Alvina Yee Lian On

(1/4) Magnetic fields are ubiquitous, permeating across all scales of the Universe - from the stars (like our Sun!), planets (such as the Earth), some moons, galaxies (like our Milky Way) and galaxy groups, galaxy clusters, to the largest-scale cosmic web of filaments and voids.

Yet the big questions remain. Where do the first magnetic fields come from, and how do they evolve with the structure formation of the Universe to what we observe today?

Seeing magnetic fields and measuring their properties are ultimately a challenge because magnetic fields are simply invisible to the eye. We can only infer their presence and diagnose their properties through indirect methods. A classic classroom example is how we can trace the magnetic field lines of a bar magnet using iron filings. In the Northern sky, somewhat analogous to these iron filings, are the spectacular dancing colours of the aurora borealis. The Northern lights are a beautiful evidence of the Earth's magnetic field interacting with the charged particles carried by the solar wind.

(2/4) Seeing the lights allow us to indirectly trace the Earth's magnetic fields, which are otherwise invisible. The closest star to us, our Sun, is also magnetised, as hinted by the solar flares - a sudden explosion of energy when the magnetic fields cross near the sunspots. Sometimes we can see coronal loops which are magnetic arches towering over the active solar surface. The galaxy we live in, the Milky Way, is also threaded by magnetic fields, as shown by interstellar dust emission.

On galactic scales and beyond, it becomes more difficult to see and measure the magnetic fields as they are relatively weaker. Faraday rotation measure (RM) at radio wavelengths is commonly used to diagnose large-scale magnetic fields in nearby galaxies (e.g. M51) and galaxy groups (e.g. Stephan's Quintet), as well as, galaxy clusters (e.g. Coma). Faraday rotation occurs when the polarisation plane of light rotates in the presence of a magnetic field. The amount of rotation is quantified by the rotation measure (RM). From the RM, we can deduce the magnetic field strength along the line-of-sight.

(3/4) It is argued that the length scales on which the magnetic fields vary can be inferred from correlations in the observed RM. The RM fluctuation (RMF) analysis is proposed as a means to probe the structures of large-scale magnetic fields, including those pervading the cosmic web of filaments and voids. The RM and RMF analyses are based on the theory of polarised radiative transfer under certain restricted conditions. It is therefore crucial to understand the information we extract from the analyses and under what conditions the interpretations from the analyses are unambiguous.

We assess the use of RMF analyses to diagnose magnetic fields in the framework of polarised radiative transfer. We show that density fluctuations could affect the correlation length of magnetic fields inferred from the conventional RMF analyses. In particular, we have to be careful in interpreting from RMF analyses when a characteristic density is ill-defined, e.g. in cases of lognormal-distributed and fractal-like density structures. These structures are common in many astrophysical systems, e.g., molecular clouds and the intracluster medium.

(4/4) In summary, the conventional RMF analyses are applicable in some, but not all, astrophysical situations. The spatial correlations are generally different along the line-of-sight and across the sky plane, hence the context of RMF must be clarified when inferring from observations. In complex situations, a covariant polarised radiative transfer calculation is essential to properly track the radiative and transport processes. Otherwise, the interpretations of magnetism in galaxy clusters and larger scale structures would be ambiguous.