Testing for spectral index variations in polarized CMB foregrounds

Abstract

ABSTRACT We present a Bayesian parametric component separation method for polarized microwave sky maps. We solve jointly for the primary cosmic microwave background (CMB) signal and the main Galactic polarized foreground components. For the latter, we consider electron-synchrotron radiation and thermal dust emission, modelled in frequency as a power law and a modified blackbody, respectively. We account for inter-pixel correlations in the noise covariance matrices of the input maps and introduce a spatial correlation length in the prior matrices for the spectral indices β. We apply our method to low-resolution polarized Planck 2018 Low and High Frequency Instrument (LFI/HFI) data, including the SRoll2 re-processing of HFI data. We find evidence for spatial variation of the synchrotron spectral index, and no evidence for depolarization of dust. Using the HFI SRoll2 maps, and applying wide priors on the spectral indices, we find a mean polarized synchrotron spectral index over the unmasked sky of $\bar{\beta }_{\rm sync}=-2.83\pm 0.62$. For polarized thermal dust emission, we obtain $\bar{\beta }_{\rm dust}=1.43\pm 0.24$. Using our recovered CMB maps and associated uncertainties, we constrain the optical depth to reionization, τ, using a cross-spectrum-based likelihood-approximation scheme (momento) to be τ = 0.0598 ± 0.0059. We confirm our findings using a pixel-based likelihood (pixLike). In both cases, we obtain a result that is consistent with that found by subtracting spatially uniform foreground templates. While the latter method is sufficient for current polarization data from Planck, next-generation space-borne CMB experiments will need more powerful schemes such as the one presented here.