Introduction to Faraday tomography and its future prospects

Faraday tomography is a new method of the study of cosmic magnetic fields enabled by broad-band low-frequency radio observations. Using Faraday tomography it is possible to obtain the Faraday dispersion function, which contains information on the line-of-sight distributions of magnetic fields, thermal electron density, and cosmic ray electron density by measuring the polarization spectrum from a source of synchrotron radiation over a wide band. Furthermore, by combining it with two-dimensional imaging, Faraday tomography allows us to explore the three-dimensional structure of polarization sources. Faraday tomography has been active over the last 20 years, since the broad-band observation has become technically feasible, and polarization sources such as interstellar space, supernova remnants, and galaxies have been investigated. However, the Faraday dispersion function is mathematically the Fourier transform of the polarization spectrum. And since the observable band is finite, it is impossible to obtain a complete Faraday dispersion function by performing a Fourier transform. For this purpose, various methods have been developed to accurately estimate the Faraday dispersion function from the observed polarization spectrum. In addition, the Faraday dispersion function does not directly reflect the distribution of magnetic field, thermal electron density, and cosmic ray electron density in the physical space, and its physical interpretation is not straightforward. Despite these two difficult problems, Faraday tomography is attracting much attention because it has great potential as a new method for studying cosmic magnetic fields and magnetized plasmas. In particular, the next-generation radio telescope SKA (Square Kilometre Array) is capable of polarization observation with unprecedented sensitivity and broad bands, and the application of Faraday tomography is expected to make dramatic progress in the field of cosmic magnetic fields. In this review, we explain the basics of Faraday tomography with simple and instructive examples. Representative algorithms to realize Faraday tomography are introduced, and some applications are shown.