and thermal and cosmic-ray electrons are reflected in the FDF and it is possible to extract information on distribution [@bec12].

Model of Galaxies {#subsection:2.2}
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In order to study FDFs of galaxies, we employ a model of the Milky Way galaxy constructed by [@arkg13]. Actually, this is a model of the Solar neighbor but we use it as a representative model because physical quantities have been better determined there. We expect that the model are reasonable also for external spiral galaxies. Below, we briefly summarize the model.

The model considers the domain toward high Galactic latitudes of the Milky Way. It consists of the global, regular component as well as the turbulent, random component. The regular component is modeled using the thermal electron density model of [@cl02] and magnetic-field models including an axi-symmetric spiral field and a halo toroidal field [@sun08] plus a dipole poloidal field that produces a coherent vertical field near the Earth [@gkss10]. The random component is modeled by piling up computational boxes of MHD turbulence simulations [@krjh99] from the Galactic mid-plane up to $\pm 10.0$ kpc, where each box size is $500~{\rm pc}$ with $512$ grids on a side. They adopted a driving scale of $250~{\rm 