Did WMAP see Moving Local Structures?

The divergence of the momentum density field of the large scale structure generates a secondary anisotropy contribution to the Cosmic Microwave Background (CMB). While the effect is best described as a non-linear extension to the well-known integrated Sachs-Wolfe effect, due to mathematical coincidences, the anisotropy contribution is also described as the lensing of the dipole seen in the rest-frame of a moving mass. Given the closeness, there is a remote possibility that local concentrations of mass in the form of the Great Attractor and the Shapley concentration generate large angular scale fluctuations in CMB and could potentially be responsible, at least partly, for some of the low-multipole anomalies in WMAP data. While the local anisotropy contribution peaks at low multipoles, for reasonable models of the mass and velocity distributions associated with local super structures we find that the amplitude of temperature anisotropies is at most at a level of 10$^{-2}$ $\mu$K and is substantially smaller than primordial fluctuations. It is extremely unlikely that the momentum density of local mass concentrations is responsible for any of the large angular scale anomalies in WMAP data.