Internal Linear Combination Method Research Articles

Foreground Removal and Angular Power Spectrum Estimation of 21 cm Signal Using Harmonic Space ILC Method

Abstract Mapping the distribution of neutral atomic hydrogen (H i) in the Universe through its 21 cm emission line provides a powerful cosmological probe to map the large-scale structures and shed light on various cosmological phenomena. The baryon acoustic oscillations at low redshifts can potentially be probed by sensitive H i intensity mapping experiments and constrain the properties of dark energy. However, the 21 cm signal detection faces formidable challenges owing to the dominance of various astrophysical foregrounds, which can be several orders of magnitude stronger. Our current work introduces a novel and model-independent internal linear combination (ILC) method in harmonic space using the principal components of the 21 cm signal for accurate foreground removal and power spectrum estimation. We estimate the principal components by incorporating prior knowledge of the theoretical 21 cm covariance matrix. We test our methodology by detailed simulations of radio observations, incorporating synchrotron emission, free–free radiation, extragalactic point sources, and thermal noise. We estimate the full-sky 21 cm angular power spectrum after application of a mask on the full-sky cleaned 21 cm signal by using the mode–mode coupling matrix. These full-sky estimates of angular spectra can be directly used to measure the cosmological parameters. For the first time, we demonstrate the effectiveness of a foreground-model-independent ILC method in harmonic space to reconstruct the 21 cm signal.

Planck CO revisited: Improved CO line-emission maps from Planck space-mission observations

The Planck space mission has observed the first three rotational lines of emission of Galactic carbon monoxide (CO). Those maps, however, are either noisy or contaminated by astrophysical emissions from different origin. We revisit those data products to deliver new full-sky CO maps with low astrophysical contamination and significantly enhanced noise properties. To that effect, a specific pipeline is designed to evaluate and postprocess the existing Planck Galactic CO maps. Specifically, we use an extension of the generalized needlet Internal Linear Combination method to extract multicomponent astrophysical emissions from multifrequency observations. Well-characterized, clean, CO full-sky maps at 10′ angular resolution are produced. These maps are made available to the scientific community and can be used to trace CO emission over the entire sky and to generate sky simulations in preparation for future cosmic microwave background (CMB) observations.

A constrained NILC method for CMB B mode observations

The Internal Linear Combination (ILC) method is commonly employed to extract the cosmic microwave background (CMB) signal from multi-frequency observation maps.However, the performance of the ILC method tends to degrade when the signal-to-noise ratio (SNR) is relatively low, particularly when measuring the primordial B-modes to detect the primordial gravitational waves. To address this issue, an enhanced version of the ILC method, known as constrained ILC, is proposed.This method is designed to be more suitable for situations with low signal-to-noise ratio (SNR) by incorporating additional prior foreground information.In our study, we have modified the constraint Needlet ILC method and successfully improved its performance at low SNR.We illustrate our methods using mock data generated from the combination of WMAP, Planck and a ground-based experiment in the northern hemisphere, and the chosen noise level for the ground-based experiment are very conservative which can be easily achieved in the very near future. The results show that the level of foreground residual can be well controlled. In comparison to the standard NILC method, which introduces a bias to the tensor-to-scalar ratio (r) of approximately 0.05, the constrained NILC method exhibits a significantly reduced bias of only around 5 × 10-3 towards r which is much smaller than the statistical error.

Recovering Cosmic Microwave Background Polarization Signals with Machine Learning

Primordial B-mode detection is one of the main goals of current and future cosmic microwave background (CMB) experiments. However, the weak B-mode signal is overshadowed by several Galactic polarized emissions, such as thermal dust emission and synchrotron radiation. Subtracting foreground components from CMB observations is one of the key challenges in searching for the primordial B-mode signal. Here, we construct a deep convolutional neural network (CNN) model, called CMBFSCNN (Cosmic Microwave Background Foreground Subtraction with CNN), which can cleanly remove various foreground components from simulated CMB observational maps at the sensitivity of the CMB-S4 experiment. Noisy CMB Q (or U) maps are recovered with a mean absolute difference of 0.018 ± 0.023 μK (or 0.021 ± 0.028 μK). To remove the residual instrumental noise from the foreground-cleaned map, inspired by the needlet internal linear combination method, we divide the whole data set into two “half-split maps,” which share the same sky signal, but have uncorrelated noise, and perform a cross-correlation technique to reduce the instrumental noise effects at the power spectrum level. We find that the CMB EE and BB power spectra can be precisely recovered with significantly reduced noise effects. Finally, we apply this pipeline to current Planck observations. As expected, various foregrounds are cleanly removed from the Planck observational maps, with the recovered EE and BB power spectra being in good agreement with the official Planck results.

A foreground model-independent Bayesian CMB temperature and polarization signal reconstruction and cosmological parameter estimation over large angular scales

ABSTRACT Recent CMB observations have resulted in very precise observational data. A robust and reliable CMB reconstruction technique can lead to efficient estimation of the cosmological parameters. We demonstrate the performance of our methodology using simulated temperature and polarization observations using cosmic variance-limited future-generation PRISM satellite mission. We generate samples from the joint distribution by implementing the CMB inverse covariance weighted internal-linear-combination (ILC) with the Gibbs sampling technique. We use the Python Sky Model (PySM), d4f1s1 to generate the realistic foreground templates. The synchrotron emission is parametrized by a spatially varying spectral index, whereas the thermal dust emission is described as a two-component dust model. We estimate the marginalized densities of CMB signal and theoretical angular power spectrum utilizing the samples from the entire posterior distribution. The best-fitting cleaned CMB map and the corresponding angular power spectrum are consistent with the CMB realization and the sky angular power spectrum, implying an efficient foreground-minimized reconstruction. The likelihood function estimated by making use of the Blackwell–Rao estimator is used for the estimation of cosmological parameters. Our methodology can estimate the tensor-to-scalar ratio r ≥ 0.0075 for the chosen foreground models and the instrumental noise levels. Our current work demonstrates an analysis pipeline starting from the reliable estimation of CMB signal and its angular power spectrum to the case of cosmological parameter estimation using the foreground model-independent Gibbs–ILC method.

Efficient ILC analysis on polarization maps after EB leakage correction

The Internal Linear Combination (ILC) is widely used to extract the cosmic microwave background (CMB) signal from multi-frequency observation maps, especially for Satellite experiments with quasi-full sky coverage. We extend ILC method to CMB polarization map analysis with a small sky patch which is especially typical for ground-based experiments, by combing ILC with a template cleaning method which can give pure B map free from EB leakage caused by partial sky coverage. The feature of our methods is that we do the ILC analysis on pseudo-scalar B maps, and the advantage is that it totally avoids the impact of EB leakage on ILC, so that it can improve the efficiency of component separation dramatically. We demonstrate our methods with mock data of a future ground-based experiment with a deep survey on a clean patch in the northern sky, and the results show that the level of foreground residual can be well controlled, it biases the tensor to scalar ratio (r) at the order of 10-3 which is comparable to the statistical error by noise.

Weak lensing magnification reconstruction with the modified internal linear combination method

Measuring weak lensing cosmic magnification signal is very challenging due to the overwhelming intrinsic clustering in the observed galaxy distribution. In this paper, we modify the Internal Linear Combination (ILC) method to reconstruct the lensing signal with an extra constraint to suppress the intrinsic clustering. To quantify the performance, we construct a realistic galaxy catalogue for the LSST-like photometric survey, covering 20 000 deg2 with mean source redshift at zs ∼ 1. We find that the reconstruction performance depends on the width of the photo-z bin we choose. Due to the correlation between the lensing signal and the source galaxy distribution, the derived signal has smaller systematic bias but larger statistical uncertainty for a narrower photo-z bin. We conclude that the lensing signal reconstruction with the Modified ILC method is unbiased with a statistical uncertainty <5% for bin width Δ zP = 0.2.

A Bayesian ILC Method for CMB B-mode Posterior Estimation and Reconstruction of Primordial Gravity Wave Signal

Abstract The cosmic microwave background (CMB) radiation B-mode polarization signal contains the unique signature of primordial metric perturbations produced during the inflation. The separation of the weak CMB B-mode signal from strong foreground contamination in observed maps is a complex task, and proposed new-generation low-noise satellite missions compete with the weak signal level of this gravitational background. In this paper, for the first time, we employ a foreground model-independent internal linear combination (ILC) method to reconstruct the CMB B-mode signal using simulated observations over large angular scales of the sky of six frequency bands of the future-generation CMB mission Probe of Inflation and Cosmic Origins (PICO). We estimate the joint CMB B-mode posterior density following the interleaving Gibbs steps of the B-mode angular power spectrum and cleaned map samples using the ILC method. We extend and improve the earlier reported Bayesian ILC method to analyze weak CMB B-mode reconstruction by introducing noise-bias corrections at two stages during the ILC weight estimation. By performing 200 Monte Carlo simulations of the Bayesian ILC method, we find that our method can reconstruct the CMB signals and the joint posterior density accurately over large angular scales of the sky. We estimate the Blackwell–Rao statistics of the marginal density of the CMB B-mode angular power spectrum and use them to estimate the joint density of the tensor-to-scalar ratio r and a lensing power spectrum amplitude A lens . Using 200 Monte Carlo simulations of the delensing approach, we find that our method can achieve an unbiased detection of the primordial gravitational-wave signal r with more than 8σ significance for levels of r ≥ 0.01 for input frequency maps with realistic lensing and foregrounds with constant spectral indices.

Partially constrained internal linear combination: A method for low-noise CMB foreground mitigation

Internal Linear Combination (ILC) methods are some of the most widely used multi-frequency cleaning techniques employed in CMB data analysis. These methods reduce foregrounds by minimizing the total variance in the coadded map (subject to a signal-preservation constraint), although often significant foreground residuals or biases remain. A modification to the ILC method is the constrained ILC (cILC), which explicitly nulls certain foreground components; however, this foreground nulling often comes at a high price for ground-based CMB datasets, with the map noise increasing significantly on small scales. In this paper we explore a new method, the partially constrained ILC (pcILC), which allows us to optimize the tradeoff between foreground bias and variance in ILC methods. In particular, this method allows us to minimize the variance subject to an inequality constraint requiring that the constrained foregrounds are reduced by at least a fixed factor, which can be chosen based on the foreground sensitivity of the intended application. We test our method on simulated sky maps for a Simons Observatory-like experiment; we find that for cleaning thermal Sunyaev-Zel'dovich (tSZ) contamination at $\ell \in [3000,4800]$, if a small tSZ residual of 20% of the standard ILC residual can be tolerated, the variance of the CMB temperature map is reduced by at least 50% over the cILC value. We also demonstrate an application of this method to reduce noise in CMB lensing reconstruction.

An accurate reconstruction of CMB E-mode signal over large angular scales using prior information of CMB covariance matrix in ILC algorithm

ABSTRACT Recently, the internal-linear-combination (ILC) method was investigated extensively in the context of reconstruction of Cosmic Microwave Background (CMB) temperature anisotropy signal using observations obtained by WMAP and Planck satellite missions. In this article, we, for the first time, apply the ILC method to reconstruct the large-scale CMB E mode polarization signal, which could probe the ionization history, using simulated observations of 15 frequency CMB polarization maps of future generation Cosmic Origin Explorer (COrE) satellite mission. We find that the clean power spectra, from the usual ILC, are strongly biased due to non-zero CMB-foregrounds chance correlations. In order to address the issues of bias and errors we extend and improve the usual ILC method for CMB E-mode reconstruction by incorporating prior information of theoretical E-mode angular power spectrum while estimating the weights for linear combination of input maps (Sudevan &amp; Saha 2018b). Using the E-mode covariance matrix effectively suppresses the CMB-foreground chance correlation power leading to an accurate reconstruction of cleaned CMB E-mode map and its angular power spectrum. We compare the performance of the usual ILC and the new method over large angular scales and show that the later produces significantly statistically improved results than the former. The new E-mode CMB angular power spectrum contains neither any significant negative bias at the low multipoles nor any positive foreground bias at relatively higher mutltipoles. The error estimates of the cleaned spectrum agree very well with the cosmic variance induced error.

Planck intermediate results

We describe an extension of the most recent version of the Planck Catalogue of Compact Sources (PCCS2), produced using a new multi-band Bayesian Extraction and Estimation Package (BeeP). BeeP assumes that the compact sources present in PCCS2 at 857 GHz have a dust-like spectral energy distribution (SED), which leads to emission at both lower and higher frequencies, and adjusts the parameters of the source and its SED to fit the emission observed in Planck’s three highest frequency channels at 353, 545, and 857 GHz, as well as the IRIS map at 3000 GHz. In order to reduce confusion regarding diffuse cirrus emission, BeeP’s data model includes a description of the background emission surrounding each source, and it adjusts the confidence in the source parameter extraction based on the statistical properties of the spatial distribution of the background emission. BeeP produces the following three new sets of parameters for each source: (a) fits to a modified blackbody (MBB) thermal emission model of the source; (b) SED-independent source flux densities at each frequency considered; and (c) fits to an MBB model of the background in which the source is embedded. BeeP also calculates, for each source, a reliability parameter, which takes into account confusion due to the surrounding cirrus. This parameter can be used to extract sub-samples of high-frequency sources with statistically well-understood properties. We define a high-reliability subset (BeeP/base), containing 26 083 sources (54.1% of the total PCCS2 catalogue), the majority of which have no information on reliability in the PCCS2. We describe the characteristics of this specific high-quality subset of PCCS2 and its validation against other data sets, specifically for: the sub-sample of PCCS2 located in low-cirrus areas; the Planck Catalogue of Galactic Cold Clumps; the Herschel GAMA15-field catalogue; and the temperature- and spectral-index-reconstructed dust maps obtained with Planck’s Generalized Needlet Internal Linear Combination method. The results of the BeeP extension of PCCS2, which are made publicly available via the Planck Legacy Archive, will enable the study of the thermal properties of well-defined samples of compact Galactic and extragalactic dusty sources.

Combining ILC and moment expansion techniques for extracting average-sky signals and CMB anisotropies

Abstract The method of weighted addition of multi-frequency maps, more commonly referred to as Internal Linear Combination (ILC), has been extensively employed in the measurement of cosmic microwave background (CMB) anisotropies and its secondaries along with similar application in 21cm data analysis. Here we argue and demonstrate that ILC methods can also be applied to data from absolutely-calibrated CMB experiments to extract average-sky signals in addition to the conventional CMB anisotropies. The performance of the simple ILC method is, however, limited, but can be significantly improved by adding constraints informed by physics and existing empirical information. In recent work, a moment description has been introduced as a technique of carrying out high precision modeling of foregrounds in the presence of inevitable averaging effects. We combine these two approaches to construct a heavily constrained form of the ILC, dubbed MILC, which can be used to recover tiny monopolar spectral distortion signals in the presence of realistic foregrounds and instrumental noise. This is a first demonstration for measurements of the monopolar and anisotropic spectral distortion signals using ILC and extended moment methods. We also show that CMB anisotropy measurements can be improved, reducing foreground biases and signal uncertainties when using the MILC. While here we focus on CMB spectral distortions, the scope extends to the 21cm monopole signal and B-mode analysis. We briefly discuss augmentations that need further study to reach the full potential of the method.

On the Impact of Random Residual Calibration Error on the Gibbs ILC CMB Estimates over Large Angular Scales

Abstract Residual errors in calibration coefficients corresponding to observed cosmic microwave background (CMB) maps are an important issue when estimating a pure CMB signal. These errors in the input-foreground-contaminated CMB maps, if not properly taken into account in a component separation method, may lead to bias in the cleaned CMB map and estimated CMB angular power spectrum. But the inability to exactly determine the calibration coefficients corresponding to each observed CMB map from a multifrequency CMB experiment makes it very difficult to incorporate their exact and actual values during the component separation method. Hence, the effect of any random and residual calibration error in the cleaned CMB map and its angular power spectrum of a component separation problem can only be understood by performing detailed Monte Carlo simulations. In this paper, we investigate the impact of using input-observed CMB maps with random calibration errors on the posterior density of a cleaned CMB map and theoretical CMB angular power spectrum over large angular scales of the sky following the Gibbs Internal-Linear-Combination (ILC) method. By performing detailed Monte Carlo simulations of WMAP and Planck temperature anisotropy observations, including their estimate on calibration errors, we show that the best-fit map corresponding to the posterior maximum is minimally biased in the Gibbs ILC method by a CMB normalization bias and residual foreground bias. The residual calibration-induced error in the best-fit power spectrum causes an overall 6% increase of the net error when added in quadrature with the cosmic-variance-induced error.

Detection of WHIM in the Planck data using Stack First approach

We detect the diffuse thermal Sunyaev-Zeldovich (tSZ) effect from the gas filaments between the Luminous Red Galaxy (LRG) pairs using a new approach relying on stacking the individual frequency maps. We apply and demonstrate our method on 08800 LRG pairs in the SDSS DR12 catalogue selected with an improved selection criterion that ensures minimal contamination by the Galactic CO emission as well as the tSZ signal from the clusters of galaxies. We first stack the Planck channel maps and then perform the Internal Linear Combination method to extract the diffuse ysz signal. Our Stack First approach makes the component separation a lot easier as the stacking greatly suppresses the noise and CMB contributions while the dust foreground becomes homogeneous in spectral-domain across the stacked patch. Thus one component, the CMB, is removed while the rest of the foregrounds are made simpler even before component separation algorithm is applied. We obtain the WHIM signal of ywhim=(3.78± 0.37)× 10−8 in the gas filaments, accounting for the electron overdensity of ∼ 13. We estimate the detection significance to be ≳ 10.2σ. This excess ysz signal is tracing the warm-hot intergalactic medium and it could account for most of the missing baryons of the Universe. We show that the Stack First approach is more robust to systematics and produces a cleaner signal compared to the methods relying on stacking the y-maps to detect weak tSZ signal currently being used by the cosmology community.

PACT

We present the optimal reconstruction of the thermal Sunyaev–Zel’dovich (tSZ) effect signal based on the combination of a heterogeneous dataset consisting of Atacama Cosmology Telescope (ACT) and Planck data, with different numbers of channels, angular resolutions, and noise levels. We combine both datasets using two different approaches, a matched multifilter (MMF) technique and an optimized internal linear combination (ILC). We show that when applying the MMF to the combination of ACT and Planck data, the size-flux degeneracy is reduced and the signal-to-noise of clusters detected with their Sunyaev–Zel’dovich (SZ) signal improves by up to a factor of three. In the case of the optimized ILC method, we show that the tSZ map is reconstructed with a resolution of ∼1.5 arcmin. This is more than a factor two improvement compared with the Planck resolution, and with a very good control of noise, meaning that it is limited only by the intrinsic noise of the individual experiments. The combination of ACT and Planck data offers a unique opportunity to improve on the study of the pressure profiles and to study substructure in clusters through their tSZ.

Data driven foreground clustering approach to component separation in multifrequency CMB experiments: a new Planck CMB map

We present a new approach to component separation in multifrequency CMB experiments by formulating the problem as that of partitioning the sky into pixel clusters such that within each pixel cluster the foregrounds have similar spectrum, using only the information available in the data. Only spectral information is used for partitioning, allowing spatially far away pixels to belong to the same cluster if their foreground properties are close. We then apply a modified internal linear combination method to each pixel cluster. Since the foregrounds have similar spectrum within each cluster, the number of components required to describe the foregrounds is smaller compared to all data taken together and simple pixel based ILC algorithm works extremely well. We test our algorithm in the full focal plane simulations provided by the Planck collaboration. We apply our algorithm to the Planck full mission data and compare our CMB maps with the CMB maps released by the Planck collaboration. We show that our CMB maps are clean and unbiased on a larger fraction of the sky, especially at the low Galactic latitudes, compared to publicly available maps released by the Planck collaboration. This is important for constraining beyond the simplest ΛCDM cosmological models and study of anomalies. Our cleaned CMB maps are made publicly available for use by the cosmology community.

A Global ILC Approach in Pixel Space over Large Angular Scales of the Sky Using CMB Covariance Matrix

Abstract We propose a new internal linear combination (ILC) method in the pixel space, applicable on large angular scales of the sky, to estimate a foreground-minimized cosmic microwave background (CMB) temperature anisotropy map by incorporating prior knowledge about the theoretical CMB covariance matrix. The usual ILC method in pixel space, on the contrary, does not use any information about the underlying CMB covariance matrix. The new approach complements the usual pixel space ILC technique specifically at low-multipole regions, using global information available from the theoretical CMB covariance matrix and from the data. Since we apply our method over the large scale on the sky containing low multipoles, we perform foreground minimization globally. We apply our methods on low-resolution Planck and WMAP foreground-contaminated CMB maps and validate the methodology by performing detailed Monte Carlo simulations. Our cleaned CMB map and its power spectrum have significantly less error than those obtained following the usual ILC technique at low resolution that does not use CMB covariance information. Another very important advantage of our method is that the cleaned power spectrum does not have any negative bias at the low multipoles because of effective suppression of CMB–foreground chance correlations on large angular scales of the sky. Our cleaned CMB map and its power spectrum match well with those estimated by other research groups.

Spin-SILC: CMB polarization component separation with spin wavelets

We present Spin-SILC, a new foreground component separation method that accurately extracts the cosmic microwave background (CMB) polarisation $E$ and $B$ modes from raw multifrequency Stokes $Q$ and $U$ measurements of the microwave sky. Spin-SILC is an internal linear combination method that uses spin wavelets to analyse the spin-2 polarisation signal $P = Q + iU$. The wavelets are additionally directional (non-axisymmetric). This allows different morphologies of signals to be separated and therefore the cleaning algorithm is localised using an additional domain of information. The advantage of spin wavelets over standard scalar wavelets is to simultaneously and self-consistently probe scales and directions in the polarisation signal $P = Q + iU$ and in the underlying $E$ and $B$ modes, therefore providing the ability to perform component separation and $E$-$B$ decomposition concurrently for the first time. We test Spin-SILC on full-mission Planck simulations and data and show the capacity to correctly recover the underlying cosmological $E$ and $B$ modes. We also demonstrate a strong consistency of our CMB maps with those derived from existing component separation methods. Spin-SILC can be combined with the pseudo- and pure $E$-$B$ spin wavelet estimators presented in a companion paper to reliably extract the cosmological signal in the presence of complicated sky cuts and noise. Therefore, it will provide a computationally-efficient method to accurately extract the CMB $E$ and $B$ modes for future polarisation experiments.

CMB polarization map derived from the WMAP 5 year data through the harmonic internal linear combination method

We have derived whole-sky cosmic microwave background polarization maps from the WMAP 5 year polarization data, using the harmonic internal linear combination (HILC) method. Our HILC method incorporates spatial variability of linear weights in a natural way and yields continuous linear weights over the entire sky. To estimate the power spectrum of HILC maps, we have derived an unbiased quadratic estimator, which is similar to the WMAP team's cross-power estimator, but in a more convenient form for HILC maps. From our cosmic microwave background polarization map, we have obtained $TE$ correlation and $E$ mode power spectra without applying any mask. They are similar to the WMAP team's estimation and consistent with the WMAP best-fit $\ensuremath{\Lambda}\mathrm{CDM}$ model. Foreground reduction by the HILC method is more effective for high resolution and low noise data. Hence, our HILC method will enable effective foreground reduction in polarization data from the Planck surveyor.

Instability of reconstruction of the low CMB multipoles

We discuss the problem of the bias of the Internal Linear Combination (ILC) CMB map and show that it is closely related to the coefficient of cross-correlation K(l) of the true CMB and the foreground for each multipole l. We present analysis of the cross-correlation for the WMAP ILC quadrupole and octupole from the first (ILC(I)) and the third (ILC(III)) year data releases and show that these correlations are about -0.52-0.6. Analysing 10^4 Monte Carlo simulations of the random Gaussian CMB signals, we show that the distribution function for the corresponding coefficient of the cross-correlation has a polynomial shape P(K,l)\propto(1-K^2)^(l-1). We show that the most probable value of the cross-correlation coefficient of the ILC and foreground quadrupole has two extrema at K ~= +/-0.58$. Thus, the ILC(III) quadrupole represents the most probable value of the coefficient K. We analyze the problem of debiasing of the ILC CMB and pointed out that reconstruction of the bias seems to be very problematic due to statistical uncertainties. In addition, instability of the debiasing illuminates itself for the quadrupole and octupole components through the flip-effect, when the even (l+m) modes can be reconstructed with significant error. This error manifests itself as opposite, in respect to the true sign of even low multipole modes, and leads to significant changes of the coefficient of cross-correlation with the foreground. We show that the CMB realizations, whose the sign of quadrupole (2,0) component is negative (and the same, as for all the foregrounds), the corresponding probability to get the positive sign after implementation of the ILC method is about 40%.