In this paper we present a detailed analysis of the Faraday depth (FD) spectrum and its clean components obtained through the application of the commonly used technique of Faraday rotation measure synthesis to analyze spectro-polarimetric data. In order to directly compare the Faraday depth spectrum with physical properties of a magneto-ionic medium, we generated synthetic broad-bandwidth spectro-polarimetric observations from magnetohydrodynamic (MHD) simulations of a transonic, isothermal, compressible turbulent medium. We find that correlated magnetic field structures give rise to a combination of spiky, localized peaks at certain FD values, and broad structures in the FD spectrum. Although the majority of these spiky FD structures appear narrow, giving an impression of a Faraday thin medium, we show that they arise from strong synchrotron emissivity at that FD. Strong emissivity at a FD can arise because of both strong spatially-local polarized synchrotron emissivity at a FD or accumulation of weaker emissions along the distance through a medium that have Faraday depths within half the width of the rotation measure spread function. Such a complex Faraday depth spectrum is a natural consequence of MHD turbulence when the lines of sight pass through a few turbulent cells. This therefore complicates the convention of attributing narrow FD peaks to presence of a Faraday rotating medium along the line of sight. Our work shows that it is difficult to extract the FD along a line of sight from the Faraday depth spectrum using standard methods for a turbulent medium in which synchrotron emission and Faraday rotation occur simultaneously.
of 30medium for a large number of sources in a much reduced amount of observing time. Broad-band spectro-polarimetry has played a crucial role in unveiling the properties of magnetic fields in nearby galaxies [1][2][3], in high redshift galaxies [4,5], in active galactic nuclei [AGN; 6-8] and the intergalactic medium [9]. In order to physically interpret such data, the technique of Faraday rotation measure (RM) synthesis [10,11] and direct fitting of the Stokes Q and U spectra of a polarized source with models of the magneto-ionic media, known as Stokes Q, U fitting [6,12,13] have been developed. It is often not straightforward to interpret the results from these techniques and connect them to the physical properties of the magnetized plasmas being investigated [14].Currently, several large-scale spectro-polarimetric campaigns are underway, mostly in the 1 to 5 GHz frequency range. On one hand, dedicated surveys with interferometers are being conducted to study the broad-band polarization properties of millions of extragalactic sources. For example, the Karl G. Jansky Very Large Array Sky Survey [VLASS; 15,16], the Polarization Sky Survey of the Universe's Magnetism [POSSUM; 17], the QU Observations at Cm wavelength with Km baselines using ATCA 1 (QUOCKA), the MeerKAT International GHz Tiered Extragalactic Exploration (MIGHTEE) Survey [18], and the recent LOFAR Two-meter Sky Survey [L...