Faraday rotation of polarised background sources is a unique probe of astrophysical magnetic fields in a diverse range of foreground objects. However, to understand the properties of the polarised sources themselves and of depolarising phenomena alon
g the line of sight, we need to complement Faraday rotation data with polarisation observations over very broad bandwidths. Just as it is impossible to properly image a complex source with limited u-v coverage, we can only meaningfully understand the magneto-ionic properties of polarised sources if we have excellent coverage in $lambda^2$-space. We here propose a set of broadband polarisation surveys with the Square Kilometre Array, which will provide a singular set of scientific insights on the ways in which galaxies and their environments have evolved over cosmic time.
Magnetic fields in the Milky Way are present on a wide variety of sizes and strengths, influencing many processes in the Galactic ecosystem such as star formation, gas dynamics, jets, and evolution of supernova remnants or pulsar wind nebulae. Observ
ation methods are complex and indirect; the most used of these are a grid of rotation measures of unresolved polarized extragalactic sources, and broadband polarimetry of diffuse emission. Current studies of magnetic fields in the Milky Way reveal a global spiral magnetic field with a significant turbulent component; the limited sample of magnetic field measurements in discrete objects such as supernova remnants and HII regions shows a wide variety in field configurations; a few detections of magnetic fields in Young Stellar Object jets have been published; and the magnetic field structure in the Galactic Center is still under debate. The SKA will unravel the 3D structure and configurations of magnetic fields in the Milky Way on sub-parsec to galaxy scales, including field structure in the Galactic Center. The global configuration of the Milky Way disk magnetic field, probed through pulsar RMs, will resolve controversy about reversals in the Galactic plane. Characteristics of interstellar turbulence can be determined from the grid of background RMs. We expect to learn to understand magnetic field structures in protostellar jets, supernova remnants, and other discrete sources, due to the vast increase in sample sizes possible with the SKA. This knowledge of magnetic fields in the Milky Way will not only be crucial in understanding of the evolution and interaction of Galactic structures, but will also help to define and remove Galactic foregrounds for a multitude of extragalactic and cosmological studies.
(abridged) We run a Faraday structure determination data challenge to benchmark the currently available algorithms including Faraday synthesis (previously called RM synthesis in the literature), wavelet, compressive sampling and $QU$-fitting. The fre
quency set is similar to POSSUM/GALFACTS with a 300 MHz bandwidth from 1.1 to 1.4 GHz. We define three figures of merit motivated by the underlying science: a) an average RM weighted by polarized intensity, RMwtd, b) the separation $Deltaphi$ of two Faraday components and c) the reduced chi-squared. Based on the current test data of signal to noise ratio of about 32, we find that: (1) When only one Faraday thin component is present, most methods perform as expected, with occasional failures where two components are incorrectly found; (2) For two Faraday thin components, QU-fitting routines perform the best, with errors close to the theoretical ones for RMwtd, but with significantly higher errors for $Deltaphi$. All other methods including standard Faraday synthesis frequently identify only one component when $Deltaphi$ is below or near the width of the Faraday point spread function; (3) No methods, as currently implemented, work well for Faraday thick components due to the narrow bandwidth; (4) There exist combinations of two Faraday components which produce a large range of acceptable fits and hence large uncertainties in the derived single RMs; in these cases, different RMs lead to the same Q, U behavior, so no method can recover a unique input model.
