Faraday rotation: effect of magnetic field reversals

TL;DR

This paper investigates the limitations of the standard Faraday rotation measure formula, especially in regions with magnetic field reversals, and introduces corrections and new polarization effects relevant at low frequencies.

Contribution

It provides a detailed analysis of QT regions where magnetic field reversals affect polarization, offering new correction estimates and identifying novel sources of circular polarization.

Findings

Additional rotation correction  is small and likely unobservable.

Mode coupling in QT regions can generate circular polarization.

New polarization-dependent correction to dispersion measure at low frequencies.

Abstract

The standard formula for the rotation measure, RM, which determines the position angle, $\psi={\rm RM}\lambda^2$, due to Faraday rotation, includes contributions only from the portions of the ray path where the natural modes of the plasma are circularly polarized. In small regions of the ray path where the projection of the magnetic field on the ray path reverses sign (called QT regions) the modes are nearly linearly polarized. The neglect of QT regions in estimating RM is not well justified at frequencies below a transition frequency where mode coupling changes from strong to weak. By integrating the polarization transfer equation across a QT region in the latter limit, I estimate the additional contribution $\Delta\psi$ needed to correct this omission. In contrast with a result proposed by \cite{BB10}, $\Delta\psi$ is small and probably unobservable. I identify a new source of circular polarization, due to mode coupling in an asymmetric QT region. I also identify a new circular-polarization-dependent correction to the dispersion measure at low frequencies.