Studying the dark matter annihilation in galaxy clusters through radio and gravitational lensing measures

Galaxy clusters are expected to be dominated by a component of Dark Matter (DM) of unknown nature. The annihilation of DM particles in a galaxy cluster can produce relativistic electrons and gamma rays, that can be used to test the properties of the DM particles and of the cluster itself. Gravitational lensing measures provide the spatial DM distribution in a cluster, and can be used to build detailed models to estimate the contribution of DM-produced electrons to the non-thermal diffuse emission observed in some galaxy clusters. Therefore putting together the information derived from radio and gravitational lensing measures in galaxy clusters can provide important information about the properties of DM and the physics of clusters. We apply this technique to two galaxy clusters where radio and gravitational lensing measurements are available. In the Bullet cluster a contribution of the DM to the diffuse radio emission is possible because of the spectral changes visible in the overall spectrum, that suggest that more than one component can be present; to better constrain this possibility information on the spectrum of the diffuse radio emission in smaller regions of the cluster is necessary. In the Coma cluster the distribution of the DM sub-halos closely resembles the radio halo surface brightness shape, and the overall radio halo spectrum is well reproduced by a DM model for the observed properties of the magnetic field, without violating the gamma ray upper limits in the cluster; however, there are open issues, like the values of the annihilation cross section and of the substructures boosting factor. On the basis of these results, we conclude that the combination of radio and gravitational lensing studies of galaxy clusters appears to be a very promising way to obtain information about the physics of galaxy clusters and the DM properties. Present results suggest that a contribution from DM to the total diffuse radio emission can be important, but require to study in detail the spectrum of the diffuse radio emission obtained in smaller regions of the clusters, and to have good contraints on the components of baryonic origin. The application of this technique to a higher number of clusters will be important to obtain better information and solve some open issues.