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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 synchrotron-heating process by multiple bursts of FRB 121102 in a self-absorbed synchrotron nebula. As 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 $3.3times10^{49},unit{erg}$, the burst injection age is over $6.7times 10^4,unit{yr}$, the nebula size is $sim0.02,unit{pc}$, and the electron number is about $3.2times10^{55}$. 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 $sim1~unit{GHz}$.
Fast Radio Bursts are millisecond-duration astronomical radio pulses of unknown physical origin that appear to come from extragalactic distances. Previous follow-up observations have failed to find additional bursts at the same dispersion measures (i
Fast radio bursts (FRBs) are extremely luminous and brief radio flashes originating from other galaxies (Petroff et al. 2019). Progressing our understanding of the FRB phenomenon is limited by their large distances and unpredictable activity. The rec
Fast radio bursts (FRBs) are millisecond-duration radio transients of unknown origin. Two possible mechanisms that could generate extremely coherent emission from FRBs invoke neutron star magnetospheres or relativistic shocks far from the central ene
The event rate, energy distribution, and time-domain behaviour of repeating fast radio bursts (FRBs) contains essential information regarding their physical nature and central engine, which are as yet unknown. As the first precisely-localized source,
Fast radio bursts (FRBs) are brief, bright, extragalactic radio flashes. Their physical origin remains unknown, but dozens of possible models have been postulated. Some FRB sources exhibit repeat bursts. Though over a hundred FRB sources have been di