Disentangling the Faraday rotation sky

Context. Magnetic fields permeate the diffuse interstellar medium (ISM) of the Milky Way, and are essential to explain the dynamical evolution and current shape of the Galaxy. Magnetic fields reveal themselves via their influence on the surrounding matter, and as such are notoriously hard to measure independently of other tracers. Aims. In this work, we attempt to disentangle an all-sky map of the line-of-sight (LoS)-parallel component of the Galactic magnetic field from the Faraday effect, utilizing several tracers of the Galactic electron density, ne. Additionally, we aim to produce a Galactic electron dispersion measure map and quantify several tracers of the structure of the ionized medium of the Milky Way. Methods. The method developed to reach these aims is based on information field theory, a Bayesian inference framework for fields, which performs well when handling noisy and incomplete data and constraining high-dimensional-parameter spaces. We rely on compiled catalogs of extragalactic Faraday rotation measures and Galactic pulsar dispersion measures, a well as data on bremsstrahlung and the hydrogen α spectral line to trace the ionized medium of the Milky Way. Results. We present the first full sky map of the LoS-averaged Galactic magnetic field. Within this map, we find LoS-parallel and LoS-averaged magnetic field strengths of up to 4 µG, with an all-sky root mean square of 1.1 µG, which is consistent with previous local measurements and global magnetic field models. Additionally, we produce a detailed electron dispersion measure map that agrees with existing parametric models at high latitudes but suffers from systematic effects in the disk. Further analysis of our results with regard to the 3D structure of ne reveals that it follows a Kolmogorov-type turbulence for most of the sky. From the reconstructed dispersion measure and emission measure maps, we construct several tracers of variability in ne along the LoS. Conclusions. This work demonstrates the power of consistent joint statistical analysis including multiple datasets and physical quantities and defines a road map toward a full three-dimensional joint reconstruction of the Galactic magnetic field and the ionized ISM.