The polarized thermal emission from diffuse Galactic dust is the main foreground present in measurements of the polarization of the cosmic microwave background ( CMB ) at frequencies above 100 GHz .
In this paper we exploit the uniqueness of the Planck HFI polarization data from 100 to 353 GHz to measure the polarized dust angular power spectra C _ { \ell } ^ { EE } and C _ { \ell } ^ { BB } over the multipole range 40 < \ell < 600 well away from the Galactic plane .
These measurements will bring new insights into interstellar dust physics and allow a precise determination of the level of contamination for CMB polarization experiments .
Despite the non-Gaussian and anisotropic nature of Galactic dust , we show that general statistical properties of the emission can be characterized accurately over large fractions of the sky using angular power spectra .
The polarization power spectra of the dust are well described by power laws in multipole , C _ { \ell } \propto \ell ^ { \alpha } , with exponents \alpha ^ { EE,BB } = -2.42 \pm 0.02 .
The amplitudes of the polarization power spectra vary with the average brightness in a way similar to the intensity power spectra .
The frequency dependence of the dust polarization spectra is consistent with modified blackbody emission with \beta _ { d } = 1.59 and T _ { d } = 19.6 \thinspace K down to the lowest Planck HFI frequencies .
We find a systematic difference between the amplitudes of the Galactic B - and E -modes , C _ { \ell } ^ { BB } / C _ { \ell } ^ { EE } = 0.5 .
We verify that these general properties are preserved towards high Galactic latitudes with low dust column densities .
We show that even in the faintest dust-emitting regions there are no “ clean ” windows in the sky where primordial CMB B -mode polarization measurements could be made without subtraction of foreground emission .
Finally , we investigate the level of dust polarization in the specific field recently targeted by the BICEP2 experiment .
Extrapolation of the Planck 353 GHz data to 150 GHz gives a dust power { \cal D _ { \ell } ^ { BB } } \equiv \ell ( \ell + 1 ) C _ { \ell } ^ { BB } / ( 2 \pi ) of 1.32 \times 10 ^ { -2 } \thinspace \mu K _ { CMB } ^ { 2 } over the multipole range of the primordial recombination bump ( 40 < \ell < 120 ) ; the statistical uncertainty is \pm 0.29 \times 10 ^ { -2 } \thinspace \mu K _ { CMB } ^ { 2 } and there is an additional uncertainty ( +0.28 , -0.24 ) \times 10 ^ { -2 } \thinspace \mu K _ { CMB } ^ { 2 } from the extrapolation .
This level is the same magnitude as reported by BICEP2 over this \ell range , which highlights the need for assessment of the polarized dust signal even in the cleanest windows of the sky .