We show the constraints set by the radio halo spectrum of Coma on the annihilation cross section for the DM models considered in this paper. Upper, middle, and lower panel refer to the 9, 60 and 500 GeV neutralino mass, respectively. We consider the case of an NFW DM profile with (solid red curve) and τ ± (dashed red curve), and the case for a cored DM profile with (solid blue curve) and τ ± (dashed blue curve). The lower panel also contains the cases of W± composition with NFW (dotted red curve) and cored DM profile (dotted blue curve). The upper curve bundles refer to a smooth DM profile, while the lower curve bundles refer to the case where substructures are considered as in Fig. 1. The shaded bands in this figure represent the upper limit to the annihilation cross-section for the DM models derived combining the limits coming from a multi-messenger analysis (see text for details). The results are obtained using B(r) ∝ nth(r).
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