Foreground-cleaned Cosmic Microwave Background Research Articles

Detection of Dipole Modulation in CMB Temperature Anisotropy Maps from WMAP and Planck using Artificial Intelligence

Breakdown of rotational invariance of the primordial power spectrum manifests in the statistical anisotropy of the observed Cosmic Microwave Background (CMB) radiation. Hemispherical power asymmetry in the CMB may be caused due to a dipolar modulation, indicating the presence of a preferred direction. Appropriately rescaled local variance maps of the CMB temperature anisotropy data effectively encapsulate this dipolar pattern. As a first-of-its-kind method, we train Artificial Neural Networks (ANNs) with such local variances as input features to distinguish statistically isotropic CMB maps from dipole-modulated ones. Our trained ANNs are able to predict components of the amplitude times the unit vector of the preferred direction for mixed sets of modulated and unmodulated maps, with goodness-of-fit (R 2) scores >0.97 for full sky and >0.96 for partial sky coverage. On all observed foreground-cleaned CMB maps, the ANNs detect the dipolar modulation signal with overall consistent values of amplitudes and directions. This detection is significant at 97.21%–99.38% C.L. for all full sky maps, and at 98.34%–100% C.L. for all partial sky maps. Robustness of the signal holds across full and partial skies, various foreground cleaning methods, inpainting algorithms, instruments, and all the different periods of observation for Planck and WMAP satellites. The significant and robust detection of the signal, in addition to the consistency of values of amplitude and directions, as found independent of any preexisting methods, further mitigates the criticisms of look-elsewhere effects and a posteriori inferences for the preferred dipole direction in the CMB.

Level correlations of CMB temperature angular power spectrum

If the principle of statistical isotropy is valid, then the angular power spectrum (APS) of cosmic microwave background (CMB) radiation is uncorrelated between different multipoles. We propose a novel technique to analyse any possible correlations of the foreground-cleaned CMB temperature APS measures (\(C_{\ell }\) and \({\mathcal {D}}_\ell =({\ell (\ell +1)})/({2\pi })C_\ell \)). This is motivated by the behaviour of level spacings between random matrix eigenvalues. This method helps to distinguish uncorrelated statistically isotropic CMB APS from correlated APS, where the latter can arise due to breakdown of isotropy or presence of some residual systematics in the foreground cleaned CMB maps. Spacings of statistically isotropic CMB \(C_\ell \)’s and \({\mathcal {D}}_\ell \)’s are seen to closely obey Poisson statistics and introduction of correlations, changes the distribution to appropriate Wigner–Dyson statistics. For foreground-cleaned CMB, we employ the average spacing of consecutive multipole APS for multipoles \(\in [2,31]\). This estimator is sensitive to departures from the null hypothesis of zero correlations between the APS measures of statistically isotropic CMB. We study full sky WMAP 9-year ILC and 2018 Planck foreground-cleaned maps (Commander, NILC and SMICA). Sans parity distinctions, average spacings are in good agreement with theoretical expectation. With parity distinctions, even multipoles indicate unusually low average spacings for both \(C_\ell \)’s (at \(\ge \)98.86% C.L.) and \({\mathcal {D}}_\ell \)’s (at \({\ge }\)95.07% C.L.). We use an inpainting method based on constrained Gaussian realisations and show that for the Planck U73 and WMAP KQ75 masks, all the foreground-cleaned inpainted CMB maps robustly confirm the existence of such unusually low average spacings of even multipole APS. In addition, this signal is independent of the non-Gaussian cold spot.

Constraining the baryon abundance with the kinematic Sunyaev-Zel’dovich effect: Projected-field detection using Planck , WMAP , and unWISE

The kinematic Sunyaev-Zel'dovich (kSZ) effect---the Doppler boosting of Cosmic Microwave Background (CMB) photons scattering off free electrons with nonzero line-of-sight velocity---is an excellent probe of the distribution of baryons in the Universe. In this paper, we measure the kSZ effect due to ionized gas traced by infrared-selected galaxies from the $unWISE$ catalog. We employ the ``projected-field'' kSZ estimator, which does not require spectroscopic galaxy redshifts. To suppress contributions from non-kSZ signals associated with the galaxies (e.g., dust emission and thermal SZ), this estimator requires foreground-cleaned CMB maps, which we obtain from $Planck$ and $WMAP$ data. Using a new ``asymmetric'' estimator that combines different foreground-cleaned CMB maps to maximize the signal-to-noise, we measure the ${\mathrm{kSZ}}^{2}$-galaxy cross-power spectrum for three subsamples of the $unWISE$ galaxy catalog. These subsamples peak at mean redshifts $z\ensuremath{\approx}0.6$, 1.1, and 1.5, have average halo mass $\ensuremath{\sim}1--5\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }\text{ }{h}^{\ensuremath{-}1}{M}_{\ensuremath{\bigodot}}$, and in total contain over 500 million galaxies. After marginalizing over contributions from CMB lensing, we measure the amplitude of the kSZ signal ${A}_{{\mathrm{kSZ}}^{2}}=0.42\ifmmode\pm\else\textpm\fi{}0.31(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.02(\mathrm{sys})$, $5.02\ifmmode\pm\else\textpm\fi{}1.01(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.49(\mathrm{sys})$, and $8.23\ifmmode\pm\else\textpm\fi{}3.23(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.57(\mathrm{sys})$, for the three subsamples, where ${A}_{{\mathrm{kSZ}}^{2}}=1$ corresponds to our fiducial theoretical model. The combined statistical significance of our kSZ detection exceeds $5\ensuremath{\sigma}$. Our theoretical model includes the first calculation of lensing magnification contributions to the ${\mathrm{kSZ}}^{2}$-galaxy cross-power spectrum, which are significant for the $z\ensuremath{\approx}1.1$ and 1.5 subsamples. We discuss possible explanations for the excess kSZ signal associated with the $z\ensuremath{\approx}1.1$ sample, and show that foreground contamination in the CMB maps is very unlikely to be the cause. From our measurements of ${A}_{{\mathrm{kSZ}}^{2}}$, we constrain the product of the baryon fraction ${f}_{b}$ and free electron fraction ${f}_{\mathrm{free}}$ to be $({f}_{b}/0.158)({f}_{\mathrm{free}}/1.0)=0.65\ifmmode\pm\else\textpm\fi{}0.24$, $2.24\ifmmode\pm\else\textpm\fi{}0.25$, and $2.87\ifmmode\pm\else\textpm\fi{}0.57$ at $z\ensuremath{\approx}0.6$, 1.1, and 1.5, respectively, consistent with a large fraction of the cosmic baryon abundance existing in an ionized state at low redshifts.

Full-sky Cosmic Microwave Background Foreground Cleaning Using Machine Learning

Abstract In order to extract cosmological information from observations of the millimeter and submillimeter sky, foreground components must first be removed to produce an estimate of the cosmic microwave background (CMB). We developed a machine-learning approach for doing so for full-sky temperature maps of the millimeter and submillimeter sky. We constructed a Bayesian spherical convolutional neural network architecture to produce a model that captures both spectral and morphological aspects of the foregrounds. Additionally, the model outputs a per-pixel error estimate that incorporates both statistical and model uncertainties. The model was then trained using simulations that incorporated knowledge of these foreground components that was available at the time of the launch of the Planck satellite. On simulated maps, the CMB is recovered with a mean absolute difference of <4 μK over the full sky after masking map pixels with a predicted standard error of >50 μK; the angular power spectrum is also accurately recovered. Once validated with the simulations, this model was applied to Planck temperature observations from its 70 GHz through 857 GHz channels to produce a foreground-cleaned CMB map at a Healpix map resolution of nside = 512. Furthermore, we demonstrate the utility of the technique for evaluating how well different simulations match observations, particularly in regard to the modeling of thermal dust.

The CMB angular power spectrum via component separation: a study on Planck data

Aims. We investigate the extent to which foreground-cleaned cosmic microwave background (CMB) maps can be used to estimate cosmological parameters at small scales. Methods. We use the SMICA method, a blind separation technique that works directly at the spectral level. In this work we focus on the small scales of the CMB angular power spectrum, which are chiefly affected by noise and extragalactic foregrounds, such as point sources. We adapt SMICA to use only cross-spectra between data maps, thus avoiding the noise bias. In this study, performed using both simulations and Planck 2015 data, we fit for extragalactic point sources by modelling them as shot noise of two independent populations. Results. In simulations, we correctly recover the point-source emission law, and obtain a CMB angular power spectrum that has an average foreground residual of one fifth of the CMB power at ℓ ≥ 2200. With Planck data, the recovered point-source emission law corresponds to external estimates, with some offsets at the highest and lowest frequencies, possibly due to frequency decoherence of point sources. The CMB angular power spectrum residuals are consistent with what we find in simulations. The cosmological parameters obtained from the simulations and the data show offsets up to 1σ on average from their expected values. Biases on cosmological parameters in simulations represent the expected level of bias in Planck data. Conclusions. The results on cosmological parameters depend on the detail of the foreground residual contamination in the spectrum, and therefore a tailored modelling of the likelihood foreground model is required.

Joint Bayesian estimation of tensor and lensing B modes in the power spectrum of CMB polarization data

We investigate the performance of a simple Bayesian fitting approach to correct the cosmic microwave background (CMB) B-mode polarization for gravitational lensing effects in the recovered probability distribution of the tensor-to-scalar ratio. We perform a two-dimensional power spectrum fit of the amplitude of the primordial B-modes (tensor-to-scalar ratio, $r$) and the amplitude of the lensing B-modes (parameter $A_{lens}$), jointly with the estimation of the astrophysical foregrounds including both synchrotron and thermal dust emissions. Using this Bayesian framework, we forecast the ability of the proposed CMB space mission LiteBIRD to constrain $r$ in the presence of realistic lensing and foreground contributions. We compute the joint posterior distribution of $r$ and $A_{lens}$, which we improve by adopting a prior on $A_{lens}$ taken from the South Pole Telescope (SPT) measurement. As it applies to the power spectrum, this approach cannot mitigate the uncertainty on $r$ that is due to E-mode cosmic variance transferred to B-modes by lensing, unlike standard delensing techniques that are performed on maps. However, the method allows to correct for the bias on $r$ induced by lensing, at the expense of a larger uncertainty due to the increased volume of the parameter space. We quantify, for different values of the tensor-to-scalar ratio, the trade-off between bias correction and increase of uncertainty on $r$. For LiteBIRD simulations, which include foregrounds and lensing contamination, we find that correcting the foreground-cleaned CMB B-mode power spectrum for the lensing bias, not the lensing cosmic variance, still guarantees a $3\sigma$ detection of $r=5\times 10^{-3}$. The significance of the detection is increased to $6\sigma$ when the current SPT prior on $A_{lens}$ is adopted.

Improved Diffuse Foreground Subtraction with the ILC Method: CMB Map and Angular Power Spectrum Using Planck and WMAP Observations

Abstract We report an improved technique for diffuse foreground minimization from Cosmic Microwave Background (CMB) maps using a new multiphase iterative harmonic space internal-linear-combination (HILC) approach. Our method nullifies a foreground leakage that was present in the old and usual iterative HILC method. In phase 1 of the multiphase technique, we obtain an initial cleaned map using the single iteration HILC approach over the desired portion of the sky. In phase 2, we obtain a final CMB map using the iterative HILC approach; however, now, to nullify the leakage, during each iteration, some of the regions of the sky that are not being cleaned in the current iteration are replaced by the corresponding cleaned portions of the phase 1 map. We bring all input frequency maps to a common and maximum possible beam and pixel resolution at the beginning of the analysis, which significantly reduces data redundancy, memory usage, and computational cost, and avoids, during the HILC weight calculation, the deconvolution of partial sky harmonic coefficients by the azimuthally symmetric beam and pixel window functions, which in a strict mathematical sense, are not well defined. Using WMAP 9 year and Planck 2015 frequency maps, we obtain foreground-cleaned CMB maps and a CMB angular power spectrum for the multipole range . Our power spectrum matches the published Planck results with some differences at different multipole ranges. We validate our method by performing Monte Carlo simulations. Finally, we show that the weights for HILC foreground minimization have the intrinsic characteristic that they also tend to produce a statistically isotropic CMB map.

Planck2013 results. XII. Diffuse component separation

Planck has produced detailed all-sky observations over nine frequency bands between 30 and 857 GHz. These observations allow robust reconstruction of the primordial cosmic microwave background (CMB) temperature fluctuations over nearly the full sky, as well as new constraints on Galactic foregrounds. This paper describes the component separation framework adopted by Planck. We test four foreground-cleaned CMB maps derived using qualitatively different component separation algorithms. The quality of our reconstructions is evaluated through detailed simulations and internal comparisons, and shown through various tests to be internally consistent and robust for CMB power spectrum and cosmological parameter estimation up to l = 2000. The parameter constraints on LambdaCDM cosmologies derived from these maps are consistent with those presented in the cross-spectrum based Planck likelihood analysis. We choose two of the CMB maps for specific scientific goals. We also present maps and frequency spectra of the Galactic low-frequency, CO, and thermal dust emission. The component maps are found to provide a faithful representation of the sky, as evaluated by simulations. For the low-frequency component, the spectral index varies widely over the sky, ranging from about beta = -4 to -2. Considering both morphology and prior knowledge of the low frequency components, the index map allows us to associate a steep spectral index (beta < -3.2) with strong anomalous microwave emission, corresponding to a spinning dust spectrum peaking below 20 GHz, a flat index of beta > -2.3 with strong free-free emission, and intermediate values with synchrotron emission.

A FOREGROUND-CLEANED COSMIC MICROWAVE BACKGROUND MAP FROM NON-GAUSSIANITY MEASUREMENT

In this paper we present a new method to estimate a foreground cleaned Cosmic Microwave Background (CMB) map at a resolution of $1^\circ$ by minimizing the non-Gaussian properties of the cleaned map which arise dominantly due to diffuse foreground emission components from the Milky Way. We employ simple kurtosis statistic as the measure of non-Gaussian properties and perform a linear combination of 5 frequency maps provided by Wilkinson Microwave Anisotropy Probe (WMAP) in its 7 year data release in such a way that the cleaned map has a minimum kurtosis which leads to a non-Gaussianity minimized, foreground cleaned CMB map. We validate the method by performing Monte-Carlo simulations. To minimize any residual foreground contamination from the cleaned map we flag out region near the galactic plane based upon results from simulations. Outside the masked region our new estimate of CMB map matches well with the WMAP's ILC map. A simple pseudo-$C_l$ based CMB TT power spectrum derived from the non-gaussianity minimized map reproduces the earlier results of WMAP's power spectrum. {\it An important advantage of the method is that it does not introduce any negative bias in angular power spectrum in low multipole regime, unlike usual ILC method.} Comparing our results with the previously published results we argue that CMB results are robust with respect to specific foreground removal algorithms employed.