Faraday dispersion functions of galaxies

The Faraday dispersion function (FDF), which can be derived from an observed polarization spec- trum 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 cosmic- ray 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 pa- rameters. 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.