Linear to circular conversion in the polarized radio emission of a magnetar

Radio emission from magnetars provides a unique probe of the relativistic, magnetized plasma within the near-field environment of these ultra-magnetic neutron stars. The transmitted waves can undergo birefringent and dispersive propagation effects that result in frequency-dependent conversions of linear to circularly polarized radiation and vice-versa, thus necessitating classification when relating the measured polarization to the intrinsic properties of neutron star and fast radio burst (FRB) emission sites. We report the detection of such behavior in 0.7-4 GHz observations of the P = 5.54 s radio magnetar XTE J1810$-$197 following its 2018 outburst. The phenomenon is restricted to a narrow range of pulse phase centered around the magnetic meridian. Its temporal evolution is closely coupled to large-scale variations in magnetic topology that originate from either plastic motion of an active region on the magnetar surface or free precession of the neutron star crust. Our model of the effect deviates from simple theoretical expectations for radio waves propagating through a magnetized plasma. Birefringent self-coupling between the transmitted wave modes, line-of-sight variations in the magnetic field direction and differences in particle charge or energy distributions above the magnetic pole are explored as possible explanations. We discuss potential links between the immediate magneto-ionic environments of magnetars and those of FRB progenitors.