A Monte Carlo comparison between template-based and Wiener-filter CMB dipole estimators
H. Thommesen, K. J. Andersen, R. Aurlien, R. Banerji, M. Brilenkov, H. K. Eriksen, U. Fuskeland, M. Galloway, L. M. Mocanu, T. L. Svalheim, I. K. Wehus
We review and compare two different CMB dipole estimators discussed in the literature, and assess their performances through Monte Carlo simulations. The first method amounts to simple template regression with partial sky data, while the second method is an optimal Wiener filter (or Gibbs sampling) implementation. The main difference between the two methods is that the latter approach takes into account correlations with higher-order CMB temperature fluctuations that arise from non-orthogonal spherical harmonics on an incomplete sky, which for recent CMB data sets (such as Planck) is the dominant source of uncertainty. For an accepted sky fraction of 81% and an angular CMB power spectrum corresponding to the best-fit Planck 2018 $Λ$CDM model, we find that the uncertainty on the recovered dipole amplitude is about six times smaller for the Wiener filter approach than for the template approach, corresponding to 0.5 and 3$~μ$K, respectively. Similar relative differences are found for the corresponding directional parameters and other sky fractions. We note that the Wiener filter algorithm is generally applicable to any dipole estimation problem on an incomplete sky, as long as a statistical and computationally tractable model is available for the unmasked higher-order fluctuations. The methodology described in this paper forms the numerical basis for the most recent determination of the CMB solar dipole from Planck, as summarized by arXiv:2007.04997.
We present the application of a new method to compute the Wiener filter solution of large and complex data sets. Contrary to the iterative solvers usually employed in signal processing, our algorithm does not require the use of preconditioners to be computationally efficient. The new scheme is conceptually very simple and therefore easy to implement, numerically absolutely stable, and guaranteed to converge. We introduce a messenger field to mediate between the different preferred bases in which signal and noise properties can be specified most conveniently, and rephrase the signal reconstruct…
We show how a neural network can be trained to Wiener filter masked CMB maps to high accuracy. We propose an innovative neural network architecture, the WienerNet, which guarantees linearity in the data map. Our method does not require Wiener filtered training data, but rather learns Wiener filtering from tailored loss functions which are mathematically guaranteed to be minimized by the exact solution. Once trained, the neural network Wiener filter is extremely fast, about a factor of 1000 faster than the standard conjugate gradient method. Wiener filtering is the computational bottleneck in m…
We present a new approach to calculate the Wiener filter solution of general data sets. It is trivial to implement, flexible, numerically absolutely stable, and guaranteed to converge. Most importantly, it does not require an ingenious choice of preconditioner to work well. The method is capable of taking into account inhomogeneous noise distributions and arbitrary mask geometries. It iteratively builds up the signal reconstruction by means of a messenger field, introduced to mediate between the different preferred bases in which signal and noise properties can be specified most conveniently. …
We present an augmented version of our dual messenger algorithm for spin field reconstruction on the sphere, while accounting for highly non-trivial and realistic noise models such as modulated correlated noise. We also describe an optimization method for the estimation of noise covariance from Monte Carlo simulations. Using simulated Planck polarized cosmic microwave background (CMB) maps as a showcase, we demonstrate the capabilities of the algorithm in reconstructing pure E and B maps, guaranteed to be free from ambiguous modes resulting from the leakage or coupling issue that plagues conve…
We present a Bayesian model for multi-resolution CMB component separation based on Wiener filtering and/or computation of constrained realizations, extending a previously developed framework. We also develop an efficient solver for the corresponding linear system for the associated signal amplitudes. The core of this new solver is an efficient preconditioner based on the pseudo-inverse of the coefficient matrix of the linear system. In the full sky coverage case, the method gives a speed-up of 2--3x in compute time compared to a simple diagonal preconditioner, and it is easier to implement in …
We describe the details of the binned bispectrum estimator as used for the official 2013 and 2015 analyses of the temperature and polarization CMB maps from the ESA Planck satellite. The defining aspect of this estimator is the determination of a map bispectrum (3-point correlator) that has been binned in harmonic space. For a parametric determination of the non-Gaussianity in the map (the so-called fNL parameters), one takes the inner product of this binned bispectrum with theoretically motivated templates. However, as a complementary approach one can also smooth the binned bispectrum using a…
Efforts to detect a primordial $B$-mode of CMB polarization generated by inflationary gravitational waves ought to mitigate the large variance associated with the $B$-modes produced by gravitational lensing, a process known as delensing. A popular approach to delensing entails building a lensing $B$-mode template by mimicking the lensing operation, either at gradient order or non-perturbatively, using high-resolution $E$-mode observations and some proxy of the lensing potential. By explicitly calculating all contributions to two-loop order in lensing to the power spectrum of $B$-modes delensed…
We present a new method for detecting the missing baryons by generating a template for the kinematic Sunyaev-Zel'dovich effect. The template is computed from the product of a reconstructed velocity field with a galaxy field; we find that the combination of a galaxy redshift survey such as SDSS and a CMB survey such as ACT and PLANCK can detect the kSZ, and thus the ionized gas, at significant signal-to-noise. Unlike other techniques that look for hot gas or metals, this approach directly detects the electrons in the IGM through their signature on the CMB. The estimated signal-to-noise for dete…
The Sunyaev-Zel'dovich (SZ) effect has long been identified as one of the most important secondary effects of the Cosmic Microwave Background (CMB). On the one hand, it is a potentially very powerful cosmological probe providing us with additional constraints and on the other hand it represents the major source of secondary fluctuations at small angular scales (l > 1000). We investigate the effects of the SZ modelling in the determination of the cosmological parameters. We explore the consequences of the SZ power spectrum computation by comparing three increasingly complex modelling, from a fi…
Accurate galaxy cluster mass measurements from the gravitational lensing of the cosmic microwave background temperature maps depend on mitigating potential biases from the cluster's own thermal Sunyaev-Zel'dovich (SZ) effect signal. Quadratic lensing estimators use a pair of maps to extract the lensing signal: a large scale gradient map and a small scale lensing map. The SZ bias can be eliminated by using an SZ-free map in the pair, with the gradient map being favored for signal-to-noise reasons. However, while this approach eliminates the bias, the SZ power in small scale lensing map adds ext…
We compute the polarized signal from atmospheric molecular oxygen due to Zeeman effect in the Earth magnetic field for various sites suitable for CMB measurements such as South Pole, Dome C (Antarctica) and Atacama desert (Chile). We present maps of this signal for those sites and show their typical elevation and azimuth dependencies. We find a typical circularly polarized signal (V Stokes parameter) level of 50 - 300 μK at 90 GHz when looking at the zenith; Atacama site shows the lowest emission while Dome C site presents the lowest gradient in polarized brightness temperature (0.3 μK/deg at …
We compute the circularly polarized signal from atmospheric molecular oxygen. Polarization of O2 rotational lines is caused by Zeeman effect in the Earth magnetic field. We evaluate the circularly polarized emission for various sites suitable for CMB measurements: South Pole and Dome C (Antarctica), Atacama (Chile) and Testa Grigia (Italy). An analysis of the polarized signal is presented and discussed in the framework of future CMB polarization experiments. We find a typical circularly polarized signal (V Stokes parameter) of ~ 50 - 300 μK at 90 GHz looking at the zenith. Among the other site…
We propose optimal estimators for bispectra from excited states. Two common properties of such bispectra are the enhancement in the collinear limit, and the prediction of oscillating features. We review the physics behind excited states and some of the choices made in the literature. We show that the enfolded template is a good template in the collinear limit, but does poorly elsewhere, establishing a strong case for an improved estimator. Although the detailed scale dependence of the bispectra differs depending on various assumptions, generally the predicted bispectra are either effectively 1…
We adapt our recently proposed dual messenger algorithm for spin field reconstruction and showcase its efficiency and effectiveness in Wiener filtering polarized cosmic microwave background (CMB) maps. Unlike conventional preconditioned conjugate gradient (PCG) solvers, our preconditioner-free technique can deal with high-resolution joint temperature and polarization maps with inhomogeneous noise distributions and arbitrary mask geometries with relative ease. Various convergence diagnostics illustrate the high quality of the dual messenger reconstruction. In contrast, the PCG implementation fa…
We use the binned bispectrum estimator to determine the bispectra of the dust, free-free, synchrotron, and AME galactic foregrounds using maps produced by the Commander component separation method from Planck 2015 data. We find that all of these peak in the squeezed configuration, allowing for potential confusion with in particular the local primordial shape. Applying an additional functionality implemented in the binned bispectrum estimator code, we then use these galactic bispectra as templates in an $f_\mathrm{NL}$ analysis of other maps. After testing and validating the method and code wit…
We present a high performance solution to the Wiener filtering problem via a formulation that is dual to the recently developed messenger technique. This new dual messenger algorithm, like its predecessor, efficiently calculates the Wiener filter solution of large and complex data sets without preconditioning and can account for inhomogeneous noise distributions and arbitrary mask geometries. We demonstrate the capabilities of this scheme in signal reconstruction by applying it on a simulated cosmic microwave background (CMB) temperature data set. The performance of this new method is compared…
Delensing, the removal of the limiting lensing B-mode background, is crucial for the success of future cosmic microwave background (CMB) surveys in constraining inflationary gravitational waves (IGWs). In recent work, delensing with large-scale structure tracers has emerged as a promising method both for improving constraints on IGWs and for testing delensing methods for future use. However, the delensing fractions (i.e., the fraction of the lensing-B mode power removed) achieved by recent efforts have been only $20-30\%$. In this work, we provide a detailed characterization of a full-sky, dus…
We present a new model of the microwave sky in polarization that can be used to simulate data from CMB polarization experiments. We exploit the most recent results from the Planck satellite to provide an accurate description of the diffuse polarized foreground synchrotron and thermal dust emission. Our model can include the two mentioned foregrounds, and also a constructed template of Anomalous Microwave Emission (AME). Several options for the frequency dependence of the foregrounds can be easily selected, to reflect our uncertainties and to test the impact of different assumptions. Small angu…
This work extends the Elsner & Wandelt (2013) iterative method for efficient, preconditioner-free Wiener filtering to cases in which the noise covariance matrix is dense, but can be decomposed into a sum whose parts are sparse in convenient bases. The new method, which uses multiple messenger fields, reproduces Wiener filter solutions for test problems, and we apply it to a case beyond the reach of the Elsner & Wandelt (2013) method. We compute the Wiener filter solution for a simulated Cosmic Microwave Background map that contains spatially-varying, uncorrelated noise, isotropic $1/f$ noise, …
Cross-correlations between Cosmic Microwave Background (CMB) temperature and $y$-spectral distortions anisotropies have been previously proposed as a way to measure the local bispectrum parameter $f_{\rm NL}^{\rm loc.}$ in a range of scales inaccessible to either CMB ($T$, $E$) bispectra or $T$-$μ$ correlations. This is useful e.g. to test scale dependence of primordial non-Gaussianity. Unfortunately, the primordial $y$-T signal is strongly contaminated by the late-time correlation between the Integrated Sachs Wolfe and Sunyaev-Zel'dovich (SZ) effects. Moreover, SZ itself generates a large noi…
SPT-3G D1: Foreground-Robust Lensing Templates for Primordial Gravitational Wave Searches
Stanford University（斯坦福大学）；California Institute of Technology（加州理工学院）；Kavli Institute for Particle Astrophysics and Cosmology, Stanford University（斯坦福大学卡弗里粒子天体物理与宇宙学研究所）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；University of Chicago（芝加哥大学）；NSF-Simons AI Institute for the Sky (SkAI)（NSF-西蒙斯天空人工智能研究所）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；University of Melbourne（墨尔本大学）
The CMB Cold Spot under the lens II: Lensing signatures in polarization and cosmic texture footprints
Center for Cosmology and Computational Astrophysics, Institute for Advanced Study in Physics, Zhejiang University（浙江大学物理学院高等研究院宇宙学与计算天体物理中心）；Institute of Astronomy, School of Physics, Zhejiang University（浙江大学物理学院天文研究所）；Observatório do Valongo, Universidade Federal do Rio de Janeiro（里约热内卢联邦大学瓦隆戈天文台）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；North Hennepin Community College（北亨内平社区学院）
In this paper we present the tools to optimally extract the Lensing-Integrated Sachs Wolfe (L-ISW) bispectrum signal from future CMB data. We implement two different methods to simulate the non-Gaussian CMB maps with the L-ISW signal: a non-perturbative method based on the FLINTS lensing code and the separable mode expansion method. We implement the Komatsu, Spergel and Wandelt (KSW) optimal estimator analysis for the Lensing-ISW bispectrum and we test it on the non-Gaussian simulations in the case of a realistic CMB experimental settings with an inhomogeneous sky coverage. We show that the es…
The Cold Spot, with an unusually cold region surrounded by a hot ring, is a statistically significant anomaly in the Cosmic Microwave Background (CMB) sky. In this work we assess whether different sets of multiple subvoids based on the 2dF-VST ATLAS Cold Spot galaxy redshift survey or a collapsing cosmic texture could have produced such an anomaly through a simultaneous search for their gravitational redshift and lensing signatures on the {\it Planck} CMB temperature anisotropies. We use patches with radii $R=10^\circ$ and $R=20^\circ$ to account for the inner cold region as well as the outer …
We reconsider the pixel-based, "template" polarized foreground removal method within the context of a next-generation, low-noise, low-resolution (0.5 degree FWHM) space-borne experiment measuring the cosmological B-mode polarization signal in the cosmic microwave background (CMB). This method was put forward by the Wilkinson Microwave Anisotropy Probe (WMAP) team and further studied by Efstathiou et al. We need at least 3 frequency channels: one is used for extracting the CMB signal, whereas the other two are used to estimate the spatial distribution of the polarized dust and synchrotron emiss…
Signals from the early Universe: a comprehensive search for primordial features in Planck CMB datasets
Università degli Studi di Ferrara（费拉拉大学）；INFN, Sezione di Ferrara（意大利国家核物理研究所费拉拉分部）；INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna（博洛尼亚天文物理与空间科学研究所）；University of the Western Cape（西开普大学）；Instituto de Física Corpuscular (IFIC), CSIC‐Universitat de València（瓦伦西亚大学西班牙国家科学研究委员会粒子物理研究所）
We cross-correlate foreground cleaned Planck Nominal Cosmic Microwave Background (CMB) maps with two templates constructed from the Two-Micron All-Sky Redshift Survey of galaxies. The first template traces the large-scale filamentary distribution characteristic of the Warm-Hot Intergalactic Medium (WHIM) out to ~90 Mpc/h. The second traces preferentially the virialized gas in unresolved halos around galaxies. We find a marginal signal from the correlation of Planck data and the WHIM template with a signal-to-noise from 0.84 to 1.39 at the different Planck frequencies, and with a frequency depe…
We constrain the deviation of adiabatic evolution of the Universe using the data on the Cosmic Microwave Background (CMB) temperature anisotropies measured by the {\it Planck} satellite and a sample of 481 X-ray selected clusters with spectroscopically measured redshifts. To avoid antenna beam effects, we bring all the maps to the same resolution. We use a CMB template to subtract the cosmological signal while preserving the Thermal Sunyaev-Zeldovich (TSZ) anisotropies; next, we remove galactic foreground emissions around each cluster and we mask out all known point sources. If the CMB black-b…
The reionization optical depth is the most poorly determined of the six $Λ$CDM parameters fit to CMB anisotropy data. Instrumental noise and systematics have prevented uncertainties from reaching their cosmic variance limit. At present, the datasets providing the most statistical constraining power are the WMAP, Planck LFI, and Planck HFI full-sky polarization maps. As the reprocessed HFI data with reduced systematics are not yet publicly unavailable, we examine determinations of $τ$ using 9-year WMAP and 2015 Planck LFI data, with an emphasis on characterizing potential systematic bias result…
We extend the internal template foreground removal method by accounting for spatially varying spectral parameters such as the spectral indices of synchrotron and dust emission and the dust temperature. As the previous algorithm had to assume that the spectral parameters are uniform over the full sky (or some significant fraction of the sky), it resulted in a bias in the tensor-to-scalar ratio parameter $r$ estimated from foreground-cleaned polarization maps of the cosmic microwave background (CMB). The new algorithm, "Delta-map method", accounts for spatially varying spectra to first order in …
Various data analyses of the Cosmic Microwave Background (CMB) provide observational hints of statistical isotropy breaking. Some of these features can be studied within the framework of primordial vector fields in inflationary theories which generally display some level of statistical anisotropy both in the power spectrum and in higher-order correlation functions. Motivated by these observations and the recent theoretical developments in the study of primordial vector fields, we develop the formalism necessary to extract statistical anisotropy information from the three-point function of the …
We present a methodology to recover cosmic microwave background (CMB) polarization in which the quantity $P = Q+ iU$ is linearly combined at different frequencies using complex coefficients. This is the most general linear combination of the $Q$ and $U$ Stokes parameters which preserves the physical coherence of the residual contribution on the CMB estimation. The approach is applied to the internal linear combination (ILC) and the internal template fitting (ITF) methodologies. The variance of $P$ of the resulting map is minimized to compute the coefficients of the linear combination. One of t…
Low Density Points (LDPs, \citet{2019ApJ...874....7D}), obtained by removing high-density regions of observed galaxies, can trace the Large-Scale Structures (LSSs) of the universe. In particular, it offers an intriguing opportunity to detect weak gravitational lensing from low-density regions. In this work, we investigate tomographic cross-correlation between Planck CMB lensing maps and LDP-traced LSSs, where LDPs are constructed from the DR8 data release of the DESI legacy imaging survey, with about $10^6$-$10^7$ galaxies. We find that, due to the large sky coverage (20,000 deg$^2$) and large…
Templates for polarised emission from Galactic foregrounds at frequencies relevant to Cosmic Microwave Background (CMB) polarisation experiments are obtained by modelling the Galactic Magnetic Field (GMF) on large scales. This work extends the results of O'Dea et al. by including polarised synchrotron radiation as a source of foreground emission. The polarisation direction and fraction in this calculation are based solely on the underlying choice of GMF model and therefore provide an independent prediction for the polarisation signal on large scales. Templates of polarised foregrounds may be o…
Modifications of the initial-state of the inflaton field can induce a departure from Gaussianity and leave a testable imprint on the higher order correlations of the CMB and large scale structures in the Universe. We focus on the bispectrum statistics of the primordial curvature perturbation and its projection on the CMB. For a canonical single-field action the three-point correlator enhancement is localized, maximizing in the collinear limit, corresponding to enfolded or squashed triangles in comoving momentum space. We show that the available local and equilateral template are very insensiti…
Using Planck polarization data, we search for and constrain spatial variations of the polarized dust foreground for cosmic microwave background (CMB) observations, specifically in its spectral index, $β_d$. Failure to account for such variations will cause errors in the foreground cleaning that propagate into errors on cosmological parameter recovery from the cleaned CMB map. It is unclear how robust prior studies of the Planck data which constrained $β_d$ variations are due to challenges with noise modeling, residual systematics, and priors. To clarify constraints on $β_d$ and its variation, …
We present a Bayesian parametric component separation method for polarised microwave sky maps. We solve jointly for the primary cosmic microwave background (CMB) signal and the main Galactic polarised foreground components. For the latter, we consider electron-synchrotron radiation and thermal dust emission, modelled in frequency as a power law and a modified blackbody respectively. We account for inter-pixel correlations in the noise covariance matrices of the input maps and introduce a spatial correlation length in the prior matrices for the spectral indices beta. We apply our method to low-…
A detection of primordial non-Gaussianity could transform our understanding of the fundamental theory of inflation. The precision promised by upcoming CMB and large-scale structure surveys raises a natural question: if a detection given a particular template is made, what does this truly tell us about the underlying theory? In this paper we present a systematic way to constrain a wide range of non-Gaussian shapes, including general single and multi-field models and models with excited initial states. We present a separable, divergent basis able to recreate many shapes in the literature to high…
Systematic effects in dual-beam, differential, radio observations of extended objects are discussed in the context of the One Centimeter Receiver Array (OCRA). We use simulated samples of Sunyaev-Zel'dovich (SZ) galaxy clusters at low ($z<0.4$) and intermediate ($0.4<z<1.0$) redshifts to study the implications of operating at a single frequency (30 GHz) on the accuracy of extracting SZ flux densities and of reconstructing comptonization parameters with OCRA. We analyze dependences on cluster mass, redshift, observation strategy, and telescope pointing accuracy. Using $Planck$ data to make prim…
We study the power of PLANCK data to constrain deviations of the Cosmic Microwave Background black body temperature from adiabatic evolution using the thermal Sunyaev-Zeldovich anisotropy induced by clusters of galaxies. We consider two types of data sets: the cosmological signal is removed in the Time Ordered Information or is removed from the final maps; and two different statistical estimators, based on the ratio of temperature anisotropies at two different frequencies and on a fit to the spectral variation of the cluster signal with frequency. To test for systematics, we construct a templa…
A crucial problem for partial sky analysis of CMB polarization is the $E$-$B$ leakage problem. Such leakage arises from the presence of `ambiguous' modes that satisfy properties of both $E$ and $B$ modes. Solving this problem is critical for primordial polarization $B$ mode detection in partial sky CMB polarization experiments. In this work we introduce a new method for reducing the leakage. We demonstrate that if we complement the $E$-mode information outside the observation patch with ancillary data from full-sky CMB observations, we can reduce and even effectively remove the $E$-to-$B$ leak…
Constructing a fast and efficient estimator for the B-mode power spectrum of cosmic microwave background (CMB) is of critical importance for CMB science. For a general CMB survey, the Quadratic Maximum Likelihood (QML) estimator for CMB polarization has been proved to be the optimal estimator with minimal uncertainties, but it is computationally very expensive. In this article, we propose two new QML methods for B-mode power spectrum estimation. We use the Smith-Zaldarriaga approach to prepare pure-B mode map, and E-mode recycling method to obtain a leakage free B-mode map. We then use the sca…
The Python Sky Model (PySM) is a Python package used by Cosmic Microwave Background (CMB) experiments to simulate maps, in HEALPix pixelization, of the various diffuse astrophysical components of Galactic emission relevant at CMB frequencies (i.e. dust, synchrotron, free-free and Anomalous Microwave Emission), as well as the CMB itself. These maps may be integrated over a given instrument bandpass and smoothed with a given instrument beam. PySM 2, released in 2016, has become the de-facto standard for simulating Galactic emission, for example it is used by CMB-S4, Simons Observatory, LiteBird,…
