Upper: histogram of obtained on simulated data assuming either (curves peaking at ) or a random value for (curves peaking at ) and noise simulated using the actual Planck noise covariance matrices. The green and black curves show the histograms over the sky fraction shown in Fig. 4 and the blue and red curves show histograms where the S/N on is larger than 3. The vertical dashed line shows , which is the value for pure random noise on Q and U. Lower: distribution of the bias-corrected ( minus the offset derived from a simulation with ), with respect to , in the region where the S/N on is larger than 3. Dashed lines show =-offset), with n = 1,2, 5, and 10. The colour scale shows the pixel density on a log₁₀ scale.