Wavelets and sparsity for Faraday tomography

TL;DR

This paper introduces CRAFT+WS, an enhanced Faraday tomography method using wavelet sparsity, which improves resolution and reveals complex magnetic structures in astronomical observations, crucial for future cosmic magnetism research.

Contribution

It combines wavelet transforms and sparsity with the CRAFT algorithm to significantly improve Faraday tomography reconstructions, enabling super-resolution and revealing hidden magnetic complexities.

Findings

CRAFT+WS outperforms original CRAFT in complex FDF reconstructions

Demonstrates super-resolution in Faraday depth

Reveals previously unseen Faraday complexities

Abstract

Faraday tomography through broadband polarimetry can provide crucial information on magnetized astronomical objects, such as quasars, galaxies, or galaxy clusters. However, the limited wavelength coverage of the instruments requires that we solve an ill-posed inverse problem when we want to obtain the Faraday dispersion function (FDF), a tomographic distribution of the magnetoionic media along the line of sight. This paper explores the use of wavelet transforms and the sparsity of the transformed FDFs in the form of wavelet shrinkage (WS) for finding better solutions to the inverse problem. We recently proposed the Constraining and Restoring iterative Algorithm for Faraday Tomography (CRAFT; Cooray et al. 2021), a new flexible algorithm that showed significant improvements over the popular methods such as Rotation Measure Synthesis. In this work, we introduce CRAFT+WS, a new version of CRAFT incorporating the ideas of wavelets and sparsity. CRAFT+WS exhibit significant improvements over the original CRAFT when tested for a complex FDF of realistic Galactic model. Reconstructions of FDFs demonstrate super-resolution in Faraday depth, uncovering previously unseen Faraday complexities in observations. The proposed approach will be necessary for effective cosmic magnetism studies using the Square Kilometre Array and its precursors.