Internal Linear Combination Research Articles

Signal-preserving CMB component separation with machine learning

Analysis of microwave sky signals, such as the cosmic microwave background, often requires component separation using multifrequency methods, whereby different signals are isolated according to their different frequency behaviors. Many so-called blind methods, such as the internal linear combination (ILC), make minimal assumptions about the spatial distribution of the signal or contaminants, and only assume knowledge of the frequency dependence of the signal. The ILC produces a minimum-variance linear combination of the measured frequency maps. In the case of Gaussian, statistically isotropic fields, this is the optimal linear combination, as the variance is the only statistic of interest. However, in many cases the signal we wish to isolate, or the foregrounds we wish to remove, are non-Gaussian and/or statistically anisotropic (in particular for the case of Galactic foregrounds). In such cases, it is possible that machine learning (ML) techniques can be used to exploit the non-Gaussian features of the foregrounds and thereby improve component separation. However, many ML techniques require the use of complex, difficult-to-interpret operations on the data. We propose a hybrid method whereby we train an ML model using only combinations of the data that , and combine the resulting ML-predicted foreground estimate with the ILC solution to reduce the error from the ILC. We demonstrate our methods on simulations of extragalactic temperature and Galactic polarization foregrounds and show that our ML model can exploit non-Gaussian features, such as point sources and spatially varying spectral indices, to produce lower-variance maps than ILC—e.g., reducing the variance of the B-mode residual by factors of up to 5—while preserving the signal of interest in an unbiased manner. Moreover, we often find improved performance even when applying our ML technique to foreground models on which it was not trained. Published by the American Physical Society 2025

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.

Expanded Generalized Needlet Internal Linear Combination (eGNILC) Framework for the 21 cm Foreground Removal

Abstract The Generalized Needlet Internal Linear Combination (GNILC) method is a nonparametric component separation algorithm to remove the foreground contamination of the 21 cm intensity mapping data. In this work, we perform the discrete cosine transform along the frequency axis in the expanded GNILC framework (denoted eGNILC), which helps reduce the power loss in low multipoles, and further demonstrates its performance. We also calculate the eGNILC bias to modify the criterion for determining the degrees of freedom (dof) of the foreground, and embed the robust principal component analysis in mixing matrix computation to obtain a blind component separation method. We find that the eGNILC bias is related to the averaged domain size and the dof of the foreground but not the underlying 21 cm signal. In the case of no beam effect, the eGNILC bias is negligible for simple power-law foregrounds outside the Galactic plane. We also examine the eGNILC performance in the SKA Phase-I in mid-frequency (SKA-MID) and Baryon Acoustic Oscillations from Integrated Neutral Gas Observations (BINGO) simulations. We show that if the adjacent frequency channels are not highly correlated, eGNILC can recover the underlying 21 cm signal with good accuracy. With the varying Airy-disk beam applied to both SKA-MID and BINGO, the power spectra of 21 cm can be effectively recovered at the multipoles ℓ ∈ [20, 250] and [20, 300], respectively. With no instrumental noise, the SKA-MID exhibits ≲20% power loss, and BINGO exhibits ~10% power loss. The varying Airy-disk beam only causes significant errors at large multipoles.

Requirements on the gain calibration for LiteBIRD polarisation data with blind component separation

The detection of primordial B modes of the cosmic microwave background (CMB) could provide information about the early stages of the Universe's evolution. The faintness of this signal requires exquisite calibration accuracy and control of instrumental systematic effects which otherwise could bias the measurements. In this work, we study the impact of an imperfect relative polarisation gain calibration on the recovered value of the tensor-to-scalar ratio r for the LiteBIRD experiment, through the application of the blind Needlet Internal Linear Combination (NILC) foreground-cleaning method. We derive requirements on the relative calibration accuracy of the overall polarisation gain (Δgν ) for each LiteBIRD frequency channel. Our results show that minimum variance techniques, as NILC, are less sensitive to systematic gain calibration uncertainties compared to a parametric approach, if the latter is not equipped with a proper modelling of these instrumental effects. In this study, the most stringent requirements are found in the channels where the CMB signal is relatively brighter, with the tightest constraints at 166 GHz (Δgν ≈ 0.16%). This differs from the outcome of an analogous analysis performed with a parametric method, where the tightest requirements are obtained for the foreground-dominated channels. Gain calibration uncertainties, corresponding to the derived requirements, are then simultaneously propagated into all frequency channels. By doing so, we find that the overall impact on estimated r is lower than the total gain systematic budget for LiteBIRD approximately by a factor 5, due to the correlations of the impacts of gain calibration uncertainties in different frequency channels. In order to decouple the systematic effect from the specific choice of the model, we derive the requirements assuming constant spectral parameters for the foreground emission. To assess the robustness of the obtained results against more realistic scenarios, we repeat the analysis assuming sky models of intermediate and high complexity. In these further cases, we adopt an optimised NILC pipeline, called the Multi-Clustering NILC (MC-NILC). We find that the impact of gain calibration uncertainties on r is lower than the LiteBIRD gain systematics budget for the intermediate-complexity sky model. For the high-complexity case, instead, it would be necessary to tighten the requirements by a factor 1.8.

Forecast of Foreground Cleaning Strategies for AliCPT-1

We report the test results of several independent foreground cleaning pipelines used in the Ali CMB Polarization Telescope experiment (AliCPT-1), a high-altitude cosmic microwave background (CMB) imager in the Northern Hemisphere with thousands of detectors dedicated to the search for a primordial CMB polarization B-mode signature. Based on simulated data from four detector modules and a single season of observation, which we refer to as Data Challenge 1 (DC1), we employ different and independent pipelines to examine the robustness and effectiveness of estimates on foreground parameters and primordial B-mode detection. The foreground cleaning strategies used in the pipelines include the parametric method of template fitting (TF) and the nonparametric methods of constrained internal linear combination (cILC), analytical blind separation (ABS), and generalized least squares (GLS). We examine the impact of possible foreground residuals on the estimate of the CMB tensor-to-scalar ratio (r) for each pipeline by changing the contamination components in the simulated maps and varying the foreground models and sky patches for various tests. According to the DC1 data with the simulation input value r true = 0.023, the foreground residual contamination levels in the TF/ABS/cILC/GLS pipelines are well within the corresponding statistical errors at the 2σ level. Furthermore, by utilizing the tension estimator, which helps identify significant residual foreground contamination in the detection of the primordial B-mode signal by quantifying the discrepancy between various r measurements, we conclude that the presence of small foreground residuals does not lead to any significant inconsistency in the estimation of r.

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.

LiteBIRD science goals and forecasts: a full-sky measurement of gravitational lensing of the CMB

We explore the capability of measuring lensing signals in LiteBIRD full-sky polarization maps. With a 30 arcmin beam width and an impressively low polarization noise of 2.16 μK-arcmin, LiteBIRD will be able to measure the full-sky polarization of the cosmic microwave background (CMB) very precisely. This unique sensitivity also enables the reconstruction of a nearly full-sky lensing map using only polarization data, even considering its limited capability to capture small-scale CMB anisotropies. In this paper, we investigate the ability to construct a full-sky lensing measurement in the presence of Galactic foregrounds, finding that several possible biases from Galactic foregrounds should be negligible after component separation by harmonic-space internal linear combination. We find that the signal-to-noise ratio of the lensing is approximately 40 using only polarization data measured over 80% of the sky. This achievement is comparable to Planck's recent lensing measurement with both temperature and polarization and represents a four-fold improvement over Planck's polarization-only lensing measurement. The LiteBIRD lensing map will complement the Planck lensing map and provide several opportunities for cross-correlation science, especially in the northern hemisphere.

Optimization of foreground moment deprojection for semi-blind CMB polarization reconstruction

Upcoming Cosmic Microwave Background (CMB) experiments, aimed at measuring primordial CMB polarization B-modes, require exquisite control of instrumental systematics and Galactic foreground contamination. Blind minimum-variance techniques, like the Needlet Internal Linear Combination (NILC), have proven effective in reconstructing the CMB polarization signal and mitigating foregrounds and systematics across diverse sky models without suffering from foreground mismodelling errors. Still, residual foreground contamination from NILC may bias the recovered CMB polarization at large angular scales when confronted with the most complex foreground scenarios.By adding constraints to NILC to deproject statistical moments of the Galactic emission, the Constrained Moment ILC (cMILC) method has been demonstrated to further enhance foreground subtraction, albeit with an associated increase in overall noise variance. Faced with this trade-off between foreground bias reduction and overall variance minimization, there is still no recipe on which moments to deproject and which are better suited for blind variance minimization. To address this, we introduce the optimized cMILC (ocMILC) pipeline, which performs full automated optimization of the required number and set of foreground moments to deproject, pivot parameter values, and deprojection coefficients across the sky and angular scales, depending on the actual sky complexity, available frequency coverage, and experiment sensitivity. The optimal number of moments for deprojection, before paying significant noise penalty, is determined through a data diagnosis inspired by the Generalized NILC (GNILC) method.Validated on B-mode simulations of the PICO space mission concept with four challenging foreground models, ocMILC exhibits lower Galactic foreground contamination compared to NILC and cMILC at all angular scales, with limited noise penalty. This multi-layer optimization enables the ocMILC pipeline to achieve unbiased posteriors of the tensor-to-scalar ratio, regardless of foreground complexity.

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.

Optimizing NILC Extractions of the Thermal Sunyaev–Zel’Dovich Effect with Deep Learning

All-sky maps of the thermal Sunyaev–Zel’dovich effect (SZ) tend to suffer from systematic features arising from the component-separation techniques used to extract the signal. In this work, we investigate one of these methods, known as needlet internal linear combination (NILC), and test its performance on simulated data. We show that NILC estimates are strongly affected by the choice of the spatial localization parameter (Γ), which controls a bias-variance trade-off. Typically, NILC extractions assume a fixed value of Γ over the entire sky, but we show there exists an optimal Γ that depends on the SZ signal strength and local contamination properties. Then we calculate the NILC solutions for multiple values of Γ and feed the results into a neural network to predict the SZ signal. This extraction method, which we call Deep-NILC, is tested against a set of validation data, including recovered radial profiles of resolved systems. Our main result is that Deep-NILC offers significant improvements over choosing fixed values of Γ.

Cross-correlation of the thermal Sunyaev-Zel’dovich and CMB lensing signals in Planck PR4 data with robust CIB decontamination

We use the full-mission PR4 data to measure the CMB lensing convergence (κ)–thermal Sunyaev-Zel’dovich (tSZ, y) cross-correlation signal, Cℓyκ. This is only the second measurement to date of this signal, following Hill and Spergel []. We perform the measurement using foreground-cleaned tSZ maps built from the PR4 frequency maps via a tailored needlet internal linear combination (NILC) code in our companion paper [F. McCarthy and J. C. Hill, companion paper, .], in combination with the PR4 κ maps and various systematic-mitigated PR3 κ maps. A serious systematic is the residual cosmic infrared background (CIB) signal in the tSZ map, as the high CIB—κ cross-correlation can significantly bias the inferred tSZ—κ cross-correlation. We mitigate this contamination by deprojecting the CIB in our NILC algorithm, using a moment deprojection approach to avoid leakage due to incorrect modeling of the CIB frequency dependence. We validate this method on mm-wave sky simulations. We fit a theoretical halo model to our measurement, finding a best-fit amplitude of A=0.82±0.21 (for the highest signal-to-noise PR4 κ map) or A=0.56±0.24 (for a PR3 κ map built from a tSZ-deprojected CMB map), indicating that the data are consistent with our fiducial model within ≈1−2σ. Although our error bars are similar to those of the previous measurement [J. C. Hill and D. N. Spergel, ], our method is significantly more robust to CIB contamination. Our moment-deprojection approach lays the foundation for future measurements of this signal with higher signal-to-noise κ and y maps from ground-based telescopes, which will precisely probe the astrophysics of the intracluster medium of galaxy groups and clusters in the intermediate-mass (M∼1013–1014h−1M⊙), high-z (z≲1.5, c.f. z≲0.8 for the tSZ auto-power signal) regime, as well as CIB-decontaminated measurements of tSZ cross-correlations with other large-scale structure probes. Published by the American Physical Society 2024

Needlet Karhunen–Loève (NKL): a method for cleaning foregrounds from 21 cm intensity maps

ABSTRACT This paper introduces a technique called needlet Karhunen–Loéve (NKL), which cleans both polarized and unpolarized foregrounds from H i intensity maps by applying a Karhunen–Loéve transform on the needlet coefficients. In NKL, one takes advantage of correlations not only along the line of sight, but also between different angular regions, referred to as ‘chunks’. This provides a distinct advantage over many of the standard techniques applied to map space that one finds in the literature, which do not consider such spatial correlations. Moreover, the NKL technique does not require any priors on the nature of the foregrounds, which is important when considering polarized foregrounds. We also introduce a modified version of Generalized Needlet Internal Linear Combination (GNILC), referred to as MGNILC, which incorporates an approximation of the foregrounds to improve performance. The NKL and MGNILC techniques are tested on simulated maps which include polarized foregrounds. Their performance is compared to the GNILC, generalized morphological component analysis, independent component analysis, and principal component analysis techniques. Two separate tests were performed. One at 1.84 < z < 2.55 and the other at 0.31 < z < 0.45. NKL was found to provide the best performance in both tests, providing a factor of 10–50 improvement over GNILC at $k \lt 0.1\, {\rm hMpc^{-1}}$ in the higher redshift case and $k \lt 0.03 \, {\rm hMpc^{-1}}$ in the lower redshift case. However, none of the methods were found to recover the power spectrum satisfactorily at all baryon acoustic oscillations scales.

An improved Compton parameter map of thermal Sunyaev–Zeldovich effect from Planck PR4 data

ABSTRACT Taking advantage of the reduced levels of noise and systematics in the data of the latest Planck release (PR4, also known as NPIPE), we construct a new all-sky Compton-y parameter map (hereafter, y-map) of the thermal Sunyaev–Zeldovich (SZ) effect from the Planck PR4 data. A tailored Needlet Internal Linear Combination (NILC) pipeline, first validated on detailed sky simulations, is applied to the nine single-frequency Planck PR4 sky maps, ranging from 30 to 857 GHz, to produce the PR4 y-map over 98 per cent of the sky. Using map comparisons, angular power spectra, and one-point statistics, we show that the PR4 NILC y-map is of improved quality compared to that of the previous PR2 release. The new y-map shows reduced levels of large-scale striations associated with 1/f noise in the scan direction. Regions near the Galactic plane also show lower residual contamination by Galactic thermal dust emission. At small angular scales, the residual contamination by thermal noise and cosmic infrared background (CIB) emission is found to be reduced by around 7 and 34 per cent, respectively, in the PR4 y-map. The PR4 NILC y-map is made publicly available for astrophysical and cosmological analyses of the thermal SZ effect.

Analysis of Needlet Internal Linear Combination performance on B-mode data from sub-orbital experiments

Context. The observation of primordial B modes in cosmic microwave background (CMB) polarisation data represents the main scientific goal of most of the future CMB experiments. This signal is predicted to be much lower than polarised Galactic emission (foregrounds) in any region of the sky, pointing to the need for effective component separation methods. Aims. Among all the techniques, the blind Needlet Internal Linear Combination (NILC) is of great relevance given our current limited knowledge of the B-mode foregrounds. In this work, we explore the possibility of employing NILC for the analysis of B modes reconstructed from partial-sky data, specifically addressing the complications that such an application yields such as E–B leakage, needlet filtering, and beam convolution. Methods. We consider two complementary simulated datasets of future experiments: the balloon-borne Short Wavelength Instrument for the Polarisation Explorer (SWIPE) of the Large Scale Polarisation Explorer, which targets the observation of both reionisation and recombination peaks of the primordial CMB B-mode angular power spectrum, and the ground-based Small Aperture Telescope of Simons Observatory, which, instead, is designed to observe only the recombination bump at ℓ ∼ 80. We assessed the performance of the following two alternative techniques to correct for the CMB E–B leakage: the recycling technique and the Zhao-Baskaran method. Results. We find that both techniques reduce the E–B leakage residuals at a negligible level given the sensitivity of the considered experiments, except for the recycling method in the SWIPE footprint at ℓ < 20. Thus, we implemented two extensions of the pipeline, the iterative B decomposition and the diffusive inpainting, which enabled us to recover the input CMB B-mode power for ℓ ≥ 5. For the considered experiments, we demonstrate that needlet filtering and beam convolution do not affect the CMB B-mode reconstruction. Finally, with an appropriate masking strategy, we find that NILC foregrounds subtraction allows one to achieve sensitivities on the tensor-to-scalar ratio in agreement with the targets of the considered CMB experiments.

Multiclustering needlet ILC for CMB B-mode component separation

ABSTRACT The Cosmic Microwave Background (CMB) primordial B-mode signal is predicted to be much lower than the polarized Galactic emission (foregrounds) in any region of the sky pointing to the need for sophisticated component separation methods. Among them, the blind Needlet Internal Linear Combination (NILC) has great relevance given our current poor knowledge of the B-mode foregrounds. However, the expected level of spatial variability of the foreground spectral properties complicates the NILC subtraction of the Galactic contamination. We therefore propose a novel extension of the NILC approach, the Multiclustering NILC (MC-NILC), which performs NILC variance minimization on separate regions of the sky (clusters) properly chosen to have similar spectral properties of the B-mode Galactic emission within them. Clusters are identified thresholding either the ratio of simulated foregrounds-only B modes (ideal case) or the one of cleaned templates of Galactic emission obtained from realistic simulations. In this work we present an application of MC-NILC to the future LiteBIRD satellite, which targets the observation of both reionization and recombination peaks of the primordial B-mode angular power spectrum with a total error on the tensor-to-scalar ratio δr < 0.001. We show that MC-NILC provides a CMB solution with residual foreground and noise contamination that is significantly lower than the NILC one and the primordial signal targeted by LiteBIRD at all angular scales for the ideal case and at the reionization peak for a realistic ratio. Thus, MC-NILC will represent a powerful method to mitigate B-mode foregrounds for future CMB polarization experiments.

Thermal Energy Census with the Sunyaev–Zel’dovich Effect of DESI Galaxy Clusters/Groups and Its Implication on the Weak-lensing Power Spectrum

We carry out a thermal energy census of hot baryons at z < 1, by cross correlating the Planck Modified Internal Linear Combination Algorithm (MILCA) y map with 0.8 million clusters/groups selected from the Yang et al. catalog. The thermal Sunyaev–Zel’dovich effect around these clusters/groups is reliably obtained, which enables us to make our model constraints based on one-halo (1h) and two-halo (2h) contributions, respectively. (1) The total measurement signal-to-noise (S/N) of the one-halo term is 63. We constrain the Y–M relation over the halo mass range of 1013–1015 M ⊙ h −1, and find Y ∝ M α with α = 1.8 at z = 0.14 (α = 2.1 at z = 0.75). The total thermal energy of gas bound to clusters/groups increases from 0.1 meV cm−3 at z = 0.14 to 0.22 meV cm−3 at z = 0.75. (2) The 2h term is used to constrain the bias-weighted electron pressure 〈b y P e 〉. We find that 〈b y P e 〉 (in units of meV cm−3) increases from 0.24 ± 0.02 at z = 0.14 to 0.45 ± 0.02 at z = 0.75. These results lead to several implications. (i) The hot gas fraction f gas in clusters/groups monotonically increase with the halo mass, where f gas of a 1014 M ⊙ h −1 halo is ∼50% (25%) of the cosmic mean at z = 0.14 (0.75). (ii) By comparing the 1h and 2h terms, we obtain a tentative constraint on the thermal energy of unbound gas. (iii) The above results lead to significant suppression of the matter and weak-lensing power spectrum at small scales. These implications are important for astrophysics and cosmology, and we will further investigate them with improved data and gas modeling.

Forecasts of CMB lensing reconstruction of AliCPT-1 from the foreground cleaned polarization data

The gravitational lensing distortion of Cosmic microwave background radiation (CMB) carries fruitful information of cosmic large-scale structure. However, CMB observations are unavoidably contaminated by emission from various extra-galactic foregrounds, which must be removed to obtain reliable measurements of the cosmological signal. In this paper, we demonstrate CMB lensing reconstruction in AliCPT-1 after foreground removal, combine the two bands of AliCPT-1 (90 and 150 GHz) with Planck HFI bands (100, 143, 217 and 353 GHz) and with the WMAP-K band (23 GHz). In order to balance contamination by instrumental noise and foreground residual bias, we adopt the Needlet Internal Linear Combination (NILC) method to clean the E-map and the constrained Internal Linear Combination (cILC) method to clean the B-map. The latter utilizes additional constraints on average frequency scaling of the dust and synchrotron to remove foregrounds at the expense of somewhat noisier maps. Assuming 4 modules observing 1 season from simulation data, the resulting effective residual noise in E- and B-map are roughly 15 μ K· arcmin and 25 μ K· arcmin, respectively. As a result, the CMB lensing reconstruction signal-to-noise ratio (SNR) from polarization data is about SNR≈4.5. This lensing reconstruction capability is comparable to that of other stage-III small aperture millimeter CMB telescopes.

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.

Testing synchrotron models and frequency resolution in BINGO 21 cm simulated maps using GNILC

Context. The 21 cm hydrogen line is arguably one of the most powerful probes with which to explore the Universe, from recombination to the present times. To recover it, it is essential to separate the cosmological signal from the much stronger foreground contributions at radio frequencies. The Baryon Acoustic Oscillations from Integrated Neutral Gas Observations (BINGO) radio telescope is designed to measure the 21 cm line and detect baryon acoustic oscillations (BAOs) using the intensity mapping (IM) technique. Aims. This work analyses the performance of the Generalized Needlet Internal Linear Combination (GNILC) method when combined with a power spectrum debiasing procedure. This method was applied to a simulated BINGO mission, building upon previous work from the collaboration. It compares two different synchrotron emission models and different instrumental configurations and takes into account ancillary data in order to optimize both the removal of foreground emission and the recovery of the 21 cm signal across the full BINGO frequency band and to determine an optimal number of frequency (redshift) bands for the signal recovery. Methods. We produced foreground emission maps using the Planck Sky Model (PSM) and generated cosmological HI emission maps using the Full-Sky Log-normal Astro-Fields simulation Kit (FLASK) package. We also created thermal noise maps according to the instrumental setup. We apply the GNILC method to the simulated sky maps to separate the HI plus thermal noise contribution and, through a debiasing procedure, recover an estimate of the noiseless 21 cm power spectrum. Results. We find a near-optimal reconstruction of the HI signal using an 80-bin configuration, which resulted in a power-spectrum reconstruction average error over all frequencies of 3%. Furthermore, our tests show that GNILC is robust against different synchrotron emission models. Finally, adding an extra channel with C-Band All-Sky Survey (CBASS) foregrounds information, we reduced the estimation error of the 21 cm signal. Conclusions. The optimization of our previous work, producing a configuration with an optimal number of channels for binning the data, significantly impacts decisions regarding BINGO hardware configuration before commissioning. We were able to recover the HI signal with good efficiency in the harmonic space, but have yet to investigate the effect of 1/f noise in the data, which will possibly impact the recovery of the HI signal. This issue will be addressed in forthcoming work.

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.