Introduction to Faraday tomography and its future prospects

Abstract

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.

CHANG-ES XXXI—A Decade of CHANG-ES: What We Have Learned from Radio Observations of Edge-on Galaxies

“…Significant results have been obtained from the individual frequency bands, as described in previous sections, but the analysis of the complete frequency range has yet to begin. This includes spectral index structure, including the radio spectrum in the separation of thermal and nonthermal emissions, spectral curvature, and Faraday tomography [59] (see Section 4.2) of the diffuse emission and background sources.…”

“…7 RM, more technically, is defined as the slope of the Φ versus λ 2 plot [14]. It has the same value as FD only in simple cases where there is only one Faraday-thin source along the line of sight [59]. 8 This was the very faint galaxy NGC 4244.…”

Faraday Tomography with CHIME: The “Tadpole” Feature G137+7

“…We focus on the narrow declination range around G137+7, +60° δ  70°. This covers zenith angles 11°-21°, a region in which the CHIME beam model is best (CHIME Collaboration 2022, 2023.…”

“…Useful λ 2 coverage typically implies low frequencies and wide bandwidths (ideally octave or more). The use of Faraday synthesis, 24 a form of Faraday tomography (Takahashi 2023), enables studies of the large-scale structure of the magnetic field (Dickey et al 2019(Dickey et al , 2022Erceg et al 2022), and also of individual objects and small regions (e.g., Schnitzeler et al 2007;Van Eck et al 2017Thomson et al 2019Thomson et al , 2021. Direct modeling of the spectra of Stokes parameters Q and U (QU fitting) has proven able to detect multiple Faraday depth components in Faraday complex spectra more reliably than Faraday synthesis, but with the drawbacks of needing considerably longer computational time for each line of sight and requiring us to assume a Faraday rotation model (Farnsworth et al 2011;O'Sullivan et al 2012;Ideguchi et al 2014;Sun et al 2015).…”