tokens: polarized emission at intermediate and high Galactic latitudes. In extrapolating the foreground contribution at the various frequencies, we take the Planck 353 and 30 GHz and WMAP--band color corrections into account to properly include the real frequency response of the instruments ( Planck Collaboration IX 2014 ; Planck Collaboration V 2016 ). We recall that synchrotron and dust maps of Fig. 3 report the actual value of the spectra in the bandpower in those pixels corresponding to regions where we have a signal detection above 3, and the upper limit on it in all the other pixels. Nevertheless, we treat detections and upper limits in the same way by rigidly extrapolating the complete maps in frequency. To distinguish among different cases, we divide the sky regions into four classes, depending on whether we reach detections or upper limits for synchrotron and dust, and in the following figures, we use different colors to distinguish them. Classes are defined in Table 2 . Figure 4 shows the minimum foreground amplitude (sum of synchrotron and dust contributions) recovered in each sky patch after frequency extrapolation, together with the associated error. Amplitudes are expressed in terms of , computed by dividing the total minimum amplitude of foreground emission in K by the value of the CMB primordial modes power spectrum with tensor-to-scalar ratio in the bandpower, which is equal to K. Therefore, a value of , for example, means a foreground contribution at the level of a CMB GWs signal with . For regions belonging to class (1), maps in Fig. 4 use colored pixels to report the estimated values of and the associated errors. For each map we also report the histogram of the retrieved values. Uncertainties are calculated as the quadratic sum of the statistical errors coming from the white noise in the sky maps and the errors coming from the uncertainties on the frequency scaling parameters. For regions in classes (2), (3), and (4), we are able to put only upper limits on , which are shown in Fig. 4 . We also report the errors on these upper limits, which as before, are the quadratic sum of the statistical errors (included only if we have a detection of at least one of the two kinds of signal) and the frequency scaling ones. Figure 5 shows the map reporting, for each region, the frequency at which we find the minimum of foreground emission, together with the associated histogram. In this map, we again distinguish the four classes of regions using different color scales. For class (1), since we are dealing with detections, the value of each pixel represents the actual frequency where the minimum of foreground emission is reached. For classes (2) and (3), the reported value represents the frequency at which we set the upper limit on in the corresponding region. This frequency should be seen as an upper (for class (2)) or a lower limit (for class (3)) on the real frequency at which the foreground emission reaches its actual minimum. For class number
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