It has been pointed out recently that the quadrupole-octupole 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 \pm 0.003 ) \times 10 ^ { -3 } , which leads to a non-negligible DQ of { \cal O } ( \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 Planck 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 2.3 \sigma to 3.3 \sigma with the frequency dependent DQ , instead of 2.9 \sigma 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 .