Conventionally, one can constrain the dark matter (DM) interaction with DM mass heavier than GeV by searching for DM induced synchrotron emission in the radio frequency band. However, an MeV DM can also generate detectable radio emission if electrons and positrons produced by DM annihilation or decay undergoes inverse Compton scattering (ICS) with the cosmic microwave background. The upcoming radio telescope Square Kilometre Array (SKA) is designed to operate with extremely high sensitivity. We investigate the capability of the SKA to detect DM particles in a board mass range from MeV to TeV, for both annihilation and decay scenarios. In this paper, we consider the sensitivities of the future SKA first and second phase (SKA1 and SKA2). As a comprehensive study, we systematically study the impacts on the DM-induced signal computation from the magnetic field strengths and particle diffusion coefficients. We compare the detection potential of four very different sources: two dwarf spheroidal galaxies (Draco and Segue 1), one radio-poor cluster (A2199), and one DM-rich ultra-diffuse galaxy (Dragonfly 44). We project the SKA1 and SKA2 sensitivities with the exposure of 100 hours on the annihilation cross section and decay time for DM mass from MeV to TeV by considering two different leptonic final states $e^+ e^-$ and $mu^+mu^-$.
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