Depolarization and Faraday effects in galaxies

Abstract

Faraday rotation and depolarization of synchrotron radio emission are considered in a consistent general approach, under conditions typical of spiral galaxies, i.e. when the magneto‐ionic medium and relativistic electrons are non‐uniformly distributed in a layer containing both regular and fluctuating components of magnetic field, thermal electron density and synchrotron emissivity. We demonstrate that non‐uniformity of the magneto‐ionic medium along the line of sight strongly affects the observable polarization patterns. The degree of polarization p and the observed Faraday rotation measure RM are very sensitive to whether or not the source is symmetric along the line of sight. The RM may change sign in a certain wavelength range in an asymmetric slab even when the line‐of‐sight magnetic field has no reversals. Faraday depolarization in a purely regular magnetic field can be much stronger than suggested by the low observed rotation measures. A twisted regular magnetic field may result in p increasing with λ— a behaviour detected in several galaxies. We derive expressions for statistical fluctuations in complex polarization and show that random fluctuations in the degree of polarization caused by Faraday dispersion are expected to become significantly larger than the mean value of p at λ ≳ 20 − 30 cm. We also discuss depolarization arising from a gradient of Faraday rotation measure across the beam, both in the source and in an external Faraday screen. We briefly discuss applications of the above results to radio polarization observations. We discuss how the degree of polarization is affected by the scaling of synchrotron emissivity ɛ with the total magnetic field strength B. We derive formulae for the complex polarization at λ → 0 under the assumption that ɛ ∝ B2B2⊥, which may arise under energy equipartition or pressure balance between cosmic rays and magnetic fields. The resulting degree of polarization is systematically larger than for the usually adopted scaling ɛ ∝ B2⊥; the difference may reach a factor of 1.5.

Multiwavelength observations of the γ-ray flaring quasar S4 1030+61 in 2009–2014

“…The resulting Gaussian fit, given in Fig. 10, is very close to the anomalous depolarization (Sokoloff et al 1998;Homan 2012) or to the smearing of multiple RM components (Conway et al 1974). …”

“…The dependence differs from the expected behavior for the optically thick region of a jet (Pacholczyk & Swihart 1967). Possible explanations for such behavior are the following: (i) anomalous (Sokoloff et al 1998) or inverse (Homan 2012) depolarization, which appears in a regular twisted or tangled magnetic fields; (ii) spectral depolarization (Conway et al 1974) due to smearing of multiple components within the observed region. Unfortunately, distinguishing between these alternatives is difficult.…”

“…10) with wavelength, with the maximum around 4.5 cm, indicating the complex polarized structure of the source. It was shown (e.g., Farnes et al 2014) that a Gaussian function reproduces well the wavelength-dependence of various number of Faraday effects (Sokoloff et al 1998). The resulting Gaussian fit, given in Fig.…”

JVLA S- and X-band polarimetry of the merging cluster Abell 2256

“…where p0 is the intrinsic fractional polarization and ǫ is the synchrotron emissivity at a depth along the line of sight (Burn 1966;Gardner & Whiteoak 1966;Sokoloff et al 1998). The polarization angle φ(x, y) is given by φ(x, y) = φ0 + 812…”

Revealing the Faraday depth structure of radio galaxy NGC 612 with broad-band radio polarimetric observations

“…However, the observation of depolarisation in Figure 4 at the location of the hot spot makes it immediately evident that it will be necessary to involve more complex models in order to accurately describe at least some of the observed polarisation. There are typically three mechanisms that can lead to depolarisation, all of which are presented with complete discussion in Sokoloff et al (1998) and references therein, and all we briefly outline below.…”