An In-depth Investigation of Faraday Depth Spectrum Using Synthetic
  Observations of Turbulent MHD Simulations
  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.
