Frequency dependence of the thermal dust E/B ratio and EB correlation: Insights from the spin-moment expansion

Abstract

The change of physical conditions across the turbulent and magnetized interstellar medium induces a 3D spatial variation of the properties of Galactic polarized emission. The observed signal results from the averaging of different spectral energy distributions (SEDs) and polarization angles along and between lines of sight. As a consequence, the total Stokes parameters Q and U will have different frequency dependencies, both departing from the canonical emission law, so that the polarization angle becomes frequency dependent. In the present work, we show how this phenomenon similarly induces a different, distorted SED for the three polarized angular power spectra 𝒟𝓁EE, 𝒟𝓁BB, and 𝒟𝓁EB, implying a variation of the 𝒟𝓁EE/𝒟𝓁BB ratio with frequency. We demonstrate how the previously introduced “spin-moment” formalism provides a natural framework to grasp these effects and enables us to derive analytical predictions for the spectral behaviors of the polarized spectra, focusing here on the example of thermal dust polarized emission. After a quantitative discussion based on a model combining emission from a filament with its background, we further reveal that the spectral complexity implemented in the dust models commonly used by the cosmic microwave background (CMB) community includes different distortions for the three polarized power-spectra. This new understanding is crucial for CMB component separation, in which extreme accuracy is required for the modeling of the dust signal to allow for the search of the primordial imprints of inflation or cosmic birefringence. For the latter, as long as the dust EB signal is not measured accurately, great caution is required regarding the assumptions made to model its spectral behavior, as it may not be inferred from the other dust angular power spectra.