  We present theoretical modelling of the electron distribution produced by
annihilating neutralino dark matter in dwarf spheroidal galaxies (dSphs). In
particular, we follow up the idea of Colafrancesco (2004) and find that such
electrons distort the cosmic microwave background (CMB) by the
Sunyaev-Zeldovich effect. For an assumed neutralino mass of 10 GeV and beam
size of 1'', the SZ temperature decrement is of the order of nano-Kelvin for
dSph models with a soft core. By contrast, it is of the order of micro-Kelvin
for the strongly cusped dSph models favoured by some cosmological simulations.
Although this is out of reach of current instruments, it may well be detectable
by future mm telescopes, such as ALMA. We also show that the upscattered CMB
photons have energies within reach of upcoming X-ray observatories, but that
the flux of such photons is too small to be detectable soon. Nonetheless, we
conclude that searching for the dark matter induced Sunyaev-Zeldovich effect is
a promising way of constraining the dark distribution in dSphs, especially if
the particles are light.
