How bad could it be? Modelling the 3D complexity of the polarised dust signal using moment expansion

TL;DR

This paper introduces a moment expansion formalism to model the 3D complexity of polarized dust emission in the galaxy, aiding CMB foreground modeling and highlighting challenges for future component separation methods.

Contribution

It applies the spin-moment expansion to thermal dust models, demonstrating its effectiveness and generating new complex dust emission models compatible with Planck data.

Findings

Moment expansion effectively compresses dust emission information.

Increased 3D complexity impacts component separation performance.

Different methods respond variably to dust model complexities.

Abstract

The variation of the physical conditions across the three dimensions of our Galaxy is a major source of complexity for the modelling of the foreground signal facing the cosmic microwave background (CMB). In the present work, we demonstrate that the spin-moment expansion formalism provides a powerful framework to model and understand this complexity, with a special focus on that arising from variations of the physical conditions along each line-of-sight on the sky. We perform the first application of the moment expansion to reproduce a thermal dust model largely used by the CMB community, demonstrating its power as a minimal tool to compress, understand and model the information contained within any foreground model. Furthermore, we use this framework to produce new models of thermal dust emission containing the maximal amount of complexity allowed by the current data, remaining compatible with the observed angular power-spectra by the $Planck$ mission. By assessing the impact of these models on the performance of component separation methodologies, we conclude that the additional complexity contained within the third dimension could represent a significant challenge for future CMB experiments and that different component separation approaches are sensitive to different properties of the moments.