Study of Vertical Magnetic Field in Face-on Galaxies using Faraday
  Tomography
  Faraday tomography allows astronomers to probe the distribution of magnetic
field along the line of sight (LOS), but that can be achieved only after
Faraday spectrum is interpreted. However, the interpretation is not
straightforward, mainly because Faraday spectrum is complicated due to
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
Faraday spectrum. In this paper, employing "simple toy models" for the magnetic
field, we describe numerically as well as analytically the characteristic
properties of Faraday spectrum. We show that Faraday spectrum along "multiple
loss" can be used to extract the global properties of magnetic field.
Specifically, considering face-on spiral galaxies and modeling turbulent
magnetic field as a random field with single coherence length, we numerically
calculate Faraday spectrum along a number of LOSs and its shape-characterizing
parameters, that is, the moments. When multiple LOSs cover a region of $\gtrsim
(10\ {\rm coherence\ length)^2}$, the shape of 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 LOS magnetic field and the coherence
length. We also consider the turbulent magnetic field modeled with power-law
spectrum, and study how the magnetic field is revealed in Faraday spectrum. Our
work suggests a way toward obtaining the information of magnetic field from
Faraday tomography study.
