Induced Polarization from Birefringent Pulse Splitting in Magnetoionic Media

Birefringence in ionized, magnetized media is usually measured as Faraday rotation of linearly polarized radiation. However, pulses propagating through regions with very large Faraday rotation measures (RMs) can split into circularly polarized components with measurable differences in arrival times $\propto \nu^{-3}\, \rm RM$, where $\nu$ is the radio frequency. Differential refraction from gradients in DM (dispersion measure) and RM can contribute a splitting time $\propto \vert \mathbf{\nabla_{\perp}} \rm DM \vert \vert \mathbf{\nabla_{\perp}}\rm RM \vert\,\nu^{-5}$. Regardless of whether the emitted pulse is unpolarized or linearly polarized, net circular polarization will be measured when splitting is a significant fraction of the pulse width. However, the initial polarization may be inferable from the noise statistics of the bursts. Extreme multipath scattering that broadens pulses can mask splitting effects. We discuss particular cases such as the Galactic center magnetar, J1749$-$2900, and the repeating fast radio burst source, FRB 121102. Both lines of sight have $\rm RM \sim 10^5~\rm rad~m^{-2}$ that yields millisecond splittings at frequencies well below $\sim 1 \text{ GHz}$. We also consider the splitting of nanosecond shot pulses in giant pulses from the Crab pulsar and the minimal effects of birefringence on precision pulsar timing. Finally, we explore the utility of two-dimensional coherent dedispersion with DM and RM as parameters.