# Dense Forests of Microshots in Bursts from FRB 20220912A

Danté M. Hewitt,1 Jason W. T. Hessels,1,2 Omar S. Ould-Boukattine,2,1 Pragya
Chawla,1 Ismaël Cognard,3,4 Akshatha Gopinath,1 Lucas Guillemot,3,4 Daniela
Huppenkothen,5,1 Kenzie Nimmo6 and Mark P. Snelders2,1
1Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science
Park 904, 1098 XH, Amsterdam, The Netherlands
2ASTRON, Netherlands Institute for Radio Astronomy, Oude Hoogeveensedijk 4,
7991 PD Dwingeloo, The Netherlands
3Station de Radioastronomie de Nançay, Observatoire de Paris, PSL University,
CNRS, Université d’Orléans, F-18330 Nançay, France
4Laboratoire de Physique et Chimie de l’Environnement et de l’Espace LPC2E
UMR7328, Université d’Orléans, CNRS, F-45071 Orléans, France
5SRON Netherlands Institute for Space Research, Niels Bohrweg 4, 2333 CA,
Leiden, Netherlands
6MIT Kavli Institute for Astrophysics and Space Research, Massachusetts
Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We report on exceptionally bright bursts ($>$400 Jy ms) detected from the
repeating fast radio burst source FRB 20220912A using the Nançay Radio
Telescope (NRT), as part of the ECLAT (Extragalactic Coherent Light from
Astrophysical Transients) monitoring campaign. These bursts exhibit extremely
luminous, broadband, short-duration structures ($\sim 16$ $\mu$s), which we
term ‘microshots’ and which can be especially well studied in the NRT data
given the excellent signal-to-noise and dynamic range (32-bit samples). The
estimated peak flux density of the brightest microshot is 450 Jy. We show that
the microshots are clustered into dense ‘forests’, by modelling them as
Weibull distributions and obtaining Weibull shape parameters of approximately
0.5. Our polarimetric analysis reveals that the bursts are nearly 100 %
linearly polarised; have $\lesssim 10$ % circular polarisation fractions; a
near-zero average rotation measure of 0.10(6) rad m-2; and varying
polarisation position angles over the burst duration. For one of the bursts,
we analyse raw voltage data from simultaneous observations with the Westerbork
RT-1 single 25-m dish. These data allow us to measure the scintillation
bandwidth, 0.30(3) MHz, and to probe the bursts on (sub-)microsecond
timescales. Some important nuances related to dedispersion are also discussed.
We propose that the emission mechanism for the broadband microshots is
potentially different from the emission mechanism of the broader burst
components which still show a residual drift of a few hundred MHz ms-1 after
correcting for dispersion using the microshots. We discuss how the observed
emission is phenomenologically analogous to different types of radio bursts
from the Sun.

###### keywords:

fast radio bursts – radio continuum: transients

††pubyear: 2015††pagerange: Dense Forests of Microshots in Bursts from FRB
20220912A–C

##  1 Introduction

Fast radio bursts (FRBs) are coherent radio transients, typically lasting a
few milliseconds. Their extragalactic origin was inferred from their excess
dispersion measures (DMs) and has been confirmed by multiple localisations to
a diverse set of host galaxies (for a recent review of FRBs, see Petroff et
al., 2022). A small fraction ($\sim 2.6$ %; Chime/Frb Collaboration et al.,
2023) of known FRBs are confirmed repeaters (Spitler et al., 2016) that emit
multiple bursts — more often than not, sporadically and infrequently. These
repeater bursts are, on average, longer in duration and narrower in observed
emission bandwidth compared to the apparently non-repeating FRBs (Pleunis et
al., 2021). Conversely, it has recently been demonstrated that the repetition
rates of repeaters and the upper limits on repetition from apparently non-
repeaters are not clearly distinct, after exposure and sensitivity corrections
(Chime/Frb Collaboration et al., 2023). There are, however, some anomalously
prolific repeaters that have appeared to suddenly awaken from quiescence,
e.g., FRB 20201124A (Chime/Frb Collabortion, 2021). A non-negligible fraction
of apparently non-repeating sources may thus in fact be repeaters (either with
low repetition rates or long periods of quiescence); if so, their shorter-
duration and wider-bandwidth bursts could arise from a different emission
mechanism and/or beaming effects (Connor et al., 2020).

Many theories advocate for highly magnetized neutron stars as the progenitors
of FRBs. This hypothesis has been strengthened by the detection of an
extremely bright, millisecond-duration radio burst from the Galactic magnetar
SGR 1935+2154 (Bochenek et al., 2020; CHIME/FRB Collaboration et al., 2020).
It is presently unclear whether the repeating and apparently non-repeating
FRBs originate from the same progenitor(s). So far, there also seems to be no
distinction in the properties of the host galaxies of repeaters and apparent
non-repeaters (Bhandari et al., 2022; Gordon et al., 2023). If assuming a
universal magnetar progenitor, however, different formation channels are
required in order to reconcile the rate of all extragalactic FRBs with the
volumetric population of magnetars (Margalit et al., 2020; Kirsten et al.,
2022a).

The repeater population itself, also boasts rich diversity. Repeaters have
been localised to various types of host galaxies, including dwarf galaxies
(e.g., FRB 20121102A and FRB 20190520B, Chatterjee et al., 2017; Niu et al.,
2022), spiral galaxies (e.g., FRB 20180916B, Marcote et al., 2020) and even a
globular cluster in the nearby M81 galactic system (Kirsten et al., 2022a).
Furthermore, the propagation effects we can measure from bursts such as
scattering times, Faraday rotation measure (RM), and DM (as well as the
evolution of these properties) suggest diverse, yet quite often chaotic,
magneto-ionic local environments for the repeaters (e.g., Michilli et al.,
2018; Mckinven et al., 2023). There are various other characteristics that can
be used to group repeaters: FRB 20121102A and FRB 20190520B are the only
repeaters so far associated with a persistent radio source (Chatterjee et al.,
2017; Marcote et al., 2017; Niu et al., 2022), potentially a nebula powered by
the FRB source; FRB 20121102A and FRB 20180916B are the only repeaters so far
that show an underlying periodicity in their activity windows (of $\sim 16$
and $\sim 160$ days, respectively; Chime/Frb Collaboration et al., 2020;
Rajwade et al., 2020; Cruces et al., 2021); FRB 20180916B and FRB 20200120E
are the only repeaters so far that exhibit (sub-)microsecond burst structure
(Nimmo et al., 2021, 2022); and only a handful of repeaters are known to enter
periods of high activity (‘burst storms’, e.g., Li et al., 2021; Hewitt et
al., 2022; Zhou et al., 2022; Nimmo et al., 2023). It is thus also unclear
whether all repeaters originate from the same progenitor(s). The relationship
between the various FRB sources we observe is clearly intricate, but detailed
studies of burst properties can help further our understanding.

On 15 October 2022, the CHIME/FRB Collaboration announced that a new repeating
FRB source, FRB 20220912A had become active. Within 3 days (with a daily
exposure time of only $\approx 10-15$ minutes) CHIME/FRB detected 9 bursts
from this source at $400-800$ MHz and report a DM of 219.46 pc cm-3 (McKinven
& Chime/Frb Collaboration, 2022). FRB 20220912A has since proven to be one of
the most active known repeaters to date. The vast majority of the bursts have
been detected around $\sim 1.4$ GHz (L-band), where multiple telescopes,
including the 100-m Green Bank Telescope (GBT), Five hundred meter Aperture
Spherical Telescope (FAST), and Effelsberg 100-m telescope have detected more
than a hundred bursts within a few hours or less of observations (e.g., Feng
et al., 2022; Zhang et al., 2022; Kirsten et al., 2022b; Feng et al., 2023;
Zhang et al., 2023). Bursts have also been detected at lower frequencies
($\sim 300-400$ MHz; Bhusare et al., 2022; Ould-Boukattine et al., 2022) and
at higher frequencies around 2 GHz (S-band; Perera et al., 2022; Rajwade et
al., 2022). Thus far, however, no bursts have been detected above 3 GHz
despite many hours of observations (Kirsten et al., 2022b; Rajwade et al.,
2022; Sheikh et al., 2022), or at the operating frequencies of the LOFAR High-
Band Antennas where other repeaters have been seen (110-190 MHz; Gopinath et
al., 2023).

The majority of repeaters exhibit high fractions of linear polarisation, and
little to no circular polarisation (e.g., Gajjar et al., 2018; Day et al.,
2020; Nimmo et al., 2021). The brightest burst detected from FRB 20220912Aby
CHIME/FRB ($\sim 600$ MHz), also exhibited 100% linear polarisation, and
showed an RM value of111Note that, when convenient, we use parentheses to
indicate the uncertainty on the least significant digits. +0.6(1) rad m-2
(McKinven & Chime/Frb Collaboration, 2022). Bursts detected at higher
frequencies ($\sim 1.4$ GHz) from FAST and the GBT show similar properties:
100% linear polarisation and relatively stable RM values close to zero rad
m-2, the latter being indicative of a clean local environment. Additionally,
approximately half of the bursts have some degree of circular polarisation,
making FRB 20220912A the repeater with the highest known fraction of bursts
that exhibit circular polarisation (Feng et al., 2023; Zhang et al., 2023).
Furthermore, some bursts have polarisation position angle (PPA) swings, which
is also scarce among the known repeaters (see Luo et al., 2020).

FRB 20220912A was localised to a host galaxy with redshift $z=0.0771(1)$ by
the Deep Synoptic Array (DSA-110) during its commissioning phase (Ravi et al.,
2023). The host, PSO J347.2702+48.70, is a massive galaxy (log
M${}_{*}=10.0(1)$) with moderate star formation (SFR $\gtrsim 0.1\,$M⊙ yr-1),
not unlike other FRB host galaxies (Gordon et al., 2023). The host galaxy is
located at a luminosity distance of 362.4(1) Mpc and classified as composite
in the Baldwin, Phillips & Terlevich (BPT) scheme.

In this paper, we present three exceptionally bright bursts detected from FRB
20220912A using the Nançay Radio Telescope (NRT). For two of the bursts, we
have simultaneous coverage with the Westerbork RT-1 single 25-m dish, which
recorded raw voltage data, allowing us to study burst properties at the
Nyquist limit, but with lower bandwidth and sensitivity compared to NRT. The
excellent quality of these combined data, together with the extraordinary
signal-to-noise (S/N) of the bursts, provide a great opportunity for an in-
depth study of burst features. In Section 2 we describe the observational
setup and data acquisition. In Section 3 we describe our search for bursts and
the analysis used to investigate the burst properties. In Section 4 we discuss
the challenges related to determining an accurate DM. This is critical for the
subsequent discussion where we probe the range of timescales of the emission
in these bursts from FRB 20220912A and provide observational evidence that
FRBs can contain short timescale (and sometimes narrow-band) shots of emission
that are tightly packed together. We then compare our findings with what is
seen from other FRBs, pulsar giant pulses, magnetar bursts, and solar radio
bursts. Finally, in Section 5 we conclude and put forward some recommendations
for future work. Throughout the paper, unless otherwise mentioned, numbers in
parentheses of our measurements are used to indicate the 3$\sigma$-uncertainty
on the least significant digits.

##  2 Observations

###  2.1 Nançay Radio Telescope

The NRT is a Kraus type meridian telescope situated in the centre of France.
At $\sim 1.4$ GHz the NRT has a system temperature of $T_{\rm sys}\approx 35$
K and a gain of $G\approx 1.4$ K/Jy, making it effectively as sensitive as a
100-m radio dish. At the beginning of 2022 we established a monitoring
campaign called ECLAT222Éclat can be translated as ‘burst’ in French.
(Extragalactic Coherent Light from Astrophysical Transients; PI: D. M. Hewitt)
on the NRT. ECLAT is conducting follow-up observations of about a dozen
repeaters with approximate weekly cadence over the course of two years. Thus
far, bursts have been detected from more than half of the sources,
establishing the NRT as a valuable instrument for FRB research. Following the
detection of FRB 20220912A by CHIME/FRB we included this source among the
repeaters that are regularly monitored. The pointing position we used was that
of the original DSA-110 localisation: RA=23h09m05.49s Dec=+48∘42′25.6′′
(J2000; Ravi, 2022). The offset from the final localization: RA=23h09m04.9s
Dec=+48∘42′25.4′′ (J2000; Ravi et al., 2023) is $5.8^{\prime\prime}$ but this
does not impact our observations as the NRT has a half-power beam width of
$4^{\prime}$ (RA) $\times$ $22^{\prime}$ (Dec) at 1.4 GHz.

These data were acquired using the Low Frequency receiver ($1.1-1.8$ GHz) of
the focal plane and receivers systems called FORT (Foyer Optimisé pour le
Radio Télescope), and have 512 MHz of bandwidth (consisting of 128 channels)
centered at a frequency of 1484 MHz. The data were recorded as 8 subbands,
each consisting of sixteen 4-MHz channels, using the Nançay Ultimate Pulsar
Processing Instrument (NUPPI; Desvignes et al., 2011) with a time resolution
of 16 $\mu$s, 32-bit sampling (which is better than most FRB observations and
hence provides excellent dynamic range for studying these bursts) and full
polarisation information in a linear basis. Coherent dedispersion, within the
4-MHz channels, was applied using a DM of 219.46 pc cm-3 for FRB 20220912A, as
reported by McKinven & Chime/Frb Collaboration (2022). The maximum DM offset
that corresponds to a temporal smearing equal to the time resolution of the
NRT data is 0.9 pc cm-3. We measure DMs for the detected bursts with a smaller
offset than this and consequently, the residual temporal smearing due to
inaccurate coherent dedispersion, even in the worst case scenario, is still
less than half the NRT sampling time (DM determination is discussed further in
Section 3.2). Additionally, each observation is accompanied by an observation
of a 3-Hz pulsed noise diode, which is used to calibrate the polarimetry.

###  2.2 Westerbork RT-1

We were also monitoring FRB 20220912A during this period using a single 25-m
Westerbork dish (RT-1) in the Netherlands. The
SEFD333www.evlbi.org/sites/default/files/shared/EVNstatus.txt at 1.4 GHz is
420 Jy. The Westerbork observations were conducted with an observing bandwidth
of 128 MHz centered at 1271 MHz. Raw voltage data were recorded as 2-bit
samples of both left and right circular polarisations with the local DBBC2 and
Flexbuff systems, and stored in VLBI Data Interchange Format (VDIF; Whitney et
al. 2010). Using digifil from the standard pulsar software package DSPSR (van
Straten & Bailes, 2011), we created Stokes I filterbanks from the voltage
data, with frequency and time resolutions of 62.5 kHz and 64 $\mu$s,
respectively, which we then used to search for bursts. We also created
filterbank data products from the raw voltages at the time of detected bursts,
with different time/frequency resolution combinations, for other analyses, as
will be explained in later sections.

##  3 Analysis and Results

###  3.1 Burst search

####  3.1.1 The ECLAT burst search pipeline

NUPPI records data as eight 64-MHz subbands, which we stitch together and
write out as 32-bit Stokes I filterbanks with 512-MHz bandwidth using custom
Python scripts that incorporate functionality from the YOUR (Your Unified
Reader) library (Aggarwal et al., 2020b). These filterbanks are converted to
8-bit samples using digifil for compatibility with the Heimdall software used
later in the pipeline. The 8-bit filterbanks are then processed in two-minute
chunks using the rfifind tool from the PRESTO pulsar software suite (Ransom,
2001), to determine which channels are most contaminated by radio frequency
interference (RFI). We flag only these channels and apply no flagging to
individual time intervals. The flagged data are then searched using Heimdall,
where we set a S/N threshold of 7. We effectively searched for boxcar widths
ranging from 16 $\mu$s to 131 ms within a DM range of $200-250\,$pc cm-3 for
FRB 20220912A. Candidates from the Heimdall search are classified by the
machine-learning classifier FETCH (Aggarwal et al., 2020a). We manually
inspect all the candidates for which any of the FETCH models A to H give a
score above 0.5. If the bursts pass this manual inspection and are considered
astrophysical, they are extracted from the original 32-bit data with full
polarisation information. The 32-bit data are used for the remainder of the
analyses.

We detected many hundreds of bursts from FRB 20220912A, and while the burst
rate drastically decreased around the end of 2022, we are still occasionally
detecting bursts at the time of writing this manuscript. The entire burst
sample and a study of the evolution of the burst properties over time will
presented in a future paper. On 29 October 2022 (MJD 59881), 1 November 2022
(MJD 59884), and 16 November 2022 (MJD 59899), we detected exceptionally
bright bursts from FRB 20220912A, which we refer to as B1, B2 and B3,
respectively, throughout the rest of this paper. These were the three bursts
with the highest detection S/N.

In Figure 1, we show the dynamic spectra, frequency-averaged burst profiles,
and time-averaged spectra of the three brightest bursts detected thus far from
FRB 20220912A in our ECLAT observations. Each frequency channel in the dynamic
spectrum has been individually normalised using off-burst statistics (i.e.,
bandpass corrected). The brightness variations in the spectra that are a few
bins wide are likely the result of unresolved scintillation. The extreme S/N
of these bursts results in some artifacts from out-of-band emission before the
first digitisation stage that can be seen in the dynamic spectra at the
highest observed frequencies, before the burst occurs.

Figure 1: Dynamic spectra of three bursts detected from FRB 20220912A with the
NRT as part of the ECLAT monitoring campaign. The burst IDs (see Table
LABEL:tab:properties) are shown in the top-left corners of each sub-figure.
The frequency and time resolution are 4 MHz and 16 $\mu$s, respectively. In
addition to being coherently dedispersed to a DM of 219.46 pc cm-3, bursts B1,
B2 and B3 have also been incoherently dedispersed to DMs of 219.356, 219.375
and 219.8 pc cm-3, respectively (see the main text for more details).
Horizontal white lines in the dynamic spectra indicate frequency channels that
have been excised due to the presence of RFI. The top panel of each sub-figure
shows the frequency-averaged time series of the burst, and the right panel
shows the time-averaged spectrum of the burst. The time series is obtained by
summing over the entire observing bandwidth, while the spectrum is obtained by
only summing over the times where the burst is present (determined by eye and
indicated by the purple bar in the top panel). The spikes in the frequency
spectra are likely due to scintillation in the Galactic ISM. Note that while
the frequency extent of each dynamic spectrum is the same, the time extent is
not. The noise is Gaussian-distributed with a standard deviation of 1 and a
mean of 0. The colour scale for all sub-figures has been logarithmically
scaled using the 99.9 quantile as the maximum and a value of 1 as the minimum.
Note that artifacts, arising from out-of-band emission before the first
digitisation stage, are visible in the highest-frequency channels, preceding
the burst.

Two of the three bright bursts exhibit clustered broadband (and sometimes
exquisitely bright) emission components that are sometimes a single 16-$\mu$s
time bin in duration. Throughout this paper we refer to these extremely short-
timescale, broadband structures as ‘microshots’. In Figure 2 the top panels
show the time profile of the entire burst envelopes, while the middle and
bottom panels display zoom-ins of the time profiles and dynamic spectra where
the microshots appear. In the middle panels we have also over-plotted, in
purple, the time profile on a logarithmic scale y-axis, which reveals many
more microshots that are less apparent in the linear scale. The microshots
have been manually identified and are indicated by vertical turquoise lines in
the figure.

Figure 2: A zoomed-in view of bursts B1 and B2 is shown in the two sub-
figures. Panels a and d show the full temporal burst profile of bursts B1 and
B2, respectively. Microshots are indicated by vertical turquoise lines. In
each of these panels, the time-span where the microshots are clustered is
indicated by a horizontal orange bar. Panels b and e show zoom-ins of these
regions. The purple profile is the same as the black, but on a logarithmic
y-scale, revealing microshots that are less visible in the black linearly
scaled profile due to the wide range of observed S/Ns. The dynamic spectra of
these zoomed-in regions are shown in panels c and f. Horizontal white lines
indicate channels that have been zapped due to the presence of RFI. Also note
the residual frequency drift present in the broader burst components that
occur after the microshot forests in panel c.

####  3.1.2 Westerbork burst search

The burst search pipeline used to search the Westerbork data has been
previously described in detail (Kirsten et al., 2021, 2022a). Westerbork was
not on source during burst B1, but on 29 October 2022 and 16 November 2022 the
ECLAT observations overlapped with Westerbork observations and B2 and B3 were
independently discovered in the search of the Westerbork data.

###  3.2 Dispersion Measure determination

We determined the DM of B1 using the three extremely bright and broadband
microshots seen in the dynamic spectrum of the NRT data. We chose a DM that
ensured that these microshots each individually arrive at all observed
frequencies at the same time. This was done by dedispersing these three
microshots to a range of trial DM values using a technique that shifts
channels by fractions of a bin. We then fitted a Gaussian to these S/N versus
DM curves to determine an optimal value and uncertainty. The microshots
slightly differ from one another in their skewness, brightness, duration and
bandwidth. Together with the intense variations in brightness as a function of
frequency (likely scintillation, as we discuss later) this complicates the DM
determination, but we attempt to mitigate this by averaging the power of a few
microshots, and fitting a Gaussian to this averaged S/N vs DM curve. The
resulting fits are shown in Appendix Figure 10. The curves are not smooth and
exhibit scalloping that differs from one microshot to another. This occurs
because the microshots have durations comparable to the time resolution of our
data and our frequency resolution is rather coarse (since coherent
dedispersion has been implemented beforehand). Artificially increasing the
time resolution of the dynamic spectrum before dedispersion (with nearest
neighbour interpolation), and then downsampling to the original time
resolution after the frequency channels have been shifted, results in slightly
less scatter in S/N versus DM. In the Westerbork data, where sub-microsecond
resolution is available, the scalloping disappears. Our fits yield a DM of
219.356(12) pc cm-3 for B1. B2 similarly has three extremely bright and
broadband microshots that were used to determine a DM of 219.377(9) pc cm-3.
Consistent measurements were obtained by performing similar analysis on the
Westerbork data of B2 (time resolution of 1 $\mu$s). B3, however, shows no
microshots, even when exploring the burst with higher time resolution in the
Westerbork data. Here we thus focused on straightening the notches (narrow
intensity dips) that are present in the burst, resulting in a DM of 219.8(1)
pc cm-3. This is likely a slight overestimation of the DM because the DM that
straightens the microshots in the other bursts does not necessarily straighten
the dips in the broader sub-bursts. For the remainder of the analyses we use
the aforementioned DM values, tabulated in Table LABEL:tab:properties, unless
stated otherwise.

In the literature, DMs are often determined using DM_phase (Seymour et al.,
2019)444https://github.com/danielemichilli/DM_phase, which maximizes the
coherent power of a burst across the bandwidth in order to determine a best
DM. For the sake of comparison, using the entire burst as input for DM_phase,
while applying a bandpass filter to limit the fluctuation frequencies between
1 and 15.625 ms-1 (i.e., timescales ranging from 2 bins to 1 ms) results in
optimal DMs of 219.35(3), 219.37(2) and 219.8(2) pc cm-3 for bursts B1, B2 and
B3, respectively (1$\sigma$-uncertainties). These values are consistent with
those we obtain from aligning the microshots to arrive at the same time at all
observed frequencies. All the aforementioned DM values are summarised in Table
LABEL:tab:more_properties.

Moreover, these DMs are generally consistent with what was reported by
CHIME/FRB and others thus far. In Section 4.1 we further justify our decision
for determining the DM in this manner and discuss other important nuances
related to FRB DM determination in general.

###  3.3 Measurement of burst properties

Some properties of the bursts are tabulated in Table LABEL:tab:properties.
Before determining any properties we first removed the bandpass: for each
channel we subtract the mean and divide by the standard deviation of the off-
burst noise, free of any obvious RFI. To convert these pixels, which are now
in S/N units, to physical flux densities we multiply by the radiometer
equation.

Table 1: Burst properties

Burst ID | TOA (MJD) a | Peak flux | Fluence | Isotropic equivalent | Drift rate | DM
---|---|---|---|---|---|---
|  | density (Jy)b | (Jy ms)b,c | energy (1040 erg)b,d | (MHz ms-1)e | (pc cm-3)
B1 | 59881.86563025384 | 281 | 1089 | 8.1 |  $-8$(3) | 219.356(12)
B2 | 59884.83394049601 | 450 | 474 | 3.5 |  $-20$(6) | 219.377(9)
B3 | 59899.78465274653 | 190 | 411 | 3.1 |  $-34$(8) | 219.8(1)

a The topocentric time-of-arrival of the burst measured at the time bin of
peak flux density, corrected to infinite frequency for a dispersion measure of
219.37 pc cm-3 and using a DM constant of 1/(2.41 $\times 10^{-4}$) MHz2 pc-1
cm3 s.
bThe estimated uncertainty is approximately 20% due to uncertainty in the
SEFD.
c Determined over the full bandwidth of the observations.
d Calculated as 4$\pi$F$\Delta\nu$D${}_{L}^{2}$/(1+$z$), where F is the
fluence, $\Delta\nu$ is the observing bandwidth, and DL and $z$ are the
luminosity distance and redshift of the host galaxy, respectively.
e Calculated as cot$(\theta)$, where $\theta$ is the angle of the 2D Gaussian
fit to the 2D ACF (see main text for details).

####  3.3.1 ACF analysis

We measured drift rates by calculating 2D autocorrelation functions (ACFs) of
the bursts. We masked the zero-lag noise spike and then fitted a 2D Gaussian
function to the ACF, following the technique detailed in Chamma et al. (2021).
Uncertainties on the drift rate are calculated as in Gopinath et al. (2023).
The ACFs of the bursts can be seen in Appendix Figure 11. The angle of the 2D
Gaussian is defined as the orientation of the semi-major axis measured
counterclockwise from the positive y-axis and the tangent of this angle gives
the burst drift rates reported in Table LABEL:tab:properties. These drift
rates are comparable to drift rates measured in other complex bursts from FRBs
such as FRB 20201124A (e.g., Zhou et al., 2022), and with the lower-end of
drifts measured for FRB 20121102A (e.g., Hessels et al., 2019). Measurement of
drift rates at other radio frequency bands are necessary to determine whether
the drift rate varies linearly with frequency for FRB 20220912A as it does for
other repeaters (e.g., Hessels et al., 2019; Gopinath et al., 2023).

The 2D ACFs can further be used to measure the frequency and time scales of
brightness variations in these bursts. The Galactic coordinates of FRB
20220912A are $l=106.1^{\circ}$, $b=-10.8^{\circ}$; it thus lies slightly
outside of the Galactic plane and scatter broadening should consequently be
moderate. The expected scattering timescale for FRB 20220912A at 1 GHz
according to the NE2001 Galactic electron density model (Cordes & Lazio, 2002)
is $2.6\,\mu$s. Assuming a frequency scaling of $\tau\propto\nu^{-4}$, the
expected scattering time at the center of the Westerbork band (1.271 GHz) is
1.0 $\mu$s, corresponding to a scintillation bandwidth of 160 kHz (using the
approximation $\Delta\nu\sim 1/2\pi\tau$). At 1.484 GHz, which is the center
of the NRT band, the scintillation bandwidth is expected to be approximately
290 kHz, which is less than a tenth of the frequency resolution of these data
(4 MHz). Since the frequency resolution of our NRT data is too coarse to
resolve the expected scintillation bandwidth we do not attempt to measure it
in the frequency ACF. The presence of a one-bin peak at the centre of the
frequency ACF, does however hint at a scintillation bandwidth of a few MHz at
most. Fortunately, as previously mentioned, voltage data were recorded for B2
with Westerbork RT-1 and we were thus able to generate coherently dedispersed
total intensity filterbanks with even higher time and/or frequency resolution
than that of the NRT data, using the Super FX Correlator, SFXC (Keimpema et
al., 2015). We constructed data products with a frequency resolution of 62.5
kHz and computed an ACF of these data, allowing us to distinguish between the
different frequency scales that are present. We then fit a Lorentzian function
to the narrow central feature present in the 1D frequency ACF and measure a
scintillation bandwidth, defined as the half-width at half-maximum of the
Lorentzian, of 300(30) kHz (see Figure 12). This corresponds to a scattering
timescale of $\sim$0.5 $\mu$s at 1.271 GHz, which is consistent within a
factor of 2 with the prediction from NE2001. Moreover, once frequency scaling
has been taken into account, our measurement is also consistent with the
scintillation bandwidth of 390(20) kHz reported from FAST observations that
were conducted at a central frequency of 1.3 GHz (Wu et al., 2023).

####  3.3.2 Power spectrum analysis

In Nimmo et al. (2021, 2022) the power spectra of bursts are computed to
determine if the bursts are consistent with red noise and to explore whether
there are any significant features present in the power spectra such as quasi-
periodic oscillations (QPOs). Following this same procedure and using the
Stingray modelling interface (Huppenkothen et al., 2019), we computed the
power spectra of bursts B1 to B3 using the NRT data, as well as B2 with the
Westerbork data (which has a 16$\times$ higher time resolution of 1 $\mu$s),
and modelled them as power laws (red noise), where the maximum-a-posteriori
model is of the form:

$f(\omega)=A\omega^{\alpha}+C$ (1)

Here, $\omega$ is the frequency, $A$ is the amplitude, $\alpha$ is the power
law index and $C$ is a white noise constant. We assume flat priors for $A$ and
$\alpha$, and a normal prior for $C$. In the case of B1 and B2 with the NRT
data, $C$ could not be well constrained, so we only fit a power law without a
white noise constant. These power law fits and residuals are shown in Figure
3. The power law indices we estimate are presented in Table
LABEL:tab:more_properties. These values are comparable to those of FRB
20180916B and FRB 20200120E (Nimmo et al., 2021, 2022). The power laws for B1
and B2 are flatter than that of B3, which is in agreement with B1 and B2
having more significant power at higher frequencies (shorter timescales) due
to the presence of microshots. Furthermore, these fits allow us to investigate
the highest fluctuation frequencies and to determine if there are any
significant outliers from the power-law fit that may suggest the presence of
QPOs. There are, however, no such outliers and we find no evidence for any
QPOs in any of these three bursts.

(a)  (b)

(c)  (d)

Figure 3: The power spectra of the NRT-detected bursts from FRB 20220912A are
shown in grey, the black line shows the same power spectra but downsampled by
a factor of 8. The power spectrum of the off-burst noise is shown in
turquoise. No normalization has been applied to any of the power spectra.
Burst IDs are labeled in the top right of each sub-figure. For B2, we also
show the spectra using the simultaneous Westerbork (Wb) voltage data, which
provided 1 $\mu$s time resolution for this analysis. The burst power spectra
have been fit with a model which consists of a power-law (purple dashed line)
and, where possible, a white noise component (purple dotted line) using the
Stingray modelling interface (Huppenkothen et al., 2019). The residuals from
these fits are shown in the bottom panels of each sub-figure. The crossover
frequency where the power-law and white noise components intersect are marked
with a solid vertical orange line, with shaded regions to illustrate the
3-$\sigma$ uncertainty (see the main text for more detail). Note that the
x-axes are different between bursts.

In an effort to quantify the shortest timescales present in the burst data, we
determine the crossover frequency $\omega_{c}$ where $A\omega^{\alpha}$ and
$C$ intersect, i.e. the frequency where the amplitude of the source variations
is smaller than the amplitude of the instrument noise and can no longer be
measured. For B1 and B2, we were unable to constrain $C$ in the NRT data, and
$\omega_{c}$ potentially lies at frequencies higher than we are capable of
probing (i.e., timescales shorter than 16 $\mu$s). In addition to the power
spectra and fits of the bursts in Figure 3, we also show a power spectrum of
off-burst noise in turquoise. The statistical properties of the off-burst
noise are different from those of the on-burst noise due to amplitude
modulation. We consequently do not normalize the spectra, and while the
comparison is imperfect, it is sufficient to demonstrate that even at the
highest fluctuation frequencies the burst power is well above the noise for B1
and B2. This suggests significant burst structure on timescales comparable to,
and even smaller than, the time resolution of our NRT data (16$\,\mu$s), which
is consistent with the presence of microshots in these bursts. For B3, which
lacks any obvious microshots, we were however able to constrain $C$ and
estimate $\omega_{c}$ to be $22(6)$ kHz ($\sim$45 $\mu$s), while for B2 with
the Westerbork data (1 $\mu$s time resolution) $\omega_{c}$ is 61(9) kHz
($\sim$16 $\mu$s). These values and their uncertainties are indicated by the
orange vertical lines and shaded regions in Figure 3. One can also see by eye
that this is approximately the fluctuation frequency where the on- and off-
burst power spectra intersect. The microshots are thus marginally resolved by
the time resolution of the NRT data, and the notches present in B3 are of the
same duration as some of the microshots.

####  3.3.3 High time resolution analysis

Using the raw voltage data recorded from the Westerbork observations, we can
construct data products using SFXC (as mentioned earlier) with even better
time resolution than the NRT data to confirm that we are marginally resolving
the microshots and to determine if there is any structure on timescales
shorter than the time resolution of the NRT data. In Figure 4 we show a
dynamic spectrum of B2 which was detected using the Westerbork RT-1 dish. The
plotted data have the same time resolution as the NRT data (16 $\mu$s) and a
frequency resolution of 62.5 kHz. The top 3 panels show zoom-ins of the
brightest three microshots at a time resolution of 1 $\mu$s. Here it can be
seen that the microshots are mostly being resolved in the NRT data, as they do
not completely break up into more components. There are, however, hints of
brightness fluctuations on the order of 1 $\mu$s timescales, particularly in
the third, brightest microshot (indicated by the purple bar).

In Figure 5 we further zoom in on this specific bright microshot. Instead of
plotting a conventional dynamic spectrum (with poor frequency resolution), we
opt to show the time series per subband sampled at the Nyquist rate at a time
resolution of 31.25 ns and a frequency resolution of 16 MHz. We find that the
emission of the burst is mostly concentrated in the form of bright scintils in
the top subbands. The top panel shows the time series of the microshot at a
time-averaged resolution of 125 ns. Here we can see hints of sub-microsecond
structure, but due to S/N limitations, the precision to which we know the true
DM and the inferred scattering timescale of about 0.5 $\mu$s, we are unable to
make concrete claims.

Figure 4: The bottom panel shows a zoom-in of the dynamic spectrum of burst
B2, which was simultaneously detected (along with NRT) by the Westerbork RT-1
dish. The time and frequency resolution are 16 $\mu$s and 62.5 kHz,
respectively, and the three brightest microshots are clearly visible. Above
the dynamic spectrum, the frequency-averaged profile is shown. The top three
panels show zoom-ins on each of these microshots (indicated by the coloured
horizontal bars), at 1 $\mu$s time resolution. These high time resolution
views of the microshots confirm that we are (mostly) resolving these
microshots even with the 16-$\mu$s time resolution of the NRT data. Note that
the S/N of the microshots indicated by the turquoise and orange bars is shown
by the left y-axis, whereas the S/N of the microshot indicated by the purple
bar is shown on the right y-axis (in purple).  Figure 5: The top panel shows
the brightest microshot in burst B2 at 125 ns time resolution. In the bottom
panel the time profile for each of the eight subbands is shown at a time
resolution of 31.25 ns, which is the best possible time resolution we can
obtain with the Westerbork data. The majority of the emission is concentrated
towards the top of the Westerbork observing band.

###  3.4 Clustering of microshots

To explore whether the microshots are clustered in time during the bursts, or
exhibit a random (Poisson) distribution, we manually identified 27 microshots
in B1 and 18 microshots in B2, and calculated the wait-time distributions of
these microshots (see Figure 6). The intervals $\delta$ between events of a
Poisson process with a constant rate $r$ follow an exponential distribution:

$f(\delta|r)=re^{-\delta r}$ (2)

In the context of FRBs, Oppermann et al. (2018) have discussed how this can be
generalized as a Weibull distribution:

$f(\delta|k,r)=\frac{k}{\delta}(\delta r\Gamma(1+k^{-1}))^{k}e^{-(\delta
r\Gamma(1+k^{-1}))^{k}}$ (3)

where $k$ is the shape parameter, $r$ is the rate parameter, and $\Gamma$ is
the gamma function. If $k=1$, the equation reduces to the exponential form and
the events are Poisson distributed. The smaller the value of $k$, the more the
distribution deviates from a Poisson distribution and the more clustered the
events are.

Here we test whether the wait times between the microshots identified in these
bursts are consistent with a Poissonian distribution (i.e., the posterior
distribution is consistent witk $k=1$) by following the methodology of
Oppermann et al. (2018) (as also implemented in Kirsten et al., 2021; Good et
al., 2023; Nimmo et al., 2023). Using a uniform prior distribution $f(k,r)$,
we calculate the posterior distribution as:

$\mathrm{Post}(k,r|d)\propto L(d|k,r)f(k,r)$ (4)

Table 2: Burst properties obtained from the power spectrum, clustering, and
polarimetric analyses.

Burst ID | $\alpha^{a}$ | $r$ | $k^{b}$ | RM${}_{\text{obs}}$ |  $\delta$RM${}_{\text{obs}}$ | Circular polarisation
---|---|---|---|---|---|---
|  | (ms-1)b |  | (rad m-2)c | (rad m-2)d | fraction
B1 | 2.08(8) | $0.87^{+1.64}_{-0.59}$ | $0.46^{+0.15}_{-0.13}$ |  $-0.93$(5) | 0.67(5) | 4(1)
B2 | 1.5(2) | $1.07^{+2.40}_{-0.76}$ | $0.51^{+0.22}_{-0.18}$ | 1.10(7) | 0.73(5) | 6(5)
B3 | 2.8(2) | - | - | 0.12(7) | 0.75(3) | 7(2)

a Power-law index determined by fitting a power-law model to B1-B3 using the
NRT data (see the main text for more detail).
b These uncertainties are the 99 % confidence intervals.
c These are the FWHM/SNR uncertainties reported by rmfit.
d The amount of ionospheric Faraday rotation estimated using IonFR (Sotomayor-
Beltran et al., 2013).

where $L(d|k,r)$ is the likelihood of the data $d$. The posterior probability
distributions of $r$ and $k$ for the microshots in B1 and B2 are shown in
Figure 7 and the values are presented in Table LABEL:tab:more_properties. For
both bursts, $k<1$, thus providing evidence that the microshots are clustered
within the bursts (and possibly even to a comparable degree in both bursts).

(a)  (b)

Figure 6: (a) The cumulative microshot distribution as a function of time
since the start of the burst, for bursts B1 and B2. (b) The wait-time
distribution of the microshots identified in B1 and B2. Each histogram bin is
0.25 ms wide.

(a)  (b)

Figure 7: Posterior probability distributions of the rate ($r$) and shape
parameters ($k$) for the Weibull distributions of the microshots identified in
B1 (a) and B2 (b). The contours and shaded regions show the 68%, 95% and 99%
confidence intervals. The white plus indicates the position of the maximum
probability density.

###  3.5 Polarimetry

We calibrated the polarimetric data by using PSRCHIVE
tools555psrchive.sourceforge.net (Hotan et al., 2004). Archive files
containing full polarisation information were created for the bursts using
DSPSR (van Straten & Bailes, 2011). These archives were then calibrated using
the pac command from PSRCHIVE in combination with a 3-Hz pulsed noise diode
scan and a polarisation calibration modeling (pcm) file. The pcm files are
constructed by analyzing observations of the pulsar PSR J0742$-$2822 during
which the receiver horn is rotated by $\sim$180∘ over the course of a 1-hr
observation. Notably, we do not simply apply single-axis calibration to
correct the differential gain and differential phase of the receptors, but
make use of the complete reception model (van Straten, 2006, 2013), which in
addition to the single-axis calibration, maps the frequency-dependent gain,
and takes into account the non-orthogonality of the receptors to more
accurately estimate the complete instrumental response (Guillemot et al.,
submitted).

To determine the RMs of the bursts, we use PSRCHIVE’s rmfit. In Figure 8 the
obtained Faraday spectra are shown for the three bursts detected with NRT. The
optimal RMs, with the FWHM/SNR uncertainties reported by rmfit, are all close
to 0 rad m-2. Using IonFR (Sotomayor-Beltran et al., 2013), we estimated the
amount of ionospheric Faraday rotation. All the aforementioned RM values are
shown in Table LABEL:tab:more_properties. Importantly, the values obtained
from rmfit are the observed RM values (RM${}_{\text{obs}}$), since they have
not been corrected for the effect of the ionosphere or redshift. These
RM${}_{\text{obs}}$ values are consistent with what has been reported in other
works (McKinven & Chime/Frb Collaboration, 2022; Feng et al., 2023; Zhang et
al., 2023). The RM also appears to be relatively stable, as Zhang et al.
(2023) demonstrated that the RM changed very little over the course of 2
months. We too find no major change in the RM between B1 and B3, which are
separated by 18 days.

Figure 8: The RM spectra produced by rmfit for the three FRB 20220912A bursts
detected with the NRT. The optimal values for RM${}_{\text{obs}}$ are
$-0.93$(5), 1.10(7) and 0.12(7) rad m-2 for B1, B2 and B3, respectively. The
vertical dashed line is at 0.6 rad m-2, the RM reported for a bright burst
from FRB 20220912A by CHIME/FRB (McKinven & Chime/Frb Collaboration, 2022).

We validated our polarimetric calibration using an observation of the pulsar
PSR B0355+54. The resulting polarimetric profiles matched those in the
European Pulsar Network666www.epta.eu.org/epndb/ (EPN) database centered at
1408, 1642 and 1710 MHz, and the RM we retrieved is $82.9(9)$ rad m-2, which
when taking into account possible ionospheric variations is consistent with
$81.5(3)$ rad m-2 reported in the ATNF catalogue (Manchester et al.,
2005)777www.atnf.csiro.au/research/pulsar/psrcat/.

Figure 9 shows the polarimetric profiles of the NRT detected bursts, assuming
an RM of 0.6 rad m-2. Before creating the frequency-averaged profiles, we
masked the frequency channels contaminated by RFI in the burst data, as well
those channels that had to be masked due to RFI in the noise diode scans.
Since the polarimetric profiles and PPAs do not significantly change if we
correct for the small range of RM values that we measure, we adopt this single
value which was previously reported and is consistent with our results. We
used unbiased linear polarisation (Everett & Weisberg, 2001) for our analyses
and plots,

$\text{L}_{\text{unbiased}}=\Bigg{\\{}\begin{array}[]{lr}\sigma_{I}\sqrt{(\frac{\text{L}}{\sigma_{I}})^{2}-1}&\rm{if}\quad\frac{L}{\sigma_{I}}\geq
1.57\\\ 0&\rm{otherwise}\end{array}$ (5)

The bursts are all about 100% linearly polarised with hints of circular
polarisation in some components. The circular polarisation fractions are
tabulated in Table LABEL:tab:more_properties. We do not believe these inklings
of circular polarisation to be astrophysical, since the circular polarisation
fraction of the bursts still retains a slight frequency dependence despite our
careful calibration procedure (see Figure 13). Nevertheless, this imperfection
in the calibration has no significant effects on our results or interpretation
thereof. Unlike many other repeating FRBs which show PPAs that are flat
across, and even between, bursts (e.g., Nimmo et al., 2021), the PPAs of these
FRB 20220912A bursts show some variability. The PPAs in B1 and B3 display
swings and vary by approximately 10 degrees across the burst duration. We also
see significant jumps in the PPA at the time of the dense microshot forest.
Feng et al. (2023) also reported PPA swings in some bursts from FRB 20220912A,
akin to those seen in FRB 20180301 (Luo et al., 2020).

Figure 9: Polarimetric profiles of the three FRB 20220912A bursts detected
with the NRT (see burst ID in each sub-figure). The total intensity is shown
by the black burst profiles and the unbiased linear and circular polarisation
in red and blue, respectively. These profiles are shown at the full 16-$\mu$s
time resolution of the data, and channels contaminated by RFI were flagged
before averaging over frequency to obtain these profiles. The probability
distribution (following Everett & Weisberg, 2001) of the PPAs are shown in the
panels above the burst profiles, and are zoomed-in to show subtle variations
with time. These profiles have been polarimetrically calibrated using the full
receptor model and de-Faradayed with an RM of 0.6 rad m-2.

##  4 Discussion

###  4.1 On dedispersion

The DM is a fundamental quantity associated with FRB sources, and knowledge of
the correct DM is critical for measuring many other attributes such as burst
widths, peak flux densities and scattering timescales, to only name a few
examples. Determining the DM accurately, however, is non-trivial as has been
noted by various other authors (e.g., Hessels et al., 2019).

One can opt to determine the DM by trying to maximise the frequency-averaged
S/N of a burst, as is effectively done in most burst searches. This method
unfortunately often results in overestimation of the DM due to downward
drifting complex frequency-time structure (‘sad-tromboning’; Hessels et al.,
2019) which is present in many FRBs (especially repeaters) and is most likely
not related to dispersion caused by intervening media. Hessels et al. (2019)
followed an alternate approach which involves trying to optimise for burst
structure by maximizing the time derivative of the peaks in frequency-averaged
burst profile. This method has been widely adopted through its implementation
in the DM_phase package (Seymour et al., 2019) and other similar techniques.
While this greatly improves upon simple S/N-maximization, it might still fail
to determine an accurate DM for weaker bursts or bursts which lack any
prominent structure.

Fortunately, bursts B1 and B2 exhibit exquisite structure. There are
exceptionally bright components present that are at most only a few bins wide
in the NRT data (tens of microseconds in duration). As was mentioned in
Section 3, we determined the DM of the bursts presented in this paper by
aligning the microshots so that the emission occurs simultaneously at all
frequencies. The DM estimates obtained from using DM_phase, with some manual
guidance on what range of times and fluctuation frequencies to use, are
consistent with our DM values.

Importantly, in accurately determining this DM a few assumptions are made that
require justification. Firstly, we are assuming that the entire burst, and all
of its components, have a single DM value. Furthermore, the structure
optimization approach assumes that in the reference frame of the source, burst
emission occurs simultaneously across a broad range of frequencies. Building
upon these two assumptions, we further assume that it only holds true for the
microshots, but not necessarily for broader components/sub-bursts. This is
motivated by our observation of a residual drift that can be seen in the
broader sub-bursts after correcting for dispersion (using a DM which we
measure using the microshots). While, effectively, a single DM value
temporally aligns the emission of multiple microshots across all observed
frequencies, it does not vertically straighten the broader components in the
dynamic spectrum. We have overdedispered bursts B1 and B2 to straighten these
broader burst components, ignoring the microshots, and find that no single DM
value can perfectly straighten all of the broader burst components, as they
have slightly different (apparent) DMs. These DMs are always slightly larger
than the DM determined using the microshots, but smaller than about $0.3$ pc
cm-3. Other authors have also noted that for some bursts not all components
can be temporally aligned using a single DM (e.g., Michilli et al., 2018; Zhou
et al., 2022). In addition to the $\lambda^{2}$ dependent delay introduced by
dispersion, there appears to be an additional drift which determines the
spectro-temporal morphology of the sub-bursts, perhaps related to the emission
mechanism. Jahns et al. (2023) and Chamma et al. (2021) have noted that this
drift increases linearly with burst duration, and that the sad-trombone effect
occurs within sub-bursts, as well as between them.

Alternatively, if we refrain from making our initial assumption and allow for
different burst components to have different DM values, the residual drift
seen in broader burst components after dedispersion (to the microshot-
determined DM) could perhaps be explained by a difference in column depth or
electron density between the microshots and the broader burst components.
Considering a scenario where FRBs are emitted within an ionised medium around
a compact progenitor, the difference in DM would arise from the broader
components being emitted deeper within the ionised medium closer to the
progenitor, and thus travelling along a longer path or through denser media
than the microshots. Furthermore, within close proximity to a magnetar
progenitor, for example, the plasma becomes relativistic and nonlinear
propagation effects start to play a significant role. The most important
nonlinear propagation effect in magnetar winds is the filamentation
instability (Sobacchi et al., 2022), which is expected to result in slight
variations of the effective DM, on the order of the variations we see in
different millisecond-duration components in these bursts.

Now, considering a scenario where the position of the burst emission can be
explained by radius-to-frequency mapping (Lyutikov, 2020; Tong et al., 2022),
it is more natural to assume that the burst emission of some components is
delayed at lower frequencies as a result of material that is propagating
radially outward from a central engine, than assuming the inverse situation
where emission is delayed at higher frequencies due to the emission region
moving towards the central engine. Consequently, if a burst is found to have a
DM that results in dedispersed emission occurring later at higher frequencies,
this DM is likely overestimated.

In short, we thus argue that the correct DM of a burst, is one that temporally
aligns short timescale emission at all observed frequencies, but may still
cause longer duration sub-bursts to have a drift where emission is delayed at
lower, but not higher, frequencies. The shortest timescales in a burst should
thus be used to quantify the uncertainty of the DM measurement. Methods that
enable accurate quantification of the uncertainty on the structure metric of a
burst, such as Sutinjo et al. (2023), are especially useful in this regard.

Reporting accurate uncertainties is especially important when individual DM
measurements are made for a large numbers of bursts. Negligence in this regard
may result in nonphysical interpretations, as significant changes in the DM of
bursts within a short period of time requires quite extreme variations in the
line-of-sight plasma local to the source (e.g., very dense filaments moving
across the line-of-sight). In the case of the Crab pulsar, DM variations of
$\sim$0.02 pc cm-3 month-1 have been seen that can be interpreted as a
scattering screen caused by filaments in the nebula (Driessen et al., 2019).
While some FRBs do originate from a very extreme magneto-ionic environment,
and large DM and RM variations between bursts are expected, true astrophysical
DM variations of a few units over the course of a few weeks seem unlikely. We
therefore argue that it is in general better and more astrophysically
motivated (although still not ideal) to dedisperse multiple bursts that were
detected from the same source within a period of weeks, to a DM which has been
determined from burst(s) that have short timescale structures, than it to
dedisperse each burst to an individual DM (regardless of the method used to
determine these inidividual DMs).

Notably, however, there are some sources, such as FRB 20121102A have been seen
to have credible DM variations on longer timescales. The DM has been seen to
increase by approximately 4 pc cm-3 over the course of $\sim$3 years (Michilli
et al., 2018; Hilmarsson et al., 2021), before decreasing by about 10 pc cm-3
over the next 3 years (Wang et al., 2022).

###  4.2 Microshots in FRB 20220912A

Two of the three FRB 20220912A bursts presented in this paper consist of burst
components with durations ranging from about ten microseconds to a few
milliseconds. Summing over the entire 512-MHz observing bandwidth, the
brightest of these microshots in B2 (when dedispersed using a DM of 219.377 pc
cm-3) has a S/N above 2000, corresponding to a peak flux density of
approximately 450 Jy. These microshots appear to be mostly resolved at around
10 $\mu$s, but there are hints of sub-microsecond time structure, as shown in
Figure 5, that require confirmation.

In addition to the microshots there are also more typical wider burst
components. Interestingly, even after the burst has been corrected for
dispersion and the microshots are aligned so that emission occurs
simultaneously at all frequencies, the wider burst components still exhibit a
residual drift apparently not associated with dispersion (see, e.g., the
components between 5 and 6 ms in B1 of Figure 2). Assuming the microshots with
comparable bandwidth are also drifting, on a conservative estimate of 5 time
bins, this results in a drift rate which is at least a factor of 6 larger than
the more typical sub-bursts.

The range of timescales we are probing is also evident in the NRT burst power
spectra, where there is power significantly above the noise level for
frequencies ranging from $\sim 40-3\times 10^{4}$ Hz (corresponding to
timescales of $\sim 32\,\mu$s $-$ 25 ms) for B1 and B2. For B3, which lacks
the microshots, the crossover frequency starts becoming visible and suggests
the shortest timescales on which there is significant burst structure is about
$35-62\,\mu$s, above the duration of the shortest microshots but corresponding
to the duration of the notches. The Westerbork B2 power spectrum indicates
that the shortest timescale where there is significant structure is around
$14-19\,\mu$s, explaining why the crossover frequency could not be determined
in the NRT data, but that the shots are being marginally resolved.

Furthermore, we have shown in Section 3.4 that these microshots are not
homogeneously spread out through the burst, but are clustered into dense
forests that can be described by a Weibull shape parameter of about 0.5. The
different timescales of burst emission and different drift rates, together
with the clustering of the microshots, require theoretical understanding

###  4.3 In comparison with FRBs

It is well known that temporal structure much shorter than the burst width can
be present in FRBs. Farah et al. (2018) showed that FRB 170827 has structures
that are only $\sim 30\,\mu$s in duration, and the total duration of one of
the FRB 20121102A bursts in Michilli et al. (2018) is only $\sim 30\,\mu$s.
FRB 20180916B bursts can have structure on the order of a few microseconds
(Nimmo et al., 2021), and even shorter timescale structure (tens of
nanoseconds) is present in some FRB 20200120E bursts (Nimmo et al., 2022).
Additionally, in a search of archival GBT data, Snelders et al. (2023)
detected isolated bursts from FRB 20121102A that are only a few microseconds
in duration. At least some repeaters are thus capable of producing such short
timescale emission independent from broad-timescale emission. We have shown
that the FRB 20220912A bursts presented in this work have structure on
timescales down to a few microseconds, and potentially even lower (see Figure
5), adding FRB 20220912A to the handful of FRBs that exhibit known
microstructure.

However, we do not see these forests of microshots in all bursts from FRB
20220912A. Similarly, Nimmo et al. (2021, 2022, 2023) noted that only some of
the bursts have microstructure. This raises the question if these microshots
are in fact a type of burst which can sometimes occur alone as with FRB
20121102A or FRB 170827, and at other times simultaneously with a different
broader type of burst, as with B1 and B2 presented here. While the isolated
microsecond duration FRBs might be ‘tips of an iceberg’ — extraordinarily
bright microshots (much brighter than the ones shown in this work) from a
broader burst too faint to be detected — this seems unlikely because of the
fine-tuning that is needed to see microshots but no broader components
(Snelders et al., 2023). Regardless, investigating emission on a wide range of
timescales provides valuable constraints for theoretical models.

The occurrence of microshots is not easily explained by propagation effects
such as fragmentation instabilities (e.g., Lu et al., 2022). One of the main
arguments for this is the lack of explanation as to why the instability would
cause the breakdown of the emission into the microshots, while not affecting
the broader emission components that occur mere milliseconds later. Ignoring
relativistic effects, these timescales correspond to small emission regions
which are more naturally explained by magnetospheric magnetar models
(Beniamini & Kumar, 2020) than the synchrotron maser models where emissions is
generated in a shock far away from the central engine (e.g., Metzger et al.,
2019).

###  4.4 In comparison with neutron stars

There are five known Galactic radio-emitting magnetars (Camilo et al., 2006;
Camilo et al., 2007; Levin et al., 2010; Eatough et al., 2013; Karuppusamy et
al., 2010). These magnetars emit radio pulsations that while semi-stable in
rotational phase, show pulse-to-pulse variability in flux density, spectral
index and the shape of the pulse profile (e.g., Lazaridis et al., 2008;
Serylak et al., 2009). Similarly to the bursts seen from repeating FRBs, the
individual magnetar radio pulses (as well as the average pulse profile) tend
to be highly linearly polarised, while having circular polarisation up to a
few tens of percent (e.g., Kramer et al., 2007), although this too can be time
variable (Dai et al., 2019). Furthermore, individual radio pulses from
magnetars have often been described as ‘spiky’ in the literature (e.g.,
Serylak et al., 2009; Caleb et al., 2022). The pulses jump around in phase
within the larger integrated profile, and are typically a few milliseconds
wide, and sometimes exceptionally bright (e.g., Yan et al., 2015; Pearlman et
al., 2018; Suresh et al., 2021). The pulses can also occasionally show hints
of more complex structure, such as features as short as $\approx 0.2$ ms
(Camilo et al., 2006) or two components with opposing spectral indices (Suresh
et al., 2021), further prompting comparison with FRBs. While the radio
pulsations are the defining characteristic of radio magnetars, these
pulsations are not necessarily ever-present and can disappear as in the case
of XTE J1810$-$197 (Camilo et al., 2016), or reawaken after years of radio-
quiescence (Lyne et al., 2018). We require long-term monitoring of more
repeaters to determine whether the burst storm behaviour is analogous to this.
Unlike FRBs that are sometimes extremely narrowband ($\sim$10$-$30% fractional
bandwidths, e.g., Gourdji et al., 2019; Kumar et al., 2021), the magnetar
pulsations have broadband flat spectra (e.g., Lazaridis et al., 2008; Dai et
al., 2019). The pulses also do not show any downward drifting or sad-
tromboning, as is evident in some bursts from repeaters. Magnetar radio bursts
have not been extensively studied on microsecond timescales, however, and the
comparison with FRBs is thus incomplete.

It is also worth noting that even the shortest timescale components in typical
magnetar pulses are still longer in duration than the microshots in the FRB
20220912A bursts presented here, or the microshots seen in giant pulses (GPs).
GPs are extremely bright pulses from pulsars that last a few microseconds or
less, and that occur within narrow phase windows. GPs have also been detected
from radio magnetars (e.g., Caleb et al., 2022). GPs from the Crab (PSR
B0531+21) have been shown to occasionally consist of nanosecond-duration
highly polarised shots of emission (Hankins et al., 2003). The main pulse (MP)
of the Crab has also been shown to resolve down to a dense forest of broadband
microsecond bursts, which sometimes can be further resolved into extremely
bright ($>10^{3}$ Jy), highly polarised and narrow-band nano-shots with sub-ns
durations (Hankins & Eilek, 2007). While morphologically similar to the spiky
emission in magnetars and the microshots in FRBs, it is important to note that
the timescales are much shorter for the GPs. Furthermore, the polarimetric
properties of the nanoshots in the MP can change drastically from one shot to
another, meaning that with sufficient averaging or a high enough density of
nanoshots, the polarization washes out and the profile becomes only weakly
polarized. As pointed out by other authors, pulses from the High-Frequency
Interpulse (HFIP) share more similarity with the repeaters in that they are
often highly linearly polarised ($\sim 80-100\%$), have little to no circular
polarisation and have polarisation positions angles that remain constant not
only throughout the pulse, but also between pulses (Hankins et al., 2016).
This thus proves to show that magnetised neutron stars such as the Crab are
capable of producing burst emission with very diverse properties.

The only Galactic radio burst brighter than GPs, are the extremely bright
isolated radio bursts that have been detected from the Galactic magnetar SGR
1935+2154 (Bochenek et al., 2020; CHIME/FRB Collaboration et al., 2020). The
brightest of these bursts had an equivalent isotropic energy approximately a
thousand times brighter than any previously detected radio magnetar burst;
this burst was indeed even more luminous than bursts detected from the
extragalactic FRB 20200120E (Nimmo et al., 2022) situated approximately 3.6
Mpc away (Bhardwaj et al., 2021; Kirsten et al., 2022a). It was further shown
in follow-up observations that SGR 1935+2154 is also capable of producing
fainter bursts, spanning 7 orders of magnitude in energies with comparable
rates (Kirsten et al., 2021). All together, this shows that at least some
fraction of the FRB population is produced by magnetars. Assuming a magnetar
progenitor, the discovery of an FRB source in a globular cluster (Kirsten et
al., 2022a), does however beckon for formation channels other than core-
collapse supernovae, such as accretion-induced collapse or binary merger.

###  4.5 In comparison with solar radio bursts

The Sun produces various types of solar radio bursts (SRBs) that bear striking
morphological similarities with FRBs, albeit on much longer timescales and
with much lower luminosity (for a review see, e.g., Wild et al., 1963; Pick &
Vilmer, 2008). In fact, Lyutikov (2002) predicted coherent radio emission
similar to SRBs during X-ray bursts from soft gamma-ray repeaters, by virtue
of comparison with solar flares. The first three types of SRBs were coined by
Wild & McCready (1950). Type I SRBs (also called ‘noise storms’) can last from
hours to days, with the emission typically observed between $50-500$ MHz and
are made up of short-duration ($\sim 1\,$s) and narrow bandwidth bursts which
occur on top of continuum emission. Type II and Type III SRBs have more
complex structure and exhibit time-frequency drifting on the order of $\sim
0.25$ and $\sim 20$ MHz s-1, respectively. Type II SRBs last approximately
minutes and are associated with coronal mass ejections that create a shock
that propagates outward through the solar corona, while Type III SRBs last
only tens of seconds and are associated with high-velocity electrons that are
accelerated along open magnetic field lines resulting from magnetic
reconnection events that cause solar flares. Ignoring the duration of the
emission, the downward drifting structure of Type II and III bursts looks very
similar to repeater FRB emission, and also specifically to the broader
emission components and microshots seen in the FRB 20220912A bursts presented
here. However, it is worth noting that SRBs can be significantly circularly
polarized (e.g., Kansabanik, 2022), whereas repeaters are more typically
highly linearly polarized. This could potentially be attributed to the
emission being relativistic in the latter case. There are also other types of
SRBs and more elaborate sub-classifications, but discussion thereof is not
required for the comparison being made in this work.

The different types of SRBs are produced by different emission mechanisms, and
while the emission physics are naturally vastly different from that of FRBs
which are many order of magnitudes more energetic and shorter in duration,
this provides an interesting analogy for the FRB 20220912A bursts presented in
this paper. Just as the Sun produces different types of bursts through
different processes, sometimes simultaneously, FRB sources could potentially
be generating different types of bursts (in terms of energy, duration,
bandwidth or drift rate), that are occasionally superimposed. In the solar
scenario the outward propagating shock of a coronal mass ejection results in
longer duration, lower drift rate Type II bursts, but around the same time
short-duration, higher-drift-rate Type III bursts can be produced along the
open field lines. One of the models that has been proposed to explain magnetar
X-ray bursts, and that has been adapted to also explain FRBs, is the magnetar
fireball model. In this model energy arising from starquakes or magnetic
reconnection is injected into a plasmoid which is enclosed by magnetic field
lines close to the surface of the magnetar. As the fireball expands along the
magnetic field lines, the energy can dissipate as coherent radio emission
resulting in FRBs (Ioka, 2020; Wada & Ioka, 2023). The observed spectrum of
the emission is dependent on the configuration of the magnetic field. In
analogy to the SRBs, the microshots and broader drifting components we observe
in these FRB 20220912A bursts could potentially be emission with different
drift rates arising from different magnetic field configurations.

##  5 Conclusions & future work

We have observed the highly active repeating FRB 20220912A using the Nançay
and Westerbork radio telescopes. We analyze a small subset of bursts with
extremely high S/N, dynamic range, and time resolution. These data allow us to
investigate effects that may likely be present in the bursts from other FRBs,
but unapparent due to their faintness or lack of time resolution used in the
data recording. We come to the following main conclusions and suggestions for
future work:

  * •

As previously pointed out by other authors (Hessels et al., 2019), the
determination of FRB DMs is non-trivial because of frequency-dependent burst
structure and time-frequency drifts that are unlikely to be related to
dispersion in the intervening media. Here we have used broadband microshots in
FRB 20220912A bursts to determine the optimal DM. We find that while the
microshots are well fit by a single DM, there is a residual drift in the
broader burst components. This means that DM determination via frequency-
averaged burst structure maximization will likely fail for bursts with lower
S/N. We thus caution that DM variation in repeating FRBs is difficult to
establish robustly, and that DM uncertainties should consider the shortest-
observable time structures (Sutinjo et al., 2023).

  * •

After accurate correction for dispersion, we still observe residual time-
frequency drifts within broader sub-bursts of FRB 20220912A. This residual
time-frequency drift may be related to an outwards propagating emission region
and radius-to-frequency mapping (Hessels et al., 2019). Alternatively, it
could be due to an additional electron column density between the emission
sites of the broad and narrow (microshots) burst components; the DM required
to straighten the broad burst components is $\lesssim 0.3$ pc cm-3.

  * •

We show that some FRB 20220912A bursts have brightness variations spanning
from a few milliseconds to less than a microsecond. Such a broad range of
timescales, within a single burst event, has also been observed in FRB
20180916B (Nimmo et al., 2021) and FRB 20200120E (Nimmo et al., 2022).
Furthermore, we find that the brightest microshots in our observed bursts are
clustered in time compared to the total duration of the bursts. The range of
timescales and clustering of microshots requires theoretical understanding.
Since the microshots show extremely high (or possibly no) time-frequency
drift, it is possible that they arise from a distinct physical mechanism
compared to the broader sub-bursts, which do drift.

  * •

Though solar radio bursts (SRBs) are obviously very different in their
luminosity and timescale, the existence of multiple types of SRBs, which
sometimes occur superimposed on each other provides an interesting analogy to
consider. The broadband microshots from FRB 20220912A could be generated in a
physically distinct way compared to the wider frequency-swept emission.
Supporting this hypothesis, Snelders et al. (2023) find isolated microshots
from FRB 20121102A, which occur at different times compared to wider, time-
frequency swept bursts. However, the similar polarimetric properties between
the microshots and wider sub-bursts suggests a physical connection.

  * •

The timescales of the FRB 20220912A microshots are compatible with those of
giant pulses from young and millisecond rotation-powered pulsars (e.g.,
Hankins et al., 2016), but the overall FRB 20220912A burst durations of tens
of milliseconds are much longer. While the overall durations and spiky burst
structure are consistent with pulses from radio magnetars, sub-millisecond
temporal structures have not been extensively studied in magnetars. We
therefore encourage microsecond-resolution studies of bright radio bursts from
magnetars.

## Acknowledgements

DMH would like to thank Pawan Kumar and Emanuele Sobacchi for helpful
discussions about the interpretation of the results presented in this work.
Research by the AstroFlash group at University of Amsterdam, ASTRON and JIVE
is supported in part by an NWO Vici grant (PI Hessels; VI.C.192.045). The
Nançay Radio Observatory is operated by the Paris Observatory, associated with
the French Centre National de la Recherche Scientifique (CNRS). We acknowledge
financial support from the “Programme National de Cosmologie et Galaxies”
(PNCG) and “Programme National Hautes Energies” (PNHE) of CNRS/INSU, France.
The Westerbork RT-1 telescope is maintained and operated by ASTRON. We express
our gratitude to the operators R. Blaauw, J.J Sluman and H. Mulder for
scheduling observations. We would like to express our gratitude to Aard
Keipema and Willem van Straten for modifying the software correlator SFXC, and
software package DSPSR, respectively, to fit our needs. DH is supported by the
Women In Science Excel (WISE) programme of the Netherlands Organisation for
Scientific Research (NWO).

## Data Availability

The relevant code and data products for this work will be uploaded on Zenodo
at the time of acceptance for publication.

## References

  * Aggarwal et al. (2020a) Aggarwal K., Law C. J., Burke-Spolaor S., Bower G., Butler B. J., Demorest P., Linford J., Lazio T. J. W., 2020a, Research Notes of the American Astronomical Society, 4, 94
  * Aggarwal et al. (2020b) Aggarwal K., et al., 2020b, Journal of Open Source Software, 5, 2750
  * Beniamini & Kumar (2020) Beniamini P., Kumar P., 2020, MNRAS, 498, 651
  * Bhandari et al. (2022) Bhandari S., et al., 2022, AJ, 163, 69
  * Bhardwaj et al. (2021) Bhardwaj M., et al., 2021, ApJ, 910, L18
  * Bhusare et al. (2022) Bhusare Y., et al., 2022, The Astronomer’s Telegram, 15806, 1
  * Bochenek et al. (2020) Bochenek C. D., Ravi V., Belov K. V., Hallinan G., Kocz J., Kulkarni S. R., McKenna D. L., 2020, Nature, 587, 59
  * CHIME/FRB Collaboration et al. (2020) CHIME/FRB Collaboration et al., 2020, Nature, 587, 54
  * Caleb et al. (2022) Caleb M., et al., 2022, MNRAS, 510, 1996
  * Camilo et al. (2006) Camilo F., Ransom S. M., Halpern J. P., Reynolds J., Helfand D. J., Zimmerman N., Sarkissian J., 2006, Nature, 442, 892
  * Camilo et al. (2007) Camilo F., Ransom S. M., Halpern J. P., Reynolds J., 2007, ApJ, 666, L93
  * Camilo et al. (2016) Camilo F., et al., 2016, ApJ, 820, 110
  * Chamma et al. (2021) Chamma M. A., Rajabi F., Wyenberg C. M., Mathews A., Houde M., 2021, MNRAS, 507, 246
  * Chatterjee et al. (2017) Chatterjee S., et al., 2017, Nature, 541, 58
  * Chime/Frb Collaboration et al. (2020) Chime/Frb Collaboration et al., 2020, Nature, 582, 351
  * Chime/Frb Collaboration et al. (2023) Chime/Frb Collaboration et al., 2023, ApJ, 947, 83
  * Chime/Frb Collabortion (2021) Chime/Frb Collabortion 2021, The Astronomer’s Telegram, 14497, 1
  * Connor et al. (2020) Connor L., Miller M. C., Gardenier D. W., 2020, MNRAS, 497, 3076
  * Cordes & Lazio (2002) Cordes J. M., Lazio T. J. W., 2002, arXiv e-prints, pp astro–ph/0207156
  * Cruces et al. (2021) Cruces M., et al., 2021, MNRAS, 500, 448
  * Dai et al. (2019) Dai S., et al., 2019, ApJ, 874, L14
  * Day et al. (2020) Day C. K., et al., 2020, MNRAS, 497, 3335
  * Desvignes et al. (2011) Desvignes G., Barott W. C., Cognard I., Lespagnol P., Theureau G., 2011, in Burgay M., D’Amico N., Esposito P., Pellizzoni A., Possenti A., eds, American Institute of Physics Conference Series Vol. 1357, Radio Pulsars: An Astrophysical Key to Unlock the Secrets of the Universe. pp 349–350, doi:10.1063/1.3615154
  * Driessen et al. (2019) Driessen L. N., Janssen G. H., Bassa C. G., Stappers B. W., Stinebring D. R., 2019, MNRAS, 483, 1224
  * Eatough et al. (2013) Eatough R. P., et al., 2013, Nature, 501, 391
  * Everett & Weisberg (2001) Everett J. E., Weisberg J. M., 2001, ApJ, 553, 341
  * Farah et al. (2018) Farah W., et al., 2018, MNRAS, 478, 1209
  * Feng et al. (2022) Feng Y., et al., 2022, The Astronomer’s Telegram, 15723, 1
  * Feng et al. (2023) Feng Y., et al., 2023, arXiv e-prints, p. arXiv:2304.14671
  * Gajjar et al. (2018) Gajjar V., et al., 2018, ApJ, 863, 2
  * Good et al. (2023) Good D. C., et al., 2023, ApJ, 944, 70
  * Gopinath et al. (2023) Gopinath A., et al., 2023, arXiv e-prints, p. arXiv:2305.06393
  * Gordon et al. (2023) Gordon A. C., et al., 2023, arXiv e-prints, p. arXiv:2302.05465
  * Gourdji et al. (2019) Gourdji K., Michilli D., Spitler L. G., Hessels J. W. T., Seymour A., Cordes J. M., Chatterjee S., 2019, ApJ, 877, L19
  * Hankins & Eilek (2007) Hankins T. H., Eilek J. A., 2007, ApJ, 670, 693
  * Hankins et al. (2003) Hankins T. H., Kern J. S., Weatherall J. C., Eilek J. A., 2003, Nature, 422, 141
  * Hankins et al. (2016) Hankins T. H., Eilek J. A., Jones G., 2016, ApJ, 833, 47
  * Hessels et al. (2019) Hessels J. W. T., et al., 2019, ApJ, 876, L23
  * Hewitt et al. (2022) Hewitt D. M., et al., 2022, MNRAS, 515, 3577
  * Hilmarsson et al. (2021) Hilmarsson G. H., et al., 2021, ApJ, 908, L10
  * Hotan et al. (2004) Hotan A. W., van Straten W., Manchester R. N., 2004, Publ. Astron. Soc. Australia, 21, 302
  * Huppenkothen et al. (2019) Huppenkothen D., et al., 2019, ApJ, 881, 39
  * Ioka (2020) Ioka K., 2020, ApJ, 904, L15
  * Jahns et al. (2023) Jahns J. N., et al., 2023, MNRAS, 519, 666
  * Kansabanik (2022) Kansabanik D., 2022, Sol. Phys., 297, 122
  * Karuppusamy et al. (2010) Karuppusamy R., Stappers B. W., van Straten W., 2010, A&A, 515, A36
  * Keimpema et al. (2015) Keimpema A., et al., 2015, Experimental Astronomy, 39, 259
  * Kirsten et al. (2021) Kirsten F., Snelders M. P., Jenkins M., Nimmo K., van den Eijnden J., Hessels J. W. T., Gawroński M. P., Yang J., 2021, Nature Astronomy, 5, 414
  * Kirsten et al. (2022a) Kirsten F., et al., 2022a, Nature, 602, 585
  * Kirsten et al. (2022b) Kirsten F., et al., 2022b, The Astronomer’s Telegram, 15727, 1
  * Kramer et al. (2007) Kramer M., Stappers B. W., Jessner A., Lyne A. G., Jordan C. A., 2007, MNRAS, 377, 107
  * Kumar et al. (2021) Kumar P., et al., 2021, MNRAS, 500, 2525
  * Lazaridis et al. (2008) Lazaridis K., Jessner A., Kramer M., Stappers B. W., Lyne A. G., Jordan C. A., Serylak M., Zensus J. A., 2008, MNRAS, 390, 839
  * Levin et al. (2010) Levin L., et al., 2010, ApJ, 721, L33
  * Li et al. (2021) Li D., et al., 2021, Nature, 598, 267
  * Lu et al. (2022) Lu W., Beniamini P., Kumar P., 2022, MNRAS, 510, 1867
  * Luo et al. (2020) Luo R., et al., 2020, Nature, 586, 693
  * Lyne et al. (2018) Lyne A., Levin L., Stappers B., Mickaliger M., Desvignes G., Kramer M., 2018, The Astronomer’s Telegram, 12284, 1
  * Lyutikov (2002) Lyutikov M., 2002, ApJ, 580, L65
  * Lyutikov (2020) Lyutikov M., 2020, ApJ, 889, 135
  * Manchester et al. (2005) Manchester R. N., Hobbs G. B., Teoh A., Hobbs M., 2005, AJ, 129, 1993
  * Marcote et al. (2017) Marcote B., et al., 2017, ApJ, 834, L8
  * Marcote et al. (2020) Marcote B., et al., 2020, Nature, 577, 190
  * Margalit et al. (2020) Margalit B., Beniamini P., Sridhar N., Metzger B. D., 2020, ApJ, 899, L27
  * McKinven & Chime/Frb Collaboration (2022) McKinven R., Chime/Frb Collaboration 2022, The Astronomer’s Telegram, 15679, 1
  * Mckinven et al. (2023) Mckinven R., et al., 2023, ApJ, 951, 82
  * Metzger et al. (2019) Metzger B. D., Margalit B., Sironi L., 2019, MNRAS, 485, 4091
  * Michilli et al. (2018) Michilli D., et al., 2018, Nature, 553, 182
  * Nimmo et al. (2021) Nimmo K., et al., 2021, Nature Astronomy, 5, 594
  * Nimmo et al. (2022) Nimmo K., et al., 2022, Nature Astronomy, 6, 393
  * Nimmo et al. (2023) Nimmo K., et al., 2023, MNRAS, 520, 2281
  * Niu et al. (2022) Niu C. H., et al., 2022, Nature, 606, 873
  * Oppermann et al. (2018) Oppermann N., Yu H.-R., Pen U.-L., 2018, MNRAS, 475, 5109
  * Ould-Boukattine et al. (2022) Ould-Boukattine O. S., et al., 2022, The Astronomer’s Telegram, 15817, 1
  * Pearlman et al. (2018) Pearlman A. B., Majid W. A., Prince T. A., Kocz J., Horiuchi S., 2018, ApJ, 866, 160
  * Perera et al. (2022) Perera B., et al., 2022, The Astronomer’s Telegram, 15734, 1
  * Petroff et al. (2022) Petroff E., Hessels J. W. T., Lorimer D. R., 2022, A&ARv, 30, 2
  * Pick & Vilmer (2008) Pick M., Vilmer N., 2008, A&ARv, 16, 1
  * Pleunis et al. (2021) Pleunis Z., et al., 2021, ApJ, 923, 1
  * Rajwade et al. (2020) Rajwade K. M., et al., 2020, MNRAS, 495, 3551
  * Rajwade et al. (2022) Rajwade K., et al., 2022, The Astronomer’s Telegram, 15791, 1
  * Ransom (2001) Ransom S. M., 2001, PhD thesis, Harvard University, Massachusetts
  * Ravi (2022) Ravi V., 2022, The Astronomer’s Telegram, 15693, 1
  * Ravi et al. (2023) Ravi V., et al., 2023, ApJ, 949, L3
  * Serylak et al. (2009) Serylak M., et al., 2009, MNRAS, 394, 295
  * Seymour et al. (2019) Seymour A., Michilli D., Pleunis Z., 2019, DM_phase: Algorithm for correcting dispersion of radio signals, Astrophysics Source Code Library, record ascl:1910.004 (ascl:1910.004)
  * Sheikh et al. (2022) Sheikh S., et al., 2022, The Astronomer’s Telegram, 15735, 1
  * Snelders et al. (2023) Snelders M. P., et al., 2023, arXiv e-prints, p. arXiv:2307.02303
  * Sobacchi et al. (2022) Sobacchi E., Lyubarsky Y., Beloborodov A. M., Sironi L., 2022, MNRAS, 511, 4766
  * Sotomayor-Beltran et al. (2013) Sotomayor-Beltran C., et al., 2013, ionFR: Ionospheric Faraday rotation, Astrophysics Source Code Library, record ascl:1303.022 (ascl:1303.022)
  * Spitler et al. (2016) Spitler L. G., et al., 2016, Nature, 531, 202
  * Suresh et al. (2021) Suresh A., Cordes J. M., Chatterjee S., Gajjar V., Perez K. I., Siemion A. P. V., Price D. C., 2021, ApJ, 921, 101
  * Sutinjo et al. (2023) Sutinjo A. T., et al., 2023, arXiv e-prints, p. arXiv:2302.06220
  * Tong et al. (2022) Tong H., Liu J., Wang H. G., Yan Z., 2022, MNRAS, 509, 5679
  * Wada & Ioka (2023) Wada T., Ioka K., 2023, MNRAS, 519, 4094
  * Wang et al. (2022) Wang P., et al., 2022, The Astronomer’s Telegram, 15619, 1
  * Whitney et al. (2010) Whitney A., Kettenis M., Phillips C., Sekido M., 2010, in Navarro R., Rogstad S., Goodhart C. E., Sigman E., Soriano M., Wang D., White L. A., Jacobs C. S., eds, Sixth International VLBI Service for Geodesy and Astronomy. Proceedings from the 2010 General Meeting. pp 192–196
  * Wild & McCready (1950) Wild J. P., McCready L. L., 1950, Australian Journal of Scientific Research A Physical Sciences, 3, 387
  * Wild et al. (1963) Wild J. P., Smerd S. F., Weiss A. A., 1963, ARA&A, 1, 291
  * Wu et al. (2023) Wu Z.-W., et al., 2023, arXiv e-prints, p. arXiv:2304.14697
  * Yan et al. (2015) Yan Z., et al., 2015, ApJ, 814, 5
  * Zhang et al. (2022) Zhang Y., et al., 2022, The Astronomer’s Telegram, 15733, 1
  * Zhang et al. (2023) Zhang Y.-K., et al., 2023, arXiv e-prints, p. arXiv:2304.14665
  * Zhou et al. (2022) Zhou D. J., et al., 2022, Research in Astronomy and Astrophysics, 22, 124001
  * van Straten (2006) van Straten W., 2006, ApJ, 642, 1004
  * van Straten (2013) van Straten W., 2013, ApJS, 204, 13
  * van Straten & Bailes (2011) van Straten W., Bailes M., 2011, Publ. Astron. Soc. Australia, 28, 1

##  Appendix A DM determination

In order to determine the DM we dedispersed the three brightest microshots in
B1 and B2 to a range of DMs in the interval $219.2-219.55$ pc cm-3. The DM is
then given by the centroid of a Gaussian fit to the sum of the S/N vs DM
curves. These curves are shown in Fiure 10. See the main text for more detail.

(a)  (b)

Figure 10: The S/N as a function of DM of the three brightest microshots in B1
and B2 are shown as black dots. Gaussian fits to these curves are overplotted
in turquoise. The combined S/N of the three microshots is also shown, with a
Gaussian fit in purple. The centroid of this Gaussian fit is indicated by the
solid vertical orange line, while the shaded region shows the 3$\sigma$
uncertainty. The scalloping in the curves is likely the result of the strongly
scintillating microshots that have a duration comparable to the time
resolution of our data.

##  Appendix B ACF analysis

In Figures 11 and 12 we show 2D ACFs of the bursts presented in this paper.
See the main text and figure captions for more detail.

(a)  (b)  (c)

Figure 11: 2D autocorrelation functions of burst B1, B2, and B3 detected with
the NRT. A 2D Gaussian is fitted to the 2D ACFs to determine the drift rate.
The top panels show the 1D time ACF, while the right hand panels show the 1D
frequency ACF. For more detail see the main text.  Figure 12: Panels a and c
show 1D time and frequency ACFs, respectively, of B2 using the data from the
Westebork RT-1 dish. Gaussian fits have been overplotted in purple. Panel b
shows the 2D ACF, with a 2D Gaussian fit overplotted in purple. The residuals
of the frequency ACF as a fraction of the normalised maximum of the 1D ACF are
shown in panel c. In panels c and d, a strong peak in the frequency ACF
corresponding to the scintillation bandwidth has been highlighted in
turquoise. Finally, we zoom in on this peak in panel e, where a Lorentzian fit
is overplotted in turquoise. The HWHM of the Lorentzian function, which
corresponds to the scintillation bandwidth, is indicated by the orange line,
with the shaded orange regions showing the 3$\sigma$ uncertainty. This value
is consistent within a factor of 2 of the NE2001 prediction.

##  Appendix C Polarisation Calibration

In Figure 13 we plot the polarisation fractions of our bursts as a function of
frequency. A similar trend in Stokes V/I for all three bursts indicates a
slight imperfection in the polarimetric calibration that does not, however,
significantly influence our results or interpretation thereof.

Figure 13: The linear (in red) and circular (in blue) polarisation fractions
of B1, B2 and B3 as a function of frequency. Gaps occur due to channels that
have been zapped to remove RFI contamination.