Stochastic Faraday Rotation

Abstract

Different ray paths through a turbulent plasma can produce stochastic Faraday rotation leading to depolarization of any linearly polarized component. Simple theory predicts that the average values of the Stokes parameters decay according to $<Q>$, $<U>\propto \exp (-{\delta }_l)$, with ${\delta }_l\propto {\lambda }^4$. It is pointed out that a definitive test for such depolarization is provided by the fact that $<Q^2+U^2>$ remains constant while $<Q{>}^2+<U{>}^2$ decreases $\propto \exp (-2{\delta }_l)$. The averages to which this effect, called polarization covariance, should apply are discussed; it should apply to spatial averages over a polarization map or temporal averages over a data set, but not to beamwidth and bandwidth averages that are intrinsic to the observation process. Observations of depolarization would provide statistical information on fluctuations in the turbulent plasma along the line of sight, specifically, the variance of the rotation measure. Other effects that can also cause depolarization are discussed.

15 pages, Accepted for publication in ApJ

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