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tokens: extrapolation to 150 GHz. The Planck 2013 best-fit CDM CMB model based on temperature anisotropies, with a tensor amplitude fixed at , is overplotted as a black line. 6.2. Statistical estimate of the dust B-mode level in the BICEP2 field We have seen in Sect. 5.2 that the dust spectra amplitudes statistically follow an empirical scaling law of the mean dust intensity for the patch on which they are computed. We can use this scaling law to assess the most probable dust value for . For this field, which has a mean dust intensity of = 0.060 , the expected value at 353 GHz is K at , taking into account the uncertainty on the fitted amplitude from Sect. 4.3 . In order to extrapolate this value to the BICEP2 observing frequency, 150 GHz, we proceed as in Sect. 5.3 , using the same typical dust SED from Planck Collaboration Int. XXII (2015) . For patches the size of the expected dispersion of (Sect. 2.2.1 ) is 0.11, which introduces an uncertainty in the extrapolation. The extrapolation, unlike in that section, is made to 150 GHz taking into account the BICEP2 bandpass 16 . The conversion factor from the Planck 353 GHz band to the 150 GHz BICEP2 band, taking into account both Planck and BICEP2 colour corrections, as well as the statistical error on , is thus in the SED, and therefore this value squared in . The resulting expected dust amplitude at 150 GHz is K at . The uncertainty quoted here applies to the most probable value for patches with a similar , but it ignores the intrinsic dispersion around this value (see Sect. 5.2 ). Therefore, a direct measurement of the dust spectrum in is required to complete the assessment of its polarized dust level. In Sect. 5.3 , we have localized the amplitudes from the analysis of patches on a map. The pixels falling inside the approximate BICEP2 deep-field region shown in Fig. 8 give a mean value of , i.e., an expected dust power of K at 150 GHz and ; we note that in this region the Planck estimate of the dust contamination is significantly higher, by a factor of about 2, than it is in some more optimal patches. Nevertheless, a more accurate estimate of the dust polarization amplitude in the BICEP2 observed field requires the direct computation of the angular power spectrum on a similar region. 6.3. BB angular power spectrum of dust in the BICEP2 field We now compute the spectrum of the dust at 150 GHz on presented in Sect. 6.1 , using the Planck 353 GHz data. For this purpose, we compute the 353 GHz spectrum by cross-correlating the two DetSets that have independent noise at this frequency in the three -bins defined by the intervals between multipoles 40, 120, 250, and 400. The -bin sizes were increased with respect to the previous sections in order to increase the S/N, especially around the range of the CMB recombination bump. Appendix D.1 confirms that the result does not depend on the method of computing the power spectrum. This power spectrum is extrapolated to 150 GHz as in Sect. 6.2 , with an