Faraday caustics: Singularities in the Faraday spectrum and their utility as probes of magnetic field properties

TL;DR

This paper investigates singularities called Faraday caustics in the Faraday spectrum caused by magnetic field reversals along the line of sight, revealing their formation, properties, and statistical distribution in turbulent magnetic fields.

Contribution

It introduces the concept of Faraday caustics, describes their formation and properties, and derives their statistical distribution in Gaussian magnetic fields, linking them to magnetic turbulence scales.

Findings

Faraday caustics appear as asymmetric peaks in the Faraday spectrum.

The probability distribution of strong Faraday caustics follows a F^{-3} power law.

Distribution depends on the Taylor microscale related to turbulence dissipation.

Abstract

We describe singularities in the distribution of polarized intensity as a function of Faraday depth (i.e. the Faraday spectrum) caused by line-of-sight (LOS) magnetic field reversals. We call these features Faraday caustics because of their similarity to optical caustics. They appear as sharply peaked and asymmetric profiles in the Faraday spectrum, that have a tail that extends to one side. The direction in which the tail extends depends on the way in which the LOS magnetic field reversal occurs (either changing from oncoming to retreating or vice versa). We describe how Faraday caustics will form three-dimensional surfaces that relate to boundaries between regions where the LOS magnetic field has opposite polarity. We present examples from simulations of the predicted polarized synchrotron emission from the Milky Way. We derive either the probability or luminosity distribution of Faraday caustics produced in a Gaussian magnetic field distribution as a function of their strength, F, and find that for strong Faraday caustics P(F)\proptoF^{-3} . If fully resolved, this distribution is also shown to depend on the Taylor microscale, which relates to the largest scale over which dissipation is important in a turbulent flow.