On the Sunyaev-Zel'dovich effect from dark matter annihilation or decay
  in galaxy clusters
  We revisit the prospects for detecting the Sunyaev Zel'dovich (SZ) effect
induced by dark matter (DM) annihilation or decay. We show that with standard
(or even extreme) assumptions for DM properties, the optical depth associated
with relativistic electrons injected from DM annihilation or decay is much
smaller than that associated with thermal electrons, when averaged over the
angular resolution of current and future experiments. For example, we find:
$\tau_{\rm DM} \sim 10^{-9}-10^{-5}$ (depending on the assumptions) for $\mchi
= 1$ GeV and a density profile $\rho\propto r^{-1}$ for a template cluster
located at 50 Mpc and observed within an angular resolution of $10"$, compared
to $\tau_{\rm th}\sim 10^{-3}-10^{-2}$. This, together with a full spectral
analysis, enables us to demonstrate that, for a template cluster with generic
properties, the SZ effect due to DM annihilation or decay is far below the
sensitivity of the Planck satellite. This is at variance with previous claims
regarding heavier annihilating DM particles. Should DM be made of lighter
particles, the current constraints from 511 keV observations on the
annihilation cross section or decay rate still prevent a detectable SZ effect.
Finally, we show that spatial diffusion sets a core of a few kpc in the
electron distribution, even for very cuspy DM profiles, such that improving the
angular resolution of the instrument, e.g. with ALMA, does not necessarily
improve the detection potential. We provide useful analytical formulae
parameterized in terms of the DM mass, decay rate or annihilation cross section
and DM halo features, that allow quick estimates of the SZ effect induced by
any given candidate and any DM halo profile.
