Dark Matter (DM) is a fundamental ingredient of our Universe and of structure formation, and yet its nature is elusive to astrophysical probes. Information on the nature and physical properties of the WIMP (neutralino) DM (the leading candidate for a cosmologically relevant DM) can be obtained by studying the astrophysical signals of their annihilation/decay. Among the various e.m. signals, secondary electrons produced by neutralino annihilation generate synchrotron emission in the magnetized atmosphere of galaxy clusters and galaxies which could be observed as a diffuse radio emission (halo or haze) centered on the DM halo. A deep search for DM radio emission with SKA in local dwarf galaxies, galaxy regions with low star formation and galaxy clusters (with offset DM-baryonic distribution, like e.g. the Bullet cluster) can be very effective in constraining the neutralino mass, composition and annihilation cross-section. For the case of a dwarf galaxy, like e.g. Draco, the constraints on the DM annihilation cross-section obtainable with SKA1-MID will be at least a factor $sim 10^3$ more stringent than the limits obtained by Fermi-LAT in the $gamma$-rays. These limits scale with the value of the B field, and the SKA will have the capability to determine simultaneously both the magnetic field in the DM-dominated structures and the DM particle properties. The optimal frequency band for detecting the DM-induced radio emission is around $sim 1$ GHz, with the SKA1-MID Band 1 and 4 important to probe the synchrotron spectral curvature at low-$ u$ (sensitive to DM composition) and at high-$ u$ (sensitive to DM mass).
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