BICEP/Keck XX: Component-separated maps of polarized CMB and thermal dust emission using Planck and BICEP/Keck Observations through the 2018 Observing Season

TL;DR

The paper tackles the challenge of separating faint CMB B-mode polarization from Galactic dust foregrounds in BICEP/Keck and Planck data by developing a map-based, maximum-likelihood component-separation framework that jointly estimates $s^{\rm CMB}$ and $s^{\rm dust}$ from multi-frequency polarization maps using an observing-matrix formalism. It provides unbiased component maps, two complementary power-spectrum estimators (pseudo-$C_{\ell}$ with matrix purification and optimal quadratic maximum likelihood), and a cross-check against the standard BK18 multi-frequency likelihood, finding an $\sim84\%$ correlation in $r$ across methods. Validation on 499 simulations demonstrates robust $E$-to-$B$ leakage control and favorable purification performance, while real-data results are consistent with the baseline $\Lambda$CDM$+$dust model. The approach yields high-fidelity CMB and dust maps and foreground templates, offering a data-vector alternative to harmonic-space foreground modeling with potential for higher-order analyses and improved foreground handling in future CMB polarization studies.

Abstract

We present component-separated polarization maps of the cosmic microwave background (CMB) and Galactic thermal dust emission, derived using data from the BICEP/Keck experiments through the 2018 observing season and Planck. By employing a maximum-likelihood method that utilizes observing matrices, we produce unbiased maps of the CMB and dust signals. We outline the computational challenges and demonstrate an efficient implementation of the component map estimator. We show methods to compute and characterize power spectra of these maps, opening up an alternative way to infer the tensor-to-scalar ratio from our data. We compare the results of this map-based separation method with the baseline BICEP/Keck analysis. Our analysis demonstrates consistency between the two methods, finding an 84% correlation between the pipelines.

Figures (20)

• Figure 1: Histogram of the maximum likelihood values of the dust spectral index $\beta_d$ obtained in the baseline BK18 BK18 auto-/cross-spectrum analysis. The black vertical line indicates the input value to the simulations, the (nearly coincident) red line indicates the mean of the recovered best-fit values, and the dashed green line marks the best-fit value of the real data.
• Figure 2: Plot of the non-zero matrix elements of the BICEP/ Keck internal maps' observing matrices, i.e., the BICEP/ Keck-specific block of the matrix $\mathbf{R}$ used in this work. Applying a vector including beam-convolved $Q$ & $U$ maps to the right of this matrix results in a vector of filtered $Q$ & $U$ maps in the flat pixelization used in BK18. The top-left block corresponds to the BICEP3 map, while the following blocks along the diagonal contain the observing matrices for the Keck 95 GHz, BICEP2/ Keck 150 GHz, Keck 210 GHz, and Keck 220 GHz channels. Within each block on the diagonal, the top row produces a BICEP/ Keck$Q$ map and the bottom row a BICEP/ Keck$U$ map from a vector of stacked $Q$ & $U$ maps. This part of the matrix contains about 5 billion non-zero elements and is the biggest computational challenge in this analysis.
• Figure 3: $Q$ maps (top row) and the logarithmic (base 10) $EE$ two-dimensional auto-power spectrum (bottom row) of one noise simulation for BICEP3 (left column), Planck HFI 100 GHz (middle column), and their combination (right column). The combination estimator corrects for filtering suppression at the map-level and hence boosts the noise compared to the filtered BICEP3 map and fills in modes from Planck for small $\ell_x$. This is why the combined $Q$ noise maps show strong horizontal stripes in the central BICEP3 map region.
• Figure 4: The relative residual $||\mathbf{A}\mathbf{s}-\mathbf{b}||/||\mathbf{b}||$, where $\mathbf{A}\equiv \mathbf{R}^T \hat{\mathbf{N}}_{B3}^{-1} \mathbf{R} + \hat{\mathbf{N}}_{P}^{-1}$ and $\mathbf{b}=\mathbf{R}^T \hat{\mathbf{N}}_{B3}^{-1} \mathbf{d}_{B3} + \hat{\mathbf{N}}_{P}^{-1} \mathbf{d}_{P}$, for each iteration of the preconditioned iterative method. We test three different iterative solvers: the classic CG, GMRES, and Bi-CGSTAB pcg. The spikes are due to numerical noise, which these iterative solvers are susceptible to Sidje2011.
• Figure 5: The relative residual as defined in Fig. \ref{['fig:pcgresidualmethods']} for each iteration of the (Bi-CGSTAB) preconditioned conjugate gradient method. We show the convergence performance for a signal-only, noise-only, and a signal-and-noise simulation.