Foreground contamination of the WMAP CMB maps from the perspective of the matched circle test

Wilkinson Microwave Anisotropy Probe has provided cosmic microwave background (CMB) maps of the full sky. The raw data are subject to foreground contamination, in particular near to the Galactic plane. Foreground‐cleaned maps have been derived, e.g. the internal linear combination map of Bennett et al., and the reduced foreground TOH map of Tegmark et al. Using S statistics, we examine whether residual foreground contamination is left over in the foreground‐cleaned maps. In particular, we specify which parts of the foreground‐cleaned maps are sufficiently accurate for the circle‐in‐the‐sky signature. We generalize the S statistic, called D statistic, such that the circle test can deal with CMB maps in which the contaminated regions of the sky are excluded with masks.