Extreme blazars as counterparts of IceCube astrophysical neutrinos
  We explore the correlation of $\gamma$-ray emitting blazars with IceCube
neutrinos by using three very recently completed, and independently built,
catalogues and the latest neutrino lists. We introduce a new observable, namely
the number of neutrino events with at least one $\gamma$-ray counterpart,
$N_{\nu}$. In all three catalogues we consistently observe a positive
fluctuation of $N_{\nu}$ with respect to the mean random expectation at a
significance level of $0.4 - 1.3$ per cent. This applies only to extreme
blazars, namely strong, very high energy $\gamma$-ray sources of the high
energy peaked type, and implies a model-independent fraction of the current
IceCube signal $\sim 10 - 20$ per cent. An investigation of the hybrid photon
-- neutrino spectral energy distributions of the most likely candidates reveals
a set of $\approx 5$ such sources, which could be linked to the corresponding
IceCube neutrinos. Other types of blazars, when testable, give null correlation
results. Although we could not perform a similar correlation study for Galactic
sources, we have also identified two (further) strong Galactic $\gamma$-ray
sources as most probable counterparts of IceCube neutrinos through their hybrid
spectral energy distributions. We have reasons to believe that our blazar
results are not constrained by the $\gamma$-ray samples but by the neutrino
statistics, which means that the detection of more astrophysical neutrinos
could turn this first hint into a discovery.
