Spectral Imaging with QUBIC: building frequency maps from Time-Ordered-Data using Bolometric Interferometry

TL;DR

The paper introduces Spectral-Imaging for QUBIC, enabling reconstruction of sub-band CMB polarization maps within the instrument bandwidth by exploiting the frequency evolution of Bolometric Interferometer beams. It formulates an inverse-model map-making framework tailored to the BI synthesized beam, addresses angular resolution changes and bandpass-binning biases, and regularizes edge effects with external data such as Planck. End-to-end simulations show that spectral-imaging improves foreground mitigation and leads to tighter forecasts for the tensor-to-scalar ratio, achieving $ ext{survey} ext{level}~ angle \\sigma(r) \,=\, 0.0225$ after component separation with external data, illustrating the practical impact of increased spectral information. The work demonstrates the unique capabilities of BI for CMB foreground characterization and motivates further development of components-map-making to jointly perform spectral imaging and component separation.

Abstract

The search for relics from the inflation era in the form of B-mode polarization of the CMB is a major challenge in cosmology. The main obstacle appears to come from the complexity of Galactic foregrounds that need to be removed. Multi-frequency observations are key to mitigating their contamination and mapping primordial fluctuations. We present spectral-imaging, a method to reconstruct sub-frequency maps of the CMB polarization within the instrument's physical bandwidth, a unique feature of Bolometric Interferometry that could be crucial for foreground mitigation as it provides an increased spectral resolution. Our technique uses the frequency evolution of the shape of the Bolometric Interferometer's synthesized beam to reconstruct frequency information from the time domain data. We reconstruct sub-frequency maps using an inverse problem approach based on detailed modeling of the instrument acquisition. We use external data to regularize the convergence of the estimator and account for bandpass mismatch and varying angular resolution. The reconstructed maps are unbiased and allow exploiting the spectral-imaging capacity of QUBIC. Using end-to-end simulations of the QUBIC instrument, we perform a cross-spectra analysis to extract a forecast on the tensor-to-scalar ratio constraint of $σ(r)= 0.0225$ after component separation.

Figures (9)

• Figure 1: Top panel: Theoretical synthesized beam for a detector at the center of the QUBIC focal plane along with with its primary beam. $\theta$ is the angle between the detector axis and the observed direction. One can clearly see the frequency-dependent position of the secondary peaks. Bottom panel: synthesized beam for one detector measured at various frequencies, from 2020.QUBIC.PAPER3.
• Figure 2: Monochromatic case - From the top to the bottom: Stokes parameters I, Q, and U; from the left to the right: input, reconstructed maps, and the difference between them respectively, in $\mu\K_\text{CMB}$.
• Figure 3: Broadband case - First row is the result of the QUBIC acquisition only with the edges effect. The second row is the merging of the QUBIC and Planck acquisitions. From the left to the right is the input, output and the difference between them respectively for the Q Stokes parameter, in $\mu\K_\text{CMB}$. This simulation integrates the 150 GHz band from 131 GHz to 169 GHz (see Table \ref{['tab: main_parameters']}).
• Figure 4: Broadband case - Profile of the residual RMS for Q (top) and U (bottom) Stokes parameter. The blue line shows the RMS using QUBIC only and the red line shows the RMS when using Planck data to regularize the edge effects.
• Figure 5: Reconstructed spectral energy distribution (SED) of Q Stokes parameter for $N_{\text{rec}} = 3$ for both physical bands. Dots are the value of a given pixel in the QUBIC patch and errorbars are the dispersion (RMS) over the whole QUBIC patch. Black dots denote Planck uncertainties on the QUBIC patch. The dashed-line is the MBB spectrum of the dust. The pixelization of the sky has been set to $N_{\text{side}} = 256$.