χ² distributions obtained from the T (left column), Q_r (middle column), and U_r (right column) mean radial profiles centred on temperature hot spots selected above the null threshold (upper row) and three times the dispersion of the map (bottom row). The black lines correspond to the theoretical χ² distribution with 12 degrees of freedom, whilst the histograms show the distributions determined from 100 simulations computed through the Commander (red), NILC (orange), SEVEM (green), and SMICA (blue) pipelines. The vertical lines represent the χ² values obtained from the data.