Cleaning Galactic foregrounds with spatially varying spectral dependence from CMB observations with \texttt{fgbuster}

TL;DR

The paper tackles foreground contamination in next-generation CMB $B$-mode searches by introducing \\texttt{fgbuster}, a spectral-likelihood, parametric component-separation method that allows foreground SED parameters to vary across pixel subsets. It couples simulation-based analyses with a semi-analytical forecasting framework to quantify how systematic and statistical residuals depend on patch definitions, foreground models, and instrument characteristics (e.g., LiteBIRD-like and PICO-like configurations). The study shows that increasing the number of pixel subsets reduces systematic residuals but elevates statistical residuals, with the balance strongly influenced by the instrument's frequency coverage and sensitivity; an optimal trade-off is achievable in realistic configurations. The semi-analytical forecasts align with full simulations, offering actionable guidance for designing subset schemes and instrument specifications to minimize residuals while preserving sensitivity to the tensor-to-scalar ratio $r$.

Abstract

In the context of maximum-likelihood parametric component separation for next-generation full-sky CMB polarization experiments, we study the impact of fitting different spectral parameters of Galactic foregrounds in distinct subsets of pixels on the sky, with the goal of optimizing the search for primordial B modes. Using both simulations and analytical arguments, we highlight how the post-component separation uncertainty and systematic foreground residuals in the cleaned CMB power spectrum depend on spatial variations in the spectral parameters. We show that allowing spectral parameters to vary across subsets of the sky pixels is essential to achieve competitive S/N on the reconstructed CMB after component separation while keeping residual foreground bias under control. Although several strategies exist to define pixel subsets for the spectral parameters, each with its advantages and limitations, we show using current foreground simulations in the context of next-generation space-borne missions that there are satisfactory configurations in which both statistical and systematic residuals become negligible. The exact magnitude of these residuals, however, depends on the mission's specific characteristics, especially its frequency coverage and sensitivity. We also show that the post-component separation statistical uncertainty is only weakly dependent on the properties of the foregrounds and propose a semi-analytical framework to estimate it. On the contrary, the systematic foreground residuals highly depend on both the properties of the foregrounds and the chosen spatial resolution of the spectral parameters.

Figures (17)

• Figure 1: Polarization amplitudes $P\equiv\sqrt{Q^2+U^2}$ between $50$ and $500$ GHz, normalized at $150$ GHz, computed for each pixel (at nside = 64) for the reference PySM3 models d0 and s0 and the more realistic PySM3 models considered in this work d1, d10 and s1, s5. Each line corresponds to a sky pixel. All the lines for the different sky pixels are overlapped for d0 (s0), being the same MBB (PL), while for the more realistic models the lines corresponding to the different pixels are spread over a wide range. Note that the frequency scalings shown here come from $P$ taken in $\mu \mathrm{K}_{\mathrm{CMB}}$ units, which explains why they do not look like what one could naively expect for a MBB and a PL.
• Figure 2: Angular power spectra of the three spectral indices studied in this work, $\beta_{\rm d}$, $\rm{T}_{\rm d}$ and $\beta_{\rm s}$, computed for various sky cuts (progressively masking more and more the Galactic plane), both for the d1 (s1) and d10 (s5) PySM3 models. The power spectra are computed with NaMasteralonso2019unified, and by apodizing the Planck HFI Galactic plane masks HFI_Mask with the "Smooth" apodization of NaMaster and an apodization scale of $2.5^\circ$. A binning of $\Delta\ell=2$ is applied for the $\mathrm{fsky}=0.49$ mask and of $\Delta\ell=7$ for the $\mathrm{fsky}=0.14$ mask. Note that, before computing the power spectrum of the $\rm{T}_{\rm d}$ maps, we subtract the mean of each map and then divide by it, in order to bring the resulting power spectrum into the same range of values as those of $\beta_{\rm d}$ and $\beta_{\rm s}$, and to make it dimensionless.
• Figure 3: Fisher-like matrix for the d0s0 foreground model full sky, with a LiteBIRD-like setup (see Sect.\ref{['subsection:sims']}), using HEALPix pixel patches with nside=[2,1,1] respectively for [$\beta_\text{d}$, $\mathrm{T}_\text{d}$, $\beta_\text{s}$]. The parameters with indices 0 to 47 correspond to $\beta_{\text{d}}$, $T_{\text{d}}$ is represented by parameters from 48 to 59 and $\beta_{\text{s}}$ by those from 60 to 71. Note that the entries of the Fisher-like matrix corresponding to $\beta_{\rm d}$ and $\beta_{\rm s}$ are dimensionless, while the ones corresponding to $\rm{T}_{\rm d}$ are in $\rm{K}^{-2}$.
• Figure 4: Frequency bands and sensitivities assumed in the analysis for the LiteBIRD-like and PICO-like instruments. Horizontal lines indicate the total combined sensitivity for each instrument, obtained by inverse-variance weighting of the sensitivities across the different frequency bands, yielding $2.16 \, \mu\mathrm{K\text{-}arcmin}$ and $0.86 \, \mu\mathrm{K\text{-}arcmin}$, respectively. Only the central frequency for each band is shown, as the bandpass widths are not relevant for the study we perform in this work. The key aspect relevant to the analysis and comparison of the results obtained for the two instruments is their differing frequency coverage and sensitivity levels.
• Figure 5: Illustration of the various sky masks used in this work, with fsky: $20\%$ (yellow), $40\%$ (yellow + green) and $60\%$ (yellow + green + blue).