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A. Bonaldi

Publications and source records attributed to A. Bonaldi.

At least 19 recordsLinked to original sources
arXiv2025

Square Kilometre Array Science Data Challenge 3a: foreground removal for an EoR experiment

We present and analyse the results of the Science data challenge 3a (SDC3a, https://sdc3.skao.int/challenges/foregrounds), an EoR foreground-removal community-wide exercise organised by the Square Kilometre Array Observatory (SKAO). The challenge ran for 8 months, from March to October 2023. Participants were provided with realistic simulations of SKA-Low data between 106 MHz and 196 MHz, including foreground contamination from extragalactic as well as Galactic emission, instrumental and systematic effects. They were asked to deliver cylindrical power spectra of the EoR signal, cleaned from all corruptions, and the corresponding confidence levels. Here we describe the approaches taken by the 17 teams that completed the challenge, and we assess their performance using different metrics. The challenge results provide a positive outlook on the capabilities of current foreground-mitigation approaches to recover the faint EoR signal from SKA-Low observations. The median error committed in the EoR power spectrum recovery is below the true signal for seven teams, although in some cases there are some significant outliers. The smallest residual overall is $4.2_{-4.2}^{+20} \times 10^{-4}\,\rm{K}^2h^{-3}$cMpc$^{3}$ across all considered scales and frequencies. The estimation of confidence levels provided by the teams is overall less accurate, with the true error being typically under-estimated, sometimes very significantly. The most accurate error bars account for $60 \pm 20$\% of the true errors committed. The challenge results provide a means for all teams to understand and improve their performance. This challenge indicates that the comparison between independent pipelines could be a powerful tool to assess residual biases and improve error estimation.

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arXiv2023

SKA Science Data Challenge 2: analysis and results

The Square Kilometre Array Observatory (SKAO) will explore the radio sky to new depths in order to conduct transformational science. SKAO data products made available to astronomers will be correspondingly large and complex, requiring the application of advanced analysis techniques to extract key science findings. To this end, SKAO is conducting a series of Science Data Challenges, each designed to familiarise the scientific community with SKAO data and to drive the development of new analysis techniques. We present the results from Science Data Challenge 2 (SDC2), which invited participants to find and characterise 233245 neutral hydrogen (Hi) sources in a simulated data product representing a 2000~h SKA MID spectral line observation from redshifts 0.25 to 0.5. Through the generous support of eight international supercomputing facilities, participants were able to undertake the Challenge using dedicated computational resources. Alongside the main challenge, `reproducibility awards' were made in recognition of those pipelines which demonstrated Open Science best practice. The Challenge saw over 100 participants develop a range of new and existing techniques, with results that highlight the strengths of multidisciplinary and collaborative effort. The winning strategy -- which combined predictions from two independent machine learning techniques to yield a 20 percent improvement in overall performance -- underscores one of the main Challenge outcomes: that of method complementarity. It is likely that the combination of methods in a so-called ensemble approach will be key to exploiting very large astronomical datasets.

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arXiv2020

Square Kilometre Array Science Data Challenge 1: analysis and results

As the largest radio telescope in the world, the Square Kilometre Array (SKA) will lead the next generation of radio astronomy. The feats of engineering required to construct the telescope array will be matched only by the techniques developed to exploit the rich scientific value of the data. To drive forward the development of efficient and accurate analysis methods, we are designing a series of data challenges that will provide the scientific community with high-quality datasets for testing and evaluating new techniques. In this paper we present a description and results from the first such Science Data Challenge (SDC1). Based on SKA MID continuum simulated observations and covering three frequencies (560 MHz, 1400MHz and 9200 MHz) at three depths (8 h, 100 h and 1000 h), SDC1 asked participants to apply source detection, characterization and classification methods to simulated data. The challenge opened in November 2018, with nine teams submitting results by the deadline of April 2019. In this work we analyse the results for 8 of those teams, showcasing the variety of approaches that can be successfully used to find, characterise and classify sources in a deep, crowded field. The results also demonstrate the importance of building domain knowledge and expertise on this kind of analysis to obtain the best performance. As high-resolution observations begin revealing the true complexity of the sky, one of the outstanding challenges emerging from this analysis is the ability to deal with highly resolved and complex sources as effectively as the unresolved source population.

astro-ph.IM↗
arXiv2018

Dust in galaxy clusters: Modeling at millimeter wavelengths and impact on Planck cluster cosmology

We have examined dust emission in galaxy clusters at millimeter wavelengths using the Planck $857 \, {\rm GHz}$ map to constrain the model based on Herschel observations that was used in studies for the Cosmic ORigins Explorer (CORE) mission concept. By stacking the emission from Planck-detected clusters, we estimated the normalization of the infrared luminosity versus mass relation and constrained the spatial profile of the dust emission. We used this newly constrained model to simulate clusters that we inject into Planck frequency maps. The comparison between clusters extracted using these gas+dust simulations and the basic gas-only simulations allows us to assess the impact of cluster dust emission on Planck results. In particular, we determined the impact on cluster parameter recovery (size, flux) and on Planck cluster cosmology results (survey completeness, determination of cosmological parameters). We show that dust emission has a negligible effect on the recovery of individual cluster parameters for the Planck mission, but that it impacts the cluster catalog completeness, reducing the number of detections in the redshift range [0.3-0.8] by up to $\sim 9\%$. Correcting for this incompleteness in the cosmological analysis has a negligible effect on cosmological parameter measurements: in particular, it does not ease the tension between Planck cluster and primary cosmic microwave background cosmologies.

astro-ph.CO↗
arXiv2018

Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts

We present cluster counts and corresponding cosmological constraints from the Planck full mission data set. Our catalogue consists of 439 clusters detected via their Sunyaev-Zeldovich (SZ) signal down to a signal-to-noise ratio of 6, and is more than a factor of 2 larger than the 2013 Planck cluster cosmology sample. The counts are consistent with those from 2013 and yield compatible constraints under the same modelling assumptions. Taking advantage of the larger catalogue, we extend our analysis to the two-dimensional distribution in redshift and signal-to-noise. We use mass estimates from two recent studies of gravitational lensing of background galaxies by Planck clusters to provide priors on the hydrostatic bias parameter, $(1-b)$. In addition, we use lensing of cosmic microwave background (CMB) temperature fluctuations by Planck clusters as an independent constraint on this parameter. These various calibrations imply constraints on the present-day amplitude of matter fluctuations in varying degrees of tension with those from the Planck analysis of primary fluctuations in the CMB; for the lowest estimated values of $(1-b)$ the tension is mild, only a little over one standard deviation, while it remains substantial ($3.7\,σ$) for the largest estimated value. We also examine constraints on extensions to the base flat $Λ$CDM model by combining the cluster and CMB constraints. The combination appears to favour non-minimal neutrino masses, but this possibility does little to relieve the overall tension because it simultaneously lowers the implied value of the Hubble parameter, thereby exacerbating the discrepancy with most current astrophysical estimates. Improving the precision of cluster mass calibrations from the current 10%-level to 1% would significantly strengthen these combined analyses and provide a stringent test of the base $Λ$CDM model.

astro-ph.CO↗
arXiv2017

Planck 2015 results. XX. Constraints on inflation

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. 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 $n_\mathrm{s} = 0.968 \pm 0.006$ and tightly constrain its scale dependence to $d n_s/d \ln k =-0.003 \pm 0.007$ when combined with the Planck lensing likelihood. When the high-$\ell$ polarization data is included, the results are consistent and uncertainties are reduced. The upper bound on the tensor-to-scalar ratio is $r_{0.002} < 0.11$ (95% CL), consistent with the B-mode polarization constraint $r< 0.12$ (95% CL) obtained from a joint BICEP2/Keck Array and Planck analysis. These results imply that $V(ϕ) \propto ϕ^2$ and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as $R^2$ inflation. Three independent methods reconstructing the primordial power spectrum are investigated. The Planck data are consistent with adiabatic primordial perturbations. We investigate inflationary models producing an anisotropic modulation of the primordial curvature power spectrum as well as generalized models of inflation not governed by a scalar field with a canonical kinetic term. The 2015 results are consistent with the 2013 analysis based on the nominal mission data.

astro-ph.CO↗
arXiv2017

Exploring cosmic origins with CORE: effects of observer peculiar motion

We discuss the effects on the CMB, CIB, and thermal SZ effect due to the peculiar motion of an observer with respect to the CMB rest frame, which induces boosting effects. We investigate the scientific perspectives opened by future CMB space missions, focussing on the CORE proposal. The improvements in sensitivity offered by a mission like CORE, together with its high resolution over a wide frequency range, will provide a more accurate estimate of the CMB dipole. The extension of boosting effects to polarization and cross-correlations will enable a more robust determination of purely velocity-driven effects that are not degenerate with the intrinsic CMB dipole, allowing us to achieve a S/N ratio of 13; this improves on the Planck detection and essentially equals that of an ideal cosmic-variance-limited experiment up to a multipole l of 2000. Precise inter-frequency calibration will offer the opportunity to constrain or even detect CMB spectral distortions, particularly from the cosmological reionization, because of the frequency dependence of the dipole spectrum, without resorting to precise absolute calibration. The expected improvement with respect to COBE-FIRAS in the recovery of distortion parameters (in principle, a factor of several hundred for an ideal experiment with the CORE configuration) ranges from a factor of several up to about 50, depending on the quality of foreground removal and relative calibration. Even for 1% accuracy in both foreground removal and relative calibration at an angular scale of 1 deg, we find that dipole analyses for a mission like CORE will be able to improve the recovery of the CIB spectrum amplitude by a factor of 17 in comparison with current results based on FIRAS. In addition to the scientific potential of a mission like CORE for these analyses, synergies with other planned and ongoing projects are also discussed.

astro-ph.CO↗
arXiv2017

Exploring cosmic origins with CORE: mitigation of systematic effects

We present an analysis of the main systematic effects that could impact the measurement of CMB polarization with the proposed CORE space mission. We employ timeline-to-map simulations to verify that the CORE instrumental set-up and scanning strategy allow us to measure sky polarization to a level of accuracy adequate to the mission science goals. We also show how the CORE observations can be processed to mitigate the level of contamination by potentially worrying systematics, including intensity-to-polarization leakage due to bandpass mismatch, asymmetric main beams, pointing errors and correlated noise. We use analysis techniques that are well validated on data from current missions such as Planck to demonstrate how the residual contamination of the measurements by these effects can be brought to a level low enough not to hamper the scientific capability of the mission, nor significantly increase the overall error budget. We also present a prototype of the CORE photometric calibration pipeline, based on that used for Planck, and discuss its robustness to systematics, showing how CORE can achieve its calibration requirements. While a fine-grained assessment of the impact of systematics requires a level of knowledge of the system that can only be achieved in a future study phase, the analysis presented here strongly suggests that the main areas of concern for the CORE mission can be addressed using existing knowledge, techniques and algorithms.

astro-ph.CO↗
arXiv2017

Exploring Cosmic Origins with CORE: B-mode Component Separation

We demonstrate that, for the baseline design of the CORE satellite mission, the polarized foregrounds can be controlled at the level required to allow the detection of the primordial cosmic microwave background (CMB) $B$-mode polarization with the desired accuracy at both reionization and recombination scales, for tensor-to-scalar ratio values of ${r\gtrsim 5\times 10^{-3}}$. We consider detailed sky simulations based on state-of-the-art CMB observations that consist of CMB polarization with $τ=0.055$ and tensor-to-scalar values ranging from $r=10^{-2}$ to $10^{-3}$, Galactic synchrotron, and thermal dust polarization with variable spectral indices over the sky, polarized anomalous microwave emission, polarized infrared and radio sources, and gravitational lensing effects. Using both parametric and blind approaches, we perform full component separation and likelihood analysis of the simulations, allowing us to quantify both uncertainties and biases on the reconstructed primordial $B$-modes. Under the assumption of perfect control of lensing effects, CORE would measure an unbiased estimate of $r=\left(5 \pm 0.4\right)\times 10^{-3}$ after foreground cleaning. In the presence of both gravitational lensing effects and astrophysical foregrounds, the significance of the detection is lowered, with CORE achieving a $4σ$-measurement of $r=5\times 10^{-3}$ after foreground cleaning and $60$% delensing. For lower tensor-to-scalar ratios ($r=10^{-3}$) the overall uncertainty on $r$ is dominated by foreground residuals, not by the 40% residual of lensing cosmic variance. Moreover, the residual contribution of unprocessed polarized point-sources can be the dominant foreground contamination to primordial B-modes at this $r$ level, even on relatively large angular scales, $\ell \sim 50$. Finally, we report two sources of potential bias for the detection of the primordial $B$-modes.[abridged]

astro-ph.CO↗
arXiv2017

Exploring Cosmic Origins with CORE: Survey requirements and mission design

Future observations of cosmic microwave background (CMB) polarisation have the potential to answer some of the most fundamental questions of modern physics and cosmology. In this paper, we list the requirements for a future CMB polarisation survey addressing these scientific objectives, and discuss the design drivers of the CORE space mission proposed to ESA in answer to the "M5" call for a medium-sized mission. The rationale and options, and the methodologies used to assess the mission's performance, are of interest to other future CMB mission design studies. CORE is designed as a near-ultimate CMB polarisation mission which, for optimal complementarity with ground-based observations, will perform the observations that are known to be essential to CMB polarisation scienceand cannot be obtained by any other means than a dedicated space mission.

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arXiv2017

Exploring Cosmic Origins with CORE: The Instrument

We describe a space-borne, multi-band, multi-beam polarimeter aiming at a precise and accurate measurement of the polarization of the Cosmic Microwave Background. The instrument is optimized to be compatible with the strict budget requirements of a medium-size space mission within the Cosmic Vision Programme of the European Space Agency. The instrument has no moving parts, and uses arrays of diffraction-limited Kinetic Inductance Detectors to cover the frequency range from 60 GHz to 600 GHz in 19 wide bands, in the focal plane of a 1.2 m aperture telescope cooled at 40 K, allowing for an accurate extraction of the CMB signal from polarized foreground emission. The projected CMB polarization survey sensitivity of this instrument, after foregrounds removal, is 1.7 μK$\cdot$arcmin. The design is robust enough to allow, if needed, a downscoped version of the instrument covering the 100 GHz to 600 GHz range with a 0.8 m aperture telescope cooled at 85 K, with a projected CMB polarization survey sensitivity of 3.2 μK$\cdot$arcmin.

astro-ph.IM↗
arXiv2017

Exploring Cosmic Origins with CORE: Extragalactic sources in Cosmic Microwave Background maps

We discuss the potential of a next generation space-borne Cosmic Microwave Background (CMB) experiment for studies of extragalactic sources. Our analysis has particular bearing on the definition of the future space project, CORE, that has been submitted in response to ESA's call for a Medium-size mission opportunity as the successor of the Planck satellite. Even though the effective telescope size will be somewhat smaller than that of Planck, CORE will have a considerably better angular resolution at its highest frequencies, since, in contrast with Planck, it will be diffraction limited at all frequencies. The improved resolution implies a considerable decrease of the source confusion, i.e. substantially fainter detection limits. In particular, CORE will detect thousands of strongly lensed high-z galaxies distributed over the full sky. The extreme brightness of these galaxies will make it possible to study them, via follow-up observations, in extraordinary detail. Also, the CORE resolution matches the typical sizes of high-z galaxy proto-clusters much better than the Planck resolution, resulting in a much higher detection efficiency; these objects will be caught in an evolutionary phase beyond the reach of surveys in other wavebands. Furthermore, CORE will provide unique information on the evolution of the star formation in virialized groups and clusters of galaxies up to the highest possible redshifts. Finally, thanks to its very high sensitivity, CORE will detect the polarized emission of thousands of radio sources and, for the first time, of dusty galaxies, at mm and sub-mm wavelengths, respectively.

astro-ph.GA↗
arXiv2017

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↗
arXiv2017

Exploring Cosmic Origins with CORE: Cluster Science

We examine the cosmological constraints that can be achieved with a galaxy cluster survey with the future CORE space mission. Using realistic simulations of the millimeter sky, produced with the latest version of the Planck Sky Model, we characterize the CORE cluster catalogues as a function of the main mission performance parameters. We pay particular attention to telescope size, key to improved angular resolution, and discuss the comparison and the complementarity of CORE with ambitious future ground-based CMB experiments that could be deployed in the next decade. A possible CORE mission concept with a 150 cm diameter primary mirror can detect of the order of 50,000 clusters through the thermal Sunyaev-Zeldovich effect (SZE). The total yield increases (decreases) by 25% when increasing (decreasing) the mirror diameter by 30 cm. The 150 cm telescope configuration will detect the most massive clusters ($>10^{14}\, M_\odot$) at redshift $z>1.5$ over the whole sky, although the exact number above this redshift is tied to the uncertain evolution of the cluster SZE flux-mass relation; assuming self-similar evolution, CORE will detect $\sim 500$ clusters at redshift $z>1.5$. This changes to 800 (200) when increasing (decreasing) the mirror size by 30 cm. CORE will be able to measure individual cluster halo masses through lensing of the cosmic microwave background anisotropies with a 1-$σ$ sensitivity of $4\times10^{14} M_\odot$, for a 120 cm aperture telescope, and $10^{14} M_\odot$ for a 180 cm one. [abridged]

astro-ph.CO↗
arXiv2016

Multi-frequency polarimetry of a complete sample of PACO radio sources

We present high sensitivity polarimetric observations in 6 bands covering the 5.5-38 GHz range of a complete sample of 53 compact extragalactic radio sources brighter than 200 mJy at 20 GHz. The observations, carried out with the Australia Telescope Compact Array (ATCA), achieved a 91% detection rate (at 5 sigma). Within this frequency range the spectra of about 95% of sources are well fitted by double power laws, both in total intensity and in polarisation, but the spectral shapes are generally different in the two cases. Most sources were classified as either steep- or peaked-spectrum but less than 50% have the same classification in total and in polarised intensity. No significant trends of the polarisation degree with flux density or with frequency were found. The mean variability index in total intensity of steep-spectrum sources increases with frequency for a 4-5 year lag, while no significant trend shows up for the other sources and for the 8 year lag. In polarisation, the variability index, that could be computed only for the 8 year lag, is substantially higher than in total intensity and has no significant frequency dependence.

astro-ph.GA↗
arXiv2016

Planck 2015 results. XXI. The integrated Sachs-Wolfe effect

This paper presents a study of the ISW effect from the Planck 2015 temperature and polarization data release. The CMB is cross-correlated with different LSS tracers: the NVSS, SDSS and WISE catalogues, and the Planck 2015 lensing map. This cross-correlation yields a detection at $4\,σ$, where most of the signal-to-noise is due to the Planck lensing and NVSS. In fact, the ISW effect is detected only from the Planck data (through the ISW-lensing bispectrum) at $\approx 3\,σ$, which is similar to the detection level achieved by combining the cross-correlation signal coming from all the catalogues. The ISW signal allow us to detect $Ω_Λ$ at more than $3\,σ$. 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, polarization data is used to study the anomalously large ISW signal previously reported through the stacking of CMB features at the locations of known superstructures. 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 LSS traced by the 2MPZ survey by directly inverting the density field into the gravitational potential field.

astro-ph.CO↗
arXiv2016

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↗
arXiv2016

Planck 2015 results. XV. Gravitational lensing

We present the most significant measurement of the cosmic microwave background (CMB) lensing potential to date (at a level of 40 sigma), using temperature and polarization data from the Planck 2015 full-mission release. Using a polarization-only estimator we detect lensing at a significance of 5 sigma. 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 best-fitting LCDM model based on the Planck temperature and polarization power spectra. Using the lensing likelihood alone we obtain a percent-level measurement of the parameter combination $σ_8 Ω_m^{0.25} = 0.591\pm 0.021$. 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 10 sigma, 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 3 sigma level, as expected due to dark energy in the concordance LCDM model.

astro-ph.CO↗