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

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.