Polarized radiative transfer, rotation measure fluctuations, and large-scale magnetic fields

Faraday rotation measure (RM) at radio wavelengths is commonly used to diagnose large-scale magnetic fields. It is argued that the length-scales on which magnetic fields vary in large-scale diffuse astrophysical media can be inferred from correlations in the observed RM. RM is a variable which can be derived from the polarized radiative transfer equations in restrictive conditions. This paper assesses the usage of rotation measure fluctuation (RMF) analyses for magnetic field diagnostics in the framework of polarized radiative transfer. We use models of various magnetic field configurations and electron density distributions to show how density fluctuations could affect the correlation length of the magnetic fields inferred from the conventional RMF analyses. We caution against interpretations of RMF analyses when a characteristic density is ill defined, e.g. in cases of lognormal-distributed and fractal-like density structures. As the spatial correlations are generally not the same in the line-of-sight longitudinal direction and the sky plane direction, one also needs to clarify the context of RMF when inferring from observational data. In complex situations, a covariant polarized radiative transfer calculation is essential to capture all aspects of radiative and transport processes, which would otherwise ambiguate the interpretations of magnetism in galaxy clusters and larger scale cosmological structures.