Induced CMB quadrupole from pointing offsets

Abstract: Recent claims in the literature have suggested that the {\it WMAP} quadrupole is not primordial in origin, and arises from an aliasing of the much larger dipole field because of incorrect satellite pointing. We attempt to reproduce this result and delineate the key physics leading to the effect. We find that, even if real, the induced quadrupole would be smaller than claimed. We discuss reasons why the {\it WMAP} data are unlikely to suffer from this particular systematic effect, including the implications for observations of point sources. Given this evidence against the reality of the effect, the similarity between the pointing-offset-induced signal and the actual quadrupole then appears to be quite puzzling. However, we find that the effect arises from a convolution between the gradient of the dipole field and anisotropic coverage of the scan direction at each pixel. There is something of a directional conspiracy here -- the dipole signal lies close to the Ecliptic Plane, and its direction, together with the {\it WMAP} scan strategy, results in a strong coupling to the $Y_{2,\,-1}$ component in Ecliptic co-ordinates. The dominant strength of this component in the measured quadrupole suggests that one should exercise increased caution in interpreting its estimated amplitude. The {\it Planck} satellite has a different scan strategy which does not so directly couple the dipole and quadrupole in this way and will soon provide an independent measurement.