Planck intermediate results XXX. The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes

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-l(EE) and C-l(BB) over the multipole range 40 < l < 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-l proportional to l(alpha), with exponents alpha(EE,BB) = -2.42 +/- 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 K down to the lowest Planck HFI frequencies. We find a systematic difference between the amplitudes of the Galactic B-and E-modes, C-l(BB) = C-l(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 D-l(BB) equivalent to l(l + 1)C-l(BB)/(2 pi) of 1.32 x 10(-2) mu K-CMB(2) over the multipole range of the primordial recombination bump (40 < l < 120); the statistical uncertainty is +/-0.29 x 10(-2) mu K-CMB(2) and there is an additional uncertainty (+0.28, -0.24) x 10(-2) mu K-CMB(2) from the extrapolation. This level is the same magnitude as reported by BICEP2 over this l range, which highlights the need for assessment of the polarized dust signal even in the cleanest windows of the sky.