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We assume that the supersymmetric lightest neutralino is a good candidate forthe CDM and explore the possibility to produce diffuse radio emission fromhigh-energy electrons arising from the neutralino annihilation in galaxyclusters whose intracluster medium is filled with a large-scale magnetic field.We show that these electrons fit the population of seed relativistic electronspostulated in many models for the origin of cluster radio halos. For magneticfields with central values $3 \div 30$ $\mu$G (depending on the DM profile),the population of seed relativistic electrons from neutralino annihilation canfit the radio halo spectra of Coma and 1E0657-56. The shape and the frequencyextension of the radio halo spectra are connected with the mass and physicalcomposition of the neutralino. A pure-gaugino neutralino with mass $M_{\chi}\geq 80$ GeV can reasonably fit the spectra of both Coma and 1E0657-56. Thismodel provides a number of extra predictions that make it definitely testable.On the one hand, it agrees with the observations that {\it (i)} the radio halois centered on the cluster dynamical center, usually coincident with the X-raycenter, {\it (ii)} the radio halo surface brightness is similar to the X-rayone, and {\it (iii)} the monochromatic radio luminosity at 1.4 GHz correlatesstrongly with the IC gas temperature. On the other hand, the model predictsthat radio halos should be present in every cluster, which is not actuallyobserved, although the predicted radio halo luminosities can change by a largeamount ($\sim 10^2 \div 10^6$), depending on the amplitude and the structure ofthe IC magnetic field. Also, neutral pions arising from neutralino annihilationshould give rise to substantial gamma-ray emission that could be tested by thenext generation gamma-ray experiments.Comment: 49 pages, 11 Figures, Latex (using epsfig), submitted to The  Astrophysical Journal. submitted to The Astrophysical Journa

Neutralinos and the Origin of Radio Halos in Clusters of Galaxies