Impact of bias correction and weighting on the uniformity of dipole directions for E-mode polarization HMHD simulation maps. Upper panel: local-variance dipole directions for the Commander simulations of E-mode polarization maps, obtained for 4° discs, when no bias correction and weighting have been applied to the maps. Middle panel: same as in the upper panel, but when the transformation X_i → (X_i − M_i)/σ_i has been applied to the polarization maps before applying the local-variance estimator. Lower panel: same as in the upper and middle panels, but when the transformation has been applied to the maps (i.e., with a square in the denominator). The results for the other component-separation methods are very similar to the ones presented here. For reference, we also show the CMB dipole direction, the north ecliptic pole (NEP), the south ecliptic pole (SEP), and the preferred dipolar modulation axis (labelled as “low-ℓ”) derived from the temperature data in Sect. 7.2.