The Faraday dispersion function (FDF), which can be derived from an observed polarization spectrum by Faraday rotation measure synthesis, is a profile of polarized emissions as a function of Faraday depth. We study intrinsic FDFs along sight lines through face-on, Milky-Way-like galaxies by means of a sophisticated galactic model incorporating 3D MHD turbulence, and investigate how much the FDF contains information intrinsically. Since the FDF reflects distributions of thermal and cosmicray electrons as well as magnetic fields, it has been expected that the FDF could be a new probe to examine internal structures of galaxies. We, however, find that an intrinsic FDF along a sight line through a galaxy is very complicated, depending significantly on actual configurations of turbulence. We perform 800 realizations of turbulence, and find no universal shape of the FDF even if we fix the global parameters of the model. We calculate the probability distribution functions of the standard deviation, skewness, and kurtosis of FDFs and compare them for models with different global parameters. Our models predict that the presence of vertical magnetic fields and large scale-height of cosmic-ray electrons tend to make the standard deviation relatively large. Contrastingly, differences in skewness and kurtosis are relatively less significant.

Faraday tomography allows astronomers to probe the distribution of the magnetic field along the line of sight (LOS), but that can be achieved only after the Faraday spectrum is interpreted. However, the interpretation is not straightforward, mainly because the Faraday spectrum is complicated due to a turbulent magnetic field; it ruins the one-to-one relation between the Faraday depth and the physical depth, and appears as many small-scale features in the Faraday spectrum. In this paper, by employing "simple toy models" for the magnetic field, we describe numerically as well as analytically the characteristic properties of the Faraday spectrum. We show that the Faraday spectrum along "multiple LOSs" can be used to extract the global properties of the magnetic field. Specifically, considering face-on spiral galaxies and modeling turbulent magnetic field as a random field with a single coherence length, we numerically calculate the Faraday spectrum along a number of LOSs and its shape-characterizing parameters, that is, the moments. When multiple LOSs cover a region of (10 coherence length) 2 , the shape of the Faraday spectrum becomes smooth and the shape-characterizing parameters are well specified. With the Faraday spectrum constructed as a sum of Gaussian functions with different means and variances, we analytically show that the parameters are expressed in terms of the regular and turbulent components of the LOS magnetic field and the coherence length. We also consider the turbulent magnetic field modeled with a power-law spectrum, and study how the magnetic field is revealed in the Faraday spectrum. Our work suggests a way to obtain information on the magnetic field from a Faraday tomography study.