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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.

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.

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 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.

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 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.

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.

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.

The European Space Agency's Planck satellite, which was dedicated to studying the early Universe and its subsequent evolution, was launched on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013, producing deep, high-resolution, all-sky maps in nine frequency bands from 30 to 857 GHz. This paper presents the cosmological legacy of Planck, which currently provides our strongest constraints on the parameters of the standard cosmological model and some of the tightest limits available on deviations from that model. The 6-parameter ΛCDM model continues to provide an excellent fit to the cosmic microwave background data at high and low redshift, describing the cosmological information in over a billion map pixels with just six parameters. With 18 peaks in the temperature and polarization angular power spectra constrained well, Planck measures five of the six parameters to better than 1% (simultaneously), with the best-determined parameter (θ∗) now known to 0.03%. We describe the multi-component sky as seen by Planck, the success of the ΛCDM model, and the connection to lower-redshift probes of structure formation. We also give a comprehensive summary of the major changes introduced in this 2018 release. The Planck data, alone and in combination with other probes, provide stringent constraints on our models of the early Universe and the large-scale structure within which all astrophysical objects form and evolve. We discuss some lessons learned from the Planck mission, and highlight areas ripe for further experimental advances.

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 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.

Context. The European Space Agency (ESA) Rosetta mission was the most comprehensive study of a comet ever performed. In particular, the Rosetta orbiter, which carried many instruments for monitoring the evolution of the dusty gas emitted by the cometary nucleus, returned an enormous volume of observational data collected from the close vicinity of the nucleus of comet 67P/Churyumov-Gerasimenko.Aims. Such data are expected to yield unique information on the physical processes of gas and dust emission, using current physical model fits to the data. We present such a model (the RZC model) and our procedure of adjustment of this model to the data.Methods. The RZC model consists of two components: (1) a numerical three-dimensional time-dependent code solving the Eulerian/Navier-Stokes equations governing the gas outflow, and a direct simulation Monte Carlo (DSMC) gaskinetic code with the same objective; and (2) an iterative procedure to adjust the assumed model parameters to best-fit the observational data at all times.Results. We demonstrate that our model is able to reproduce the overall features of the local neutral number density and composition measurements of Rosetta Orbiter Spectrometer for Ion and Neutral Analysis (ROSINA) Comet Pressure Sensor (COPS) and Double Focusing Mass Spectrometer (DFMS) instruments in the period August 1–November 30, 2014. The results of numerical simulations show that illumination conditions on the nucleus are the main driver for the gas activity of the comet. We present the distribution of surface inhomogeneity best-fitted to the ROSINA COPS and DFMS in situ measurements.

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.

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.

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.

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.

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.

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.

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 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.

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.

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).

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

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

We discuss the Galactic foreground emission between 20 and 100 GHz based on observations by Planck and WMAP. The total intensity in this part of the spectrum is dominated by free-free and spinning dust emission, whereas the polarized intensity is dominated by synchrotron emission. The Commander component-separation tool has been used to separate the various astrophysical processes in total intensity. Comparison with radio recombination line templates verifies the recovery of the free-free emission along the Galactic plane. Comparison of the high-latitude Hα emission with our free-free map shows residuals that correlate with dust optical depth, consistent with a fraction (≠30%) of Hα having been scattered by high-latitude dust. We highlight a number of diffuse spinning dust morphological features at high latitude. There is substantial spatial variation in the spinning dust spectrum, with the emission peak (in Iν) ranging from below 20 GHz to more than 50 GHz. There is a strong tendency for the spinning dust component near many prominent H ii regions to have a higher peak frequency, suggesting that this increase in peak frequency is associated with dust in the photo-dissociation regions around the nebulae. The emissivity of spinning dust in these diffuse regions is of the same order as previous detections in the literature. Over the entire sky, the Commander solution finds more anomalous microwave emission (AME) than the WMAP component maps, at the expense of synchrotron and free-free emission. This can be explained by the difficulty in separating multiple broadband components with a limited number of frequency maps. Future surveys, particularly at 5-20 GHz, will greatly improve the separation by constraining the synchrotron spectrum. We combine Planck and WMAP data to make the highest signal-to-noise ratio maps yet of the intensity of the all-sky polarized synchrotron emission at frequencies above a few GHz. Most of the high-latitude polarized emission is associated with distinct large-scale loops and spurs, and we re-discuss their structure. We argue that nearly all the emission at 40deg > l >-90deg is part of the Loop I structure, and show that the emission extends much further in to the southern Galactic hemisphere than previously recognised, giving Loop I an ovoid rather than circular outline. However, it does not continue as far as the "Fermi bubble/microwave haze", making it less probable that these are part of the same structure. We identify a number of new faint features in the polarized sky, including a dearth of polarized synchrotron emission directly correlated with a narrow, roughly 20deg long filament seen in Hα at high Galactic latitude. Finally, we look for evidence of polarized AME, however many AME regions are significantly contaminated by polarized synchrotron emission, and we find a 2σ upper limit of 1.6% in the Perseus region.

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.

The Second Planck Catalogue of Compact Sources is a list of discrete objects detected in single-frequency maps from the full duration of the Planck mission and supersedes previous versions. It consists of compact sources, both Galactic and extragalactic, detected over the entire sky. Compact sources detected in the lower frequency channels are assigned to the PCCS2, while at higher frequencies they are assigned to one of two subcatalogues, the PCCS2 or PCCS2E, depending on their location on the sky. The first of these (PCCS2) covers most of the sky and allows the user to produce subsamples at higher reliabilities than the target 80% integral reliability of the catalogue. The second (PCCS2E) contains sources detected in sky regions where the diffuse emission makes it difficult to quantify the reliability of the detections. Both the PCCS2 and PCCS2E include polarization measurements, in the form of polarized flux densities, or upper limits, and orientation angles for all seven polarization-sensitive Planck channels. The improved data-processing of the full-mission maps and their reduced noise levels allow us to increase the number of objects in the catalogue, improving its completeness for the target 80% reliability as compared with the previous versions, the PCCS and the Early Release Compact Source Catalogue (ERCSC).

This paper presents cosmological results based on full-mission Planck observations of temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation. Our results are in very good agreement with the 2013 analysis of the Planck nominal-mission temperature data, but with increased precision. The temperature and polarization power spectra are consistent with the standard spatially-flat 6-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations (denoted "base ΛCDM" in this paper). From the Planck temperature data combined with Planck lensing, for this cosmology we find a Hubble constant, H0 = (67.8 ± 0.9) km s-1Mpc-1, a matter density parameter Ωm = 0.308 ± 0.012, and a tilted scalar spectral index with ns = 0.968 ± 0.006, consistent with the 2013 analysis. Note that in this abstract we quote 68% confidence limits on measured parameters and 95% upper limits on other parameters. We present the first results of polarization measurements with the Low Frequency Instrument at large angular scales. Combined with the Planck temperature and lensing data, these measurements give a reionization optical depth of τ = 0.066 ± 0.016, corresponding to a reionization redshift of \hbox{$z-{\rm re}=8.8{+1.7}-{-1.4}$}. These results are consistent with those from WMAP polarization measurements cleaned for dust emission using 353-GHz polarization maps from the High Frequency Instrument. We find no evidence for any departure from base ΛCDM in the neutrino sector of the theory; for example, combining Planck observations with other astrophysical data we find Neff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value Neff = 3.046 of the Standard Model of particle physics. The sum of neutrino masses is constrained to â'mν < 0.23 eV. The spatial curvature of our Universe is found to be very close to zero, with | ΩK | < 0.005. Adding a tensor component as a single-parameter extension to base ΛCDM we find an upper limit on the tensor-to-scalar ratio of r0.002< 0.11, consistent with the Planck 2013 results and consistent with the B-mode polarization constraints from a joint analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP B-mode data to our analysis leads to a tighter constraint of r0.002 < 0.09 and disfavours inflationarymodels with a V(φ) φ2 potential. The addition of Planck polarization data leads to strong constraints on deviations from a purely adiabatic spectrum of fluctuations. We find no evidence for any contribution from isocurvature perturbations or from cosmic defects. Combining Planck data with other astrophysical data, including Type Ia supernovae, the equation of state of dark energy is constrained to w =-1.006 ± 0.045, consistent with the expected value for a cosmological constant. The standard big bang nucleosynthesis predictions for the helium and deuterium abundances for the best-fit Planck base ΛCDM cosmology are in excellent agreement with observations. We also constraints on annihilating dark matter and on possible deviations from the standard recombination history. In neither case do we find no evidence for new physics. The Planck results for base ΛCDM are in good agreement with baryon acoustic oscillation data and with the JLA sample of Type Ia supernovae. However, as in the 2013 analysis, the amplitude of the fluctuation spectrum is found to be higher than inferred from some analyses of rich cluster counts and weak gravitational lensing. We show that these tensions cannot easily be resolved with simple modifications of the base ΛCDM cosmology. Apart from these tensions, the base ΛCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.

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.

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 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.

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

We present foreground-reduced cosmic microwave background (CMB) maps derived from the full Planck data set in both temperature and polarization. Compared to the corresponding Planck 2013 temperature sky maps, the total data volume is larger by a factor of 3.2 for frequencies between 30 and 70 GHz, and by 1.9 for frequencies between 100 and 857 GHz. In addition, systematic errors in the forms of temperature-to-polarization leakage, analogue-to-digital conversion uncertainties, and very long time constant errors have been dramatically reduced, to the extent that the cosmological polarization signal may now be robustly recovered on angular scales â"" μ 40. On the very largest scales, instrumental systematic residuals are still non-negligible compared to the expected cosmological signal, and modes with â"" < 20 are accordingly suppressed in the current polarization maps by high-pass filtering. As in 2013, four different CMB component separation algorithms are applied to these observations, providing a measure of stability with respect to algorithmic and modelling choices. The resulting polarization maps have rms instrumental noise ranging between 0.21 and 0.27μK averaged over 55′ pixels, and between 4.5 and 6.1μK averaged over \hbox{$3\parcm4$} pixels. The cosmological parameters derived from the analysis of temperature power spectra are in agreement at the 1σ level with the Planck 2015 likelihood. Unresolved mismatches between the noise properties of the data and simulations prevent a satisfactory description of the higher-order statistical properties of the polarization maps. Thus, the primary applications of these polarization maps are those that do not require massive simulations for accurate estimation of uncertainties, for instance estimation of cross-spectra and cross-correlations, or stacking analyses. However, the amplitude of primordial non-Gaussianity is consistent with zero within 2σ for all local, equilateral, and orthogonal configurations of the bispectrum, including for polarization E-modes. Moreover, excellent agreement is found regarding the lensing B-mode power spectrum, both internally among the various component separation codes and with the best-fit Planck 2015 Λ cold dark matter model.

The Planck full mission cosmic microwave background (CMB) temperature and E-mode polarization maps are analysed to obtain constraints on primordial non-Gaussianity (NG). Using three classes of optimal bispectrum estimators-separable template-fitting (KSW), binned, and modal-we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result from temperature alone localNL = 2.5 ± 5.7, equilNL=-16 ± 70, fNLlocal=2.5±5.7, fNLequil=-16±70, and orthoNL =-34 ± 32fNLortho=-34±33 (68% CL, statistical). Combining temperature and polarization data we obtain fNLlocal=0.8±5.0, fNLequil=-4±43, and fNLortho=-26±21localNL = 0.8 ± 5.0, equilNL=-4 ± 43, and orthoNL =-26 ± 21 (68% CL, statistical). The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are consistent with estimators based on measuring the Minkowski functionals of the CMB. The effect of time-domain de-glitching systematics on the bispectrum is negligible. In spite of these test outcomes we conservatively label the results including polarization data as preliminary, owing to a known mismatch of the noise model in simulations and the data. Beyond estimates of individual shape amplitudes, we present model-independent, three-dimensional reconstructions of the Planck CMB bispectrum and derive constraints on early universe scenarios that generate primordial NG, including general single-field models of inflation, axion inflation, initial state modifications, models producing parity-violating tensor bispectra, and directionally dependent vector models. We present a wide survey of scale-dependent feature and resonance models, accounting for the "look elsewhere" effect in estimating the statistical significance of features. We also look for isocurvature NG, and find no signal, but we obtain constraints that improve significantly with the inclusion of polarization. The primordial trispectrum amplitude in the local model is constrained to be glocalNL = (-0.9 ± 7.7) X 104(68% CL statistical), and we perform an analysis of trispectrum shapes beyond the local case. The global picture that emerges is one of consistency with the premises of the ΛCDM cosmology, namely that the structure we observe today was sourced by adiabatic, passive, Gaussian, and primordial seed perturbations.

We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be ns = 0.968 ± 0.006 and tightly constrain its scale dependence to dns/dlnk =-0.003 ± 0.007 when combined with the Planck lensing likelihood. When the Planck high-â"" polarization data are included, the results are consistent and uncertainties are further reduced. The upper bound on the tensor-to-scalar ratio is r0.002< 0.11 (95% CL). This upper limit is consistent with the B-mode polarization constraint r< 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. These results imply that V(φ) â φ2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R2 inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth \hbox{${\cal P}-{\cal{R}}(k)$} over the range of scales 0.008 Mpc-1 â‰2 k â‰2 0.1 Mpc-1. At large scales, each method finds deviations from a power law, connected to a deficit at multipoles â"" ≠20-40 in the temperature power spectrum, but at an uncompelling statistical significance owing to the large cosmic variance present at these multipoles. By combining power spectrum and non-Gaussianity bounds, we constrain models with generalized Lagrangians, including Galileon models and axion monodromy models. The Planck data are consistent with adiabatic primordial perturbations, and the estimated values for the parameters of the base Λ cold dark matter (ΛCDM) model are not significantly altered when more general initial conditions are admitted. In correlated mixed adiabatic and isocurvature models, the 95% CL upper bound for the non-adiabatic contribution to the observed CMB temperature variance is | αnon-adi | < 1.9%, 4.0%, and 2.9% for CDM, neutrino density, and neutrino velocity isocurvature modes, respectively. We have tested inflationary models producing an anisotropic modulation of the primordial curvature power spectrum findingthat the dipolar modulation in the CMB temperature field induced by a CDM isocurvature perturbation is not preferred at a statistically significant level. We also establish tight constraints on a possible quadrupolar modulation of the curvature perturbation. These results are consistent with the Planck 2013 analysis based on the nominal mission data and further constrain slow-roll single-field inflationary models, as expected from the increased precision of Planck data using the full set of observations.

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 present the 8th full focal plane simulation set (FFP8), deployed in support of the Planck 2015 results. FFP8 consists of 10 fiducial mission realizations reduced to 18 144 maps, together with the most massive suite of Monte Carlo realizations of instrument noise and CMB ever generated, comprising 104 mission realizations reduced to about 106 maps. The resulting maps incorporate the dominant instrumental, scanning, and data analysis effects, and the remaining subdominant effects will be included in future updates. Generated at a cost of some 25 million CPU-hours spread across multiple high-performance-computing (HPC) platforms, FFP8 is used to validate and verify analysis algorithms and their implementations, and to remove biases from and quantify uncertainties in the results of analyses of the real data.

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

We present the all-sky Planck catalogue of Sunyaev-Zeldovich (SZ) sources detected from the 29 month full-mission data. The catalogue (PSZ2) is the largest SZ-selected sample of galaxy clusters yet produced and the deepest systematic all-sky surveyof galaxy clusters. It contains 1653 detections, of which 1203 are confirmed clusters with identified counterparts in external data sets, and is the first SZ-selected cluster survey containing >103 confirmed clusters. We present a detailed analysis of the survey selection function in terms of its completeness and statistical reliability, placing a lower limit of 83% on the purity. Using simulations, we find that the estimates of the SZ strength parameter Y5R500are robust to pressure-profile variation and beam systematics, but accurate conversion to Y500 requires the use of prior information on the cluster extent. We describe the multi-wavelength search for counterparts in ancillary data, which makes use of radio, microwave, infra-red, optical, and X-ray data sets, and which places emphasis on the robustness of the counterpart match. We discuss the physical properties of the new sample and identify a population of low-redshift X-ray under-luminous clusters revealed by SZ selection. These objects appear in optical and SZ surveys with consistent properties for their mass, but are almost absent from ROSAT X-ray selected samples.

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.

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.