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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. The 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 (VLA), 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 $H_{\alpha}$ 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 $B_\parallel\gtrsim1~{\rm mG}$ and FRB 20190520B with $B_\parallel\gtrsim0.1~{\rm mG}$., Comment: 16 pages, 7 figures, accepted by ApJ

We report the radio observations of the eclipsing black widow pulsar J1720-0534, a 3.26 ms pulsar in orbit with a low mass companion of mass 0.029 to 0.034 M$_{\odot}$. We obtain the phase-connected timing ephemeris and polarization profile of this millisecond pulsar (MSP) using the Five-hundred-meter Aperture Spherical Radio Telescope (FAST), the Green Bank Telescope (GBT), and the Parkes Telescope. For the first time from such a system, an oscillatory polarisation angle change was observed from a particular eclipse egress with partial depolarization, indicating 10-milliGauss-level reciprocating magnetic fields oscillating in a length scale of 5000 km (assuming an orbital inclination angle of 90 degrees) outside the companion's magnetosphere. The dispersion measure variation observed during the ingresses and egresses shows the rapid raising of the electron density in the shock boundary between the companion's magnetosphere and the surrounding pulsar wind. We suggest that the observed oscillatory magnetic fields originate from the pulsar wind outside the companion's magnetosphere., Comment: 15 pages, 8 figures, 1 table, accepted by RAA

The origin of fast radio bursts (FRBs), the brightest cosmic explosion in radio bands, remains unknown. We introduce here a novel method for a comprehensive analysis of active FRBs' behaviors in the time-energy domain. Using ``Pincus Index'' and ``Maximum Lyapunov Exponent'', we were able to quantify the randomness and chaoticity, respectively, of the bursting events and put FRBs in the context of common transient physical phenomena, such as pulsar, earthquakes, and solar flares. In the bivariate time-energy domain, repeated FRB bursts' behaviors deviate significantly (more random, less chaotic) from pulsars, earthquakes, and solar flares. The waiting times between FRB bursts and the corresponding energy changes exhibit no correlation and remain unpredictable, suggesting that the emission of FRBs does not exhibit the time and energy clustering observed in seismic events. The pronounced stochasticity may arise from a singular source with high entropy or the combination of diverse emission mechanisms/sites. Consequently, our methodology serves as a pragmatic tool for illustrating the congruities and distinctions among diverse physical processes., Comment: 8 pages, 6 figures, accepted for publication in Science Bulletin

Fast radio bursts (FRBs) are bright radio bursts originating at cosmological distances. Only three repeating FRBs FRB 20121102A, FRB 20190520B and FRB 20201124A among $\sim$ 60 known repeating FRBs have circular polarization. We observed the FRB 20220912A with the Robert C. Byrd Green Bank Telescope (GBT) at L-band on 24 October 2022 and detected 128 bursts in 1.4 hours, corresponding to a burst rate of about 90 hr$^{-1}$, which is the highest yet for FRBs observed by the GBT. The average rotation measure (RM) was $-$0.4$\pm$0.3$\,$rad$\,$m$^{-2}$ with negligible intraday RM change, indicating a likely non-magneto-ionic environment. 61% bursts have linear polarization fraction greater than 90%. Approximately 56% of the bright bursts have circular polarization. A downward drift in frequency and polarization angle swings were found in our sample. The characterization of FRB 20220912A indicates that the circular polarization is unlikely to be caused by the magneto-ionic environment for at least some of the repeating FRB population., Comment: accepted to ApJ

Fast radio bursts (FRBs) are bright millisecond radio bursts at cosmological distances. Only a small fraction of FRBs apparently repeat. Polarization, a fundamental property of electromagnetic signals, often carries critical information about the radiation processes, the environment, and the intervening medium of FRBs. Here we report circular polarization detections of two active repeating FRBs, namely FRBs 20121102A and 20190520B, with the Five-hundred-meter Aperture Spherical radio Telescope. We detect circular polarization in both active repeating FRBs, which increases the number of repeating FRBs with circular polarization to three. In one of the bursts of FRB 20121102A, we detect 64% degree of circular polarization. The observed circular polarization is unlikely induced by multipath propagation. Our observations favor circular polarization induced by Faraday conversion or radiation mechanism intrinsic to the FRB source. The conditions to generate circular polarization have to be rare in either case., Comment: 9pages, 3 figures, and 1 table, published in Science Bulletin

We report the properties of more than 800 bursts detected from the repeating fast radio burst (FRB) source FRB 20201124A with the Five-hundred-meter Aperture Spherical radio Telescope (FAST) during an extremely active episode on UTC September 25-28, 2021 in a series of four papers. In this second paper of the series, we mainly focus on the energy distribution of the detected bursts. The event rate initially increased exponentially but the source activity stopped within 24 hours after the 4th day. The detection of 542 bursts in one hour during the fourth day marked the highest event rate detected from one single FRB source so far. The bursts have complex structures in the time-frequency space. We find a double-peak distribution of the waiting time, which can be modeled with two log-normal functions peaking at 51.22 ms and 10.05 s, respectively. Compared with the emission from a previous active episode of the source detected with FAST, the second distribution peak time is smaller, suggesting that this peak is defined by the activity level of the source. We calculate the isotropic energy of the bursts using both a partial bandwidth and a full bandwidth and find that the energy distribution is not significantly changed. We find that an exponentially connected broken-power-law function can fit the cumulative burst energy distribution well, with the lower and higher-energy indices being $-1.22\pm0.01$ and $-4.27\pm0.23$, respectively. Assuming a radio radiative efficiency of $\eta_r = 10^{-4}$, the total isotropic energy of the bursts released during the four days when the source was active is already $3.9\times10^{46}$ erg, exceeding $\sim 23\%$ of the available magnetar dipolar magnetic energy. This challenges the magnetar models invoking an inefficient radio emission (e.g. synchrotron maser models)., Comment: 26 pages, 7 figures, accepted for publication in Research in Astronomy and Astrophysics

As the third paper in the multiple-part series, we report the statistical properties of radio bursts detected from the repeating fast radio burst (FRB) source FRB 20201124A with the Five-hundred-meter Aperture Spherical radio telescope (FAST) during an extremely active episode between the 25th and the 28th of September 2021 (UT). We focus on the polarisation properties of 536 bright bursts with $\mathrm{S/N}>50$. We found that the Faraday rotation measures (RMs) monotonically dropped from $-579 \ {\rm rad \ m^{-2}}$ to $-605 \ {\rm rad \ m^{-2}}$ in the 4-day window. The RM values were compatible with the values ($-300$ to $-900\ {\rm rad \ m^{-2}}$ ) reported 4 month ago (Xu et al. 2022). However, the RM evolution rate in the current observation window was at least an order of magnitude smaller than the one ($\sim 500\ {\rm rad \ m^{-2}\, day^{-1}}$) previously reported during the rapid RM-variation phase, but is still higher than the one ($\le 1\ {\rm rad \ m^{-2} day^{-1}}$ ) during the later RM no-evolution phase. The bursts of FRB 20201124A were highly polarised with the total degree of polarisation (circular plus linear) greater than 90% for more than 90\% of all bursts. The distribution of linear polarisation position angles (PAs), degree of linear polarisation ($L/I$), and degree of circular polarisation ($V/I$) can be characterised with unimodal distribution functions. During the observation window, the distributions became wider with time, i.e. with larger scatter, but the centroids of the distribution functions remained nearly constant. For individual bursts, significant PA variations (confidence level 5-$\sigma$) were observed in 33% of all bursts. The polarisation of single pulses seems to follow certain complex trajectories on the Poincar\'e sphere, which may shed light on the radiation mechanism at the source or the plasma properties along the path of FRB propagation., Comment: 25 pages, 16 figures. Accepted by Research in Astronomy and Astrophysics (RAA)