2022ApJ...928L..16Y

Some repeating fast radio burst (FRB) sources exhibit complex polarization behaviors, including frequency-dependent depolarization, variation of rotation measure (RM), and oscillating spectral structures of polarized components. Very recently, Feng et al. reported that active repeaters exhibit conspicuous frequency-dependent depolarization and a strong correlation between RM scatter (σ_RM) and the temporal scattering time (τ_s), σ_RM∝τ_{s}^{1.0±0.2}, both of which can be well described by multipath propagation through a magnetized inhomogeneous plasma screen. This observation strongly suggests that the temporal scattering and RM scatter originate from the same region. Besides, a particular finding of note in Feng et al. is that the FRBs with compact persistent radio sources (PRSs) tend to have extreme σ_RM. In this work, we focus on some theoretical predictions of the relations among temporal scattering, depolarization by RM scatter, and PRSs contributed by the magnetized plasma environment close to a repeating FRB source. The behaviors of the RM scatter imply that the magnetized plasma environment is consistent with a supernova remnant or pulsar wind nebula, and the predicted σ_RM-τ_s relation is σ_RM∝τ_{s}^{(0.54-0.83)} for different astrophysical scenarios. We further make a general discussion of PRSs that does not depend on specific astrophysical scenarios. We show that the specific luminosity of a PRS should have a positive correlation with the RM contributed by the plasma screen. This is consistent with the observations of FRB 121102 and FRB 190520B.