Non-Gaussianity in SMICA

TL;DR

This paper tackles the problem of separating CMB from foregrounds when those foregrounds exhibit non-Gaussianity, by extending SMICA with a Multivariate Edgeworth Expansion (MEE) to include the bispectrum in a joint framework and by building a multi-frequency, multi-component bispectrum estimator. The authors test these ideas on 400 LiteBIRD-like simulations for E- and B-mode polarization, using dust and synchrotron foregrounds, and find that the MEE-based addition does not improve power-spectrum or spectral-parameter constraints. To address foreground uncertainties more robustly, they develop an independent, multi-frequency bispectrum likelihood and a binned, even/odd bispectrum estimator that can recover the foreground bispectra and provide constraints on primordial non-Gaussianity, such as the local $f_{ ext{NL}}$. The work demonstrates a coherent approach to combining power-spectrum and bispectrum information in component separation and PNG inference, with clear future directions toward Planck-like data, multiple polarizations, and inclusion of linear corrections.

Abstract

We develop a new formalism for the component separation method Spectral Matching Independent Component Analysis (SMICA) in order to include the information contained in the foregrounds beyond second-order statistics. We also develop a binned bispectrum estimator that works directly using maps of different frequency channels, capable of determining the bispectrum of multiple components at the same time, shifting the traditional approach to non-Gaussianity estimation from a cleaned map to the component separation step, for a better handling of foreground uncertainty. We test our method on 400 E and B polarization simulations based on the LiteBIRD experiment, containing the two main sources of contamination for CMB polarization experiments: polarized dust and synchrotron emission. We show that the bispectrum does not improve the precision of the power spectrum estimation or of the spectral parameters. However, we are capable of recovering the correct 3-point correlator of the foregrounds and standard constraints on primordial non-Gaussianity in a coherent multi-frequency and multi-component framework. The advantage of our approach is that it combines data in an optimal way accounting for the power spectrum and the bispectrum of the various components, which is not true for the standard approach.

Figures (14)

• Figure 1: The B-mode power spectra computed from the template maps (left) and the mixing matrix representing the emission laws of the components included in our simulations (right).
• Figure 2: The signal-to-noise ratio of the bispectrum for the two masked foreground maps d0 and s0.
• Figure 3: The three bispectrum models implemented to describe the bispectra of d0 and s0. These three models peak in the configurations indicated.
• Figure 4: The $f_{\text{NL}}$ values for the three shapes as a function of $f_{\text{sky}}$, both for dust and synchrotron.
• Figure 5: Comparison between the original gaussian likelihood and the non-Guassian corrective term for the mixing matrix component $A^{402\text{GHz, dust}}$.