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Over 700 bright millisecond-duration radio transients, known as fast radio bursts (FRBs), have been identified to date. Nevertheless, the origin of FRBs remains unknown. Two repeating FRBs (FRB 20121102A and FRB 20190520B) have been verified to be associated with persistent radio sources (PRSs), making them the best candidates to study the nature of FRBs. Monitoring the variability in PRSs is essential for understanding their physical nature. We conducted 22 observations of the PRSs linked to FRB 20121102A and FRB 20190520B using the Karl G. Jansky Very Large Array, to study their variability. We have observed significant flux variability for the PRSs of FRB 20121102A and FRB 20190520B, with a confidence level exceeding 99.99%, based on the observations covering the longest timescale recorded to date. The observed variability of the two PRSs exhibits no significant difference in amplitude across both short and long timescales. We found that the radio-derived star formation rates of the two FRB hosts are significantly higher than those measured by the optical H α emissions, indicating that their host galaxies are highly obscured or most radio emissions are not from star formation processes. The observed timescale of PRS flux evolution constrained the magnetic field of FRB 20121102A with B ∥ ≳ 1 mG and FRB 20190520B with B ∥ ≳ 0.1 mG. [ABSTRACT FROM AUTHOR]

Fast radio bursts (FRBs) are millisecond-duration, bright (approximately Jy) extragalactic bursts, whose production mechanism is still unclear 1 . Recently, two repeating FRBs were found to have a physically associated persistent radio source of non-thermal origin 2,3 . These two FRBs have unusually large Faraday rotation measure values 2,3 , probably tracing a dense magneto-ionic medium, consistent with synchrotron radiation originating from a nebula surrounding the FRB source 4-8 . Recent theoretical arguments predict that, if the observed Faraday rotation measure mostly arises from the persistent radio source region, there should be a simple relation between the persistent radio source luminosity and the rotation measure itself 7,9 . Here we report the detection of a third, less luminous persistent radio source associated with the repeating FRB source FRB 20201124A at a distance of 413 Mpc, substantially expanding the predicted relation into the low luminosity-low Faraday rotation measure regime (<1,000 rad m -2 ). At lower values of the Faraday rotation measure, the expected radio luminosity falls below the limit-of-detection threshold for present-day radio telescopes. These findings support the idea that the persistent radio sources observed so far are generated by a nebula in the FRB environment and that FRBs with low Faraday rotation measure may not show a persistent radio source because of a weaker magneto-ionic medium. This is generally consistent with models invoking a young magnetar as the central engine of the FRB, in which the surrounding ionized nebula-or the interacting shock in a binary system-powers the persistent radio source., (© 2024. The Author(s), under exclusive licence to Springer Nature Limited.)