Neutrinos in IceCube/KM3NeT as probes of Dark Matter Substructures in
  Galaxy Clusters
  Galaxy clusters are one of the most promising candidate sites for dark matter
annihilation. We focus on dark matter with mass in the range 10 GeV - 100 TeV
annihilating to muon pairs, neutrino pairs, top pairs, or two neutrino pairs,
and forecast the expected sensitivity to the annihilation cross section into
these channels by observing galaxy clusters at IceCube/KM3NeT. Optimistically,
the presence of dark matter substructures in galaxy clusters is predicted to
enhance the signal by 2-3 orders of magnitude over the contribution from the
smooth component of the dark matter distribution. Optimizing for the angular
size of the region of interest for galaxy clusters, the sensitivity to the
annihilation cross section of heavy DM with mass in the range 300 GeV - 100 TeV
will be of the order of 10^{-24} cm^3 s^{-1}, for full IceCube/KM3NeT live time
of 10 years, which is about one order of magnitude better than the best limit
that can be obtained by observing the Milky Way halo. We find that neutrinos
from cosmic ray interactions in the galaxy cluster, in addition to the
atmospheric neutrinos, are a source of background. We show that significant
improvement in the experimental sensitivity can be achieved for lower DM masses
in the range 10 GeV - 300 GeV if neutrino-induced cascades can be reconstructed
to approximately 5 degrees accuracy, as may be possible in KM3NeT. We therefore
propose that a low-energy extension "KM3NeT-Core", similar to DeepCore in
IceCube, be considered for an extended reach at low DM masses.
