The correct sense of Faraday rotation

Abstract

The phenomenon of Faraday rotation of linearly polarized synchrotron emission in a magneto-ionized medium has been understood and studied for decades. But since the sense of the rotation itself is irrelevant in most contexts, some uncertainty and inconsistencies have arisen in the literature about this detail. Here, we start from basic plasma theory to describe the propagation of polarized emission from a background radio source through a magnetized, ionized medium in order to re-derive the correct sense of Faraday rotation. We present simple graphics to illustrate the decomposition of a linearly polarized wave into right and left circularly polarized modes, the temporal and spatial propagation of the phases of those modes, and the resulting physical rotation of the polarization orientation. We then re-examine the case of a medium that both Faraday rotates and emits polarized radiation and show how a helical magnetic field can construct or destruct the Faraday rotation. This paper aims to resolve a source of confusion that has arisen between the plasma physics and radio astronomy communities and to help avoid common pitfalls when working with this unintuitive phenomenon.