# A Nançay Radio Telescope study of the hyperactive repeating FRB 20220912A

David C. Konijn ,1,2,3 Danté M. Hewitt ,1 Jason W. T. Hessels ,1,2,4,5 Ismaël
Cognard ,6,7 Jeff Huang ,1 Omar S. Ould-Boukattine , 1,2 Pragya Chawla ,2
Kenzie Nimmo ,8 Mark P. Snelders ,2,1 Akshatha Gopinath ,1 and Ninisha
Manaswini 9

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
3Kapteyn Astronomical Institute, University of Groningen, Kapteynborg 5419,
9747 AD, Groningen, The Netherlands
4Trottier Space Institute, McGill University, 3550 rue University, Montréal,
QC H3A 2A7, Canada
5Department of Physics, McGill University, 3600 rue University, Montréal, QC
H3A 2T8, Canada
6Station de Radioastronomie de Nançay, Observatoire de Paris, PSL University,
CNRS, Université d’Orléans, F-18330 Nançay, France
7Laboratoire de Physique et Chimie de l’Environnement et de l’Espace LPC2E
UMR7328, Université d’Orléans, CNRS, F-45071 Orléans, France
8MIT Kavli Institute for Astrophysics and Space Research, Massachusetts
Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA
9Max Planck Institute for Radio Astronomy, University of Bonn, Auf dem Hügel
69, D-53121, Bonn, Germany
E-mail<EMAIL_ADDRESS>0009-0000-7084-9956 0000-0002-5794-2360
0000-0003-2317-1446 0000-0002-1775-9692 0000-0002-8043-0048
0000-0001-9381-8466 0000-0002-3426-7606 0000-0003-0510-0740
0000-0001-6170-2282 0000-0002-1836-0771 0009-0005-1319-9586

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The repeating fast radio burst source FRB 20220912A was remarkably active in
the weeks after its discovery. Here we report 696 bursts detected with the
Nançay Radio Telescope (NRT) as part of the Extragalactic Coherent Light from
Astrophysical Transients (ÉCLAT) monitoring campaign. We present 68
observations, conducted from October 2022 to April 2023, with a total duration
of 61 hours and an event rate peaking at $75^{+10}_{-9}$ bursts per hour above
a fluence threshold of 0.59 Jy ms in the $1.2-1.7$-GHz band. Most bursts in
the sample occur towards the bottom of the observing band. They follow a
bimodal wait-time distribution, with peaks at 33.4 ms and 67.0 s. We find a
roughly constant dispersion measure (DM) over time ($\delta$DM $\lesssim$ 2 pc
cm-3) when taking into account ‘sad-trombone’ drift, with a mean drift rate of
$-8.8\,$MHz ms-1. Nonetheless, we confirm small $\sim 0.3$ pc cm-3 DM
variations using microshot structure, while finding that microstructure is
rare in our sample – despite the 16 $\upmu$s time resolution of the data. The
cumulative spectral energy distribution shows more high-energy bursts
($E_{\nu}\gtrsim 10^{31}$ erg/Hz) than would be expected from a simple power-
law distribution. The burst rate per observation appears Poissonian, but the
full set of observations is better modelled by a Weibull distribution, showing
clustering. We discuss the various observational similarities that FRB
20220912A shares with other (hyper)active repeaters, which as a group are
beginning to show a common set of phenomenological traits that provide
multiple useful dimensions for their quantitative comparison and modelling.

###### keywords:

fast radio bursts – radio continuum: transients

††pubyear: 2024††pagerange: A Nançay Radio Telescope study of the hyperactive
repeating FRB 20220912A–3

##  1 Introduction

Fast radio bursts (FRBs) are short-duration, extremely luminous pulses of
coherent radio emission originating from unknown extragalactic sources
(Lorimer et al., 2007; Thornton et al., 2013; Petroff et al., 2022). FRBs
typically have durations ranging from microseconds (Snelders et al., 2023) to
milliseconds, and have been observed at radio frequencies ranging from 110 MHz
(Pleunis et al., 2021a) to 8 GHz (Gajjar et al., 2018). Thousands of sources
of FRBs have been detected, with $\sim$97 per cent observed as (apparently)
one-off events (CHIME/FRB Collaboration et al., 2023). The remaining small
fraction of FRBs are known to repeat (e.g., Spitler et al., 2016), often in a
clustered manner (e.g., Li et al., 2019; Hewitt et al., 2022) and showing
band-limited emission (Gourdji et al., 2019).

The bursts from these repeaters are, on average, longer in duration and
narrower in bandwidth than those seen from apparently non-repeating FRBs
(Pleunis et al., 2021b). Despite these spectro-temporal differences between
the repeaters and non-repeaters, some factors point towards a single
population of FRBs with a continuous distribution of repetition rates that are
capable of producing bursts with different (observed) morphologies. Most
importantly, the upper limits on repetition for the apparent non-repeating
FRBs are not clearly distinct from the repetition rates observed in the vast
majority of repeaters, though with with some notable exceptions (CHIME/FRB
Collaboration et al., 2023). To then consolidate the implied relationship
between repetition rate and burst duration, beaming could be invoked to
explain temporal differences (Connor et al., 2020; Kumar et al., 2024). Most
notably, the high end of the burst energy distribution from the repeating FRB
20201124A resembles that of the non-repeating FRB population (Kirsten et al.,
2024).

The source(s) and emission mechanism(s) behind repeating and non-repeating
FRBs remain unknown, but given the diversity observed in FRB host
environments, burst properties and repetition rates, attributing all observed
FRBs to a single progenitor is likely an oversimplification. Nevertheless,
among the various models, magnetically powered neutron stars, commonly
referred to as ‘magnetars’, are among the most promising candidates (e.g.,
Margalit et al., 2019; Gourdji et al., 2020). The energetics (Margalit et al.,
2020a), timescales (Camilo et al., 2008; Nimmo et al., 2021, 2022; Hewitt et
al., 2023), and emission frequencies (e.g., Dai et al., 2019) of magnetars and
FRBs suggest a connection between them. The most important observational
connection to magnetar theories is the high-luminosity radio burst that was
detected from the Galactic magnetar SGR 1935+2154, which showed similarities
to FRBs in terms of its duration, spectrum and luminosity (Bochenek et al.,
2020; CHIME/FRB Collaboration, 2020; Kirsten et al., 2021). However, the rate
of SGR 1935+2154-like bursts alone is insufficient to account for the observed
FRB rate and repetition fraction (Margalit et al., 2020b). These authors argue
that an additional population of magnetars is required, with stronger magnetic
fields than Galactic magnetars, but lower birth rates. Indeed, the discovery
of an FRB source in a globular cluster (Kirsten et al., 2022a), further
advocates for diverse formation channels, assuming magnetars as the
progenitors of FRBs.

On 2022 September 12, FRB 20220912A was discovered by the CHIME/FRB
Collaboration (McKinven & CHIME/FRB Collaboration et al., 2022). In only three
days, nine bursts were detected, indicating an exceptionally high burst rate —
especially considering that, after six years of monitoring by CHIME/FRB, the
median number of bursts detected per repeater is three (CHIME/FRB
Collaboration et al., 2023). Shortly after the discovery of FRB 20220912A, the
source was localised by the Deep Synoptic Array (DSA-110) to its host galaxy
PSO J347.2702+48.7066 at a redshift of $z=0.0771$ (Ravi et al., 2023).
Thereafter, the European VLBI Network (EVN) localised the source to
milliarcsecond precision, with coordinates RA (J2000) = $23^{\rm h}09^{\rm
m}04.8989^{\rm s}\pm 5\,$mas Dec (J2000) =
$48^{\circ}42^{\prime}23.9078^{\prime\prime}\pm 5\,$mas (Hewitt et al., 2024).
These observations also ruled out the presence of a compact persistent radio
source (PRS), as has been associated with some other active repeaters (Marcote
et al., 2020; Niu et al., 2022; Bhandari et al., 2023). Multiple telescopes
have detected more than a hundred bursts within a few hours of observation
around $\sim$ 1.4 GHz (e.g., Feng et al., 2022; Kirsten et al., 2022b; Zhang
et al., 2022). Remarkably, at the peak of its activity, the burst rate of FRB
20220912A (above a fluence threshold of 100 Jy ms) constituted up to a few per
cent of the all-sky rate of FRBs in general (Sheikh et al., 2022). This rate
of high-fluence bursts is comparable to another hyperactive repeater, FRB
20201124A (Kirsten et al., 2024). Such high activity is short-lived, however,
with considerable daily fluctuations (Zhang et al., 2023). In terms of
spectral range, in addition to the detections at 1.4 GHz (Pelliciari et al.,
2024), FRB 20220912A has been detected at $300-400$ MHz (Bhusare et al., 2022;
Ould-Boukattine et al., 2022), and around 2 GHz (Perera et al., 2022; Rajwade
et al., 2022), yet no bursts have been found in searches above 3 GHz or below
200 MHz (Kirsten et al., 2022b; Rajwade et al., 2022; Sheikh et al., 2022).

The activity of repeaters is often clustered in time (Oppermann et al., 2018)
and triggered by an unknown mechanism (peharps starquakes or magnetar flares;
e.g., Wang et al., 2018), as there have been numerous reported ‘burst storms’
where a repeating FRB produces bursts at a rate of dozens to hundreds per hour
(e.g., Li et al., 2021; Nimmo et al., 2023; Jahns et al., 2023). FRB 20220912A
is the second FRB, after FRB 20201124A (Lanman et al., 2022; Xu et al., 2022),
that has seemingly awoken from quiesence before entering a hyperactive state
during which it exhibits prolonged activity for weeks to months, observable by
numerous telescopes in multiple frequency bands. More recently, FRB 20240114A
has been seen to do the same (Shin et al., 2024). CHIME/FRB monitored these
sources for years without detecting any bursts, before their spontanteous
flare ups. Roughly speaking, the discovery rate of hyperactive FRBs is
currently on the order of $\sim$1 per year. It is not known whether these
intense periods of activity signal an awakening from quiescence, or the birth
of a new source, but studying the evolution of the burst properties during
these periods can inform theory.

In this paper, we report on 696 bursts that have been detected from the
hyperactive repeating FRB 20220912A, using the Nançay Radio Telescope (NRT) as
part of the Extragalactic Coherent Light from Astrophysical Transients (ÉCLAT)
monitoring campaign. Three of these bursts were the subject of in-depth
analysis in Hewitt et al. (2023), which revealed that some bursts from FRB
20220912A feature extremely bright, broadband, clustered shots of emission
with durations on the order of microseconds. These shots are potentially
produced by a different emission mechanism than the broader burst components
that show substantial drift not related to dispersion – i.e., the time-
frequency drift (Hessels et al., 2019) that is colloquially referred to as the
‘sad-trombone’ effect. Here, we have analysed the spectro-temporal properties
and the energetics of all 696 bursts in our NRT data, drawing population-wide
statistics for comparison with other FRB sources. Section 2 outlines the
observational setup and data acquisition, followed by a description of how we
obtained the burst sample in Section 3. The burst property analyses are
explained in Section 4. We discuss the results in Section 5, in the context of
other FRB 20220912A observations, and finally present our main conclusions in
Section 6.

##  2 Observations

We observed FRB 20220912A as part of the ÉCLAT (PI: D. M. Hewitt) FRB-
monitoring campaign on the NRT. The NRT is a Kraus-type transit telescope
located in Nançay, France; it is operated by the Observatoire de Paris, and
associated with the French Centre National de la Recherche Scientifique
(CNRS). At 1.4 GHz, the NRT has a system temperature of $T_{\text{sys}}\sim
35$ K and a gain of $G\sim 1.4$ K Jy-1, making it effectively as sensitive as
a radio dish with a diameter of 94 m. ÉCLAT was established at the start of
2022 and has since been monitoring about a dozen FRB sources with
approximately weekly cadence to constrain their activity levels and map the
evolution of burst properties. Between 2022 October 15 and 2023 April 20, we
observed FRB 20220912A at a cadence of $\sim$2.5 times per week. There were 68
observations in total, each lasting $\sim$1 hour, as shown in Table 3.

Our observations used the NRT’s Low-Frequency receiver ($1.1-1.8$ GHz total
span) and the Nançay Ultimate Pulsar Processing Instrument (NUPPI; Desvignes
et al., 2011). We recorded data at a central observing frequency of 1.484 GHz,
with 512 MHz of bandwidth (from $1.228-1.740$ GHz) split into 128 4-MHz
channels, with 16 channels from each of the 8 NUPPI nodes. NUPPI provided a
time resolution of 16 $\upmu$s and full Stokes information in a linear basis.
For pointing, we used the original DSA-110 localisation of FRB 20220912A: RA
(J2000) = $23^{\rm h}09^{\rm m}05.49^{\rm s}$ and Dec (J2000) =
$48^{\circ}42^{\prime}25.6^{\prime\prime}$ (Ravi et al., 2023). This position
is 5.8′′ offset from the EVN localisation (Hewitt et al., 2024), but the true
position is still well within the half-power beam width of the NRT, which is
at least a few arcminutes at 1.4 GHz.

To maintain the best possible time resolution, our observations were
coherently dedispersed within each 4-MHz channel, to a DM of $219.46$ pc cm-3
(McKinven & CHIME/FRB Collaboration et al., 2022). The maximum DM offset at
the bottom of the observing band that corresponds to a temporal smearing equal
to the time resolution of the NRT data (16 $\upmu$s) is 0.9 pc cm-3. In other
words, any burst with a DM lower than $218.56$ pc cm-3 or higher than $220.36$
pc cm-3 will experience residual temporal smearing due to imperfect coherent
dedispersion. Since the best-fit DM falls within this range, we can be
confident that the bursts do not experience significant intra-channel DM
smearing.

##  3 Search and Discovery of Bursts

In this work, we have expanded on the ÉCLAT pipeline presented by Hewitt et
al. (2023), to find bursts from FRB 20220912A. In short, the pipeline combines
the coherence products AA and BB from the eight recorded subbands to create
Stokes I filterbanks with the full 512-MHz bandwidth, before flagging radio
frequency interference (RFI), in frequency but not time, using the rfifind
tool from the PRESTO pulsar software suite (Ransom, 2011). Thereafter, a
boxcar match-filter search is conducted for impulsive transient signals,
between a DM of 200 and 250 pc cm-3, using the GPU-accelerated software
HEIMDALL111https://sourceforge.net/projects/heimdall-astro/. Heimdall searches
the full 512-MHz band, using a S/N threshold that we set at seven. The
resulting burst candidates are classified as being either astrophysical or RFI
using the deep-learning models ‘A’ to ‘H’ from the machine-learning classifier
FETCH (Fast Extragalactic Transient Candidate Hunter, Agarwal et al., 2020;
Agarwal & Aggarwal, 2020). Finally, all candidates assigned a $>0.5$
probability of being astrophysical are manually inspected to confirm they are
from FRB 20220912A.

In our pipeline, FETCH frequently assigned a $>0.5$ probability of being an
astrophysical transient to RFI and, less often, FRBs were misclassified as
RFI. Konijn (2023) established that within a sample of 7100 Heimdall
candidates containing 263 FRBs from FRB 20220912A, FETCH incorrectly
classified 54 FRBs (though note that FETCH has not been retrained specifically
on the NRT data). To mitigate this, we incorporated FETCH into a new
classification method which we term CATCH (Classification Algorithm and
Transient Candidate Handler; Konijn, 2023). CATCH classifies FRB candidates
based on the structure in the DM-time space. A detailed description of CATCH
is presented in Appendix A.

Heimdall has identified a total of 34546 potential FRB candidates, after which
our CATCH classification found 696 FRBs with a subband S/N $>$7.0. Here, the
subband S/N is the S/N value calculated only in the exact frequency and time
region of the burst. At the start of the observations, the event rate was
$\sim$60 burst per hour, which decreased and stabilised near the end of the
observations to $\sim$1.3 bursts per hour. A subset of the bursts is shown in
Figure 1. These bursts are not representative of the complete set, but were
selected to showcase bursts with high S/N and detailed structures.

Figure 1: A subset of the 696 NRT-detected bursts from FRB 20220912A. This
sample consists of very bright bursts, some of which show multiple sub-bursts
and/or microsecond-time-scale intensity fluctuations. Each thumbnail shows a
dynamic spectrum (bottom-left panel; $\Delta t=16\,\upmu$s and
$\Delta\nu=4\,$MHz), frequency-integrated lightcurve (top panel; integrated
over the entire frequency band), and time-integrated spectrum (bottom right
panel; integrated over the entire time range). All bursts have been coherently
dedispersed within each channel to DM = 219.46 pc cm-3 during recording.
Additionally, each burst has been incoherently dedispersed between channels to
the DM value (units pc cm-3) reported in the top-right of every thumbnail.
Also noted in the top-right of each thumbnail is the burst ID, which
corresponds to the entries in Tables 1 and 2. Horizontal white lines in the
dynamic spectra represent channels removed due to the presence of RFI. For
visual purposes, the colour maps of the dynamic spectrum range from the value
0.0 to the 99th percentile. The plotted S/N values for these bursts are lower
than those indicated in Table 1 because this data has not been downsampled,
and the S/N is calculated across the entire bandwidth. A detailed analysis of
bursts B411, B491, and B582 was previously presented in Hewitt et al. (2023).

##  4 Burst properties and analysis

Table 1 summarises the burst properties. In the following sub-sections we
describe how these properties were measured. While the ÉCLAT observations
include full polarimetric information, we differ the polarimetric analysis of
these data to a future paper.

Table 1:  Properties of our sample of 696 NRT-detected bursts from FRB 20220912A (full table available online). Burst ID | Time of arrival${}^{\text{a}}$ | Detection DM${}^{\text{b}}$ | Temporal width${}^{\text{c}}$ | Frequency extent${}^{\text{c}}$ | Central observed frequency${}^{\text{c}}$ | S/N${}^{\text{c, d}}$ | Fluence${}^{\text{c}}$
---|---|---|---|---|---|---|---
| (MJD) | (pc cm-3) | (ms) | (MHz) | (GHz) |  | (Jy ms)
B000 | 59867.90178241 | 222.94 | 5.63 | 140 | 1.462 | 26.8 | 3.06
B001 | 59867.90178356 | 222.94 | 9.12 | 132 | 1.322 | 16.1 | 2.90
B002 | 59867.90209490 | 226.96 | 5.89 | 120 | 1.286 | 22.1 | 4.02
B003 | 59867.90456018 | 218.94 | 6.66 | 216 | 1.538 | 24.1 | 2.83
B004 | 59867.90456053 | 218.94 | 8.32 | 200 | 1.398 | 23.2 | 2.83
B005 | 59867.90502314 | 226.96 | 5.38 | 348 | 1.414 | 14.1 | 1.18
… | … | … | … | … | … | … | …
${}^{\text{a}}$ Quoted to $\sim 1$ ms precision. Corrected to the Solar System
Barycentre at infinite frequency using the per-burst determined DM, a
dispersion constant of
${}^{\text{\ \ }}$ 1/(2.41$\times$104) MHz2 pc-1 cm3 s, and the EVN-derived
FRB 20220912A position (Hewitt et al.,
2024)222https://github.com/MSnelders/FRB-Burst-TOA. The times quoted are
dynamical times (TDB).
${}^{\text{b}}$ As determined by Heimdall.
${}^{\text{c}}$ As defined by CATCH (see Appendix A).
${}^{\text{d}}$ Subband S/N values calculated on data downsampled by a factor
of eight.

###  4.1 Spectro-temporal properties

Our transient classification method, CATCH, determined the frequency extent
($\Delta\nu$) and temporal width ($\tau_{\rm{burst}}$) of each burst by
outlining a rectangular box around the burst region in the dynamic spectrum.
The positioning of this box was verified manually for each FRB to ensure that
the box encompasses all burst emission, but not any high-intensity RFI. We
define the middle of the box in frequency extent as the central observed
frequency ($\nu_{\rm mid}$) of a burst.

Figure 2: The temporal width distribution for our sample of 696 NRT-detected
bursts from FRB 20220912A. The vertical dashed blue line indicates the median
at 7.68 ms.

Figure 2 shows the temporal width distribution for the 696 bursts we detected
from FRB 20220912A. Here, the temporal width of the burst is the width of the
box that was fitted to the burst, hence it encompasses the earliest and latest
times of emission in the case of multi-component bursts. The median temporal
width is 7.68 ms and the distribution is slightly skewed towards longer
durations.

Figure 3: The frequency extent, $\Delta\nu$, of each detected burst from FRB
20220912A is plotted against its central observed frequency $\nu_{\rm mid}$,
and coloured by its fluence. The right and top panels show the distritbutions
of $\Delta\nu$ and $\nu_{\rm mid}$, respectively, where the NRT bandpass has
been added to the top histogram. The error bars represent the Poissonian
uncertainty, with a 1$\sigma$ confidence interval. The dashed black triangular
shape in the middle panel represents the limits of our observing band (see the
text for more details). The colour of the bins of the side histograms
represents the median fluence of the bursts within each bin.

Figure 3 shows $\Delta\nu$ against $\nu_{\rm mid}$ for each burst, coloured by
fluence. Given that $\nu_{\rm mid}$ represents the middle of the frequency
extent where burst emission is visible within our observing band, bursts with
larger frequency extents will naturally have $\nu_{\rm mid}$ approaching the
center frequency of our observing band. The maximum allowed frequency extent
as a function of central frequency is shown by dashed black lines that
constrain the 2D distribution to a triangular region. The frequency extent
distribution exhibits an artificial peak at the maximum value, which is the
result of many bursts having a frequency extent larger than our observing
band. The median frequency extent is 248 MHz, while the central frequency
distribution demonstrates a preference for lower central frequencies. The top
histogram shows that more bursts are present at lower frequencies.

###  4.2 Fluence and energetics

The S/N and fluence of a burst are calculated within the spectro-temporal box
determined by CATCH. We note that for some bursts the emission clearly extends
beyond our observing band, but we refrain from extrapolating and estimating
frequency extents and fluences outside of the observing band. In these cases,
the quoted values are thus lower limits. We calculated the fluence of a burst,
$F$ (Jy ms), by integrating the flux with respect to time, using the
radiometer equation (Lorimer & Kramer, 2005):

$F=\text{S/N}\cdot\text{SEFD}\cdot\sqrt{\frac{\tau_{\text{burst}}}{{\rm
n}_{\text{pol}}\Delta\nu}}$ (1)

where SEFD is the system equivalent flux density ($\sim$ 25 Jy for the NRT)
and ${\rm n}_{\text{pol}}$ is the number of polarisations recorded in the
observation (2 in this case).

Figure 4: The burst fluence distribution for completeness thresholds 0.59,
0.69, 0.82 Jy ms, calculated for three temporal widths: 5.63, 7.68 and 10.79
ms. The grey areas indicate the incompleteness regions, whereas the purple
areas indicate the 1$\sigma$ fit error of a log-normal function to the
distributions. Fit residuals are shown in the smaller panels beneath each
fluence distribution.

Figure 4 shows the fluence distribution of our NRT-detected bursts for the
completeness thresholds that depend on assumed burst width. We estimated these
completeness thresholds using Equation 1, assuming a S/N $=7$, a frequency
extent of 248 MHz (the median value from fitting our burst sample), and three
different temporal widths: the first-quartile value from our burst temporal
duration distribution (5.63 ms), the second quartile (or median; 7.68 ms), and
the third quartile (10.79 ms). We then fit a log-normal distribution to the
data above the three aforementioned completeness thresholds. In all cases the
reduced $\chi^{2}$ values (1.31, 1.57 and 1.03) do not exceed the critical
$\chi^{2}$ values (1.58, 1.60 and 1.60), confirming that the fluence
distribution is well fit by a log-normal function regardless of the assumed
completeness threshold.

22footnotetext: https://github.com/MSnelders/FRB-Burst-TOA

The main panel of Figure 5 shows the bursts’ spectral energy densities,
$E_{\text{spectral}}$, which we calculated as follows (See Macquart & Ekers,
2018, Equation 10):

$E_{\text{spectral}}=1\times 10^{-23}\cdot\frac{F\cdot 4\pi
D_{L}^{2}}{(1+z)^{2}}\hskip 5.69046pt\text{erg/Hz},$

where $z$ and $D_{L}$ are the redshift and luminosity distance to the source
(0.0771 and 362.4 Mpc, respectively; Ravi et al., 2022).

Figure 5: Temporal evolution of the spectral energy distribution of FRB
20220912A bursts detected with the NRT. Slashes through Panels A and B
indicate a break in the continuity of the plotted timeline. Panel A: The green
bars show the duration of each observation, while the solid purple line
indicates the cumulative burst count with time. Panel B: The green data points
display the spectral energy of each detected burst, while the purple data
points show the bursts’ median spectral energy on each observing day. The
vertical dashed black line indicates the time when CHIME/FRB reported the
discovery of FRB 20220912A and when we started observing with NRT. Panel C:
The spectral energy distribution, considering all the detected bursts, is
shown in green with a log-normal fit and the 1$\sigma$ fit error indicted by
the purple line and shaded region. The mean lies at $10^{29.48}$ erg/Hz, with
a standard deviation of $10^{0.33}$ erg/Hz. Panel D: The cumulative spectral
energy distribution plotted in green and fitted with a power law, show by the
black dot-dashed line. The horizontal green lines indicate the theoretical
completeness thresholds for various assumed burst widths, assuming a minimal
S/N$=7$ detection, as in Figure 4. The solid green line indicates the
completeness threshold for assumed burst widths at 5.63 ms; the dash-dotted
line at 7.68 ms; and the dashed line at 10.79 ms. The distribution is seen to
flatten at higher energies, indicating that bursts with these energies happen
more frequently than predicted by extrapolating a simple power law based on
fitting lower-energy bursts. This effect is less obviously present in Panel C,
as several one-burst bins are obscured by the fit line.

In this figure, Panel A shows the duration of each observation (median of 0.92
hr) together with the cumulative burst count, illustrating the high cadence of
our observations. The majority of the bursts that were detected at the
beginning of the observational campaign have spectral energy densities in the
$10^{29}-10^{30}$ erg/Hz range. The distribution of spectral energies is shown
in Panel C, where a log-normal function is fitted to the data. The reduced
$\chi^{2}$ value is 1.09, which does not exceed the critical value of 1.39,
indicating a good fit. Panel D shows the cumulative distribution of spectral
energies. It depicts the burst rate per hour with spectral energies larger
than a specific threshold. The errors on the rate are Poissonian, and we
assume a fractional error of 20 per cent for the derived fluence values. The
apparent turnover visible at lower energies is a reflection of bursts being
detected close to the completeness threshold of the telescope, where it is
easier to miss some bursts.

We fit a power law to the distribution using the powerlaw package (Clauset et
al., 2009). In addition to performing power-law fits, this package identifies
the initial turnover point in the cumulative distribution to determine the
appropriate minimum spectral energy from which to start the fit. In the case
of a perfectly log-normal spectral energy distribution, the start of the
power-law fit (i.e., the mimimum spectral energy being fit) should coincide
with the completeness threshold. The three completeness thresholds for bursts
with temporal widths of 5.63 ms 7.68 ms, and 10.79 ms deviate from the start
of the power law by approximately $10^{0.61},10^{0.54},$ and $10^{0.47}$
erg/Hz, respectively. This could, in principle, indicate that the spectral
energy distribution flattens at lower energies. Note that the completeness
threshold can also deviate even more from its estimated value, in which case
the log-normal distribution would not fit the data well. The fitted power law
has a slope of $-1.67\pm 0.01\pm 0.06$, where the first error is determined as
the quadrature sum of the error on the fit using the fractional 20 per cent
fluence errors and the second error is determined by bootstrapping. The data
follows the power law until spectral energies of $10^{30.5}$ erg Hz-1, after
which the distribution appears to flatten. This flattening of the cumulative
spectral energy distribution has been seen in other repeaters such as FRB
20121102A (Hewitt et al., 2022) and FRB 20201124A (Kirsten et al., 2024), and
will be discussed in more detail for FRB 20220912A by Ould-Boukattine et al.
(in prep.), using additional data from several other telescopes.

The isotropic-equivalent energy (in erg) is the total energy released,
assuming that the energy is radiated isotropically. We assume isotropic
emission due to the unknown beaming angle, despite the expectation that FRB
emission is highly directional. The isotropic-equivalent energy can be
determined by multiplying the spectral energy by the bandwidth of the burst in
Hz. Figure 6 shows the temporal widths of the bursts plotted against their
isotropic-equivalent energies. The colours of the histograms are based on the
median of the bursts inside each bin. Bursts with higher isotropic-equivalent
energies and greater temporal widths tend to span larger bandwidths, whereas
bursts with lower isotropic-equivalent energies tend to span smaller
bandwidths.

Figure 6: The temporal widths of bursts plotted against their isotropic-
equivalent energy. The histograms are coloured based on the median value of
the bursts within each bin.

###  4.3 Dispersion measure and time-frequency drift

Determining the DM of a burst is non-trivial, due to the complex spectro-
temporal morphology seen in many FRBs, along with the lack of a priori
knowledge about how the burst should look. There is no exact model for each
individual FRB and effects such as scintilation, the sad-trombone effect
(Hessels et al., 2019), and the residual intra-burst drift not related to
dispersion seen in many bursts (e.g., Rajabi et al., 2020; Chamma et al.,
2021; Jahns et al., 2023) make it difficult and ultimately ambiguous to
accurately determine the ‘true’ DM. In this paper, we determined the DMs using
DM_phase (Seymour et al., 2019)333https://github.com/danielemichilli/DM_phase,
which maximizes the coherent power of a burst across the bandwidth in order to
determine a best DM. Using 32-bit, coherently dedispersed (DM = 219.46 pc
cm-3) filterbank data, we estimated the DM for 15 bursts with subband S/N
$>100$ and visible (sub-)millisecond temporal structure, carefully selecting a
suitable range of fluctuation frequencies to consider in DM_phase. The
selected bursts are: B038, B050, B090, B267, B318, B384, B411, B491, B510,
B528, B578, B582, B602, B664, and B669. Our DM measurements are tabulated in
Table 2.

Table 2:  Properties of the FRB 20220912A bursts with fluctuation frequencies $>2.5$ ms-1 Burst ID | Time of arrival${}^{\text{a}}$ | DM${}^{\text{b}}$ | DM error${}^{\text{c}}$ | Min. fluctuation frequency | Max. fluctuation frequency | Temporal width${}^{\text{d}}$ | Spectral extent${}^{\text{d}}$
---|---|---|---|---|---|---|---
| (MJD) | (pc cm-3) | (pc cm-3) | ($1\times 10^{-1}$ ms-1) | ($1\times 10^{-1}$ ms-1) | (ms) | (MHz)
B038 | 59870.88721446 | 219.51 | 0.06 | 60 | 175 | 8.37 | 380
B050 | 59871.87238284 | 219.37 | 0.10 | 50 | 120 | 1.42 | 348
B090 | 59873.88115071 | 219.58 | 0.20 | 10 | 51 | 5.44 | 128
B267 | 59877.86661735 | 219.47 | 0.05 | 120 | 244 | 5.14 | 444
B318 | 59879.83220702 | 219.45 | 0.23 | 21 | 57 | 3.49 | 404
B384 | 59881.86993869 | 219.36 | 0.01 | 850 | 2050 | 47.78 | 452
B411${}^{\text{e}}$ | 59881.83351237 | 219.39 | 0.10 | 29 | 102 | 26.08 | 308
B491${}^{\text{e}}$ | 59884.83816794 | 219.38 | 0.01 | 1000 | 3125 | 10.50 | 500
B510 | 59889.82448343 | 219.40 | 0.01 | 1000 | 3125 | 8.67 | 412
B528 | 59891.81058320 | 219.64 | 0.10 | 33 | 112 | 8.21 | 248
B578 | 59898.82970864 | 219.62 | 0.22 | 10 | 50 | 1.98 | 220
B582${}^{\text{e}}$ | 59899.78833990 | 219.72 | 0.02 | 200 | 550 | 9.73 | 492
B602 | 59900.82699925 | 219.68 | 0.06 | 40 | 220 | 7.95 | 484
B664 | 59917.75117914 | 222.53 | 0.48 | 7 | 27 | 6.42 | 440
B669 | 59919.74566971 | 223.09 | 0.28 | 20 | 50 | 6.66 | 392
${}^{\text{a}}$ Quoted to $\sim 1$ ms precision. Corrected to the Solar System
Barycentre at infinite frequency using the per-burst determined DM, a
dispersion constant of
${}^{\text{\ \ }}$ 1/(2.41$\times$104) MHz2 pc-1 cm3 s, and the EVN-derived
FRB 20220912A position (Hewitt et al., 2024)blue2. The times quoted are
dynamical times (TDB).
${}^{\text{b}}$ Computed using DM_phase within the spectro-temporal confines
of the burst defined by CATCH.
${}^{\text{c}}$ See Appendix B.
${}^{\text{d}}$ The temporal width and frequency extent of the burst defined
by CATCH (see Appendix A).
${}^{\text{e}}$ These three bursts are presented in detail in Hewitt et al.
(2023). The DMs reported here are consistent with the DMs those authors
determined,
${}^{\text{\ \ }}$ where they ensured that the extremely short time-scale,
broad-band structures (microshots) arrived at all observed frequencies at the
same time.

In Figure 7 the DM is plotted as a function of time. The DM appears constant
over the majority of our campaign. However, towards the end of our campaign,
we observe an apparent increase in the DM of 2.86$\pm$0.54 pc cm-3 from
Modified Julian Date (MJD) 59900 to MJD 59917. We can determine the validity
of this increase in DM by looking at the total drift rate of each bright
(S/N$>30$) burst.

Figure 7: DM measurements for all bursts above a CATCH S/N of 120 and with the
maximum fluctuation frequencies exceeding $2.5$ ms-1. This fluctuation
frequency limit ensures that the timescales on which the intensity
significantly changes are smaller than 4 ms. The colour of each point
indicates the subband S/N of the respective bursts. The dashed horizontal
line, along with the shaded region, indicates the original DM and its
associated error reported by McKinven & CHIME/FRB Collaboration et al. (2022).
There appears to be a jump in the DM between MJDs 59900 and 59917.

The total drift of a burst is mainly determined by three factors: the DM, the
sad-trombone-induced drift between sub-bursts, and the intra-(sub-)burst
drift. Assuming the influence of the sad-trombone drift and the intra-burst
drift remains constant over time, any observed increase in the total drift
over time could then be attributed to an increase in the DM. To determine the
total drift, we follow the methodology presented in Gopinath et al. (2024),
where we fix the DM to 219.46 pc cm-3 (the DM used for coherent dedispersion),
and measured the burst drift for all bursts that have a S/N$>30$. This entails
fitting a 2D Gaussian function to the auto-correlation function (ACF) of the
bursts, where the zero-lag noise spike has been masked. The drift rate is then
essentially $cot(\theta)$, where $\theta$ is the angle of the 2D Gaussian,
measured counterclockwise from the positive y-axis to the semi-major axis. The
total drift is shown in Figure 8.

Figure 8: The total drift of each burst with S/N $>30$, where the DM has been
fixed at 219.46 pc cm-3. The dashed grey line indicates no drift. The
histogram bars are coloured based on the median value of the bursts within
each bin.

We find a median drift rate of $-8.8\,$ MHz ms-1. The drift rate appears to
stay more or less constant throughout our campaign. As the burst rate
(apparently) decreases, fewer measurements are available. We performed a
Kolmogorov-Smirnov test using scipy.stats.kstest, comparing the drift
measurements before and after MJD 60000, to see if there is a statistically
significant decline in the magnitude of the drifts over time. We find
$p=0.0986$ and $K=0.38$, and thus cannot reject the null hypthesis that the
samples are drawn from the same distribution. This lack of an increase in
drift, given a fixed DM, also argues for a DM that is (roughly) constant over
time. An increase in DM by $\sim 2$ pc cm-3 would result in significant
differences between the samples before and after MJD 60000. It is likely that
we have absorbed some of the sad-trombone drift or intra-burst drift in bursts
B664 and B669 when determining the DM – thus leading to an apparently higher
DM when naively fitting those bursts.

###  4.4 Wait-times

The time between successive bursts is referred to as the ‘wait-time’. We
consider two bursts to be separate, rather than multiple components of a
single burst, if the signal between the two high-intensity regions returns to
the level of the noise. In Figure 9 we show the wait-time distribution for our
sample of NRT-detected bursts. As for several other repeaters, e.g. FRB
20121102 (Li et al., 2021), FRB 20201124A (Xu et al., 2022), and FRB 20200120E
(Nimmo et al., 2023), the distribution is bimodal. We fit two log-normal
functions to the peaks, yielding a reduced $\chi^{2}$ value of 1.08, which is
below the critical threshold of 1.36, indicating a good fit. To minimise the
effect of outlier data points, and to more robustly estimate uncertainties, we
have bootstrapped the data by randomly selecting 90 per cent of the data
without replacement 1000 times, and only fitting that sample with a log-normal
function. From our bootstrapping analysis, we find wait-time peaks at
$33.40\pm 6.41$ ms and $67.03\pm 2.61$ s. Note that the quoted error is the
uncertainty on the location of the wait-time peak. The full width at half
maximum of the shorter-timescale (left) peak at 33.40 ms is 63.30 ms.

Figure 9: The distribution of the wait-times from FRB 20220912A plotted on a
logarithmic scale. A double log-normal distribution has been fitted to the
data, and the peaks of the wait-time distribution are at $33.40\pm 6.41$ ms
and $67.03\pm 2.61$ s, respectively. Note that the quoted error is the
uncertainty on the location of the wait-time peak. The purple areas indicate
the 1$\sigma$ fit error and the bottom plot shows the fit residuals. The top
plot shows the cumulative wait-time distribution of the second wait-time peak,
to which a Weibull cumulative distribution function has been fitted. The total
error on the shape parameter $k$ is a combination of the error on the fit, and
the error derived from bootstrapping 1000 times. The burst rate deviates from
a Poisson distribution, as the shape parameter of the fitted Weibull CDF
$k=0.88\pm 0.01\pm 0.01$ is not equal to 1.0.

Also shown in Figure 9 is the cumulative wait-time distribution for wait-times
corresponding to the second peak at longer times. We can use this cumulative
wait-time distribution to test if the burst rate is Poissonian, over the
course of our observing campaign, or if there is clustering in time. If the
bursts are distributed in time according to a Poisson process, then the
distribution of intervals $t_{\text{wait}}$ between subsequent bursts would
have an exponential distribution. One generalisation of an exponential
distribution of intervals is the Weibull distribution

$\mathcal{W}(t_{\text{wait}}|k,r)=k\,t_{\text{wait}}^{-1}\,[t_{\text{wait}}\,r\,\Gamma(1+1/k)]^{k}~{}\text{e}^{-[t_{\text{wait}}\,r\,\Gamma(1+1/k)]^{k}},$
(2)

where $r$ is the burst rate, $\Gamma$ is the gamma function, and $k$ is the
shape parameter (Papoulis & Unnikrishna Pillai, 2002). The cumulative density
function (CDF) of the Weibull distribution can be fitted to the cumulative
wait-time distribution to test for possible burst clustering (e.g., Oppermann
et al., 2018). The Weibull CDF is defined as:

$P_{\text{Weibull}}=1-e^{-(t_{\text{wait}}\,r\,\Gamma(1+1/k))^{k}}.$ (3)

This function is identical to the Poisson CDF when $k=1$, while $k\neq 1$
implies that the bursts have a variable rate and cluster in time.

We find that the best-fit Weibull burst rate is $31.7\pm 0.4$ bursts/hour,
with a shape parameter of $0.88\pm 0.01\pm 0.01$. The total error on the shape
parameter is a combination of the error on the fit and the error derived from
bootstrapping. As before, the data is bootstrapped 1000 times.

###  4.5 Burst rate

Figure 10: The activity of FRB 20220912A during our observing campaign. The
error bars on the burst rate represent the Poissonian uncertainty, with a
1-$\sigma$ confidence interval. Panel A shows the duration of each
observation, $T_{\text{obs}}$, in hours. Panel B shows the average burst width
per observation, where the errors indicate the root-mean-square deviation.
Panel D stacks the frequency band of each burst per observation to illustrate
the total number of bursts within each frequency channel.

We mapped the burst activity and spectral evolution of FRB 20220912A bursts in
Figure 10. The main panel shows the average burst rate per hour, with
1-$\sigma$ Poissonian errors, for each observation against the corresponding
MJD. Shortly after the beginning of the observation campaign (MJD 59880), the
burst rate peaked at $75^{+10}_{-9}$ bursts per hour, as seen by NRT. The
burst rate was highly time-variable, with consecutive observations fluctuating
by up to 90 per cent. The gap in observations between MJD 59935 and MJD 60007
is due to a holiday break followed by maintenance. In Panel A, we show the
duration of each observation in hours. Despite our observations having more or
less the same duration throughout the campaign, we witness a significant drop
in the burst rate around MJD 59910. The burst rate rapidly peaked and then
gradually diminished over a period of $\sim 80$ days, displaying variations in
burst rate during this period.

Panel D of Figure 10 is a density plot displaying a superposition of the
frequency extent of each individual burst for every observation. When multiple
bursts overlap, the coloured lines appear stronger. There is no obvious
correlation with the burst rate and the location of the bursts in frequency
space.

##  5 Discussion

###  5.1 Burst morphology

Most of the bursts we detected are narrowband, as is often the case for
repeating FRBs (e.g., CHIME/FRB Collaboration et al., 2023). A few bright
bursts in our sample show ‘microshots’, extremely short-time-scale, broader-
band structures. These events are rare ($\lesssim 1$% of the bursts in our
sample show this), and we have only identified them in high-S/N bursts that
also show millisecond-scale sub-bursts as well. The best examples in our
sample were previously discussed in detail by Hewitt et al. (2023), who also
showed that the occurrence of microshots is clustered in two high-fluence
bursts (B411 and B491 in our naming convention). Such microshots have
previously been observed superimposed on millisecond-duration bursts from
repeaters FRB 20180916B (Nimmo et al., 2021) and FRB 20200120E (Nimmo et al.,
2023). In the case of FRB 20121102A, isolated microshots were seen at high
frequencies ($3.9-9.3$ GHz; Snelders et al., 2023). Overall, microshots appear
to be a rare phenomenon in repeating FRBs, compared to the more typical
millisecond-duration bursts, and they may have a different emission mechanism
that is triggered by the same underlying event that creates the bursts in
general (Hewitt et al., 2023).

The NRT bandpass is calculated using the NRT noise diode scans, and is visible
in the top histogram of Figure 3. It shows greater sensitivity at lower
frequencies, potentially (partially) explaining the higher occurrence of
bursts at lower frequencies. However, these lower frequencies are also more
susceptible to RFI, significantly influencing the bandpass. Therefore, the
bandpass may also somewhat reflect the higher levels of RFI, instead of the
innate higher sensitivity. The apparent preference for burst emission at lower
frequencies in the NRT observing band agrees with observations of FRB
20220912A by the Five-hundred-meter Aperture Spherical Telescope (FAST; Zhang
et al., 2023) and the Allen Telescope Array (ATA; Sheikh et al., 2024). The
top histogram of Figure 3 also indicates that bursts at these lower
frequencies were generally more energetic. Observations by FAST and ATA were
conducted with an observing band that stretches to slightly lower frequencies
($1000-1500$ MHz and $900-2244$ MHz for FAST and ATA, respectively) than our
NRT data. The central frequency of the bursts was found to be drifting down by
6.12 $\pm$ 0.76 MHz per day (Sheikh et al., 2024). Furthermore, the majority
of burst emission seems to occur just below the NRT observing band which, in
combination with the decreasing central frequencies of the bursts, gives rise
to a more rapid drop in burst rate observed by NRT (around MJD 59900),
compared to FAST and ATA.

###  5.2 Energetics

Plotted in Panel D of Figure 5 is the cumulative spectral energy distribution,
where the three representative completeness thresholds deviate from the start
of the power law by approximately $10^{0.61},10^{0.54},$ and $10^{0.47}$
erg/Hz. This could indicate that the spectral energy distribution flattens at
lower energies. Zhang et al. (2023) observe a bimodality of the energy
distribution for FRB 20220912A, and other repeating FRBs, like FRB 20121102A
and FRB 20201124A, also show this bimodal energy distribution (e.g., Aggarwal
et al., 2021; Li et al., 2021; Jahns et al., 2023). Due to our limited
sensitivity compared with FAST, we are likely only sampling the tail of the
distribution at lower energies, which is why the distribution also seems to
flatten at lower energies and which is likely why the completeness thresholds
and start of the power-law fit are misaligned. We do not attempt to model a
low-energy turnover in the burst rate.

The cumulative spectral energy distribution also flattens at higher energies,
showing that higher-energy FRBs occur more often than would be expected based
on an extrapolation from a simple power law. This aspect of FRB 20220912A’s
behaviour will be discussed in more detail by Ould-Boukattine et al. (in
prep.), who incorporate additional data from several other telescopes as well
as more advanced modelling.

###  5.3 Wait-times

Figure 9 shows the burst wait-time distribution. Similar to many other
repeaters (e.g., Li et al., 2021; Hewitt et al., 2022; Nimmo et al., 2023),
the distribution seen from FRB 20220912A is bimodal. We find that the longer-
timescale (right) peak of the wait-time distribution lies at 67.03 s, which is
at longer timescales than the equivalent wait-time peak seen from FAST
observations of FRB 20220912A (18.05 s; Zhang et al., 2023). The fluctuating
burst rate, 20-fold sensitivity difference between the NRT and FAST, and the
fact that FAST observations are typically half as long on average, all
influence the position of this peak. Aggarwal et al. (2021), e.g., have shown
how this right peak shifts to shorter timescales as more bursts are detected
in a constant-length observation.

The shorter-timescale (left) peak in the wait-time distribution (33.40 ms) is
comparable not only to what has been found by other telescopes observing this
source, e.g. 50.98 ms (Zhang et al., 2023), but also to other sources such as
FRB 20201124A (51 ms in Zhang et al. 2022 and 39 ms in Xu et al. 2022), and
FRB 20121102A (24 ms in Hewitt et al., 2022). Note that we classify candidates
as separate bursts if the intensity between the peaks returns to the noise
level. Other authors have used different methods to distinguish between a
single multi-component burst and multiple bursts, which could result in
different peaks in the wait-time distribution (e.g., see Jahns et al., 2023,
for a discussion and distinction). The increased likelihood of detecting a
burst very shortly ($<$ 100 ms) after another burst, appears to be universal
among the most active repeaters, with the exception of FRB 20200120E, the
globular cluster repeater. FRB 20200120E also shows a potential bimodality in
its wait-time distribution, but rather than at tens of milliseconds, the
short-wait-time peak is at 0.94 seconds (Nimmo et al., 2023). Future studies
should aim to constrain whether the short-wait-time peak is constant with time
for a particular source, and how the timescale compares between sources.
Additionally, the existing datasets need to be reanalyzed with consistent
assumptions above what constitutes a sub-burst versus a separate burst.

The timescales of the short-wait-time peaks seen from repeaters might be
associated with the physical size of the region where bursts are generated, or
perhaps the time required for perturbations to propagate through this region
(Nimmo et al., 2023; Totani & Tsuzuki, 2023). Such a bimodality in the wait-
time distribution has also been seen in short X-ray bursts from magnetars
(e.g., Huppenkothen et al., 2015). While Huppenkothen et al. (2015) suggest
that these wait-times align with both repeated crust failure and
magnetospheric reconnection models, Wadiasingh & Chirenti (2020) propose that
the shorter timescales observed in the wait-time distributions of magnetars
are more likely associated with crustal magnetar oscillations. Another
alternative that might explain the presence of the short-wait-time peak is the
occurrence of aftershocks following a starquake within a neutron star crust
(Totani & Tsuzuki, 2023). If consecutive bursts were indeed the result of
aftershocks, one might expect a trend where fluence of the first burst is
consistently higher; however, this relation has not been found in this work,
or in previous studies (e.g. Gourdji et al., 2019).

###  5.4 Burst rate

High variability in the burst rate, as illustrated for FRB 20220912A in Figure
10, has also been seen in other repeating FRBs, namely: FRB 20121102, FRB
20200120E, FRB 20201124A, and FRB 20240114A (e.g., Li et al., 2021; Nimmo et
al., 2023; Lanman et al., 2022; Shin et al., 2024). This variability is not
only seen in other FRBs but also in magnetars and pulsars that emit giant
pulses. Magnetars can exhibit outbursts during which they emit numerous short
X-ray bursts within a short time frame, typically ranging from tens to
hundreds of bursts per hour (Gavriil et al., 2004; Israel et al., 2008; Van
der Horst et al., 2012). An excellent example of this high variablity was seen
in 2020 from the magnetar, SGR 1935+2154, when it generated a millisecond-
duration radio burst with a luminosity comparable to the lowest-luminosity
FRBs (CHIME/FRB Collaboration, 2020; Bochenek et al., 2020). During its
outburst phase, the X-ray burst rate was approximately 720 bursts per hour
(Fletcher & Fermi GBM Team, 2020; Palmer, 2020; Younes et al., 2020), but
rapidly declined to approximately 29 bursts per hour within a mere 3-hour
period. In the context of giant pulse emitters, significant variations in the
rate of giant pulses have also been observed across different observing
epochs. For instance, in the case of the Crab pulsar (PSR B0531+21), the rate
of giant pulses with high fluence ($>$ 130 Jy ms) has been found to vary by up
to a factor of five between consecutive observing days (Bera & Chengalur,
2019).

Motivated by the lack of clear bimodality in the repetition rate distribution
of FRB sources (repeaters versus non-repeaters; CHIME/FRB Collaboration et
al., 2023), and the potential of a correlation between repetition rate and
burst width (Connor et al., 2020), we searched for a correlation between the
burst rate and burst width in our sample. Such a correlation across a
population of sources could be attributed to differences in the beaming angle,
whereby FRBs with a broader beaming angle would exhibit higher observed
repetition rates. The top panel of Figure 10 shows the median burst width per
observation against the burst rate of that observation. We see no correlation
between the median burst width and burst rate on a per-observation basis,
concluding that for our sample of bursts from FRB 20220912A the burst width is
independent of activity rate. While this correlation does not exist for our
sample of bursts from FRB 20220912A, it might still exist across a larger
sample of different sources and we encourage future works to investigate this.

The total wait-time distribution, considered over the entire observing
campaign, shows clustering, but individual observations on hour-long
timescales appear Poissonian (see Appendix C). To investigate further, we
applied an identical Weibull analysis to the wait-time distribution of the
FAST data presented in Zhang et al. (2023). These observations have higher
burst rates, and have shorter observation durations ($\sim$30 minutes). Using
the total set of observations, we obtained a shape parameter of $k=0.93\pm
0.003\pm 0.01$. Despite FAST’s increased sensitivity, higher burst rate, and
the shorter duration of the observations, it also demonstrates clustering in
the wait-times.

###  5.5 DM and Drift

Figure 7 shows the DM of bursts with S/N$>120$ and fluctuation frequencies
exceeding 2.5 ms-1, where we observed an apparent increase in the DM from MJD
59900 to MJD 59920. However, this apparent increase in the DM was not
corroborated when we looked at the total drift rate of a set of bright
(S/N$>30$) bursts, shown in Figure 8. We therefore conclude that we have
incorporated the sad-trombone drift or intra-burst drift into the DM
calculation when determining the DMs of bursts B664 and B669. Figure 11 shows
both B664 and B669 dedispersed to a DM of 219.46 pc cm-3 and to the DM
optimized for maximising coherent power in each burst. Here, both bursts
appear consistent with a DM of 219.46 pc cm-3. Although we do not find any
large DM variations over time, (Hewitt et al., 2023) reported robust evidence
for DM variations on the level of $\sim 0.3$ pc cm-3 on the timescale of weeks
– using broad-band microshots to unambiguously determine the DM accurately and
precisely.

We find a mean drift rate for FRB 20220912A of $-8.8\,$MHz ms-1, which is a
combination of the excess DM beyond 219.46 pc cm-3, the drift induced by the
sad-trombone effect, and the intra-burst drift. Our mean drift is more than an
order-of-magnitude smaller than those quoted for FRB 20121102A in Hessels et
al. (2019) ($\sim-200\,$MHz ms-1), where the sad trombone effect dominated the
drift rate. Our mean drift rate is comparable with the drift rate from FRB
20180916B quoted in Pastor-Marazuela et al. (2021) at similar frequencies
($-39\pm 7\,$MHz ms-1). Note that our quoted drift rate is likely smaller, due
to the fact that we have fixed our DM to a constant value. Our drift rate is
also comparable to FRB 20201124A, where Zhou et al. (2022) quotes a mean
single component drift rate of $-61\pm 9\,$MHz ms-1, and a mean multi-
component drift rate of $-21\pm 4\,$MHz ms-1.

(a) Dynamic spectrum of burst B664 dedispersed to a DM of 219.46 pc cm-3 and
to a DM of 222.539 pc cm-3.

(b) Dynamic spectrum of burst B669 dedispersed to a DM of 219.46 pc cm-3 and
to a DM of 223.090 pc cm-3.

Figure 11: Dynamic spectra of bursts B664 and B669, dedispersed to a DM of
219.46 pc cm-3 and to the DM optimized for maximising coherent power in each
burst. The black dotted line marks the onset of each burst. Visual inspection
suggests consistency with a DM of 219.46 pc cm-3 for both bursts.

##  6 Conclusions & Future work

We performed a study of the repeating FRB 20220912A using the NRT, where a
total of 61 hours of observations were conducted over the course of 6 months.
Employing the new CATCH pipeline, a total of 696 bursts were detected, with an
observed event rate up to $75^{+10}_{-9}$ bursts per hour (above fluence 0.59
Jy ms), demonstrating the remarkably high activity of the source, which has
also been noted by other studies (e.g., Zhang et al., 2023; Feng et al., 2022;
McKinven & CHIME/FRB Collaboration et al., 2022). FRB 20220912A shows various
features which appear to be common among (hyper)active repeaters:

  * •

The wait-time distribution is bimodal, showing peaks at 33.4 ms and 67.0 s.
The short-wait-time peak at 33.4 ms is roughly consistent between repeating
FRB sources, to within a factor $\sim 2$ (e.g., Hewitt et al., 2022).

  * •

The cumulative spectral energy distribution flattens towards the highest
energies ($E_{\nu}\gtrsim 10^{31}$ erg/Hz), as also seen for another
hyperactive repeater (Kirsten et al., 2024). We will analyse and discuss this
in more detail in an upcoming paper (Ould-Boukattine et al., in prep.).

  * •

The DM is roughly constant in time when taking into account the confusing
factor of ‘sad-trombone’ time-frequency drift ($\delta$DM $\lesssim$ 2 pc
cm-3). Nonetheless, we confirm the results of Hewitt et al. (2023), and find
that small DM variations, on the order of $\sim 0.3$ pc cm-3, are occurring.

  * •

The bursts show a mean ‘sad trombone’ drift rate of $-8.8\,$MHz ms-1 (for
bursts with S/N$>30$). This is comparable to some known repeaters, but much
less compared to others measured in the same frequency range (e.g., Hessels et
al., 2019).

  * •

We observe that more bursts occur towards the bottom of the NRT observing
band, at around 1350 MHz, consistent with quasi-contemporaneous observations
from FAST (Zhang et al., 2023) and ATA (Sheikh et al., 2024).

  * •

While the burst rate within $\sim$1-hr observations appears Poissonian, we
find that the rate in the entire observing campaign is better modelled by a
Weibull distribution, with shape parameter $k=0.88\,\pm\,0.01\,\pm\,0.01$,
showing clustering.

  * •

The 16-$\upmu$s time resolution of the data allows us to probe microshots in
the bursts, but we find that these occur in only $\lesssim 1$% of the bursts
in our sample. The rare occurrence of microshots has also been seen in other
repeaters (e.g. Nimmo et al., 2023).

The breadth of phenomena displayed by repeating FRBs provides multiple
dimensions to quantitatively compare their properties and to constrain
theoretical models of their nature. ÉCLAT is continuing to monitor repeating
FRBs at $1218-1740$ MHz (and sometimes also at $>2$ GHz) with approximately
weekly cadence, providing a valuable complement to CHIME/FRB’s daily
monitoring of these sources at $400-800$ MHz.

## Acknowledgements

The AstroFlash research group at McGill University, University of Amsterdam,
ASTRON, and JIVE is supported by: a Canada Excellence Research Chair in
Transient Astrophysics (CERC-2022-00009); the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme
(‘EuroFlash’; Grant agreement No. 101098079); and an NWO-Vici grant
(‘AstroFlash’; 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 INSU, CNRS, France. K. N. is an MIT Kavli Fellow.

## Data Availability

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

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##  Appendix A The Classification Algorithm and Transient Candidate Handler

Ideally, each FRB candidate from the search pipeline is validated by eye.
However, conducting a manual review of tens of thousands of candidates,
generated from tens of hours of observations, is not feasible or reproducible.
In most FRB searches, convolutional neural network classifiers (e.g., FETCH)
have been employed to greatly reduce the number of candidates requiring manual
inspection. However, these classifiers are not perfect (especially when not
retrained) and occasionally misclassify real FRBs.

In an attempt to address this issue, we developed a classifier algorithm
called "The Classification Algorithm and Transient Candidate Handler" (CATCH,
for short). CATCH parses all candidates created by Heimdall that fulfill any
of the following criteria: i) FETCH’s deep-learning models ‘A’ to ‘H’ indicate
a probability larger than 0.5 that the candidate is astrophysical; ii)
candidates that have a subband S/N larger than 200; iii) candidates identified
based on their brightness distribution in the DM-time space through a method
we will refer to as the ‘bow tie’ method (Konijn, 2023).

###  A.1 Identification of the bow tie feature

The bow tie method tries to classify candidates based on their brightness
distribution in the DM-time spectrum, i.e. the frequency-integrated burst
brightness as a function of DM and time. The DM-time spectrum is created by
dedispersing the dynamic spectrum of a burst for a range of trial DM values,
and then integrating across all frequencies. In this parameter space, an
astrophysical transient with a large non-zero DM, gives rise to a symmetric
‘bow tie’-like shape, as visible in Figure 12.

Figure 12: Frequency-integrated burst brightness as a function of DM and time
for burst B049. The defining ‘bow tie’-shaped feature of an impulsive and
dispersive astrophysical signal is clearly visible. Fine ‘spokes’ are also
visible in the bow tie, indicating time-frequency structure in the dynamic
spectrum.

Terrestrial RFI is not significantly dispersed (though it can be frequency-
swept), effectively allowing for the identification of astrophysical
candidates based on the presence of the bow tie shape in the DM-time spectrum.
In an ideal case, the bow tie can be identified by comparing the intensity at
the centre of the bow tie (at the true DM) with the intensity at the edges (at
some other trial DM). However, this comparison is difficult because the bow
tie can vary in size, intensity, opening angle, and pointing angle. To ensure
consistency in our comparison, given the different spectro-temporal features
of bursts, we first vertically align the bow tie, after which we estimate the
size of the bow tie based on the duration and bandwidth of the burst in the
dynamic spectrum (frequency-time space).

The bow tie can be vertically aligned by correcting for the temporal delay
between the highest and lowest frequency of the burst caused by the
dispersion. These frequencies can be obtained by placing a box around the
burst in the dynamic spectrum, after masking those channels contaminated by
RFI. The optimal location and size of this box are determined by maximising
the summed intensity divided by the square root of its area. An example of an
optimised box is shown in 13.

Figure 13: Dynamic spectrum of burst B049. A box has been placed surrounding
the highest intensity areas, and is plotted as the red dashed rectangle. The
horizontal white bands are the zapped frequency channels, which complicates
the process of determining the frequency range of the box. Added to the top
and the side of the dynamic spectrum are the one dimensional integrated
spectra, where the dashed red lines again indicate the location of the box.

###  A.2 Bow tie size

The next step involves determining the size of the bow tie, primarily
influenced by the frequency extent and temporal width of the burst. Bursts
with large frequency ranges or narrow temporal widths have their frequency-
integrated intensity significantly affected by slight variations in DM,
resulting in a smaller bow tie. We can calculate this change in intensity due
to different DM values per burst and use it to characterise the size of the
bow tie.

Due to dispersion, there is a frequency-dependent time-smearing effect (Cordes
& McLaughlin, 2003). This is equal to

$\Delta
t_{\rm{DM}}=8.3\cdot\upmu\text{s}\cdot\text{DM}\cdot\Delta\nu_{\text{MHz}}\cdot\nu_{\text{GHz}}^{-3},$
(4)

for a frequency extent $\Delta\nu_{\text{MHz}}$, an observing frequency
$\nu_{\text{GHz}}$, and a dispersion measure DM. Using a DM value that is
incorrect by an amount $\delta$DM increases the temporal width of the pulse by

$\Delta t_{\delta\text{DM}}=\Delta t_{\text{DM}}(\delta\text{DM}/\text{DM}).$
(5)

By combining these equations, an expression for the time smearing as a
function of incorrect DM value can be found:

$\Delta t_{\delta\text{DM}}=8.3\
\upmu\text{s}\cdot\Delta\nu_{\text{MHz}}\cdot\nu_{\text{GHz}}^{-3}\cdot\delta\text{DM}.$
(6)

Reordering terms results in an equation for $\delta$DM as a function of the
temporal smearing:

$\delta\text{DM}=\Delta t_{\delta\text{DM}}/(8.3\
\upmu\text{s}\cdot\Delta\nu_{\text{MHz}}\cdot\nu_{\text{GHz}}^{-3}).$ (7)

Since the total power of the burst remains constant, time smearing that will
increase the width of the burst by a factor N will decrease the per-pixel
intensity in the DM-time spectrum by a factor sqrt(N). By assuming $\Delta
t_{\delta\text{DM}}=10\times t_{\text{burst}}$, we can compute the error
associated with the DM required to achieve this temporal width. Thus, for each
burst, we can calculate the number of DM trials where the bow tie width will
be smeared by a factor of ten and the intensity reduced by a factor of
$\sqrt{10}$. We define the size of the symmetrical bow tie as the number of DM
units on both sides that reduce the intensity with a factor of $\sqrt{10}$.

To identify the bow tie, we compare the intensity in the centre of the bow tie
with the intensity at the top and bottom of the bow tie. The width of the box
is equal to the temporal width of the burst in the dynamic spectrum, and the
height of the box is calculated using the above equations where $\Delta
t_{\delta\text{DM}}=3\times t_{\text{burst}}$, to take into account the
smearing of the burst. The amount of DM units between the centre of the box
and the top and bottom has been calculated using $10\times t_{\text{burst}}$.
Here, the box is slid across the spectrum at the calculated trial DM using a
sliding window of $10\times t_{\text{burst}}$ ms, where the box with the
highest intensity is selected for comparison with the box in the centre.

An example is shown in Figures 14(a) and 14(b) for an RFI candidate and for
burst B049, respectively. For the RFI candidate, the intensity remains
relatively consistent at both the top and bottom of the plot, whereas, for
burst B049, there is a substantial decrease in intensity. The ratio between
these intensities is a reliable indicator for distinguishing between FRBs and
RFI, and we dub this the ‘bow tie intensity ratio’. For the RFI candidate, the
bow tie intensity ratio will never exceed 1.0. However, for burst B049, as the
intensity decreases away from the centre, the bow tie intensity ratio will
consistently be greater than one.

(a) The DM-time spectrum of an RFI candidate from FRB 20220912A detected by
the NRT.

(b) The DM-time spectrum for burst B049.

Figure 14: Frequency-integrated brightness as a function of DM and time (‘DM-
time spectrum’) are shown for an RFI candidate and for burst B049. In the
center of the plot, a box is placed at Heimdall’s estimated DM value.
Additionally, at the top and bottom of the plot, a set of boxes is positioned
at the trial DM values where the burst would be smeared in time by a factor of
ten. The dotted lines indicate the width of the region for which the intensity
is calculated. The intensity of the RFI candidate does not decrease in the top
and bottom regions compared to the central box. In contrast, for the FRB
candidate, the intensity does decrease, signifying that this candidate is
indeed an FRB.

###  A.3 Classification of burst candidates

To assess the validity of our algorithm, we must look at the sensitivity. In
this context, ‘sensitivity’ is a classification metric that represents the
number of true positives divided by the number of true positives plus the
number of false negatives:

$\text{Sensitivity}=\frac{\text{TP}}{\text{TP}+\text{FN}}.$ (8)

This metric penalises false negative predictions, thus penalising the
misclassification of real FRBs. A perfect classifier would achieve a
sensitivity of 1.0, as it would not misidentify any FRBs.

Sensitivity is unaffected by the number of false positives, so optimising for
sensitivity often results in a large number of potential FRB candidates that
require manual examination. For instance, an algorithm can achieve a
sensitivity of 1.0 by classifying all potential candidates as FRBs. We
therefore try to optimise the sensitivity for our classifier while keeping the
number of false positives below a manageable threshold. We have placed this
threshold at 15 per cent of the total number of candidates.

CATCH classifies candidates based on the ratio between the average intensity
in the central box and the highest average intensity in one of the boxes at
the trial DM value that would smear the burst width by a factor of ten. To
find this ratio, we have trained the algorithm using 7104 manually inspected
burst candidates from eleven randomly selected datasets from FRB 20220912A.
CATCH classified these candidates based on whether their bow tie intensity
ratios exceeded a specific threshold value. By analysing CATCH’s performance
at varying threshold levels, we can find the threshold at which the algorithm
optimally performs. Figure 15 shows the sensitivity of this bow tie method
plotted against the number of false positives, where the colour of the crosses
indicates the thresholds. The best performance is achieved at a treshold level
of 1.24.

Figure 15: The sensitivity of the bow tie classifier (at different bow tie
ratio thresholds) as a function of the percentage of false positives. The
colour of the crosses indicates at what value the classification threshold has
been placed. The dashed grey line representes the maximum fractional false
positive limit, which has been set at 15 per cent of the total number of
candidates.

Machine learning algorithms, like the conventionally used FETCH, demonstrate a
higher level of robustness when confronted with singular noisy frequency
channels in the DM-time spectrum, but have difficulty with large RFI
structures. To create a classifier that achieves the highest sensitivity
possible, CATCH includes the candidates that FETCH identifies as FRBs with a
probability higher than 50 per cent, all the candidates which have a S/N ratio
above 200, and all candidates that are selected by the bow tie method. The
result is a significant increase in sensitivity, without exceeding the 15 per
cent limit for false positives. Figure 16 shows the sensitivity of CATCH
plotted against the number of false positives using varied classification
ratios, like in Figure 15. The sensitivity of FETCH has been plotted for
comparison, visualised with crosses, which includes the static classification
threshold across all models and randomly sampled classification thresholds for
each model separately. At the aforementioned 15 per cent maximum false
positive threshold, CATCH attains a sensitivity of 99.62 per cent on the test
dataset, surpassing the sensitivity of the conventionally used machine
learning algorithm by $\sim$29 times.

CATCH has proven valuable, finding bursts in the training data set with a
sensitivity of 99.6 per cent, and an accuracy of 88.8 per cent, while
achieving a false positive total below the 15 per cent imposed limit. In the
60.99 hours of data obtained from the hyperactive FRB 20220912A, CATCH
successfully detected 696 FRBs, surpassing the number that the standard method
would have found by 26 per cent. Although CATCH displays promise, it is
pertinent to acknowledge the identified limitations and challenges. First, to
achieve such high sensitivity, CATCH classifies a greater number of candidates
as FRBs, leading to a higher number of false positives. This approach proves
valuable when analysing data containing many FRBs, as it vastly reduces the
likelihood of missing real FRBs. However, for real-time systems where the
false positive rate must be low, or when monitoring sources that are not
hyperactive, this method is not preferable. Secondly, when evaluating the
types of bursts that conventional classification algorithms (such as FETCH)
misclassify but CATCH correctly identifies, we find that lower S/N bursts are
typically misclassified. However, the conventional classification algorithm
also misclassified several brighter bursts (S/N $\sim$ 20). A comprehensive
discussion of these issues has been undertaken by Konijn (2023), and for
brevity, we will refrain from further delving into the details here.

Figure 16: The sensitivity of CATCH and FETCH plotted against the percentage
of false positives. FETCH has been plotted as crosses, including the static
classification threshold across all models and randomly sampled thresholds.
CATCH has been plotted as circles. The dashed grey line marks the 15 per cent
fractional limit on the total number of candidates. At the dashed grey line
limit, CATCH vastly outperforms FETCH in terms of sensitivity.

##  Appendix B Determining the dispersion measure uncertainty

We estimated the error associated with the DM by calculating the $\delta$DM
that corresponds to the inverse of the highest fluctuation frequency at which
the burst still exhibits significant intensity in the power spectrum. Figure
17 shows the coherent power of burst B586, plotted for various fluctuation
frequencies against a range of DM values. At the DM of 219.717 pc cm-3, we can
see that the coherent power extends to fluctuation frequencies of $\sim$5.5
ms-1. The inverted fluctuation frequency indicates the shortest intensity
fluctuations of the burst (182 $\upmu$s). Subsequently, we can calculate the
number of DM units required to induce a variation on this timescale,
corresponding to the error on the DM.

Figure 17: The coherent power of burst B586, plotted for a range of
fluctuation frequencies against a range of DM values. The higher-intensity
areas indicate vertically aligned structures across the frequency band. At the
lower-end of the fluctuation frequencies, the burst exhibits vertical
structures across the entire range of DM values. However, at higher
fluctuation frequencies, only the small-scale structures align, specifically
when the DM is 219.717 pc cm-3, indicative of the true DM of the burst. There
is no apparent coherent power above fluctuation frequencies of 5.5 ms-1, which
is the maximum fluctuation frequency of this burst.

##  Appendix C Wait-times of individual observations

The wait-time distribution for the observation at MJD 59877 is plotted in
Figure 18. During a period of 0.96 h, a total of 72 FRBs were detected,
indicating a burst rate of $75^{+10}_{-9}$ bursts per hour, where the errors
are Poissonian. The best-fit Weibull CDF indicates a burst rate of $76.7\pm
5.7$ bursts per hour, which is consistent with the calculated burst rate. The
shape parameter of the Weibull CDF is $1.08\pm 0.10\pm 0.04$, which is
consistent with $k=1$, indicating that the Poisson distribution hypothesis can
not be rejected. Thus, for this observation, there is no significant evidence
for clustering.

Figure 18: The distribution of the wait-times from the observation on MJD
59877, with a Poisson burst rate of $75^{+10}_{-9}$ bursts per hour. The
cumulative wait-time distribution is shown in the top plot and fitted with a
Weibull CDF. The shape parameter $k=1.08\pm 0.10\pm 0.04$ does not
significantly deviate from $k=1$, which indicates the Poisson distribution can
not be rejected as a potential fit to the data. Thus, for this observation,
there is no significant evidence for clustering.

The wait-times for the observation on MJD 59879 are shown in Figure 19. During
a period of 1.37 h, a total of 82 FRBs were detected, giving rise to a Poisson
burst rate of $60.06^{+7.35}_{-6.58}$ bursts per hour. The best-fit Weibull
CDF indicates a burst rate of $78.3\pm 5.2$ bursts per hour, which is not
consistent with the calculated burst rate. The shape parameter of the Weibull
CDF is $1.16\pm 0.11\pm 0.05$, which is within errors consistent with $k=1$,
again indicating that the Poisson distribution can not be rejected. Also for
this observation, there is no significant evidence for clustering.

Figure 19: The distribution of the wait-times from the observation on MJD
59879, with a Poisson burst rate of $60^{+7}_{-7}$ bursts per hour. The
cumulative wait-time distribution is shown in the top plot and fitted with a
Weibull CDF. The shape parameter $k=1.16\pm 0.11\pm 0.05$ does not
significantly deviate from $k=1$, which indicates the Poisson distribution can
not be rejected as an accurate fit to the data. Thus, for this observation,
there is no significant evidence for clustering.

##  Appendix D Observation Durations

The 68 total observations, each lasting approximately 1 hour, are summarized
in Table 3.

Table 3:  NRT observation log for FRB 20220912A  Observation ID | Start (MJD)${}^{\text{a}}$ | Duration (s) |  | Observation ID | Start (MJD)${}^{\text{a}}$ | Duration (s)
---|---|---|---|---|---|---
O1 | 59867.90178 | 1298.7 |  | O35 | 59906.76284 | 2425.7
O2 | 59869.87766 | 939.6 |  | O36 | 59907.77528 | 2660.7
O3 | 59870.86635 | 2004.7 |  | O37 | 59909.75402 | 3952.2
O4 | 59871.86137 | 3649.0 |  | O38 | 59911.74708 | 4103.1
O5 | 59873.85096 | 4138.0 |  | O39 | 59912.73449 | 3417.0
O6 | 59874.84975 | 2429.7 |  | O40 | 59915.73991 | 3792.0
O7 | 59875.85090 | 3578.9 |  | O41 | 59917.73277 | 3980.9
O8 | 59876.84022 | 2172.6 |  | O42 | 59919.72279 | 4285.1
O9 | 59877.84736 | 3451.9 |  | O43 | 59921.72711 | 3451.9
O10 | 59878.83732 | 2560.8 |  | O44 | 59923.71440 | 4139.1
O11 | 59879.82461 | 4915.2 |  | O45 | 59925.70626 | 4285.0
O12 | 59881.82641 | 4286.1 |  | O46 | 59927.69795 | 4541.1
O13 | 59882.82632 | 2562.8 |  | O47 | 59931.68961 | 4340.2
O14 | 59883.84423 | 2390.7 |  | O48 | 59935.68565 | 3826.6
O15 | 59884.82111 | 1884.6 |  | O49 | 60007.49410 | 2948.7
O16 | 59884.84769 | 1849.9 |  | O50 | 60011.47434 | 2559.7
O17 | 59885.81839 | 2559.8 |  | O51 | 60012.47868 | 3451.9
O18 | 59887.80276 | 3418.0 |  | O52 | 60014.47088 | 3649.0
O19 | 59888.81363 | 3792.0 |  | O53 | 60016.46052 | 4138.1
O20 | 59889.80460 | 2848.8 |  | O54 | 60019.46660 | 3652.0
O21 | 59890.80948 | 3648.1 |  | O55 | 60020.44704 | 2846.8
O22 | 59891.80041 | 2706.8 |  | O56 | 60021.45762 | 3199.8
O23 | 59892.80272 | 1748.7 |  | O57 | 60023.45200 | 3182.9
O24 | 59892.82765 | 1696.8 |  | O58 | 60026.44155 | 3335.9
O25 | 59893.79641 | 2560.8 |  | O59 | 60030.41960 | 4284.0
O26 | 59894.78365 | 4915.3 |  | O60 | 60033.41924 | 3274.9
O27 | 59896.78825 | 4136.1 |  | O61 | 60036.41660 | 2678.8
O28 | 59897.78272 | 2897.0 |  | O62 | 60040.40335 | 2950.0
O29 | 59898.78065 | 4272.2 |  | O63 | 60042.40042 | 2671.4
O30 | 59899.78016 | 2559.8 |  | O64 | 60044.39492 | 2678.8
O31 | 59900.77444 | 4336.1 |  | O65 | 60047.38420 | 2950.0
O32 | 59901.76453 | 3417.0 |  | O66 | 60049.38117 | 3199.9
O33 | 59903.76904 | 4178.0 |  | O67 | 60051.37340 | 3314.9
O34 | 59904.76995 | 2288.6 |  | O68 | 60054.36522 | 3314.8
${}^{\text{a}}$ Topocentric at NRT. |  |  |  |  |  |