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.
