The ISW effect is linear in the perturbations. Cancellation of the ISW effect on small scales leaves second order and non-linear analogues in its wake [Rees & Sciama, 1968]. From a single isolated structure, the potential along the line of sight can change not only from evolution in the density profile but more importantly from its bulk motion across the line of sight. In the context of clusters of galaxies, this is called the moving cluster effect [Birkinshaw & Gull, 1983]. More generally, the bulk motion of dark matter halos of all masses contribute to this effect [Tuluie & Laguna, 1995,Seljak, 1996b], and their clustering gives rise to a low level of anisotropies on a range of scales but is never the leading source of secondary anisotropies on any scale (see Plate 5a).
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