Separation of polarized dust emission in Planck observations with Scattering Transforms
Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，ENS，PSL大学，CNRS，索邦大学，巴黎西岱大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Department of Astronomy and Astrophysics, University of Chicago（芝加哥大学天文学与天体物理学系）；CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL 2007, CPB-IN2P3（CNRS-UCB国际研究实验室，皮埃尔·比内屈中心，IRL 2007，CPB-IN2P3）
Alexandros Tsouros, Elisa Russier, Erwan Allys, Constant Auclair, François Boulanger, Jacques Delabrouille
Polarized dust emission is a major astrophysical foreground contaminant of the cosmic microwave background polarization (CMB), which must be accurately measured to look for the faint primordial polarization B-modes of inflationary origin. The available maps to date, obtained from Planck space mission data, are noise-dominated in the high Galactic latitude regions that are most relevant for CMB observations. The goal of this work is to obtain better dust polarization maps from Planck observations, by exploiting both the dependence between polarization and total intensity, as well as the non-Gaussian filamentary structure of the dust emission. To this end, we use scattering transforms, which provide a stable and interpretable representation of complex non-Gaussian textures, allowing for a data-driven analysis approach requiring no explicit priors on dust. The analysis is performed locally on Cartesian patches of sky, where Stokes linear polarization parameters, redefined in a local reference frame, are modeled as the sum of a signal of interest and a nuisance term. Using multiple realizations of the random nuisance term, we recover the polarized dust maps by minimizing a composite objective function that enforces multiple statistical constraints in scattering space. The proposed algorithm reconstructs maps of polarized dust emission whose statistics are consistent with those expected from the Planck data once random nuisance realizations are added. This is confirmed in a validation test using a high signal-to-noise sky region as a test case. Comparisons with existing dust polarization maps and models show that our approach better recovers small-scale polarized dust emission, and that our reconstructed power and cross-spectra closely match those of the dust polarization maps. A second set of maps that deterministically reproduce the features of the dust polarized emission is also produced.
Dust emission is the main foreground for cosmic microwave background (CMB) polarization. Its statistical characterization must be derived from the analysis of observational data because the precision required for a reliable component separation is far greater than what is currently achievable with physical models of the turbulent magnetized interstellar medium. This letter takes a significant step toward this goal by proposing a method that retrieves non-Gaussian statistical characteristics of dust emission from noisy Planck polarization observations at 353 GHz. We devised a statistical denois…
This work is point of the preparation to the analysis of the PLANCK satellite data. The PLANCK satellite is an ESA mission which has been launched the 14th of may 2009 and is dedicaced to the measurement of the Cosmic Microwave Background (CMB) in temperature and polarization. The presence of diffuse Galactic polarized emissions disturb the measurement of the CMB anisotropies, in particular in polarization. Therefore a precise knowledge of these emissions is needed to obtain the level of accuracy required for PLANCK. In this context, we have developed and implemented a coherent 3D model of the…
Understanding the properties of dust emission in the microwave domain is an important premise for the next generation of cosmic microwave background (CMB) experiments, devoted to the measurement of the primordial $B$-modes of polarization. In this paper, we compare three solutions to thermal dust emission by the Planck Collaboration \cite{PlanckDust03,planck_16,planck_com} to point out significant differences between their respective parameters (the spectral index $β$, the optical depth $τ$ and the dust temperature $T_d$). These differences originate from e.g. the priors on the parameters or t…
The polarized Galactic thermal dust emission constitutes a major probe for the study and the characterization of the Galactic Magnetic Field (GMF). In this paper, we apply the maximum-likelihood analysis that we established in our companion paper (Pelgrims, Macías-Pérez & Ruppin) to model the large-scale regular-component of the GMF from the polarized diffuse emission from Galactic thermal dust as measured by $Planck$ at 353 GHz. As a first attempt, we consider three models to describe the dust density distribution across the whole Galaxy and four models for the GMF. All models are parametric …
The PLANCK satellite mission has been launched the 14th of May 2009 and is dedicated to the measurement of the Cosmic Microwave Background (CMB) in temperature and polarization. The presence of diffuse galactic polarized emission contaminates the measurement of the CMB anisotropies, in particular in polarization. Therefore a good knowledge of these emissions is needed to the accuracy required for PLANCK. In this context, we have developed and implemented a coherent 3D model of the two main polarized galactic emissions : synchrotron radiation and thermal dust. We have compared these models to t…
The polarized Galactic synchrotron and thermal dust emission constitutes a major tool in the study of the Galactic magnetic field (GMF) and in constraining its strength and geometry for the regular and turbulent components. In this paper, we review the modeling of these two components of the polarized Galactic emission and present our strategy for optimally exploiting the currently existing data sets. We investigate a Markov Chain Monte Carlo (MCMC) method to constrain the model parameter space through maximum-likelihood analysis, focusing mainly on dust polarized emission. Relying on simulati…
We have examined dust emission in galaxy clusters at millimeter wavelengths using the Planck $857 \, {\rm GHz}$ map to constrain the model based on Herschel observations that was used in studies for the Cosmic ORigins Explorer (CORE) mission concept. By stacking the emission from Planck-detected clusters, we estimated the normalization of the infrared luminosity versus mass relation and constrained the spatial profile of the dust emission. We used this newly constrained model to simulate clusters that we inject into Planck frequency maps. The comparison between clusters extracted using these g…
The Planck satellite experiment, which was launched the 14th of may 2009, will give an accurate measurement of the anisotropies of the Cosmic Microwave Background (CMB) in temperature and polarization. This measurement is polluted by the presence of diffuse galactic polarized foreground emissions. In order to obtain the level of accuracy required for the Planck mission it is necessary to deal with these foregrounds. In order to do this, have develloped and implemented coherent 3D models of the two main galactic polarized emissions : the synchrotron and thermal dust emissions. We have optimized…
Constraints on inflationary $B$-modes using Cosmic Microwave Background polarization data commonly rely on either template cleaning or cross-spectra between maps at different frequencies to disentangle galactic foregrounds from the cosmological signal. Assumptions about how the foregrounds scale with frequency are therefore crucial to interpreting the data. Recent results from the Planck satellite collaboration claim significant evidence for a decorrelation in the polarization signal of the spatial pattern of galactic dust between 353 GHz and 217 GHz. Such a decorrelation would suppress power …
Using the Planck 2015 data release (PR2) temperature maps, we separate Galactic thermal dust emission from cosmic infrared background (CIB) anisotropies. For this purpose, we implement a specifically tailored component-separation method, the so-called generalized needlet internal linear combination (GNILC) method, which uses spatial information (the angular power spectra) to disentangle the Galactic dust emission and CIB anisotropies. We produce significantly improved all-sky maps of Planck thermal dust emission, with reduced CIB contamination, at 353, 545, and 857 GHz. By reducing the CIB con…
Scattering transforms have been successfully used to describe dust polarization for flat-sky images. This paper expands this framework to noisy observations on the sphere with the aim of obtaining denoised Stokes Q and U all-sky maps at 353GHz, as well as a non-Gaussian model of dust polarization, from the Planck data. To achieve this goal, we extend the computation of scattering coefficients to the Healpix pixelation and introduce cross-statistics that allow us to make use of half-mission maps as well as the correlation between dust temperature and polarization. Introducing a general framewor…
The study of polarized dust emission has become entwined with the analysis of the cosmic microwave background (CMB) polarization. We use new Planck maps to characterize Galactic dust emission as a foreground to the CMB polarization. We present Planck EE, BB, and TE power spectra of dust polarization at 353 GHz for six nested sky regions covering from 24 to 71 % of the sky. We present power-law fits to the angular power spectra, yielding evidence for statistically significant variations of the exponents over sky regions and a difference between the values for the EE and BB spectra. The TE corre…
The Planck survey has quantified polarized Galactic foregrounds and established that they are a main limiting factor in the quest for the cosmic microwave background (CMB) B-mode signal induced by primordial gravitational waves during cosmic inflation. Accurate separation of the Galactic foregrounds therefore binds this quest to our understanding of the magnetized interstellar medium (ISM). The two most relevant empirical results from analysis of Planck data are line of sight depolarization arising from fluctuations of the Galactic magnetic field orientation and alignment of filamentary dust s…
We combine Planck HFI data at 857, 545, 353 & 217GHz with data from WISE, Spitzer, IRAS & Herschel to investigate the properties of a flux limited sample of local star-forming galaxies. A 545GHz flux density limit was chosen so that the sample is 80% complete at this frequency, giving a sample of 234 local galaxies. We investigate the dust emission and star formation properties of the sample via various models & calculate the local dust mass function. Although 1-component modified black bodies fit the dust emission longward of 80um very well (median beta=1.83) the degeneracy between dust temp …
Angular power spectra computed from Planck HFI 353 GHz intensity and polarization maps produce a TB correlation that can be approximated by a power law. Whether the observed TB correlation is an induced systematic feature or a physical property of Galactic dust emission is of interest both for cosmological and Galactic studies. We investigate the large angular scale E- and B-mode morphology of microwave polarized thermal dust emission, and relate it to physical quantities of polarization angle and polarization fraction. We use empirical models of polarized dust to show that dust polarization a…
Recent measurements of Galactic polarized dust emission have found a nonzero $TB$ signal, a correlation between the total intensity and the $B$-mode polarization component. We present evidence that this parity-odd signal is driven by the relative geometry of the magnetic field and the filamentary interstellar medium in projection. Using neutral hydrogen morphology and Planck polarization data, we find that the angle between intensity structures and the plane-of-sky magnetic field orientation is predictive of the signs of Galactic $TB$ and $EB$. Our results suggest that magnetically misaligned …
Dark Matter (DM) annihilation in our Galaxy may produce a linearly polarized synchrotron signal. We use, for the first time, synchrotron polarization to constrain the DM annihilation cross section by comparing theoretical predictions with the latest polarization maps obtained by the Planck satellite collaboration. We find that synchrotron polarization is typically more constraining than synchrotron intensity by about one order of magnitude, independently of uncertainties in the modeling of electron and positron propagation, or of the Galactic magnetic field. Our bounds compete with Cosmic Micr…
If a single line of sight (LOS) intercepts multiple dust clouds of different spectral energy distributions and magnetic field orientations, the frequency scaling of each of the Stokes $Q$ and $U$ parameters of thermal dust emission may be different ("LOS frequency decorrelation"). We present first evidence for LOS frequency decorrelation in $Planck$ data. We use independent, neutral-hydrogen--measurements of the number of clouds per LOS and the magnetic field orientation in each cloud to select two sets of sightlines: (i) a target sample (pixels likely to exhibit LOS frequency decorrelation); …
Recent Planck results have shown that radiation from the cosmic microwave background passes through foregrounds in which aligned dust grains produce polarized dust emission, even in regions of the sky with the lowest level of dust emission. One of the most commonly used ways to remove the dust foreground is to extrapolate the polarized dust emission signal from frequencies where it dominates (e.g., ~ 350 GHz) to frequencies commonly targeted by cosmic microwave background experiments (e.g., ~150 GHz). In this paper, we describe an interstellar medium effect that can lead to decorrelation of th…
Using high-resolution data from the Galactic Arecibo L-Band Feed Array HI (GALFA-HI) survey, we show that linear structure in Galactic neutral hydrogen (HI) correlates with the magnetic field orientation implied by Planck 353 GHz polarized dust emission. The structure of the neutral interstellar medium is more tightly coupled to the magnetic field than previously known. At high Galactic latitudes, where the Planck data are noise-dominated, the HI data provide an independent constraint on the Galactic magnetic field orientation, and hence the local dust polarization angle. We detect strong cros…
$Ab$ $initio$ modeling of Galactic dust polarized CMB foreground
Nanjing University（南京大学）；University of California, San Diego（加州大学圣迭戈分校）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣巴巴拉分校卡弗里理论物理研究所）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
The purpose of this work is to characterize the diffuse Galactic polarized synchrotron. We present EE, BB, and EB power spectra estimated cross-correlating Planck and WMAP polarization frequency maps at 23 and 30 GHz, for a set of six sky regions covering from 30% to 94% of the sky. The EE and BB angular power spectra show a steep decay of the spectral amplitude as a function of multipole, approximated by a power law with power indices around -2.9 for both components. The B/E ratio is about 0.22. The EB cross-component is compatible with zero at 1$σ$, with upper constraint on the EB/EE ratio o…
We analyze BICEP2 and Planck data using a model that includes CMB lensing, gravity waves, and polarized dust. Planck dust polarization maps have highlighted the difficulty of estimating the dust polarization in low intensity regions, suggesting that the polarization fractions have considerable uncertainties and may be significantly higher than previous predictions. In this paper, we start by assuming nothing about the dust polarization except for the power spectrum shape, which we take to be $C_{l}^{BB} \propto l^{-2.42}$. The resulting joint BICEP2+Planck analysis favors solutions without gra…
Context: The Planck data releases have provided the community with sub-millimetre and radio observations of the full-sky at unprecedented resolutions. We make use of the Planck 353, 545 and 857 GHz maps alongside the IRAS 3000 GHz map. These maps contain information on the cosmic microwave background (CMB), cosmic infrared background (CIB), extragalactic point sources and diffuse thermal dust emission. Aims: We aim to determine the modified black body (MBB) model parameters of thermal dust emission in total intensity and produce all sky maps of pure thermal dust, having separated this Galactic…
We calculate weighted mosaic correlations between the recently published Planck 2015 foreground maps - both anomalous microwave emission (AME) maps, free-free emission, synchrotron radiation and thermal dust emission. The weighting coefficients are constructed taking account of the signal-to-error ratio given by the data product. Positive correlation is found for AME compared with thermal dust emission as well as synchrotron radiation. We find AME and free-free emission tending to be anti-correlated, however, when investigating different scales, their relationship appears to be more complex. W…
Science opportunities and recommendations concerning optical/infrared polarimetry for the upcoming decade in the field of cosmology. Community-based White Paper to Astro2010 in response to the call for such papers.
We use Bayesian component estimation methods to examine the prospects for large-scale polarized map and cosmological parameter estimation with simulated Planck data assuming simplified white noise properties. The sky signal is parametrized as the sum of the CMB, synchrotron emission, and thermal dust emission. The synchrotron and dust components are modelled as power-laws, with a spatially varying spectral index for synchrotron and a uniform index for dust. Using the Gibbs sampling technique, we estimate the linear polarisation Q and U posterior amplitudes of the CMB, synchrotron and dust maps…
Recent Planck observations have revealed some of the important statistical properties of synchrotron and dust polarisation, namely, the $B$ to $E$ mode power and temperature-$E$ (TE) mode cross-correlation. In this paper, we extend our analysis in Kandel et al. (2017) that studied $B$ to $E$ mode power ratio for polarised dust emission to include TE cross-correlation and develop an analogous formalism for synchrotron signal, all using a realistic model of magnetohydrodynamical (MHD) turbulence. Our results suggest that the Planck results for both synchrotron and dust polarisation can be unders…
We present an analysis of the level of polarized dust and synchrotron emission using the WMAP9 and Planck data. The primary goal of this study is to inform the assessment of foreground contamination in the cosmic microwave background (CMB) measurements below $\ell\sim200$ from 23 to 353 GHz. We compute angular power spectra as a function of sky cut based on the Planck 353 GHz polarization maps. Our primary findings are the following. (1) There is a spatial correlation between the dust emission as measured by Planck at 353 GHz and the synchrotron emission as measured by WMAP at 23 GHz with $ρ\a…
We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at $95%$ confidence level in the base $Λ$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.116$ at $95%$ confidence level. Our results imply that the inflation model with a single monomial potential is marginally disfavored at around $95%$ confidence level. Especially, the $m^2ϕ^2/2$ infla…
Characterizing accurately the polarized dust emission from our Galaxy will be decisive for the quest for the Cosmic Microwave Background (CMB) primordial $B$-modes. The incomplete modeling of its potentially complex spectral properties could lead to biases in the CMB polarization analyses and to a spurious detection of the tensor-to-scalar ratio $r$. Variations of the dust properties along and between lines of sight lead to unavoidable distortions of the spectral energy distribution (SED) that can not be easily anticipated by standard component separation methods. This issue can be tackled usi…
(abridged) We report the discovery of PHz G95.5-61.6, a complex structure detected in emission in the Planck all-sky survey that corresponds to two over-densities of high-redshift galaxies. This is the first source from the Planck catalogue of high-z candidates that has been completely characterised with follow-up observations from the optical to the sub-millimetre domain. Herschel/SPIRE observations at 250, 350 and 500 microns reveal the existence of five sources producing a 500 microns emission excess that spatially corresponds to the candidate proto-clusters discovered by Planck. Further ob…
We present an iterative scheme designed to recover calibrated I, Q, and U maps from Planck-HFI data using the orbital dipole due to the satellite motion with respect to the Solar System frame. It combines a map reconstruction, based on a destriping technique, juxtaposed with an absolute calibration algorithm. We evaluate systematic and statistical uncertainties incurred during both these steps with the help of realistic, Planck-like simulations containing CMB, foreground components and instrumental noise, and assess the accuracy of the sky map reconstruction by considering the maps of the resi…
Untangling dust emission and cosmic infrared background anisotropies with the scattering transform statistics
National Institute of Science Education and Research（印度科学教育研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室）；Laboratoire d’Océanographie Physique et Spatiale (LOPS), Univ. Brest, CNRS, Ifremer, IRD（布列斯特大学海洋物理与空间实验室）
We present 3D models of the Galactic magnetic field including regular and turbulent components, and of the distribution of matter in the Galaxy including relativistic electrons and dust grains. By integrating along the line of sight, we construct maps of the polarized Galactic synchrotron and thermal dust emissions for each of these models. We perform a likelihood analysis to compare the maps of the Ka, Q, V and W bands of the Wilkinson Microwave Anisotropy Probe (Wmap) and the 353 GHz Archeops data to the models obtained by varying the pitch angle of the regular magnetic field, the relative a…
We present for the first time a coherent model of the polarized Galactic synchrotron and thermal dust emissions which are the main diffuse foreground for the measurement of the polarized power spectra of the CMB fluctuations with the Planck satellite mission. We produce 3D models of the Galactic magnetic field including regular and turbulent components, and of the distribution of matter in the Galaxy, relativistic electrons and dust grains. By integrating along the line of sight we construct maps of the polarized Galactic synchrotron and thermal dust emission for each of these models and compa…
Gigaparsec scale alignments of the quasar optical polarization vectors have been proven to be robust against a scenario of contamination by the Galactic interstellar medium (ISM). This claim has been established by means of optical polarization measurements of the starlight surrounding the lines of sight of the 355 quasars for which reliable optical polarization measurements are available. In this paper, we take advantage of the full-sky and high quality polarization data released by the \textit{Planck} satellite to provide an independent, complementary, and up-to-date estimation of the contam…
The Internal Linear Combination (ILC) method has been extensively used to extract the cosmic microwave background (CMB) anisotropy map from foreground contaminated multi-frequency maps. However, the performance of simple ILC is limited and can be significantly improved by heavily constraint equations, dubbed cILC. The standard ILC and cILC works on the spin-0 field. Recently, a generalized version of ILC is developed to estimate polarization maps in which the quantity $Q \pm iU$ is combined at multiple frequencies using complex coefficients called Polarization ILC (PILC). A statistical moment …
We present new measurements of the power spectra of the cosmic infrared background (CIB) anisotropies using the Planck 2015 full-mission HFI data at 353, 545, and 857 GHz over 20000 square degrees. We use techniques similar to those applied for the cosmological analysis of Planck, subtracting dust emission at the power spectrum level. Our analysis gives stable solutions for the CIB power spectra with increasing sky coverage up to about 50% of the sky. These spectra agree well with Hi cleaned spectra from Planck measured on much smaller areas of sky with low Galactic dust emission. At 545 and 8…
The search for the primordial B-modes of the cosmic microwave background (CMB) relies on the separation from the brighter foreground dust signal. In this context, the characterisation of the spectral energy distribution (SED) of thermal dust in polarization has become a critical subject of study. We present a power-spectra analysis of Planck data, which improves on previous studies by using the newly released SRoll2 maps that correct residual data systematics, and by extending the analysis to regions near the Galactic plane. Our analysis focuses on the lowest multipoles between l=4 and 32, and…
The characterization of the dust polarization foreground to the Cosmic Microwave Background (CMB) is a necessary step towards the detection of the B-mode signal associated with primordial gravitational waves. We present a method to simulate maps of polarized dust emission on the sphere, similarly to what is done for the CMB anisotropies. This method builds on the understanding of Galactic polarization stemming from the analysis of Planck data. It relates the dust polarization sky to the structure of the Galactic magnetic field and its coupling with interstellar matter and turbulence. The Galac…
This paper introduces a new Planck Catalog of Polarized and Variable Compact Sources (PCCS-PV) comprising 153 sources, the majority of which are extragalactic. The data include both the total flux density and linear polarization measured by Planck with frequency coverage from 30 to 353 GHz, and temporal spacing ranging from days to years. We classify most sources as beamed, extragalactic radio sources; the catalog also includes several radio galaxies, Seyfert galaxies, and Galactic and Magellanic Cloud sources, including H IIi regions and planetary nebulae. An advanced extraction method applie…
We develop an analytic model for the power spectra of polarized filamentary structures as a way to study the Galactic polarization foreground to the Cosmic Microwave Background. Our approach is akin to the cosmological halo-model framework, and reproduces the main features of the Planck 353 GHz power spectra. We model the foreground as randomly-oriented, three-dimensional, spheroidal filaments, accounting for their projection onto the sky. The main tunable parameters are the distribution of filament sizes, the filament physical aspect ratio, and the dispersion of the filament axis around the l…
Using Planck polarization data, we search for and constrain spatial variations of the polarized dust foreground for cosmic microwave background (CMB) observations, specifically in its spectral index, $β_d$. Failure to account for such variations will cause errors in the foreground cleaning that propagate into errors on cosmological parameter recovery from the cleaned CMB map. It is unclear how robust prior studies of the Planck data which constrained $β_d$ variations are due to challenges with noise modeling, residual systematics, and priors. To clarify constraints on $β_d$ and its variation, …
We quantify the contamination from polarized diffuse Galactic synchrotron and thermal dust emissions to the B-modes of the CMB anisotropies on the degree angular scale, using data from the Planck and WMAP satellites. We compute power spectra of foreground polarized emissions in 352 circular sky patches located at Galactic latitude |b|>20°, each of which covering a fraction of the sky of about 1.5%. We make use of the spectral properties derived from Planck and WMAP data to extrapolate, in frequency, the amplitude of synchrotron and thermal dust B-modes spectra in the multipole bin centered at …
The measurement and characterization of the lensing of the cosmic microwave background (CMB) is key goal of the current and next generation of CMB experiments. We perform a case study of a three-channel balloon-borne CMB experiment observing the sky at (l,b)=(250deg,-38deg) and attaining a sensitivity of 5.25 muK-arcmin with 8' angular resolution at 150 GHz, in order to assess whether the effect of polarized Galactic dust is expected to be a significant contaminant to the lensing signal reconstructed using the EB quadratic estimator. We find that for our assumed dust model, polarization fracti…
We use a model of polarized Galactic emission developed by the the Planck collaboration to assess the impact of foregrounds on B-mode detection at low multipoles. Our main interest is to applications of noisy polarization data and in particular to assessing the feasibility of B-mode detection by Planck. This limits the complexity of foreground subtraction techniques that can be applied to the data. We analyze internal linear combination techniques and show that the offset caused by the dominant E-mode polarization pattern leads to a fundamental limit of r approximately 0.1 for the tensor-scala…
We present results of deep polarization imaging at 1.4 GHz with the Dominion Radio Astrophysical Observatory as part of the DRAO Planck Deep Fields project. This deep extragalactic field covers 15.16 square degrees centered at RA = 16h 14m and DEC = 54d 56', has an angular resolution of 42" x 62" at the field center, and reaches a sensitivity of 55 microJy/beam in Stokes I and 45 microJy/beam in Stokes Q and U. We detect 958 radio sources in Stokes I of which 136 are detected in polarization. We present the Euclidean-normalized polarized differential source counts down to 400 microJy. These co…
The characterization of the spectral energy distribution (SED) of dust emission has become a critical issue in the quest for primordial B-modes. The dust SED is often approximated by a modified black body (MBB) emission law but the extent to which this is accurate is unclear. This paper addresses this question, expanding the dust SED at the power spectrum level. The expansion is performed by means of moments around the MBB law, related to derivatives with respect to the dust spectral index. We present the mathematical formalism and apply it to simulations and Planck total intensity data, from …
The dust polarization is parameterized as a power law form of the multipole $l$: $D^{XX}_{l}=A^{XX}l(l+1)l^{α_{XX}}/(2π)$ ($XX$ denotes $BB$ or $EE$), where $A^{XX}$ is its amplitude with the ratio $A^{BB}/A^{EE}=0.52\pm 0.02$ and $α_{BB,EE}=-2.42\pm 0.02$. Extrapolating to $150$GHz from $353$GHz yields a value of $D^{BB}_{l=80}=(1.32\pm 0.29)\times 10^{-2}μK^2$ (and an additional uncertainty $(+0.28,-0.24)\times 10^{-2}μK^2$) over the range $40<l<120$. Based on these data, we report the tensor-to-scalar ratio $r=A_{t}/A_{s}$ defined at $k_0=0.05 \text{Mpc} ^{-1}$ by joining the BICEP2+{\it Pl…
The purpose of this work is to characterize the diffuse Galactic polarized synchrotron, which is the dominant CMB foreground emission at low frequency. We present EE, BB, and EB power spectra estimated from polarization frequency maps at 23 and 30 GHz as observed respectively by the WMAP K-band and the Planck lowest frequency channel, for a set of six sky regions covering from 30% to 94% of the sky. We study the synchrotron polarization angular distribution and spectral energy distribution (SED) by means of the so-called pseudo-$C_\ell$ formalism, provided by the NaMaster package, in the multi…
