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Quasi-normal mode of a Planck star

Highlights: • We have derived the Regge–Wheeler equations for a Planck star. • We have calculated the perturbed Einstein equations for a Planck star. • We have calculated the Quasi Normal Modes of a Planck star. In this work we present a calculation of the quasi-normal modes of a Planck star, a supposed state in the life of a large mass star in which quantum effects should reverse the collapse causing the star to explode. In order to solve the Regge–Wheeler equations and to calculate the quasi-normal modes, we apply the shooting method.

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Planck 2013 results. IX. HFI spectral response

The Planck High Frequency Instrument (HFI) spectral response was determined through a series of ground based tests conducted with the HFI focal plane in a cryogenic environment prior to launch. The main goal of the spectral transmission tests was to measure the relative spectral response (includingthe level of out-of-band signal rejection) of all HFI detectors to a known source of electromagnetic radiation individually. This was determined by measuring the interferometric output of a continuously scanned Fourier transform spectrometer with all HFI detectors. As there is no on-board spectrometer within HFI, the ground-based spectral response experiments provide the definitive data set for the relative spectral calibration of the HFI. Knowledge of the relative variations in the spectral response between HFI detectors allows for a more thorough analysis of the HFI data. The spectral response of the HFI is used in Planck data analysis and component separation, this includes extraction of CO emission observed within Planck bands, dust emission, Sunyaev-Zeldovich sources, and intensity to polarization leakage. The HFI spectral response data have also been used to provide unit conversion and colour correction analysis tools. While previous papers describe the pre-flight experiments conducted on the Planck HFI, this paper focusses on the analysis of the pre-flight spectral response measurements and the derivation of data products, e.g. band-average spectra, unit conversion coefficients, and colour correction coefficients, all with related uncertainties. Verifications of the HFI spectral response data are provided through comparisons with photometric HFI flight data. This validation includes use of HFI zodiacal emission observations to demonstrate out-of-band spectral signal rejection better than 10 8 . The accuracy of the HFI relative spectral response data is verified through comparison with complementary flight-data based unit conversion coefficients and colour correction coefficients. Furthermore, these coefficients include those based upon HFI observations of CO, dust, and Sunyaev-Zeldovich emission. General agreement is observed between the ground-based spectral characterization of HFI and corresponding in-flight observations, within the quoted uncertainty of each; explanations are provided for any discrepancies.

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Planck 2013 results. XXVI. Background geometry and topology of the Universe

The new cosmic microwave background (CMB) temperature maps from Planck provide the highest-quality full-sky view of the surface of last scattering available to date. This allows us to detect possible departures from the standard model of a globally homogeneous and isotropic cosmology on the largest scales. We search for correlations induced by a possible non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance χ rec ), both via a direct search for matched circular patterns at the intersections and by an optimal likelihood search for specific topologies. For the latter we consider flat spaces with cubic toroidal (T3), equal-sided chimney (T2) and slab (T1) topologies, three multi-connected spaces of constant positive curvature (dodecahedral, truncated cube and octahedral) and two compact negative-curvature spaces. These searches yield no detection of the compact topology with the scale below the diameter of the last scattering surface. For most compact topologies studied the likelihood maximized over the orientation of the space relative to the observed map shows some preference for multi-connected models just larger than the diameter of the last scattering surface. Since this effect is also present in simulated realizations of isotropic maps, we interpret it as the inevitable alignment of mild anisotropic correlations with chance features in a single sky realization; such a feature can also be present, in milder form, when the likelihood is marginalized over orientations. Thus marginalized, the limits on the radius R i of the largest sphere inscribed in topological domain (at log-likelihood-ratio Δln L > -5 relative to a simply-connected flat Planck best-fit model) are: in a flat Universe, R i > 0.92χ rec for the T3 cubic torus; R i > 0.71χ rec for the T2 chimney; R i > 0.50χ rec for the T1 slab; and in a positively curved Universe, R i > 1.03χ rec for the dodecahedral space; R i > 1.0χ rec for the truncated cube; and R i > 0.89χ rec for the octahedral space. The limit for a wider class of topologies, i.e., those predicting matching pairs of back-to-back circles, among them tori and the three spherical cases listed above, coming from the matched-circles search, is R i > 0.94χ rec at 99% confidence level. Similar limits apply to a wide, although not exhaustive, range of topologies. We also perform a Bayesian search for an anisotropic global Bianchi VII h geometry. In the non-physical setting where the Bianchi cosmology is decoupled from the standard cosmology, Planck data favour the inclusion of a Bianchi component with a Bayes factor of at least 1.5 units of log-evidence. Indeed, the Bianchi pattern is quite efficient at accounting for some of the large-scale anomalies found in Planck data. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone. In the physically motivated setting where the Bianchi parameters are coupled and fitted simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VII h cosmology and constrain the vorticity of such models to (ω/H) 0 < 8.1 × 10 -10 (95% confidence level).

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Planck 2013 results. XIII. Galactic CO emission

Rotational transition lines of CO play a major role in molecular radio astronomy as a mass tracer and in particular in the study of star formation and Galactic structure. Although a wealth of data exists for the Galactic plane and some well-known molecular clouds, there is no available high sensitivity all-sky survey of CO emission to date. Such all-sky surveys can be constructed using the Planck HFI data because the three lowest CO rotational transition lines at 115, 230 and 345 GHz significantly contribute to the signal of the 100, 217 and 353 GHz HFI channels, respectively. Two different component separation methods are used to extract the CO maps from Planck HFI data. The maps obtained are then compared to one another and to existing external CO surveys. From these quality checks the best CO maps, in terms of signal to noise ratio and/or residual contamination by other emission, are selected. Three different sets of velocity-integrated CO emission maps are produced with different trade-offs between signal-to-noise, angular resolution, and reliability. Maps for the CO J = 1 → 0, J = 2 → 1, and J = 3 → 2 rotational transitions are presented and described in detail. They are shown to be fully compatible with previous surveys of parts of the Galactic plane as well as with under-sampled surveys of the high latitude sky. The Planck HFI velocity-integrated CO maps for the J = 1 → 0, J = 2 → 1, and J = 3 →2 rotational transitions provide an unprecedented all-sky CO view of the Galaxy. These maps are also of great interest to monitor potential CO contamination of the Planck studies of the cosmological microwave background.

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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 CDM 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 Σ$m_v$ ≤0:26 eV (95% confidence) from the CMB+lensing+BAO data combination.

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Planck 2013 results. XI. All-sky model of thermal dust emission

This work introduces an all-sky model of dust emission from the Planck 353, 545, and 857 GHz, and IRAS 100 μm data. Using a modified blackbody fit to the data we present all-sky maps of the dust optical depth, temperature, and spectral index over the 353-3000 GHz range. This model is a good representation of the IRAS and Planck data at 5' between 353 and 3000 GHz (850 and 100 μm). It shows variations of the order of 30% compared with the widely-used model of Finkbeiner, Davis, and Schlegel. The Planck data allow us to estimate the dust temperature uniformly over the whole sky, down to an angular resolution of 5', providing an improved estimate of the dust optical depth compared to previous all-sky dust model, especially in high-contrast molecular regions where the dust temperature varies strongly at small scales in response to dust evolution, extinction, and/or local production of heating photons. An increase of the dust opacity at 353 GHz, τ 353 / N H , from the diffuse to the denser interstellar medium (ISM) is reported. It is associated with a decrease in the observed dust temperature, T obs , that could be due at least in part to the increased dust opacity. We also report an excess of dust emission at H I column densities lower than 10 20 cm -2 that could be the signature of dust in the warm ionized medium. In the diffuse ISM at high Galactic latitude, we report an anticorrelation between τ 353 / N H and T obs while the dust specific luminosity, i.e., the total dust emission integrated over frequency (the radiance) per hydrogen atom, stays about constant, confirming one of the Planck Early Results obtained on selected fields. This effect is compatible with the view that, in the diffuse ISM, T obs responds to spatial variations of the dust opacity, due to variations of dust properties, in addition to (small) variations of the radiation field strength. The indication is that in the diffuse high-latitude ISM τ 353 is not as reliable a tracer of dust column density as we conclude it is in molecular clouds where the correlation of τ 353 with dust extinction estimated using colour excess measurements on stars is strong. To estimate Galactic E(B-V) in extragalactic fields at high latitude we develop a new method based on the thermal dust radiance, instead of the dust optical depth, calibrated to E(B -V) using reddening measurements of quasars deduced from Sloan Digital Sky Survey data.

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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 ( p max = 19.8%), in particular in some regions of moderate hydrogen column density ( N H < 2 × 10 21 cm -2 ). The polarization fraction displays a large scatter at N H below a few 10 21 cm -2 . There is a general decrease in the dust polarization fraction with increasing column density above N H ≃ 1 × 10 21 cm -2 and in particular a sharp drop above N H ≃ 1.5 × 10 22 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&deg;, 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.

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Planck 2015 results: XIV. Dark energy and modified gravity

For this research, we study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state w(a), as well as principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar field. When estimating the density of DE at early times, we significantly improve present constraints and find that it has to be below ~2% (at 95% confidence) of the critical density, even when forced to play a role for z < 50 only. We then move to general parameterizations of the DE or MG perturbations that encompass both effective field theories and the phenomenology of gravitational potentials in MG models. Lastly, we test a range of specific models, such as k-essence, f(R) theories, and coupled DE. In addition to the latest Planck data, for our main analyses, we use background constraints from baryonic acoustic oscillations, type-Ia supernovae, and local measurements of the Hubble constant. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. These additional probes are important tools for testing MG models and for breaking degeneracies that are still present in the combination of Planck and background data sets. All results that include only background parameterizations (expansion of the equation of state, early DE, general potentials in minimally-coupled scalar fields or principal component analysis) are in agreement with ΛCDM. Finally, when testing models that also change perturbations (even when the background is fixed to ΛCDM), some tensions appear in a few scenarios: the maximum one found is ~2σ for Planck TT+lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to, at most, 3σ when external data sets are included. It however disappears when including CMB lensing.

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Planck 2015 results: XVIII. Background geometry and topology of the Universe

We report that maps of cosmic microwave background (CMB) temperature and polarization from the 2015 release of Planck data provide the highestquality full-sky view of the surface of last scattering available to date. This enables us to detect possible departures from a globally isotropic cosmology. We present the first searches using CMB polarization for correlations induced by a possible non-trivial topology with a fundamental domain that intersects, or nearly intersects, the last-scattering surface (at comoving distance χ rec ), both via a direct scan for matched circular patterns at the intersections and by an optimal likelihood calculation for specific topologies. We specialize to flat spaces with cubic toroidal (T3) and slab (T1) topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology with a scale below the diameter of the last-scattering surface. The limits on the radius R i of the largest sphere inscribed in the fundamental domain (at log-likelihood ratio ΔlnL > -5 relative to a simply-connected flat Planck best-fit model) are: R i > 0.97 χ rec for the T3 cubic torus; and R i > 0.56 χ rec for the T1 slab. The limit for the T3 cubic torus from the matched-circles search is numerically equivalent, R i > 0.97 χ rec at 99% confidence level from polarization data alone. We also perform a Bayesian search for an anisotropic global Bianchi VII h geometry. In the non-physical setting, where the Bianchi cosmology is decoupled from the standard cosmology, Planck temperature data favour the inclusion of a Bianchi component with a Bayes factor of at least 2.3 units of log-evidence. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone. Fitting the induced polarization pattern for this model to the Planck data requires an amplitude of -0.10 ± 0.04 compared to the value of + 1 if the model were to be correct. In the physically motivated setting, where the Bianchi parameters are coupled and fitted simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VII h cosmology and constrain the vorticity of such models to (ω/H) 0 < 7.6 × 10 -10 (95% CL).

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Planck intermediate results: XXXV. Probing the role of the magnetic field in the formation of structure in molecular clouds

Within ten nearby (d < 450 pc) Gould belt molecular clouds we evaluate in this paper statistically the relative orientation between the magnetic field projected on the plane of sky, inferred from the polarized thermal emission of Galactic dust observed by Planck at 353 GHz, and the gas column density structures, quantified by the gradient of the column density, N H . The selected regions, covering several degrees in size, are analysed at an effective angular resolution of 10' FWHM, thus sampling physical scales from 0.4 to 40 pc in the nearest cloud. The column densities in the selected regions range from N H ≈ 10 21 to10 23 cm -2 , and hence they correspond to the bulk of the molecular clouds. The relative orientation is evaluated pixel by pixel and analysed in bins of column density using the novel statistical tool called “histogram of relative orientations”. Throughout this study, we assume that the polarized emission observed by Planck at 353 GHz is representative of the projected morphology of the magnetic field in each region, i.e., we assume a constant dust grain alignment efficiency, independent of the local environment. Within most clouds we find that the relative orientation changes progressively with increasing N H , from mostly parallel or having no preferred orientation to mostly perpendicular. In simulations of magnetohydrodynamic turbulence in molecular clouds this trend in relative orientation is a signature of Alfvénic or sub-Alfvénic turbulence, implying that the magnetic field is significant for the gas dynamics at the scales probed by Planck. Finally, we compare the deduced magnetic field strength with estimates we obtain from other methods and discuss the implications of the Planck observations for the general picture of molecular cloud formation and evolution.

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Planck 2015 results: IX. Diffuse component separation: CMB maps

In this paper, we present foreground-reduced cosmic microwave background (CMB) maps derived from the full Planck data set in both temperature and polarization. Compared to the corresponding Planck 2013 temperature sky maps, the total data volume is larger by a factor of 3.2 for frequencies between 30 and 70 GHz, and by 1.9 for frequencies between 100 and 857 GHz. In addition, systematic errors in the forms of temperature-to-polarization leakage, analogue-to-digital conversion uncertainties, and very long time constant errors have been dramatically reduced, to the extent that the cosmological polarization signal may now be robustly recovered on angular scales ℓ ≳ 40. On the very largest scales, instrumental systematic residuals are still non-negligible compared to the expected cosmological signal, and modes with ℓ< 20 are accordingly suppressed in the current polarization maps by high-pass filtering. As in 2013, four different CMB component separation algorithms are applied to these observations, providing a measure of stability with respect to algorithmic and modelling choices. Additionally, the resulting polarization maps have rms instrumental noise ranging between 0.21 and 0.27μK averaged over 55' pixels, and between 4.5 and 6.1μK averaged over 3$'\atop{.}$4 pixels. The cosmological parameters derived from the analysis of temperature power spectra are in agreement at the 1σ level with the Planck 2015 likelihood. Unresolved mismatches between the noise properties of the data and simulations prevent a satisfactory description of the higher-order statistical properties of the polarization maps. Thus, the primary applications of these polarization maps are those that do not require massive simulations for accurate estimation of uncertainties, for instance estimation of cross-spectra and cross-correlations, or stacking analyses. However, the amplitude of primordial non-Gaussianity is consistent with zero within 2σ for all local, equilateral, and orthogonal configurations of the bispectrum, including for polarization E-modes. Moreover, excellent agreement is found regarding the lensing B-mode power spectrum, both internally among the various component separation codes and with the best-fit Planck 2015 Λ cold dark matter model.

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Planck 2015 results: XVI. Isotropy and statistics of the CMB

In this paper, we test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived from the multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we find excellent agreement between results based on these sky maps over both a very large fraction of the sky and a broad range of angular scales, establishing that potential foreground residuals do not affect our studies. Tests of skewness, kurtosis, multi-normality, N-point functions, and Minkowski functionals indicate consistency with Gaussianity, while a power deficit at large angular scales is manifested in several ways, for example low map variance. The results of a peak statistics analysis are consistent with the expectations of a Gaussian random field. The “Cold Spot” is detected with several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe the large-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a posteriori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at a significance that is dependent on the details of the approach. We perform the first examination of polarization data, finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations. Finally, where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data and provide our most thorough view of the statistics of the CMB fluctuations to date.

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Planck 2015 results: I. Overview of products and scientific results

The European Space Agency’s Planck satellite, which is dedicated to studying the early Universe and its subsequent evolution, was launched on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013. In February 2015, ESA and the Planck Collaboration released the second set of cosmology products based ondata from the entire Planck mission, including both temperature and polarization, along with a set of scientific and technical papers and a web-based explanatory supplement. This study gives an overview of the main characteristics of the data and the data products in the release, as well as the associated cosmological and astrophysical science results and papers. The data products include maps of the cosmic microwave background (CMB), the thermal Sunyaev-Zeldovich effect, diffuse foregrounds in temperature and polarization, catalogues of compact Galactic and extragalactic sources (including separate catalogues of Sunyaev-Zeldovich clusters and Galactic cold clumps), and extensive simulations of signals and noise used in assessing uncertainties and the performance of the analysis methods. The likelihood code used to assess cosmological models against the Planck data is described, along with a CMB lensing likelihood. Finally, scientific results include cosmological parameters derived from CMB power spectra, gravitational lensing, and cluster counts, as well as constraints on inflation, non-Gaussianity, primordial magnetic fields, dark energy, and modified gravity, and new results on low-frequency Galactic foregrounds.

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Planck intermediate results: XL. The Sunyaev-Zeldovich signal from the Virgo cluster

The Virgo cluster is the largest Sunyaev-Zeldovich (SZ) source in the sky, both in terms of angular size and total integrated flux. Planck’s wide angular scale and frequency coverage, together with its high sensitivity, enable a detailed study of this big object through the SZ effect. Virgo is well resolved by Planck, showing an elongated structure that correlates well with the morphology observed from X-rays, but extends beyond the observed X-ray signal. We find good agreement between the SZ signal (or Compton parameter, y c ) observed by Planck and the expected signal inferred from X-ray observations and simple analytical models. Owing to its proximity to us, the gas beyond the virial radius in Virgo can be studied with unprecedented sensitivity by integrating the SZ signal over tens of square degrees. In this paper, we study the signal in the outskirts of Virgo and compare it with analytical models and a constrained simulation of the environment of Virgo. Planck data suggest that significant amounts of low-density plasma surround Virgo, out to twice the virial radius. We find the SZ signal in the outskirts of Virgo to be consistent with a simple model that extrapolates the inferred pressure at lower radii, while assuming that the temperature stays in the keV range beyond the virial radius. The observed signal is also consistent with simulations and points to a shallow pressure profile in the outskirts of the cluster. This reservoir of gas at large radii can be linked with the hottest phase of the elusivewarm/hot intergalactic medium. Taking the lack of symmetry of Virgo into account, we find that a prolate model is favoured by the combination of SZ and X-ray data, in agreement with predictions. In conclusion, based on the combination of the same SZ and X-ray data, we constrain the total amount of gas in Virgo. Under the hypothesis that the abundance of baryons in Virgo is representative of the cosmic average, we also infer a distance for Virgo of approximately 18 Mpc, in good agreement with previous estimates.

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Planck intermediate results: XLI. A map of lensing-induced B -modes

The secondary cosmic microwave background (CMB) B-modes stem from the post-decoupling distortion of the polarization E-modes due to the gravitational lensing effect of large-scale structures. These lensing-induced B-modes constitute both a valuable probe of the dark matter distribution and an important contaminant for the extraction of the primary CMB B-modes from inflation. Planck provides accurate nearly all-sky measurements of both the polarization E-modes and the integrated mass distribution via the reconstruction of the CMB lensing potential. By combining these two data products, we have produced in this paper an all-sky template map of the lensing-induced B-modes using a real-space algorithm that minimizes the impact of sky masks. The cross-correlation of this template with an observed (primordial and secondary) B-mode map can be used to measure the lensing B-mode power spectrum at multipoles up to 2000. In particular, when cross-correlating with the B-mode contribution directly derived from the Planck polarization maps, we obtain lensing-induced B-mode power spectrum measurement at a significance level of 12σ, which agrees with the theoretical expectation derived from the Planck best-fit Λ cold dark matter model. This unique nearly all-sky secondary B-mode template, which includes the lensing-induced information from intermediate to small (10 ≲ ℓ ≲ 1000) angular scales, is delivered as part of the Planck 2015 public data release. Finally, it will be particularly useful for experiments searching for primordial B-modes, such as BICEP2/Keck Array or LiteBIRD, since it will enable an estimate to be made of the lensing-induced contribution to the measured total CMB B-modes.

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Planck intermediate results: XLII. Large-scale Galactic magnetic fields

Recent models for the large-scale Galactic magnetic fields in the literature have been largely constrained by synchrotron emission and Faraday rotation measures. In this paper, we use three different but representative models to compare their predicted polarized synchrotron and dust emission with that measured by the Planck satellite. We first update these models to match the Planck synchrotron products using a common model for the cosmic-ray leptons. We discuss the impact on this analysis of the ongoing problems of component separation in the Planck microwave bands and of the uncertain cosmic-ray spectrum. In particular, the inferred degree of ordering in the magnetic fields is sensitive to these systematic uncertainties, and we further show the importance of considering the expected variations in the observables in addition to their mean morphology. We then compare the resulting simulated emission to the observed dust polarization and find that the dust predictions do not match the morphology in the Planck data but underpredict the dust polarization away from the plane. We modify one of the models to roughly match both observables at high latitudes by increasing the field ordering in the thin disc near the observer. Finally, though this specific analysis is dependent on the component separation issues, we present the improved model as a proof of concept for how these studies can be advanced in future using complementary information from ongoing and planned observational projects.

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Planck intermediate results: XLIII. Spectral energy distribution of dust in clusters of galaxies

Although infrared (IR) overall dust emission from clusters of galaxies has been statistically detected using data from the Infrared Astronomical Satellite (IRAS), it has not been possible to sample the spectral energy distribution (SED) of this emission over its peak, and thus to break the degeneracy between dust temperature and mass. By complementing the IRAS spectral coverage with Planck satellite data from 100 to 857 GHz, we provide in this paper new constraints on the IR spectrum of thermal dust emission in clusters of galaxies. We achieve this by using a stacking approach for a sample of several hundred objects from the Planck cluster sample. This procedure averages out fluctuations from the IR sky, allowing us to reach a significant detection of the faint cluster contribution. We also use the large frequency range probed by Planck, together with component-separation techniques, to remove the contamination from both cosmic microwave background anisotropies and the thermal Sunyaev-Zeldovich effect (tSZ) signal, which dominate at ν ≤ 353 GHz. By excluding dominant spurious signals or systematic effects, averaged detections are reported at frequencies 353 GHz ≤ ν ≤ 5000 GHz. We confirm the presence of dust in clusters of galaxies at low and intermediate redshifts, yielding an SED with a shape similar to that of the Milky Way. Planck’s resolution does not allow us to investigate the detailed spatial distribution of this emission (e.g. whether it comes from intergalactic dust or simply the dust content of the cluster galaxies), but the radial distribution of the emission appears to follow that of the stacked SZ signal, and thus the extent of the clusters. Finally, the recovered SED allows us to constrain the dust mass responsible for the signal and its temperature.

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Planck 2018 results XII. Galactic astrophysics using polarized dust emission

Observations of the submillimetre emission from Galactic dust, in both total intensity I and polarization, have received tremendous interest thanks to the Planck full-sky maps. In this paper we make use of such full-sky maps of dust polarized emission produced from the third public release of Planck data. As the basis for expanding on astrophysical studies of the polarized thermal emission from Galactic dust, we present full-sky maps of the dust polarization fraction p, polarization angle ψ, and dispersion function of polarization angles S . The joint distribution (one-point statistics) of p and NH confirms that the mean and maximum polarization fractions decrease with increasing NH. The uncertainty on the maximum observed polarization fraction, pmax = 22.0 -1.4 +3.5% at 353 GHz and 80' resolution, is dominated by the uncertainty on the Galactic emission zero level in total intensity, in particular towards diffuse lines of sight at high Galactic latitudes. Furthermore, the inverse behaviour between p and S found earlier is seen to be present at high latitudes. This follows the S ∝ p -1 relationship expected from models of the polarized sky (including numerical simulations of magnetohydrodynamical turbulence) that include effects from only the topology of the turbulent magnetic field, but otherwise have uniform alignment and dust properties. Thus, the statistical properties of p, ψ, and S for the most part reflect the structure of the Galactic magnetic field. Nevertheless, we search for potential signatures of varying grain alignment and dust properties. First, we analyse the product map S × p, looking for residual trends. While the polarization fraction p decreases by a factor of 3-4 between NH = 10 20 cm -2 and NH = 2 x 10 22 cm -2 , out of the Galactic plane, this product S × p only decreases by about 25%. Because S is independent of the grain alignment efficiency, this demonstrates that the systematic decrease in p with N H is determined mostly by the magnetic-field structure and not by a drop in grain alignment. This systematic trend is observed both in the diffuse interstellar medium (ISM) and in molecular clouds of the Gould Belt. Second, we look for a dependence of polarization properties on the dust temperature, as we would expect from the radiative alignment torque (RAT) theory. We find no systematic trend of S × p with the dust temperature T d , whether in the diffuse ISM or in the molecular clouds of the Gould Belt. In the diffuse ISM, lines of sight with high polarization fraction p and low polarization angle dispersion S tend, on the contrary, to have colder dust than lines of sight with low p and high S . We also compare the Planck thermal dust polarization with starlight polarization data in the visible at high Galactic latitudes. The agreement in polarization angles is remarkable, and is consistent with what we expect from the noise and the observed dispersion of polarization angles in the visible on the scale of the Planck beam. The two polarization emission-to-extinction ratios, R P/p and R S/V , which primarily characterize dust optical properties, have only a weak dependence on the column density, and converge towards the values previously determined for translucent lines of sight. We also determine an upper limit for the polarization fraction in extinction, p V /E(B - V), of 13% at high Galactic latitude, compatible with the polarization fraction p ≈ 20% observed at 353 GHz. Taken together, these results provide strong constraints for models of Galactic dust in diffuse gas.

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