# Characterization of the Repeating FRB 20220912A with the Allen Telescope
Array

Sofia Z. Sheikh1,2,3, Wael Farah1,2, Alexander W. Pollak1,2, Andrew, P. V.,
Siemion1,2,4,5, Mohammed A. Chamma6, Luigi F. Cruz1,2, Roy H. Davis1, David R.
DeBoer1,2, Vishal Gajjar1,2, Phil Karn1, Jamar Kittling1,7, Wenbin Lu8, Mark
Masters1, Pranav Premnath1,9, Sarah Schoultz1, Carol Shumaker1, Gurmehar
Singh1,10, Michael Snodgrass1

1SETI Institute, 339 Bernardo Ave, Suite 200 Mountain View, CA 94043, USA
2Berkeley SETI Research Center, University of California, Berkeley, CA 94720,
USA 3Penn State Extraterrestrial Intelligence Center, 525 Davey Laboratory,
The Pennsylvania State University, University Park, PA, 16802, USA 4Department
of Physics and Astronomy, University of Manchester, UK 5University of Malta,
Institute of Space Sciences and Astronomy, Msida, MSD2080, Malta 6Department
of Physics & Astronomy, McMaster University, 1280 Main Street West, Hamilton,
ON, L8S 4M1, Canada 7Wesleyan University, Middletown, CT 06459, USA
8Departments of Astronomy and Theoretical Astrophysics Center, UC Berkeley,
Berkeley, CA 94720, USA 9Department of Physics & Astronomy, The University of
California, Irvine, Irvine, CA 92697, USA 10Purdue University, West Lafayette,
IN 47907, USA E-mail<EMAIL_ADDRESS>
(Accepted 2023 November 20. Received 2023 November 17; in original form 2023
May 19)

###### Abstract

FRB 20220912A is a repeating Fast Radio Burst (FRB) that was discovered in
Fall 2022 and remained highly active for several months. We report the
detection of 35 FRBs from 541 hours of follow-up observations of this source
using the recently refurbished Allen Telescope Array, covering 1344 MHz of
bandwidth primarily centered at 1572 MHz. All 35 FRBs were detected in the
lower half of the band with non-detections in the upper half and covered
fluences from 4–431 Jy-ms (median$=$48.27 Jy-ms). We find consistency with
previous repeater studies for a range of spectrotemporal features including:
bursts with downward frequency drifting over time; a positive correlation
between bandwidth and center frequency; and a decrease in sub-burst duration
over time. We report an apparent decrease in the center frequency of observed
bursts over the 2 months of the observing campaign (corresponding to a drop of
$6.21\pm 0.76$ MHz per day). We predict a cut-off fluence for FRB 20220912A of
$F_{\textrm{max}}\lesssim 10^{4}$ Jy-ms, for this source to be consistent with
the all-sky rate, and find that FRB 20220912A significantly contributed to the
all-sky FRB rate at a level of a few percent for fluences of $\sim$100 Jy-ms.
Finally, we investigate characteristic timescales and sub-burst periodicities
and find a) a median inter-subburst timescale of 5.82$\pm$1.16 ms in the
multi-component bursts and b) no evidence of strict periodicity even in the
most evenly-spaced multi-component burst in the sample. Our results
demonstrate the importance of wideband observations of FRBs, and provide an
important set of observational parameters against which to compare FRB
progenitor and emission mechanism models.

###### keywords:

radio continuum: transients – instrumentation: interferometers – methods: data
analysis

††pubyear: 2023††pagerange: Characterization of the Repeating FRB 20220912A
with the Allen Telescope Array–Characterization of the Repeating FRB 20220912A
with the Allen Telescope Array

##  1 Introduction

FRBs, subsecond-duration coherent flashes in the radio spectrum that originate
at cosmological distances, are one of the most intriguing phenomena in the
last decade of time-domain astronomy. FRBs have been detected at radio
frequencies from 120 MHz (Pastor-Marazuela et al., 2021) all the way up to 8
GHz (Gajjar et al., 2018; Michilli et al., 2018), with isotropic-equivalent
spectral luminosities of $10^{27}$ to $10^{34}$ erg s-1Hz-1 (Nimmo et al.,
2022), and excess Dispersion Measures (subtracting the galactic contribution
using electron density models) of several tens to a few thousand pc cm-3
(Petroff et al., 2022). Most FRBs have only been observed a single time, but
some, known as “repeaters,” are seen more than once; the repeater fraction is
still evolving with more observation, but, at the moment, only 2.6% of the
Canadian Hydrogen Intensity Mapping Experiment (CHIME) FRB sources have been
seen to repeat (CHIME/FRB Collaboration et al., 2023). The first of these
repeaters discovered, FRB20121102A (e.g., Spitler et al., 2016; Scholz et al.,
2016; Zhang et al., 2018; Gourdji et al., 2019; Hessels et al., 2019; Majid et
al., 2020; Pearlman et al., 2020; Agarwal et al., 2020; Li et al., 2021;
CHIME/FRB Collaboration et al., 2023) has now produced thousands of recorded
bursts across different instruments and frequency ranges. As of the writing of
this paper, 46 FRB sources have been confirmed to repeat, the majority of
which do not show any burst-to-burst periodicity (though two sources,
FRB121102 and FRB180916, show periodic activity windows, e.g., CHIME/FRB
Collaboration et al., 2020a; Pilia et al., 2020). Many FRB sources have been
precisely localized by interferometric arrays (Bannister et al., 2019; Marcote
et al., 2020; Kirsten et al., 2022; Ravi & DSA-110 Collaboration, 2023), which
provide important clues to the nature of the emitting objects and their host
environments. Repeaters are particularly valuable for interrogating the
emission mechanism of FRBs, as their bursts can be analyzed as a self-
contained sample of observational data arising from a single physical object
(e.g., Hessels et al., 2019; Li et al., 2021; Chamma et al., 2023; Jahns et
al., 2023).

The emission mechanism of FRBs still remains a mystery (see Cordes &
Chatterjee, 2019; Zhang, 2020; Petroff et al., 2022; Bailes, 2022, for recent
reviews), though a consensus is emerging that magnetars are likely responsible
for at least a sub-population due to an FRB-like event from a galactic
magnetar (Bochenek et al., 2020; CHIME/FRB Collaboration et al., 2020b). For
magnetar-related classes of models, there is still considerable debate on the
detailed radiation mechanism, with various explanations distinguished by,
among other things, their distance from the progenitor magnetar (Petroff et
al., 2022). Magnetospheric models operate at a few neutron star radii from the
magnetar (e.g., Lu et al., 2020), while shock models operate much further out,
at characteristic scales of $10^{10}$ cm (e.g., Metzger et al., 2019). Most
radiation mechanism models for repeaters sufficiently explain the broad
features of repeating FRB emission (e.g., coherent emission, an energy budget
consistent with repeating bursts, non-cataclysmic sources) and therefore will
likely be differentiated via more specific spectrotemporal behaviour.

The observed population of repeating FRBs does show consistent spectrotemporal
features, such as the tendency of emission from a single burst to decrease in
frequency over the duration of the burst, often in discrete steps associated
with distinct “subpulses” or “sub-bursts” (Hessels et al., 2019). This so-
called “sad trombone” effect, or downward drift, is not an unbreakable rule,
however, as others have reported positive drift rates in some bursts (e.g.,
Kumar et al., 2022; Zhou et al., 2022). For each FRB, features such as the
duration, central frequency, frequency extent, and drift rate can be combined
with flux and polarization information to reveal consistent properties across
bursts and sources. Specific spectrotemporal features such as upward-drifting
“happy trombones,” sub-burst periodicities (CHIME/FRB Collaboration et al.,
2023), or $<$100 ns sub-burst structure (Majid et al., 2021; Nimmo et al.,
2022) might provide the clues necessary to understand the full nature of FRBs.
For example, Zhou et al. (2022) notes the similarity of drifting behaviour in
FRBs to that of certain pulsars, hinting at a potential similarity in emission
mechanism or environment. Similarly, the small emission regions (tens to
thousands of meters) implied by $<$100 ns sub-burst structure lends itself to
a magnetospheric origin (Nimmo et al., 2022).

On 2022 October 15, a new repeating source, FRB 20220912A, was reported by
McKinven & CHIME/FRB Collaboration (2022); nine bursts at 400 MHz were
detected by CHIME in a three day period in September 2022. The original
detection had inferred J2000 coordinates of RA $=347.29(4)^{\circ}$, Dec
$=+48.70(3)^{\circ}$. Other Astronomer’s Telegrams (ATels) soon followed,
showing detections at L-band (Herrmann, 2022) and an improved localization
from the Deep Synoptic Array (DSA-110) at 23h09m04.9s +48d42m25.4s (J2000)
(Ravi, 2022). This location is coincident with the potential host galaxy PSO
J347.2702+48.7066 (McKinven & CHIME/FRB Collaboration, 2022; Ravi, 2022). The
repeating FRB has since been detected at frequencies from 300 MHz (Bhusare et
al., 2022)111There is also a claimed marginal detection at 111 MHz (Fedorova &
Rodin, 2022) to 2.3 GHz (Rajwade et al., 2022; Perera et al., 2022), with some
large single-dish telescopes seeing L-band burst rates of over 100 bursts per
hour (e.g., Feng et al., 2022). Recent published work on the source in Zhang
et al. (2023) and Feng et al. (2023) characterize this source as the fourth
extremely active FRB, but the first one in a relatively clean environment as
derived from its polarization information and steady DM, providing a unique
laboratory for understanding which FRB properties come from the emission
mechanism intrinsically.

Repeating FRBs show varying behaviour across wide bandwidths, for instance,
periodicity in activity that is phase-delayed in time over frequency for FRB
20180916B (e.g., Sand et al., 2022). They are also limited in bandwidth
($100$s of MHz up to a few GHz; e.g., Gourdji et al., 2019) around their
unpredictable center frequencies. Given these characteristics, wide bandwidth
receivers and simultaneous observation at different bands will be critical to
characterize them. The Allen Telescope Array (ATA) has both of these features,
making it a uniquely suited instrument for FRB observation.

In this paper, we report an observing campaign of FRB 20220912A conducted with
the ATA between October and December of 2022. In Section 2, we summarize the
current status of the refurbishment of the ATA, describe the observational
campaign of FRB 20220912A, and detail the search pipeline used to detect and
validate FRBs. In Section 3, we discuss our methods for data pre-processing
and extraction of spectrotemporal properties. In Section 4, we use the data
and properties from the previous section to compute the all-sky rate, quantify
correlations between spectrotemporal properties, and investigate potential
sub-burst periodicity. Finally, we discuss our results and conclude in Section
5.

##  2 Observations and Data

###  2.1 The Allen Telescope Array: Instrument Specifications

The ATA is a 42-element interferometer consisting of 6.1m dishes hosted on the
Hat Creek Radio Observatory in northern California owned and operated by the
SETI Institute, Mtn. View, CA. In late 2019, the instrument began a
refurbishment program aimed at improving the sensitivity and robustness of the
telescope feeds and revamping the Digital Signal Processing (DSP) system. A
full description of the analog and DSP upgrades will be presented in Pollak et
al. (in prep.) and Farah et al. (in prep.) respectively, but here we will
include the essential details to accompany the observations of FRB 20220912A.

Each ATA dish is an offset Gregorian and can slew in both the azimuth and
elevation direction. The refurbished “Antonio” log-periodic feeds are dual-
polarization and sensitive to a large instantaneous frequency range covering
the 1 to 11 GHz band (Welch et al., 2009). Each feed is placed in a cryostat
and is cooled to a temperature of $\sim 70$K. Analog signals from each antenna
are amplified and sent over optical fiber. Each antenna’s signal is then split
and mixed to produce up to 4 independently tunable signal chains, denoted ‘a’,
‘b’, ‘c’, and ‘d’.

Digitization of the antenna signals is performed on 16-channel input Xilinx
ZYNQ UltraScale+ Radio Frequency System-on-Chip (RFSoC) boards, where data get
channelized, packetized, and transmitted to the network on a 100 GB ethernet
link. A delay engine and fringe rotator are also included as part of the
firmware on the Field Programmable Gate Array (FPGA) boards such that voltage
data from all antennas are delayed and phase-centered relative to a user-
defined sky coordinate (usually the center of the ATA antenna primary beam).
Five RFSoC boards are currently deployed as part of the prototype DSP system
which supports the digitisation of 20 dual-polarization antennas over 2
frequency tunings. Upgrades to outfit the entire ATA with newly refurbished
feeds and deploy more digitizers to cover all the available tunings are
planned for the near future.

Channelized voltages are received by a cluster of 8 compute nodes where data
are processed depending on the observer-selected DSP backend. An xGPU-based,
which accelerates cross-correlations (x) using Graphical Processing Units
(GPUs) (Clark et al., 2011), can be selected to generate interferometric
visibilities that can be used for imaging and for delay and phase calibrating
the beamformer. Our beamformer, Breakthrough Listen Accelerated DSP Engine
(BLADE), is a custom-built GPU-based beamformer that was developed in-house,
tested, and deployed on the ATA cluster (Cruz et al., in prep.) and has since
been used for novel science, such as tracking the reverse shock emission of
gamma-ray burst 221009A (Bright et al., 2023). Telescope users can customise
the ATA backend according to science cases. This includes selecting the time-
integration length of the correlator, setting the number of beams to produce
with the beamformer, and setting the polarization data output.

Table 1 contains a summary of the relevant instrument properties for the FRB
observations described here.

Table 1: Specifications of the Allen Telescope Array in Fall 2022

.  Parameter Value Antenna diameter 6.1 meter Longest baseline 300 meter
Frequency coverage 1-11 GHz Primary beam FWHM (at 1GHz; at 11GHz) 3.5∘; 0.3∘
Synthesized beam FWHM (at 1GHz; at 11GHz) 4.2′; 0.38′ Processed bandwidth per
tuning 672 MHz Number of available simultaneous tunings 2 Number of
simultaneous polarizations 2 Number of beamformed antennas 20

###  2.2 Observing Campaign

Just 56 minutes after the initial announcement of FRB 20220912A by McKinven &
CHIME/FRB Collaboration (2022), the ATA began a follow-up campaign of the
source. During the time period between 15 October 2022 and 31 December 2022,
we observed the source in a series of 70 observations, with a median
observation length of 8 hours, divided into 30 minute scans. This led to a
total observing time of 541 hours on-source. We ended the campaign when the
source’s activity had decreased, but not fully ceased, due to observing
resource constraints. We recorded data with the 20-element beamformer, placing
a single phase-centered synthesized beam on the target at the center of the
primary beam; initially, we used the inferred J2000 coordinates from the CHIME
detection of FRB 20220912A, then switched coordinates to the updated DSA-110
coordinates once they were available on 25 October 2022. Given the synthesized
beamsize of the ATA at 2 GHz (approximately 2 arcmin), the original FRB
coordinates would have placed the true source at the edge of the beamformed
beam, which affected the first 31 hours of observation. Sheikh et al. (2022)
described the detection of 8 bursts from FRB 20220912A with the ATA; the 8
bursts in that announcement are included in this work.

We exercised the ATA’s tuning flexibility to observe the source at two
different 672 MHz tunings simultaneously. The center frequencies of the
tunings varied at the beginning of the campaign, but settled at their final
values of 1236 MHz and 1908 MHz on 4 November 2022. This setting allows for
the two tunings to provide continuous frequency coverage from 900–2244 MHz.
Before 4 November 2022, 12 sessions had tunings of 1400 MHz and 3000 MHz, 2
sessions had tunings of 1400 MHz and 6000 MHz, and 1 session had tunings of
1150 MHz and 1850 MHz — this amounts to 76 / 541 hours of data recorded at the
non-final central frequencies.

Before every observing session, we observed a phase calibrator (3C48, 3C286,
or 3C147) in the correlator mode to assess sensitivity and calibrate the
instrument with updated delay and phase solutions prior to science
observations. In addition, from 7 November 2022 until the end of the campaign,
we added an observation of pulsar J0332+5434 for general system validation and
validation of the SPANDAK pulse detection pipeline described in Section 2.3.

###  2.3 Searching for FRBs

The ATA beamformer used for the observations described in the previous section
currently produces Stokes I 32-bit SIGPROC
“filterbank”222https://sigproc.sourceforge.net/sigproc.pdf files at a
frequency and time resolution of 0.5 MHz and $64\upmu\textrm{s}$,
respectively. These data were not coherently dedispersed to any particular DM
during data-recording, but were stored for off-line FRB searching. The
beamformer is capable of producing cross-polarisation data products that can
enable polarization studies. However, given the intricate nature of
polarisation calibration, we deliberately chose not to record individual
polarisations for this work (though we intend to do so in future studies).
Moreover, efforts are currently underway to implement a beamformer mode which
supports coherent dedispersion.

In this project, we used the SPANDAK pipeline (Gajjar et al., 2022), which is
a wrapper for HEIMDALL, a GPU-accelerated search code for dispersed signals in
radio astronomical data (Barsdell, 2012). SPANDAK implements additional
filtering and candidate evaluation procedures on the HEIMDALL outputs and
produces tables of burst candidates along with diagnostic plots that are later
visually reviewed by an observer.

We first decimate the filterbank files in bit depth from 32-bit to 8-bit so
they are compatible with the existing format requirements for HEIMDALL. We
then splice the seven nodes of data for each of the two tunings together,
creating one 8-bit filterbank file covering the entirety of the tuning
centered at Local Oscillator (LO) b and another covering the entirety of the
tuning centered at LOc. Due to the data volume and processing time, we opted
not to perform Radio Frequency Interference (RFI) removal before searching.

We assign a DM search range of $\pm 10\%$ from the nominal dispersion measure
of 219.46 pc cm-3 as reported by the CHIME repeater
catalog333https://www.chime-frb.ca/repeaters, with a DM step size calculated
such that the Signal-to-Noise Ratio (SNR) loss between DM trials is no more
than 0.1%. We then run SPANDAK with a SNR threshold of 10, a boxcar maximum
width of $2^{16}$ samples (4.194 seconds), and a maximum-candidates-per-second
(maxCsec) value of 15, which is slightly higher than the SPANDAK default. The
maxCsec parameter is observatory and band dependent as it is strongly
correlated with the RFI environment. For these frequencies at the ATA, we
determined that 15 was an appropriate value via test observations of
J0332+5434. We execute the search code over each spliced tuning independently,
corresponding to a fixed search bandwidth of 672 MHz. The incoherent
dedispersion and searching code is then executed and logged. More information
about how the SPANDAK candidate plots are constructed can be found in Figure 9
of Gajjar et al. (2021).

The median number of top candidates per observing session was 9, where a top
candidate is a HEIMDALL candidate given at least a B–C rank by SPANDAK due to
its broadband characteristics and trial DM-vs-SNR response. The low number of
candidates made additional filtering for false-positive RFI unnecessary in
most cases.

In 541 hours of observation, we detect 35 bursts from FRB 20220912A. All 35
bursts were detected in LOb, the lower 672 MHz tuning, with none detected (or
visible simultaneously in dedispersed archives) in LOc. This is consistent
with low detection rates at S-band and non-detections in C-band (e.g., Kirsten
et al., 2022). Dynamic spectra for all the bursts detected with the ATA are
shown in Figure 2. As suggested by the single-tuning detections, the bursts
from FRB 20220912A are highly spectrally limited, which was similarly observed
in FRB 20180916B (Sand et al., 2022) and FRB 20121102A (Law et al., 2017) — a
deeper investigation of spectral extent is performed in Section section 4.

Figure 1: Dynamic spectra (or “waterfall” plots) for all the bursts from FRB
20220912A detected using the Allen Telescope Array, the frequency-averaged
pulse profiles, and the time-averaged spectra. The red-shaded regions in the
time series plots denote the time span of the defined sub-bursts, with red
vertical lines demarcating adjacent sub-bursts.

Figure 2: Continued.

The timeline of our detections is visualized in Figure 3.

Figure 3: Cumulative observing time on FRB 20220912A over the months of the
campaign (black line), with detections marked in dashed blue lines. The red
shaded region indicates observations for which the higher tuning was
unavailable, restricting our bandwidth by a factor of two. The average
interval between observations was 1.11 days, with a maximum interval of 3.80
days and a minimum interval of a few hours.

##  3 Data Reduction

###  3.1 File Preparation

Once we have identified an FRB within one of the 30-minute long filterbank
files as described in Section section 2.3, we crop the filterbank in time,
centering on SPANDAK’s reported trigger time for the burst. We choose a
10-second cropping length, to capture the entire burst with dispersive delay
and provide context for noise and RFI properties.

Next we convert the cropped filterbanks to archive files with DSPSR (van
Straten & Bailes, 2011), using the best-fit SNR-maximizing DM of the burst
from SPANDAK contained in the metadata. This choice visually corresponded with
structure-maximizing in the dedispersed waterfall plots for all but two of the
bursts. For these two bursts (#24 and #25), we found that the SPANDAK over-
disperses the burst, as evidenced by the morphology of the subcomponents and
the anomalously large reported DMs (224.94 and 223.24 pc cm-3, respectively).
We thus set their archive file DM to the average from the other 33 bursts, at
219.775 pc cm-3. All archive files have the time axis of the file (10 seconds)
read in as “phase” but are otherwise equivalent to archive files used for
other radio pulsar applications.

###  3.2 Calculating Flux and Fluence

Using the calibration measurements described in Section 2.2, we calculate the
flux and fluence of each of the 35 FRBs in the sample. First, we obtain the
System Equivalent Flux Density (SEFD) of each observation. All three flux
calibrators in this dataset have flux models from Perley & Butler (2017), from
which we obtain expected spectral flux densities $S_{\mathrm{exp}}$ at the
central frequencies of both LOs. We calculate the SEFD for each antenna-
polarization combination (antenna $x$, polarization $y$) as follows:

$\mathrm{SEFD}_{x,y}=(G_{\mathrm{cal}}^{2}\times S_{\mathrm{exp}})^{-1}$ (1)

Where $G_{\mathrm{cal}}$ is the gain from the associated calibrator file, in
units of $\textrm{Jy}^{-1}$, computed using the Common Astronomy Software
Application (CASA) gaincal task (Bean et al., 2022). We then average each of
the antenna-polarization SEFDs to get the beamformer SEFD:

$\mathrm{SEFD}_{\mathrm{beamformer}}=\frac{\frac{\Sigma_{x,y}\mathrm{SEFD}_{x,y}}{N_{x,y}}}{N_{\textrm{el}}}$
(2)

Where $N_{x,y}$ = 40 (the number of antenna-polarization combinations) and
$N_{\textrm{el}}$ = 20 (the number of elements in the beamformer). This
results in a polarization-averaged SEFD${}_{\textrm{beamformer}}$ of $387\,\pm
38$ Jy. This number is in agreement with earlier tests conducted with the
instrument, and details about recovering flux scales and beamformer efficiency
for the ATA will be presented in a forthcoming paper (Farah et al., in prep.).
For observations listed here, we used a uniform weighting of all antennas for
the beamformer.

From this SEFD, we can use the radiometer equation to get the minimum
detectable flux density $S_{\nu,\mathrm{min}}$ of this work:

$S_{\nu,\mathrm{min}}=\frac{(\mathrm{SNR})(\mathrm{SEFD})}{\sqrt{n_{\mathrm{pol}}\tau\Delta\nu}}$
(3)

Where $\tau$ is the duration of an FRB, $\Delta\nu$ is its frequency extent,
and $n_{\mathrm{pol}}$ is the number of recorded polarizations (in this case,
2). Therefore, $S_{\nu,\mathrm{min}}$ for a SNR threshold of 10, an SEFD of
387 Jy, and a fiducial FRB duration and bandwidth of 1 ms and 672 MHz, is 4.7
Jy.

We detected 35 bursts in 541 hours of observing, implying an average burst
rate above 4.7 Jy of $6.47^{{}^{+1.29}}_{{}_{-1.09}}\times
10^{-2}\,\textrm{h}^{-1}$, where the uncertainties represent 1-sigma Poisson
errors (Gehrels, 1986).

We use the Python binding for PSRCHIVE (Hotan et al., 2004) to load the data
as dynamic spectra, incoherently dedisperse each array to the SPANDAK DM
described in Section 3.1, and remove the baseline. We then average each array
in frequency to get a timeseries burst profile, and normalize it by
subtracting the median and dividing by the standard deviation of a noise
region consisting of $\pm 1000$ time bins (64 ms) on either side of the burst.

At this point, we define the boundaries in the timeseries from which to
extract SNRs, fluxes, and fluences. Only 7 FRBs consist of a single component;
the rest of the sample shows complex sub-burst structure. A sub-burst is
qualitatively defined here as a significant local maximum in intensity in an
FRB’s profile, especially if that structure seems distinct in frequency from
the neighboring emission in the dynamic spectrum. We opt here to measure each
of the sub-bursts individually, as not to downweight the flux by averaging
over the periods between sub-bursts. The sub-burst delineations determined
here are the same ones that are used in the process of extracting spectral
properties of sub-bursts, described in Section 3.3.

Using the sub-burst bounds and the normalized profile defined above, we obtain
the SNR with $\mathrm{SNR}=\frac{\Sigma p}{\sqrt{N}}$, where $p$ is the
normalized profile and $N$ is the number of points across the profile (i.e.,
the duration of the sub-burst). To transform the SNR into the flux in Jy, we
can incorporate the SEFD as follows:

$S_{\textrm{Jy}}=\frac{\mathrm{SEFD}\times\mathrm{SNR}}{\sqrt{B\times
N_{P}\times N\times t_{\textrm{samp}}}}$ (4)

where $B$ is bandwidth of the sub-burst, $N_{\textrm{P}}$ is the number of
polarizations, and $t_{\textrm{samp}}$ is the sampling time. Finally, we
convert $N$, the duration in bins, into a duration in ms and multiply by
$S_{\textrm{Jy}}$ to get the fluences in Jy-ms.

The SNRs, fluxes, and fluences derived here are included in Table
LABEL:tab:frb_detections (at the end of the paper). Uncertainties in the DM
were derived by applying a sliding boxcar with the parameters used by SPANDAK
in the original detection and providing the width of the best-fit Gaussian to
the DM-SNR curve. Uncertainties in the fluxes and fluences are calculated by
propagating the uncertainty on the mean SEFD.

It should be noted that the first 3 FRBs in the sample were detected while the
synthesized beam was centered on the original, offset coordinates. To address
that, we modeled the shape of the synthesized beam at the topocentric
coordinates for the aforementioned bursts. We then corrected the measured flux
densities with the calculated attenuation values of 0.5 dB, 0.5 dB, and 1 dB
for bursts 1, 2, and 3 respectively.

Some of the flux values in the downsampled 8-bit filterbank files were clipped
to the highest intensity bin, implying that we were underestimating the total
flux by some amount for the brightest FRBs. To estimate the impact of the
clipping, we looked at the percentage of pixels in the highest intensity bin
for the highest SNR FRB (#25). For this particular FRB, approximately 3% of
the pixels were clipped as seen when plotting the pixel intensity distribution
histogram. Recovering the original values (i.e. before resizing to 8-bit
depth) is almost impossible given that the original 32-bit, higher dynamic
range data products were deleted. However, we still attempted to quantify the
effects of pixel clipping by assuming that the intensity distribution, at the
top end, follows a continuous dampened trend. We fit the intensity histogram,
and “redistribute” the clipped pixels by extrapolating beyond the 8-bit
clipping point, and then integrate the intensities and measure the flux. By
doing so, we found that we were only underestimating the flux by approximately
3% for this FRB. Given that this is the most extreme example in our sample, we
do not correct for this effect in the dataset.

###  3.3 Extracting Spectral Properties with frbgui

Some parameters of interest for the 35 FRB sample are calculated from the
original archive files, but some spectrotemporal properties such as bandwidth
and duration must be extracted with additional processing, especially for
bursts with multiple sub-components. We used the spectrotemporal FRB code
frbgui (Chamma et al., 2023) to extract these parameters.

We load the archive files into Python, dedisperse, and remove baseline as
described in the previous Section 3.2. For each FRB, we defined start time and
end time indexes in the original archive file — we crop the array to $\pm$ 100
bins (6.4 ms) on this range. Finally, the files are written out as dynamic
spectra with accompanying metadata containing information about the time axis,
frequency axis, dispersion measure, and various units.

We open these dedispersed and cropped files with frbgui. For each file, we
define a DM grid covering the original SPANDAK DM $\pm$ 0.5 pc cm-3, sampled
at 0.01 pc cm-3 intervals. If the average DM of the whole sample would fall
outside of this grid, we extend it by another $\pm$ 0.5 pc cm-3 in the
relevant direction. We then optionally perform a series of tasks to improve
the SNR of the burst:

  * •

Subtract a background sample from the entire dynamic spectrum: This background
sample is usually selected to be the first few milliseconds of the file before
the burst begins. This helps remove narrowband RFI.

  * •

Add a frequency mask range: For bursts that do not cover the entire bandwidth
(most of them, as per Figure 2), we can mask up to hundreds of MHz of bandpass
where there is no FRB signal in order to improve the SNR.

  * •

Remove remaining RFI: For bursts with significant RFI, we implemented built-in
RFI-masking with a spectral kurtosis - Savitzky–Golay (SK-SG) filter (with a
polynomial order of $\sigma=3$ and a a window-size of 15 samples), which
improved the SNR. For less affected bursts, however, this removed the
brightest parts of the true FRB signal and was not used.

  * •

Downsample in time and frequency: By downsampling, or frequency averaging and
time integrating the dynamic spectrum, we can improve the SNR — this is
especially necessary for faint FRBs and was already part of SPANDAK’s routine
for finding these fainter FRBs. We select time and frequency downsampling
factors that are evenly divisible into the length of the array axes, while
still endeavoring to keep enough resolution to be confident of e.g., drift
rates.

We then manually demarcate burst splitting with frbgui’s interactive
interface. Given that FRBs have been shown to have sub-bursts and structure on
the order of microseconds (Nimmo et al., 2022), and that we are downsampling
to increase SNR, there are likely fine-structure details that we cannot
resolve in our dataset. Nevertheless, we do delineate the sub-bursts that are
visible given our resolution, and find FRBs with up to 7 distinct components
in our 35 burst dataset.

Finally, we use a non-linear least squares algorithm444Via
scipy.optimize.curve_fit to perform a 6-parameter 2D Gaussian fit to the 2D
auto-correlation of the dynamic spectrum for the entire array, and then for
the limited sub-arrays delineated in time by each sub-burst start and stop
defined previously. Fitting to the auto-correlation increases the SNR and
mitigates the effect of e.g., scintillation and RFI in the parameter
measurements (see Chamma et al., 2023, for more details about this operation).
For each DM in the grid, the fitter returns the bandwidth, duration, and sub-
burst slope for each of the sub-bursts, as well as the bandwidth, duration,
and drift rate (in MHz ms-1) of the overall burst, with their associated
errors. In some cases, the fitter does not converge on the correct parameters
for the burst. We visually reviewed each fit (for every DM-sub-burst
combination) in the frbgui interface and, where necessary, implemented a refit
by manually inputting an initial guess based on the correct preceding fits.

The center frequency, duration, and bandwidth information for each sub-burst
are shown in Table LABEL:tab:frb_detections. Reported uncertainties in the
duration are equal to the time bin size after scrunching in the dynamic
spectrum used for the spectral property fitting.

##  4 Data Analysis

###  4.1 Spectrotemporal Analysis

Using the FRB and sub-burst characteristics extracted in Section 3, we can
investigate population-scale features of our dataset. The center frequencies,
durations, and bandwidths for all 101 sub-bursts in the set are displayed in
Figure 4.

Figure 4: The distributions of center frequency in MHz, duration in ms, and
bandwidths in MHz for each of the 101 sub-bursts in the dataset. We see the
majority of FRBs reside at the lower end of the bandpass, have $<2$ ms
durations and show bandwidths of a few 100 MHz.

For all linear fits in Sections 4.1.2–4.1.5, we use the following methodology.
In most cases, we have an independent variable $x$, a dependent variable $y$,
and heteroscedastic errors in each variable $x_{\mathrm{err}}$ and
$y_{\mathrm{err}}$. We account for this heteroscedasticity with a
bootstrapping technique. We employ an ordinary least squares (OLS) fitting
method that incorporates robust covariance estimators (specifially, the HC1
estimator from MacKinnon & White, 1985). In each of 10000 bootstrapped trials,
we draw each value of $x$ or $y$ from a normal distribution with a width of
$x_{\mathrm{err}}$ or $y_{\mathrm{err}}$ respectively, and then use the OLS
fitting method to get a value for the slope and its associated $R^{2}$ value
(the square of the Pearson correlation coefficient, to quantify how much
variance in the dependent variable is explained by the independent variable).

For each fit, we report a) the mean of the 10000 slopes from the trials above
b) the mean of the 10000 standard errors of the slope, and c) the mean of the
$R^{2}$ values of the 10000 trials. We calculate the significance of these
correlations by running an additional 10000 trials where we permute the data,
i.e., randomly shuffle the $y$ values and then re-assign them to the $x$
values. The p-value is then the percentage of permuted outcomes that meet or
exceed the absolute value of the mean $R^{2}$ described above. Here, we use
$p<0.05$ as our threshold for statistical significance.

####  4.1.1 Burst Energy

To compare our sample with the energy distribution of 128 bursts seen by the
Green Bank Telescope (GBT) (Feng et al., 2023), we can convert the fluences
from Section 3.2 into isotropic equivalent sub-burst energies, using the
redshift and luminosity distance from Planck Collaboration et al. (2016); Ravi
et al. (2022), which assumes Planck 2016 cosmology. We find a median sub-burst
energy for our sample of 1 $\times$ $10^{39}$ erg, approximately two orders-
of-magnitude greater than the median from Feng et al. (2023), although
approximately on-par with their brightest bursts. This is consistent with the
lower sensitivity of the ATA. The brightest sub-burst in our sample, from #25,
has an energy of $1.8\times~{}$ $10^{40}$ erg; the brightest burst, combining
all subbursts (also #25), has an isotropic energy of $5\times~{}10^{40}$ erg.

####  4.1.2 Center Frequency vs. Bandwidth

To test the correlation between the center frequency of a sub-burst and its
bandwidth, we first remove any FRB from the set whose sub-bursts significantly
intersect the edge of the band by visual inspection of the de-dispersed
dynamic spectra. This results in a set of 55 sub-bursts for which we evaluate
a linear fit. We find a positive, linear correlation between center frequency
and bandwidth with a slope of $0.28\pm 0.04$, as shown in Figure 5. The
$R^{2}$ for the fit between the center frequency and bandwidth is 0.533 and
the p-value is $<10^{-4}$.

This slope is consistent within a factor of two of the slope of $0.14\pm
0.004$ found by Chamma et al. (2023) for FRB 20121102A, although different
sources would not necessarily be expected to have the same slope. The center
frequency and bandwidth relationship described here also appears consistent
with the 1000-burst dataset from Zhang et al. (2023).

Figure 5: Center frequency in MHz versus bandwidth in MHz for 55 sub-bursts
from FRB 20220912A (black) and their best-fit line (blue). 1-$\sigma$ fit
errors derived by frbgui are shown in both center frequency and bandwidth for
the points used in the linear fit, which were accounted for during the
bootstrapping. We confirm the expected positive linear relationship between
these two properties.

####  4.1.3 Center Frequency and Bandwidth vs. Time

A unique feature of our dataset was the relatively steady rate of data
acquisition over the two months of the campaign; this can be seen in the
smooth slope of the cumulative observing time in Figure 3. This allows us to
interrogate changes in the properties of the 101 sub-bursts from FRB 20220912A
over time. We see a decrease in both the center frequency and bandwidth over
the course of the campaign (Figure 6). The center frequency decreases at a
rate of $6.21\pm 0.76$ MHz per day, with a corresponding $R^{2}$ of 0.311 and
a p-value of $<10^{4}$. This trend is echoed by the bandwidth, which decreases
$2.08\pm 0.38$ MHz per day, with a corresponding $R^{2}$ of 0.191 and a
p-value of $<10^{4}$, due to their inherent relationship shown in Figure 5.
There were no similarly obvious changes in flux, duration, or DM over the
campaign.

Other repeaters have been observed to have varying activity levels at
different frequency ranges. For example, FRB 20180916B shows activity in the
1000 MHz range 3 days before activity peaks in the 100 MHz range (Pleunis et
al., 2021a). Pearlman et al. (2020) also find that apparent FRB activity is
strongly affected by which frequencies are being recorded, with FRB 20180916B
again showing this behaviour particularly strongly. However, this marks the
first trend in frequency over time for a so-far non-periodic (as per Zhang et
al., 2023) repeating FRB.

Figure 6: Two FRB 20220912A dataset parameters — center frequency and
bandwidth — plotted over time, in MJD, from the beginning of the campaign to
the end of the campaign (a time period of approximately 60 days). Panel a)
indicates that the central frequency of the FRB decreases through the campaign
(with residuals from the fit and a LOWESS non-parametric guideline shown below
in blue). Panel b) shows the same decrease over time for bandwidth, which is
understandable given the relationship between bandwidth and center frequency
shown in Figure 5.

The residuals from the linear fit of central frequency over time in Figure 6
do merit discussion. We find some remaining structure in the residuals, where
the best-fit model underestimates the center frequency at the beginning of the
campaign and overestimates the center frequency at MJD 59890. Without an
underlying model to compare to, we do not attempt to fit a more complex
function to the data, but do note this behaviour as something to be
investigated in future studies. In addition, the residuals in this linear fit
are not homoskedastic: the scatter around the best-fit line decreases over the
campaign. These heteroskedastic errors should raise some questions about the
extension of this trend past the bottom of our bandpass. Specifically, it
seems possible that there is a several hundred MHz wide, downward drifting
“activity window” in frequency, that drifts out of our bandpass over the
campaign. This leads to the apparent shrinking of the scatter at the end of
the linear fit, and implies that the actual slope in the central frequency may
be steeper than 6.2 MHz per day.

####  4.1.4 Center Frequency vs. Drift Rate

Other repeaters have shown a correlation between center frequency and drift
rate, the linear decrease in sub-burst center frequency over time. We use the
values derived by frbgui in Section 3.3 to assess whether we see this same
correlation in the FRB 20220912A data. It should be noted that no FRBs in our
sample show upward-drifting bursts (e.g., Kumar et al., 2022).

To construct a subsample with reliable drift rate measurements, we must first
remove all of the single-component FRBs, which do not have a defined drift
rate. In addition, the Auto-Correlation Function (ACF) method for sub-burst
center frequency determination will underestimate the center frequencies of
components that intersect the top edge of the bandpass, and correspondingly
overestimate the center frequencies of components that intersect the bottom
edge of the bandpass. Both effects lead to an underestimation of the drift
rate: therefore, we remove any FRBs that intersect the edges of the bandpass,
bringing the subsample to 11 FRBs. Finally, we wish to remove any FRB where
the ACF measured the sub-burst slope of the brightest component instead of the
drift rate across multiple components, which can occur in FRBs with large SNR
variation across sub-bursts. This effect is visible in the 2D-ACFs, and can be
confirmed as an anomalously high drift rate that is consistent with a single
sub-burst’s slope. For this reason, we additionally remove FRBs #3, #6, and
#18.

We plot the drift rates for the 8 remaining FRBs (#1, #4, #8, #10, #20, #23,
#24, and #25) against their center frequencies in Figure 7 and do not find a
statistically-significant correlation. We used a $N=10^{5}$ trial bootstrap
for this correlation, due to p-values that were near the threshold. The
bootstrapping OLS routine finds a slope of -0.189$\pm$0.07 MHz ms-1MHz-1 and
an $R^{2}$ of 0.502, but the p-value of 0.052 is not significant. This is
consistent with the data, considering the small-number statistics resulting
from only 8 FRBs in the fit.

Other repeating FRBs demonstrate a trend of steeper drift rates with
frequency. For FRB 20180916B, compilations of studies across wide bandwidths
have shown a drift rate change of $-0.02$–$-0.03$ MHz ms-1MHz-1 with frequency
(Pastor-Marazuela et al., 2021; Sand et al., 2022). Meanwhile, for FRB
20180301A (at frequencies an order-of-magnitude higher), Kumar et al. (2023)
find a drift rate change of $-0.14$ MHz ms-1MHz-1 with frequency, over
approximately the same frequency range as this work. Using MeerKAT, Platts et
al. (2021) find a similar drift rate change with frequency, -0.147 $\pm$ 0.014
MHz ms -1MHz-1, for FRB 121102. It should be noted that a quadratic fit is
favoured when data covers a larger range of frequencies (Wang et al., 2022;
Chamma et al., 2023). Given that our measurement was not significant, we
cannot add to this population of results with FRB 20220912A in this work;
regardless, the consistency of the sign and general relationship of frequency
and drift rate over this population of repeaters hints at a persistent feature
in at least a subclass of FRBs that must be explained by any proposed emission
mechanism.

Figure 7: Drift rates in MHz ms-1 plotted against frequency in MHz for 8 FRBs
from FRB 20220912A that a) had more than 1 subcomponent b) did not intersect
either edge of the bandpass and c) had subcomponents of similar-enough SNRs to
allow for a correct drift rate fit from the 2D ACF of the dynamic spectrum.
Visually, there is a downward trend (increasing magnitude of drift) with
increasing frequency and we show the best-fit line from a linear fit (black),
but we do not find that this trend is significant

.

Sub-burst slope and drift rate can follow similar relationships (e.g., Rajabi
et al., 2020; Chamma et al., 2023). However, we see no correlation between
subburst slope and duration, or subburst slope and center frequency, in this
dataset. Given the scatter in the measurements and the lack of bursts at other
bands to constrain model fits, this is not unexpected.

####  4.1.5 Center Frequency vs. Temporal Duration

It has been noted that higher frequency sub-bursts seem to have shorter
temporal durations, which is only observable across GHz of bandwidth (e.g.,
Platts et al., 2021). Gajjar et al. (2018) notes that the widths are
considerably narrower (about an order of magnitude) at 8 GHz compared to 1 GHz
for FRB 121102, but that the effect does not seem consistent with broadening
due to scattering from turbulent plasma along the line-of-sight. Here, we do
observe a slight downward trend in duration with increasing frequency, as
shown in Figure 8. The associated linear fit has a slope of $(-9.3\pm
3.3)\times 10^{-4}$ MHz ms-1, an R2 value of 0.067 (indicating wide scatter
over the $\sim$700 MHz available in these observations), and a p-value of
0.0098. Given the low correlation, this result should be taken only as an
indication of consistency with the previously-observed trend of shorter
durations at higher central frequencies. Given the channel width and the FRB
DM, the expected smearing due to dispersion at the bottom of the ATA band is
$\sim 0.9$ ms.

Figure 8: Duration in ms plotted against frequency in MHz for our full sample
of 101 sub-bursts from FRB 20220912A. Note the slight decrease in duration
over the bandpass.

####  4.1.6 Scattering

We do not observe any significant scattering behaviour in the waterfall plots
in Figure 2, though we cannot constrain scattering timescales less than
several hundred $\upmu$s at these frequencies, due to our sampling time of 64
$\upmu$s. This is consistent with the nominal scattering value of $\leq 15$ ms
at 400 MHz for this source as reported by Bhusare et al. (2022), which would
imply, given a Kolmogorov scaling with $\alpha$ = 4.4, an expected scattering
timescale of $\leq$60 $\upmu$s.

###  4.2 Repeating Rate Function and All-Sky Rate

We show the cumulative repeating rate function $R(>F)$ for FRB 20220912A in
Figure 9, where $F$ is the fluence of each FRB (which may contain multiple
sub-bursts). We fit the observed fluence distribution with a power-law
function using the $\mathtt{powerlaw}$ package provided by Alstott et al.
(2014) based on Clauset et al. (2009). The package uses the maximum likelihood
method to optimize the power-law slope
$\gamma\equiv-\mathrm{d}\,\mathrm{ln}[R(>F)]/\mathrm{d}\,\mathrm{ln}F$ and
further uses the Kologorov-Smirnov test to optimize the minimum fluence
$F_{\rm min}$ above which a power-law provides the best description (see
Clauset et al., 2009, for the method descriptions).

When restricting the minimum fluence to be in the range from $40$ to
$150\rm\,Jy\,ms$ (roughly corresponding to a minimum SNR between $\sim$40 and
$\sim$150 for burst duration of $\sim$1 ms), we find the optimized minimum
fluence to be $F_{\rm min}\simeq 130\rm\,Jy\,ms$. We also find the best power-
law above this minimum fluence to be

$R(>F)=3.3\times 10^{-2}\mathrm{\,h^{-1}}\,(F/F_{\rm
min})^{\gamma},\gamma=1.08,$ (5)

and the standard deviation of the power-law slope is $\sigma=0.25$. The slope
is not well constrained by the current small sample but it is consistent with
the power-law slope of the FRB luminosity (or energy) function (e.g., Luo et
al., 2018; Lu & Piro, 2019; James et al., 2022; Shin et al., 2023). We also
tried fitting the ATA sample by an exponentially truncated power-law described
by $R(>F)\propto F^{\gamma}\exp(-F/F_{\rm max})$, and the best fit result is
$\gamma\simeq 0.0$ and $F_{\rm max}\simeq 570\rm\,Jy\,ms$. Although the
likelihood ratio test shows that a truncated power-law fit is preferred with a
$p$-value of 0.06 — meaning that there is a 6% chance that the improvement in
the likelihood is due to random fluctuations, the truncated power-law model
has an additional free parameter and hence a truncation is not required by the
current data.

We then compared the repeating rate function for FRB 20220912A with the
cumulative all-sky rate function at high fluences, which is provided by the
ASKAP Fly’s Eye survey (Shannon et al., 2018). Using the same method as
outlined above, we find that the all-sky rate function can be described by the
following best-fit power-law function above an optimized minimum fluence of
$F_{\rm min}=50.6\rm\,Jy\,ms$,

$R_{\rm as}(>F)=1.6\mathrm{\,h^{-1}}\,(F/F_{\rm min})^{\gamma_{\rm
as}},\gamma_{\rm as}=1.54,$ (6)

and the standard deviation of the power-law slope is $\sigma_{\rm as}=0.34$.
Despite that $\gamma_{\rm as}$ is statistically weakly constrained, we do
theoretically expect the fluence distribution to be close to the Euclidean
value of $\gamma=1.5$ because the ASKAP bursts are from the local Universe and
the entire FRB population has a maximum specific energy (see e.g., Macquart &
Ekers, 2018; Lu & Piro, 2019; Shin et al., 2023).

It should be noted that the specific energy of the brightest burst
($F=1128\rm\,Jy\,ms$) detected in our sample is

$E\simeq{F\times 4\pi D_{\rm L}^{2}(z)\over(1+z)^{2}}\simeq 1.5\times
10^{32}\rm\,erg\,Hz^{-1},$ (7)

where we have used the Planck Collaboration et al. (2016) cosmological
parameters for the luminosity distance $D_{\rm L}$ and a source redshift of
$z=0.077$ provided by Ravi et al. (2022). This burst is among the most
intrinsically bright ones observed to-date (e.g., Ryder et al., 2022; Shin et
al., 2023). As can be seen in Figure 9, the repeating rate function of FRB
20220912A must have a cut-off at fluence $F_{\rm max}\lesssim
10^{4}\rm\,Jy\,ms$ for this source to be consistent with the all-sky fluence
distribution extrapolated from the ASKAP measurement assuming $\gamma_{\rm
as}=1.5$ (and additionally assuming that the repetition rate of this source is
constant). Such a cut-off is also consistent with the inferred maximum
specific energy $E_{\rm max}\sim 10^{32}\mbox{ to }10^{33}\rm\,erg\,Hz^{-1}$
in the FRB luminosity/energy function (Shin et al., 2023). Further long-term
monitoring of FRB 20220912A is needed to test if the repeating rate function
indeed has a cut-off.

On the other hand, we also see from Figure 9 that FRB 20220912A contributes at
least a few percent of the all-sky rate above fluence of
$\sim\rm\,100\,Jy\,ms$. Although prolific repeaters like FRB 20220912A and FRB
20121102A represent a minority of all FRB sources, they contribute a
significant fraction of the all-sky rate. On the other hand, many of the
$>100\rm\,Jy\,ms$ sources detected by the ASKAP Fly’s Eye did not show
repetitions even with sensitive follow-up observations. This means that the
brightest FRBs in the sky are contributed by the most active repeaters as well
as by the less active ones. This further restricts the maximum fluence of FRB
20220912A to be likely significantly less than $10^{4}\rm\,Jy\,ms$.

Figure 9: Fluence distributions of the ATA sample of bursts from FRB 20220912A
(thick black line) and the ASKAP Fly’s Eye sample (thin black line). The
vertical axis shows the cumulative rate, as computed by the raw number of
detections divided by the total on-source time. The total exposure of the
ASKAP Fly’s Eye survey is $5.1\times 10^{5}\rm\,deg^{2}\,h$ (Shannon et al.,
2018), which is converted into an all-sky equivalent exposure time of
$12.4\rm\,hr$ — the thin black line shows the all-sky rate as inferred from
the ASKAP sample. The flattening of the distributions at the low fluence end
($\lesssim 100\rm\,Jy\,ms$ for the ATA sample and $\lesssim 50\rm\,Jy\,ms$ for
the ASKAP sample) is likely due to incompleteness of the surveys. The
steepening at the high fluence end is due to insufficient exposure times. The
blue dashed and orange dash-dotted lines show the best-fit power-law and
truncated power-law models to the ATA data, respectively. The red dotted line
shows the best-fit power-law model for the ASKAP data.

###  4.3 Characteristic Timescales and Sub-burst Periodicity

Given that so many of our FRBs are multi-component (29/35), we investigate
whether or not the sub-bursts show any consistent inter-pulse spacings. In
particular, FRB #10 shows 4 sub-bursts that are bright and appear evenly-
spaced, hinting at sub-burst periodicity. For both a general characteristic
timescale analysis and a periodicity analysis, we begin with the numpy arrays
produced in Section 3.3, and average over the frequency axis to get a
timeseries profile. We then median-subtract and apply a 5th-degree polynomial
Savitzky-Golay filter with a window-size of 21 samples (Savitzky & Golay,
1964). The smoothing filter is applied to make peak-finding possible in
Section 4.3.1, but does attenuate potential short-period behaviour ($\lesssim
0.13$ ms) in the FRB profile.

####  4.3.1 Characteristic Timescales

To characterize significant timescales in each FRB, we calculate the ACF of
the smoothed FRB profile with scipy. This allows us to be more sensitive to
non-sinusoidal signals with fewer repetitions in short timeseries than a power
spectrum (e.g., a Leahy-normalized power spectrum, see CHIME/FRB Collaboration
et al., 2022) while still performing a similar function.

We then find the tallest local maximum in the ACF with a required minimum peak
width of $w_{{}_{\textrm{ACF}}}>2$ bins (to avoid single-bin noise
fluctuations).This corresponds to the lag time $p_{{}_{\textrm{ACF}}}$ which
contains the most power in the ACF — if the FRB is generating the peak in the
ACF, this is likely representative of the delay in sub-bursts for a two-
component FRB. At this stage, 2 of the 35 FRBs were removed from the sample
due to not having any peaks in their ACFs.

RFI is often periodic and could create a false-positive periodicity in the
ACFs from the previous step. Therefore, we perform a bootstrap resampling
noise-permutation test as a crude filter for ACF peaks that are not coming
from the FRB signal itself. Each file contains 100 channels of noise before
and after the FRB, which constitutes 25% or more of each file (depending on
the variable FRB duration; mean=42%). For each FRB, we perform 1000 trials
where the noise arrays before and after the FRB signal are randomly shuffled,
and then perform the median-removal, smoothing, ACF, and peak-finding steps as
for the original FRB profile. If the mean of the set of 1000 noise-scrambled
ACF peaks still falls within 10% of the original, with a standard deviation
that is less than the width of the peak $w_{{}_{\textrm{ACF}}}$ from the
original ACF, we treat this as a spacing that is inherent to the FRB itself.
We find that 21 of the remaining 33 FRBs pass this filter. Those 21 ACF peak
spacings were then visually checked against the timeseries profiles, to ensure
that the above methodology returned results that were consistent with the
visual appearance of the FRB. It should be noted that peaks in an ACF can be
difficult to interpret or assign significances to; for example, for FRBs with
complex quasi-periodic structure, this could be representative of the distance
between the two brightest sub-bursts, or an indication of evenly-spaced
components.

The median and median absolute deviation of the distribution of ACF-derived
timescales is $5.82\pm 1.16$ ms. This implies that, while individual bursts
may have preferred periods or spacings, we do not see a sharp mode or
otherwise tightly-clustered distribution providing evidence of a shared,
strict periodicity between sub-bursts across the sample, which corroborates
the report of no 1 ms–1000 s periodicity from Zhang et al. (2023).

In the future, this sort of technique would be improved by fitting for the FRB
shape, subtracting it from the data, and then fully permuting the remaining
profile, instead of the “bookend” noise-permutation method described above.

####  4.3.2 Sub-Burst Periodicity

As noted by Petroff et al. (2022), strict periodicity even within a single
sub-burst (as in CHIME/FRB Collaboration et al., 2022) supports a
magnetospheric origin of FRB emission, given that it is difficult to produce
with an external shock model. Visually, FRB # 10 is a candidate for this kind
of strict periodicity. To assess the statistical significance of the
periodicity in this particular burst, we employ methodology similar to
CHIME/FRB Collaboration et al. (2022), as follows.

We first check for a peak in the squared Fourier transform, which we find at
6.4 ms (the ACF peak for this FRB was at 5.7 ms). To find actual times-of-
arrival (ToAs) of each of the four subbursts, we perform a least-squares fit
of a function containing four Gaussians (each with independent amplitude,
width, and central time) and a constant vertical offset. Using the results of
that fit, we extract the central times as the ToAs; we then re-fit while
enforcing a constant spacing between peaks, letting only period and start time
of the first subburst vary while fixing the amplitudes, widths, and offset to
the best-fit values from the previous fit. The resulting best-fit period is
6.1 ms.

To assess the significance of this result, we calculate the $\hat{L}[n]$
statistic from CHIME/FRB Collaboration et al. (2022), a metric of how well the
ToAs approximate the linear relationship expected for arrival time vs. integer
multiples of the best-fit period (where larger scores equal better
approximation). Using the ToAs obtained in the first 4-Gaussian fit and a 6.1
ms period, we find $\hat{L}[n]_{FRB10}=3.459$. Then, we simulate 10000 arrays
of four ToAs each, with the following conditions:

  1. 1.

Average spacings $\bar{d}$ that would enforce all four pulses falling within
the length of the timeseries

  2. 2.

An “exclusion factor” (minimum spacing factor) of $\chi=0.2$

  3. 3.

ToAs drawn from a uniform probability distribution between $\chi\bar{d}\leq
d\leq(2-\chi)\bar{d}$

This creates series of four ToAs that are not drawn from a periodic
distribution, but will have a range of scores in $\hat{L}[n]$ which could, in
cases, approach periodicity. When we compare $\hat{L}[n]_{FRB10}$ to the
distribution of $\hat{L}[n]$ values from the simulations, we find that it is
larger than 81% of values in the simulation, giving a generous “false alarm
probability” of 19%. From this result, we cannot reject the null hypothesis of
a non-periodic emission mechanism. Note that the first two sub-pulses are
particularly low SNR, so their Gaussian-fitted ToAs may be contributing to the
lower $\hat{L}[n]$ score.

We also see no obvious periodicity between bursts. However, we note that,
because the ATA can only observe the part of the FRB’s energy distribution
that is above both bimodal peaks seen by Zhang et al. (2023) and Feng et al.
(2023), our sampling of periodicity or patterns in wait-time will be
incomplete.

##  5 Discussion and Conclusion

As described in Section 2.3, we detect 35 bursts from the FRB 20220912A in 541
hours of observation with the ATA, using the SPANDAK detection pipeline. The
FRBs appear throughout the 672 MHz bandpass, biased towards the lower ($\sim
1$ GHz) frequency end, with an average sub-burst duration of 1.2 ms and an
average sub-burst bandwidth of $\sim 200$ MHz. In Section 3, we used the
frbgui package, which leverages 2D fits to the ACF of the dynamic spectrum of
each bursts, to measure spectrotemporal features from each FRB. In Section 4,
we described the following features in our dataset:

  1. 1.

A median dispersion measure of 219.775 pc cm-3 (Section 3.1)

  2. 2.

A median isotropic equivalent burst energy of 1 $\times$ $10^{39}$ erg
(Section 4.1.1)

  3. 3.

A positive, linear correlation between center frequency and bandwidth (Section
4.1.2)

  4. 4.

A decrease in center frequency and bandwidth over the two months of the
campaign (Section 4.1.3)

  5. 5.

A slight decrease in duration with increasing center frequency (Section 4.1.5)

  6. 6.

No evidence for scattering (Section 4.1.6)

  7. 7.

FRB 20220912A must have a cut-off fluence $F_{\rm max}\lesssim 10^{4}$ Jy-ms
to be consistent with the all-sky fluence distribution (Section 4.2)

  8. 8.

FRB 20220912A significantly contributed to the all-sky FRB rate at a level of
a few percent for fluences $\gtrsim$100 Jy-ms (Section 4.2)

  9. 9.

The majority of bursts in the observed sample were multi-component FRBs, with
median component spacings of 5.82$\pm$1.16 ms (Section 4.3.1)

  10. 10.

No bursts showed statistically significant sub-burst periodicity (Section
4.3.2)

Broadly speaking, there are two classes of FRB models depending on whether the
radio bursts are created within the magnetosphere of a neutron star (or black
hole) or far from the magnetosphere.

One of the close-in models is coherent curvature emission, where charged
particles in macroscopic clumps of longitudinal sizes $\lesssim\lambda$ (the
FRB wavelength) radiate coherently when moving along curved magnetic field
lines (e.g., Lu & Kumar, 2018; Lu et al., 2020). In this model, the FRB
spectrum is set by the spatial distribution of currents in the longitudinal
direction. By Fourier transformation, a narrow spectrum of
$\Delta\omega/\omega_{\rm center}\simeq 0.3$ can be produced by a modestly
long ($N\sim\mbox{few}$) chain of current islands.

One class of the far-away models relies on synchrotron maser emission when an
ultra-relativistic outflow interacts with strongly magnetized plasma forming a
quasi-perpendicular shock (Hoshino & Arons, 1991; Metzger et al., 2019;
Plotnikov & Sironi, 2019). The synchrotron maser model predicts
$\Delta\omega/\omega_{\rm center}\gtrsim 1$ for two reasons: (1) the ring-like
particle distribution function is not infinitely thin in phase space but with
a fractional momentum spread of order unity — this allows the rapid growth of
modes at a rather broad range of frequencies
$\Delta\omega^{\prime}/\omega_{\rm center}^{\prime}\sim 1$ (here, primes ′
mean in the comoving frame of the shocked plasma) instead of a narrow spectral
line (Plotnikov & Sironi, 2019; Sironi et al., 2021); (2) the Doppler beaming
for viewing angles of $\lesssim 1/\Gamma$ across a quasi-spherical shock front
creates a broad spectrum $\Delta\omega/\omega_{\rm center}\sim 1$ in the
observer’s frame (Metzger et al., 2019; Beniamini & Kumar, 2020). Previous
observations show that many bursts, especially those from repeaters (Pleunis
et al., 2021b), have narrow bandwidths $\Delta\omega/\omega_{\rm center}\ll
1$. For the synchrotron maser model to be viable for these narrow-banded
bursts, external propagation effects (e.g., Cordes et al., 2017; Sobacchi et
al., 2022) must be playing a role at modulating the spectral intensity across
narrow frequency intervals.

While magnetar models are currently favoured, other exotic repeater models do
exist. For example, superradiance models rely on a narrowband emitter similar
to a molecular maser, and triggered superradiance models invoke FRBs initiated
in the system by a more distant coherent emitter such as a pulsar (Dicke,
1954; Houde et al., 2019).

The conclusions in the list above do not strongly favour or disfavour any of
the described classes of models, but do provide a benchmark against which to
compare future observations. For example, it remains to be shown how (and if
possible at all) propagation effects in the synchrotron maser model would
create a linear correlation between the bandwidth and the central frequency as
seen in this work. This same observation, as well as the tentative decrease in
duration with center frequency, is consistent with a narrowband emission
process such as that in the superradiance model (Rajabi et al., 2020).

Regardless of the model’s location of emission, our results underscore the
conclusions found in Feng et al. (2023) and Zhang et al. (2023): low-
efficiency models (with efficiencies of order $10^{-4}$ or lower) for the
emission mechanism are not compatible with the immense energy being released
and the high activity rate of this FRB source, especially given that our
sample consists of bursts with a median energy $\sim 100\times$ that of the
previous literature.

All of the published bursts for this source, our 35 included, are downward-
drifting, potentially indicating that downward frequency drift is inherent to
the emission mechanism; this is a feature consistent with both close-in and
far-away magnetar models.

This work emphasizes the importance of the ATA in FRB science, given its wide
bandwidth recording capabilities and potential to engage in unique modes of
observation, for example, a “Fly’s Eye” strategy covering up to a 389 sq. deg.
field-of-view on the sky at 1 GHz (Siemion et al., 2011). As the refurbishment
continues, additional FRB-relevant features, such as a fast imaging mode will
be re-implemented on the upgraded system (Law & ATA Team, 2009). More
observations of the source, especially at higher frequencies with instruments
like the ATA, will help to differentiate between the various classes of FRB
progenitor models.

## Acknowledgements

The Allen Telescope Array (ATA) refurbishment program and its ongoing
operations have received substantial support from Franklin Antonio. Additional
contributions from Frank Levinson, Greg Papadopoulos, the Breakthrough Listen
Initiative and other private donors have been instrumental in the renewal of
the ATA. Breakthrough Listen is managed by the Breakthrough Initiatives,
sponsored by the Breakthrough Prize Foundation. The Paul G. Allen Family
Foundation provided major support for the design and construction of the ATA,
alongside contributions from Nathan Myhrvold, Xilinx Corporation, Sun
Microsystems, and other private donors. The ATA has also been supported by
contributions from the US Naval Observatory and the US National Science
Foundation. S.Z.S. acknowledges that this material is based upon work
supported by the National Science Foundation MPS-Ascend Postdoctoral Research
Fellowship under Grant No. 2138147. Participation of J.K. made possible by
SETI Institute REU program (NSF award #2051007). The authors would also like
to thank Ron Maddalena for his help in measuring the sensitivity of the ATA
feeds. We acknowledge use of the CHIME/FRB Public Database, provided at
https://www.chime-frb.ca/ by the CHIME/FRB Collaboration. We also acknowledge
use of the software packages pandas (pandas development team, 2023), numpy
(Harris et al., 2020), astropy (Astropy Collaboration et al., 2022), and YOUR
(Aggarwal et al., 2020).

FRB

    Fast Radio Burst
CHIME

    the Canadian Hydrogen Intensity Mapping Experiment
ATA

    Allen Telescope Array
ATel

    Astronomer’s Telegram
DSA-110

    Deep Synoptic Array
DM

    Dispersion Measure
DSP

    Digital Signal Processing
RF

    Radio Frequency
LO

    Local Oscillator
IF

    Intermediate Frequency
FPGA

    Field Programmable Gate Array
BLADE

    Breakthrough Listen Accelerated DSP Engine
RFI

    Radio Frequency Interference
SNR

    Signal-to-Noise Ratio
SEFD

    System Equivalent Flux Density
ACF

    Auto-Correlation Function
GBT

    Green Bank Telescope
RFSoC

    Radio Frequency System-on-Chip
ToAs

    times-of-arrival

## Data Availability

The extracted FRB properties are available in the article and in its online
supplementary material. The dynamic spectra in archive or filterbank formats
will be shared on reasonable request to the corresponding author.

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Table 2: Properties of the 35 bursts from FRB 20220912A detected by the Allen Telescope Array. Index |  MJD |  DM |  Width |  Flux |  Fluence |  S/N |  Center Frequency |  Bandwidth
---|---|---|---|---|---|---|---|---
|  (day) |  (pc cm-3) |  (ms) |  (Jy) |  (Jy-ms) |  |  (MHz) |  (MHz)
1 |  59872.4423299306 |  219.81 $\pm$ 1.22 |  2.56 |  6.30 $\pm$ 0.57 |  16.13 $\pm$ 1.45 |  18.53 |  1289.66 $\pm$ 8.39 |  301.39 $\pm$ 0.87
|  |  |  1.92 |  3.00 $\pm$ 0.27 |  5.75 $\pm$ 0.52 |  6.08 |  1220.00 $\pm$ 15.03 |  191.81 $\pm$ 2.42
2 |  59873.3504993634 |  219.63 $\pm$ 1.61 |  2.56 |  65.74 $\pm$ 5.77 |  168.30 $\pm$ 14.78 |  177.38 |  1652.05 $\pm$ 4.62 |  266.21 $\pm$ 0.01
|  |  |  3.20 |  14.71 $\pm$ 1.29 |  47.04 $\pm$ 4.13 |  53.61 |  1568.95 $\pm$ 4.64 |  389.06 $\pm$ 0.19
3 |  59875.2672106481 |  219.46 $\pm$ 0.90 |  0.77 |  25.60 $\pm$ 1.88 |  19.66 $\pm$ 1.45 |  29.29 |  1311.63 $\pm$ 5.00 |  227.51 $\pm$ 0.35
|  |  |  0.64 |  11.26 $\pm$ 0.83 |  7.21 $\pm$ 0.53 |  12.52 |  1326.39 $\pm$ 16.55 |  257.39 $\pm$ 4.28
4 |  59880.2720233796 |  219.98 $\pm$ 1.95 |  3.20 |  5.90 $\pm$ 0.59 |  18.87 $\pm$ 1.90 |  25.10 |  1545.38 $\pm$ 4.69 |  405.03 $\pm$ 0.92
|  |  |  1.92 |  25.14 $\pm$ 2.53 |  48.27 $\pm$ 4.85 |  74.93 |  1491.42 $\pm$ 4.65 |  330.73 $\pm$ 0.07
|  |  |  3.20 |  44.74 $\pm$ 4.50 |  143.16 $\pm$ 14.39 |  147.75 |  1453.30 $\pm$ 4.62 |  243.71 $\pm$ 0.01
|  |  |  1.60 |  108.09 $\pm$ 10.86 |  172.95 $\pm$ 17.38 |  259.44 |  1427.25 $\pm$ 4.62 |  257.44 $\pm$ 0.01
|  |  |  2.88 |  59.11 $\pm$ 5.94 |  170.22 $\pm$ 17.11 |  194.19 |  1418.31 $\pm$ 4.62 |  267.98 $\pm$ 0.01
|  |  |  3.84 |  21.01 $\pm$ 2.11 |  80.69 $\pm$ 8.11 |  79.35 |  1280.43 $\pm$ 4.62 |  265.50 $\pm$ 0.03
5 |  59880.3955575231 |  219.81 $\pm$ 1.12 |  3.20 |  8.48 $\pm$ 0.85 |  27.12 $\pm$ 2.73 |  29.47 |  1398.85 $\pm$ 4.69 |  270.24 $\pm$ 0.29
|  |  |  1.60 |  24.64 $\pm$ 2.48 |  39.42 $\pm$ 3.96 |  63.59 |  1318.60 $\pm$ 4.63 |  297.62 $\pm$ 0.08
|  |  |  2.88 |  35.13 $\pm$ 3.53 |  101.18 $\pm$ 10.17 |  122.56 |  1304.51 $\pm$ 4.62 |  302.13 $\pm$ 0.02
6 |  59880.4029308449 |  219.78 $\pm$ 1.82 |  7.68 |  12.60 $\pm$ 1.27 |  96.78 $\pm$ 9.73 |  65.43 |  1236.88 $\pm$ 2.32 |  250.98 $\pm$ 0.02
|  |  |  6.40 |  19.80 $\pm$ 1.99 |  126.70 $\pm$ 12.73 |  79.22 |  1136.83 $\pm$ 2.31 |  178.88 $\pm$ 0.01
7 |  59882.2707171412 |  219.72 $\pm$ 1.43 |  2.56 |  9.43 $\pm$ 0.94 |  24.15 $\pm$ 2.40 |  18.76 |  1683.63 $\pm$ 4.62 |  113.21 $\pm$ 0.12
8 |  59882.4726475694 |  219.23 $\pm$ 0.55 |  1.60 |  2.79 $\pm$ 0.28 |  4.47 $\pm$ 0.44 |  5.73 |  1381.16 $\pm$ 6.14 |  192.61 $\pm$ 2.94
|  |  |  1.60 |  7.53 $\pm$ 0.75 |  12.05 $\pm$ 1.20 |  17.13 |  1337.40 $\pm$ 7.50 |  237.15 $\pm$ 0.92
9 |  59883.1097671759 |  221.16 $\pm$ 1.39 |  6.40 |  3.95 $\pm$ 0.36 |  25.31 $\pm$ 2.32 |  15.90 |  1059.68 $\pm$ 8.55 |  217.32 $\pm$ 1.40
|  |  |  6.40 |  4.18 $\pm$ 0.38 |  26.75 $\pm$ 2.45 |  12.51 |  1003.38 $\pm$ 7.99 |  120.38 $\pm$ 1.10
10 |  59883.4502390046 |  219.60 $\pm$ 0.68 |  6.40 |  2.79 $\pm$ 0.26 |  17.86 $\pm$ 1.64 |  12.75 |  1301.65 $\pm$ 5.71 |  280.61 $\pm$ 5.38
|  |  |  6.40 |  2.87 $\pm$ 0.26 |  18.38 $\pm$ 1.68 |  10.73 |  1200.97 $\pm$ 9.44 |  187.49 $\pm$ 1.11
|  |  |  6.40 |  4.24 $\pm$ 0.39 |  27.14 $\pm$ 2.49 |  17.26 |  1120.52 $\pm$ 6.76 |  222.49 $\pm$ 0.78
|  |  |  5.12 |  5.57 $\pm$ 0.51 |  28.51 $\pm$ 2.61 |  20.53 |  1094.15 $\pm$ 6.03 |  228.34 $\pm$ 1.10
11 |  59887.3512349537 |  219.60 $\pm$ 2.23 |  9.60 |  15.66 $\pm$ 1.57 |  150.34 $\pm$ 15.05 |  84.69 |  1126.54 $\pm$ 4.62 |  219.55 $\pm$ 0.04
|  |  |  3.84 |  10.03 $\pm$ 1.00 |  38.53 $\pm$ 3.86 |  35.02 |  1008.34 $\pm$ 4.62 |  228.68 $\pm$ 0.45
|  |  |  2.56 |  14.88 $\pm$ 1.49 |  38.08 $\pm$ 3.81 |  37.65 |  974.84 $\pm$ 4.62 |  180.38 $\pm$ 0.39
|  |  |  3.84 |  6.78 $\pm$ 0.68 |  26.04 $\pm$ 2.61 |  19.09 |  966.87 $\pm$ 4.91 |  148.70 $\pm$ 1.85
|  |  |  5.76 |  10.29 $\pm$ 1.03 |  59.28 $\pm$ 5.93 |  27.37 |  946.64 $\pm$ 4.62 |  88.50 $\pm$ 0.20
12 |  59887.4423248843 |  219.86 $\pm$ 1.35 |  2.88 |  11.63 $\pm$ 1.16 |  33.48 $\pm$ 3.35 |  34.26 |  1153.26 $\pm$ 4.62 |  217.24 $\pm$ 0.09
|  |  |  6.08 |  27.24 $\pm$ 2.73 |  165.64 $\pm$ 16.58 |  120.94 |  1114.70 $\pm$ 4.62 |  233.57 $\pm$ 0.01
|  |  |  5.12 |  12.46 $\pm$ 1.25 |  63.81 $\pm$ 6.39 |  43.26 |  967.08 $\pm$ 4.62 |  169.55 $\pm$ 0.04
13 |  59889.1244077662 |  220.03 $\pm$ 0.98 |  4.48 |  5.92 $\pm$ 0.60 |  26.53 $\pm$ 2.70 |  20.98 |  1469.10 $\pm$ 4.64 |  195.59 $\pm$ 0.28
|  |  |  6.40 |  4.80 $\pm$ 0.49 |  30.71 $\pm$ 3.12 |  26.32 |  1355.54 $\pm$ 4.66 |  328.12 $\pm$ 0.31
14 |  59889.3744443403 |  219.77 $\pm$ 1.35 |  7.68 |  13.49 $\pm$ 1.37 |  103.60 $\pm$ 10.54 |  46.63 |  947.01 $\pm$ 4.64 |  108.60 $\pm$ 0.76
|  |  |  6.40 |  5.17 $\pm$ 0.53 |  33.11 $\pm$ 3.37 |  11.77 |  929.49 $\pm$ 4.66 |  56.48 $\pm$ 6.54
15 |  59890.3176200116 |  219.57 $\pm$ 1.64 |  2.56 |  2.58 $\pm$ 0.26 |  6.60 $\pm$ 0.67 |  7.63 |  1423.93 $\pm$ 12.58 |  242.58 $\pm$ 8.22
|  |  |  7.68 |  16.86 $\pm$ 1.70 |  129.51 $\pm$ 13.06 |  88.89 |  1409.52 $\pm$ 4.62 |  256.73 $\pm$ 0.03
|  |  |  5.12 |  28.24 $\pm$ 2.85 |  144.57 $\pm$ 14.58 |  125.74 |  1308.04 $\pm$ 4.63 |  274.81 $\pm$ 0.02
16 |  59890.3637615394 |  220.34 $\pm$ 1.43 |  16.64 |  4.60 $\pm$ 0.46 |  76.52 $\pm$ 7.72 |  19.92 |  948.73 $\pm$ 4.79 |  80.03 $\pm$ 0.05
17 |  59891.3109625000 |  219.49 $\pm$ 1.00 |  3.84 |  9.85 $\pm$ 1.05 |  37.82 $\pm$ 4.01 |  30.63 |  978.96 $\pm$ 4.82 |  161.54 $\pm$ 0.51
|  |  |  7.04 |  16.30 $\pm$ 1.73 |  114.76 $\pm$ 12.18 |  55.80 |  950.16 $\pm$ 4.62 |  106.73 $\pm$ 0.06
|  |  |  1.92 |  20.17 $\pm$ 2.14 |  38.72 $\pm$ 4.11 |  33.33 |  944.70 $\pm$ 4.65 |  91.18 $\pm$ 0.27
|  |  |  3.84 |  38.79 $\pm$ 4.12 |  148.96 $\pm$ 15.81 |  94.28 |  939.47 $\pm$ 4.62 |  98.62 $\pm$ 0.02
|  |  |  3.84 |  11.40 $\pm$ 1.21 |  43.79 $\pm$ 4.65 |  25.54 |  932.68 $\pm$ 4.89 |  83.77 $\pm$ 0.43
18 |  59891.3164585648 |  219.29 $\pm$ 0.61 |  1.92 |  7.66 $\pm$ 0.81 |  14.71 $\pm$ 1.56 |  19.17 |  1043.39 $\pm$ 4.62 |  209.05 $\pm$ 0.32
|  |  |  1.92 |  9.09 $\pm$ 0.96 |  17.46 $\pm$ 1.85 |  22.55 |  1038.36 $\pm$ 5.53 |  205.43 $\pm$ 0.26
19 |  59897.0712164352 |  219.40 $\pm$ 1.11 |  3.20 |  16.15 $\pm$ 1.61 |  51.69 $\pm$ 5.16 |  40.72 |  971.51 $\pm$ 2.37 |  144.12 $\pm$ 1.01
|  |  |  4.48 |  55.00 $\pm$ 5.49 |  246.42 $\pm$ 24.58 |  146.33 |  955.11 $\pm$ 2.31 |  114.66 $\pm$ 0.05
|  |  |  5.12 |  24.72 $\pm$ 2.47 |  126.58 $\pm$ 12.62 |  63.69 |  949.56 $\pm$ 2.31 |  94.08 $\pm$ 0.22
|  |  |  3.84 |  17.51 $\pm$ 1.75 |  67.22 $\pm$ 6.70 |  37.72 |  940.87 $\pm$ 2.32 |  87.74 $\pm$ 0.49
20 |  59898.4399226852 |  219.91 $\pm$ 1.65 |  4.16 |  2.48 $\pm$ 0.25 |  10.32 $\pm$ 1.03 |  9.12 |  1218.58 $\pm$ 4.79 |  233.42 $\pm$ 10.08
|  |  |  5.44 |  10.64 $\pm$ 1.07 |  57.86 $\pm$ 5.80 |  47.43 |  1151.51 $\pm$ 4.77 |  262.89 $\pm$ 0.23
21 |  59900.1470432060 |  220.03 $\pm$ 1.45 |  2.56 |  9.37 $\pm$ 0.93 |  24.00 $\pm$ 2.38 |  24.36 |  1059.62 $\pm$ 4.17 |  194.06 $\pm$ 1.14
|  |  |  2.56 |  22.82 $\pm$ 2.26 |  58.42 $\pm$ 5.79 |  58.10 |  1056.02 $\pm$ 2.32 |  186.19 $\pm$ 0.12
|  |  |  3.84 |  30.42 $\pm$ 3.01 |  116.82 $\pm$ 11.58 |  94.34 |  1030.33 $\pm$ 2.31 |  184.12 $\pm$ 0.03
|  |  |  14.08 |  28.78 $\pm$ 2.85 |  405.15 $\pm$ 40.15 |  147.22 |  959.33 $\pm$ 2.31 |  136.69 $\pm$ 0.00
22 |  59900.2719472685 |  220.00 $\pm$ 1.47 |  5.76 |  13.64 $\pm$ 1.35 |  78.57 $\pm$ 7.79 |  48.58 |  963.68 $\pm$ 4.63 |  161.91 $\pm$ 0.01
23 |  59901.4354073148 |  219.66 $\pm$ 1.76 |  10.24 |  6.69 $\pm$ 0.69 |  68.46 $\pm$ 7.09 |  49.16 |  1262.87 $\pm$ 4.62 |  354.94 $\pm$ 1.52
|  |  |  6.40 |  4.11 $\pm$ 0.43 |  26.28 $\pm$ 2.72 |  18.64 |  1169.06 $\pm$ 4.68 |  216.43 $\pm$ 7.03
|  |  |  8.32 |  15.62 $\pm$ 1.62 |  129.93 $\pm$ 13.46 |  80.24 |  1108.69 $\pm$ 4.62 |  213.32 $\pm$ 0.27
|  |  |  5.76 |  16.99 $\pm$ 1.76 |  97.86 $\pm$ 10.14 |  52.06 |  1040.13 $\pm$ 7.50 |  109.59 $\pm$ 11.58
24 |  59903.1278839120 |  224.94 $\pm$ 1.76 |  5.76 |  5.13 $\pm$ 0.51 |  29.53 $\pm$ 2.93 |  22.38 |  1091.56 $\pm$ 4.64 |  242.03 $\pm$ 1.30
|  |  |  4.48 |  11.86 $\pm$ 1.18 |  53.15 $\pm$ 5.28 |  41.54 |  1039.08 $\pm$ 4.77 |  200.17 $\pm$ 0.29
|  |  |  4.16 |  11.31 $\pm$ 1.12 |  47.07 $\pm$ 4.68 |  34.67 |  983.03 $\pm$ 4.62 |  165.10 $\pm$ 0.21
25 |  59903.2531478009 |  223.24 $\pm$ 1.62 |  3.20 |  23.33 $\pm$ 2.32 |  74.64 $\pm$ 7.42 |  86.56 |  1240.18 $\pm$ 4.62 |  314.81 $\pm$ 0.12
|  |  |  4.48 |  96.10 $\pm$ 9.55 |  430.55 $\pm$ 42.77 |  407.73 |  1274.37 $\pm$ 4.62 |  293.91 $\pm$ 0.00
|  |  |  2.88 |  97.12 $\pm$ 9.65 |  279.71 $\pm$ 27.79 |  329.37 |  1211.68 $\pm$ 4.62 |  292.13 $\pm$ 0.00
|  |  |  3.52 |  44.98 $\pm$ 4.47 |  158.33 $\pm$ 15.73 |  155.80 |  1187.19 $\pm$ 4.62 |  249.33 $\pm$ 0.02
|  |  |  1.92 |  20.92 $\pm$ 2.08 |  40.17 $\pm$ 3.99 |  49.47 |  1116.64 $\pm$ 4.64 |  213.09 $\pm$ 0.22
|  |  |  4.48 |  32.35 $\pm$ 3.21 |  144.93 $\pm$ 14.40 |  127.18 |  1080.22 $\pm$ 4.62 |  252.39 $\pm$ 0.02
26 |  59904.2669536921 |  219.46 $\pm$ 1.15 |  10.24 |  17.17 $\pm$ 1.71 |  175.87 $\pm$ 17.48 |  108.96 |  1413.36 $\pm$ 4.62 |  287.34 $\pm$ 0.34
|  |  |  8.96 |  41.23 $\pm$ 4.10 |  369.43 $\pm$ 36.71 |  253.34 |  1337.74 $\pm$ 4.62 |  308.05 $\pm$ 0.08
|  |  |  6.40 |  9.60 $\pm$ 0.95 |  61.44 $\pm$ 6.11 |  47.50 |  1229.29 $\pm$ 4.63 |  279.59 $\pm$ 2.61
|  |  |  6.40 |  2.82 $\pm$ 0.28 |  18.05 $\pm$ 1.79 |  11.79 |  1160.55 $\pm$ 4.84 |  199.84 $\pm$ 38.37
27 |  59907.2594524074 |  219.77 $\pm$ 0.43 |  3.84 |  2.21 $\pm$ 0.21 |  8.48 $\pm$ 0.82 |  6.39 |  1067.12 $\pm$ 9.71 |  168.12 $\pm$ 1.44
28 |  59912.2962470023 |  219.83 $\pm$ 1.76 |  3.20 |  12.44 $\pm$ 1.26 |  39.82 $\pm$ 4.03 |  22.08 |  925.77 $\pm$ 4.64 |  69.26 $\pm$ 0.02
|  |  |  3.84 |  13.22 $\pm$ 1.34 |  50.77 $\pm$ 5.14 |  24.26 |  920.02 $\pm$ 4.63 |  61.70 $\pm$ 0.01
29 |  59914.2529407407 |  220.31 $\pm$ 2.56 |  6.40 |  30.83 $\pm$ 3.15 |  197.31 $\pm$ 20.15 |  93.40 |  936.72 $\pm$ 4.62 |  99.31 $\pm$ 0.06
|  |  |  5.76 |  3.53 $\pm$ 0.36 |  20.31 $\pm$ 2.07 |  7.49 |  940.03 $\pm$ 4.64 |  54.19 $\pm$ 7.29
30 |  59915.2896052546 |  219.60 $\pm$ 1.11 |  9.60 |  2.44 $\pm$ 0.25 |  23.47 $\pm$ 2.39 |  13.22 |  1013.09 $\pm$ 7.50 |  211.43 $\pm$ 4.31
|  |  |  7.04 |  15.45 $\pm$ 1.58 |  108.78 $\pm$ 11.09 |  61.20 |  951.36 $\pm$ 4.62 |  154.67 $\pm$ 0.15
|  |  |  4.48 |  5.26 $\pm$ 0.54 |  23.58 $\pm$ 2.40 |  16.52 |  954.24 $\pm$ 4.67 |  152.58 $\pm$ 2.56
|  |  |  8.32 |  2.92 $\pm$ 0.30 |  24.30 $\pm$ 2.48 |  8.34 |  956.78 $\pm$ 6.55 |  68.03 $\pm$ 1.25
31 |  59916.3118642361 |  220.11 $\pm$ 1.20 |  6.40 |  5.25 $\pm$ 0.52 |  33.59 $\pm$ 3.32 |  22.81 |  1162.06 $\pm$ 5.44 |  218.62 $\pm$ 0.20
32 |  59920.2334853009 |  219.83 $\pm$ 1.25 |  4.48 |  12.14 $\pm$ 0.79 |  54.38 $\pm$ 3.55 |  25.46 |  1080.98 $\pm$ 4.71 |  166.28 $\pm$ 0.11
33 |  59930.1239017014 |  219.55 $\pm$ 0.98 |  3.20 |  7.75 $\pm$ 0.79 |  24.81 $\pm$ 2.52 |  20.48 |  970.46 $\pm$ 4.74 |  152.34 $\pm$ 1.21
|  |  |  3.20 |  8.53 $\pm$ 0.87 |  27.31 $\pm$ 2.78 |  17.46 |  968.14 $\pm$ 4.67 |  91.45 $\pm$ 1.13
|  |  |  1.28 |  5.64 $\pm$ 0.57 |  7.21 $\pm$ 0.73 |  4.47 |  986.71 $\pm$ 4.89 |  34.28 $\pm$ 1.41
34 |  59931.2705442477 |  219.77 $\pm$ 1.43 |  5.12 |  4.27 $\pm$ 0.43 |  21.87 $\pm$ 2.22 |  15.82 |  999.10 $\pm$ 4.73 |  188.25 $\pm$ 1.60
|  |  |  2.56 |  3.74 $\pm$ 0.38 |  9.58 $\pm$ 0.97 |  5.15 |  966.17 $\pm$ 5.40 |  51.96 $\pm$ 2.06
|  |  |  2.56 |  21.32 $\pm$ 2.16 |  54.58 $\pm$ 5.53 |  35.14 |  936.37 $\pm$ 4.91 |  74.58 $\pm$ 0.11
35 |  59933.1711922801 |  219.86 $\pm$ 1.12 |  3.20 |  2.07 $\pm$ 0.22 |  6.62 $\pm$ 0.69 |  7.28 |  1041.30 $\pm$ 9.47 |  254.05 $\pm$ 6.32
|  |  |  5.12 |  24.94 $\pm$ 2.62 |  127.72 $\pm$ 13.40 |  90.72 |  979.10 $\pm$ 4.62 |  169.45 $\pm$ 0.03
|  |  |  3.20 |  58.65 $\pm$ 6.15 |  187.69 $\pm$ 19.69 |  162.29 |  968.05 $\pm$ 4.62 |  156.93 $\pm$ 0.01
|  |  |  3.20 |  84.50 $\pm$ 8.86 |  270.39 $\pm$ 28.37 |  234.56 |  963.53 $\pm$ 4.62 |  157.97 $\pm$ 0.01
|  |  |  3.20 |  33.11 $\pm$ 3.47 |  105.94 $\pm$ 11.11 |  79.37 |  948.45 $\pm$ 4.62 |  117.81 $\pm$ 0.03
|  |  |  4.48 |  26.32 $\pm$ 2.76 |  117.92 $\pm$ 12.37 |  68.89 |  940.82 $\pm$ 4.62 |  100.29 $\pm$ 0.05
|  |  |  8.00 |  25.42 $\pm$ 2.67 |  203.35 $\pm$ 21.33 |  85.77 |  935.08 $\pm$ 4.62 |  93.35 $\pm$ 0.01
  *[FRB]: Fast Radio Burst
  *[FRBs]: Fast Radio Burst
  *[CHIME]: the Canadian Hydrogen Intensity Mapping Experiment
  *[DSA-110]: Deep Synoptic Array
  *[DM]: Dispersion Measure
  *[ATA]: Allen Telescope Array
  *[DSP]: Digital Signal Processing
  *[RFSoC]: Radio Frequency System-on-Chip
  *[FPGA]: Field Programmable Gate Array
  *[BLADE]: Breakthrough Listen Accelerated DSP Engine
  *[LO]: Local Oscillator
  *[RFI]: Radio Frequency Interference
  *[SNR]: Signal-to-Noise Ratio
  *[SEFD]: System Equivalent Flux Density
  *[GBT]: Green Bank Telescope
  *[ACF]: Auto-Correlation Function
  *[ToAs]: times-of-arrival