active galactic nuclei (AGN): one by Koers & Tinyakov (KT) and another by Becker & Biermann (BB). Our observable has been the number of upgoing muon-neutrinos expected in the 86-string IceCube detector, after 5 years of exposure, in the range 10⁵ ⩽ E_ν/GeV ⩽ 10⁸. We have used the latest estimated discovery potential of the IceCube-86 array at the 5σ level to determine the lower boundary of the regions, while for the upper boundary we have used either the AMANDA upper bound on the neutrino flux or the more recent preliminary upper bound given by the half-completed IceCube-40 array (IC40). We have varied the spectral index of the proposed power-law fluxes, α, and two parameters of the BB model: the ratio between the boost factors of neutrinos and cosmic rays, Γ_ν/Γ_CR, and the maximum redshift of the sources that contribute to the cosmic-ray flux,z_CR^max. For the KT model, we have considered two scenarios: one in which the number density of AGN does not evolve with redshift and another in which it evolves strongly, following the star formation rate. Using the IC40 upper bound, we have found that the models are visible in IceCube-86 only inside very thin strips of parameter space and that both of them are discarded at the preferred value of α = 2.7 obtained from fits to cosmic-ray data. Lower values of α, notably the values 2.0 and 2.3 proposed in the literature, fare better. In addition, we have analysed the capacity of IceCube-86 to discriminate between the models within the small regions of parameter space where both of them give testable predictions. Within these regions, discrimination at the 5σ level or more is guaranteed.