Main

The vast majority of fast radio burst (FRB) sources have been detected only once1, but a small subpopulation (~2.6%) is known to burst repeatedly2,3. Nonetheless, many apparent non-repeaters may be capable of repeating. In particular, recent results have shown that there is a wide range of FRB activity levels, with only very few sources being highly active3. This suggests that the apparent non-repeaters are simply the least active FRB sources. However, statistical studies have shown that the average emission bandwidth and burst duration differ between repeaters and non-repeaters1,4. This suggests that repeaters and non-repeaters have different origins, either a physically distinct progenitor or that a single type of source can produce different types of bursts.

Probing the burst energy distribution of FRBs across many orders of magnitude, for both individual sources and the entire population, could help determine whether repeaters and non-repeaters have the same burst engines.

Typically, FRBs have isotropic-equivalent burst energies E in the range5 E ≈ 1036–41 erg, though burst energies as high as E = 2 × 1042 erg have been reported for distant sources6. Telescope sensitivity strongly limits our ability to detect weaker bursts and on-sky time limits our ability to detect the rarest, most energetic bursts. In this Article, we will consider the spectral energy density Eν = E/ν, where ν is the observed bandwidth of the emission. To convert energies quoted in the literature to spectral energies, we adopt a fiducial bandwidth of 300 MHz (unless specified otherwise) as a ‘middle ground’ between the statistically different bandwidths of repeating and apparently non-repeating FRBs4.

The cumulative burst spectral energy distribution of repeating FRBs can be modelled by a single or broken power law7,8, \(R( {>} {E}_{\nu })\propto {E}_{\nu }^{\gamma }\), with the slope γ sometimes steepening towards the high-energy tail, reaching values as extreme as γ = −4.9 (ref. 9). The measured value of γ varies between sources and between observing epochs. For example, for FRB 20121102A, γ ranges10,11 between −0.61 and −1.8. There is also a hint that the burst energy distribution of FRB 20121102A flattens10,11 at the highest spectral energies (Eν ≳ 3 × 1031 erg Hz−1), although the low number of observed events precludes a robust conclusion.

In contrast, for apparently non-repeating FRBs, modelling of the population12,13,14 shows a much flatter energy distribution, with γ between about 0 and −1. Hyperactive repeating sources provide an opportunity to probe the high-energy burst distribution and compare it with that of apparently non-repeating sources. This is an important way to investigate whether repeaters and non-repeaters have the same progenitors. It also provides key input for FRB population simulations and applications for probing cosmology because the highest-achievable burst energies directly relate to the maximum distances from which we can observe FRBs.

One of the most hyperactive FRB sources to date is FRB 20201124A (ref. 15), with >3,000 bursts detected in ~25 h of observations with the FAST telescope16. In addition, the source has been reported to emit high-fluence bursts17 that are detectable with relatively small 25–32 m class radio telescopes. FRB 20201124A is in a region of enhanced star formation18 in a massive star-forming galaxy at redshift19 z = 0.098. The known distance allows us to infer burst energies from measured fluences.

Observations and results

We observed FRB 20201124A between modified Julian date (MJD) 59,309 and MJD 59,641 (April 2021 to March 2022; Fig. 1) for 2,281 h, spread over a 1-year time span. Four radio telescopes were used: the 25 m dish in Onsala, Sweden (O8); RT1, a 25 m dish in Westerbork, the Netherlands (Wb); the 32 m dish in Toruń, Poland (Tr); and the 25 m telescope in Stockert, Germany (St). The observations were coordinated between the four telescopes with the aim of covering as broad a radio-frequency bandwidth as possible during contemporaneous observations while increasing the overall time on source (Table 1). During times of high source activity, we observed for up to 12 h daily over the course of several weeks. We recorded raw voltages (amplitude and phase data) at Wb, O8 and Tr, whereas St recorded total-intensity data (Methods). The data were processed and searched for bursts using standard techniques and tools (Methods).

Fig. 1: Overview of the FRB 20201124A monitoring campaign.
figure 1

a, MJD range 59,300–59,600. b, MJD 59,600–59,645. The corresponding calendar dates are listed on the top x axes. Each coloured vertical block indicates an observation and associated telescope (annotated in the figure legend). The placement and extent along the y axes indicate the observing band. Note that the frequency axis is discontinuous. The vertical black dashed lines denote detections of bursts from FRB 20201124A in the frequency range 1,202–1,714 MHz (despite spanning the entire frequency axis for visualization purposes). The horizontal grey bar along the bottom of a highlights the time range overlapping the FAST observations20 discussed in the text.

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Table 1 Observational set-up
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We detected 46 unique bursts in the frequency range 1,200–1,750 MHz (L-band), after accounting for events that were detected by several telescopes simultaneously (Table 2). We consider subcomponents to be part of a single burst if they are separated by no more than 100 ms from each other. This choice is driven by the observed wait-time distribution8,20 of FRB 20201124A. Among our detections is the highest-fluence burst ever detected from this source (fluence F ≈ 1,600 Jy ms; Fig. 2). Fourteen bursts were detected simultaneously at more than one dish. No bursts were discovered at P-band (300–364 MHz) or at C-band (4,550–4,806 MHz), and none of the bursts discovered at L-band had a counterpart in the other frequency bands (Methods and Extended Data Table 1). During our campaign, Apertif21 reported the detection of two bursts from FRB 20201124A, one of which we detected as well (B23-wb), whereas the other occurred when Wb was observing at P-band. The dynamic spectra, time series and spectra for a subset of bursts are shown in Fig. 2 (the full set is shown in Extended Data Figs. 1–3). Almost half of the bursts (18/46) were composed of two or more components, most of which (13/18, that is ~70%) show the canonical ‘sad trombone’ effect22 in which burst emission at lower frequencies arrives later in time, even after correcting for the dispersive delay. We used the structure-optimizing code DM-phase23 on one of our brightest multi-component bursts (B13-o8; Fig. 2) to obtain a dispersion measure DM = 410.8 ± 0.3 pc cm−3 (Methods and Extended Data Table 2). This DM is used throughout the rest of the analysis for all bursts. The burst properties listed in Extended Data Table 3 were obtained from incoherently dedispersed data, except for the time of arrival (TOA), which was measured using coherently dedispersed data products when baseband data were available, that is, for all bursts detected by Tr, Wb and O8. For the St bursts, incoherently dedispersed data products were used for the TOAs (Methods). Particular care was given to the computation of the burst fluences because the large brightness and strong scintillation of the bursts systematically affects the recorded data through saturation effects (Methods and Extended Data Figs. 4 and 5). The median scintillation bandwidth νs, scaled to a canonical observing frequency of 1 GHz, \({\nu }_{s}^{1{{{\rm{GHz}}}}}=0.4\pm 0.1\,{{{\rm{MHz}}}}\), is consistent with previous observations24. Furthermore, we measured the characteristic temporal separation between individual burst components to be \(\delta t=4.{1}_{-2.1}^{+4.4}\,{{{\rm{ms}}}}\) (Extended Data Fig. 6). This value is a factor 2–10 larger than the one reported22 for FRB 20121102A.

Table 2 Observing hours and number of bursts detected per active period and dish
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Fig. 2: Subset of bursts detected in this campaign.
figure 2

a–d, Dedispersed dynamic spectra for St (a), Tr (b), O8 (c) and Wb (d). For Tr, O8 and Wb, the spectra were coherently dedispersed using SFXC, whereas the spectrum for St was incoherently dedispersed with DSPSR as no baseband data were available. The horizontal white lines with the red marker on the left denote the frequency ranges that were flagged because of RFI. For visualization, the data were capped at the 98th percentile. e–h, Frequency-averaged time series for St (e), Tr (f), O8 (g) and Wb (h). The pulse ID is given in the top left corner. The time and frequency resolutions used for the plots are given in the top right corner. i-l, Spectra of the time-averaged ‘on-time’ of the pulses for St (i), Tr (j), O8 (k) and Wb (l). This on-time is indicated by the coloured horizontal bar under each time series. The colour encodes the telescope at which the pulse was detected: purple for St, orange for Tr, green for O8 and blue for Wb. The same on-time was used to compute the fluences in Extended Data Table 3. The full set of bursts is shown in Extended Data Figs. 1–3.

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The vast majority of bursts were detected during two time ranges, lasting roughly 60 and 40 d each (Fig. 1 and Extended Data Table 3). Figure 3a shows the distributions of the burst spectral energy densities Eν during the first activity window compared with those observed with FAST during the same time range20 (MJD 59,305–59,363). The energy distribution of our bursts shows no break, so we fitted a simple power law to the cumulative burst rate as a function of spectral energy density, \(R( {>} {E}_{\nu })\propto {E}_{\nu }^{\gamma }\), using a least-squares technique (Methods). Jointly fitting the O8 and St data yields a power-law index γ = −0.48 ± 0.11 ± 0.03 (where the first error is the formal fitting uncertainty and the second error is derived from bootstrapping; Methods). This value is a factor 3 lower (flatter) than that observed by FAST20 for Eν > 5.9 × 1029 erg Hz−1 (Methods), where γ2 = −1.5 ± 0.1 ± 0.1. The value of γ2 was derived by fitting a broken power law to the data split into energy bins20, an approach that is not applicable for the relatively low number of bursts we detected. Therefore, for better comparability, we refitted the FAST data following our technique (Methods) to find γFAST = −1.947 ± 0.011 ± 0.063, which agrees with γ2 within 2σ. The bursts and the associated cumulative burst rates that we detected with O8, Wb and St during the second activity window after MJD 59,602 are shown in Fig. 3b. We fitted the data from Wb and St in the same way as described above and found power-law slopes γSt = −1.43 ± 0.09 ± 0.41 and γWb = −0.85 ± 0.05 ± 0.09 for the St and Wb bursts, respectively. These energy distribution slopes are steeper than that from the first activity window but are still much flatter for the Wb data than that of the high-energy tail in the FAST data20. The slope of the St data during this epoch agrees with the one from Wb within the summed 1σ uncertainties but also agrees with γ2 from ref. 20. Since the sensitivity thresholds of O8, Wb and St during the second activity window are comparable, we combined the data from all three telescopes from both activity windows (excluding the data from St during the first window as its detection threshold was a factor ~3 higher at that time; Methods) to get an estimate of the average slope γav of the energy distribution around an observing frequency of 1.3 GHz. Fitting the combined data yields γav = −1.09 ± 0.03 ± 0.06 (Fig. 4).

Fig. 3: Burst spectral energy density distribution in different epochs.
figure 3

a, Cumulative burst rate distribution measured during the time range MJD 59,305–59,363 in comparison to those reported by FAST during the same epoch20. The vertical green and purple dotted lines indicate the completeness threshold for O8 and St, respectively, beyond which we jointly fitted the data with a simple power law (grey solid line). Pale coloured data points were excluded from the fit. The vertical black dotted and dash-dotted lines indicate the threshold beyond which the FAST data no longer follow a simple power law, as determined with the Python package powerlaw, and the break point of the broken power law as determined by Xu et al.20, respectively. We fitted simple power laws to the data beyond the respective limits, as shown by the solid and dotted black lines. b, Coloured circles indicate the burst rates observed after MJD 59,602, as measured by Wb (blue), St (purple) and O8 (green). The coloured lines are the respective power-law fits. We did not fit the O8 data as there were too few detections. Note that in this time range, the St SEFD improved by a factor of ~3 compared to the data taken in 2021, lowering the completeness threshold compared to what is shown in a. For comparison, we also show the burst rates measured by O8 and St during the first activity window (pale coloured squares, same as a). The quoted uncertainties are composed of the statistical 1σ error of the least-squares fit (first error) and the 1σ uncertainty on the fitted slope from bootstrapping.

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Fig. 4: Burst energy distribution averaged over both activity windows.
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We excluded the data from St from the first activity window because of the large discrepancy in the detection threshold compared to the other stations. The solid black line denotes the best-fitting power law.

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Discussion

Lensing cannot explain FRB 20201124A’s high-energy bursts

The highest-energy bursts (Eν ≳ 1031 erg Hz−1) observed from FRB 20201124A occurred at a much higher rate than expected based on the energy distribution of lower-energy bursts. One possible explanation is that burst brightness is boosted by propagation effects, such as lensing in an inhomogeneous plasma25 local to FRB 20201124A or an intervening gravitational potential26. However, if all bursts were affected equally by such a lens, the energy distribution would be shifted as a whole and no difference between the power-law slopes of low- and high-energy bursts would be seen. Moreover, in the limit of strong magnification with magnification factor μ ≫ 1, the lensing cross section σ(μ) ∝ μ−2 would be independent of the lensing potential26,27. Thus, if the brightest bursts that we see were caused by lensing, we would expect γ ≈ −2, which is inconsistent with our measurements. If the amplification due to plasma lensing has a temporal dependence28, one would expect a burst rate distribution that is variable in time. However, as shown in Fig. 1, we detected high-energy bursts throughout the entirety of the time range that was covered by FAST, and there is no evidence for a variable energy distribution within the time range MJD 59,305–59,363. Thus, we conclude that the flattening of the burst energy distribution at high energies is most probably not a propagation effect. Rather, it more probably indicates that there is a difference in the emission mechanism, emission site or beaming angle between low- and high-energy bursts.

FRB 20201124A as a link between repeaters and non-repeaters

Burst rates as a function of energy have been reported for several repeating FRB sources, with the measured slopes of the fitted power-law distribution ranging from as steep as −4.9 (ref. 9) to as flat as −0.5 (ref. 11). The slopes vary both as a function of time and as a function of the energy range that is considered. In general, the slope is apparently flatter towards lower energies11,20 (Eν ≲ 1029 erg Hz−1). However, this can often be attributed to a lower completeness near the detection threshold of the telescope that is measuring the bursts. Nonetheless, in some cases, the low-energy turnover appears to be intrinsic to the emission process7,8,20. The slope usually steepens towards the high-energy end (Eν ≳ 3 × 1029 erg Hz−1) of the distribution8, but a slight gradual flattening of the burst rates for very high-energy bursts (Eν ≳ 1031 erg Hz−1) has been observed for at least one source10,11. Here we observe a strong flattening of the burst rate slope in a previously unexplored ultra-high-energy range for FRB 20201124A.

Unaffected by the limited bandwidth of our observations (Methods), the average high-energy slope that we measure (Fig. 4) broadly agrees with that found for non-repeating FRBs14, and our value also agrees with various empirical models12,13 that find a power-law slope γ ≈ −1 for non-repeating FRBs. This indicates that the distribution of the ultra-high-energy tail (Eν ≳ 1031 erg Hz−1) of FRB 20201124A bursts resembles that of non-repeaters, whereas the low-energy bulk of the bursts does not. Thus, we are seeing both repeater- and non-repeater-like behaviour from a single FRB source.

For apparently non-repeating FRBs, we may be observing bursts from a similar high-energy tail as what we report here for FRB 20201124A. As such bursts are extremely rare, occurring once per hundreds to thousands of hours or more (we see no high-energy cutoff in the burst energy distribution), such a source would appear to be non-repeating.

However, the low- and high-energy ends of the burst distribution for FRB 20201124A are currently statistically indistinguishable in terms of burst morphology, width and bandwidth. This contradicts what has been shown for the repeater and non-repeater populations as a whole4. A careful comparison of, for example, the polarimetric properties of high-energy bursts from FRB 20201124A with those of non-repeaters may shed further light on their possible connections. If non-repeaters are indeed drawn from the high-energy tail of a repeater’s burst energy distribution, then approximately 1,000 h of observing time, or more, is required to detect a repeat burst from a given source. Very few FRB sources have been observed in this way. On the other hand, if the observed flattening is a peculiarity of FRB 20201124A—and if the overall population of FRBs generally follows the steeper rate distribution as observed by FAST (and assuming all FRBs repeat)—then we can extrapolate this rate to the spectral energy density of our brightest burst, B06-st. Assuming a similar energy distribution as that observed by FAST, the rate of this burst is approximately 10−6 h−1.

FRB 20201124A contributes strongly to the overall sky rate

The ASKAP FRB survey29 was conducted in a similar frequency band as our observations. Based on modelled number counts30 for 20 ASKAP bursts, N(>F) = 20(F/50 Jy ms)−1.5, and the total exposure (5.1 × 105 deg2 h) of the ASKAP survey, an FRB all-sky rate above a fluence F > 100 Jy ms, Rsky(F > 100 Jy ms) = 5 × 103 sky−1 year−1 was reported29. During our campaign, we found 17 bursts from FRB 20201124A above this threshold, which, considering the amount of time spent on source, corresponds to 1.3% of Rsky(F > 100 Jy ms). Moreover, considering only the three brightest bursts in our sample (those with F > 500 Jy ms), the contribution of FRB 20201124A to Rsky(F > 500 Jy ms) during its active state is even twice as high, at 2.6%. Since the spectral energy distribution that we observe is shallower than the assumed power-law slope of −1.5 used in the modelled number counts30, these fractional contributions are only a lower limit. This demonstrates that hyperactive repeaters may account for a substantial fraction of all observed FRBs.

FRB 20201124A would be observable even at very high redshift

The emission from FRB sources is subject to dispersion, scattering and Faraday rotation as it travels through the cold plasma of interstellar and intergalactic space. As such, the signals carry the imprints of the matter density structure along a particular line of sight, allowing measurements of, for example, galaxy halo matter densities31. As the DM provides a complete measurement of the free electrons along the path, FRBs have already been used to trace the diffuse intergalactic medium and, thereby, have contributed to solving32 the ‘missing baryon problem’. Furthermore, it has been suggested33 that individual, well-localized, gravitationally lensed, repeating FRBs could be used to measure the Hubble constant due to the change in the delays between the arrival times of lensed versions of subsequent bursts. As such, FRBs are proven cosmological probes with great future potential. How far back in cosmic history we can probe the Universe with FRBs is directly related to their energetics.

Assuming a burst bandwidth of 1 GHz, recent empirical models of the FRB population14 find a characteristic spectral energy cutoff of \({{{{{E}}}}}_{\nu }^{{{{\rm{char}}}}}=2.3{8}_{-1.64}^{+5.35}\times 1{0}^{32}\,{{{\rm{erg}}}}\,{{{{\rm{Hz}}}}}^{-1}\). The most energetic burst that we report here, B06-st, had an isotropic-equivalent spectral energy of \({{{{{E}}}}}_{\nu }=3.{1}_{-0.7}^{+0.6}\times 1{0}^{32}\,{{{\rm{erg}}}}\,{{{{\rm{Hz}}}}}^{-1}\), consistent with the estimated \({{{{{E}}}}}_{\nu }^{{{{\rm{char}}}}}\). For the FAST data shown in Fig. 3, the completeness threshold20 was 53 mJy ms. Thus, given the spectral energy that we measured for B06-st, such a burst would have been observable out to redshift \(z=12.{9}_{-1.5}^{+1.4}\) with a telescope such as FAST.

At that redshift, the emitted frequency of the pulse would need to be ~19 GHz to be observable at 1.4 GHz from Earth. This is plausible, considering that FRB 20121102A has been detected at 8 GHz (ref. 34), which corresponds to an emission frequency of ~10 GHz at the source given its redshift35 z = 0.19273. Similarly, to be observable in the CHIME band (400–800 MHz), pulses emitted at redshift z = 12.9 would need to be emitted at ~8 GHz at the source. Employing the Macquart relation32, such a high redshift would imply DM ≈ 5,700 pc cm−3. This is close to double the DM seen from any other FRB1 to date. The largest measured FRB redshift6 is currently z = 1.016 ± 0.002. Nevertheless, purely from an energetics point of view, it is not implausible to expect hyperactive FRBs like FRB 20201124A at redshifts beyond 3, allowing for novel cosmological studies using repeat bursts. However, it has been pointed out36 that at such high redshifts, individual bursts might be subject to scatter broadening as large as 300 ms at 1 GHz due to intervening galaxies. This would reduce the detectability of high-redshift FRBs.

Conclusions

Using four small 25–32 m class radio telescopes, we present a multi-frequency observing campaign targeting the hyperactive, repeating FRB 20201124A. This campaign is unprecedented in terms of the amount of observing time spent on source, and we conclude that ultra-high-energy bursts (Eν ≳ 1031 erg Hz−1) occur much more frequently than would have been expected based on previous observations of lower-energy bursts20. We argue that our detected bursts are intrinsically higher in energy, as opposed to being boosted in brightness by propagation effects like lensing.

Given our results, FRB 20201124A generates bursts spanning at least 6 orders of magnitude in spectral energy density, a similar span to the Galactic magnetar SGR 1935+2154 (ref. 37) but reaching much higher energies. Moreover, the burst energy distribution flattens towards the highest-observed energies. This high-energy distribution resembles that seen from the population of non-repeating FRBs as a whole, suggesting that observations of apparently non-repeating FRBs may simply be sampling the rare high-energy events of sources that are capable of repeating. The highest-energy bursts may originate from a separate emission mechanism or emission region at the progenitor source. Further evidence for such a scenario might be found by comparing the polarimetric properties of low- and high-energy bursts.

We also showed that FRB 20201124A’s extremely energetic bursts, although rare, mean that a similar hyperactive repeating source would be detectable out to very high redshift (z = 12) using the world’s most sensitive radio telescopes, although considerable on-sky time would be necessary to detect repeat bursts.

Lastly, the large number of high-fluence bursts (F > 500 Jy ms) that we detected from FRB 20201124A constitute an important fraction (at least ~2.6%) of the estimated all-sky FRB rate29,30. This shows that, in this high-fluence range, the all-sky rate is significantly influenced by a small number of hyperactive sources.

Methods

Observations and data reduction

Onsala, Westerbork and Toruń

O8, Wb and Tr recorded raw voltages (referred to as baseband data, providing both the amplitude and phase of the electromagnetic signal) in VDIF format38 using the local DBBC2 and Flexbuff systems. Both left and right circular polarizations were sampled at the Nyquist rate and recorded as 2-bit samples. Depending on observing frequency and set-up, the recorded bandwidth varied between 64 and 512 MHz and was divided into sub-bands of 8, 16 or 32 MHz (Table 1). All observations made by O8 were conducted at L-band (between 1,202 and 1,714 MHz for various bandwidths). Wb covered P-band (300–364 MHz) when co-observing with the O8 and L-band when observing on its own. Tr observed at C-band (4,500–4,800 MHz for various bandwidths) when co-observing with another dish, or otherwise, it also covered a part of L-band. For the exact frequency ranges and observed hours per station, see Table 1.

All the data from Wb and O8 and a subset of the data from Tr were transferred using the internet to a dedicated processing machine, ebur, at the Onsala Space Observatory in Sweden. The processing pipeline37 performed the following steps:

  • Generate total-intensity (Stokes I) filterbanks (8-bit encoding) with various time and frequency resolutions from the baseband data.

  • Search the filterbank data for bursts using Heimdall.

  • Classify the candidates found by Heimdall using the machine learning classifier FETCH39.

  • Manually inspect the diagnostic plots generated by FETCH.

The time and frequency resolutions of the total-intensity filterbanks varied depending on the observing frequency: 1.024 ms and 7.8125 kHz at P-band, 0.128 ms and 62.5 kHz at L-band, and 0.064 ms and 500.0 kHz at C-band. These values were chosen as a compromise between the Nyquist limit and the maximal residual DM smearing in the lowest frequency channel of each observing band. In the Heimdall search, the DM range over which the search was conducted was limited to DMFRB ± 50 pc cm−3, where \({{{{{\rm{DM}}}}}_{{{{\rm{FRB}}}}}}=413.0\) pc cm−315. To mitigate the radio-frequency interference (RFI), we implemented a static frequency mask that was obtained through a manual inspection of parts of the data. The detection threshold was set to 7σ, which translates to fluence limits of roughly 42, 7 and 3 Jy ms at P-, L- and C- bands, respectively. When classifying the Heimdall-generated burst candidates as either astronomical signals or RFI, we used FETCH models39 a and h with a probability threshold of 0.5.

Stockert

The recording set-up and burst detection pipeline at St were developed independently from the one for O8, Wb and Tr, and hence, it uses different tools and detection thresholds. At St, we observed in the frequency range 1,332.5–1,430.5 MHz, recording total-intensity 32-bit data with a pulsar fast Fourier transform back end40. The data were initially stored as PFFTS files, which is the instrument’s specific format. These were subsequently converted to the standardized filterbank format using the tool filterbank, which is part of the SIGPROC package41. The resulting data had time and frequency resolutions of 218.45 μs and 586 kHz and were stored as 32-bit floats. We used the tools rfifind, prepsubband and single_pulse_search from the PRESTO package42 to subsequently remove RFI, incoherently dedisperse the data (using DM = 412.0 pc cm−3) and search for bursts. Between 24 November 2021 and 8 February 2022, the St dish underwent an upgrade, reducing the system equivalent flux density (SEFD) by almost a factor of 3 (Table 1), thereby improving the sensitivity of the dish substantially. We used a detection threshold of 8σ in the pulse searches, which corresponds to fluence limits of 21 and 7 Jy ms before and after the upgrade, respectively.

Digitization artefacts

As discussed above, we recorded 2-bit baseband data at O8, Wb and Tr. The limited dynamic range of these samples in combination with the large fluences of some of the bursts (signal-to-noise (S/N) ratio ≈ 100) leads to digitization artefacts in the data whereby power is ‘scattered’ in time and frequency43. Most notably this manifests as ‘depressions’ in the data around the times of the bursts (for example, burst B08-o8 in Extended Data Fig. 4). A similar digitization artefact was also found and described44 for a burst from FRB 20201124A detected at 2.2 GHz. As a result, the measured overall fluences will be underestimated. To quantify this effect and compensate for it, we measured the fluences from data products generated from the baseband data in three different ways. For case i, we created coherently dedispersed total-intensity filterbanks with SFXC, the Super FX Correlator45. These filterbank data were subsequently converted to archive files with DSPSR, the standard pulsar software package46. For case ii, we used the tool digifil that is part of DSPSR to generate total-intensity filterbanks (no dedispersion applied), which we then converted to archives with DSPSR (applying incoherent dedispersion). For case iii, we applied a scattered power correction (SPC) algorithm47 that is part of PSRCHIVE48,49 to the archives generated in case ii.

The reason for implementing case iii is that digifil applies a 2-bit correction to the baseband data43 that effectively overcompensates for the limited dynamic range of bright bursts. The effect is that the overall measured fluence is overestimated compared to the real fluence. Extended Data Fig. 4 compares the burst profiles for B08-o8 generated in these three ways. The profile generated from SFXC dips below the mean of the off-pulse region between components. In contrast, the profile generated by the regular digifil stays above the mean. Even though this could be intrinsic to the pulse, that the profile appears to begin/rise early compared to the SFXC profile indicates that there is an overall ‘skirt’ around the burst that is due to the 2-bit correction implemented in digifil. The profile generated from the archive corrected with the SPC algorithm (case iii) does not show this skirt and also does not drop below the mean between components. Thus, we conclude that this data product provides the best estimate of the true fluence of the burst. Extended Data Fig. 5 shows a relative comparison of the measured fluences scaled by the SPC-corrected fluences. Overall, compared to the case iii fluences, the case ii fluences (uncorrected digifil) are 5–10% higher, whereas the case i fluences (SFXC generated) are lower by a factor 1.5–2.0. There is no clear fluence threshold above which the quantization limitation shows its effects. Rather, it is the range in the time–frequency space over which power is concentrated that determines whether or not ‘depressions’ occur. A single bright scintil can result in scattered power whereas the overall band-integrated fluence is not higher compared to other bursts. Although making these corrections is important for achieving the most accurate fluences possible, note that the factor of 2 uncertainties in the burst energies do not affect the conclusions that we draw in this paper.

For the data recorded at St, the 2-bit quantization limitations did not apply, and we measured the burst properties directly from the recorded filterbanks and the archive files generated for case ii.

Analysis and results

DM optimization

We used the structure-optimizing code DM-phase23 on one of our brightest multi-component bursts (B13-o8, Fig. 2) to obtain DM = 410.8 ± 0.3 pc cm−3 (DM-phase uses a DM constant of 1/0.000241 GHz2 cm3 pc−1 μs). To assess any potential evolution of the DM over the roughly 1-year time span of our observing campaign, we ran DM-phase on nine other bright, multi-component bursts detected throughout the campaign. We did not measure any significant evolution nor any DM values that disagree beyond their respective 2σ uncertainties with our initial measurement (Extended Data Table 2). Any DM offsets on the order of our measurement uncertainties have only a negligible impact on the values listed in Extended Data Table 3 (the most notable would be a difference in the TOA of ~1.2 ms for a DM offset of 0.5 pc cm−3). Thus, given the challenges in measuring the ‘correct’ DM of an FRB50, we used this DM value in the rest of the analysis for all detected bursts.

The effect of bandwidth on the number of detected bursts

During our campaign, we detected bursts spanning more than an order of magnitude in spectral energy Eν. A power-law slope like the one observed with FAST20 would require a difference in rate of a factor of ≳102 between the high- and low-energy bursts, that is a factor ≳10 larger than what we find. Previous studies11 of FRB 20121102A reported that low-energy bursts (Eν ≲ 3 × 1029 erg Hz−1) were typically narrower in bandwidth than high-energy bursts. In our case, this could imply that due to our limited bandwidth of ~100 MHz, we might miss low-energy bursts as they might be bright outside of our observing band. In contrast, the high-energy bursts are sufficiently broadband to always fall within our frequency window. Conversely, the FAST L-band receiver covers a frequency range of 1.0–1.5 GHz, and the median bandwidth20 of the bursts (185 MHz) indicates that bursts with different central frequencies appear in different parts of the FAST L-band so that these may be outside our limited frequency range. However, the cumulative burst rate that we derive for our ‘low-energy’ bursts (Eν ≈ 1031 erg Hz−1) is in good agreement with similarly energetic bursts detected with FAST20 in the same time range. Therefore, we exclude the possibility that we missed a large fraction of bursts because of a frequency ‘windowing’ effect. Even if we had missed some of the low-energy bursts because of RFI, we deem it highly unlikely that we had missed 90% of the possible low-energy bursts. Instead, we conclude that we detected a factor of ~10 ‘too many’ bursts compared to what one would expect from the FAST slope20 in the spectral energy range ~1030–1032 erg Hz−1 during this period.

Burst properties

Except for the TOA, all burst properties listed in Extended Data Table 3 were obtained from the archive files that were corrected with the SPC algorithm (case iii above). First, we manually determined a flagging mask using the PSRCHIVE tools pazi and psrzap. This mask excises RFI and discards 5% of bandwidth at the top and bottom of each sub-band. We subsequently downsampled the data to time and frequency resolutions of 256 μs and 500 kHz, respectively, inspected the dedispersed burst profiles by eye and manually selected the start and stop bins of burst components. For each of these (component-based) time ranges, we computed the two-dimensional autocorrelation function in time and frequency. The resulting autocorrelation spectra and time series were fitted separately with a one-dimensional Gaussian to determine the component width in time (the time Gaussian) and in frequency (the frequency Gaussian). To measure the scintillation bandwidth for each burst component, we first subtracted the frequency Gaussian from the autocorrelation spectra and then fitted a Lorentzian to the central component of the residuals. The half-width at half-maximum of this Lorentzian is an estimate of the scintillation bandwidth νs (ref. 51). We list these values scaled to a frequency of 1 GHz in Extended Data Table 3. For the scaling of νs with central frequency νc, \({\nu }_\mathrm{s}\propto {\nu }_\mathrm{c}^{\alpha }\), we adopted a canonical power-law slope α = 4.0. The median of \({\nu }_{\mathrm{s}}^{1\,\mathrm{GHz}}=0.4\pm 0.1\,{\rm{MHz}}\) is consistent with earlier measurements24. Finally, we took the burst frequency extent to be the total observing bandwidth, unless twice the full-width at half-maximum (FWHM) of the frequency Gaussian was less than 75% of the total bandwidth (BW, that is 2 × FWHM < 0.75 × BW), in which case we determined by eye the burst frequency extent. This approach was chosen to ensure that no flux was lost due to flagged channels (which in either case would lead to an underestimated FWHM of the frequency Gaussian). The fluences were computed by first determining the flux densities per time bin using the radiometer equation52. We assumed a constant gain and constant system temperature, yielding the SEFDs listed in Table 1. Subsequently, we summed over the manually selected on-time region. From the fluences, we then determined the isotropic-equivalent spectral luminosity of the bursts using the known luminosity distance53 DL = 453 ± 0.1 Mpc (z = 0.098) of FRB 20201124A.

Burst times of arrival

It is not uncommon for some data loss to occur during recording (of the order of a few seconds accumulated over a 15 min recording). digifil has currently no functionality to detect and account for such data loss, which eventually leads to inaccurate timestamps in the generated filterbanks. Having been developed for correlating interferometric observations, SFXC has the required functionality to compensate for such losses. Therefore. we used SFXC to generate coherently dedispersed filterbanks (SFXC uses the same DM constant as DM-phase) to compute the TOA of each burst component. We fitted multi-component Gaussians to the frequency-averaged profile (time resolution of 64 μs) of each burst and took the centre of each Gaussian component as the component’s TOA. The timestamps in the SFXC-generated filterbanks were referenced to the geocentre. The reference frequency used for coherently dedispersing the pulses was the centre frequency of the highest sub-band. In Extended Data Table 3, the listed TOAs are referenced to the barycentre (using the barycentric dynamical time) at infinite frequency. The times designate either the middle between the first and the last component of a multi-component burst or the centre of the fitted Gaussian for single-component bursts. Extended Data Fig. 6 displays the log-normal distribution of time separation between components of multi-component bursts. The Gaussian fit yields a characteristic separation of \(\delta t=4.{1}_{-2.1}^{+4.4}\,{{{\rm{ms}}}}\) between burst components, which is a factor 2–10 larger than that reported22 for FRB 20121102A.

Burst rates

The distribution of bursts that we detected shows no evidence of a broken power law, which is why we fitted a simple power law for the cumulative burst rate as a function of spectral energy density, \(R( > {E}_{\nu })\propto {E}_{\nu }^{\gamma }\), using a least-squares method. For the fitting, we set conservative 15σ completeness limits (assuming a canonical burst width of 1 ms) of 10 and 39 Jy ms for O8 and St, respectively, and we adopted a 20% uncertainty on the derived spectral energy density. To better estimate the uncertainties of the fitted parameters, we fitted the entire dataset and we also ran a bootstrapping algorithm for which we randomly selected 90% of the data points (without replacement) and performed the least-squares fit on this subset of data. We repeated the bootstrapping step 1,000 times and took the standard deviation of the fitted parameters as the additional bootstrapping error. Jointly fitting the O8 and St data yielded a power-law index γ = −0.48 ± 0.11 ± 0.03. We also fitted the contemporaneous FAST data20 in a similar fashion. We first applied our definition of a unique burst to the FAST data by summing fluences of bursts that are separated by less than 100 ms. This affected a total of 148 bursts detected by FAST. We then determined the threshold \({E}_{\nu }^{\min }\) below which the high-energy part of the FAST bursts no longer followed a simple power law using the Python powerlaw54 package and fitted the data for which \(E > {E}_{\nu }^{\min }=1.7\times 1{0}^{30}\,{{{\rm{erg}}}}\,{{{{\rm{Hz}}}}}^{-1}\), in the same way as described above. We found γFAST = −2.254 ± 0.019 ± 0.114, which is even steeper than the reported20 γ2 = −1.5 ± 0.1 ± 0.1. Xu et al.20 found the break point between the low- and high-energy ranges of their burst distribution to be ~1.1 × 1038 erg ( = 5.9 × 1029 erg Hz−1 using their median bandwidth of 185 MHz to convert from energy to spectral energy density), roughly a factor 3 lower than our adopted \({{{{{E}}}}}_{\nu }^{\rm{min}}\). Using the break point from Xu et al.20 as the limiting energy for the fit, we found γFAST = −1.947 ± 0.011 ± 0.063, which agrees with γ2 within 2σ.

For completeness, we also fitted the FAST data without summing components that are separated by less than 100 ms. This yielded values for γFAST of −2.318 ± 0.018 ± 0.116 (when determining the power-law break point with the software powerlaw) and −1.997 ± 0.011 ± 0.067 (using the published break point20), which agree within the uncertainties for the values found when applying our definition of a unique burst.

The bursts and the associated cumulative burst rates that we detected with O8, Wb and St after MJD 59,602 are shown in Fig. 3b. We fitted the data from Wb and St in the same way as described above, using, however, a 15σ completeness limit of 14 Jy ms for both telescopes (because of the upgrade at St discussed above). We did not fit the bursts detected at O8 separately because of the low number of detections. The burst rates we found are γWb = −1.43 ± 0.09 ± 0.41 and γSt = −0.85 ± 0.05 ± 0.09 for the Wb and St bursts, respectively.

Implications of non-detections at P- and C-band

As listed in Table 1, we spent about 650 h observing FRB 20201124A at P-band with Westerbork, and another 244 h observing at C-band with Toruń. If we consider the time windows with enhanced activity only, that is MJD 59,305–59,363 and MJD 59,602–59,641 (Fig. 1), these numbers reduce to 274 and 36 h for P-band and to 115 h and 86 h for the C-band observations, respectively. During the same two time ranges, we spent a total of 513 and 351 h of non-overlapping time on source at L-band. The completeness thresholds for the P- and C-bands are ~91 and ~5 Jy ms, respectively. Extended Data Table 1 lists the number of bursts that we detected at L-band above a given fluence threshold; once assuming a flat spectrum for the bursts and once assuming a steep spectrum with α = −1.5. Given the number of bursts detected at L-band and the time that each band was observed for, we also list the number of bursts that we would have expected to detect at P- and C-bands if we assume that the activity rates are the same across all observed frequencies. The expected number of bursts ranges between 0.6 and 7.6, depending on the observing band and epoch considered. That we did not detect a single burst outside L-band clearly shows that the bursts are narrowband in nature55,56 and that the activity rates and, potentially, even the activity windows are frequency dependent57,58. Alternatively, besides the spectral index, the emission process might be such that the amplitude of the bursts is modulated as a function of frequency, peaking in the range 1,200–1,700 MHz during our observations. Whatever the modulation mechanism might be (intrinsic to the source or a propagation effect such as refractive scintillation), it has to be time variable as the source was first detected by CHIME/FRB in the band between 400 and 800 MHz (ref. 15).

The notch in burst B08

We note a curious feature in burst B08, which is highlighted in Supplementary Fig. 1 for B08-tr (this can also be seen in Extended Data Fig. 4, which shows the same burst detected by O8, B08-o8). We call this sudden, sharp dip in flux density a ‘notch’. The B08 notch, lasting ~0.5 ms, is somewhat reminiscent of the notches seen in the average profiles of a few very bright radio pulsars59, which also happen to have exceptionally wide pulse profiles that cover a large range of rotational phases. However, pulsar notches are double notches (two closely spaced dips), whereas the limited S/N ratio of B08 makes it impossible to see more subtle features in the notch profile. This limits the degree to which we can compare the two phenomena.

For pulsars, the notches have been modelled as coming from an absorbing region in an outer magnetosphere that co-rotates with the neutron star60. This model requires that the pulsar has both emitting and absorbing regions at heights that are a large fraction of the light cylinder radius. In another model61, the pulsar itself is the absorber and the emission is a combination of inward- and outward-travelling components.

FRBs often show quite well-defined sub-bursts with cessation of emission between these components22. This is also clearly visible in B08 (Supplementary Fig. 1, left panel). However, the notch we detect in B08 appears qualitatively different. It is a sudden, sharp dip on the shoulder of a bright component, much like what is seen in pulsar notches (Supplementary Fig. 1, right panel). We speculate that notches may be generally visible in the profiles of high S/N ratio, wide FRBs observed at high time resolution, and that this effect could plausibly probe magnetospheric physics, assuming such an origin for FRB emission. Furthermore, if notches can be detected in several bursts from a single repeater, then these could provide a stable marker of rotational phase that could allow the spin rate of the neutron star to be determined. This assumes that the absorber is locked in rotational phase with respect to the neutron star. For pulsars, the notches indeed occur at stable rotational phases, which can be explained by the models60,61 mentioned above. FRB notches would also potentially be excellent reference points for determining accurate DMs. As can be seen in Supplementary Fig. 1, the notch occurs at the same time across the observed radio-frequency band for the DM we have chosen to dedisperse all bursts in the paper.