On the proper kinetic quadrupole CMB removal and the quadrupole
  anomalies
  It has been pointed out recently that the quadrupole-octopole alignment in
the CMB data is significantly affected by the so-called kinetic Doppler
quadrupole (DQ), which is the temperature quadrupole induced by our proper
motion. Assuming our velocity is the dominant contribution to the CMB dipole we
have v/c = beta = (1.231 +/- 0.003) * 10^{-3}, which leads to a non-negligible
DQ of order beta^2. Here we stress that one should properly take into account
that CMB data are usually not presented in true thermodynamic temperature,
which induces a frequency dependent boost correction. The DQ must therefore be
multiplied by a frequency-averaged factor, which we explicitly compute for
several CMB maps finding that it varies between 1.67 and 2.47. This is often
neglected in the literature and turns out to cause a small but non-negligible
difference in the significance levels of some quadrupole-related statistics.
For instance the alignment significance in the SMICA 2013 map goes from
2.3sigma to 3.3sigma, with the frequency dependent DQ, instead of 2.9sigma
ignoring the frequency dependence in the DQ. Moreover as a result of a proper
DQ removal, the agreement across different map-making techniques is improved.
