Gamma-ray bounds from EAS detectors and heavy decaying dark matter
  constraints
  The very high energy Galactic $\gamma$-ray sky is partially opaque in the
($0.1-10$) PeV energy range. In the light of the recently detected high energy
neutrino flux by IceCube, a comparable very high energy $\gamma$-ray flux is
expected in any scenario with a sizable Galactic contribution to the neutrino
flux. Here we elaborate on the peculiar energy and anisotropy features imposed
upon these very high energy $\gamma$-rays by the absorption on the cosmic
microwave background photons and Galactic interstellar light. As a notable
application of our considerations, we study the prospects of probing the
PeV-scale decaying DM scenario, proposed as a possible source of IceCube
neutrinos, by extensive air shower (EAS) cosmic ray experiments. In particular,
we show that anisotropy measurements at EAS experiments are already sensitive
to $\tau_{\rm DM}\sim {\cal O}(10^{27})$~s and future measurements, using
better gamma/hadron separation, can improve the limit significantly.
