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 linearized formula for
relating them to the temperature blackbody fluctuations. However, this
procedure also generates a signal in the maps in the form of y-type distortions
which is degenerate with the thermal Sunyaev Zel'dovich (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 primordial y-distortions. They can nevertheless be well-modeled and
accounted for. We show that the distortions arise from a leakage of the CMB
dipole into the y-channel which couples to all multipoles, mostly affecting the
range $\ell$ < ~400. This should be visible in Planck's y-maps with an
estimated signal-to-noise ratio of about 12. 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 reported by the collaboration. Finally, we
quantify the level of contamination in tSZ and primordial y-type distortions
and show that it is above the sensitivity of proposed next generation CMB
experiments.
