Effect of turbulent reacceleration on electrons produced by dark matter annihilation in the Coma cluster

In this paper, we study the effect of reacceleration provided by turbulences on electrons produced by dark matter (DM) annihilation in the Coma cluster. We use a simplified phenomenological model to describe the effect of the turbulences, and explore a limited subset of three possible DM models for neutralino particles with different mass and annihilation channel. We find that, for values of the annihilation cross-section of the order of the upper limits found with Fermi-LAT measurements in astrophysical objects, and for conservative values of the boosting factor due to DM substructures, the reacceleration due to turbulences can enhance the radio emission produced by DM-originated electrons up to the level of the observed flux of the radio halo in Coma, for moderate reacceleration intensity in relatively short times. Therefore, we conclude that, even if it is not possible to distinguish between the fits obtained in this paper because of the scattering present in the radio flux data, the electrons produced by DM annihilation can be possible seed electrons for the reacceleration, as well as secondary electrons of hadronic origin. A possible discriminant between these two classes of models is the flux produced in the gamma ray band, which in the case of DM-originated electrons should be more than two orders of magnitude smaller than the present Fermi-LAT upper limits, whereas in the hadronic case the expected gamma ray flux should be close to the value of present upper limits.