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.

Planck 2013 results. XXX. Cosmic infrared background measurements and implications for star formation

Fabio Finelli, Julien Lesgourgues

We present new measurements of cosmic infrared background (CIB) anisotropies using Planck. Combining HFI data with IRAS, the angular auto-and cross-frequency power spectrum is measured from 143 to 3000 GHz, and the auto-bispectrum from 217 to 545 GHz. The total areas used to compute the CIB power spectrum and bispectrum are about 2240 and 4400 deg(2), respectively. After careful removal of the contaminants (cosmic microwave background anisotropies, Galactic dust, and Sunyaev-Zeldovich emission), and a complete study of systematics, the CIB power spectrum is measured with unprecedented signal to noise ratio from angular multipoles l similar to 150 to 2500. The bispectrum due to the clustering of dusty, star-forming galaxies is measured from l similar to 130 to 1100, with a total signal to noise ratio of around 6, 19, and 29 at 217, 353, and 545 GHz, respectively. Two approaches are developed for modelling CIB power spectrum anisotropies. The first approach takes advantage of the unique measurements by Planck at large angular scales, and models only the linear part of the power spectrum, with a mean bias of dark matter haloes hosting dusty galaxies at a given redshift weighted by their contribution to the emissivities. The second approach is based on a model that associates star-forming galaxies with dark matter haloes and their subhaloes, using a parametrized relation between the dust-processed infrared luminosity and (sub-) halo mass. The two approaches simultaneously fit all auto-and cross-power spectra very well. We find that the star formation history is well constrained up to redshifts around 2, and agrees with recent estimates of the obscured star-formation density using Spitzer and Herschel. However, at higher redshift, the accuracy of the star formation history measurement is strongly degraded by the uncertainty in the spectral energy distribution of CIB galaxies. We also find that the mean halo mass which is most efficient at hosting star formation is log (M-eff/ M-circle dot) = 12.6 and that CIB galaxies have warmer temperatures as redshift increases. The CIB bispectrum is steeper than that expected from the power spectrum, although well fitted by a power law; this gives some information about the contribution of massive haloes to the CIB bispectrum. Finally, we show that the same halo occupation distribution can fit all power spectra simultaneously. The precise measurements enabled by Planck pose new challenges for the modelling of CIB anisotropies, indicating the power of using CIB anisotropies to understand the process of galaxy formation.

Edp Sciences S A2014

CMB power spectra and likelihood

Fabio Finelli, Julien Lesgourgues

This paper presents the Planck 2013 likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations that accounts for all known relevant uncertainties, both instrumental and astrophysical in nature. We use this likelihood to derive our best estimate of the CMB angular power spectrum from Planck over three decades in multipole moment, t, covering 2 2500. The main source of uncertainty at S 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher Es. For < 50, our likelihood exploits all Planck frequency channels from 30 to 353 GHz, separating the cosmological CMB signal from diffuse Galactic foregrounds through a physically motivated Bayesian component separation technique. At 50, we employ a correlated Gaussian likelihood approximation based on a fine-grained set of angular cross-spectra derived from multiple detector combinations between the 100, 143, and 217 GHz frequency channels, marginalising over power spectrum foreground templates. We validate our likelihood through an extensive suite of consistency tests, and assess the impact of residual foreground and instrumental uncertainties on the final cosmological parameters. We find good internal agreement among the high- cross-spectra with residuals below a few fiK2 at S 1000, in agreement with estimated calibration uncertainties. We compare our results with foreground-cleaned CMB maps derived from all Planck frequencies, as well as with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. We further show that the best-fit ACDM cosmology is in excellent agreement with preliminary Planck EE and T E polarisation spectra. We find that the standard ACDM cosmology is well constrained by Planck from the measurements at C 1500. One specific example is the spectral index of scalar perturbations, for which we report a 5.4o- deviation from scale invariance, ns = 1. Increasing the multipole range beyond = 1500 does not increase our accuracy for the ACDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the ACDM framework. Finally, we report a tension between the Planck best-fit ACDM model and the low- spectrum in the form of a power deficit of 5-10% at 40, with a statistical significance of 2.5-3o-. Without a theoretically motivated model for this power deficit, we do not elaborate further on its cosmological implications, but note that this is our most puzzling finding in an otherwise remarkably consistent data set.

Edp Sciences S A2014

Planck 2013 results. IV. Low Frequency Instrument beams and window functions

Fabio Finelli, Julien Lesgourgues

This paper presents the characterization of the in-flight beams, the beam window functions, and the associated uncertainties for the Planck Low Frequency Instrument (LFI). Knowledge of the beam profiles is necessary for determining the transfer function to go from the observed to the actual sky anisotropy power spectrum. The main beam distortions affect the beam window function, complicating the reconstruction of the anisotropy power spectrum at high multipoles, whereas the sidelobes affect the low and intermediate multipoles. The in-flight assessment of the LFI main beams relies on the measurements performed during Jupiter observations. By stacking the data from multiple Jupiter transits, the main beam profiles are measured down to -20 dB at 30 and 44 GHz, and down to -25 dB at 70 GHz. The main beam solid angles are determined to better than 0.2% at each LFI frequency band. The Planck pre-launch optical model is conveniently tuned to characterize the main beams independently of any noise effects. This approach provides an optical model whose beams fully reproduce the measurements in the main beam region, but also allows a description of the beams at power levels lower than can be achieved by the Jupiter measurements themselves. The agreement between the simulated beams and the measured beams is better than 1% at each LFI frequency band. The simulated beams are used for the computation of the window functions for the effective beams. The error budget for the window functions is estimated from both main beam and sidelobe contributions, and accounts for the radiometer bandshapes. The total uncertainties in the effective beam window functions are: 2% and 1.2% at 30 and 44 GHz, respectively (at l approximate to 600), and 0.7% at 70 GHz (at l approximate to 1000).

Edp Sciences S A2014

CMB power spectra and likelihood

Fabio Finelli, Julien Lesgourgues

Edp Sciences S A2014

Planck 2013 results. XXX. Cosmic infrared background measurements and implications for star formation

Fabio Finelli, Julien Lesgourgues

Edp Sciences S A2014