Magnetic field and Faraday rotation from large-scale interstellar medium to plasma near the black-hole horizon

Magnetic fields appear to be ubiquitous in the astrophysical environments of our Universe, but are still poorly understood despite playing an important role in understanding different-scale celestial objects (e.g., Earth, planets, stars, normal galaxies, active galactic nuclei, clusters etc.). We briefly review the results and progress in magnetic field estimation based on rotation measures from the large-scale interstellar medium, megaparsec-scale radio jets to the plasma near the black-hole horizon. We find that there is no evident correlation between electron density and magnetic field in warm ionized plasma, which suggests that the estimation of the magnetic field from the ratio of the rotation measure and dispersion measure correctly reflects the intrinsic field. The estimation of the magnetic field from the rotation measure is also discussed near the black hole horizon in M 87. The Square Kilometre Array will greatly improve the understanding of the magnetic field in our Universe, which will provide high-quality polarization imaging and extragalactic rotation measures in the near future.