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 $12\,\sigma$, which agrees with the theoretical expectation derived from the Planck best-fit $\Lambda$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.Comment: 20 pages, 12 figures; Accepted for publication in A&A; The B-mode map is part of the PR2-2015 Cosmology Products; available as Lensing Products in the Planck Legacy Archive http://pla.esac.esa.int/pla/#cosmology; and described in the 'Explanatory Supplement' https://wiki.cosmos.esa.int/planckpla2015/index.php/Specially_processed_maps#2015_Lensing-induced_B-mode_ma

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 0.25 m =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 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

Euclid: The reduced shear approximation and magnification bias for Stage IV cosmic shear experiments

Context: Stage IV weak lensing experiments will offer more than an order of magnitude leap in precision. We must therefore ensure that our analyses remain accurate in this new era. Accordingly, previously ignored systematic effects must be addressed. / Aims: In this work, we evaluate the impact of the reduced shear approximation and magnification bias on information obtained from the angular power spectrum. To first-order, the statistics of reduced shear, a combination of shear and convergence, are taken to be equal to those of shear. However, this approximation can induce a bias in the cosmological parameters that can no longer be neglected. A separate bias arises from the statistics of shear being altered by the preferential selection of galaxies and the dilution of their surface densities in high-magnification regions. / Methods: The corrections for these systematic effects take similar forms, allowing them to be treated together. We calculated the impact of neglecting these effects on the cosmological parameters that would be determined from Euclid, using cosmic shear tomography. To do so, we employed the Fisher matrix formalism, and included the impact of the super-sample covariance. We also demonstrate how the reduced shear correction can be calculated using a lognormal field forward modelling approach. / Results: These effects cause significant biases in Ωm, σ8, ns, ΩDE, w0, and wa of −0.53σ, 0.43σ, −0.34σ, 1.36σ, −0.68σ, and 1.21σ, respectively. We then show that these lensing biases interact with another systematic effect: the intrinsic alignment of galaxies. Accordingly, we have developed the formalism for an intrinsic alignment-enhanced lensing bias correction. Applying this to Euclid, we find that the additional terms introduced by this correction are sub-dominant

Euclid: the selection of quiescent and star-forming galaxies using observed colours

The Euclid mission will observe well over a billion galaxies out to z ∼ 6 and beyond. This will offer an unrivalled opportunity to investigate several key questions for understanding galaxy formation and evolution. The first step for many of these studies will be the selection of a sample of quiescent and star-forming galaxies, as is often done in the literature by using well-known colour techniques such as the ‘UVJ’ diagram. However, given the limited number of filters available for the Euclid telescope, the recovery of such rest-frame colours will be challenging. We therefore investigate the use of observed Euclid colours, on their own and together with ground-based u-band observations, for selecting quiescent and star-forming galaxies. The most efficient colour combination, among the ones tested in this work, consists of the (u − VIS) and (VIS − J) colours. We find that this combination allows users to select a sample of quiescent galaxies complete to above ∼70 per cent and with less than 15 per cent contamination at redshifts in the range 0.75 65 per cent completeness level and contamination below 20 per cent at 1 < z < 2 for finding quiescent galaxies. In comparison, the sample of quiescent galaxies selected with the traditional UVJ technique is only ∼20 per cent complete at z < 3, when recovering the rest-frame colours using mock Euclid observations. This shows that our new methodology is the most suitable one when only Euclid bands, along with u-band imaging, are available

Euclid preparation: XXVII. A UV-NIR spectral atlas of compact planetary nebulae for wavelength calibration

The Euclid mission will conduct an extragalactic survey over 15 000 deg2 of the extragalactic sky. The spectroscopic channel of the Near-Infrared Spectrometer and Photometer (NISP) has a resolution of R~450 for its blue and red grisms that collectively cover the 0.93-1.89 μm range. NISP will obtain spectroscopic redshifts for 3 107 galaxies for the experiments on galaxy clustering, baryonic acoustic oscillations, and redshift space distortion. The wavelength calibration must be accurate within 5 A to avoid systematics in the redshifts and downstream cosmological parameters. The NISP pre-flight dispersion laws for the grisms were obtained on the ground using a Fabry-Perot etalon. Launch vibrations, zero gravity conditions, and thermal stabilisation may alter these dispersion laws, requiring an in-flight recalibration. To this end, we use the emission lines in the spectra of compact planetary nebulae (PNe), which were selected from a PN database. To ensure completeness of the PN sample, we developed a novel technique to identify compact and strong line emitters in Gaia spectroscopic data using the Gaia spectra shape coefficients. We obtained VLT/X-shooter spectra from 0.3 to 2.5 μm for 19 PNe in excellent seeing conditions and a wide slit, mimicking Euclid's slitless spectroscopy mode but with a ten times higher spectral resolution. Additional observations of one northern PN were obtained in the 0.80- 1.90 μm range with the GMOS and GNIRS instruments at the Gemini North Observatory. The collected spectra were combined into an atlas of heliocentric vacuum wavelengths with a joint statistical and systematic accuracy of 0.1 A in the optical and 0.3 A in the near-infrared. The wavelength atlas and the related 1D and 2D spectra are made publicly available

Euclid preparation LI. Forecasting the recovery of galaxy physical properties and their relations with template-fitting and machine-learning methods

Euclid will collect an enormous amount of data during the mission’s lifetime, observing billions of galaxies in the extragalactic sky. Along with traditional template-fitting methods, numerous machine learning (ML) algorithms have been presented for computing their photometric redshifts and physical parameters (PPs), requiring significantly less computing effort while producing equivalent performance measures. However, their performance is limited by the quality and amount of input information entering the model (the features), to a level where the recovery of some well-established physical relationships between parameters might not be guaranteed – for example, the star-forming main sequence (SFMS). To forecast the reliability of Euclid photo-zs and PPs calculations, we produced two mock catalogs simulating the photometry with the UNIONS ugriz and Euclid filters. We simulated the Euclid Wide Survey (EWS) and Euclid Deep Fields (EDF), alongside two auxiliary fields. We tested the performance of a template-fitting algorithm (Phosphoros) and four ML methods in recovering photo-zs, PPs (stellar masses and star formation rates), and the SFMS on the simulated Euclid fields. To mimic the Euclid processing as closely as possible, the models were trained with Phosphoros-recovered labels and tested on the simulated ground truth. For the EWS, we found that the best results are achieved with a mixed labels approach, training the models with wide survey features and labels from the Phosphoros results on deeper photometry, that is, with the best possible set of labels for a given photometry. This imposes a prior to the input features, helping the models to better discern cases in degenerate regions of feature space, that is, when galaxies have similar magnitudes and colors but different redshifts and PPs, with performance metrics even better than those found with Phosphoros. We found no more than 3% performance degradation using a COSMOS-like reference sample or removing u band data, which will not be available until after data release DR1. The best results are obtained for the EDF, with appropriate recovery of photo-z, PPs, and the SFMS

Euclid: Estimation of the impact of correlated readout noise for flux measurements with the euclid NISP instrument

The Euclid satellite, to be launched by ESA in 2022, will be a major instrument for cosmology for the next decades. Euclid is composed of two instruments: the Visible instrument and the Near Infrared Spectrometer and Photometer (NISP). In this work, we estimate the implications of correlated readout noise in the NISP detectors for the final in-flight flux measurements. Considering the multiple accumulated readout mode, for which the UTR (Up The Ramp) exposure frames are averaged in groups, we derive an analytical expression for the noise covariance matrix between groups in the presence of correlated noise. We also characterize the correlated readout noise properties in the NISP engineering-grade detectors using long dark integrations. For this purpose, we assume a (1/f)α-like noise model and fit the model parameters to the data, obtaining typical values of $\sigma ={19.7}_{-0.8}^{+1.1}$ e− Hz−0.5, ${f}_{\mathrm{knee}}=({5.2}_{-1.3}^{+1.8})\times {10}^{-3}\,\mathrm{Hz}$ and $\alpha ={1.24}_{-0.21}^{+0.26}$. Furthermore, via realistic simulations and using a maximum likelihood flux estimator we derive the bias between the input flux and the recovered one. We find that using our analytical expression for the covariance matrix of the correlated readout noise we diminish this bias by up to a factor of four with respect to the white noise approximation for the covariance matrix. Finally, we conclude that the final bias on the in-flight NISP flux measurements should still be negligible even in the white readout noise approximation, which is taken as a baseline for the Euclid on-board processing to estimate the on-sky flux

Euclid: The importance of galaxy clustering and weak lensing cross-correlations within the photometric Euclid survey

Context. The data from the Euclid mission will enable the measurement of the angular positions and weak lensing shapes of over a billion galaxies, with their photometric redshifts obtained together with ground-based observations. This large dataset, with well-controlled systematic effects, will allow for cosmological analyses using the angular clustering of galaxies (GCph) and cosmic shear (WL). For Euclid, these two cosmological probes will not be independent because they will probe the same volume of the Universe. The cross-correlation (XC) between these probes can tighten constraints and is therefore important to quantify their impact for Euclid. Aims. In this study, we therefore extend the recently published Euclid forecasts by carefully quantifying the impact of XC not only on the final parameter constraints for different cosmological models, but also on the nuisance parameters. In particular, we aim to decipher the amount of additional information that XC can provide for parameters encoding systematic effects, such as galaxy bias, intrinsic alignments (IAs), and knowledge of the redshift distributions. Methods. We follow the Fisher matrix formalism and make use of previously validated codes. We also investigate a different galaxy bias model, which was obtained from the Flagship simulation, and additional photometric-redshift uncertainties; we also elucidate the impact of including the XC terms on constraining these latter. Results. Starting with a baseline model, we show that the XC terms reduce the uncertainties on galaxy bias by ∼17% and the uncertainties on IA by a factor of about four. The XC terms also help in constraining the γ parameter for minimal modified gravity models. Concerning galaxy bias, we observe that the role of the XC terms on the final parameter constraints is qualitatively the same irrespective of the specific galaxy-bias model used. For IA, we show that the XC terms can help in distinguishing between different models, and that if IA terms are neglected then this can lead to significant biases on the cosmological parameters. Finally, we show that the XC terms can lead to a better determination of the mean of the photometric galaxy distributions. Conclusions. We find that the XC between GCph and WL within the Euclid survey is necessary to extract the full information content from the data in future analyses. These terms help in better constraining the cosmological model, and also lead to a better understanding of the systematic effects that contaminate these probes. Furthermore, we find that XC significantly helps in constraining the mean of the photometric-redshift distributions, but, at the same time, it requires more precise knowledge of this mean with respect to single probes in order not to degrade the final “figure of merit”

Euclid preparation: XXXI. The effect of the variations in photometric passbands on photometric-redshift accuracy

The technique of photometric redshifts has become essential for the exploitation of multi-band extragalactic surveys. While the requirements on photometric redshifts for the study of galaxy evolution mostly pertain to the precision and to the fraction of outliers, the most stringent requirement in their use in cosmology is on the accuracy, with a level of bias at the sub-percent level for the Euclid cosmology mission. A separate, and challenging, calibration process is needed to control the bias at this level of accuracy. The bias in photometric redshifts has several distinct origins that may not always be easily overcome. We identify here one source of bias linked to the spatial or time variability of the passbands used to determine the photometric colours of galaxies. We first quantified the effect as observed on several well-known photometric cameras, and found in particular that, due to the properties of optical filters, the redshifts of off-axis sources are usually overestimated. We show using simple simulations that the detailed and complex changes in the shape can be mostly ignored and that it is suficient to know the mean wavelength of the passbands of each photometric observation to correct almost exactly for this bias; the key point is that this mean wavelength is independent of the spectral energy distribution of the source. We use this property to propose a correction that can be computationally eficiently implemented in some photometric-redshift algorithms, in particular template-fitting. We verified that our algorithm, implemented in the new photometric-redshift code Phosphoros, can effectively reduce the bias in photometric redshifts on real data using the CFHTLS T007 survey, with an average measured bias Δz over the redshift range 0:4 ≤ z ≤ 0:7 decreasing by about 0.02, specifically from Δz ≈ 0:04 to Δz ≈ 0:02 around z = 0:5. Our algorithm is also able to produce corrected photometry for other applications

Euclid preparation: XXXII. Evaluating the weak-lensing cluster mass biases using the Three Hundred Project hydrodynamical simulations

The photometric catalogue of galaxy clusters extracted from ESA Euclid data is expected to be very competitive for cosmological studies. Using dedicated hydrodynamical simulations, we present systematic analyses simulating the expected weak-lensing profiles from clusters in a variety of dynamic states and for a wide range of redshifts. In order to derive cluster masses, we use a model consistent with the implementation within the Euclid Consortium of the dedicated processing function and find that when we jointly model the mass and concentration parameter of the Navarro–Frenk–White halo profile, the weak-lensing masses tend to be biased low by 5–10% on average with respect to the true mass, up to z = 0.5. For a fixed value for the concentration c200 = 3, the mass bias is decreases to lower than 5%, up to z = 0.7, along with the relative uncertainty. Simulating the weak-lensing signal by projecting along the directions of the axes of the moment of inertia tensor ellipsoid, we find that orientation matters: when clusters are oriented along the major axis, the lensing signal is boosted, and the recovered weak-lensing mass is correspondingly overestimated. Typically, the weak-lensing mass bias of individual clusters is modulated by the weak-lensing signal-to-noise ratio, which is related to the redshift evolution of the number of galaxies used for weak-lensing measurements: the negative mass bias tends to be stronger toward higher redshifts. However, when we use a fixed value of the concentration parameter, the redshift evolution trend is reduced. These results provide a solid basis for the weak-lensing mass calibration required by the cosmological application of future cluster surveys from Euclid and Rubin