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

TL;DR

This paper delivers the first nearly all-sky characterization of polarized Galactic dust emission in the Planck era, quantifying the angular power spectra of dust polarization (EE and BB) over $40<\ell<600$ using Planck HFI data. It establishes that dust polarization spectra follow a simple power-law in $\ell$ with a common slope near $-2.42$, and their amplitudes scale with the mean dust brightness as $\langle I_{353}\rangle^{1.9}$, while the BB/EE amplitude ratio is about 0.53. The frequency dependence of the dust spectra from 100 to 353 GHz is well described by a modified blackbody with $\beta_d=1.59$, $T_d=19.6$ K, implying substantial dust contamination in the B-mode channel even in high-latitude “clean” patches and in the BICEP2 field. The results stress the necessity of accurate dust modeling and joint Planck–BICEP2 analyses to separate primordial B-modes from Galactic foregrounds, particularly around the recombination peak at $\ell\sim80$.

Abstract

The polarized thermal emission from Galactic dust is the main foreground present in measurements of the polarization of the cosmic microwave background (CMB) at frequencies above 100GHz. We exploit the Planck HFI polarization data from 100 to 353GHz to measure the dust angular power spectra $C_\ell^{EE,BB}$ over the range $40<\ell<600$ well away from the Galactic plane. These will bring new insights into interstellar dust physics and a precise determination of the level of contamination for CMB polarization experiments. We show that statistical properties of the emission can be characterized over large fractions of the sky using $C_\ell$. For the dust, they are well described by power laws in $\ell$ with exponents $α^{EE,BB}=-2.42\pm0.02$. The amplitudes of the polarization $C_\ell$ vary with the average brightness in a way similar to the intensity ones. The dust polarization frequency dependence is consistent with modified blackbody emission with $β_d=1.59$ and $T_d=19.6$K. We find a systematic ratio between the amplitudes of the Galactic $B$- and $E$-modes of 0.5. We show that even in the faintest dust-emitting regions there are no "clean" windows where primordial CMB $B$-mode polarization could be measured without subtraction of dust emission. Finally, we investigate the level of dust polarization in the BICEP2 experiment field. Extrapolation of the Planck 353GHz data to 150GHz gives a dust power $\ell(\ell+1)C_\ell^{BB}/(2π)$ of $1.32\times10^{-2}μ$K$_{CMB}^2$ over the $40<\ell<120$ range; the statistical uncertainty is $\pm0.29$ and there is an additional uncertainty (+0.28,-0.24) from the extrapolation, both in the same units. This 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.

Figures (20)

• Figure 1: Masks and complementary selected large regions that retain fractional coverage of the sky _ sky $f_{\rm sky}$ from 0.8 to 0.3 (see details in Sect. \ref{['intlat_masks']}). The gray is the CO mask, whose complement is a selected region with $f{\rm sky}$f_ sky$= 0.8$. In increments of $f_{\rm sky}=0.1$, the retained regions can be identified by the colours yellow (0.3) to black (0.8), inclusively. Also shown is the (unapodized) point source mask used.
• Figure 2: Planck HFI 353GHz ${\cal D}_\ell^{EE}$ (red, top) and ${\cal D}_\ell^{BB}$ (blue, bottom) power spectra (in $\mu$K$_{\rm CMB}^2$) computed on three of the selected LR analysis regions that have $f{\rm sky}$f_ sky$=0.3$ (circles, lightest), $f{\rm sky}$f_ sky$=0.5$ (diamonds, medium) and $f{\rm sky}$f_ sky$=0.7$ (squares, darkest). The uncertainties shown are $\pm 1\sigma$. The best-fit power laws in $\ell$ are displayed for each spectrum as a dashed line of the corresponding colour. The Planck 2013 best-fit $\Lambda$CDM ${\cal D}_\ell^{EE}$ expectation planck2013-p11 and the corresponding $r=0.2$${\cal D}_\ell^{BB}$ CMB model are displayed as solid black lines; the rise for $\ell >200$ is from the lensing contribution. In the lower parts of each panel, the global estimates of the power spectra of the systematic effects responsible for intensity-to-polarization leakage (Sect. \ref{['systematics']}) are displayed in different shades of grey, with the same symbols to identify the three regions. Finally, absolute values of the null-test spectra anticipated in Sect. \ref{['systematics']}, computed here from the cross-spectra of the HalfRing/DetSet differences (see text), are represented as dashed-dotted, dashed, and dotted grey lines for the three LR regions.
• Figure 3: Best-fit power-law exponents $\alpha_{EE}$ (red squares) and $\alpha_{BB}$ (blue circles) fitted to the 353GHz dust ${\cal D}_\ell^{EE}$ and ${\cal D}_\ell^{BB}$ power spectra for the different LR regions defined in Sect. \ref{['intlat_masks']}, distinguished here with $f_{\rm sky}$. Although the values in the regions are not quite independent, simple means have been calculated and are represented as red and blue dashed lines.
• Figure 4: Amplitude of the dust $A^{EE}$ (red squares) and $A^{BB}$ (blue circles) power spectra, normalized with respect to the largest amplitude for each mode. These are plotted versus the mean dust intensity $\left\langle I_{353}\right\rangle$ for the six LR regions (top panel). A power-law fit of the form $A^{XX}($$\left\langle I_{353}\right\rangle$$)=K_{XX}$$\left\langle I_{353}\right\rangle$$^{1.9}$, $X\in\{E,B\}$, is overplotted as a dashed line of the corresponding colour (these almost overlap). The bottom panel presents the ratio of the data and the fitted $\left\langle I_{353}\right\rangle$$^{1.9}$ power law; the range associated with the $\pm1\sigma$ uncertainty in the power-law exponent of 1.9 is displayed in grey. For details see Sect. \ref{['nhi-dependence']}.
• Figure 5: Ratio of the amplitudes of the ${\cal D}_\ell^{BB}$ and ${\cal D}_\ell^{EE}$ dust power spectra at 353GHz for the different LR regions defined in Sect. \ref{['intlat_masks']}, distinguished here with $f_{\rm sky}$. The mean value $\langle A^{BB}/A^{EE}\rangle=0.52$ is plotted as a dashed line.