# Probing magnetic fields with multi-frequency polarized synchrotron emission

## TL;DR

This paper presents a method to reconstruct the three-dimensional structure of the Galactic magnetic field using multi-frequency polarized synchrotron emission data, leveraging internal depolarization and inverse problem techniques.

## Contribution

It introduces a novel approach combining multi-band radio spectroscopy with Maximum A Posteriori reconstruction to recover large-scale magnetic field structures.

## Key findings

- Successful recovery of magnetic field structures from simulated data.
- Identification of optimal frequency sampling strategies.
- Prediction of anisotropic posterior error distribution.

## Abstract

We investigate the problem of probing the local spatial structure of the magnetic field of the interstellar medium using multi-frequency polarized maps of the synchrotron emission at radio wavelengths. We focus in this paper on the three-dimensional reconstruction of the largest scales of the magnetic field, relying on the internal depolarization (due to differential Faraday rotation) of the emitting medium as a function of electromagnetic frequency. We argue that multi-band spectroscopy in the radio wavelengths, developed in the context of high-redshift extragalactic HI lines, can be a very useful probe of the 3D magnetic field structure of our Galaxy when combined with a Maximum A Posteriori reconstruction technique. When starting from a fair approximation of the magnetic field, we are able to recover the true one by using a linearized version of the corresponding inverse problem. The spectral analysis of this problem allows us to specify the best sampling strategy in electromagnetic frequency and predicts a spatially anisotropic distribution of posterior errors. The reconstruction method is illustrated for reference fields extracted from realistic magneto-hydrodynamical simulations.