Determination of polarization angles in CMB experiments and application to CMB component separation analyses

• Published in: Journal of cosmology and astroparticle physics 2022-03, Vol.2022 (3), p.32
• Main Authors: de la Hoz, E., Diego-Palazuelos, P., Martínez-González, E., Vielva, P., Barreiro, R.B., Bilbao-Ahedo, J.D.
• Format: Article
• Language: English
• Subjects: Bayesian reasoning; Calibration; CMBR polarisation; Covariance matrix; Frequentist statistics; Iterative methods; Polarization; Power spectra; Rotation; Separation; Systematics
• ISSN: 1475-7516; 1475-7516
• DOI: 10.1088/1475-7516/2022/03/032

The new generation of CMB polarization experiments will reach limits of sensitivity never achieved before in order to detect the elusive primordial B -mode signal. However, all these efforts will be futile if we lack a tight control of systematics. Here, we focus on the systematic that arises from the uncertainty on the calibration of polarization angles. Miscalibrated polarization angles induce a mixing of E - and B -modes that obscures the primordial B -mode signal. We introduce an iterative angular power spectra maximum likelihood-based method to calculate the polarization angles (α̂) from the multi-frequency signal. The basis behind this methodology grounds on nulling the C ℓ EB power spectra. In order to simplify the likelihood, we assume that the rotation angles are small (≲ 6°) and, the maximum likelihood solution for the rotation angles α̂ is obtained by applying an iterative process where the covariance matrix does not depend on α̂ per iteration, i.e., the rotation angles are fixed to the estimated α̂ in the previous iteration. With these assumptions, we obtain an analytical linear system which leads to a very fast computational implementation. We show that with this methodology we are able to determine the rotation angle for each frequency with sufficiently good accuracy. To prove the latter point we perform component separation analyses using the parametric component separation method B-SeCRET with two different approaches. In the first approach we apply the B-SeCRET pipeline to the signal de-rotated with the estimation of α̂, while in the second, the rotation angles are treated as model parameters using the estimation of α̂ as a prior information. We obtain that the rotation angles estimations improve after applying the second approach, and show that the systematic residuals due to the non-null calibration polarization angles are mitigated to the order of a 1% at the power spectrum level.