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In the original version, the bounds given in Eqs. (87a) and (87b) on the contribution to the early-time optical depth, (15,30), contained a numerical error in deriving the 95th percentile from the Monte Carlo samples. The corrected 95% upper bounds are: τ(15,30) < 0:018 (lowE, flat τ(15, 30), FlexKnot), (1) τ(15, 30) < 0:023 (lowE, flat knot, FlexKnot): (2) These bounds are a factor of 3 larger than the originally reported results. Consequently, the new bounds do not significantly improve upon previous results from Planck data presented in Millea & Bouchet (2018) as was stated, but are instead comparable. Equations (1) and (2) give results that are now similar to those of Heinrich & Hu (2021), who used the same Planck 2018 data to derive a 95% upper bound of 0.020 using the principal component analysis (PCA) model and uniform priors on the PCA mode amplitudes.

The largest temperature anisotropy in the cosmic microwave background (CMB) is the dipole, which has been measured with increasing accuracy for more than three decades, particularly with the Planck satellite. The simplest interpretation of the dipole is that it is due to our motion with respect to the rest frame of the CMB. Since current CMB experiments infer temperature anisotropies from angular intensity variations, the dipole modulates the temperature anisotropies with the same frequency dependence as the thermal Sunyaev-Zeldovich (tSZ) effect. We present the first, and significant, detection of this signal in the tSZ maps and find that it is consistent with direct measurements of the CMB dipole, as expected. The signal contributes power in the tSZ maps, which is modulated in a quadrupolar pattern, and we estimate its contribution to the tSZ bispectrum, noting that it contributes negligible noise to the bispectrum at relevant scales.

We report a measurement of the E-mode polarization power spectrum of the cosmic microwave background (CMB) using 150 GHz data taken from 2014 July to 2016 December with the POLARBEAR experiment. We reach an effective polarization map noise level of 32 mK-arcmin across an observation area of 670 square degrees. We measure the EE power spectrum over the angular multipole range 500 ≤ ℓ < 3000, tracing the third to seventh acoustic peaks with high sensitivity. The statistical uncertainty on E-mode bandpowers is ∼2.3 μK2 at ℓ ∼ 1000, with a systematic uncertainty of 0.5 mK2. The data are consistent with the standard ΛCDM cosmological model with a probability-to-exceed of 0.38. We combine recent CMB E-mode measurements and make inferences about cosmological parameters in ΛCDM as well as in extensions to ΛCDM. Adding the ground-based CMB polarization measurements to the Planck data set reduces the uncertainty on the Hubble constant by a factor of 1.2 to H0 = 67.20 ±0.57 km s- Mpc- 1 1. When allowing the number of relativistic species (Neff ) to vary, we find Neff = 2.94 ±0.16, which is in good agreement with the standard value of 3.046. Instead allowing the primordial helium abundance (YHe) to vary, the data favor YHe = 0.248 ±0.012. This is very close to the expectation of 0.2467 from big bang nucleosynthesis. When varying both YHe and Neff , we find Neff = 2.70 ±0.26 and YHe = 0.262 ±0.015.

We present the NPIPE processing pipeline, which produces calibrated frequency maps in temperature and polarization from data from the Planck Low Frequency Instrument (LFI) and High Frequency Instrument (HFI) using high-performance computers. NPIPE represents a natural evolution of previous Planck analysis efforts, and combines some of the most powerful features of the separate LFI and HFI analysis pipelines. For example, following the LFI 2018 processing procedure, NPIPE uses foreground polarization priors during the calibration stage in order to break scanning-induced degeneracies. Similarly, NPIPE employs the HFI 2018 time-domain processing methodology to correct for bandpass mismatch at all frequencies. In addition, NPIPE introduces several improvements, including, but not limited to: inclusion of the 8% of data collected during repointing manoeuvres; smoothing of the LFI reference load data streams; in-flight estimation of detector polarization parameters; and construction of maximally independent detector-set split maps. For component-separation purposes, important improvements include: maps that retain the CMB Solar dipole, allowing for high-precision relative calibration in higher-level analyses; well-defined single-detector maps, allowing for robust CO extraction; and HFI temperature maps between 217 and 857 GHz that are binned into 0′.9 pixels (Nside = 4096), ensuring that the full angular information in the data is represented in the maps even at the highest Planck resolutions. The net effect of these improvements is lower levels of noise and systematics in both frequency and component maps at essentially all angular scales, as well as notably improved internal consistency between the various frequency channels. Based on the NPIPE maps, we present the first estimate of the Solar dipole determined through component separation across all nine Planck frequencies. The amplitude is (3366.6 ± 2.7) μK, consistent with, albeit slightly higher than, earlier estimates. From the large-scale polarization data, we derive an updated estimate of the optical depth of reionization of τ = 0.051 ± 0.006, which appears robust with respect to data and sky cuts. There are 600 complete signal, noise and systematics simulations of the full-frequency and detector-set maps. As a Planck first, these simulations include full time-domain processing of the beam-convolved CMB anisotropies. The release of NPIPE maps and simulations is accompanied with a complete suite of raw and processed time-ordered data and the software, scripts, auxiliary data, and parameter files needed to improve further on the analysis and to run matching simulations.

We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E-mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results: flocalNL= -0.9 ± 5.1; fequilNL= -26 ± 47; and forthoNL= -38 ± 24 (68% CL, statistical). These results include low-multipole (4 ≤ ℓ < 40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarizationonly bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The nonprimordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5σ. Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of the Planck CMB bispectrum. Our final constraint on the local primordial trispectrum shape is glocalNL= (-5.8 ± 6.5) × 104(68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the CDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations.

Analysis of the Planck 2018 data set indicates that the statistical properties of the cosmic microwave background (CMB) temperature anisotropies are in excellent agreement with previous studies using the 2013 and 2015 data releases. In particular, they are consistent with the Gaussian predictions of the ΛCDM cosmological model, yet also confirm the presence of several so-called "anomalies"on large angular scales. The novelty of the current study, however, lies in being a first attempt at a comprehensive analysis of the statistics of the polarization signal over all angular scales, using either maps of the Stokes parameters, Q and U, or the E-mode signal derived from these using a new methodology (which we describe in an appendix). Although remarkable progress has been made in reducing the systematic effects that contaminated the 2015 polarization maps on large angular scales, it is still the case that residual systematics (and our ability to simulate them) can limit some tests of non-Gaussianity and isotropy. However, a detailed set of null tests applied to the maps indicates that these issues do not dominate the analysis on intermediate and large angular scales (i.e., ℓ 400). In this regime, no unambiguous detections of cosmological non-Gaussianity, or of anomalies corresponding to those seen in temperature, are claimed. Notably, the stacking of CMB polarization signals centred on the positions of temperature hot and cold spots exhibits excellent agreement with the ΛCDM cosmological model, and also gives a clear indication of how Planck provides state-of-the-art measurements of CMB temperature and polarization on degree scales.

We present a final description of the data-processing pipeline for the Planck Low Frequency Instrument (LFI), implemented for the 2018 data release. Several improvements have been made with respect to the previous release, especially in the calibration process and in the correction of instrumental features such as the effects of nonlinearity in the response of the analogue-to-digital converters. We provide a brief pedagogical introduction to the complete pipeline, as well as a detailed description of the important changes implemented. Self-consistency of the pipeline is demonstrated using dedicated simulations and null tests. We present the final version of the LFI full sky maps at 30, 44, and 70 GHz, both in temperature and polarization, together with a refined estimate of the solar dipole and a final assessment of the main LFI instrumental parameters.

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 < 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 θMC, ωc, ωb, and H0 by more than 30%, and ns 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 0.5σ level on the λCDM parameters, as well as classical single-parameter extensions for the joint likelihood (to be compared to the 0.3σ 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 < 800 and ℓ > 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.

This paper presents the High Frequency Instrument (HFI) data processing procedures for the Planck 2018 release. Major improvements in mapmaking have been achieved since the previous Planck 2015 release, many of which were used and described already in an intermediate paper dedicated to the Planck polarized data at low multipoles. These improvements enabled the first significant measurement of the reionization optical depth parameter using Planck-HFI data. This paper presents an extensive analysis of systematic effects, including the use of end-to-end simulations to facilitate their removal and characterize the residuals. The polarized data, which presented a number of known problems in the 2015 Planck release, are very significantly improved, especially the leakage from intensity to polarization. Calibration, based on the cosmic microwave background (CMB) dipole, is now extremely accurate and in the frequency range 100-353 GHz reduces intensity-to-polarization leakage caused by calibration mismatch. The Solar dipole direction has been determined in the three lowest HFI frequency channels to within one arc minute, and its amplitude has an absolute uncertainty smaller than 0.35 μK, an accuracy of order 10-4. This is a major legacy from the Planck HFI for future CMB experiments. The removal of bandpass leakage has been improved for the main high-frequency foregrounds by extracting the bandpass-mismatch coefficients for each detector as part of the mapmaking process; these values in turn improve the intensity maps. This is a major change in the philosophy of "frequency maps", which are now computed from single detector data, all adjusted to the same average bandpass response for the main foregrounds. End-to-end simulations have been shown to reproduce very well the relative gain calibration of detectors, as well as drifts within a frequency induced by the residuals of the main systematic effect (analogue-to-digital convertor non-linearity residuals). Using these simulations, we have been able to measure and correct the small frequency calibration bias induced by this systematic effect at the 10-4 level. There is no detectable sign of a residual calibration bias between the first and second acoustic peaks in the CMB channels, at the 10-3 level.

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 βd = 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 βs = -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.

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 «. 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 « found earlier is seen to be present at high latitudes. This follows the «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 « 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 « × p, looking for residual trends. While the polarization fraction p decreases by a factor of 3-4 between NH = 1020 cm-2 and NH = 2 × 1022 cm-2, out of the Galactic plane, this product « × p only decreases by about 25%. Because « is independent of the grain alignment efficiency, this demonstrates that the systematic decrease in p with NH 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 « × p with the dust temperature Td, 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 « tend, on the contrary, to have colder dust than lines of sight with low p and high «. 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, RP/p and RS/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, pV/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.

We report on the implications for cosmic inflation of the 2018 release of the Planck cosmic microwave background (CMB) anisotropy measurements. The results are fully consistent with those reported using the data from the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles. Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be ns = 0.9649 ± 0.0042 at 68% CL. We find no evidence for a scale dependence of ns, either as a running or as a running of the running. The Universe is found to be consistent with spatial flatness with a precision of 0.4% at 95% CL by combining Planck with a compilation of baryon acoustic oscillation data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, r0.002 < 0.10, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain r0.002 < 0.056. In the framework of standard single-field inflationary models with Einstein gravity, these results imply that: (a) the predictions of slow-roll models with a concave potential, V″(φ) < 0, are increasingly favoured by the data; and (b) based on two different methods for reconstructing the inflaton potential, we find no evidence for dynamics beyond slow roll. Three different methods for the non-parametric reconstruction of the primordial power spectrum consistently confirm a pure power law in the range of comoving scales 0.005 Mpc-1 k 0.2 Mpc-1. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectra. For the case of oscillatory features that are logarithmic or linear in k, this result is further strengthened by a new combined analysis including the Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions for the cosmological fluctuations. In correlated, mixed adiabatic and isocurvature models, the non-adiabatic contribution to the observed CMB temperature variance is constrained to 1.3%, 1.7%, and 1.7% at 95% CL for cold dark matter, neutrino density, and neutrino velocity, respectively. Planck power spectra plus lensing set constraints on the amplitude of compensated cold dark matter-baryon isocurvature perturbations that are consistent with current complementary measurements. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadupolar modulation of the primordial fluctuations. However, the polarization data do not support physical models for a scale-dependent dipolar modulation. All these findings support the key predictions of the standard single-field inflationary models, which will be further tested by future cosmological observations.

We present cosmological parameter results from the final full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters. Improved modelling of the small-scale polarization leads to more robust constraints on many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base ΛCDM"in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density ωch2 = 0.120 ± 0.001, baryon density ωbh2 = 0.0224 ± 0.0001, scalar spectral index ns = 0.965 ± 0.004, and optical depth τ = 0.054 ± 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100θ∗ = 1.0411 ± 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H0 = (67.4 ± 0.5) km s-1 Mpc-1; matter density parameter ωm = 0.315 ± 0.007; and matter fluctuation amplitude σ8 = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be Neff = 2.99 ± 0.17, in agreement with the Standard Model prediction Neff = 3.046, and find that the neutrino mass is tightly constrained to mν < 0.12 eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2σ, which pulls some parameters that affect the lensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, ωK = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = -1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r0.002 < 0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey's combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6σ, tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data.

We present measurements of the cosmic microwave background (CMB) lensing potential using the final Planck 2018 temperature and polarization data. Using polarization maps filtered to account for the noise anisotropy, we increase the significance of the detection of lensing in the polarization maps from 5σ to 9σ. Combined with temperature, lensing is detected at 40σ. We present an extensive set of tests of the robustness of the lensingpotential power spectrum, and construct a minimum-variance estimator likelihood over lensing multipoles 8 ≤ L ≤ 400 (extending the range to lower L compared to 2015), which we use to constrain cosmological parameters. We find good consistency between lensing constraints and the results from the Planck CMB power spectra within the σCDM model. Combined with baryon density and other weak priors, the lensing analysis alone constrains σ8Ω0.25m= 0.589 ± 0.020 (1σ errors). Also combining with baryon acoustic oscillation data, we find tight individual parameter constraints, σ8 = 0.811 ± 0.019, H0 = 67.9+1.2-1.3km s-1Mpc-1, and m = 0.303+0.016-0.018. Combining with Planck CMB power spectrum data, we measure σ8 to better than 1% precision, finding σ8 = 0.811 ± 0.006. CMB lensing reconstruction data are complementary to galaxy lensing data at lower redshift, having a different degeneracy direction in σ8 - m space; we find consistency with the lensing results from the Dark Energy Survey, and give combined lensing-only parameter constraints that are tighter than joint results using galaxy clustering. Using the Planck cosmic infrared background (CIB) maps as an additional tracer of high-redshift matter, we make a combined Planck-only estimate of the lensing potential over 60% of the sky with considerably more small-scale signal.We additionally demonstrate delensing of the Planck power spectra using the joint and individual lensing potential estimates, detecting a maximum removal of 40% of the lensing-induced power in all spectra. The improvement in the sharpening of the acoustic peaks by including both CIB and the quadratic lensing reconstruction is detected at high significance.

The study of polarized dust emission has become entwined with the analysis of the cosmic microwave background (CMB) polarization in the quest for the curl-like B-mode polarization from primordial gravitational waves and the low-multipole E-mode polarization associated with the reionization of the Universe. We used the new Planck PR3 maps to characterize Galactic dust emission at high latitudes as a foreground to the CMB polarization and use end-to-end simulations to compute uncertainties and assess the statistical significance of our measurements. We present Planck EE, BB, and TE power spectra of dust polarization at 353 GHz for a set of six nested high-Galactic-latitude 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, which for the largest sky region are αEE = -2.42 ± 0.02 and αBB = -2.54 ± 0.02, respectively. The spectra show that the TE correlation and E/B power asymmetry discovered by Planck extend to low multipoles that were not included in earlier Planck polarization papers due to residual data systematics. We also report evidence for a positive TB dust signal. Combining data from Planck and WMAP, we have determined the amplitudes and spectral energy distributions (SEDs) of polarized foregrounds, including the correlation between dust and synchrotron polarized emission, for the six sky regions as a function of multipole. This quantifies the challenge of the component-separation procedure that is required for measuring the low-ℓ reionization CMB E-mode signal and detecting the reionization and recombination peaks of primordial CMB B modes. The SED of polarized dust emission is fit well by a single-temperature modified black-body emission law from 353 GHz to below 70 GHz. For a dust temperature of 19.6 K, the mean dust spectral index for dust polarization is βdP = 1.53±0.02. The difference between indices for polarization and total intensity is βdP-βdI = 0.05±0.03. By fitting multi-frequency cross-spectra between Planck data at 100, 143, 217, and 353 GHz, we examine the correlation of the dust polarization maps across frequency. We find no evidence for a loss of correlation and provide lower limits to the correlation ratio that are tighter than values we derive from the correlation of the 217- and 353 GHz maps alone. If the Planck limit on decorrelation for the largest sky region applies to the smaller sky regions observed by sub-orbital experiments, then frequency decorrelation of dust polarization might not be a problem for CMB experiments aiming at a primordial B-mode detection limit on the tensor-to-scalar ratio r≃ 0.01 at the recombination peak. However, the Planck sensitivity precludes identifying how difficult the component-separation problem will be for more ambitious experiments targeting lower limits on r.

This paper presents the Planck Multi-frequency Catalogue of Non-thermal (i.e. synchrotron-dominated) Sources (PCNT) observed between 30 and 857 GHz by the ESA Planck mission. This catalogue was constructed by selecting objects detected in the full mission all-sky temperature maps at 30 and 143 GHz, with a signal-to-noise ratio (S/N)> 3 in at least one of the two channels after filtering with a particular Mexican hat wavelet. As a result, 29 400 source candidates were selected. Then, a multi-frequency analysis was performed using the Matrix Filters methodology at the position of these objects, and flux densities and errors were calculated for all of them in the nine Planck channels. This catalogue was built using a different methodology than the one adopted for the Planck Catalogue of Compact Sources (PCCS) and the Second Planck Catalogue of Compact Sources (PCCS2), although the initial detection was done with the same pipeline that was used to produce them. The present catalogue is the first unbiased, full-sky catalogue of synchrotron-dominated sources published at millimetre and submillimetre wavelengths and constitutes a powerful database for statistical studies of non-thermal extragalactic sources, whose emission is dominated by the central active galactic nucleus. Together with the full multi-frequency catalogue, we also define the Bright Planck Multi-frequency Catalogue of Non-thermal Sources (PCNTb), where only those objects with a S/N > 4 at both 30 and 143 GHz were selected. In this catalogue 1146 compact sources are detected outside the adopted Planck GAL070 mask; thus, these sources constitute a highly reliable sample of extragalactic radio sources. We also flag the high-significance subsample (PCNThs), a subset of 151 sources that are detected with S/Na, >, 4 in all nine Planck channels, 75 of which are found outside the Planck mask adopted here. The remaining 76 sources inside the Galactic mask are very likely Galactic objects.

Using the Planck full-mission data, we present a detection of the temperature (and therefore velocity) dispersion due to the kinetic Sunyaev-Zeldovich (kSZ) effect from clusters of galaxies. To suppress the primary CMB and instrumental noise we derive a matched filter and then convolve it with the Planck foreground-cleaned "2D-ILC" maps. By using the Meta Catalogue of X-ray detected Clusters of galaxies (MCXC), we determine the normalized rms dispersion of the temperature fluctuations at the positions of clusters, finding that this shows excess variance compared with the noise expectation. We then build an unbiased statistical estimator of the signal, determining that the normalized mean temperature dispersion of 1526 clusters is ((ΔT/T)2) = (1.64 ± 0.48) × 10-11. However, comparison with analytic calculations and simulations suggest that around 0.7 σ of this result is due to cluster lensing rather than the kSZ effect. By correcting this, the temperature dispersion is measured to be ((ΔT/T)2) = (1.35 ± 0.48) × 10-11, which gives a detection at the 2.8 σ level. We further convert uniform-weight temperature dispersion into a measurement of the line-of-sight velocity dispersion, by using estimates of the optical depth of each cluster (which introduces additional uncertainty into the estimate). We find that the velocity dispersion is (υ2) = (123 000 ± 71 000) (km s-1)2, which is consistent with findings from other large-scale structure studies, and provides direct evidence of statistical homogeneity on scales of 600 h-1 Mpc. Our study shows the promise of using cross-correlations of the kSZ effect with large-scale structure in order to constrain the growth of structure.

Measurements of flux density are described for five planets, Mars, Jupiter, Saturn, Uranus, and Neptune, across the six Planck High Frequency Instrument frequency bands (100-857 GHz) and these are then compared with models and existing data. In our analysis, we have also included estimates of the brightness of Jupiter and Saturn at the three frequencies of the Planck Low Frequency Instrument (30, 44, and 70 GHz). The results provide constraints on the intrinsic brightness and the brightness time-variability of these planets. The majority of the planet flux density estimates are limited by systematic errors, but still yield better than 1% measurements in many cases. Applying data from Planck HFI, the Wilkinson Microwave Anisotropy Probe (WMAP), and the Atacama Cosmology Telescope (ACT) to a model that incorporates contributions from Saturn's rings to the planet's total flux density suggests a best fit value for the spectral index of Saturn's ring system of βring = 2.30 ± 0.03 over the 30-1000 GHz frequency range. Estimates of the polarization amplitude of the planets have also been made in the four bands that have polarization-sensitive detectors (100-353 GHz); this analysis provides a 95% confidence level upper limit on Mars's polarization of 1.8, 1.7, 1.2, and 1.7% at 100, 143, 217, and 353 GHz, respectively. The average ratio between the Planck-HFI measurements and the adopted model predictions for all five planets (excluding Jupiter observations for 353 GHz) is 1.004, 1.002, 1.021, and 1.033 for 100, 143, 217, and 353 GHz, respectively. Model predictions for planet thermodynamic temperatures are therefore consistent with the absolute calibration of Planck-HFI detectors at about the three-percent level. We compare our measurements with published results from recent cosmic microwave background experiments. In particular, we observe that the flux densities measured by Planck HFI and WMAP agree to within 2%. These results allow experiments operating in the mm-wavelength range to cross-calibrate against Planck and improve models of radiative transport used in planetary science.

The six parameters of the standard ΛCDM model have best-fit values derived from the Planck temperature power spectrum that are shifted somewhat from the best-fit values derived from WMAP data. These shifts are driven by features in the Planck temperature power spectrum at angular scales that had never before been measured to cosmic-variance level precision. We have investigated these shifts to determine whether they are within the range of expectation and to understand their origin in the data. Taking our parameter set to be the optical depth of the reionized intergalactic medium, the baryon density ωb, the matter density ωm, the angular size of the sound horizon the spectral index of the primordial power spectrum, ns, and Ase-2τ (where As is the amplitude of the primordial power spectrum), we have examined the change in best-fit values between a WMAP-like large angular-scale data set (with multipole moment < 800 in the Planck temperature power spectrum) and an all angular-scale data set (< 2500Planck temperature power spectrum), each with a prior on τ of 0.07 ± 0.02. We find that the shifts, in units of the 1σ expected dispersion for each parameter, are {value of 8.0. We find that this χ2 value is exceeded in 15% of our simulated data sets, and that a parameter deviates by more than 2.2σ in 9% of simulated data sets, meaning that the shifts are not unusually large. Comparing < 800 instead to > 800, or splitting at a different multipole, yields similar results. We examined the < 800 model residuals in the > 800 power spectrum data and find that the features there that drive these shifts are a set of oscillations across a broad range of angular scales. Although they partly appear similar to the effects of enhanced gravitational lensing, the shifts in ΛCDM parameters that arise in response to these features correspond to model spectrum changes that are predominantly due to non-lensing effects; the only exception is, which, at fixed Ase-2τ, affects the > 800 temperature power spectrum solely through the associated change in As and the impact of that on the lensing potential power spectrum. We also ask, "what is it about the power spectrum at < 800 that leads to somewhat different best-fit parameters than come from the full range?" We find that if we discard the data at < 30, where there is a roughly 2σ downward fluctuation in power relative to the model that best fits the full range, the < 800 best-fit parameters shift significantly towards the < 2500 best-fit parameters. In contrast, including < 30, this previously noted "low-deficit" drives ns up and impacts parameters correlated with ns, such as ωm and H0. As expected, the < 30 data have a much greater impact on the < 800 best fit than on the < 2500 best fit. So although the shifts are not very significant, we find that they can be understood through the combined effects of an oscillatory-like set of high-residuals and the deficit in low-power, excursions consistent with sample variance that happen to map onto changes in cosmological parameters. Finally, we examine agreement between PlanckTT data and two other CMB data sets, namely the Planck lensing reconstruction and the TT power spectrum measured by the South Pole Telescope, again finding a lack of convincing evidence of any significant deviations in parameters, suggesting that current CMB data sets give an internally consistent picture of the ΛCDM model.

We report an improved measurement of the cosmic microwave background B-mode polarization power spectrum with the Polarbear experiment at 150 GHz. By adding new data collected during the second season of observations (2013-2014) to re-analyzed data from the first season (2012-2013), we have reduced twofold the band-power uncertainties. The band powers are reported over angular multipoles 500 ≤ ℓ ≤ 2100, where the dominant B-mode signal is expected to be due to the gravitational lensing of E-modes. We reject the null hypothesis of no B-mode polarization at a confidence of 3.1σ including both statistical and systematic uncertainties. We test the consistency of the measured B-modes with the Λ Cold Dark Matter (ΛCDM) framework by fitting for a single lensing amplitude parameter A L = 0.60 +0.26-0.24(stat)+0.00-0.04 (inst) ± 0.14(foreground) ± 0.04(multi), where A L = 1 relative to the Planck 2015 best-fit model prediction. We obtain ±0.14(foreground) ±0.04(multi), where is the fiducial ΛCDM value.

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 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.

We investigate constraints on cosmic reionization extracted from the Planck cosmic microwave background (CMB) data. We combine the Planck CMB anisotropy data in temperature with the low-multipole polarization data to fit ΛCDM models with various parameterizations of the reionization history. We obtain a Thomson optical depth τ = 0.058 ± 0.012 for the commonly adopted instantaneous reionization model. This confirms, with data solely from CMB anisotropies, the low value suggested by combining Planck 2015 results with other data sets, and also reduces the uncertainties. We reconstruct the history of the ionization fraction using either a symmetric or an asymmetric model for the transition between the neutral and ionized phases. To determine better constraints on the duration of the reionization process, we also make use of measurements of the amplitude of the kinetic Sunyaev-Zeldovich (kSZ) effect using additional information from the high-resolution Atacama Cosmology Telescope and South Pole Telescope experiments. The average redshift at which reionization occurs is found to lie between z = 7.8 and 8.8, depending on the model of reionization adopted. Using kSZ constraints and a redshift-symmetric reionization model, we find an upper limit to the width of the reionization period of Δz < 2.8. In all cases, we find that the Universe is ionized at less than the 10% level at redshifts above z ≅ 10. This suggests that an early onset of reionization is strongly disfavoured by the Planck data. We show that this result also reduces the tension between CMB-based analyses and constraints from other astrophysical sources.

Parity-violating extensions of the standard electromagnetic theory cause in vacuo rotation of the plane of polarization of propagating photons. This effect, also known as cosmic birefringence, has an impact on the cosmic microwave background (CMB) anisotropy angular power spectra, producing non-vanishing T-B and E-B correlations that are otherwise null when parity is a symmetry. Here we present new constraints on an isotropic rotation, parametrized by the angle α, derived from Planck 2015 CMB polarization data. To increase the robustness of our analyses, we employ two complementary approaches, in harmonic space and in map space, the latter based on a peak stacking technique. The two approaches provide estimates for α that are in agreement within statistical uncertainties and are very stable against several consistency tests.Considering the T-B and E-B information jointly, we find α = 0°310°05(stat.)±0°28 (syst.) from the harmonic analysis and α = 0°350°05(stat.)±0°28 (syst.) from the stacking approach. These constraints are compatible with no parity violation and are dominated by the systematic uncertainty in the orientation of Planck's polarization-sensitive bolometers.

This paper describes the identification, modelling, and removal of previously unexplained systematic effects in the polarization data of the Planck High Frequency Instrument (HFI) on large angular scales, including new mapmaking and calibration procedures, new and more complete end-to-end simulations, and a set of robust internal consistency checks on the resulting maps. These maps, at 100, 143, 217, and 353 GHz, are early versions of those that will be released in final form later in 2016. The improvements allow us to determine the cosmic reionization optical depth τ using, for the first time, the low-multipole EE data from HFI, reducing significantly the central value and uncertainty, and hence the upper limit. Two different likelihood procedures are used to constrain τ from two estimators of the CMB E-and B-mode angular power spectra at 100 and 143 GHz, after debiasing the spectra from a small remaining systematic contamination. These all give fully consistent results. A further consistency test is performed using cross-correlations derived from the Low Frequency Instrument maps of the Planck 2015 data release and the new HFI data. For this purpose, end-to-end analyses of systematic effects from the two instruments are used to demonstrate the near independence of their dominant systematic error residuals. The tightest result comes from the HFI-based τ posterior distribution using the maximum likelihood power spectrum estimator from EE data only, giving a value 0.055 ± 0.009. In a companion paper these results are discussed in the context of the best-fit PlanckΛCDM cosmological model and recent models of reionization.

Recent models for the large-scale Galactic magnetic fields in the literature have been largely constrained by synchrotron emission and Faraday rotation measures. 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. 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.

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 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. 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.

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 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 componentseparation 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. The recovered SED allows us to constrain the dust mass responsible for the signal and its temperature.

The Planck mission, thanks to its large frequency range and all-sky coverage, has a unique potential for systematically detecting the brightest, and rarest, submillimetre sources on the sky, including distant objects in the high-redshift Universe traced by their dust emission. A novel method, based on a component-separation procedure using a combination of Planck and IRAS data, has been validated and characterized on numerous simulations, and applied to select the most luminous cold submillimetre sources with spectral energy distributions peaking between 353 and 857 GHz at 5' resolution. A total of 2151 Planck high-z source candidates (the PHZ) have been detected in the cleanest 26% of the sky, with flux density at 545 GHz above 500 mJy. Embedded in the cosmic infrared background close to the confusion limit, these high-z candidates exhibit colder colours than their surroundings, consistent with redshifts z > 2, assuming a dust temperature of Txgal = 35 K and a spectral index of βxgal = 1.5. Exhibiting extremely high luminosities, larger than 1014Lo, the PHZ objects may be made of multiple galaxies or clumps at high redshift, as suggested by a first statistical analysis based on a comparison with number count models. Furthermore, first follow-up observations obtained from optical to submillimetre wavelengths, which can be found in companion papers, have confirmed that this list consists of two distinct populations. A small fraction (around 3%) of the sources have been identified as strongly gravitationally lensed star-forming galaxies at redshift 2 to 4, while the vast majority of the PHZ sources appear as overdensities of dusty star-forming galaxies, having colours consistent with being at z > 2, and may be considered as proto-cluster candidates. The PHZ provides an original sample, which is complementary to the Planck Sunyaev-Zeldovich Catalogue (PSZ2); by extending the population of virialized massive galaxy clusters detected below z < 1.5 through their SZ signal to a population of sources at z > 1.5, the PHZ may contain the progenitors of today's clusters. Hence the Planck list of high-redshift source candidates opens a new window on the study of the early stages of structure formation, particularly understanding the intensively star-forming phase at high-z.

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, yc) 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. 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. Finally, 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.

Continuum spectra covering centimetre to submillimetre wavelengths are presented 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. Variability can generally be approximated by achromatic variations, while sources with clear signatures of evolving shocks appear to be limited to the strongest outbursts.

Using data from the Planck satellite, we study the statistical properties of interstellar dust polarization at high Galactic latitudes around the south pole (b

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 powerspectra) 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 contamination of the thermal dust maps, we provide more accurate estimates of the local dust temperature and dust spectral index over the sky with reduced dispersion, especially at high Galactic latitudes above b = ±20°. We find that the dust temperature is T = (19.4 ± 1.3) K and the dust spectral index is β = 1.6 ± 0.1 averaged over the whole sky, while T = (19.4 ± 1.5) K and β = 1.6 ± 0.2 on 21% of the sky at high latitudes. Moreover, subtracting the new CIB-removed thermal dust maps from the CMB-removed Planck maps gives access to the CIB anisotropies over 60% of the sky at Galactic latitudes |b| > 20°. Because they are a significant improvement over previous Planck products, the GNILC maps are recommended for thermal dust science. The new CIB maps can be regarded as indirect tracers of the dark matter and they are recommended for exploring cross-correlations with lensing and large-scale structure optical surveys. The reconstructed GNILC thermal dust and CIB maps are delivered as Planck products.

This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlationfunctions of the cosmic microwave background (CMB) temperature and polarization fluctuations that account for relevant uncertainties, both instrumental and astrophysical in nature. They are based on the same hybrid approach used for the previous release, i.e., a pixel-based likelihood at low multipoles (ℓ < 30) and a Gaussian approximation to the distribution of cross-power spectra at higher multipoles. The main improvements are the use of more and better processed data and of Planck polarization information, along with more detailed models of foregrounds and instrumental uncertainties. The increased redundancy brought by more than doubling the amount of data analysed enables further consistency checks and enhanced immunity to systematic effects. It also improves the constraining power of Planck, in particular with regard to small-scale foreground properties. Progress in the modelling of foreground emission enables the retention of a larger fraction of the sky to determine the properties of the CMB, which also contributes to the enhanced precision of the spectra. Improvements in data processing and instrumental modelling further reduce uncertainties. Extensive tests establish the robustness and accuracy of the likelihood results, from temperature alone, from polarization alone, and from their combination. For temperature, we also perform a full likelihood analysis of realistic end-to-end simulations of the instrumental response to the sky, which were fed into the actual data processing pipeline; this does not reveal biases from residual low-level instrumental systematics. Even with the increase in precision and robustness, the ΛCDM cosmological model continues to offer a very good fit to the Planck data. The slope of the primordial scalar fluctuations, ns, is confirmed smaller than unity at more than 5σ from Planck alone. We further validate the robustness of the likelihood results against specific extensions to the baseline cosmology, which are particularly sensitive to data at high multipoles. For instance, the effective number of neutrino species remains compatible with the canonical value of 3.046. For this first detailed analysis of Planck polarization spectra, we concentrate at high multipoles on the E modes, leaving the analysis of the weaker B modes to future work. At low multipoles we use temperature maps at all Planck frequencies along with a subset of polarization data. These data take advantage of Planck's wide frequency coverage to improve the separation of CMB and foreground emission. Within the baseline ΛCDM cosmology this requires τ = 0.078 ± 0.019 for the reionization optical depth, which is significantly lower than estimates without the use of high-frequency data for explicit monitoring of dust emission. At high multipoles we detect residual systematic errors in E polarization, typically at the μK2 level; we therefore choose to retain temperature information alone for high multipoles as the recommended baseline, in particular for testing non-minimal models. Nevertheless, the high-multipole polarization spectra from Planck are already good enough to enable a separate high-precision determination of the parameters of the ΛCDM model, showing consistency with those established independently from temperature information alone.

We have constructed all-sky Compton parameters maps, y-maps, of the thermal Sunyaev-Zeldovich (tSZ) effect by applying specifically tailored component separation algorithms to the 30 to 857 GHz frequency channel maps from the Planck satellite. These reconstructed y-maps are delivered as part of the Planck 2015 release. The y-maps are characterized in terms of noise properties and residual foreground contamination, mainly thermal dust emission at large angular scales, and cosmic infrared background and extragalactic point sources at small angular scales. Specific masks are defined to minimize foreground residuals and systematics. Using these masks, we compute the y-map angular power spectrum and higher order statistics. From these we conclude that the y-map is dominated by tSZ signal in the multipole range, 20

This paper presents the characterization of the in-flight beams, the beam window functions, and the associated uncertainties for the Planck Low Frequency Instrument (LFI). The structure of the paper is similar to that presented in the 2013 Planck release; the main differences concern the beam normalization and the delivery of the window functions to be used for polarization analysis. The in-flight assessment of the LFI main beams relies on measurements performed during observations of Jupiter. By stacking data from seven Jupiter transits, the main beam profiles are measured down to -25 dB at 30 and 44 GHz, and down to -30 dB at 70 GHz. It has been confirmed that the agreement between the simulated beams and the measured beams is better than 1% at each LFI frequency band (within the 20 dB contour from the peak, the rms values are 0.1% at 30 and 70 GHz; 0.2% at 44 GHz). Simulated polarized beams are used for the computation of the effective beam window functions. The error budget for the window functions is estimated from both main beam and sidelobe contributions, and accounts for the radiometer band shapes. The total uncertainties in the effective beam window functions are 0.7% and 1% at 30 and 44 GHz, respectively (at ℓ ≈ 600); and 0.5% at 70 GHz (at ℓ ≈ 1000).

This paper describes the mapmaking procedure applied to Planck Low Frequency Instrument (LFI) data. The mapmaking step takes as input the calibrated timelines and pointing information. The main products are sky maps of I, Q, and U Stokes components. For the first time, we present polarization maps at LFI frequencies. The mapmaking algorithm is based on a destriping technique, which is enhanced with a noise prior. The Galactic region is masked to reduce errors arising from bandpass mismatch and high signal gradients. We apply horn-uniform radiometer weights to reduce the effects of beam-shape mismatch. The algorithm is the same as used for the 2013 release, apart from small changes in parameter settings. We validate the procedure through simulations. Special emphasis is put on the control of systematics, which is particularly important for accurate polarization analysis. We also produce low-resolution versions of the maps and corresponding noise covariance matrices. These serve as input in later analysis steps and parameter estimation. The noise covariance matrices are validated through noise Monte Carlo simulations. The residual noise in the map products is characterized through analysis of half-ring maps, noise covariance matrices, and simulations.

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. 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.

We present the most significant measurement of the cosmic microwave background (CMB) lensing potential to date (at a level of 40σ), using temperature and polarization data from the Planck 2015 full-mission release. Using a polarization-only estimator, we detect lensing at a significance of 5σ. We cross-check the accuracy of our measurement using the wide frequency coverage and complementarity of the temperature and polarization measurements. Public products based on this measurement include an estimate of the lensing potential over approximately 70% of the sky, an estimate of the lensing potential power spectrum in bandpowers for the multipole range 40≤L≤400, and an associated likelihood for cosmological parameter constraints. We find good agreement between our measurement of the lensing potential power spectrum and that found in the ΛCDM model that best fits the Planck temperature and polarization power spectra. Using the lensing likelihood alone we obtain a percent-level measurement of the parameter combination σ8ω0.25m = 0:591 ± 0:021. We combine our determination of the lensing potential with the E-mode polarization, also measured by Planck, to generate an estimate of the lensing B-mode. We show that this lensing B-mode estimate is correlated with the B-modes observed directly by Planck at the expected level and with a statistical significance of 10σ, confirming Planck's sensitivity to this known sky signal. We also correlate our lensing potential estimate with the large-scale temperature anisotropies, detecting a cross-correlation at the 3σ level, as expected because of dark energy in the concordance ΛCDM model.

We present the current accounting of systematic effect uncertainties for the Low Frequency Instrument (LFI) that are relevant to the 2015 release of the Planck cosmological results, showing the robustness and consistency of our data set, especially for polarization analysis. We use two complementary approaches: (i) simulations based on measured data and physical models of the known systematic effects; and (ii) analysis of difference maps containing the same sky signal ("null-maps"). The LFI temperature data are limited by instrumental noise. At large angular scales the systematic effects are below the cosmic microwave background (CMB) temperature power spectrum by several orders of magnitude. In polarization the systematic uncertainties are dominated by calibration uncertainties and compete with the CMB E-modes in the multipole range 10-20. Based on our model of all known systematic effects, we show that these effects introduce a slight bias of around 0.2σ on the reionization optical depth derived from the 70GHz EE spectrum using the 30 and 353GHz channels as foreground templates. At 30GHz the systematic effects are smaller than the Galactic foreground at all scales in temperature and polarization, which allows us to consider this channel as a reliable template of synchrotron emission. We assess the residual uncertainties due to LFI effects on CMB maps and power spectra after component separation and show that these effects are smaller than the CMB amplitude at all scales. We also assess the impact on non-Gaussianity studies and find it to be negligible. Some residuals still appear in null maps from particular sky survey pairs, particularly at 30 GHz, suggesting possible straylight contamination due to an imperfect knowledge of the beam far sidelobes.

This paper presents a study of the integrated Sachs-Wolfe (ISW) effect from the Planck 2015 temperature and polarization data release. This secondary cosmic microwave background (CMB) anisotropy caused by the large-scale time-evolving gravitational potential is probed from different perspectives. The CMB is cross-correlated with different large-scale structure (LSS) tracers: radio sources from the NVSS catalogue; galaxies from the optical SDSS and the infrared WISE surveys; and the Planck 2015 convergence lensing map. The joint cross-correlation of the CMB with the tracers yields a detection at 4σ where most of the signal-to-noise is due to the Planck lensing and the NVSS radio catalogue. In fact, the ISW effect is detected from the Planck data only at ≠3σ (through the ISW-lensing bispectrum), which is similar to the detection level achieved by combining the cross-correlation signal coming from all the galaxy catalogues mentioned above. We study the ability of the ISW effect to place constraints on the dark-energy parameters; in particular, we show that ΩΛ is detected at more than 3σ. This cross-correlation analysis is performed only with the Planck temperature data, since the polarization scales available in the 2015 release do not permit significant improvement of the CMB-LSS cross-correlation detectability. Nevertheless, the Planck polarization data are used to study the anomalously large ISW signal previously reported through the aperture photometry on stacked CMB features at the locations of known superclusters and supervoids, which is in conflict with ΛCDM expectations. We find that the current Planck polarization data do not exclude that this signal could be caused by the ISW effect. In addition, the stacking of the Planck lensing map on the locations of superstructures exhibits a positive cross-correlation with these large-scale structures. Finally, we have improved our previous reconstruction of the ISW temperature fluctuations by combining the information encoded in all the previously mentioned LSS tracers. In particular, we construct a map of the ISW secondary anisotropies and the corresponding uncertainties map, obtained from simulations. We also explore the reconstruction of the ISW anisotropies caused by the large-scale structure traced by the 2MASS Photometric Redshift Survey (2MPZ) by directly inverting the density field into the gravitational potential field.

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 paper 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. Angular cross-power spectra using data sets that are decorrelated in time are immune to the main systematic effects.

This paper describes the processing applied to the cleaned, time-ordered information obtained from the Planck High Frequency Instrument (HFI) with the aim of producing photometrically calibrated maps in temperature and (for the first time) in polarization. The data from the entire 2.5-year HFI mission include almost five full-sky surveys. HFI observes the sky over a broad range of frequencies, from 100 to 857 GHz. To obtain the best accuracy on the calibration over such a large range, two different photometric calibration schemes have been used. The 545 and 857 GHz data are calibrated using models of planetary atmospheric emission. The lower frequencies (from 100 to 353 GHz) are calibrated using the time-variable cosmological microwave background dipole, which we call the orbital dipole. This source of calibration only depends on the satellite velocity with respect to the solar system. Using a CMB temperature of TCMB = 2.7255 ± 0.0006 K, it permits an independent measurement of the amplitude of the CMB solar dipole (3364.3 ± 1.5 μK), which is approximatively 1σ higher than the WMAP measurement with a direction that is consistent between the two experiments. We describe the pipeline used to produce the maps ofintensity and linear polarization from the HFI timelines, and the scheme used to set the zero level of the maps a posteriori. We also summarize the noise characteristics of the HFI maps in the 2015 Planck data release and present some null tests to assess their quality. Finally, we discuss the major systematic effects and in particular the leakage induced by flux mismatch between the detectors that leads to spurious polarization signal.

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 χrec), 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 i of the largest sphere inscribed in the fundamental domain (at log-likelihood ratio Δ >-5 relative to a simply-connected flat Planck best-fit model) are: i > 0.97 χrec for the T3 cubic torus; and i > 0.56 χrec for the T1 slab. The limit for the T3 cubic torus from the matched-circles search is numerically equivalent, i > 0.97 χrec at 99% confidence level from polarization data alone. We also perform a Bayesian search for an anisotropic global Bianchi VIIh 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 VIIh cosmology and constrain the vorticity of such models to (ω/H)0 < 7.6 × 10-10 (95% CL).

We present an updated description of the Planck Low Frequency Instrument (LFI) data processing pipeline, associated with the 2015 data release. We point out the places where our results and methods have remained unchanged since the 2013 paper and we highlight the changes made for the 2015 release, describing the products (especially timelines) and the ways in which they were obtained. We demonstrate that the pipeline is self-consistent (principally based on simulations) and report all null tests. For the first time, we present LFI maps in Stokes Q and U polarization. We refer to other related papers where more detailed descriptions of the LFI data processing pipeline may be found if needed.

We present the Planck Catalogue of Galactic Cold Clumps (PGCC), an all-sky catalogue of Galactic cold clump candidates detected by Planck. This catalogue is the full version of the Early Cold Core (ECC) catalogue, which was made available in 2011 with the Early Release Compact Source Catalogue (ERCSC) and which contained 915 high signal-to-noise sources. It is based on the Planck 48-month mission data that are currently being released to the astronomical community. The PGCC catalogue is an observational catalogue consisting exclusively of Galactic cold sources. The three highest Planck bands (857, 454, and 353 GHz) have been combined with IRAS data at 3 THz to perform a multi-frequency detection of sources colder than their local environment. After rejection of possible extragalactic contaminants, the PGCC catalogue contains 13188 Galactic sources spread across the whole sky, i.e., from the Galactic plane to high latitudes, following the spatial distribution of the main molecular cloud complexes. The median temperature of PGCC sources lies between 13 and 14.5 K, depending on the quality of the flux density measurements, with a temperature ranging from 5.8 to 20 K after removing the sources with the top 1% highest temperature estimates. Using seven independent methods, reliable distance estimates have been obtained for 5574 sources, which allows us to derive their physical properties such as their mass, physical size, mean density, and luminosity.The PGCC sources are located mainly in the solar neighbourhood, but also up to a distance of 10.5 kpc in the direction of the Galactic centre, and range from low-mass cores to large molecular clouds. Because of this diversity and because the PGCC catalogue contains sources in very different environments, the catalogue is useful for investigating the evolution from molecular clouds to cores. Finally, it also includes 54 additional sources located in the Small and Large Magellanic Clouds.

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. We provide a detailed description of the impact of all the changes implemented in the calibration since the previous data release.

We compute and investigate four types of imprint of a stochastic background of primordial magnetic fields (PMFs) on the cosmic microwave background (CMB) anisotropies: the impact of PMFs on the CMB temperature and polarization spectra, which is related to their contribution to cosmological perturbations; the effect on CMB polarization induced by Faraday rotation; the impact of PMFs on the ionization history; magnetically-induced non-Gaussianities and related non-zero bispectra; and the magnetically-induced breaking of statistical isotropy. We present constraints on the amplitude of PMFs that are derived from different Planck data products, depending on the specific effect that is being analysed. Overall, Planck data constrain the amplitude of PMFs to less than a few nanoGauss, with different bounds that depend on the considered model. In particular, individual limits coming from the analysis of the CMB angular power spectra, using the Planck likelihood, are B1 Mpc < 4.4 nG (where B1 Mpc is the comoving field amplitude at a scale of 1 Mpc) at 95% confidence level, assuming zero helicity. By considering the Planck likelihood, based only on parity-even angular power spectra, we obtain B1 Mpc < 5.6 nG for a maximally helical field. For nearly scale-invariant PMFs we obtain B1 Mpc < 2.0 nG and B1 Mpc < 0.9 nG if the impact of PMFs on the ionization history of the Universe is included in the analysis. From the analysis of magnetically-induced non-Gaussianity, we obtain three different values, corresponding to three applied methods, all below 5 nG. The constraint from the magnetically-induced passive-tensor bispectrum is B1 Mpc < 2.8 nG. A search for preferred directions in the magnetically-induced passive bispectrum yields B1 Mpc < 4.5 nG, whereas the compensated-scalar bispectrum gives B1 Mpc < 3 nG. The analysis of the Faraday rotation of CMB polarization by PMFs uses the Planck power spectra in EE and BB at 70 GHz and gives B1 Mpc < 1380 nG. In our final analysis, we consider the harmonic-space correlations produced by Alfvén waves, finding no significant evidence for the presence of these waves. Together, these results comprise a comprehensive set of constraints on possible PMFs with Planck data.

We use Planck data to detect the cross-correlation between the thermal Sunyaev-Zeldovich (tSZ) effect and the infrared emission from the galaxies that make up the the cosmic infrared background (CIB). We first perform a stacking analysis towards Planck-confirmed galaxy clusters. We detect infrared emission produced by dusty galaxies inside these clusters and demonstrate that the infrared emission is about 50% more extended than the tSZ effect. Modelling the emission with a Navarro-Frenk-White profile, we find that the radial profile concentration parameter is c500 = 1.00+0.18-0.15 c500=1.00-0.15+0.18. This indicates that infrared galaxies in the outskirts of clusters have higher infrared flux than cluster-core galaxies. We also study the cross-correlation between tSZ and CIB anisotropies, following three alternative approaches based on power spectrum analyses: (i) using a catalogue of confirmed clusters detected in Planck data; (ii) using an all-sky tSZ map built from Planck frequency maps; and (iii) using cross-spectra between Planck frequency maps. With the three different methods, we detect the tSZ-CIB cross-power spectrum at significance levels of (i) 6σ; (ii) 3σ; and (iii) 4σ. We model the tSZ-CIB cross-correlation signature and compare predictions with the measurements. The amplitude of the cross-correlation relative to the fiducial model is AtSZ-CIB = 1.2 ± 0.3. This result is consistent with predictions for the tSZ-CIB cross-correlation assuming the best-fit cosmological model from Planck 2015 results along with the tSZ and CIB scaling relations.

The role of the magnetic field in the formation of the filamentary structuresobserved in the interstellar medium (ISM) is a debated topic. The Planckall-sky maps of linearly polarized emission from dust at 353GHz provide therequired combination of imaging and statistics to study the correlation betweenthe structures of the Galactic magnetic field and of interstellar matter, bothin the diffuse ISM and in molecular clouds. The data reveal structures, orridges, in the intensity map with counterparts in the Stokes Q and/or U maps.We focus on structures at intermediate and high Galactic latitudes with columndensity from $10^{20}$ to $10^{22}$ cm$^{-2}$. We measure the magnetic fieldorientation on the plane of the sky from the polarization data, and present analgorithm to estimate the orientation of the ridges from the dust intensitymap. We use analytical models to account for projection effects. Comparingpolarization angles on and off the structures, we estimate the mean ratiobetween the strengths of the turbulent and mean components of the magneticfield to be between 0.6 and 1.0, with a preferred value of 0.8. We find thatthe ridges are preferentially aligned with the magnetic field measured on thestructures. This trend becomes more striking for increasing polarizationfraction and decreasing column density. We interpret the increase of alignmentwith polarization fraction as a consequence of projections effects. Thedecrease of alignment for high column density is not due to a loss ofcorrelation between the structures and the geometry of the magnetic field. Inmolecular complexes, we observe structures perpendicular to the magnetic field,which cannot be accounted for by projection effects. We discuss our results inthe context of models and MHD simulations, which describe the formation ofstructures in the magnetized ISM.

By looking at the kinetic Sunyaev-Zeldovich effect (kSZ) in Planck nominal mission data, we present a significant detection of baryons participating in large-scale bulk flows around central galaxies (CGs) at redshift z ≈ 0.1. We estimate the pairwise momentum of the kSZ temperature fluctuations at the positions of the Central Galaxy Catalogue (CGC) samples extracted from Sloan Digital Sky Survey (SDSS-DR7) data. For the foreground-cleaned SEVEM, SMICA, NILC, and COMMANDER maps, we find 1.8-2.5σ detections of the kSZ signal, which are consistent with the kSZ evidence found in individual Planck raw frequency maps, although lower than found in the WMAP-9yr W-band (3.3σ). We further reconstruct the peculiar velocity field from the CG density field, and compute for the first time the cross-correlation function between kSZ temperature fluctuations and estimates of CG radial peculiar velocities. This correlation function yields a 3.0-3.7σ detection of the peculiar motion of extended gas on Mpc scales in flows correlated up to distances of 80-100 h-1 Mpc. Both the pairwise momentum estimates and the kSZ temperature-velocity field correlation find evidence for kSZ signatures out to apertures of 8 arcmin and beyond, corresponding to a physical radius of >1 Mpc, more than twice the mean virial radius of halos. This is consistent with the predictions from hydrodynamical simulations that most of the baryons are outside the virialized halos. We fit a simple model, in which the temperature-velocity cross-correlation is proportional to the signal seen in a semi-analytic model built upon N-body simulations, and interpret the proportionality constant as an effective optical depth to Thomson scattering. We find τT = (1.4 ± 0.5) × 10-4; the simplest interpretation of this measurement is that much of the gas is in a diffuse phase, which contributes little signal to X-ray or thermal Sunyaev-Zeldovich observations.