Temporal Scattering, Depolarization, and Persistent Radio Emission from Magnetized Inhomogeneous Environments near Repeating Fast Radio Burst Sources

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 (σRM) and the temporal scattering time (τs), ${\sigma }_{\mathrm{RM}}\propto {\tau }_{{\rm{s}}}^{1.0\pm 0.2}$, 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 σRM. 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 σRM–τs relation is ${\sigma }_{\mathrm{RM}}\propto {\tau }_{{\rm{s}}}^{(0.54-0.83)}$ 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.