High precision modeling of polarized signals: Moment expansion method generalized to spin-2 fields

Abstract

The modeling and removal of foregrounds poses a major challenge to searches for signals from inflation using the cosmic microwave background (CMB). In particular, the modeling of CMB foregrounds including various spatial averaging effects introduces multiple complications that will have to be accounted for in upcoming analyses. In this work, we introduce the generalization of the intensity moment expansion to the spin-2 field of linear polarization: the spin-moment expansion. Within this framework, moments become spin-2 objects that are directly related to the underlying spectral parameters and polarization angle distribution functions. In obtaining the required expressions for the polarization modeling, we highlight the similarities and differences with the intensity moment methods. A spinor rotation in the complex plane with frequency naturally arises from the first order moment when the signal contains both spectral parameters and polarization angle variations. Additional dependencies are introduced at higher order, and we demonstrate how these can be accounted with several illustrative examples. Our new modeling of the polarized signals reveals to be a powerful tool to model the frequency dependence of the polarization angle. As such, it can be immediately applied to numerous astrophysical situations.

Accepted by A&A

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Cited by in corpus (7)

• Frequency dependence of the thermal dust $E/B$ ratio and $EB$ correlation: insights from the spin-moment expansion
• Dust polarization spectral dependence from Planck HFI data. Turning point on CMB polarization foregrounds modelling
• A hybrid map-$C_{\ell }$ component separation method for primordial CMB $B$-mode searches
• Mitigating the impact of the CIB on galaxy cluster SZ detection with spectrally constrained matched filters
• Generative Models of Multi-channel Data from a Single Example -- Application to Dust Emission
• Extended Delta-map: a map-based foreground removal method for CMB polarization observations
• Self-supervised component separation for the extragalactic submillimeter sky