SearcharxivSearch

arXiv subjects

T. S. Kisner

Publications and source records attributed to T. S. Kisner.

At least 19 recordsLinked to original sources

Planck 2013 results X. Energetic particle effects: characterization, removal, and simulation

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

astro-ph.CO

Improved limits on the tensor-to-scalar ratio using BICEP and Planck

We present constraints on the tensor-to-scalar ratio r using a combination of BICEP/Keck 2018 and Planck PR4 data allowing us to fit for r consistently with the six parameters of the $Λ$CDM model without fixing any of them. In particular, we are able to derive a constraint on the reionization optical depth $τ$ and thus propagate its uncertainty onto the posterior distribution for r. While Planck sensitivity to r is no longer comparable with ground-based measurements, combining Planck with BK18 and BAO gives results consistent with r = 0 and tightens the constraint to r < 0.032.

astro-ph.CO

Planck 2018 results. VI. Cosmological parameters

We present cosmological parameter results from the final full-mission Planck measurements of the CMB anisotropies. We find good consistency with the standard spatially-flat 6-parameter $Λ$CDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base $Λ$CDM" in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density $Ω_c h^2 = 0.120\pm 0.001$, baryon density $Ω_b h^2 = 0.0224\pm 0.0001$, scalar spectral index $n_s = 0.965\pm 0.004$, and optical depth $τ= 0.054\pm 0.007$ (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 $100θ_*=1.0411\pm 0.0003$. 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-$Λ$CDM cosmology, the inferred late-Universe parameters are: Hubble constant $H_0 = (67.4\pm 0.5)$km/s/Mpc; matter density parameter $Ω_m = 0.315\pm 0.007$; and matter fluctuation amplitude $σ_8 = 0.811\pm 0.006$. We find no compelling evidence for extensions to the base-$Λ$CDM model. Combining with BAO we constrain the effective extra relativistic degrees of freedom to be $N_{\rm eff} = 2.99\pm 0.17$, and the neutrino mass is tightly constrained to $\sum m_ν< 0.12$eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base -$Λ$CDM at over $2\,σ$, which pulls some parameters that affect the lensing amplitude away from the base-$Λ$CDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. (Abridged)

astro-ph.CO

Planck constraints on the tensor-to-scalar ratio

We present constraints on the tensor-to-scalar ratio r using Planck data. We use the latest release of Planck maps (PR4), processed with the NPIPE code, which produces calibrated frequency maps in temperature and polarization for all Planck channels from 30 GHz to 857 GHz using the same pipeline. We computed constraints on r using the BB angular power spectrum, and we also discuss constraints coming from the TT spectrum. Given Planck's noise level, the TT spectrum gives constraints on r that are cosmic-variance limited (with $σ$(r)=0.093), but we show that the marginalized posterior peaks towards negative values of r at about the 1.2$σ$ level. We derived Planck constraints using the BB power spectrum at both large angular scales (the 'reionization bump') and intermediate angular scales (the 'recombination bump') from $\ell$=2 to 150, and find a stronger constraint than that from TT, with $σ$(r)=0.069. The Planck BB spectrum shows no systematic bias, and is compatible with zero, given both the statistical noise and the systematic uncertainties. The likelihood analysis using B modes yields the constraint r<0.158 at 95% confidence using more than 50% of the sky. This upper limit tightens to r<0.069 when Planck EE, BB, and EB power spectra are combined consistently, and it tightens further to r<0.056 when the Planck TT power spectrum is included in the combination. Finally, combining Planck with BICEP2/Keck 2015 data yields an upper limit of r<0.044.

astro-ph.CO

Planck 2018 results. IV. Diffuse component separation

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

astro-ph.CO

Planck 2018 results. V. CMB power spectra and likelihoods

This paper describes the 2018 Planck CMB likelihoods, following a hybrid approach similar to the 2015 one, with different approximations at low and high multipoles, and implementing several methodological and analysis refinements. With more realistic simulations, and better correction and modelling of systematics, we can now make full use of the High Frequency Instrument polarization data. The low-multipole 100x143 GHz EE cross-spectrum constrains the reionization optical-depth parameter $τ$ to better than 15% (in combination with with the other low- and high-$\ell$ likelihoods). We also update the 2015 baseline low-$\ell$ joint TEB likelihood based on the Low Frequency Instrument data, which provides a weaker $τ$ constraint. At high multipoles, a better model of the temperature-to-polarization leakage and corrections for the effective calibrations of the polarization channels (polarization efficiency or PE) allow us to fully use the polarization spectra, improving the constraints on the $Λ$CDM parameters by 20 to 30% compared to TT-only constraints. Tests on the modelling of the polarization demonstrate good consistency, with some residual modelling uncertainties, the accuracy of the PE modelling being the main limitation. Using our various tests, simulations, and comparison between different high-$\ell$ implementations, we estimate the consistency of the results to be better than the 0.5$σ$ level. Minor curiosities already present before (differences between $\ell$<800 and $\ell$>800 parameters or the preference for more smoothing of the $C_\ell$ peaks) are shown to be driven by the TT power spectrum and are not significantly modified by the inclusion of polarization. Overall, the legacy Planck CMB likelihoods provide a robust tool for constraining the cosmological model and represent a reference for future CMB observations. (Abridged)

astro-ph.CO

Planck intermediate results. LV. Reliability and thermal properties of high-frequency sources in the Second Planck Catalogue of Compact Sources

We describe an extension of the most recent version of the Planck Catalogue of Compact Sources (PCCS2), produced using a new multi-band Bayesian Extraction and Estimation Package (BeeP). BeeP assumes that the compact sources present in PCCS2 at 857 GHz have a dust-like spectral energy distribution, which leads to emission at both lower and higher frequencies, and adjusts the parameters of the source and its SED to fit the emission observed in Planck's three highest frequency channels at 353, 545, and 857 GHz, as well as the IRIS map at 3000 GHz. In order to reduce confusion regarding diffuse cirrus emission, BeeP's data model includes a description of the background emission surrounding each source, and it adjusts the confidence in the source parameter extraction based on the statistical properties of the spatial distribution of the background emission. BeeP produces the following three new sets of parameters for each source: (a) fits to a modified blackbody (MBB) thermal emission model of the source; (b) SED-independent source flux densities at each frequency considered; and (c) fits to an MBB model of the background in which the source is embedded. BeeP also calculates, for each source, a reliability parameter, which takes into account confusion due to the surrounding cirrus. We define a high-reliability subset (BeeP/base), containing 26 083 sources (54.1 per cent of the total PCCS2 catalogue), the majority of which have no information on reliability in the PCCS2. The results of the BeeP extension of PCCS2, which are made publicly available via the PLA, will enable the study of the thermal properties of well-defined samples of compact Galactic and extra-galactic dusty sources.

astro-ph.GA

Planck intermediate results. LVI. Detection of the CMB dipole through modulation of the thermal Sunyaev-Zeldovich effect: Eppur si muove II

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

astro-ph.CO

Planck intermediate results. LVII. Joint Planck LFI and HFI data processing

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. The net effect of the 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 ($3366.6 \pm 2.7$)$μ$K, 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 $τ= 0.051 \pm 0.006$, 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.

astro-ph.CO

Planck 2018 results. I. Overview and the cosmological legacy of Planck

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 857GHz. 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 LCDM 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 (theta_*) now known to 0.03%. We describe the multi-component sky as seen by Planck, the success of the LCDM 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.

astro-ph.CO

Planck 2018 results. X. Constraints on inflation

We report on the implications for cosmic inflation of the 2018 Release of the Planck CMB anisotropy measurements. The results are fully consistent with 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 $n_\mathrm{s}=0.9649\pm 0.0042$ at 68% CL and show no evidence for a scale dependence of $n_\mathrm{s}.$ Spatial flatness is confirmed at a precision of 0.4% at 95% CL with the combination with BAO data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, $r_{0.002}<0.10$, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain $r_{0.002}<0.056$. In the framework of single-field inflationary models with Einstein gravity, these results imply that: (a) slow-roll models with a concave potential, $V" (ϕ) < 0,$ are increasingly favoured by the data; and (b) two different methods for reconstructing the inflaton potential find no evidence for dynamics beyond slow roll. Non-parametric reconstructions of the primordial power spectrum consistently confirm a pure power law. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectrum, a result further strengthened for certain oscillatory models by a new combined analysis that includes Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadrupolar modulation of the primordial fluctuations. However, the polarization data do not confirm physical models for a scale-dependent dipolar modulation.

astro-ph.CO

Planck intermediate results. LIV. The Planck Multi-frequency Catalogue of Non-thermal Sources

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, 29400 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. 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/N>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.

astro-ph.CO

Planck 2018 results. II. Low Frequency Instrument data processing

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.

astro-ph.CO

Planck intermediate results. LIII. Detection of velocity dispersion from the kinetic Sunyaev-Zeldovich effect

Using the ${\it Planck}$ full-mission data, we present a detection of the temperature (and therefore velocity) dispersion due to the kinetic Sunyaev-Zeldovich (kSZ) effect from clusters of galaxies. To suppress the primary CMB and instrumental noise we derive a matched filter and then convolve it with the ${\it Planck}$ foreground-cleaned `${\tt 2D-ILC\,}$' maps. By using the Meta Catalogue of X-ray detected Clusters of galaxies (MCXC), we determine the normalized ${\it rms}$ dispersion of the temperature fluctuations at the positions of clusters, finding that this shows excess variance compared with the noise expectation. We then build an unbiased statistical estimator of the signal, determining that the normalized mean temperature dispersion of $1526$ clusters is $\langle \left(ΔT/T \right)^{2} \rangle = (1.64 \pm 0.48) \times 10^{-11}$. However, comparison with analytic calculations and simulations suggest that around $0.7\,σ$ of this result is due to cluster lensing rather than the kSZ effect. By correcting this, the temperature dispersion is measured to be $\langle \left(ΔT/T \right)^{2} \rangle = (1.35 \pm 0.48) \times 10^{-11}$, which gives a detection at the $2.8\,σ$ level. We further convert uniform-weight temperature dispersion into a measurement of the line-of-sight velocity dispersion, by using estimates of the optical depth of each cluster (which introduces additional uncertainty into the estimate). We find that the velocity dispersion is $\langle v^{2} \rangle =(123\,000 \pm 71\,000)\,({\rm km}\,{\rm s}^{-1})^{2}$, which is consistent with findings from other large-scale structure studies, and provides direct evidence of statistical homogeneity on scales of $600\,h^{-1}{\rm Mpc}$. Our study shows the promise of using cross-correlations of the kSZ effect with large-scale structure in order to constrain the growth of structure.

astro-ph.CO

Planck 2018 results. III. High Frequency Instrument data processing and frequency maps

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

astro-ph.CO

Planck intermediate results. LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters

The six parameters of the standard $Λ$CDM model have best-fit values derived from the Planck temperature power spectrum that are shifted somewhat from the best-fit values derived from WMAP data. These shifts are driven by features in the Planck temperature power spectrum at angular scales that had never before been measured to cosmic-variance level precision. We investigate these shifts to determine whether they are within the range of expectation and to understand their origin in the data. Taking our parameter set to be the optical depth of the reionized intergalactic medium $τ$, the baryon density $ω_{\rm b}$, the matter density $ω_{\rm m}$, the angular size of the sound horizon $θ_*$, the spectral index of the primordial power spectrum, $n_{\rm s}$, and $A_{\rm s}e^{-2τ}$ (where $A_{\rm s}$ is the amplitude of the primordial power spectrum), we examine the change in best-fit values between a WMAP-like large angular-scale data set (with multipole moment $\ell<800$ in the Planck temperature power spectrum) and an all angular-scale data set ($\ell<2500$ Planck temperature power spectrum), each with a prior on $τ$ of $0.07\pm0.02$. We find that the shifts, in units of the 1$σ$ expected dispersion for each parameter, are $\{Δτ, ΔA_{\rm s} e^{-2τ}, Δn_{\rm s}, Δω_{\rm m}, Δω_{\rm b}, Δθ_*\} = \{-1.7, -2.2, 1.2, -2.0, 1.1, 0.9\}$, with a $χ^2$ value of 8.0. We find that this $χ^2$ value is exceeded in 15% of our simulated data sets, and that a parameter deviates by more than 2.2$σ$ in 9% of simulated data sets, meaning that the shifts are not unusually large. Comparing $\ell<800$ instead to $\ell>800$, or splitting at a different multipole, yields similar results. We examine the $\ell<800$ model residuals in the $\ell>800$ power spectrum data and find that the features there... [abridged]

astro-ph.CO

Planck intermediate results. LII. Planet flux densities

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 $β_\mathrm{ring} = 2.30\pm0.03$ over the 30-1000 GHz frequency range. The average ratio between the Planck-HFI measurements and the adopted model predictions for all five planets (excluding Jupiter observations for 353 GHz) is 0.997, 0.997, 1.018, and 1.032 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.

astro-ph.EP

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

The secondary cosmic microwave background (CMB) $B$-modes stem from the post-decoupling distortion of the polarization $E$-modes due to the gravitational lensing effect of large-scale structures. These lensing-induced $B$-modes constitute both a valuable probe of the dark matter distribution and an important contaminant for the extraction of the primary CMB $B$-modes from inflation. Planck provides accurate nearly all-sky measurements of both the polarization $E$-modes and the integrated mass distribution via the reconstruction of the CMB lensing potential. By combining these two data products, we have produced 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 $12\,σ$, which agrees with the theoretical expectation derived from the Planck best-fit $Λ$CDM model. This unique nearly all-sky secondary $B$-mode template, which includes the lensing-induced information from intermediate to small ($10\lesssim \ell\lesssim 1000$) 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.

astro-ph.CO