Planck intermediate results: XVI. Profile likelihoods for cosmological parameters

We explore the 2013 Planck likelihood function with a high-precision multi-dimensional minimizer (Minuit). This allows a refinement of the ΛCDM best-fit solution with respect to previously-released results, and the construction of frequentist confidence intervals using profile likelihoods. The agreement with the cosmological results from the Bayesian framework is excellent, demonstrating the robustness of the Planck results to the statistical methodology. We investigate the inclusion of neutrino masses, where more significant differences may appear due to the non-Gaussian nature of the posterior mass distribution. By applying the Feldman-Cousins prescription, we again obtain results very similar to those of the Bayesian methodology. However, the profile-likelihood analysis of the cosmic microwave background (CMB) combination (Planck+WP+highL) reveals a minimum well within the unphysical negative-mass region. We show that inclusion of the Planck CMB-lensing information regularizes this issue, and provide a robust frequentist upper limit ∑ mν ≤ 0.26 eV (95% confidence) from the CMB+lensing+BAO data combination. Reproduced with permission from Astronomy & Astrophysics, © ESO 201

Planck intermediate results. XIX. An overview of the polarized thermal emission from Galactic dust

This paper presents an overview of the polarized sky as seen by Planck HFI at 353 GHz, which is the most sensitive Planck channel for dust polarization. We construct and analyse maps of dust polarization fraction and polarization angle at 1° resolution, taking into account noise bias and possible systematic effects. The sensitivity of the Planck HFI polarization measurements allows for the first time a mapping of Galactic dust polarized emission on large scales, including low column density regions. We find that the maximum observed dust polarization fraction is high (pmax = 19.8%), in particular in some regions of moderate hydrogen column density (NH < 2 × 1021 cm-2). The polarization fraction displays a large scatter at NH below a few 1021 cm-2. There is a general decrease in the dust polarization fraction with increasing column density above NH ≃ 1 × 1021 cm-2 and in particular a sharp drop above NH ≃ 1.5 × 1022 cm-2. We characterize the spatial structure of the polarization angle using the angle dispersion function. We find that the polarization angle is ordered over extended areas of several square degrees, separated by filamentary structures of high angle dispersion function. These appear as interfaces where the sky projection of the magnetic field changes abruptly without variations in the column density. The polarization fraction is found to be anti-correlated with the dispersion of polarization angles. These results suggest that, at the resolution of 1°, depolarization is due mainly to fluctuations in the magnetic field orientation along the line of sight, rather than to the loss of grain alignment in shielded regions. We also compare the polarization of thermal dust emission with that of synchrotron measured with Planck, low-frequency radio data, and Faraday rotation measurements toward extragalactic sources. These components bear resemblance along the Galactic plane and in some regions such as the Fan and North Polar Spur regions. The poor match observed in other regions shows, however, that dust, cosmic-ray electrons, and thermal electrons generally sample different parts of the line of sight. Reproduced with permission, © ESO, 201

Planck intermediate results. XV. A study of anomalous microwave emission in Galactic clouds

Anomalous microwave emission (AME) is believed to be due to electric dipole radiation from small spinning dust grains. The aim of this paper is a statistical study of the basic properties of AME regions and the environment in which they emit. We used WMAP and Planck maps, combined with ancillary radio and IR data, to construct a sample of 98 candidate AME sources, assembling SEDs for each source using aperture photometry on 1°-smoothed maps from 0.408 GHz up to 3000 GHz. Each spectrum is fitted with a simple model of free-free, synchrotron (where necessary), cosmic microwave background (CMB), thermal dust, and spinning dust components. We find that 42 of the 98 sources have significant (>5σ) excess emission at frequencies between 20 and 60 GHz. An analysis of the potential contribution of optically thick free-free emission from ultra-compact H ii regions, using IR colour criteria, reduces the significant AME sample to 27 regions. The spectrum of the AME is consistent with model spectra of spinning dust. Peak frequencies are in the range 20−35 GHz except for the California nebula (NGC 1499), which appears to have a high spinning dust peak frequency of (50 ± 17) GHz. The AME regions tend to be more spatially extended than regions with little or no AME. The AME intensity is strongly correlated with the sub-millimetre/IR flux densities and comparable to previous AME detections in the literature. AME emissivity, defined as the ratio of AME to dust optical depth, varies by an order of magnitude for the AME regions. The AME regions tend to be associated with cooler dust in the range 14−20 K and an average emissivity index, βd, of +1.8, while the non-AME regions are typically warmer, at 20−27 K. In agreement with previous studies, the AME emissivity appears to decrease with increasing column density. This supports the idea of AME originating from small grains that are known to be depleted in dense regions, probably due to coagulation onto larger grains. We also find a correlation between the AME emissivity (and to a lesser degree the spinning dust peak frequency) and the intensity of the interstellar radiation field, G0. Modelling of this trend suggests that both radiative and collisional excitation are important for the spinning dust emission. The most significant AME regions tend to have relatively less ionized gas (free-free emission), although this could be a selection effect. The infrared excess, a measure of the heating of dust associated with H ii regions, is typically >4 for AME sources, indicating that the dust is not primarily heated by hot OB stars. The AME regions are associated with known dark nebulae and have higher 12 μm/25 μm ratios. The emerging picture is that the bulk of the AME is coming from the polycyclic aromatic hydrocarbons and small dust grains from the colder neutral interstellar medium phase. Reproduced with permission from Astronomy & Astrophysics, © ESO 201

SymPix: a spherical grid for efficient sampling of rotationally invariant operators

We present SymPix, a special-purpose spherical grid optimized for efficiently sampling rotationally invariant linear operators. This grid is conceptually similar to the Gauss–Legendre (GL) grid, aligning sample points with iso-latitude rings located on Legendre polynomial zeros. Unlike the GL grid, however, the number of grid points per ring varies as a function of latitude, avoiding expensive oversampling near the poles and ensuring nearly equal sky area per grid point. The ratio between the number of grid points in two neighboring rings is required to be a low-order rational number (3, 2, 1, 4/3, 5/4, or 6/5) to maintain a high degree of symmetries. Our main motivation for this grid is to solve linear systems using multi-grid methods, and to construct efficient preconditioners through pixel-space sampling of the linear operator in question. © American Astronomical Society. All rights reserved

Joint Bayesian estimation of tensor and lensing B modes in the power spectrum of CMB polarization data

We investigate the performance of a simple Bayesian fitting approach to correct the cosmic microwave background (CMB) B-mode polarization for gravitational lensing effects in the recovered probability distribution of the tensor-to-scalar ratio. We perform a two-dimensional power spectrum fit of the amplitude of the primordial B modes (tensor-to-scalar ratio, r) and the amplitude of the lensing B modes (parameter Alens), jointly with the estimation of the astrophysical foregrounds including both synchrotron and thermal dust emissions. Using this Bayesian framework, we forecast the ability of the proposed CMB space mission LiteBIRD to constrain r in the presence of realistic lensing and foreground contributions. We compute the joint posterior distribution of r and Alens, which we improve by adopting a prior on Alens taken from the South Pole Telescope (SPT) measurement. As it applies to the power spectrum, this approach cannot mitigate the uncertainty on r that is due to E-mode cosmic variance transferred to B modes by lensing, unlike standard delensing techniques that are performed on maps. However, the method allows us to correct for the bias on r induced by lensing, at the expense of a larger uncertainty due to the increased volume of the parameter space. We quantify, for different values of the tensor-to-scalar ratio, the trade-off between bias correction and increase of uncertainty on r. For LiteBIRD simulations, which include foregrounds and lensing contamination, we find that correcting the foreground-cleaned CMB B-mode power spectrum for the lensing bias, not the lensing cosmic variance, still guarantees a 3σ detection of r = 5 × 10−3. The significance of the detection is increased to 6σ when the current SPT prior on Alens is adopted. © 2017 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Societ

POWER ASYMMETRY IN WMAP AND PLANCK TEMPERATURE SKY MAPS AS MEASURED BY A LOCAL VARIANCE ESTIMATOR

We revisit the question of hemispherical power asymmetry in the WMAP and Planck temperature sky maps by measuring the local variance over the sky and on disks of various sizes. For the 2013 Planck sky map we find that none of the 1000 available isotropic Planck "Full Focal Plane" simulations have a larger variance asymmetry than that estimated from the data, suggesting the presence of an anisotropic signature formally significant at least at the 3.3σ level. For the WMAP 9 year data we find that 5 out of 1000 simulations have a larger asymmetry. The preferred direction for the asymmetry from the Planck data is (l, b) = (212°, –13°), in good agreement with previous reports of the same hemispherical power asymmetry. © American Astronomical Society. All rights reserved

WALOP-South: A wide-field one-shot linear optical polarimeter for PASIPHAE survey

WALOP (Wide-Area Linear Optical Polarimeter)-South, to be mounted on the 1m SAAO telescope in South Africa, is first of the two WALOP instruments currently under development for carrying out the PASIPHAE survey. Scheduled for commissioning in the year 2021, the WALOP instruments will be used to measure the linear polarization of around 106 stars in the SDSS-r broadband with 0.1 % polarimetric accuracy, covering 4000 square degrees in the Galactic polar regions. The combined capabilities of one-shot linear polarimetry, high polarimetric accuracy (< 0.1 %) and polarimetric sensitivity (< 0.05 %), and a large field of view (FOV) of 35 35 arcminutes make WALOP-South a unique astronomical instrument. In a single exposure, it is designed to measure the Stokes parameters I, q and u in the SDSS-r broadband and narrowband filters between 500-700 nm. During each measurement, four images of the full field corresponding to the polarization angles of 0°, 45°, 90° and 135° will be imaged on four detectors and carrying out differential photometry on these images will yield the Stokes parameters. Major challenges in designing WALOP-South instrument include- (a) in the optical design, correcting for the spectral dispersion introduced by large split angle Wollaston Prisms used as polarization analyzers as well as aberrations from the wide field, and (b) making an optomechanical design adherent to the tolerances required to obtain good imaging and polarimetric performance under all temperature conditions as well as telescope pointing positions. We present the optical and optomechanical design for WALOP-South which overcomes these challenges

Planck 2018 results: V. CMB power spectra and likelihoods

We describe the legacy Planck cosmic microwave background (CMB) likelihoods derived from the 2018 data release. The overall approach is similar in spirit to the one retained for the 2013 and 2015 data release, with a hybrid method using different approximations at low ( ℓ  &lt;  30) and high ( ℓ  ≥ 30) multipoles, implementing several methodological and data-analysis refinements compared to previous releases. With more realistic simulations, and better correction and modelling of systematic effects, we can now make full use of the CMB polarization observed in the High Frequency Instrument (HFI) channels. The low-multipole EE cross-spectra from the 100 GHz and 143 GHz data give a constraint on the ΛCDM reionization optical-depth parameter τ to better than 15% (in combination with the TT low- ℓ data and the high- ℓ temperature and polarization data), tightening constraints on all parameters with posterior distributions correlated with τ . We also update the weaker constraint on τ from the joint TEB likelihood using the Low Frequency Instrument (LFI) channels, which was used in 2015 as part of our baseline analysis. At higher multipoles, the CMB temperature spectrum and likelihood are very similar to previous releases. A better model of the temperature-to-polarization leakage and corrections for the effective calibrations of the polarization channels (i.e., the polarization efficiencies) allow us to make full use of polarization spectra, improving the ΛCDM constraints on the parameters θ MC , ω c , ω b , and H 0 by more than 30%, and n s by more than 20% compared to TT-only constraints. Extensive tests on the robustness of the modelling of the polarization data demonstrate good consistency, with some residual modelling uncertainties. At high multipoles, we are now limited mainly by the accuracy of the polarization efficiency modelling. Using our various tests, simulations, and comparison between different high-multipole likelihood implementations, we estimate the consistency of the results to be better than the 0.5  σ level on the ΛCDM parameters, as well as classical single-parameter extensions for the joint likelihood (to be compared to the 0.3  σ levels we achieved in 2015 for the temperature data alone on ΛCDM only). Minor curiosities already present in the previous releases remain, such as the differences between the best-fit ΛCDM parameters for the ℓ  &lt;  800 and ℓ  &gt;  800 ranges of the power spectrum, or the preference for more smoothing of the power-spectrum peaks than predicted in ΛCDM fits. These are shown to be driven by the temperature power spectrum and are not significantly modified by the inclusion of the polarization data. Overall, the legacy Planck CMB likelihoods provide a robust tool for constraining the cosmological model and represent a reference for future CMB observations

Planck intermediate results: L. Evidence of spatial variation of the polarized thermal dust spectral energy distribution and implications for CMB B-mode analysis

The characterization of the Galactic foregrounds has been shown to be the main obstacle in thechallenging quest to detect primordial B-modes in the polarized microwave sky. We make use of the Planck-HFI 2015 data release at high frequencies to place new constraints on the properties of the polarized thermal dust emission at high Galactic latitudes. Here, we specifically study the spatial variability of the dust polarized spectral energy distribution (SED), and its potential impact on the determination of the tensor-to-scalar ratio, r. We use the correlation ratio of the CBBℓ angular power spectra between the 217 and 353 GHz channels as a tracer of these potential variations, computed on different high Galactic latitude regions, ranging from 80% to 20% of the sky. The new insight from Planck data is a departure of the correlation ratio from unity that cannot be attributed to a spurious decorrelation due to the cosmic microwave background, instrumental noise, or instrumental systematics. The effect is marginally detected on each region, but the statistical combination of all the regions gives more than 99% confidence for this variation in polarized dust properties. In addition, we show that the decorrelation increases when there is a decrease in the mean column density of the region of the sky being considered, and we propose a simple power-law empirical model for this dependence, which matches what is seen in the Planck data. We explore the effect that this measured decorrelation has on simulations of the BICEP2-Keck Array/Planck analysis and show that the 2015 constraints from these data still allow a decorrelation between the dust at 150 and 353 GHz that is compatible with our measured value. Finally, using simplified models, we show that either spatial variation of the dust SED or of the dust polarization angle are able to produce decorrelations between 217 and 353 GHz data similar to the values we observe in the data