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

¹ IRAP, Université de Toulouse, CNRS, CNES, UPS, 9 Av. du Colonel Roche, 31400 Toulouse, France
e-mail: leo.vacher@irap.omp.eu
² Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 24 rue Lhomond, 75005 Paris, France
³ Institut d’Astrophysique Spatiale, CNRS, Université Paris-Saclay, CNRS, Rue Jean-Dominique Cassini, Bât. 121, 91405 Orsay, France
⁴ Laboratoire Univers et Particules de Montpellier, Université de Montpellier, CNRS/IN2P3, CC 72, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France
⁵ INAF-Osservatorio Astronomico di Cagliari, Via della Scienza 5, 09047 Selargius, Italy
⁶ Jodrell Bank Centre for Astrophysics, Alan Turing Building, University of Manchester, Oxford Rd M13 9PL, Manchester, UK

Received: 25 October 2022
Accepted: 11 February 2023

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 𝒟_𝓁^EE, 𝒟_𝓁^BB, and 𝒟_𝓁^EB, implying a variation of the 𝒟_𝓁^EE/𝒟_𝓁^BB 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.