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Dark matter annihilation and non-thermal Sunyaev-Zel'dovich effect: II. dwarf spheroidal galaxy

We calculate the CMB temperature distortion due to the energetic electrons and positrons produced by dark matter annihilation (Sunyaev-Zel'dovich effect), in dwarf spheroidal galaxies (dSphs). In the calculation we have included two important effects which were previously ignored. First we show that the electron-positron pairs with energy less than GeV, which were neglected in previous calculation, could contribute a significant fraction of the total signal. Secondly we also consider the full effects of diffusion loss, which could significantly reduce the density of electron-positron pairs at the center of cuspy halos. For neutralinos, we confirm that detecting such kind of SZ effect is beyond the capability of the current or even the next generation experiments. In the case of light dark matter (LDM) the signal is much larger, but even in this case it is only marginally detectable with the next generation of experiment such as ALMA. We conclude that similar to the case of galaxy clusters, in the dwarf galaxies the $SZ_2DM}$ effect is not a strong probe of DM annihilations.