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Now Broadcasting in Planck Definition

If reality has finite information content, space has finite fidelity. The quantum wave function that encodes spatial relationships may be limited to information that can be transmitted in a "Planck broadcast", with a bandwidth given by the inverse of the Planck time, about $2\times 10^{43}$ bits per second. Such a quantum system can resemble classical space-time on large scales, but locality emerges only gradually and imperfectly. Massive bodies are never perfectly at rest, but very slightly and slowly fluctuate in transverse position, with a spectrum of variation given by the Planck time. This distinctive new kind of noise associated with quantum geometry would not have been noticed up to now, but may be detectable in a new kind of experiment.

Hogan, Craig↗

Predictive drug dosage control through a Fokker–Planck observer

During the years, various techniques have been presented for optimal control of tumor growth for which its stochastic behavior has rarely been considered. This article uses the well-known Gompertz stochastic model, for describing tumor growth, and by receding horizon model predictive control (RH-MPC) scheme computes the drug dosage for minimizing the tumor-cell population. To do this, a predictive control problem is defined based on the difference between the probability density function of tumor-cell population and the desired probability density function. In the model, both the drug dosage limitation and the Fokker–Planck equation have been considered as constraints. By solving this problem, the drug dosage which is considered as an external input to tumor model, is computed. In this article, the Fokker–Planck equation is used (1) as a nonlinear observer of probability density function of tumor-cell population and (2) a mapping vehicle from stochastic to deterministic domain. The Fokker–Planck equation is written for the Gompertz stochastic model of tumor growth. The equation is then solved through the path integral method. In this way, the probability density function of tumor-cell population, which contains the entire stochastic characteristics of the tumor growth, is obtained for any instance of time. The simulation results have also been presented for the evaluation of the suggested approach. The results show that the tumor-cell population can be controlled within a number of time windows (15 time windows in our case study) if an appropriate desired PDF is selected.

97 MATHEMATICS AND COMPUTING↗

Simultaneous Planck , Swift , and Fermi observations of X-ray and γ -ray selected blazars

We present simultaneous Planck, Swift, Fermi, and ground-based data for 105 blazars belonging to three samples with flux limits in the soft X-ray, hard X-ray, and γ-ray bands, with additional 5GHz flux-density limits to ensure a good probability of a Planck detection. We compare our results to those of a companion paper presenting simultaneous Planck and multi-frequency observations of 104 radio-loud northern active galactic nuclei selected at radio frequencies. While we confirm several previous results, our unique data set allows us to demonstrate that the selection method strongly influences the results, producing biases that cannot be ignored. Almost all the BL Lac objects have been detected by the Fermi Large AreaTelescope (LAT), whereas 30% to 40% of the flat-spectrum radio quasars (FSRQs) in the radio, soft X-ray, and hard X-ray selected samples are still below the γ-ray detection limit even after integrating 27 months of Fermi-LAT data. The radio to sub-millimetre spectral slope of blazars is quite flat, with >α> ~ 0 up to about 70GHz, above which it steepens to <α> ~ -0.65. The BL Lacs have significantly flatter spectra than FSRQs at higher frequencies. The distribution of the rest-frame synchrotron peak frequency (ν peak S ) in the spectral energy distribution (SED) of FSRQs is the same in all the blazar samples with <ν peak S > = 10 13.1 ± 0.1 Hz, while the mean inverse Compton peak frequency, >ν peak IC >, ranges from 1021 to 1022 Hz. The distributions of ν peak S and ν peak IC of BL Lacs are much broader and are shifted to higher energies than those of FSRQs; their shapes strongly depend on the selection method. The Compton dominance of blazars, defined as the ratio of the inverse Compton to synchrotron peak luminosities, ranges from less than 0.2 to nearly 100, with only FSRQs reaching values larger than about 3. Its distribution is broad and depends strongly on the selection method, with γ-ray selected blazars peaking at ~7 or more, and radio-selected blazars at values close to 1, thus implying that the common assumption that the blazar power budget is largely dominated by high-energy emission is a selection effect. A comparison of our multi-frequency data with theoretical predictions shows that simple homogeneous SSC models cannot explain the simultaneous SEDs of most of the γ-ray detected blazars in all samples. The SED of the blazars that were not detected by Fermi-LAT may instead be consistent with SSC emission. Our data challenge the correlation between bolometric luminosity and ν peak S predicted by the blazar sequence.

79 ASTRONOMY AND ASTROPHYSICS↗

Planck intermediate results: XI. The gas content of dark matter halos: the Sunyaev-Zeldovich-stellar mass relation for locally brightest galaxies

We present the scaling relation between Sunyaev-Zeldovich (SZ) signal and stellar mass for almost 260,000 locally brightest galaxies (LBGs) selected from the Sloan Digital Sky Survey (SDSS). These are predominantly the central galaxies of their dark matter halos. We calibrate the stellar-to-halo mass conversion using realistic mock catalogues based on the Millennium Simulation. Applying a multi-frequency matched filter to the Planck data for each LBG, and averaging the results in bins of stellar mass, we measure the mean SZ signal down to M * &sim; 2 × 10 11 M &odot; , with a clear indication of signal at even lower stellar mass. We derive the scaling relation between SZ signal and halo mass by assigning halo properties from our mock catalogues to the real LBGs and simulating the Planck observation process. This relation shows no evidence for deviation from a power law over a halo mass range extending from rich clusters down to M 500 ~ 2 × 10 13 M &odot; , and there is a clear indication of signal down to M 500 ~ 4 × 10 12 M &odot; . Planck's SZ detections in such low-mass halos imply that about a quarter of all baryons have now been seen in the form of hot halo gas, and that this gas must be less concentrated than the dark matter in such halos in order to remain consistent with X-ray observations. At the high-mass end, the measured SZ signal is 20% lower than found from observations of X-ray clusters, a difference consistent with the magnitude of Malmquist bias effects that were previously estimated for the X-ray sample.

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Planck 2013 results. XIX. The integrated Sachs-Wolfe effect

Based on cosmic microwave background (CMB) maps from the 2013 Planck Mission data release, this paper presents the detection of the integrated Sachs-Wolfe (ISW) effect, that is, the correlation between the CMB and large-scale evolving gravitational potentials. The significance of detection ranges from 2 to 4σ, depending on which method is used. We investigated three separate approaches, which essentially cover all previous studies, and also break new ground. (i) We correlated the CMB with the Planck reconstructed gravitational lensing potential (for the first time). This detection was made using the lensing-induced bispectrum between the low-&ell; and high-&ell; temperature anisotropies; the correlation between lensing and the ISW effect has a significance close to 2.5σ. (ii) We cross-correlated with tracers of large-scale structure, which yielded a significance of about 3σ, based on a combination of radio (NVSS) and optical (SDSS) data. (iii) We used aperture photometry on stacked CMB fields at the locations of known large-scale structures, which yielded and confirms a 4σ signal, over a broader spectral range, when using a previously explored catalogue, but shows strong discrepancies in amplitude and scale when compared with expectations. More recent catalogues give more moderate results that range from negligible to 2.5σ at most, but have a more consistent scale and amplitude, the latter being still slightly higher than what is expected from numerical simulations within ΛCMD. Where they can be compared, these measurements are compatible with previous work using data from WMAP, where these scales have been mapped to the limits of cosmic variance. Planck's broader frequency coverage allows for better foreground cleaning and confirms that the signal is achromatic, which makes it preferable for ISW detection. As a final step we used tracers of large-scale structure to filter the CMB data, from which we present maps of the ISW temperature perturbation. Lastly, these results provide complementary and independent evidence for the existence of a dark energy component that governs the currently accelerated expansion of the Universe.

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Planck 2013 results. XXIV. Constraints on primordial non-Gaussianity

The Planck nominal mission cosmic microwave background (CMB) maps yield unprecedented constraints on primordial non-Gaussianity (NG). Using three optimal bispectrum estimators, separable template-fitting (KSW), binned, and modal, we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result f NL local = 2.7 ± 5.8, f NL equil = -42 ± 75, and f NL orth = -25 ± 39 (68% CL statistical). Non-Gaussianity is detected in the data; using skew-C &ell; statistics we find a nonzero bispectrum from residual point sources, and the integrated-Sachs-Wolfe-lensing bispectrum at a level expected in the ΛCDM scenario. The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are confirmed by skew-C &ell; , wavelet bispectrum and Minkowski functional estimators. Beyond estimates of individual shape amplitudes, we present model-independent, three-dimensional reconstructions of the Planck CMB bispectrum and thus derive constraints on early-Universe scenarios that generate primordial NG, including general single-field models of inflation, excited initial states (non-Bunch-Davies vacua), and directionally-dependent vector models. We provide an initial survey of scale-dependent feature and resonance models. These results bound both general single-field and multi-field model parameter ranges, such as the speed of sound, c s ≥ 0.02 (95% CL), in an effective field theory parametrization, and the curvaton decay fraction r D ≥ 0.15 (95% CL). The Planck data significantly limit the viable parameter space of the ekpyrotic/cyclic scenarios. The amplitude of the four-point function in the local model τ NL < 2800 (95% CL). Taken together, these constraints represent the highest precision tests to date of physical mechanisms for the origin of cosmic structure.

79 ASTRONOMY AND ASTROPHYSICS↗

Planck 2013 results. X. HFI energetic particle effects: Characterization, removal, and simulation

We describe the detection, interpretation, and removal of the signal resulting from interactions of high energy particles with the Planck High Frequency Instrument (HFI). There are two types of interactions: heating of the 0.1 K bolometer plate; and glitches in each detector time stream. The transient responses to detector glitch shapes are not simple single-pole exponential decays and fall into three families. The glitch shape for each family has been characterized empirically in flight data and these shapes have been used to remove glitches from the detector time streams. The spectrum of the count rate per unit energy is computed for each family and a correspondence is made to the location on the detector of the particle hit. Most of the detected glitches are from Galactic protons incident on the die frame supporting the micro-machined bolometric detectors. In the Planck orbit at L2, the particle flux is around 5 cm -2 s -1 and is dominated by protons incident on the spacecraft with energy >39 MeV, at a rate of typically one event per second per detector. Different categories of glitches have different signatures in the time stream. Two of the glitch types have a low amplitude component that decays over nearly 1 s. This component produces excess noise if not properly removed from the time-ordered data. We have used a glitch detection and subtraction method based on the joint fit of population templates. The application of this novel glitch subtraction method removes excess noise from the time streams. Using realistic simulations, we find that this method does not introduce signal bias into the Planck data.

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Planck 2013 results. XXV. Searches for cosmic strings and other topological defects

Planck data have been used to provide stringent new constraints on cosmic strings and other defects. We describe forecasts of the CMB power spectrum induced by cosmic strings, calculating these from network models and simulations using line-of-sight Boltzmann solvers. We have studied Nambu-Goto cosmic strings, as well as field theory strings for which radiative effects are important, thus spanning the range of theoretical uncertainty in the underlying strings models. We have added the angular power spectrum from strings to that for a simple adiabatic model, with the extra fraction defined as f 10 at multipole = 10. This parameter has been added to the standard six parameter fit using COSMOMC with flat priors. For the Nambu-Goto string model, we have obtained a constraint on the string tension of G μ/c 2 < 1.5 × 10 -7 and f 10 < 0.015 at 95% confidence that can be improved to G μ/c 2 < 1.3 × 10-7 and f 10 < 0.010 on inclusion of high-&ell; CMB data. For the Abelian-Higgs field theory model we find, G μ AH /c 2 < 3.2 × 10 -7 and f 10 < 0.028. The marginalised likelihoods for f 10 and in the f 10 -Ω b h 2 plane are also presented. We have additionally obtained comparable constraints on f 10 for models with semilocal strings and global textures. In terms of the effective defect energy scale these are somewhat weaker at G μ/c 2 < 1.1 × 10 -6 . We have made complementarity searches for the specific non-Gaussian signatures of cosmic strings, calibrating with all-sky Planck resolution CMB maps generated from networks of post-recombination strings. We have validated our non-Gaussian searches using these simulated maps in a Planck -realistic context, estimating sensitivities of up to Δ G μ/c 2 &approx; 4 × 10 -7 . We have obtained upper limits on the string tension at 95% confidence of G μ/c 2 < 9.0 × 10 -7 with modal bispectrum estimation and G μ/c 2 < 7.8 × 10 -7 for real space searches with Minkowski functionals. These are conservative upper bounds because only post-recombination string contributions have been included in the non-Gaussian analysis.

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

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 &ell; ~ 150 to 2500. The bispectrum due to the clustering of dusty, star-forming galaxies is measured from &ell; ~ 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 &odot; ) = 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.

79 ASTRONOMY AND ASTROPHYSICS↗

Planck intermediate results. XXII. Frequency dependence of thermal emission from Galactic dust in intensity and polarization

Planck has mapped the intensity and polarization of the sky at microwave frequencies with unprecedented sensitivity. We use these data to characterize the frequency dependence of dust emission. We utilize the Planck 353 GHz I, Q, and U Stokes maps as dust templates, and cross-correlate them with the Planck and WMAP data at 12 frequencies from 23 to 353 GHz, over circular patches with 10° radius. The cross-correlation analysis is performed for both intensity and polarization data in a consistent manner. The conclusions are corrected for the chance correlation between the templates and the anisotropies of the cosmic microwave background. We use a mask that focuses our analysis on the diffuse interstellar medium at intermediate Galactic latitudes. We determine the spectral indices of dust emission in intensity and polarization between 100 and 353 GHz, for each sky patch. Both indices are found to be remarkably constant over the sky. The mean values, 1.59 ± 0.02 for polarization and 1.51 ± 0.01 for intensity, for a mean dust temperature of 19.6 K, are close, but significantly different (3.6σ). We determine the mean spectral energy distribution (SED) of the microwave emission, correlated with the 353 GHz dust templates, by averaging the results of the correlation over all sky patches. We find that the mean SED increases for decreasing frequencies at ν< 60 GHz for both intensity and polarization. The rise of the polarization SED towards low frequencies may be accounted for by a synchrotron component correlated with dust, with no need for any polarization of the anomalous microwave emission. We use a spectral model to separate the synchrotron and dust polarization and to characterize the spectral dependence of the dust polarization fraction. The polarization fraction (p) of the dust emission decreases by (21 ± 6)% from 353 to 70 GHz. We discuss this result within the context of existing dust models. The decrease in p could indicate differences in polarization efficiency among components of interstellar dust (e.g., carbon versus silicate grains). Our observational results provide inputs to quantify and optimize the separation between Galactic and cosmological polarization.

79 ASTRONOMY AND ASTROPHYSICS↗

Planck intermediate results: XXIV. Constraints on variations in fundamental constants*

Any variation in the fundamental physical constants, more particularly in the fine structure constant, α, or in the mass of the electron, me, affects the recombination history of the Universe and cause an imprint on the cosmic microwave background angular power spectra. We demonstrate that the Planck data allow one to improve the constraint on the time variation of the fine structure constant at redshift z &sim; 10 3 by about a factor of 5 compared to WMAP data, as well as to break the degeneracy with the Hubble constant, H 0 . In addition to α, we can set a constraint on the variation in the mass of the electron, me, and in the simultaneous variation of the two constants. We study in detail the degeneracies between fundamental constants and the cosmological parameters, in order to compare the limits obtained from Planck and WMAP and to determine the constraining power gained by including other cosmological probes. We conclude that independent time variations of the fine structure constant and of the mass of the electron are constrained by Planck to Δα/α = (3.6 ± 3.7) × 10 -3 and Δme/me = (4 ± 11) × 10 -3 at the 68% confidence level. We also investigate the possibility of a spatial variation of the fine structure constant. The relative amplitude of a dipolar spatial variation in α (corresponding to a gradient across our Hubble volume) is constrained to be δα/α = (-2.4 ± 3.7) × 10 -2 .

79 ASTRONOMY AND ASTROPHYSICS↗

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 study 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 ∝ ℓ α , with exponents α 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 β 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 ≡ ℓ(ℓ+1)C ℓ BB /(2π) of 1.32 × 10 -2 μK CMB 2 over the multipole range of the primordial recombination bump (40 <ℓ< 120); the statistical uncertainty is ± 0.29 × 10 -2 μK CMB 2 and there is an additional uncertainty (+0.28, -0.24) × 10 -2 μK CMB 2 from the extrapolation. Finally, 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.

79 ASTRONOMY AND ASTROPHYSICS↗

Planck 2015 results: VII. High Frequency Instrument data processing: Time-ordered information and beams

The Planck High Frequency Instrument (HFI) has observed the full sky at six frequencies (100, 143, 217, 353, 545, and 857 GHz) in intensity and at four frequencies in linear polarization (100, 143, 217, and 353 GHz). In order to obtain sky maps, the time-ordered information (TOI) containing the detector and pointing samples must be processed and the angular response must be assessed. The full mission TOI is included in the Planck 2015 release. This study describes the HFI TOI and beam processing for the 2015 release. HFI calibration and map making are described in a companion paper. The main pipeline has been modified since the last release (2013 nominal mission in intensity only), by including a correction for the nonlinearity of the warm readout and by improving the model of the bolometer time response. The beam processing is an essential tool that derives the angular response used in all the Planck science papers and we report an improvement in the effective beam window function uncertainty of more than a factor of 10 relative to the2013 release. Noise correlations introduced by pipeline filtering function are assessed using dedicated simulations. Finally, angular cross-power spectra using data sets that are decorrelated in time are immune to the main systematic effects.

79 ASTRONOMY AND ASTROPHYSICS↗

Planck 2015 results: X. Diffuse component separation: Foreground maps

We report that Planck has mapped the microwave sky in temperature over nine frequency bands between 30 and 857 GHz and in polarization over seven frequency bands between 30 and 353 GHz in polarization. In this paper we consider the problem of diffuse astrophysical component separation, and process these maps within a Bayesian framework to derive an internally consistent set of full-sky astrophysical component maps. Component separation dedicated to cosmic microwave background (CMB) reconstruction is described in a companion paper. For the temperature analysis, we combine the Planck observations with the 9-yr Wilkinson Microwave Anisotropy Probe (WMAP) sky maps and the Haslam et al. 408 MHz map, to derive a joint model of CMB, synchrotron, free-free, spinning dust, CO, line emission in the 94 and 100 GHz channels, and thermal dust emission. Full-sky maps are provided for each component, with an angular resolution varying between 7.5 and 1deg. Global parameters (monopoles, dipoles, relative calibration, and bandpass errors) are fitted jointly with the sky model, and best-fit values are tabulated. For polarization, the model includes CMB, synchrotron, and thermal dust emission. These models provide excellent fits to the observed data, with rms temperature residuals smaller than 4μK over 93% of the sky for all Planck frequencies up to 353 GHz, and fractional errors smaller than 1% in the remaining 7% of the sky. The main limitations of the temperature model at the lower frequencies are internal degeneracies among the spinning dust, free-free, and synchrotron components; additional observations from external low-frequency experiments will be essential to break these degeneracies. The main limitations of the temperature model at the higher frequencies are uncertainties in the 545 and 857 GHz calibration and zero-points. For polarization, the main outstanding issues are instrumental systematics in the 100–353 GHz bands on large angular scales in the form of temperature-to-polarization leakage, uncertainties in the analogue-to-digital conversion, and corrections for the very long time constant of the bolometer detectors, all of which are expected to improve in the near future.

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Planck 2015 results: V. LFI calibration

In this paper, we present a description of the pipeline used to calibrate the Planck Low Frequency Instrument (LFI) timelines into thermodynamic temperatures for the Planck 2015 data release, covering four years of uninterrupted operations. As in the 2013 data release, our calibrator is provided by the spin-synchronous modulation of the cosmic microwave background dipole, but we now use the orbital component, rather than adopting the Wilkinson Microwave Anisotropy Probe (WMAP) solar dipole. This allows our 2015 LFI analysis to provide an independent Solar dipole estimate, which is in excellent agreement with that of HFI and within 1σ (0.3% in amplitude) of the WMAP value. This 0.3% shift in the peak-to-peak dipole temperature from WMAP and a general overhaul of the iterative calibration code increases the overall level of the LFI maps by 0.45% (30 GHz), 0.64% (44 GHz), and 0.82% (70 GHz) in temperature with respect to the 2013 Planck data release, thus reducing the discrepancy with the power spectrum measured by WMAP. We estimate that the LFI calibration uncertainty is now at the level of 0.20% for the 70 GHz map, 0.26% for the 44 GHz map, and 0.35% for the 30 GHz map. Finally, we provide a detailed description of the impact of all the changes implemented in the calibration since the previous data release.

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Planck intermediate results: XLV. Radio spectra of northern extragalactic radio sources

Continuum spectra covering centimetre to submillimetre wavelengths are presented in this paper for a northern sample of 104 extragalactic radio sources, mainly active galactic nuclei, based on four-epoch Planck data. The nine Planck frequencies, from 30 to 857 GHz, are complemented by a set of simultaneous ground-based radio observations between 1.1 and 37 GHz. The single-survey Planck data confirm that the flattest high-frequency radio spectral indices are close to zero, indicating that the original accelerated electron energy spectrum is much harder than commonly thought, with power-law index around 1.5 instead of the canonical 2.5. The radio spectra peak at high frequencies and exhibit a variety of shapes. For a small set of low-z sources, we find a spectral upturn at high frequencies, indicating the presence of intrinsic cold dust. Finally, variability can generally be approximated by achromatic variations, while sources with clear signatures of evolving shocks appear to be limited to the strongest outbursts.

79 ASTRONOMY AND ASTROPHYSICS↗

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. In this paper, 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 C BB ℓ 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. In conclusion, 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.

79 ASTRONOMY AND ASTROPHYSICS↗

Planck 2018 results - IV. Diffuse component separation

We present full-sky maps of the cosmic microwave background (CMB) and polarized synchrotron and thermal dust emission, derived from the third set of Planck frequency maps. These products have significantly lower contamination from instrumental systematic effects than previous versions. The methodologies used to derive these maps follow closely those described in earlier papers, adopting four methods (Commander, NILC, SEVEM, and SMICA) to extract the CMB component, as well as three methods (Commander, GNILC, and SMICA) to extract astrophysical components. Our revised CMB temperature maps agree with corresponding products in the Planck 2015 delivery, whereas the polarization maps exhibit significantly lower large-scale power, reflecting the improved data processing described in companion papers; however, the noise properties of the resulting data products are complicated, and the best available end-to-end simulations exhibit relative biases with respect to the data at the few percent level. Using these maps, we are for the first time able to fit the spectral index of thermal dust independently over 3° regions. We derive a conservative estimate of the mean spectral index of polarized thermal dust emission of β d = 1.55 ± 0.05, where the uncertainty marginalizes both over all known systematic uncertainties and different estimation techniques. For polarized synchrotron emission, we find a mean spectral index of β s = -3.1 ± 0.1, consistent with previously reported measurements. We note that the current data processing does not allow for construction of unbiased single-bolometer maps, and this limits our ability to extract CO emission and correlated components. The foreground results for intensity derived in this paper therefore do not supersede corresponding Planck 2015 products. For polarization the new results supersede the corresponding 2015 products in all respects.

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