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We revisit the prospects for detecting the Sunyaev Zel'dovich (SZ) effectinduced by dark matter (DM) annihilation or decay. We show that with standard(or even extreme) assumptions for DM properties, the optical depth associatedwith relativistic electrons injected from DM annihilation or decay is muchsmaller than that associated with thermal electrons, when averaged over theangular 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 clusterlocated at 50 Mpc and observed within an angular resolution of $10"$, comparedto $\tau_{\rm th}\sim 10^{-3}-10^{-2}$. This, together with a full spectralanalysis, enables us to demonstrate that, for a template cluster with genericproperties, the SZ effect due to DM annihilation or decay is far below thesensitivity of the Planck satellite. This is at variance with previous claimsregarding heavier annihilating DM particles. Should DM be made of lighterparticles, the current constraints from 511 keV observations on theannihilation 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 theelectron distribution, even for very cuspy DM profiles, such that improving theangular resolution of the instrument, e.g. with ALMA, does not necessarilyimprove the detection potential. We provide useful analytical formulaeparameterized in terms of the DM mass, decay rate or annihilation cross sectionand DM halo features, that allow quick estimates of the SZ effect induced byany given candidate and any DM halo profile.

On the Sunyaev-Zel'dovich effect from dark matter annihilation or decay in galaxy clusters