A fast radio burst source at a complex magnetised site in a barred galaxy


 Fast radio bursts (FRBs) are highly dispersed radio bursts prevailing in the 
universe. The recent detection of FRB~200428 from a Galactic magnetar suggested 
that at least some FRBs originate from magnetars, but it is unclear whether the 
majority of cosmological FRBs, especially the actively repeating ones, are 
produced from the magnetar channel. Here we report the detection of 1863 
polarised bursts from the repeating source FRB~20201124A during a dedicated 
radio observational campaign of Five-hundred-meter Aperture Spherical radio 
Telescope (FAST). The large sample of radio bursts detected in 88 hr over 54 
days indicate a significant, irregular, short-time variation of the Faraday 
rotation measure (RM) of the source during the first 36 days, followed by a 
constant RM during the later 18 days. Significant circular polarisation up to 
75\% was observed in a good fraction of bursts. Evidence suggests that some 
low-level circular polarisation originates from the conversion from linear 
polarisation during the propagation of the radio waves, but an intrinsic 
radiation mechanism is required to produce the higher degree of circular 
polarisation. All of these features provide evidence for a more complicated, 
dynamically evolving, magnetised immediate environment around this FRB source. 
Its host galaxy was previously known. Our optical observations reveal that it is 
a Milky-Way-sized, metal-rich, barred-spiral galaxy at redshift 
z=0.09795+-0.00003, with the FRB residing in a low stellar density, interarm 
region at an intermediate galactocentric distance, an environment not directly 
expected for a young magnetar formed during an extreme explosion of a massive 
star.

Fast radio bursts (FRBs) are highly dispersed radio bursts prevailing in the universe 1-3 . The recent detection of FRB 200428 from a Galactic magnetar [4][5][6][7][8] suggested that at least some FRBs originate from magnetars, but it is unclear whether the majority of cosmological FRBs, especially the actively repeating ones, are produced from the magnetar channel. Here we report the detection of 1863 polarised bursts from the repeating source FRB 20201124A 9 during a dedicated radio observational campaign of Five-hundred-meter Aperture Spherical radio Telescope (FAST). The large sample of radio bursts detected in 88 hr over 54 days indicate a significant, irregular, short-time variation of the Faraday rotation measure (RM) of the source during the first 36 days, followed by a constant RM during the later 18 days. Significant circular polarisation up to 75% was observed in a good fraction of bursts. Evidence suggests that some low-level circular polarisation originates from the conversion from linear polarisation dur-ing the propagation of the radio waves, but an intrinsic radiation mechanism is required to produce the higher degree of circular polarisation. All of these features provide evidence for a more complicated, dynamically evolving, magnetised immediate environment around this FRB source. Its host galaxy was previously known 10-12 . Our optical observations reveal that it is a Milky-Waysized, metal-rich, barred-spiral galaxy at redshift z = 0.09795 ± 0.00003, with the FRB source residing in a low stellar density, interarm region at an intermediate galactocentric distance, an environment not directly expected for a young magnetar formed during an extreme explosion of a massive star.
Triggered by observations of the Canadian Hydrogen Intensity Mapping Experiment (CHIME) 9 , we used the FAST 13 to monitor FRB 20201124A from 2021 April 1 to June 11 (UT dates are used throughout this paper) with a 96.9 hr total observation time. The 19-beam receiver was used to cover the frequency range from 1.0 GHz to 1.5 GHz. From 2021 April 1 to April 2, we performed a grid of 9 observations using all 19 beams around the position (α = 05 h 08 m , δ = +26 • 11 ′ ) reported by the CHIME team 9 and detected multiple bursts in 2 to 4 beams simultaneously. We then used the differential intensity in each beam to compute a refined location 14 , which agrees with the position measured by the European Very Long Baseline Interferometry Network (EVN) team 15 . Our later observation was carried out nearly daily by pointing the FAST central beam at the EVN position (α = 05 h 08 m 03.507 s , δ = +26 • 03 ′ 38.50 ′′ ).
In total, 1863 bursts were detected with a signal-to-noise ratio S/N > 7, among which 913 bright bursts reach S/N > 50. The burst flux ranges from 0.005 to 11.5 Jy, and the inferred isotropic luminosity spans 5 × 10 37 erg s −1 to 3 × 10 40 erg s −1 . The daily luminosity distributions show little evolution during our observations (Figure 1), while pulse-to-pulse isotropic luminosities fluctuate by more than two orders of magnitude. The daily event rate evolved slowly from a minimal value of 5.6 +0.9 −1.1 hr −1 to a maximal value of 45.8 +7.8 −8.2 hr −1 , making FRB 20201124A among the most active FRBs known so far. During our monitoring program, we witnessed the sudden quenching of burst activity, when the source stopped emitting any bursts above the flux limit of 4.3 mJy at a fiducial pulse width of 5 ms on 2021 May 29. Before this abrupt cessation of emission, the burst event rate did not show any sign of a monotonic decrease. We continued to observe the source over the next 16 days and did not detected any single burst during the 9 hr of observations ( Figure 1).
The polarisation properties of FRB 20201124A show a great diversity. Even though most bursts exhibit a flat polarisation angle (PA) across each burst, similar to FRB 20121102A 16 , some bursts show significant PA swings similar to the case of FRB 20180301A 17 . Interest-ingly, FRB 20201124A had shown a high degree of circular polarisation in a good fraction of bursts, with a maximal percentage of 75%. This is in contrast to most FRBs 1 or radioemitting magnetars 18 which do not show significant circular polarisation. One possible way of generating circular polarisation in FRBs is through the Faraday conversion mechanism 19, 20 , which rotates the linear and circular polarisation on the Poincaré sphere. We therefore searched for evidence of Faraday conversion in our data. For some bursts with moderate circular polarisation, the frequency spectra of both circular polarisation and linear polarisation indeed show clear oscillating structures (e.g., bursts 779 and 926 in Figure 2). The oscillation phases of the linear and circular polarisation are approximately offset by 180 o . All of these are consistent with the Faraday conversion theory, suggesting that Faraday conversion is indeed one mechanism for producing circular polarisation in FRBs. On the other hand, we also detected highly circularly polarised bursts that lack quasiperiodic structures (e.g., burst 1472 in Figure 2). This suggests that there must be an intrinsic physical mechanism for producing circular polarisation other than Faraday conversion. Since circular polarisation is commonly observed in pulsar radio emission that has a magnetospheric origin, and since the synchrotron maser model invoking relativistic shocks does not predict circular polarisation, our results again offer support for a magnetospheric origin of FRB emission 3,17,21,22 .
We monitored the evolution of the RM of FRB 20201124A, which shows a significant, irregular temporal variation from −887.2 ± +0.7 to −362.7 +2.9 −1.4 rad m − 2 on a timescale of months (see Figure 1 and details in Methods). A pulse-to-pulse RM variation with a rootmean-square (RMS) value of 75.2 rad m −2 is also detected. Similar to pulsar observations, we note that the apparent RM value changing by ∼ 15.6 rad m −2 across a single pulse is allowed owing to profile evolution. No significant dispersion measure (DM) variation is detected with a 95% confidence level upper limit of ∆DM ≤ 2.9 cm −3 pc. The RM variation suddenly stopped ∼ 20 days before the quenching of radio bursts, while the event rate slowly increased from 5.6 +0.9 −1.1 hr −1 to 27.2 +6.7 −7.5 hr −1 . We measured the daily burst rate together with a shape parameter using the Weibul distribution. The shape parameter, with fluctuations, is generally smaller than 1 ( Figure 1). Thus, the bursts tend to cluster compared to a Poisson distribution where no correlation is expected among bursts. The logarithmic waiting time follows a bimodal distribution with timescales peaking at 39 ms and 135.2 s (see Methods). Using the Lomb-Scargle periodogram algorithm, we can exclude periodicity from 30 ms to 10 days at the 95% confidence level.
We measured the scintillation bandwidth from the autocorrelation of the dynamic spectra. The measured scintillation bandwidth (∼ 0.7 MHz) agrees with previously reported values 23 . A pulse-to-pulse fluctuation of scintillation bandwidth with an RMS of 3 MHz is detected, but no systematic evolution of scintillation bandwidth is detected yet. Owing to the limited frequency coverage, we cannot exclude the possibility that such variation resulted from temporal evolution of the pulse profile.
We performed optical and near-infrared observations of the galaxy SDSS J050803.48+260338.0 identified as the FRB host 10-12 using the 10 m Keck telescopes. We took high-and lowdispersion spectra with the Echellette Spectrograph Imager (ESI) and the Low Resolution Imaging Spectrometer (LRIS), respectively, on 2021 April 7, g-and i-band images with LRIS on 2021 April 13, and K ′ -band images with the NIRC2 camera using the laser guidestar adaptive-optics (AO) system on 2021 August 17. We detected multiple emission lines (Figure 3(a)) and derive a precise redshift z = 0.09795 ± 0.00003, which corresponds to a luminosity distance of 453.3 ± 0.1 Mpc (or an angular size distance of 376.0 ± 0.1 Mpc) adopting the standard Planck cosmological model 24 . Similar to the hosts of several other repeaters (e.g., FRB 20121102A 25 , FRB 20180916B 26 , FRB 20180301A 27 ), this host is in the star-forming branch of the Baldwin-Phillips-Terlevich (BPT) diagram 28 (Extended Data Figure 8(a)). Our AO image (Figure 3(b)) with a full width at half-maximum intensity (FWHM) resolution of 0.12", shows that the host is a barred galaxy with apparent spiral features, and the FRB's apparent location is in the disk but offset from the bar and spiral arms. The galaxy's stellar mass 10,11 , M * ≈ 3 × 10 10 M ⊙ , is about half as massive as the Milky Way (MW), which is also a barred spiral galaxy; in contrast, we find that its starformation rate (SFR = 3.4 ± 0.3 M ⊙ yr −1 ) is about twice of that of MW, and its metallicity (12 + log (O/H) = 9.07 +0.03 −0.04 ) is approximately twice the solar abundance (see Methods). As shown in Extended Data Figure 8(b), the projected offset of the FRB location from the galaxy center and the specific SFR appear to be typical compared with known FRB hosts, and its metallicity is higher than that of any FRB host reported previously 29,30 .
We also identify another galaxy at z = 0.5534 ± 0.0001 with multiple emission lines detected in our spectra. The centroid of the background galaxy, which is measured using its [O iii] emission line detected at two slit orientations, is separated by 0.36" from the foreground galaxy's center and 0.72" from the FRB. If the background galaxy were the FRB host, it would have a large projected separation of 4.7 kpc, and this scenario is disfavoured by the constraint imposed by the FRB's DM (see Methods). The close proximity of the two galaxies raises the curious possibility of gravitational lensing, since their separation is comparable to the angular Einstein radius of ∼ 0.2", but more data are needed to verify this.

5
The large sample of radio bursts and the peculiar polarisation properties offer clues to the origin of this repeating FRB. If the central engine is an isolated young magnetar, the RM is predicted to show a secular monotonic decline with time, as the pulsar wind nebula expands 31,32 . The short-term RM evolution is not straightforwardly expected. Rather, it points toward a dynamically evolving, magnetised immediate environment around this FRB. One can place some interesting constraints on the magnetic field strength based on observations. First, the significant evolution of |RM| and the nondetection of DM evolution places a lower limit of B > 0.1 mG in the FRB environment (see Methods). Next, in the cold plasma limit the magnetic field of Faraday conversion may be estimated 20 using B ∼ 7(Π V0 /0.1) (RM ′ /1000 rad m −2 ) −1/2 (λ/21 cm) −2 G, where the oscillation amplitude (Π V0 ) and the RM up to the Faraday conversion position (RM ′ ) are defined in Methods. The estimated magnetic field in the Faraday conversion medium is much higher than previously estimated for FRB 20121102A 19 .
The month-timescale, significant RM variation could be caused by a change of either the magnetic field configuration or density profile along the line of sight close to the source region. One may estimate the characteristic size of the Faraday screen as ∼ 0.2 AU(τ /month)(v/10 km s −1 ), with τ and v being the timescale of RM variation and relative transverse velocity of the Faraday screen and the FRB source, respectively. The relative motion between the source and screen could be due to binary motion or proper motion of the source neutron star. The lack of periodicity may not rule out the binary scenario, since a known Galactic binary pulsar system also shows irregular RM evolution, probably related to irregular mass ejection from the companion star 33 . The cessation of RM variation in a later part of the observing window suggests that the line of sight is less contaminated by the varying component of the medium density.
The repeater FRB 20121102A is hosted by a metal-poor dwarf galaxy with high specific SFR 25 . These properties resemble those of the typical hosts for long-duration gammaray bursts (LGRBs) and hydrogen-poor superluminous supernovae (SLSNe-I), motivating a hypothesized connection between repeater FRBs and young, millisecond magnetars 34 . In contrast, the host of FRB 20201124A is more metal-rich and massive than almost all known hosts of LGRBs/SLSNe-I 30 , and the location of the FRB does not coincide with an apparent active star-forming region in the host, so the hypothesis that the source is a young magnetar born during an extreme explosion such as an LGRB or an SLSN-I is not supported. A regular magnetar similar to those in the MW is still possible, but special conditions are needed to interpret the high FRB burst rate not possessed by Galactic magnetars.

Radio observations and burst detection
We started our observations using the 19-beam receiver of FAST on 2021 April 1, which was triggered by the CHIME alarm 9 . The 19-beam receiver spans from 1.0 GHz to 1.5 GHz with a system temperature of 20-25 K 35 . During the April 1 and 2 observations, we performed a grid observation of FRB 20201124, where 9 pointings around the position reported by CHIME 9 were used to cover the 28 ′ × 35 ′ area around the source. After the source was localised, we used the central beam and continued observing the source since April 3. The epochs and durations of all observations are shown in Figure 1. The data of April 1 and 2 were used only for localisation purposes 14 ; they are excluded in other analyses in this paper, as the beam center was not aligned with the source position.
The data were recorded with a frequency resolution of 122.07 kHz and a temporal resolution of 49.152 µs or 196.608 µs. The full polarisation 4-channel Stokes intensity is derived with the linear polarisation feed 35 . Before and after each observation session, we recorded a 1 min noise calibrator signal for the purpose of polarisation calibration.
We used the software transientx 1 to perform the off-line burst searches. For FRB 20201124A, the data were dedispersed in the range of 380-440 cm −3 pc with a step of 0.1 cm −3 pc and the pulse width was searched with a boxcar filter, of which the pulsar width ranges from 0.1 ms to 100 ms. After candidate plots were formed, we visually inspected all candidates with S/N ≥ 7. A total of 1863 bursts were detected in our observations; the detected numbers of bursts for each observation session are plotted in Figure 1. We also verified the search results using the software BEAR 36 . No difference can be found for bursts with S/N ≥ 7.

Event-rate evolution and the sudden quenching
We adopted the Weibull distribution 37 to describe the probability density of time intervals between bursts. The Weibull distribution of time interval δ is where the Gamma function is defined as Γ(x) ≡ ∫ ∞ 0 t x−1 e −t dt, r is the expected event rate, and k is the shape parameter. When k = 1, the Weibull distribution reduces to the Poisson distribution and burst events are independent of each other. When burst events tend to cluster together, the shape parameter k < 1.
The statistical inferences for the parameters r and k were carried out using a Bayesian method based on the likelihood described by Oppermann et al. 37 . The software package multinest 38 was used to perform posterior sampling. The event rate and shape parameter inferred with daily data are shown in panels (c) and (d) in Figure 1. For most of the observations we have k < 1, which indicates that the bursts tend to cluster together. With all the data, the inferred average event rate and shape parameter are r = 20.5 ± 1.6 hr −1 and k = 0.60 ± 0.02 for a 95% confidence level.
As shown in Figure 1, the burst rate increased from 10.

Flux, fluence, and energy of bursts
We estimated the flux densities (S) through the radiometer equation where the digitisation correction is neglected owing to the 8-bit sampling scheme at FAST 39 , T sys ≈ 20 K, and G ≈ 16 K Jy −1 are the typical system temperature and telescope gain for FAST 35 , t samp is the sampling time, and S/N is the signal-to-noise ratio. BW is the bandwidth of the burst derived from the Gaussian fitting method 40 . The dominant uncertainty (∼ 20%) in flux-density estimation comes from the variation of system temperature 35 .
Our pulse fluence (F ) was computed by integrating the pulse flux with respect to time, while the equivalent width W eq was computed by dividing the fluence by the pulse peak flux. The sample completeness was determined with the following recipe. We simulated 10,000 mock FRB bursts. The mock bursts were simulated with a Gaussian profile and bandpass, where the pulse width and bandwidth of the injections were controlled to match the distributions of detected bursts. We then injected the mock bursts into the original FAST data when no FRB was detected. The injection epoch is random but follows a uniform distribution. The simulated data were then fed to our burst-searching pipeline to compute the detection rate. Averaging over the pulse width and bandpass distributions, the fluence threshold to achieve the 95% detection rate with S/N ≥ 7 is 53 mJy ms.
With the fluence, the isotropic burst energy E was calculated through where D L = 453.3 ± 0.1 Mpc is the luminosity distance computed with z = 0.09795 ± 0.00003 and the standard Planck cosmological model 24 , and F is the fluence. We obtained a population of energies for the 1863 bursts; the histogram of burst energies and the cumulative distribution function of the burst energy above a given threshold (i.e., N (> E)) are shown in Extended Data Figure 1.

Temporal aspects of the bursts
The burst times of arrival (TOAs) were measured from the centroid of the best-matched boxcar filter 36 as the complex morphology of the pulse shape prevents us from using the standard template-matching technique 41 . We then converted the site arrival times to the barycentric arrival times using the software package tempo2 42 .
The waiting times (∆T wait ) were calculated by subtracting pairs of two adjacent barycentric TOAs within the same observing session. The distribution of the waiting time is shown in Extended Data Figure 2. One can find a clear bimodal distribution in the logarithmic waiting time. We modeled the distribution using the superposition of three log-normal distributions, where the best-fitting curve to the histogram is also shown in Extended Data We searched for burst periodicity from FRB 20201124A using the Lomb-Scargle periodogram 44 in the range from 30 ms to 10 days, as shown in Extended Data Figure 3. No obvious period above the 95% confidence level is detected, except for the artificial period around 1 day and its harmonics induced by the observation cadence.

Scintillation and scattering
The dynamic spectra of FRB 20201124A show a complex morphology, such as frequency drifting, single/multiple components, and small-scale voids, similar to other cases 17, [45][46][47] . We investigated scintillation and scattering only with the single-peak pulses, where the measurements were less affected by the pulse structure.
The scintillation bandwidth (i.e., decorrelation bandwidth) is the frequency range over which the pulse intensity falls to half its maximum value. We measured the scintillation bandwidth using the autocorrelation function (ACF) method 48 . The measurement was performed for selected pulses with S/N ≥ 50. Our procedures is as follows. (1) Split the data into 8 evenly spaced subbands across the 500 MHz raw bandwidth; (2) clip channels RFI and 20 MHz band edges (i.e., 1.0-1.02 GHz and 1.48-1.5 GHz); (3) for each subband with S/N ≥ 10, integrate the pulse intensities over time and then compute the ACFs along the frequency axis; (4) a Lorentzian function is fitted to the measured ACFs, and the half width at half-maximum intensity of the Lorentzian function is the decorrelation bandwidth of the given subband; and (5) a power-law function is fitted to the decorrelation bandwidth measured in subbands (i.e., BW sc = BW sc,1 GHz (ν/1 GHz) −γ , with ν being the central frequency of each subband and γ the power-law index). The power-law function fitting aids to compute BW sc,1 GHz (i.e., the decorrelation bandwidth with a reference frequency of 1 GHz). As seen a posteriori, the decorrelation bandwidth (∼ 1 MHz) is two orders of magnitude smaller than the signal bandwidth (∼ 100 MHz), the finite-sample error 49 can be neglected, and the dominant error comes from statistical errors or pulse intrinsic evolution.
The measured decorrelation bandwidth is summarised in Extended Data Figure 4. No visible long-term trend of decorrelatiton bandwidth variation is detected, but we cannot exclude the short-term fluctuations. The average and RMS values of decorrelation bandwidth are 0.7 MHz and 3.0 MHz (respectively), consistent with the previous result of ∼ 0.5 MHz measured with wider frequency coverage 23 (dual bands of 650 MHz and 1.5 GHz). We note that the index γ (average value of 4.9) is fluctuating with an RMS of 6.4. Such a fluctuation in γ is a caution that our measurement for the correlation bandwidth may be affected by the FRB intrinsic radiation properties, and that multiband observations with a wider frequency coverage are required to reduce such systematics. The corresponding scattering timescale according to the scintillation bandwidth will be at the level of 1/0.7 MHz ≈ 1.4 µs, which is much smaller than the pulse width or temporal resolution of our data.

Dispersion measure
Owing to the complex time-frequency structure of FRB pulses, the DM of an FRB is usually derived by maximising the structure or contrast instead of aligning the pulse centroid 45 . This can be done in the time domain 45 or the Fourier domain 40 . In this paper, we used the Fourier-domain method, where the DM is measured by maximising the time derivative of "intensity" computed only with the Fourier phase 2 . After the best DM value is computed, we dedisperse the pulses and perform visual inspection to verify that the pulse structure is aligned in the time domain.
The DM vales as a function of time are collected in Figure 1. Although there is a significant change (maximal fluctuation ∼ 10 cm −3 pc) in the burst-to-burst DM, a linear fitting to the trend in DM variation produces no obvious DM variation rate with dDM/dt = −3(4) × 10 −3 cm −3 pc day −1 (i.e., there seems to be little systematic evolution of DM). In total, the mean value is 413.2 cm −3 pc and the RMS deviation is 2.0 cm −3 pc. Despite little long-term DM evolution, we note that the RMS of daily DM is not stationary. In particular, on May 7 (MJD 59341) and May 10 (MJD 59344) the daily RMS of DM dropped by a factor of ∼ 4 and ∼ 14, as shown in Figure 1. Using the DM template technique 53 together with host galaxy parameters of Hα luminosity L Hα = 7 × 10 41 erg s −1 and effective radius R e = 1.5 kpc (see the section on optical observations), the predicted most probable host galaxy DM is DM host /(1 + z) = 60 cm −3 pc with a 68% confidence level range of 10 ≤ DM host /(1 + z) ≤ 310 cm −3 pc. Assuming a Galactic halo contribution of 30 cm −3 pc (ref. 54 ), the expected DM of the FRB will be in the range of 260 to 620 cm −3 pc, in agreement with the observed DM ≈ 413 cm −3 pc. Basing on the DM measurement, the background galaxy (z = 0.5534) is disfavoured as the FRB host, of which the expected DM IGM = 660 cm −3 pc is already larger than the measured DM. However, the possibility cannot be fully ruled out, as a high anisotropy of the intergalactic medium may allow a low DM IGM value along a particular line of sight.

Polarisation properties
Our polarisation data are calibrated with the single-axis model using the software package psrchive 55 . Both the differential gain and phase between the two polarisation channels are calibrated using noise diode signal injected in the feed. The polarisation fidelity and calibration scheme have been described and tested in previous work 17, 35 .
We measure the RM with bursts of S/N ≥ 30 (1103 in total) using the Q-U fitting method 56 . Our curve fitting is carried out using a Bayesian method 56 , where the posterior sampling is performed with the software package multinest 38 . We corrected the ionosphere contribution with values computed from the software package ionFR 57 . For our data, the maximal ionosphere RM correction is 3 rad m −2 .
The result of the measured RM (for an Earth observer) is shown in Figure 1. We note that the RM can have pulse-to-pulse fluctuations in daily observations; for example, the data taken on April 22 (MJD 59325) show the largest RM fluctuation with an RMS of 75.2 rad m −2 . On top of the pulse-to-pulse fluctuations, one also observes significant RM evolution during the observing span. Previously, a long-term RM variation was reported in FRB 20121102A 58 , where its RM value dropped by 34% over 2.6 yr. For FRB 20201124A, from April 23 (MJD 59327) to May 2 (MJD 59336), RM varied from −887.2 ± 0.7 to −362.7 +2.9 −1.4 rad m −2 , nearly a factor of two RM variation within 10 days. On a longer timescale, the RM variation is also different between FRB 20201124A and FRB 20121102A, with FRB 20201124A showing red-noise-like variations instead of a quasimonotonic decreasing trend as in the case of FRB 20121102A.
The RM variation on a monthly timescale cannot be explained with the RM contribution in the Milky Way, which is −51(5) rad m −2 along the direction of FRB 20201124A; the maximal variation is a few tens of radians per square meter 59 . Given the redshift z = 0.09795 ± 0.00003 of the host galaxy (see Properties of the Foreground Galaxy part of Methods), RM in the source rest frame is RM host = (1+z) 2 (RM obs −RM Gal ) = −380 rad m −2 to −1010 rad m −2 . Considering the monthly timescale of RM variation, we expect that the major RM variation comes from the FRB local environment, over a distance scale ∼ 100 km s −1 × 1 month ≈ 1.8 au. Since no long-term DM variation is measured, we can derive a very conservative bound on the parallel magnetic field from ⟨B ∥ ⟩ ≥ 1.23 uG × ∆RM Host /∆DM host ≈ 0.1mG.
The RM variation is not caused by instrumental artifacts. In polarisation studies, we have excluded the data of April 1 and 2, where the observations were carried out with off-axis illumination. The FAST polarimetry stability has been checked 17 to show that the RM measurement is stable with ∆RM ≤ 0.2 rad m −2 . Because of the high sensitivity of FAST, we also checked if saturation or nonlinearity affected our polarimetry. The radiofrequency frontend of FAST has a dynamic range of ∼ 30 dB with the major limitation introduced by the microwave-optical transducer (product model GL7430 of foxcom). The digital sampling and data recording is done with an 8-bit sampling scheme at FAST. Thus, the major nonlinearity comes from the digital part. We tested the nonlinearity by comparing the differences in results between including and removing the data above 250 (maximal digital value is 255 for an 8-bit system). The differences are tiny, so the results and conclusions of this paper are not affected.
As already noted in studies of pulsars 60 and FRBs 61 , there is an apparent RM variation across the phase of a single pulse owing to the intrinsic frequency evolution of the pulse profile. We check if the RM variation of FRB 20201124A is induced by such an effect. We find that the maximum amplitude of RM variations within single pulses for FRB 20201124A is at the level of 15 rad m −2 . Examples of the 9 brightest bursts are shown in Extended Data Figure 6. The long-term RM variation with an amplitude of ∼ 500 rad m −2 is much larger than the RM variation amplitude within single-pulse profiles; thus, it does not seem to be caused by the frequency evolution of the FRB pulse profile. We also checked if the rotation of linear polarisation agrees with the cold plasma Faraday rotation model. To do so, we relaxed the power-law index of wavelength and fit for the RM index β using the model ∆Ψ = RM λ β . One expects β = 2 if the cold plasma Faraday rotation model can be applied, while the index β would not necessarily equal 2 if the apparent RM is caused by intrinsic profile evolution. As shown in Extended Data Figure 5, we found that for 83% bursts (920 out of 1103 bursts) the deviations of measured RM index values are within 1σ errorbars. Visual inspection revealed that the β ̸ = 2 deviation was mainly caused by overlapping of multiple components in the dynamic spectrum. The trend of RM variation is hardly affected by the small deviations as shown in Extended Data Figure 5, where one can see that the RM variation is very similar when including or removing the data with more than 1σ deviations of β from 2. The above tests indicate that the long-term RM variation is indeed caused by the cold plasma Faraday rotation. To further reduce the profile-evolution effects, only the measurements with RM index within 1σ of β = 2 are included in Figure 1.
We note that polarised emission dominates in the pulse of FRB 20201124A after correcting for Faraday rotation. In particular, 50% of the pulses have linear polarisation higher than 77.9% and circular polarisation higher than 3.3%. A low degree of polarisation is also detected, and the minimal linear and circular polarisation is 8.7% and below the detection threshold, respectively. On the one hand, we note that the circular polarisation is generally weaker than linear polarisation; 95% of the pulses have V /I ≤ 32.4%. On the other hand, certain pulses show a high degree of circular polarisation with a maximal value of 75.1% in the frequency-integrated profile (see pulse 1472 in Figure 2), which is rarely detected in other FRBs 2 .
For a limited number of bursts, we have discovered a λ 2 -dependent oscillation of circular and linear degrees of polarisation. The occurrence epochs of such bursts are indicated in Figure 1, with two examples (bursts 779 and 926) presented in Figure 2. We compute the Lomb-Scargle periodogram 44 for the degree of total, linear, and circular polarisation. With the technique, we find common peaks corresponding to the same conjugate frequency (ω λ 2 ). We then perform a χ 2 fitting to the following model simultaneously for circular and linear polarisation intensity, where parameters Π L0 ,Π L , Π V0 , andΠ V are the average value and slope of linear and circular degree of polarisation, respectively, while A and ω λ 2 are the amplitude and angular frequency of oscillation. Two independent phase parameters (φ L and φ V ) are introduced in the modeling, such that we can check the phase difference between the oscillation of Π L ≡ L/I and Π V ≡ V /I. Here, we perform the fitting with polarisation intensity instead of directly fitting with degree of polarisation. This can be justified with the similar arguments in Q-U fitting 56 . The best fitting conjugate frequency of burst 779 and 926 are ω λ 2 = 2400 ± 30 rad m −2 and 1800 ± 10 rad m −2 . In the framework of mild Faraday conversion, one have |RM ′ | = ω λ 2 /2, which is the Faraday rotation accumulated up to a given position where the conversion occurs. The total observed RM should be of the same order of magnitude. For such a scenario, this corresponds to RM ′ = 1200 ± 15 rad m −2 , 900 ± 5 rad m −2 , respectively.
We plot the best-fit curves against the data in Figure 2, where we convert the model to degree of polarisation for better visualisation. The best-fit phase differences between the linear and circular oscillations are given in panel (e) of Figure 2. For burst 779, the oscillation of Π V and Π L decrease significantly above 1160 MHz (indicated by the shaded area in Figure 2), where the best-fit amplitudes of oscillation below and above 1160 MHz are 0.16 ± 0.01 and 0.008 ± 0.005, respectively.
We checked the power index of oscillation with respect to λ by replacing terms of ω λ 2 λ 2 in Eq. (4) and (5) to a generalised form of ω λ 2k λ 2k and fit the index k simultaneously. For burst 779 and 926, we had k = 0.998 ± 0.005 and 1.0 ± 0.1, which verifies the λ 2 -dependent oscillation of polarisation degree.
As shown in Figure 2, the fitting model sinusoidal curves trace the variation of Π L and Π V . The phase differences between the Π L and Π V curves are ∼ 180 • . Such a phenomenon is in agreement with the prediction of Faraday conversion 20 . We note that the total degree of polarisation, Π P ≡ √ L 2 + V 2 /I, is also oscillating. Such behaviour was not explicitly claimed in the papers addressing the Faraday conversion effects in the FRB context 19, 20 . To fully understand the physics of the oscillating Π P , a complete modeling of polarisation transfer is required, which is beyond the scope of the current paper. Instead, we present a qualitative analysis. We caution that the discussion below can only apply to the local behaviour of radiation transfer.
Neglecting spontaneous emission, the radiative-transfer equation takes the form of 62, 63 where the anti-Hermitian terms f describe Faraday rotation, g and h describe Faraday conversion, and the Hermitian terms µ, ρ, and η describe wave absorption or amplification. S = (I, Q, U, V ) is the vector presentation of the Stokes parameters. We can write the components of the Stokes parameters as with the initial Faraday rotation angle Φ = 2RM ′ λ 2 . Substituting the above equations into Eq. (6), one can show that We can see from the above equations that both the sin Φ or cos Φ terms induce the λ 2dependent oscillation. In order to get the λ 2 -dependent Π P , the Hermitian coefficient µ must be nonzero. Faraday conversion involves terms containing g and h. They introduce interactions between the linear and the circular polarisations, which are λ 2 -dependent. To keep Π L and Π P in phase, we need (i) the term containing sin Φ to be negligible compared with the terms containing cos Φ , and (ii) the same sign holds for the terms gΠ V + µ(1 − Π 2 L ) and µ. To keep the phases of Π V and Π L off by 180 • , we need (iii) the sign of g + µΠ V and L ) to be the same. As we see from bursts 779 and 926 in Figure 2, the phase differences between Π L and Π V are both close to 180 • regardless of the sign of Π V . In this way, according to condition (iii), g should not be zero; otherwise, the phase between Π L and Π V depends on the sign of Π V . A nonzero value of g means that Faraday conversion processes exist. Lacking detailed modeling, we cannot conclude whether the Faraday conversion is relativistic or nonrelativistic at this stage. We expect that future modeling may reveal more details on the magnetoionic environment close to the FRB emission site.
Besides Faraday conversion, polarisation-dependent scintillation can also induce such λ 2 oscillations in degree of polarisation 64 . However, special conditions are required to reproduce the reduction of oscillations in Π L and Π V above 1160 MHz for burst 779, the characteristic frequency of a uniformly magnetised plasma 63 may provide a natural mechanism. One expects that the Lorentz factor of the corresponding relativistic electrons is γ = 15(f /GHz) 1/2 (B/G) −1/2 . That is, an environment with mildly relativistic electrons and a Gauss-level magnetic field may provide the conditions for such polarisation oscillations.
The occurrence of oscillatory polarisation appears less frequently during the time window when RM is stable. Such a behaviour can be understood in the framework of nonrelativistic Faraday conversion, which requires the reversal of longitudinal magnetic fields. When RM is stable, one expects fewer field reversals, and so less Faraday conversion occurrence.
We note that not all bursts with the measured nonzero Π V show the above oscillatory behaviour. Some bursts exhibit slow variations with opposite phases of Π V and Π L , such as burst 1112 in Figure 2. The variation may come from Faraday conversion or an intrinsic radiation mechanism of FRBs. Interestingly, the burst with the highest Π V in our sample (burst 1472 in Figure 2) shows no significant oscillation. Therefore, on top of Faraday conversion, an alternative, intrinsic radiation mechanism may be required to generate circular polarisation.

Keck optical and near-infrared observations
The LRIS 65,66 spectroscopic observations were taken with a slit width of 1.0 ′′ at a position angle PA = 53.4 • , and there were 750+920 s and 2×750 s exposures on the blue and red sides, respectively. LRIS has an atmospheric dispersion corrector. The data were reduced using LPipe 67 , and the fluxes were scaled to match Pan-STARRS1 68  We obtained 4 × 120 s K ′ -band images (dithered by 3-4 ′′ between exposures) with the NIRC2 camera (0.04 ′′ pixel −1 scale and 40 ′′ field) via the Keck II laser guide-star AO system 73 . An R = 15.9 mag star 36 ′′ NW of the FRB host served as the tip-tilt reference star. The near-infrared images were reduced following a standard iterative procedure 4 , and the final combined image reaches a FWHM resolution of 0.12 ′′ . The astrometry is calibrated using the SDSS coordinates of bright unsaturated stars.

Properties of the foreground galaxy
Star-formation rate and gas-phase metallicity We use the emission lines detected in the high-S/N LRIS spectrum to infer the star-formation rate (SFR) and the gas-phase metallicity of the galaxy. We measure line fluxes of Hα   10,11 , the specific SFR is log(sSFR/yr −1 ) = −9.86 ± 0.11. We also cross-check it by estimating sSFR using EW(Hα) = 48Å and obtain log(sSFR/yr −1 ) = −9.65 ± 0.19 by following ref. 76 , and it is higher than our L(Hα)-based estimate by ∼ 1 σ.

Morphology and kinematic
The left and middle subpanels of Extended Data Figure 7(a) show the LRIS i-band and the NIRC2 K-band AO images, respectively. The AO image with FWHM = 0.12 ′′ enables resolving the bar and spiral features of the galaxy, which is not possible with natural seeing. We used GALFIT 79 to model the host galaxy in the NIRC2 image with a single-component model composed of a Sérsic profile in the radial direction and a generalized ellipse function in the azimuthal direction. We obtain the best-fit effective radius R e = 1.5 kpc and axis ratio b/a = 0.62, which suggests cos (i) = 0.6 (where i is disk inclination angle) 80,81 . After subtracting the disk component, the galaxy bar and spiral features can be clearly seen in the residual NIRC2 image shown in the right-most subpanel of Extended Data Figure 7(a). We measure the centroid of the galaxy bar by fitting a 2D Gaussian model and obtain refined coordinates of the galaxy center (RA = 05 h 08 m 03.484 s , Dec = +26 • 03 ′ 37.90 ′′ ). The FRB is 0.32 ± 0.06 ′′ and 0.61 ± 0.06 ′′ to the East and North of the galaxy center, respectively, and its apparent position is on the disk, while does not appear to coincide with any other visible structures.
As shown in Extended Data Figure 7(b), the Hα line in the ESI spectrum has a doublepeaked profile with a peak-to-peak separation of ∼ 100 km s −1 , which may be due to disk rotation; however, since the ESI slit was oriented along the minor axis of the galaxy, it may alternatively be caused by gas outflow. We study the disk rotation with LRIS, for which the slit was oriented 60 • with respect to the major axis. As shown in the left subpanels of Extended Data Figure 7(c), the wavelength centroids of Hα emission vary along the LRIS slit direction. We extract Hα lines with a step size of 3 pixels (0.4 ′′ ) along the slit direction, and we measure their projected galactocentric distance r ⊥ and line-of-sight velocities v to the continuum center shown as the black dots in the right subpanel of Extended Data Figure 7(c).
Then we fit the data using a simple rotational disk model, in which velocity scales linearly with galactocentric distance r for r < r break (the velocity zero point is a free parameter) and stays constant at v ROT for r > r break . The best-fit model, which is shown as the red line in the right subpanel of Extended Data Figure 7(c), has the deprojected rotation velocity v ROT = 139 ± 19 km s −1 and r break = 3.0 ± 0.5 kpc. Our v ROT estimate suggests a galaxy stellar mass M * ≈ 2 × 10 10 M ⊙ using the Tully-Fisher relation 81,82 . This is consistent with our adopted value M * = 2.5 ± 0.7 × 10 10 M ⊙ from averaging two previous estimates 10,11 . iii]λ5007 = 27.6 ± 2.6 km s −1 ; such a low velocity dispersion favors that it is a star-forming galaxy 83 . Using IZI, we find that its gas-phase metallicity 12 + log(O/H) = 8.29 +0.26 −0.28 and E(B − V ) = 0.27 +0.12 −0.13 mag. The extinction-corrected Hα luminosity is L(Hα) = 1.14 +0. 51 −0.38 × 10 42 erg s −1 , which yields SFR = 5.7 +2.5 −1.9 M ⊙ yr −1 . As shown in the right sub-panels of Figure 3(b), the centers of [O iii] λ5007 emission from the background galaxy are offset from the center of the continuum dominated by the foreground galaxy in the 2D spectroscopic image. We determine that the center of the background galaxy is 0.29 ′′ to the West and 0.22 ′′ to the North of foreground galaxy's center. Their angular proximity gives rise to an interesting possibility that the background galaxy might be gravitationally lensed by the foreground galaxy. Assuming a simple Singular Isothermal Sphere (SIS) model with σ v = v ROT / √ 2 = 98 km s −1 for the foreground galaxy, the angular Einstein radius 84 can be estimated as θ E ≈ 0.2 ′′ . Further data and analysis will be required to verify lensing.

Simultaneous high-energy observations
Piro et al. 12 placed lower bounds for the radio-to-X-ray luminosity ratio of ≥ 2 × 10 −6 based on the null detection of the transient in Swift/XRT and Chandra data. We focus on γ-ray counterparts of the 1863 radio bursts using Fermi/GBM, Insight-HXMT, and GECAM, of which the observational sessions covered 1119, 1226, and 456 bursts, respectively. In total, 1708 radio bursts were covered by at least one instrument. The searching methods of Zou et al. 85 and Cai et al. 86 were used for Fermi and Insight-HXMT/GECAM data, respectively.

Data availability
Raw data are available from the FAST data center: http://fast.bao.ac.cn. Owing to the large data volume, we encourage contacting the corresponding author for the data transfer. The directly related data that support the findings of this study can be found from PSRPKU website: https://psr.pku.edu.cn/index.php/publications/frb20201124a/.       The properties (FRB-galaxy offset in the units of galaxy effective radius R e , gas-phase metallicity, sSFR, and stellar mass) of the FRB 20201124A z = 0.098 galaxy (red star) compared with a literature sample of FRB hosts (available at https://frbhosts.org/) shown with dots (black, nonrepeaters; red, repeaters).