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CMB all-scale blackbody distortions induced by linearizing temperature

Cosmic Microwave Background (CMB) experiments, such as WMAP and Planck, measure intensity anisotropies and build maps using a \emph{linearized} formula for relating them to the temperature blackbody fluctuations. However such a procedure also generates a signal in the maps in the form of y-type distortions, and thus degenerate with the thermal SZ (tSZ) effect. These are small effects that arise at second-order in the temperature fluctuations not from primordial physics but from such a limitation of the map-making procedure. They constitute a contaminant for measurements of: our peculiar velocity, the tSZ and of primordial y-distortions, but they can nevertheless be well-modelled and accounted for. We show that the largest distortions arises at high ell from a leakage of the CMB dipole into the y-channel which couples to all multipoles, but mostly affects the range ell <~ 400. This should be visible in Planck's y-maps with an estimated signal-to-noise ratio of about 9. We note however that such frequency-dependent terms carry no new information on the nature of the CMB dipole. This implies that the real significance of Planck's Doppler coupling measurements is actually lower than quoted. Finally, we quantify the relevance of the removal of such effects in order improve future measurements of tSZ and of primordial y-type distortions.