We investigate the IceCube detection potential of very high energy neutrinos
from blazars, for different classes of "hadronic" models, taking into account
the limits imposed on the neutrino flux by the recent Fermi telescope
observations. Assuming the observed gamma-ray emission is produced by the decay
of neutral pions from proton-proton interactions, the measurement of the
time-averaged spectral characteristics of blazars in the GeV energy band
imposes upper limits on the time-averaged neutrino flux. Comparing these upper
limits to the 5 sigma discovery threshold of IceCube for different neutrino
spectra and different source locations in the sky, we find that several BL Lacs
with hard spectra in the GeV band are within the detection potential of
IceCube. If the gamma-ray emission is dominated by the neutral pion decay flux,
none of the flat-spectrum radio quasars are detectable with IceCube. If the
primary high energy proton spectrum is very hard and/or neutrinos are produced
in proton-photon, rather than proton-proton reactions, the upper limit on the
neutrino flux imposed by the measured gamma-ray spectra is relaxed and
gamma-ray observations impose only lower bounds on the neutrino flux. We
investigate whether these lower bounds guarantee the detection of blazars with
very hard neutrino spectra, expected in the latter type model. We show that all
the "hadronic" models of activity of blazars are falsifiable with IceCube.
Furthermore, we show that models with gamma-ray emission produced by the decay
of neutral pions from proton-proton interactions can be readily distinguished
from the models based on proton-gamma interactions and/or models predicting
very hard high energy proton spectra via a study of the distribution of
spectral indices of gamma-ray spectra of sources detected with IceCube.Comment: 10 pages, 5 figure
