Faraday rotation in fast radio bursts

Abstract

Fast Radio Bursts (FBRs) show highly different polarization properties: high/small RMs, high/small circular/linear fractions. We outline a complicated picture of polarization propagation in the inner parts of the magnetars' winds, at scales $\sim$ few to hundreds of light cylinder radii. The key point is the Faraday rotation of linear polarization in highly magnetized symmetric pair plasma, a $\propto B^2$ effect. Position angle (PA) rotation rate is maximal for propagation across the magnetic field and disappears only for parallel propagation. In the highly magnetized regime, $\omega \ll \omega_B$, it becomes independent of the magnetic field. Very specific properties of PA($\lambda$) (scaling of the rotation angle with the observed wavelength $\lambda$) can help identify/sort out the propagation effects. Two basic regimes in pair plasma predict PA $\propto \lambda$ and $\propto \lambda^3$ (depending on the magnetic dominance); both are different from the conventional plasma's PA = RM $ \lambda^2$. This is the main prediction of the model. A number of effects, all sensitive to the underlying parameters, contribute to the observed complicated polarization patterns: streaming of plasma along magnetic field lines near the light cylinder, Faraday depolarization, effects of limiting polarization, the associated effect of linear-circular conversion, and synchrotron absorption.