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

Fast radio bursts (FRBs) are highly dispersed millisecond-duration radio bursts. Recent observations of a Galactic FRB suggest that at least some FRBs originate from magnetars, but the origin of cosmological FRBs is still not settled. Here we report the detection of 1863 bursts in 82 hr over 54 days from the repeating source FRB~20201124A. These observations show irregular short-time variation of the Faraday rotation measure (RM), which probes the density-weighted line-of-sight magnetic field strength, of individual bursts during the first 36 days, followed by a constant RM. We detected circular polarisation in more than half of the burst sample, including one burst reaching a high fractional circular polarisation of 75%. Oscillations in fractional linear and circular polarisations as well as polarisation angle as a function of wavelength were detected. All of these features provide evidence for a complicated, dynamically evolving, magnetised immediate environment within about an astronomical unit (au; Earth-Sun distance) of the source. Our optical observations of its Milky-Way-sized, metal-rich host galaxy reveal a barred spiral, with the FRB source residing in a low stellar density, interarm region at an intermediate galactocentric distance. This environment is inconsistent with a young magnetar engine formed during an extreme explosion of a massive star that resulted in a long gamma-ray burst or superluminous supernova.

siding in a low stellar density, interarm region at an intermediate galactocentric distance. This environment is inconsistent with a young magnetar engine formed during an extreme explosion of a massive star that resulted in a long gamma-ray burst or superluminous supernova.
Triggered by observations of the Canadian Hydrogen Intensity Mapping Experiment 9 , we used the Five-hundred-meter Aperture Spherical radio Telescope (FAST) 13 to monitor FRB 20201124A from 2021 April 1 to June 11 (UT) with 91 hr total observing time. The 19-beam receiver was used to cover the frequency range 1.0-1.5 GHz. Our detection threshold was a signal-to-noise ratio S/N > 7, and 1103 bright bursts reached S/N > 30 among a total of 1863 detected bursts. The burst flux is 0.005-11.5 Jy, and the inferred isotropic luminosity after integrating signal bandwidth spans from 5×10 37 erg s −1 to 3×10 40 erg s −1 . The daily burst energy distribution shows no secular trend (Methods), while the burst-to-burst fluctuation exceeds two orders of magnitude.
The daily event rate varies slowly ( Figure 1), with minimal and maximal values of 6 ± 1 and 46 ± 8 hr −1 , respectively. Throughout paper, the error bars are for the 68% confidence level unless otherwise specified. The waiting time follows a bimodal distribution with timescales peaking at 39 ms and 135.2 s (Methods). Similar bimodality in waiting time had also been detected in the repeating FRB 20121102A 14 , which may indicate a common mechanism. The high event rate makes FRB 20201124A among the most active known FRBs. We witnessed the quenching of the burst activity on a timescale < 74 hr, when the source stopped emitting any bursts above the flux limit of 4.3 mJy at the fiducial burst width of 5 ms on 2021 May 29. We continued to observe the source over the next 16 days and did not detect a single burst during the 9 hr of observations ( Figure 1). Counterintuitively, the burst rate did not show any sign of a monotonic decrease, but a slow increase from 6 ± 1 hr −1 to 27 +7 −8 hr −1 during the last 20 days before the quenching.
FRB 20201124A bursts show diverse polarisation properties, including nearly constant polarisation angle (PA) across the phase 15,16 , significant PA swings 17 , and a high amount of circular polarisation ( Figure 2). In our burst sample, 50% of the bright bursts (S/N > 30) had circular polarisation higher than 3.3%, while the maximal circular polarisation reaches 75%, higher than the 47% reported previously 18 . This is in contrast to most FRBs 1 or radio-emitting magnetars 19 showing little circular polarisation.
For some bursts with moderate circular polarisation, the frequency spectra of both circular and linear polarisations show oscillating features (e.g., bursts 779 and 926 in Figure 2), which indicate Faraday conversion (i.e., generalised Faraday rotation) or polarisation-dependent absorption. The oscillation phases of the linear and circular polarisations are approximately offset by 180 • . We also detected highly circularly polarised bursts without such quasiperiodic structures (burst 1472 in Figure 2). This suggests that there is likely an alternative mechanism for producing circular polarisation in addition to the polarisation oscillations. Since the synchrotron maser model invoking relativistic shocks does not predict circular polarisation, our results support the magnetospheric origin of FRB emission 3,17,20,21 .
The RM shows a stochastic temporal variation between −889.5 +0. 7 −0.7 and −365.1 +2.9 −1.4 rad m − 2 , on a timescale of 10 days ( Figure 1) and the largest burst-to-burst RM variation per session with a root-mean-square (RMS) value of 77.2 rad m −2 . Within a single burst, the profile evolution induced apparent RM variation is ∼ 15.6 rad m −2 . The detected stochastic RM variations on 10-day timescale are more than 40 times larger, suggesting that stochastic RM variations do not result from the profile evolution. Compared with the case of FRB 20121102A 16,22 , the fractional amplitude of RM variation in FRB 20201124A is larger, while the absolute amplitude is smaller. The RM variation quickly stopped ∼ 20 days before the quenching of the radio bursts, with the 95% confidence level upper limit of ∆RM ≤ 9.1 rad m − 2 , a factor of 50 smaller than the amplitude of stochastic RM variations detected earlier.
The significant RM variation on a 10-day timescale could be caused by a change of either the magnetic field configuration or the density profile along the line of sight close to the source region. The sub-au size of the Faraday screen is estimated as ∼ 0.6 au(τ /10d)(v/100 km s −1 ), where τ is the timescale of RM variation and v is the relative transverse velocity between the screen and the FRB source. Similar to the FRB 20201124A, the Galactic binary pulsar system PSR B1259−63 shows irregular RM evolution 23 . Thus, the lack of periodicity in RM variation may not rule out the binary scenario, and is probably related to irregular mass ejection from the companion star. The cessation of RM variation suggests that the line of sight is less contaminated by the varying component of the medium density. If the central engine is an isolated young magnetar, the RM is predicted to show a secular monotonic decline with time 24,25 .
The oscillations of the linear and circular polarisation fractions as well as the linear polarisation angle as functions of radio wavelength probe the magnetic field and the relativistic plasma close to the FRB central engine. They are likely a consequence of the polarisation-dependent absorption or conversion, which requires B ≥ 3(γ/10) −2 Gauss, where γ is the kinetic Lorentz factor of the plasma (Methods). Owing to the burst-to-burst variation of polarisation oscillation phenomena, the distance scale associated with the oscillation in polarisation is 0.1 au (τ /min) assuming that the bursts propagate at the speed of light. The polarisation oscillation suggests that the vicinity of the FRB source is occupied by a variable Gauss-level magnetic field together with both a cold and a relativistic plasma (Methods).
We performed optical and near-infrared observations of the host galaxy SDSS J050803.48+260338.0 [10][11][12] using the 10 m Keck telescopes, including high-and low-dispersion spectra with the Echellette Spectrograph Imager (ESI) and the Low Resolution Imaging Spectrometer (LRIS), respectively, and K -band images with the NIRC2 camera using the laser guide-star adaptive-optics (AO) system. In the optical spectra, we detected multiple emission lines (Figure 3(a)) and derived z = 0.09795 ± 0.00003, which corresponds to a luminosity distance of 453.3 ± 0.1 Mpc adopting the standard Planck cosmological model 26 . Similar to the hosts of several other repeaters (e.g., FRB 20121102A 27 , FRB 20180916B 28 , FRB 20180301A 29 ), this host is in the star-forming branch of the Baldwin-Phillips-Terlevich diagram 30 (Methods). Our adaptive-optics (AO) image (Figure 3(b)), with a full width at half-maximum resolution of 0.12 , shows that the host is a barred galaxy with spiral features, and the FRB's apparent location is in the disc but offset from the bar and spiral arms.
The galaxy's stellar mass 10,11 , M * ≈ 3 × 10 10 M , is about half that of the Milky Way (MW); in contrast, its star-formation rate (SFR = 3.4 ± 0.3 M yr −1 ) is about twice that of the MW, and its metallicity (12 + log (O/H) = 9.07 +0.03 −0.04 ) is approximately twice the solar abundance (Methods). The projected offset of the FRB location from the galaxy centre and the specific SFR appear to be typical compared with known FRB hosts (Methods), and its metallicity is higher than that of any FRB host reported previously (most were for non-repeating FRBs) 31,32 . One active repeater, FRB 20121102A, is hosted by a metal-poor dwarf galaxy with a high specific SFR 27,33 , which is similar to the hosts of long gamma-ray bursts or hydrogen-poor superluminous supernovae. This has motivated a hypothesised connection between active repeating 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 long gamma-ray bursts or hydrogen-poor superluminous supernovae 32 . It has been speculated that FRB 20201124A may reside in a star-forming region in the host galaxy [10][11][12] . However, the interarm location of the source revealed by our image does not support such a possibility, so a young magnetar engine born from an extreme explosion is disfavoured. Nonetheless, a regular magnetar similar to those in the MW is still possible, although the high burst rate, not seen in the Galactic magnetars, requires unusual intrinsic or environmental conditions.

Radio observations and burst detection
We carried out our observations using the 19-beam receiver of FAST on 2021 April 1. The 19beam receiver spans from 1.0 GHz to 1.5 GHz with a system temperature of 20-25 K 36 . 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/FRB team 37 and detected multiple bursts in 2 to 4 beams simultaneously. We then used the differential intensity in each beam to compute a refined location: α = 05 h 08 m 03.50 s , δ = +26 • 03 37.80 38 Figure 1. The data of April 1 and 2 were used only for localisation purposes 38 ; they are excluded in other analyses in this paper, as the beam centre was misaligned 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 FAST receiver uses the dual-polarisation linear polarisation feed 36 , with which the 4-channel Stokes intensity was measured. Before and after each observation session, we recorded a 1 minute noise diode signal for the polarisation calibration.
We used the software TRANSIENTX (https://github.com/ypmen/TransientX) to perform the off-line burst searches. The data were dedispersed in the range of 380-440 cm −3 pc with a step of 0.1 cm −3 pc and the burst width was searched with a boxcar filter, of which the filter width ranges from 0.1 ms to 100 ms. After candidate plots were formed, we visually inspected all 3364 candidates with S/N ≥ 7 39 . A total of 1863 bursts were detected in our observations; the detected number of bursts for each observation session is plotted in Figure 1. We also verified the search results using the software BEAR 40 . No difference can be found for bursts with S/N ≥ 7.

Event-rate evolution and the quenching
We adopted the Weibull distribution 41 to describe the probability density of time intervals between bursts. The Weibull distribution of time interval δ is where the function Γ(x) ≡ ∞ 0 t x−1 e −t dt; r and k are the event rate and shape parameter, respectively. The statistical inferences were carried out using the Bayesian method 41 implemented with the software package MULTINEST 42 . The inferred daily event rate and shape parameter are shown in Figure 1 and Extended Data Figure 1. The inferred average event rate and shape parameter are r = 21 ± 2 hr −1 and k = 0.60 ± 0.02 for a 95% confidence level, where k < 1 indicates that the bursts tend to cluster together. The Poisson rate, implicitly assuming no temporal correlation, is computed by fixing k = 1. As shown in Figure 1, the two rates are consistent with each other within the 68% confidence-level error. The event rate is not constant as the reduced χ 2 , assuming constant rate, for all 45 measurements are 6.3 and 12.0 (the corresponding P -values are 10 −35 and 10 −83 ) for the Weibull and Poission cases, respectively. On May 29 (MJD 59363), the FRB source was quenched. No more bursts were detected with S/N ≥ 7 thereafter in 20 days with a total of 9 hr observations. The corresponding 95% confidence level upper limit of the event rate is r ≤ 0.3 hr −1 .

Flux, fluence, and energy of bursts
We estimated the flux densities (S) through the radiometer equation with a typical system temperature of 20 K and telescope gain G ≈ 16 K Jy −1 for FAST 36 . We calculate the flux density at a frequency resolution of 7.8125 MHz and a time resolution of 196.608 µs. The dominant uncertainty (∼ 20%) in flux-density estimation comes from the temporal variation of system temperature 36 . The average flux density is derived from the Gaussian fitting method 43 . Since the average flux will depend on the definition of "signal bandwidth", we choose the 3σ width from the Gaussian fitting as our signal bandwidth. The average burst fluence (F ) is computed by integrating the average burst flux with respect to time, and the equivalent width W eq is computed by dividing the fluence by the burst peak flux. The measured distributions F and W eq are shown in Extended Data Figure 2. The average and the RMS deviation of W eq are 7.6 ms and 3.3 ms, respectively, while the average F and its RMS fluctuation are 0.5 Jy ms and 1.0 Jy ms.
The sample completeness was determined with the following method. We simulated 10,000 mock bursts with Gaussian profile and bandpass matching the detected distributions. We then randomly injected the mock bursts into the original FAST data when no FRB was detected. The mock burst injected data are then fed to our burst-searching pipeline to compute the detection rate. The procedure shows that the fluence threshold achieving the 95% detection probability with S/N ≥ 7 is 53 mJy ms.
The isotropic burst energy E was calculated by integrating over the 4π solid angle and the signal bandwidth, E = 4πD 2 Mpc is the luminosity distance 26 , and F is the fluence. The energy inference is little affected by the choice of BW, as it is integrated. We evaluate the systematics by comparing the energy measured from integrating 2σ and 3σ Gaussian-fitting BW. The difference (∆E/E ≤10%) is smaller than the 20% uncertainty in the system temperature.
The histogram of burst energies and the cumulative distribution function (CDF) of the burst energy are shown in Extended Data Figure 2. We note that the CDF of burst energy is better fitted by a broken power law rather than by a single power law; i.e., we use where γ 1 and γ 2 are the power-law indices, and E 0 is the turning-over energy. The inferred parameters for the broken power law model are Here, the former uncertainty is for the 95% confidence-level statistical error, while the later one comes from the 20% T sys variation. The natural logarithmic Bayesian factor (ln B) of the broken power law model over the single power law model is 1275, which indicates a strong preference for the former. Our measured power-law index at the higherenergy end (γ 2 ) is close to that of FRB 20121102A 14 (i.e., γ ∼ 1.4 for E > 3 × 10 38 erg), and it is also close to the power-law index (γ ≈ 1.3) of the bright bursts of FRB 20180916B detected by CHIME 43 . The power-law index at the lower-energy end (γ 1 ) is shallower than that measured in FRB 20121102A 14 with γ = 0.61 ± 0.04 for 4 × 10 36 < E < 3 × 10 38 . We tested the effects of Gaussian fitting BW on γ by comparing the value derived using 2σ and 3σ BW values, where δγ 1 = 0.02 and δγ 2 = 0.06 are comparable to the systematics of T sys variation. We searched for the corresponding high-energy transients in both Fermi and Insight-HXMT/GECAM data 44,45 , and the null detection places loose bounds that the ratio between the luminosity in radio and γ-ray bands, i.e. L radio /L γ ≥ 1.4 × 10 −7 (8-200 keV) and ≥ 6.3 × 10 −7 (200-3,000 keV).

Waiting time between the bursts
The burst times of arrival (TOAs) were measured from the centroid of the best-matched boxcar filter 40 . We then converted the site arrival times to the barycentric coordinate time at the reference frequency of 1500 MHz using the software package TEMPO2 46 . The waiting times (∆T wait ) were calculated by subtracting two adjacent barycentric TOAs. The distribution of the waiting time is shown in Extended Data Figure 3. We modeled it using the superposition of three log-normal distributions, where the best-fitting curve to the histogram is in Extended Data Figure 3. The waitingtime distribution shows local maxima at 39 ms, 45.1 s, and 162.3 s. We note that a superposition of two log-normal distributions is insufficient to describe the data (Extended Data Figure 3 51 , which predicted that the 68%-confidence-level range of the host-galaxy DM is 10 ≤ DM host /(1+z) ≤ 300 cm −3 pc, where the host-galaxy Hα luminosity L Hα = 7×10 41 erg s −1 and the effective radius R e = 1.5 kpc are from our optical observations (see the optical observation section in Methods).

Polarisation properties
Our polarisation data are calibrated with the single-axis model using the software package PSRCHIVE 52 , where 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 17,36 .
We measure the RM for high-quality bursts only with S/N ≥ 30 (1103 in total) using the Q − U fitting method 53 . We corrected the ionosphere contribution with values computed from the software package IONFR 54  We can exclude a few common origins for the RM variation. (1) The RM variation cannot be explained with the RM contribution in the MW, 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 within a 2 • field of view 57 . (2) 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 . We also checked if saturation or nonlinearity affected our polarimetry. The digital sampling and data recording is done with an 8-bit sampling scheme at FAST. We tested the nonlinearity by comparing the differences in results between including and removing the data above 250 (the maximal digital value is 255 for an 8-bit system); the differences are tiny. (3) RM variation is not from the apparent RM variation across the phase of a burst as found in pulsars 58 and in FRBs 59 . We find that the maximum amplitude of RM variations within single bursts for FRB 20201124A is at the level of 15 rad m −2 (examples are shown in Extended Data Figure 4), which is too small to explain the RM variation of FRB 20201124A at the level of ∼ 500 rad m −2 . (4) RM variation is not caused by the intrinsic frequency evolution of individual bursts, as the PA rotation matches the cold plasma Faraday rotation relation. We relaxed the power-law index of wavelength in Q − U fitting and also 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 57% of the bursts (631 out of 1103 bursts), the deviations of measured RM index values are within 1σ error bars. Visual inspection revealed that the β = 2 deviation was mainly caused by overlapping of multiple components in the dynamic spectrum. The detected trend of RM variation is hardly affected by the β = 2 deviation as shown in Extended Data Figure 5. To further reduce the profile-evolution effects, only the measurements with RM index within 1σ of β = 2 are included in Figure 1.
Considering the 10-day timescale of RM variation, we expect that the major RM variation comes from the FRB local environment, over a distance scale of ∆X ≈ 0.6 au (τ /10 day)(v/100 km s −1 ), where we normalised velocity to the typical value of binary motion or proper motion of neutron stars. We can derive a bound on the parallel magnetic field by using the constraint induced by free-free absorption at such a small distance scale. The detection of FRB emission requires that the free-free absorption optical depth should be smaller than unity 60,61 , which means that the local DM contributing to the RM variation meets where we converted the DM to EM via the filling factor η ≡ ∆DM 2 ∆XEM ≤ 1. One finds Here RM is defined in the source rest frame. Such a mG-level lower bound of the magnetic field was also reported for FRB 20121102A 16, 62 based on the host-galaxy DM estimation.
For 41 of the total 1863 bursts, we have discovered oscillations of fractional circular/linear polarisation (Π V ≡ V /I, Π L ≡ L/I), and linear PA. The oscillation can be characterised with periodicity in the square of wavelength, and we use the Lomb-Scargle periodogram 63 to find such features. A χ 2 fitting to the following model simultaneously for circular and linear polarisation intensities is used to infer the oscillation parameters: where the parameters Π L0 ,Π L , Π V0 , andΠ V are the average values and the slopes of the fractional linear and circular polarisation, A is the amplitude of oscillation in the fractional polarisation, PA 0 is the mean PA, and A PA is the amplitude of the oscillation in PA. A common angular frequency of oscillation (ω λ 2 ) is assumed for Π V ,Π L and PA. The φ L , φ V , and φ PA are oscillation phases. The best-fitting conjugate frequencies of bursts 779 and 926 are ω λ 2 = 2400 ± 30 rad m −2 and 1800 ± 10 rad m −2 . In the framework of mild polarisation absorption or Faraday conversion, one has |RM | = ω λ 2 /2, which is the Faraday rotation accumulated from the FRB, along the line of sight, up to the position where the absorption or conversion occurs: RM = 1200 ± 15 rad m −2 , 900 ± 5 rad m −2 , respectively. We note that the total observed RM is of the same order of magnitude, which indicates that a significant amount of RM comes from the vicinity of the FRB source, where, at the same time, Faraday conversion or synchrotron absorption is still important 64, 65 , i.e. a cold and a relativistic plasma coexist.
We plot the best-fit curves against the data in Figure 2, where we convert the model to fractional polarisation for better visualisation. The best-fit phase differences between the linear and circular oscillations are given in panel (d) of Figure 2. For burst 779, the oscillations of Π V and Π L decrease significantly above 1160 MHz (λ 2 0.067 m 2 as 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. Such frequency-dependent oscillation can be explained with the characteristic frequency of a uniformly magnetised plasma 65 that the plasma effects are important when wave frequency bellow the characteristic frequency, i.e. f ≤ 0.04 GHz (B/G)γ 2 , with γ the electron kinetic Lorentz factor. In the polarisation-dependent radiative transfer framework, the constraint for magnetic field becomes B ≥ 3 G(f /1.1GHz)(γ/10) −2 .
We checked the power-law index of oscillation with respect to λ by replacing terms of ω λ 2 λ 2 in Eq. (5) and (6) to a generalised form of ω λ 2k λ 2k and fit the index k simultaneously. For bursts 779 and 926, we had k = 0.998 ± 0.005 and 1.0 ± 0.1, which verifies the λ 2 -dependent oscillation of polarisation.
Besides Faraday conversion, polarisation-dependent scintillation can also induce such λ 2dependent oscillations 66 , if the number of slits on the scintillation screen is limited. However, special conditions are required in this model to reproduce the observation. First, polarisationdependent absorption is still required to induce oscillation in total polarisation Π P . Second, contrived fine tuning is required to achieve a 40% Π V variation for a < 10 • PA change as seen in burst 779. Also, an extra mechanism is needed to cease the polarisation oscillations above 1160 MHz for burst 779.
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
We obtained Keck I low-and high-dispersion spectra with the Low Resolution Imaging Spectrometer (LRIS) 67,68 and the Echellette Spectrograph Imager (ESI) 69 , respectively. The LRIS spectra were taken with a slit width of 1.0 at 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 70 , and the fluxes were scaled to match Pan-STARRS1 71 griz photometry. Galactic extinction corrections 72,73 were applied with R V = 3.1 and E(B − V ) MW = 0.652 mag. We took 8 × 320 s exposures with ESI in the cross-dispersed echelle mode with resolving power R ≈ 10, 000 and a slit width of 1.0 at the parallactic angle 74 of 87 • . They were reduced with ESIRedux (https://www2.keck.hawaii.edu/inst/ esi/ESIRedux/index.html), with only relative-flux calibration performed.
The LRIS imaging consisted of 4 × 180 s exposures in the g band and 2 × 180 s in the i band. They were reduced following standard procedures of bias subtraction, flat fielding, and coadding.
We obtained 4 × 120 s near-infrared 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 75 . An R = 15.9 mag star 36 NW of the FRB host served as the tip-tilt reference star. The images were reduced following a standard iterative procedure implemented in an IDL package (https://github.com/fuhaiastro/nirc2), and the final combined image reaches a full width at half-maximum intensity (FWHM) resolution of 0.12 . The astrometry is calibrated using five stars in the field to the Gaia reference frame (Gaia-CRF2 76 ), which is tied to the International Celestial Reference System (ICRF) reference system using accurate VLBI positions of quasars at sub-mas precision.
Morphology and kinematics: The left and middle subpanels of Extended Data Figure 6(a) show the LRIS i-band image and the NIRC2 K -band AO image, respectively. The AO image with FWHM = 0.12 enables us to resolve the bar and spiral features of the galaxy, which is not possible with natural seeing. We used GALFIT 82 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 generalised 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 disc inclination angle) 83,84 .
After subtracting the disc 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 6(a). We measure the centroid of the galaxy bar by fitting a two-dimensional (2D) Gaussian model and obtain refined J2000 coordinates of the galaxy centre (RA = 05 h 08 m 03.4896 s , Dec = +26 • 03 37.869 ). The FRB is 0.239 ± 0.013 and 0.636 ± 0.007 to the east and north of the galaxy centre, respectively. The uncertainties are estimated by adding the localisation uncertainties from EVN (∆RA EVN = 4.5 mas and ∆Dec EVN = 3.6 mas 35 ) and optical observations (∆RA opt = 12.0 mas and ∆Dec opt = 6.5 mas) in quadrature. The error budget of optical astrometry is dominated by the uncertainties from the Keck-Gaia frame transformation, whereas the centroiding errors in Keck (2 mas) and Gaia (from a fraction of 1 mas to ∼ 2 mas for the five reference stars) are relatively minor.
The object's projected position is on the disc, although it does not seem to coincide with any other visible structures. We measure the one-dimensional intensity profile of a chord slicing through the FRB position and perpendicular to the major axis of the bar on the NIR2 image. We find that it is well described by a model of concentric double Gaussian functions with the broader (σ = 511 mas) and narrower (σ = 96 mas) Gaussians describing the disc and the bar contributions, respectively. We subtract the broader Gaussian (i.e., the disc contribution) and find that at the position of the FRB, which is 260 ± 13 mas from the bar centre, its light has only 7% of the peak bar intensity, which is very small.
As shown in Extended Data Figure 6(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 disc 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 disc 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 6(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 centre shown as the black dots in the right subpanel of Extended Data Figure 6(c). Then we fit the data using a simple rotational disc 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 6(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 84,85 . This is consistent with our adopted value M * = (2.5 ± 0.7) × 10 10 M from averaging two previous estimates 10,11 .

Background galaxy
Fong et al. 10  The centres of [O III] λ5007 emission from the background galaxy are offset from the centre of the continuum dominated by the host (foreground) galaxy in the 2D spectroscopic image. We measure the centroid of the background galaxy by using its [O III] emission line detected at two slit orientations, which are shown in Figure 3(b); it is 0.29 west and 0.22 north of foreground galaxy's centre. Owing to the large projected separation of 4.7 kpc, and inconsistency of the expected DM and scattering timescale 87 , it is unlikely that the background galaxy is the FRB host.

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 at the PSRPKU website, https://psr.       Extended Data Figure 7: Properties of the galaxies and comparisons with other FRB hosts (a) FRB repeaters' hosts in the BPT diagram plotted with the SDSS DR8 MPA-JHU sample (black); parameter spaces of galaxies dominated by star formation and active galactic nuclei are separated by the black dashed and solid lines, respectively 88,89 . The host and background galaxies of FRB 2020124A are shown in red and yellow, respectively. (b) The properties (FRB-galaxy offset in units of galaxy effective radius R e , gas-phase metallicity, sSFR, and stellar mass) of the FRB 20201124A host galaxy (red star) compared with a literature sample of FRB hosts (available at https://web.archive.org/web/20211015143528/https: //frbhosts.org/#explore) shown with dots (black, non-repeaters; red, repeaters). (c) Emission lines from the background galaxy at z = 0.553 in the LRIS (blue) and ESI (red) spectra with regions contaminated by Earth's atmosphere marked in green.