Faraday Conversion in Pair-symmetric Winds of Magnetars and Fast Radio Bursts

We consider the propagation of polarization in the inner parts of pair-symmetric magnetar winds, close to the light cylinder. Pair plasmas in magnetic field is birefringent, a ∝ B2 effect. As a result, such plasmas work as phase retarders: Stokes parameters follow a circular trajectory on the Poincare sphere. In the highly magnetized regime, ω, ωp ≪ ωB, the corresponding rotation rates are independent of the magnetic field. A plasma screen with dispersion measure DM ∼ 10−6 pc cm−3 can induce large polarization changes, including large effective rotation measures (RMs). The frequency scaling of the (generalized) RM, ∝ λα, mimics the conventional RM with α = 2 for small phase shifts, but can be as small as α = 1. In interpreting observations, the frequency scaling of polarization parameters should be fitted independently. The model offers explanations for (i) the large circular polarization component observed in FRBs, with right–left switching; (ii) large RM, with possible sign changes (when the observation bandwidth is small); and (iii) time-dependent variable polarization. A relatively dense and slow wind is needed—the corresponding effect in regular pulsars is small.