The physical origin of fast radio bursts (FRBs) is still unknown. Multiwavelength and polarization observations of an FRB source would be helpful to diagnose its progenitor and environment. So far only the first repeating source FRB 121102 appears to be spatially coincident with a persistent radio emission. Its bursts also have very large values of the Faraday rotation measure (RM), i.e., . We show that theoretically there should be a simple relation between RM and the luminosity of the persistent source of an FRB source if the observed RM mostly arises from the persistent emission region. FRB 121102 follows this relation given that the magnetic field in the persistent emission region is highly ordered and that the number of relativistic electrons powering the persistent emission is comparable to that of nonrelativistic electrons that contribute to RM. The nondetections of persistent emission sources from all other localized FRB sources are consistent with their relatively small RMs ( ) according to this relation. Based on this picture, the majority of FRBs without a large RM are not supposed to be associated with bright persistent sources.
The first repeating fast radio burst (FRB), FRB 121102, was found to be associated with a spatially coincident, persistent nonthermal radio source, but the origin of the persistent emission remains unknown. In this paper, we propose that the persistent emission is produced via a synchrotron-heating process by multiple bursts of FRB 121102 in a self-absorbed synchrotron nebula. With a population of bursts of the repeating FRB absorbed by the synchrotron nebula, the energy distribution of electrons in the nebula will change significantly. As a result, the spectrum of the nebula will show a hump steadily. For the persistent emission of FRB 121102, the total energy of bursts injecting into the nebula is required to be about 3.3 × 1049 erg, the burst injection age is over 6.7 × 104 yr, the nebula size is ∼0.02 pc, and the electron number is about 3.2 × 1055. We predict that as more bursts inject, the brightness of the nebula would be brighter than the current observation, and meanwhile, the peak frequency would become higher. Due to the synchrotron absorption of the nebula, some low-frequency bursts would be absorbed, which may explain why most bursts were detected above ∼1 GHz.
The physical origin of fast radio bursts (FRBs) remains unclear. Finding multiwavelength counterparts of FRBs can provide a breakthrough for understanding their nature. In this work, we perform a systematic search for astronomical transients whose positions are consistent with FRBs. We find an unclassified optical transient AT2020hur (α = 01h58m00.ˢ750 ± 1″, δ = 65 ° 43 ′ 00 .″ 30 ± 1 ″ ) that is spatially coincident with the repeating FRB 180916B (α = 01h58m00.ˢ7502 ± 2.3 mas, δ = 65 ° 43 ′ 00 .″ 3152 ± 2.3 mas; Marcote et al. 2020). The chance possibility of the AT2020hur–FRB 180916B association is about 0.04%, which corresponds to a significance of 3.5σ. We develop a giant flare (GF) afterglow model to fit AT2020hur. Although the GF afterglow model can interpret the observations of AT2020hur, the derived kinetic energy of such a GF is at least three orders of magnitude larger than that of a typical GF, and a lot of fine-tuning and coincidences are required for this model. Another possible explanation is that AT2020hur might consist of two or more optical flares originating from the FRB source, e.g., fast optical bursts produced by the inverse Compton scattering of FRB emission. Besides, AT2020hur is located in one of the activity windows of FRB 180916B, which provides independent support for the association. This coincidence may be due to the optical counterparts being subject to the same periodic modulation as FRB 180916B, as implied by the prompt FRB counterparts. Future simultaneous observations of FRBs and their optical counterparts may help to reveal their physical origin.
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