The role of Dark Matter sub-halos in the non-thermal emission of galaxy
  clusters
  Annihilation of Dark Matter (DM) particles has been recognized as one of the
possible mechanisms for the production of non-thermal particles and radiation
in galaxy clusters. Previous studies have shown that, while DM models can
reproduce the spectral properties of the radio halo in the Coma cluster, they
fail in reproducing the shape of the radio halo surface brightness because they
produce a shape that is too concentrated towards the center of the cluster with
respect to the observed one. However, in previous studies the DM distribution
was modeled as a single spherically symmetric halo, while the DM distribution
in Coma is found to have a complex and elongated shape. In this work we
calculate a range of non-thermal emissions in the Coma cluster by using the
observed distribution of DM sub-halos. We find that, by including the observed
sub-halos in the DM model, we obtain a radio surface brightness with a shape
similar to the observed one, and that the sub-halos boost the radio emission by
a factor between 5 and 20%, thus allowing to reduce the gap between the
annihilation cross section required to reproduce the radio halo flux and the
upper limits derived from other observations, and that this gap can be
explained by realistic values of the boosting factor due to smaller
substructures. Models with neutralino mass of 9 GeV and composition $\tau^+
\tau^-$, and mass of 43 GeV and composition $b \bar b$ can fit the radio halo
spectrum using the observed properties of the magnetic field in Coma, and do
not predict a gamma-ray emission in excess compared to the recent Fermi-LAT
upper limits. These findings make these DM models viable candidate to explain
the origin of radio halos in galaxy clusters. [abridged]
