# A burst storm from the repeating FRB 20200120E in an M81 globular cluster

K. Nimmo,1,2 J. W. T. Hessels,2,1 M. P. Snelders,1,2 R. Karuppusamy,3 D. M.
Hewitt,2 F. Kirsten,1,4B. Marcote,5 U. Bach,3 A. Bansod,3 E. D. Barr,3 J.
Behrend,3 V. Bezrukovs,6 S. Buttaccio,7 R. Feiler,8M. P. Gawroński,8 M.
Lindqvist,4 A. Orbidans,6 W. Puchalska,8 N. Wang,9 T. Winchen,3 P. Wolak,8J.
Wu,3 and J. Yuan9
1ASTRON, Netherlands Institute for Radio Astronomy, Oude Hoogeveensedijk 4,
7991 PD Dwingeloo, The Netherlands
2Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science
Park 904, 1098 XH, Amsterdam, The Netherlands
3Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn,
Germany
4Department of Space, Earth and Environment, Chalmers University of
Technology, Onsala Space Observatory, 439 92, Onsala, Sweden
5Joint Institute for VLBI ERIC, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The
Netherlands
6Engineering Research Institute Ventspils International Radio Astronomy Centre
(ERI VIRAC) of Ventspils University of Applied Sciences (VUAS),
Inzenieru street 101, Ventspils, LV-3601, Latvia
7Istituto Nazionale di Astrofisica, Istituto di Radioastronomia
Radiotelescopio di Noto, Noto, Italy
8Institute of Astronomy, Faculty of Physics, Astronomy and Informatics,
Nicolaus Copernicus University, Grudziadzka 5, 87-100, Toruń, Poland
9Xinjiang Astronomical Observatory, Chinese Academy of Sciences, 150 Science
1-Street, Urumqi, Xinjiang 830011, People’s Republic of China E-mail:
<EMAIL_ADDRESS>
(Accepted 2023 January 21. Received 2023 January 20; in original form 2022
June 8)

###### Abstract

The repeating fast radio burst (FRB) source FRB 20200120E is exceptional
because of its proximity and association with a globular cluster. Here we
report $60$ bursts detected with the Effelsberg telescope at 1.4 GHz. We
observe large variations in the burst rate, and report the first FRB 20200120E
‘burst storm’, where the source suddenly became active and 53 bursts (fluence
$\geq 0.04$ Jy ms) occurred within only 40 minutes. We find no strict
periodicity in the burst arrival times, nor any evidence for periodicity in
the source’s activity between observations. The burst storm shows a steep
energy distribution (power-law index $\alpha=2.39\pm 0.12$) and a bi-modal
wait-time distribution, with log-normal means of 0.94${}^{+0.07}_{-0.06}$ s
and 23.61${}^{+3.06}_{-2.71}$ s. We attribute these wait-time distribution
peaks to a characteristic event timescale and pseudo-Poisson burst rate,
respectively. The secondary wait-time peak at $\sim 1$ s is $\sim 50\times$
longer than the $\sim 24$ ms timescale seen for both FRB 20121102A and FRB
20201124A — potentially indicating a larger emission region, or slower burst
propagation. FRB 20200120E shows order-of-magnitude lower burst durations and
luminosities compared with FRB 20121102A and FRB 20201124A. Lastly, in
contrast to FRB 20121102A, which has observed dispersion measure (DM)
variations of $\Delta{\rm DM}>1$ pc cm-3 on month-to-year timescales, we
determine that FRB 20200120E’s DM has remained stable ($\Delta{\rm DM}<0.15$
pc cm-3) over $>10$ months. Overall, the observational characteristics of FRB
20200120E deviate quantitatively from other active repeaters, but it is
unclear whether it is qualitatively a different type of source.

###### keywords:

Fast Radio Bursts

††pubyear: 2022††pagerange: A burst storm from the repeating FRB 20200120E in
an M81 globular cluster–A burst storm from the repeating FRB 20200120E in an
M81 globular cluster

##  1 Introduction

Fast radio bursts (FRBs) are highly luminous, millisecond-duration radio
transients, originating at extragalactic distances (Lorimer et al., 2007;
Thornton et al., 2013). Despite 15 years of research in the field (for recent
reviews see, e.g., Petroff et al. 2019, 2022; Cordes & Chatterjee 2019), and
more than $600$ FRBs discovered to date (e.g., CHIME/FRB Collaboration et al.
2021), their nature is still debated. The diverse burst phenomenology (Pleunis
et al., 2021b), including a relatively small fraction ($\sim 4$%) of FRB
sources exhibiting repeating bursts (Spitler et al., 2016), potentially
indicates multiple FRB origins. Athough FRBs are highly luminous, their large
extragalactic distances (typically hundreds of megaparsecs to gigaparsecs)
mean that we are strongly sensitivity limited, and therefore only observe the
bright end of the distribution of potentially observable fast radio
transients.

FRBs in the local Universe (luminosity distance $d_{L}<$ a few hundred Mpc)
provide us with the unique opportunity to connect our knowledge of fast radio
transients in the Milky Way and its satellites — e.g., the Crab pulsar
(Hankins & Eilek, 2007), the ‘Crab twin’ in the Large Magellanic Cloud PSR
B0540$-$69 (Geyer et al., 2021) and the Galactic magnetar SGR 1935+2154
(CHIME/FRB Collaboration et al., 2020; Bochenek et al., 2020) — to the much
more distant FRB population. We can do this through detailed characterisation
of their local environments (e.g., Marcote et al. 2020; Tendulkar et al. 2021;
Kirsten et al. 2022), by applying strong constraints on multi-wavelength
counterparts to the radio emission (Scholz et al., 2020), and by conducting
higher-sensitivity searches for low-luminosity FRBs (Kirsten et al., 2022;
Nimmo et al., 2022a; Majid et al., 2021).

The closest known extragalactic FRB discovered to date, FRB 20200120E
(Bhardwaj et al., 2021), was discovered by the Canadian Hydrogen Intensity
Mapping Experiment FRB project (CHIME/FRB; CHIME/FRB Collaboration et al.
2018) and subsequently precisely localised using the European Very long
baseline interferometry (VLBI) Network (EVN) to a globular cluster in the M81
galactic system (Kirsten et al., 2022). Not only is the globular cluster
origin of FRB 20200120E in stark contrast to the star-forming environments of
other well-studied repeating FRBs (Chatterjee et al., 2017; Marcote et al.,
2017; Bassa et al., 2017; Marcote et al., 2020; Tendulkar et al., 2021; Nimmo
et al., 2022b; Fong et al., 2021; Ravi et al., 2022), but the luminosities of
the bursts are 1–2 orders of magnitude weaker than those observed from other
repeaters, and even less luminous than the bright FRB-like transient from SGR
1935$+$2154 (CHIME/FRB Collaboration et al., 2020; Bochenek et al., 2020).
Furthermore, the FRB 20200120E burst widths are atypically narrow (a factor of
$\sim 30$ shorter than typical FRB 20121102A bursts at a comparable frequency;
Nimmo et al. 2022a; Majid et al. 2021; Li et al. 2021).

Nimmo et al. (2022a) discuss the observational connections between FRB
20200120E, the Crab pulsar, the Galactic magnetar SGR 1935+2154, and the more
distant FRBs using the measured luminosities, range of burst timescales, burst
morphologies, and polarimetry. In doing so, they highlight the spectrum of
short-duration radio emission spanning many orders of magnitude in luminosity
and timescales, and emphasise that the exact division between transient types
(e.g., pulsar and FRB emission) is presently unclear.

To date, only $14$ bursts from FRB 20200120E have been reported in the
literature (Bhardwaj et al., 2021; Nimmo et al., 2022a; Majid et al.,
2021)111Additional CHIME/FRB bursts are reported on in the CHIME/FRB public
database.. A larger sample of bursts from FRB 20200120E provides the ability
to probe its time-variable activity, search for any underlying periodicity and
study the energy and wait-time distributions to compare with similar studies
of Galactic neutron stars, and other repeating FRBs.

Here we report the detection of $60$ new bursts from FRB 20200120E, detected
via monitoring with the 100-m Effelsberg telescope at 1.4 GHz from 2021 April
to 2022 April. During this monitoring, we report the first observed ‘burst
storm’ from FRB 20200120E where $53$ of the $60$ bursts occurred within a
$\sim 40$ minute time window. In Section 2 we describe the Effelsberg
monitoring observations, and the data products. In Section 3 we describe the
search for bursts, followed by a description of the burst analysis and results
in Section 4. In Section 5, we discuss our results in the context of previous
FRB observations, and compare with observations of Galactic neutron stars,
before presenting the conclusions of this work in Section 6.

##  2 Observations

Figure 1: Summary of the observations of FRB 20200120E presented in this work,
in addition to those reported in Kirsten et al. (2022) and Nimmo et al.
(2022a). The coloured lines show the observation epochs (where colour
signifies the observation type, as described in Section 2). The cross markers
show the average burst rate per observing epoch, unless there were no
detections. For a tabular version of this information, see Table 1.

Between December 11 2021 and April 24 2022, we monitored FRB 20200120E (using
the EVN-PRECISE222Pinpointing Repeating Chime Sources with the EVN position;
Kirsten et al. 2022) with the 100-m Effelsberg telescope using the recently
developed Effelsberg Direct Digitization (EDD) backend operating in baseband-
mode. This allowed us to simultaneously record total intensity pulsar backend
psrfits (Hotan et al., 2004) data with time and frequency resolution of 40.96
$\upmu$s and 0.1953 MHz, respectively (exceptions to this are noted in Table
1), alongside the raw voltages (‘baseband’ data, dual circular polarisation)
in Data Acquisition and Distributed Analysis (DADA) format (van Straten et
al., 2021) sampled at 1/$400$ MHz. We used the central pixel of the 7-beam
21-cm receiver, with an observing bandwidth from 1.2–1.6 GHz. In total, we
have observed for 28.4 hr using this observing setup, which is summarised in
Table 1. We recorded psrfits data of the test pulsar B0355+54. Due to an
incorrect observing set-up, the raw voltages of 2022 February 21 and 22 (MJDs
59631, 59632) were not recorded.

We add the EVN-PRECISE observations originally reported in Kirsten et al.
(2022) and Nimmo et al. (2022a) to Table 1, with an additional three PRECISE
observations using the VLBI backend that occurred on 2021 June 6, September 2
and September 5. Using the VLBI Digital Base Band Converter (DBBC2; Tuccari et
al. 2010) backend at Effelsberg, these observations recorded baseband data
with dual circular polarisation (2-bit sampling) in VDIF (Whitney et al.,
2010) format. Additionally, we recorded total intensity filterbank data with
the PSRIX pulsar backend (Lazarus et al., 2016) with a time and frequency
resolution of 102.4 $\upmu$s and 0.49 MHz, respectively. The observing
bandwidth is 1255–1505 MHz and the total observing time using this observing
setup is 63.6 hr (all but 12.1 hr originally reported in Kirsten et al. 2022
and Nimmo et al. 2022a). Note that these are VLBI observations, and therefore
had frequent scans of calibrator sources. In such cases, the time on source is
therefore approximately 65 % of the reported times.

Furthermore, we also report on observations obtained through Director’s
Discretionary Time at Effelsberg between 2021 April 9 and 2021 May 1. These
observations were using the PSRIX pulsar backend in baseband-mode: recording
total intensity filterbank data products with time and frequency resolution of
65.5 $\upmu$s and 0.24 MHz, respectively, simultaneously with the raw voltages
(dual circular). The observing bandwidth is 1233–1483 MHz, and total observing
time with this setup is 13.7 hr.

All of the observations are summarised in Table 1 and Figure 1.

Table 1:  FRB 20200120E Effelsberg monitoring observation details. Start MJDa | Duration [hr] | Observation type | Number of bursts | Average burst rate [/hr]
---|---|---|---|---
59265.708b | 4.99 | PRECISE, VLBI backend | 2 | $0.4^{+2.0}_{-0.4}$
59280.656b | 4.99 | PRECISE, VLBI backend | 2 | $0.4^{+2.0}_{-0.4}$
59283.792b | 4.99 | PRECISE, VLBI backend | 0 | $0.0^{+1.8}_{-0.0}$
59289.750b | 4.99 | PRECISE, VLBI backend | 0 | $0.0^{+1.8}_{-0.0}$
59295.667b | 4.99 | PRECISE, VLBI backend | 0 | $0.0^{+1.8}_{-0.0}$
59313.437 | 0.07 | PSRIX baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59313.458 | 1.00 | PSRIX baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59314.508 | 2.21 | PSRIX baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59314.887b | 2.04 | PRECISE, VLBI backend | 0 | $0.0^{+1.8}_{-0.0}$
59315.191 | 0.89 | PSRIX baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59316.235 | 1.17 | PSRIX baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59320.828 | 2.22 | PSRIX baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59322.514 | 2.00 | PSRIX baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59332.458b | 4.99 | PRECISE, VLBI backend | 1 | $0.2^{+1.9}_{-0.2}$
59334.807 | 2.08 | PSRIX baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59335.634 | 2.01 | PSRIX baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59336.708b | 7.01 | PRECISE, VLBI backend | 0 | $0.0^{+1.8}_{-0.0}$
59344.771b | 2.50 | PRECISE, VLBI backend | 0 | $0.0^{+1.8}_{-0.0}$
59347.625b | 4.99 | PRECISE, VLBI backend | 0 | $0.0^{+1.8}_{-0.0}$
59360.708b | 4.99 | PRECISE, VLBI backend | 0 | $0.0^{+1.8}_{-0.0}$
59371.234 | 2.48 | PRECISE, VLBI backend | 0 | $0.0^{+1.8}_{-0.0}$
59459.027 | 4.50 | PRECISE, VLBI backend | 0 | $0.0^{+1.8}_{-0.0}$
59462.168 | 5.11 | PRECISE, VLBI backend | 0 | $0.0^{+1.8}_{-0.0}$
59559.584c | 2.00 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59564.902 | 2.00 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59571.573 | 2.00 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59575.735 | 1.38 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59578.622 | 2.00 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59582.677 | 0.20 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59582.785 | 0.50 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59593.650 | 2.00 | EDD baseband-mode | 53 | $26.5^{+6.2}_{-5.1}$
59596.262 | 0.85 | EDD baseband-mode | 1 | $1.2^{+2.4}_{-0.9}$
59598.871 | 2.50 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59602.235 | 0.03 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59631.818d | 2.50 | EDD baseband-mode | 2 | $0.8^{+2.2}_{-0.7}$
59632.673d | 2.15 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59633.599 | 1.99 | EDD baseband-mode | 2 | $1.0^{+2.3}_{-0.8}$
59655.950 | 2.50 | EDD baseband-mode | 2 | $0.8^{+2.2}_{-0.7}$
59668.052 | 0.78 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59678.079 | 1.36 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59680.974 | 1.65 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
59693.655 | 0.85 | EDD baseband-mode | 0 | $0.0^{+1.8}_{-0.0}$
a Topocentric. |
b Originally reported in Kirsten et al. (2022) and Nimmo et al. (2022a). |
c Frequency resolution of these data is 0.4 MHz. |
d No raw voltages due to incorrect observing set-up. |

##  3 Burst search and discovery

###  3.1 EDD baseband-mode

The total intensity EDD psrfits data were first converted to filterbank format
using digifil (van Straten & Bailes, 2011), at the native resolution of the
data, to be compatible with
Heimdall333https://sourceforge.net/projects/heimdall-astro/. Frequency
channels in our observing band that frequently contain radio frequency
interference (RFI) were masked before searching for single pulses with
Heimdall, using a S/N threshold of 7. Candidates found in the Heimdall search
were then classified using FETCH (models A and H, probability threshold 0.5;
Agarwal et al. 2020). We inspected the FETCH candidate plots by eye, and also
the plots of any Heimdall candidate within $\pm 3$ pc cm-3 of the known FRB
dispersion measure (DM) and above a S/N threshold of 10.

In this search, we found 37 bursts on 2022 January 14 (MJD 59593), 1 burst on
2022 January 17 (MJD 59596), and 2 bursts on each of 2022 February 21, 23 and
March 17 (MJDs 59631, 59633, and 59655, respectively). On closer inspection of
the Heimdall candidates on 2022 January 14 (pre-FETCH), with DMs $\pm 1$ pc
cm-3 around the best-known value of 87.7527 pc cm-3 (Nimmo et al., 2022a), an
additional 7 bursts were discovered. These bursts were all reported with
relatively low Heimdall S/N values of $<10$. Therefore the low S/N, combined
with the narrow temporal burst widths, are likely the cause of the
misclassification by FETCH. A similar exercise was repeated on the other
observations, and no additional bursts were discovered. Note that post 2022
January 14, we altered the analysis pipeline to keep candidate plots for
inspection for any Heimdall candidate within $\pm 3$ pc cm-3 of the known FRB
DM and above a S/N threshold of 7.

Due to the high density of bursts discovered on 2022 January 14, we saved the
raw voltages for the entire 2 hr observation for further inspection. This was
not possible for all observations due to the high data volume of the raw
voltages (1 hr is approximately 5.5 TB of raw voltage data). Therefore, for
the bursts discovered at other epochs, we saved only the 2.048 s baseband
recording containing the burst (and sometimes also the neighbouring recording
if the dispersion sweep crossed between recordings).

Table 2: The success of burst searches on 2022 January 14 EDD data. ✓ indicates that a burst was classified as astrophysical by FETCH (models A and H, probability threshold 0.5). The S/N values quoted for both Heimdall and PRESTO searches are boxcar S/N ratios.  |  $40.96$ $\upmu$s pulsar |  $40.96$ $\upmu$s baseband |  $1.28$ $\upmu$s baseband
---|---|---|---
Burst |  Heimdall S/N | FETCH |  Heimdall S/N |  PRESTO S/N |  PRESTO S/N
B1 | 13.6 | ✓ | 12.4 | 13.4 | 9.3
4-6 B2 | 36.6 | ✓ | Lost baseband data
4-6 B3 | 12.8 | ✓ | 10.8 | 10.8 | –
B4 | 7.9 | – | 7.5 | 8.6 | –
B5 | 21.6 | ✓ | 17.8 | 21.6 | 9.6
B6 | – | – | 7.3 | – | –
B7 | 8.7 | ✓ | 8.7 | 9.6 | –
B8 | 9.3 | ✓ | 8.4 | 10.3 | –
B9 | 8.4 | ✓ | 7.6 | 8.7 | –
B10 | 20.2 | ✓ | 19.0 | 20.6 | 12.9
B11 | 7.8 | ✓ | – | 8.7 | –
B12 | 16.7 | ✓ | 16.5 | 17.9 | 14.7
B13 | 20.8 | ✓ | 16.7 | 18.6 | 14.5
B14 | – | – | 9.7 | 10.9 | 8.7
B15 | – | – | – | – | 7.7
B16 | 7.2 | – | 7.7 | 8.0 | 7.0
B17 | 24.7 | ✓ | 22.3 | 25.0 | 17.2
B18 | – | – | 11.9 | 13.1 | 10.6
B19 | – | – | 7.0 | 7.8 | 9.6
B20 | 19.8 | ✓ | 18.8 | 21.7 | 16.3
B21 | 17.2 | ✓ | 14.2 | 17.2 | 15.4
B22 | 7.6 | ✓ | – | 7.2 | –
B23 | 11.0 | ✓ | 9.0 | 10.5 | 9.8
B24 | 10.2 | ✓ | 9.1 | 10.3 | 7.4
B25 | 7.6 | ✓ | – | – | –
B26 | 17.0 | ✓ | 15.1 | 16.2 | 14.6
B27 | 7.1 | ✓ | – | 7.4 | –
B28 | 8.9 | – | – | – | 7.1
B29 | 8.1 | ✓ | 7.7 | 8.5 | –
B30 | – | – | – | 8.0 | –
B31 | 22.5 | ✓ | 21.1 | 24.3 | 18.3
B32 | – | – | – | 7.8 | 9.0
B33 | 25.2 | ✓ | 19.4 | 26.4 | 15.3
B34 | 16.2 | ✓ | 14.4 | 17.3 | 17.3
B35 | 21.8 | ✓ | 19.8 | 22.2 | 15.2
B36 | 8.9 | – | 7.4 | 7.9 | 7.2
B37 | 20.7 | ✓ | 19.8 | 23.0 | 25.4
B38 | 9.5 | ✓ | 7.1 | 11.0 | 9.5
B39 | 7.7 | ✓ | – | – | –
B40 | 12.9 | ✓ | 10.4 | 11.4 | 10.0
B41 | 9.2 | – | 7.4 | 9.0 | 8.0
B42 | 8.6 | – | 7.0 | 8.0 | 9.2
B43 | 21.6 | ✓ | 19.5 | 23.3 | 15.0
B44 | 15.1 | ✓ | 12.4 | 14.2 | 12.8
B45 | 7.1 | ✓ | – | – | –
B46 | – | – | – | 7.2 | 7.1
B47 | 20.6 | ✓ | 16.8 | 21.0 | 18.7
B48 | 10.8 | ✓ | 9.0 | 11.5 | 9.4
B49 | 14.5 | ✓ | 12.1 | 17.1 | 16.9
B50 | 14.0 | ✓ | 14.5 | 17.6 | 18.1
B51 | 8.2 | ✓ | – | 9.0 | 8.7
B52 | 7.7 | – | – | 9.2 | –
B53 | – | – | – | 9.7 | –

####  3.1.1 January 14 baseband data re-search

Using digifil, we created 8-bit total intensity filterbank data from the
baseband DADA data at a resolution of 40.96 $\upmu$s and 0.1953 MHz in time
and frequency, respectively. This resolution matches that of the pulsar data.
The goal of searching these data products was to ensure that we understood the
filterbank data created and could recover the same bursts discovered in the
search of the pulsar data. These data products were searched for single pulses
using both Heimdall and PRESTO (Ransom, 2001). For the Heimdall-based search,
we mask frequency channels that frequently exhibit RFI before searching for
single pulses, and inspect the candidates with a DM within $\pm 1$ pc cm-3 of
the known DM of FRB 20200120E. For PRESTO-based searches, we use the PRESTO
tool rfifind to mask time and frequency blocks that contain RFI before
searching for single pulses using single_pulse_search.py. The PRESTO single-
pulse candidates were then grouped into events using a modified version of SpS
(Michilli et al., 2018a), and events with a DM within $\pm 1$ pc cm-3 of the
known DM were inpected by eye.

The Heimdall search of the baseband data returned $34$ of the $44$ bursts
found in the pulsar data: $9$ of those missing all have S/N $<9$, and $1$ (B2)
falls within a $\sim 4$ minute gap in the baseband data where we have missing
data. The loss of some low-S/N bursts in the baseband search is likely because
of different scalings applied in the creation of the filterbank data. We did,
however, find $4$ previously undiscovered bursts in the Heimdall search of the
baseband data. These bursts also have relatively low S/N, and likely were
missed in the search of the pulsar data for the same reasons as above. The
different scalings applied to create the pulsar data and baseband data
products, combined with time-dependent RFI, is likely also the reason for the
differing S/N values for the Heimdall searches of these data (Table 2).

The PRESTO search of the baseband data returned $39$ of the original $44$
bursts, where, again, B2 falls within the data loss region. The other missing
$4$ bursts are a subset of the missing bursts in the Heimdall search. Of the 4
new Heimdall-discovered bursts, PRESTO found $3$. Furthermore, PRESTO
discovered an additional $4$ low-S/N bursts, bringing the number of bursts
discovered in the 2022 January 14 observation to $52$. In general, the PRESTO
S/N values appear higher than Heimdall, which is likely how PRESTO found
additional bursts that Heimdall missed above our detection threshold of $7$.
Additionally, the RFI flagging method and boxcar width trialling is different
between the Heimdall and PRESTO searches, which could impact the discovery of
bursts, especially in the low-S/N regime. Note there is a timestamp
mislabelling in the pulsar backend data, creating a fictitious 125 ms delay
between the baseband recording and pulsar backend recording. This was
identified, measured and calibrated for using bursts detected in both the
pulsar and baseband data.

(a)

(b)

Figure 2: Burst profiles, dynamic spectra and time-averaged spectra for a
subset of the FRB 20200120E bursts presented in this work. The filterbank data
plotted is created by channelising the raw voltages to a resolution of 5.12
$\upmu$s and 0.1953 MHz in time and frequency, respectively, for sub-figure
(a), and 1.28 $\upmu$s and 0.7813 MHz for sub-figure (b). Sub-figure (b) shows
the burst discovered in the microsecond search of the data (see Section
3.1.2); this is the narrowest burst in this sample. The frequency resolution
has been downsampled by a factor of 32 (sub-figure (a)) and 8 (sub-figure (b))
for visualisation purposes. The data are coherently (within frequency
channels) and incoherently (between channels) corrected for dispersion using a
DM of 87.7527 pc cm-3 (Nimmo et al., 2022a). The coloured bars highlight the
1-$\sigma$ (dark) and 2-$\sigma$ (light) error regions on the burst extent in
both frequency and time, where the different colours represent different
observing epochs: 2022 January 14 (purple), 2022 January 17 (blue) and 2022
February 23 (green). Time $=0$ represents the burst centroid in time, and the
horizontal coloured line in the burst spectrum represents the frequency
centroid. Frequency channels that have been masked due to RFI have been
omitted from the dynamic spectra (white horizontal lines). The burst profile
is created by averaging the dynamic spectrum within the 2-$\sigma$ burst
extent in frequency, and similarly the burst spectrum is created by averaging
the dynamic spectrum within the 2-$\sigma$ burst extent in time.

####  3.1.2 January 14 1.28 $\upmu$s search

Motivated by the clear microsecond timescales seen in a burst from FRB
20200120E (Nimmo et al., 2022a), we re-searched the 2022 January 14
observation at 1.28 $\upmu$s time resolution. We used digifil to create
coherently dedispersed (using a DM of $87.7527$ pc cm-3; Nimmo et al. 2022a)
8-bit total intensity filterbank data with time and frequency resolution 1.28
$\upmu$s and 0.78 MHz, respectively. The true DM value must be within $\sim
0.3$ pc cm-3 of the DM used for coherent dedispersion to ensure that the
dispersion smearing within a channel is smaller than the time resolution.
Fortunately, $0.3$ pc cm-3 is much greater than the uncertainty on the known
DM (Nimmo et al., 2022a), and we confirm in Section 4 that the DM has not
significantly changed from the previous measurement.

The Heimdall search of the 1.28 $\upmu$s data returned none of the $52$
bursts, and no additional bursts. For the PRESTO-based search, we incoherently
dedispersed using trial DMs from 87.6 to 87.9 pc cm-3 in steps of 0.01 pc
cm-3. This results in maximal DM step-size smearing of $\sim 6$ $\upmu$s
across the entire 400 MHz band, or $\sim 3$ $\upmu$s for the centre 200 MHz,
where the bursts in our sample reside. We, therefore, downsample to 2.56
$\upmu$s for the search. The PRESTO search returned $35$ of the $52$, and
discovered an additional burst, bringing the total burst count to 53 on 2022
January 14. The additional burst found in our high-time-resolution search is
the narrowest burst in our sample, with a temporal scale of $\sim 14$
$\upmu$s, which combined with its low S/N is the reason it was not caught in
either of the 40.96 $\upmu$s searches. The behaviour of Heimdall is not well-
studied at extremely high time resolutions (e.g. $\upmu$s) and the fact that
we recover a significant fraction of the bursts using PRESTO, implies that
Heimdall has significantly lost sensitivity at this resolution.

Table 2 summarises the results of the searches on the 2022 January 14
observation. The burst profiles, dynamic spectra and time-averaged spectra for
selected FRB 20200120E bursts can be found in Figure 2, highlighting the
diverse burst morphology observed including the exceptionally narrow $\sim 14$
$\upmu$s burst. In Figure A1(a) and (b) we show the complete time-ordered
burst plot for the entire $60$ burst sample presented in this work.

###  3.2 PRECISE observations

The VDIF data from the VLBI backend were searched using a Heimdall and FETCH
pipeline, while the PSRIX pulsar data were searched with a PRESTO pipeline.
Details of this analysis can be found in Kirsten et al. (2021, 2022). No
additional bursts were found in these data beyond the $5$ reported in Kirsten
et al. (2022) and Nimmo et al. (2022a), down to a fluence limit of 0.05 Jy ms
(for a 7 $\sigma$, 100 $\upmu$s duration burst).

###  3.3 PSRIX baseband-mode

The PSRIX filterbank data were searched for single pulses using tools in the
PRESTO software suite, matching the analysis of the PRECISE PSRIX data in
Section 3.2. No bursts were found down to a fluence limit of 0.05 Jy ms (for a
7 $\sigma$, 100 $\upmu$s duration burst).

##  4 Burst analysis

###  4.1 Dispersion measure

Figure 3: Peak S/N of 1.28 $\upmu$s burst profile (left) and peak S/N of the
smoothed burst envelope (right) as a function of DM. The bursts were selected
based on their S/N values and fine structure observed in the 5.12 $\upmu$s
profiles. Gaussian fits are overplotted for each burst, matching the colour of
the burst markers, and the mean of each Gaussian fit are shown by the coloured
vertical lines. For comparison, a similar analysis of burst B3 from Nimmo et
al. (2022a) is overplotted in black (left panel). The best DM measurement from
Nimmo et al. (2022a), is shown by the black dashed line in both panels
(DM$=87.7527$ pc cm-3).

Radio waves interact with free electrons on their journey to Earth, causing
the lower frequencies to be delayed with respect to the higher frequencies
(this relationship is quadratic in frequency; see Lorimer & Kramer (2004)).
Due to the complex morphology of FRB signals in time and frequency,
constraining the quadratic sweep of dispersion can be challenging (Hessels et
al., 2019). Conversely, without accurately correcting for dispersion,
structure in the burst profiles could be unresolved. Using the sharp,
relatively broadband, temporal features in one burst from FRB 20200120E (on
timescales of microseconds), Nimmo et al. (2022a) constrained the DM to
$87.7527\pm 0.0003$ pc cm-3, which was sufficient to resolve sub-microsecond
timescales. This measurement is $>9\sigma$ lower than the previous measurement
from Bhardwaj et al. (2021), which could be due to temporal evolution,
spectral evolution, or unresolved burst structure in the Bhardwaj et al.
(2021) results. While it is possible that this DM difference reflects changes
in the local environment of FRB 20200120E, it is also possible that it is the
result of a turbulent interstellar medium (ISM) in the Milky Way, as observed
for pulsars (e.g. Hobbs et al. 2004), or in M81. We note that the DM
measurements have not accounted for Doppler shifting from Earth’s orbital
motion and rotation, although this should likely only contribute a $\sim
0.009$ pc cm-3 difference in DM measurements between our observations and the
previous DM measurement.

We selected bursts in our sample that have both a high S/N, and sharp
structure in the 5.12 $\upmu$s profile (Figure A1): namely B18, B19, B21, B34,
B37, B47, B49 and B50 from 2022 January 14, as well as the narrowest burst in
our sample (B15 from 2022 January 14, despite it having a relatively low S/N).
Using digifil, we created 32-bit, coherently dedispersed (DM$=$87.7527 pc
cm-3) total intensity filterbank data containing the selected bursts, with
1.28 $\upmu$s time resolution and 0.7813 MHz frequency resolution. To measure
the DM, we incoherently shifted the frequency channels using DMs in the range
87.65–87.85 pc cm-3 in steps of 0.01 pc cm-3. In Figure 3 we plot the peak S/N
of the 1.28 $\upmu$s profile as a function of DM. In contrast to the results
of Nimmo et al. (2022a), there is no clear micro-structure observed in these
bursts, meaning the S/N does not rise and fall with DM as sharply. Note that
the peak S/N versus DM mean of burst B36 is $<87.65$ pc cm-3 (the lower limit
of the x-axis scale in Figure 3), and we confirm the burst is visibly
undercorrected at that ‘best-fit’ DM. We also plot the peak of the burst
envelope as a function of DM, created by smoothing the 1.28 $\upmu$s profile
using a low-pass filter. The envelopes more clearly rise and fall with DM. In
the absence of burst structure on microsecond (or shorter) timescales, we used
the burst envelopes to measure a S/N weighted average DM of $87.77\pm 0.05$ pc
cm-3, which is in agreement with the results of Nimmo et al. (2022a). We
therefore conclude that the DM of FRB 20200120E has not changed by more than
0.15 pc cm-3 ($3$-$\sigma$) over the $\sim$ 1 year period of observation, and
proceed using a DM of 87.7527 pc cm-3 (Nimmo et al., 2022a) for the analysis
of the burst sample presented in this work. As mentioned in Section 3.1.2,
this uncertainty in the DM results in a maximum smearing within frequency
channels less than the time resolution for both 512 channel (1.28 $\upmu$s)
and 2048 channel (5.12 $\upmu$s) data products created in this work.

###  4.2 Burst characterisation

For each burst, we coherently dedispersed and channelised the DADA baseband
data to 2048 channels (0.1953 MHz and 5.12 $\upmu$s frequency and time
resolution, respectively) using digifil. This 32-bit Stokes I data is used to
determine the burst properties for all bursts, with the exception of burst B2
on 2022 January 14, and both B1 and B2 on 2022 February 21, where only the
40.96 $\upmu$s/0.1953 MHz pulsar data were retained. Frequency channels
contaminated by RFI were masked manually for each burst. The data were
downsampled before measuring their properties: a summary of the resolutions
used for the analysis can be found in Table LABEL:tab:burst_properties. The
frequency channels are shifted to correct for dispersion, and normalised such
that the mean and standard deviation of the noise in each channel is 0 and 1,
respectively.

To measure the burst extent in time and frequency we computed the
2-dimensional autocorrelation function (ACF) of the dynamic spectra. We fitted
a 2-dimensional Gaussian to the ACF, from which we derived the burst width and
frequency extent reported in Table LABEL:tab:burst_properties. In a few cases
(marked in Table LABEL:tab:burst_properties), the low S/N and strong
scintillation structure resulted in visibly under-estimated burst extents from
the ACF analysis. For these bursts, we do not report burst widths and
frequency extents, and instead assume the average values from the other bursts
at that observing epoch, to use for fluence calculations. For all bursts, we
fitted a 2-dimensional Gaussian to the dynamic spectrum to determine the
centroid of the burst in time and frequency. The coloured bars in Figures 2
and A1 highlight the 1-$\sigma$ (dark) and 2-$\sigma$ (light) burst extents,
Time $=0$ represents the burst centroid in time, which we define as the time
of arrival (ToA) of the burst, and the horizontal coloured line on the burst
spectrum represents the frequency centroid. Note for B13 and B51 on 2022
January 14, we observe $2$ clear burst components. The ToA and frequency
centroid are, therefore, the centre of the means of a Gaussian fit to each
component. In Figure 4 we show histograms of the central frequencies, temporal
widths and frequency extents of the bursts, with mean values of 1.38 GHz, 129
$\upmu$s and $111$ MHz, respectively.

Figure 4: Histograms of the burst central frequencies (left panel), temporal
widths (middle panel) and frequency extents (right panel). The colours
represent the different observing epochs and match the colours used throughout
this work (see, e.g., Figure A1). In the middle panel, the hatched bins
represent the two bursts where we have clearly identified multiple distinct
components (B13 and B51 on 2022 January 14). The longer temporal widths are
therefore a reflection of the sub-burst separation, while the individual burst
components are in fact more narrow. The black dashed line represents the mean
value.

The central frequencies are potentially influenced by scintillation from the
Milky Way’s ISM since FRB 20200120E bursts exhibit strong scintillation
spectral structure (visible in their dynamic spectra; see Figure 2). The
strong scintles can skew the 2-dimensional Gaussian fit, used to determine the
burst centroid. In addition, the central frequencies of the $2$ bursts
detected on each of February 21, 23 and March 17, fall to the same side of the
mean value in the distribution during a single epoch. The influence of
scintillation on the central frequency must be minimal, however, since the
bursts on January 17, February 21, 23 and March 17 agree well with the January
14 distribution (Figure 4). The expected frequency scale arising due to ISM
scintillation is $\sim 3$ MHz (Cordes & Lazio, 2002), consistent with the
single-bin spectral structure observed in the 6.25 MHz-resolution spectra
(Figure 5), that persists through individual observations. Since the measured
burst spectral extents are $\sim 100$ MHz, a factor of $\sim 30$ higher than
the scintillation scale, the burst frequency extents are likely not heavily
influenced by scintillation from the Milky Way interstellar medium.

Figure 5: Burst spectra at 6.25 MHz resolution. As shown in the legend, the
colours represent bursts detected on different days. Strong single-bin
spectral features due to scintillation are apparent and persistent through
individual observing epochs. The average burst spectra (weighted by burst S/N)
for 2022 January 14 bursts (black) and for bursts detected on the other days
(grey) are shown in the top panel. In addition to the narrow-band spectral
structure due to scintillation, there is also spectral structure on the scale
of $\sim 100$ MHz, consistent with the measured burst frequency extents
(Figure 4). On 2022 January 14, two $\sim 100$ MHz bumps are visible in the
stacked spectrum at $\sim 1300$ and $\sim 1450$ MHz, reminiscent of the
spectral structure seen in the single burst presented in Majid et al. (2021).
Note the flattening of the burst spectra at $\sim 1550$ MHz arises from
frequent flagging of data in that spectral range due to persistent RFI.

The burst ToAs (Table LABEL:tab:burst_properties) are corrected to the Solar
System Barycentre at infinite frequency (using a dispersion constant of
1/($2.41\times 10^{-4}$) MHz2 pc-1 cm3 s, and the VLBI position of FRB
20200120E; Kirsten et al. 2022). The burst profiles are converted to S/N units
by subtracting the mean of local noise data (containing no signal), and then
dividing by the standard deviation of the noise. The burst profiles are then
converted to physical units (Jy) using the radiometer equation (Cordes &
McLaughlin, 2003), and typical values for Effelsberg’s system temperature (20
K) and gain (1.54 Jy K-1). These values are uncertain at the 20% level, which
dominates the errors on the flux density. We also add a 3 K contribution from
the cosmic microwave background (Mather et al., 1994), and a sky background
temperature of 0.8 K, which is derived by extrapolating from the 408 MHz sky
map (Remazeilles et al., 2015), using a spectral index of $-2.7$ (Reich &
Reich, 1988). The fluence is then calculated by summing over the $\pm 2\sigma$
burst extent in time and frequency. Using the known distance to FRB 20200120E
(3.63 Mpc; Kirsten et al. 2022), we computed the isotropic-equivalent spectral
luminosity of each burst and report these values alongside the burst fluences
in Table LABEL:tab:burst_properties.

There are no clear trends of the burst properties with time through the 2022
January 14 observation (Figure A2). Perhaps the burst widths and fluences are
slightly decreasing through the observation,

Table 3: Burst properties. Burst | Time of Arrivala | Fluenceb | S/Nc | Spectral Luminosity | Widthd | Frequency Extentd | Time/Frequency
---|---|---|---|---|---|---|---
|  |  |  |  |  |  | Resolution
| [MJD] | [Jy ms] |  | [1028 erg s-1 Hz-1] | [$\upmu$s] | [MHz] | [$\upmu$s / MHz]
2022 January 14 |  |  |  |
B1 | 59593.70900072 | 0.13 $\pm$ 0.03 | 11.7 | 0.50 $\pm$ 0.10 | 171 $\pm$ 2 | 188.1 $\pm$ 1.6 | 5.12 / 12.5
B2 | 59593.71119049 | 0.54 $\pm$ 0.11 | 33.1 | 1.04 $\pm$ 0.21 | 346 $\pm$ 2 | 176.0 $\pm$ 0.8 | 40.96 / 6.2
B3 | 59593.72152561 | 0.14 $\pm$ 0.03 | 12.6 | 0.64 $\pm$ 0.13 | 152 $\pm$ 2 | 166.8 $\pm$ 2.1 | 5.12 / 12.5
B4 | 59593.72163241 | 0.08 $\pm$ 0.02 | 10.8 | 0.81 $\pm$ 0.16 | 133 $\pm$ 4 | 138.9 $\pm$ 1.9 | 40.96 / 6.2
B5 | 59593.72285434 | 0.36 $\pm$ 0.07 | 23.2 | 0.80 $\pm$ 0.16 | 302 $\pm$ 1 | 166.5 $\pm$ 0.5 | 5.12 / 6.2
B6 | 59593.72347595 | 0.09 $\pm$ 0.02 | 6.4 | 0.28 $\pm$ 0.06 | 207 $\pm$ 7 | 168.2 $\pm$ 5.0 | 20.48 / 12.5
B7 | 59593.72366265 | 0.11 $\pm$ 0.02 | 9.2 | 0.36 $\pm$ 0.07 | 240 $\pm$ 8 | 245.5 $\pm$ 7.4 | 40.96 / 12.5
B8 | 59593.72377264 | 0.10 $\pm$ 0.02 | 9.7 | 0.44 $\pm$ 0.09 | 161 $\pm$ 4 | 213.1 $\pm$ 4.5 | 10.24 / 12.5
B9 | 59593.72393352 | 0.15 $\pm$ 0.03 | 7.8 | 0.22 $\pm$ 0.04 | 445 $\pm$ 7 | 169.6 $\pm$ 2.3 | 20.48 / 12.5
B10 | 59593.72402411 | 0.26 $\pm$ 0.05 | 19.7 | 0.71 $\pm$ 0.14 | 245 $\pm$ 1 | 192.5 $\pm$ 0.7 | 5.12 / 6.2
B11 | 59593.72406203 | 0.10 $\pm$ 0.02 | 6.2 | 0.18 $\pm$ 0.04 | 384 $\pm$ 10 | 241.7 $\pm$ 5.9 | 20.48 / 12.5
B12 | 59593.72564746 | 0.22 $\pm$ 0.04 | 14.7 | 0.46 $\pm$ 0.09 | 322 $\pm$ 2 | 192.7 $\pm$ 0.8 | 5.12 / 6.2
B13 | 59593.72597616 | 0.32 $\pm$ 0.06 | 17.8 | 0.49 $\pm$ 0.10 | 431 $\pm$ 3 | 195.0 $\pm$ 1.1 | 5.12 / 6.2
B14 | 59593.72658502 | 0.17 $\pm$ 0.03 | 10.5 | 0.35 $\pm$ 0.07 | 328 $\pm$ 5 | 195.9 $\pm$ 2.5 | 10.24 / 12.5
B15 | 59593.72694393 | 0.05 $\pm$ 0.01 | 12.2 | 2.29 $\pm$ 0.46 | 14 $\pm$ 1 | 99.8 $\pm$ 6.7 | 1.28 / 6.2
B16 | 59593.72696785 | 0.08 $\pm$ 0.02 | 7.0 | 0.28 $\pm$ 0.06 | 192 $\pm$ 6 | 212.9 $\pm$ 6.5 | 10.24 / 6.2
B17 | 59593.72767015 | 0.32 $\pm$ 0.06 | 26.2 | 1.03 $\pm$ 0.21 | 211 $\pm$ 1 | 177.0 $\pm$ 0.5 | 5.12 / 6.2
B18 | 59593.72777136 | 0.16 $\pm$ 0.03 | 12.6 | 0.50 $\pm$ 0.10 | 217 $\pm$ 2 | 185.8 $\pm$ 1.5 | 5.12 / 6.2
B19 | 59593.72778012 | 0.06 $\pm$ 0.01 | 8.9 | 0.71 $\pm$ 0.14 | 55 $\pm$ 2 | 171.5 $\pm$ 5.6 | 5.12 / 6.2
B20 | 59593.72835081 | 0.21 $\pm$ 0.04 | 20.9 | 0.99 $\pm$ 0.20 | 140 $\pm$ 1 | 187.9 $\pm$ 0.8 | 5.12 / 6.2
B21 | 59593.72836174 | 0.18 $\pm$ 0.04 | 19.9 | 1.01 $\pm$ 0.20 | 124 $\pm$ 1 | 180.3 $\pm$ 1.0 | 5.12 / 6.2
B22 | 59593.72876785 | 0.06 $\pm$ 0.01 | 8.5 | 0.59 $\pm$ 0.12 | 99 $\pm$ 4 | 167.1 $\pm$ 5.6 | 20.48 / 6.2
B23 | 59593.72956599 | 0.08 $\pm$ 0.02 | 10.7 | 0.68 $\pm$ 0.14 | 84 $\pm$ 2 | 205.6 $\pm$ 3.8 | 5.12 / 6.2
B24 | 59593.72966465 | 0.11 $\pm$ 0.02 | 8.3 | 0.30 $\pm$ 0.06 | 251 $\pm$ 4 | 218.5 $\pm$ 3.0 | 10.24 / 6.2
B25 | 59593.72978254 | 0.11 $\pm$ 0.02 | 7.2 | 0.22 $\pm$ 0.04 | 366 $\pm$ 12 | 270.3 $\pm$ 9.0 | 20.48 / 12.5
B26 | 59593.73021930 | 0.17 $\pm$ 0.03 | 16.8 | 0.87 $\pm$ 0.17 | 133 $\pm$ 1 | 177.7 $\pm$ 1.0 | 5.12 / 6.2
B27 | 59593.73065954 | 0.09 $\pm$ 0.02 | 7.4 | 0.29 $\pm$ 0.06 | 215 $\pm$ 9 | 224.1 $\pm$ 8.7 | 20.48 / 12.5
B28 | 59593.73098736 | 0.08 $\pm$ 0.02 | 9.5 | 0.65 $\pm$ 0.13 | 89 $\pm$ 3 | 171.5 $\pm$ 3.0 | 5.12 / 6.2
B29 | 59593.73118289 | 0.12 $\pm$ 0.02 | 9.7 | 0.74 $\pm$ 0.15 | 111 $\pm$ 3 | 96.2 $\pm$ 2.5 | 20.48 / 6.2
B30e | 59593.73118737 | 0.12 $\pm$ 0.02 | 9.4 | 0.39 $\pm$ 0.08 | – | – | 40.96 / 25.0
B31 | 59593.73127253 | 0.27 $\pm$ 0.05 | 27.4 | 1.49 $\pm$ 0.30 | 126 $\pm$ 1 | 146.5 $\pm$ 0.5 | 5.12 / 6.2
B32 | 59593.73139847 | 0.07 $\pm$ 0.01 | 9.8 | 0.64 $\pm$ 0.13 | 76 $\pm$ 4 | 193.5 $\pm$ 8.0 | 10.24 / 12.5
B33 | 59593.73162219 | 0.45 $\pm$ 0.09 | 30.4 | 1.19 $\pm$ 0.24 | 249 $\pm$ 1 | 137.3 $\pm$ 0.4 | 5.12 / 6.2
B34 | 59593.73176535 | 0.16 $\pm$ 0.03 | 20.9 | 1.38 $\pm$ 0.28 | 80 $\pm$ 1 | 168.0 $\pm$ 1.1 | 5.12 / 6.2
B35 | 59593.73215265 | 0.24 $\pm$ 0.05 | 20.8 | 0.86 $\pm$ 0.17 | 187 $\pm$ 1 | 187.4 $\pm$ 0.7 | 5.12 / 6.2
B36e | 59593.73228158 | 0.09 $\pm$ 0.02 | 5.9 | 0.27 $\pm$ 0.05 | – | – | 10.24 / 25.0
B37 | 59593.73230289 | 0.19 $\pm$ 0.04 | 27.4 | 1.86 $\pm$ 0.37 | 71 $\pm$ 1 | 185.4 $\pm$ 0.8 | 5.12 / 6.2
B38e | 59593.73244190 | 0.11 $\pm$ 0.02 | 9.4 | 0.37 $\pm$ 0.07 | – | – | 20.48 / 12.5
B39 | 59593.73245115 | 0.11 $\pm$ 0.02 | 6.7 | 0.26 $\pm$ 0.05 | 280 $\pm$ 8 | 192.1 $\pm$ 5.5 | 10.24 / 12.5
B40 | 59593.73278832 | 0.17 $\pm$ 0.03 | 13.2 | 0.84 $\pm$ 0.17 | 139 $\pm$ 2 | 101.0 $\pm$ 0.0 | 5.12 / 6.2
B41 | 59593.73324614 | 0.04 $\pm$ 0.01 | 2.5 | 0.07 $\pm$ 0.01 | 405 $\pm$ 1 | 214.8 $\pm$ 3.9 | 20.48 / 12.5
B42 | 59593.73325516 | 0.08 $\pm$ 0.02 | 4.7 | 0.13 $\pm$ 0.03 | 380 $\pm$ 9 | 215.7 $\pm$ 4.7 | 10.24 / 6.2
B43 | 59593.73364935 | 0.27 $\pm$ 0.05 | 23.3 | 0.95 $\pm$ 0.19 | 192 $\pm$ 1 | 199.9 $\pm$ 0.6 | 5.12 / 6.2
B44 | 59593.73369348 | 0.19 $\pm$ 0.04 | 14.6 | 0.54 $\pm$ 0.11 | 231 $\pm$ 2 | 200.6 $\pm$ 1.1 | 5.12 / 6.2
B45e | 59593.73403931 | 0.11 $\pm$ 0.02 | 8.0 | 0.35 $\pm$ 0.07 | – | – | 20.48 / 25.0
B46 | 59593.73420280 | 0.07 $\pm$ 0.01 | 3.9 | 0.11 $\pm$ 0.02 | 468 $\pm$ 14 | 203.5 $\pm$ 6.0 | 10.24 / 12.5
B47 | 59593.73421902 | 0.24 $\pm$ 0.05 | 27.7 | 2.33 $\pm$ 0.47 | 69 $\pm$ 1 | 126.7 $\pm$ 0.6 | 5.12 / 6.2
B48 | 59593.73505336 | 0.10 $\pm$ 0.02 | 9.8 | 0.50 $\pm$ 0.10 | 135 $\pm$ 3 | 206.4 $\pm$ 3.5 | 5.12 / 12.5
B49 | 59593.73520064 | 0.13 $\pm$ 0.03 | 15.1 | 0.80 $\pm$ 0.16 | 111 $\pm$ 1 | 193.6 $\pm$ 1.4 | 5.12 / 6.2
B50 | 59593.73588107 | 0.13 $\pm$ 0.03 | 17.1 | 1.03 $\pm$ 0.21 | 92 $\pm$ 1 | 178.6 $\pm$ 1.2 | 5.12 / 6.2
B51 | 59593.73632506 | 0.17 $\pm$ 0.03 | 7.5 | 0.16 $\pm$ 0.03 | 704 $\pm$ 20 | 274.7 $\pm$ 7.3 | 20.48 / 6.2
B52e | 59593.73726150 | 0.09 $\pm$ 0.02 | 6.9 | 0.29 $\pm$ 0.06 | – | – | 10.24 / 12.5
B53 | 59593.73726998 | 0.11 $\pm$ 0.02 | 9.3 | 0.51 $\pm$ 0.10 | 150 $\pm$ 2 | 131.8 $\pm$ 2.5 | 10.24 / 12.5
2022 January 17 |  |  |  |
B1 | 59596.29769138 | 0.56 $\pm$ 0.11 | 49.9 | 3.06 $\pm$ 0.61 | 127 $\pm$ 1 | 134.6 $\pm$ 0.3 | 5.12 / 6.2
2022 February 21 |  |  |  |
B1 | 59631.91114554 | 0.10 $\pm$ 0.02 | 10.2 | 0.49 $\pm$ 0.10 | 196 $\pm$ 6 | 216.2 $\pm$ 5.0 | 40.96 / 12.5
B2 | 59631.91878154 | 0.32 $\pm$ 0.06 | 30.3 | 1.54 $\pm$ 0.31 | 150 $\pm$ 0 | 160.7 $\pm$ 1.0 | 40.96 / 6.2
2022 February 23 |  |  |  |
B1 | 59633.63710622 | 0.21 $\pm$ 0.04 | 24.6 | 2.36 $\pm$ 0.47 | 63 $\pm$ 0 | 102.7 $\pm$ 0.6 | 5.12 / 6.2
B2 | 59633.64288987 | 0.27 $\pm$ 0.05 | 20.9 | 1.10 $\pm$ 0.22 | 163 $\pm$ 0 | 119.0 $\pm$ 0.5 | 5.12 / 6.2
2022 March 17 |  |  |  |
B1 | 59655.95339151 | 0.35 $\pm$ 0.07 | 26.4 | 0.95 $\pm$ 0.19 | 245 $\pm$ 0 | 199.6 $\pm$ 0.6 | 5.12 / 6.2
B2 | 59655.95391696 | 0.10 $\pm$ 0.02 | 11.0 | 0.67 $\pm$ 0.13 | 115 $\pm$ 0 | 148.8 $\pm$ 6.3 | 10.24 / 12.5
a Corrected to the Solar System Barycentre at infinite frequency using a DM of
87.7527 pc cm-3 (Nimmo et al., 2022a),
a dispersion constant of 1/($2.41\times 10^{-4}$) MHz2 pc-1 cm3 s, and the
VLBI FRB 20200120E position (Kirsten et al., 2022).
The times quoted are dynamical times (TDB).
b Computed within the $\pm 2\sigma$ region of the burst temporal width
assuming Effelsberg’s system temperature and gain is 20 K
and 1.54 Jy K-1, respectively, and also considering a cosmic microwave
background temperature of 3 K and
additional sky background temperature of 0.8 K (see Section 4.2).
c Boxcar S/N: defined as the sum of the burst profile in S/N units within $\pm
2\sigma$ of the burst temporal width normalised
by the $\pm 2\sigma$ width in time bins.
d Defined as the full-width at half maximum of the Gaussian fit to the ACF
divided by $\sqrt{2}$.
e Burst extents in time and frequency could not be measured accurately due to
low S/N and temporal/spectral structure.
We assume the mean values from the remaining January 14 burst sample (132
$\upmu$s and 113 MHz) to compute the fluence.
Table 3: *

but the scatter on the data points is too large to confirm a downward trend.
The bursts on other observing days tend to have lower burst widths and
frequency extents than the mean values of the January 14 observation, while in
general they show higher fluences than average (Figure A2). More observations
are required to test whether the burst properties are drawn from different
distributions as the burst rate changes.

Motivated by the high S/N microstructure and sub-microsecond structure seen in
bursts from FRB 20200120E (Nimmo et al., 2022a; Majid et al., 2021), we
created higher-time-resolution filterbank data for bursts which have
sufficient S/N at 5.12 $\upmu$s to explore the structure on microsecond
timescales. Using digifil, we created 32-bit coherently dedispersed total
intensity filterbank data containing the bursts with a resolution of 1.28
$\upmu$s and 0.7813 MHz in time and frequency, respectively. The burst
profiles are created by averaging over the $\pm 2\sigma$ burst extent in
frequency. In Figure 6, the 1.28 $\upmu$s burst profiles are shown and
compared with the 1 $\upmu$s profile of burst B3 from Nimmo et al. (2022a),
which shows very clear microstructure. We caution that if the DM has changed
by $\sim 0.1$ pc cm-3 ($<3\sigma$ from the DM uncertainty measured in Section
4.1), this will result in $\sim 60\upmu$s of smearing from 1.5 GHz to 1.3 GHz,
therefore washing out microsecond structure. It is clear, however, from Figure
3 that the 1.28 $\upmu$s peak S/N does not rapidly increase in S/N close to
$\pm 0.1$ pc cm-3 around the DM used (B36 is increasing towards 87.65 pc cm-3,
but as noted in Section 4.1 is visibly undercorrected at its best-fit value).
If the bursts presented in this work had similarly high S/N microstructure as
seen in B3 from Nimmo et al. (2022a), this would be evident in the 5.12
$\upmu$s burst dynamic spectra (Figure A1). We cannot rule out the presence of
low S/N microstructure; however, it is evident that the sample of bursts
presented in this work do not exhibit the same high-S/N microstructure that
has been observed previously from this source.

Figure 6: 1.28 $\upmu$s burst profiles of a sample of high S/N bursts
presented in this work (burst names are shown on the y-axis). The burst
profiles are created by averaging over the $\pm 2\sigma$ burst extent in
frequency. The burst profiles are normalised such that they have the same off-
burst noise statistics. Overplotted on the 1.28 $\upmu$s profiles are the
smoothed burst profiles, using a Savitzky-Golay filter (Savitzky & Golay 1964;
11 bins, and polynomial order 2). The top burst profile is B3 from Nimmo et
al. (2022a) at 1 $\upmu$s time resolution, which has clear high-S/N
microstructure visible.

Since this burst sample does not allow us to explore a range of timescales, as
in Nimmo et al. (2022a), we instead compute the rise and decay timescales of
the high S/N bursts. We use a fluence threshold of $0.16$ Jy ms, which we
measure to be the completeness limit for the fluence distribution (see Section
4.5). Using this conservative fluence threshold limits the effect of noise on
the measurements, while also giving a sufficient sample to study the
distribution of rise and decay times (Figure 7). We define the rise time as
the time it takes the burst to increase from 10% to 90% of the burst energy
computed between the peak and peak$-2\sigma_{\rm wid}$, where $\sigma_{\rm
wid}$ is the 1 $\sigma$ burst width. Likewise, the decay time is the time
between 90% to 10% of the burst energy computed between the peak and
peak$+2\sigma_{\rm wid}$. We performed this analysis with time resolution of
20.48 $\upmu$s (with the exception of B2 on January 14 and both bursts on
February 21, where only the 40.96 $\upmu$s pulsar data is available). We find
that the rise times are preferentially lower than the decay times (Figure 7).
As the fluence decreases, the rise and decay times approach equality, and
occasionally the rise time exceeds the decay time. This evolution with fluence
is likely a reflection of the increased influence of noise in the data as the
fluence decreases. The range of rise times measured is from 47 to 356
$\upmu$s, and decay times from 37 to 266 $\upmu$s.

Figure 7: Rise and decay times of bursts above a fluence threshold of 0.16 Jy
ms. Left panels are as a function of time from the beginning of the 2022
January 14 observation, and the colour of the scatter points represent the
burst fluence. The right panels are histograms of the rise and decay times
(top), and the ratio of rise/decay (bottom), where the colours represent the
multiple observing epochs (matching the colour scheme of other plots in this
work). The horizontal black line in the bottom plots show the divide between
bursts that rise faster than they decay, and vice versa.

###  4.3 Burst rates, wait times and clustering

Reported in Table 1 are the average burst rates per observation during our FRB
20200120E monitoring campaign. For burst rates throughout this paper we report
Poisson errors. Even during the observation on 2022 January 14, the burst rate
is changing: all of the 53 bursts were discovered in the final $\sim 40$
minutes of a 2-hr observation. We computed the burst rate in 200-s time chunks
(Figure 8) to monitor the evolution of burst rate through the observation. We
find that the burst rate ramps up to a maximum of $252^{+17}_{-16}$ bursts/hr,
before falling back down towards the end of the observation. Excluding the
first two bursts, which occur significantly earlier than the remaining 50, the
burst storm has an approximate duration of 20 min. We do caution that the
storm extends to the end of our observation, beyond which we do not know the
activity behaviour of FRB 20200120E.

The distribution of the time difference between consecutive bursts, the so-
called ‘wait times’, of the 2022 January 14 burst storm is bi-modal (Figure
9). We fitted two log-normal functions to the wait-time distribution using
least-squares fitting. The best fit log-normal means are
0.94${}^{+0.07}_{-0.06}$ s and 23.61${}^{+3.06}_{-2.71}$ s. We also included
bins in the wait time distribution for the time separation of bursts from
other observing epochs (Figure 9), which are all longer than the
23.61${}^{+3.06}_{-2.71}$ s log-normal mean. This is likely a reflection of
the highly varying burst rates between observing epochs (Table 1). The median
duration of the $5$ observations with burst detections from our monitoring
campaign is $\sim 2$ hr, meaning we are unable to measure wait times longer
than this. The fact that the wait time distribution appears to tail off at
$\sim$ 1000 s is a reflection of being naturally less sensitive to longer wait
times due to the limited observation durations.

Figure 8: Cumulative burst distribution (top) and evolution of burst rate per
200 s time interval (bottom) during the 2022 January 14 FRB 20200120E burst
storm. The error bars on the rate are Poissonian. The x-axis is broken to show
that there were no bursts detected in the first $\sim$4700 s of the
observation.  Figure 9: Wait time distribution (right sub-figure, bottom
panel) and cumulative distribution of wait times (right sub-figure, top
panel). The purple wait time histogram is that of the bursts on 2022 January
14. We fit the sum of two log-normal distributions to the 2022 January 14
histogram (excluding the sub-burst separations), shown by the black line, and
the means of the two log-normals are shown by the purple dashed
(0.94${}^{+0.07}_{-0.06}$ s) and black dashed (23.61${}^{+3.06}_{-2.71}$ s)
lines. The open grey, green and yellow bins represent the time separation of
bursts on 2022 February 21, 23 and March 17, respectively (as highlighted in
the figure legend). The burst profiles of the two identified multi-component
bursts in our sample, bursts B13 and B51 on 2022 January 14, are shown in the
left sub-figure at 40.96 $\upmu$s time resolution. Overplotted on the profiles
are double Gaussian fits to the profiles, and shown in the legend are the
measured separations of the Gaussian means. The open purple histogram at short
wait times plotted on the wait time distribution represents the measured sub-
burst separations. Overplotted on the cumulative wait time distribution (right
sub-figure, top panel) are the best-fit Poisson cumulative density function
(CDF) in purple, and the best-fit Weibull CDF in blue.

Also shown in Figure 9 is the cumulative wait time distribution for the burst
storm on 2022 January 14. We test for burst clustering during the burst storm
by comparing the cumulative density function (CDF) for a Poisson distribution

$P_{\rm Poisson}=1-e^{-t_{\rm wait}R},$ (1)

with the CDF for a Weibull distribution

$P_{\rm Weibull}=1-e^{-(t_{\rm wait}R_{W}\Gamma(1+1/k))^{k}},$ (2)

where $t_{\rm wait}$ are the wait times between consecutive bursts, $R$ and
$R_{W}$ are the rates for a Poisson and Weibull distribution, respectively,
$k$ is the Weibull shape parameter and $\Gamma$ is the gamma function
(Oppermann et al., 2018). The Weibull distribution is equivalent to a Poisson
distribution when $k=1$, while $k<1$ implies that the bursts are clustered,
with more clustering implied for lower $k$. We performed a least-squares fit
of both the Poisson and Weibull distributions to the wait time cumulative
distribution. The best-fit Poissonian rate is $131\pm 1$ bursts/hr, and the
best-fit Weibull rate is $111\pm 3$ bursts/hr, with shape parameter $0.79\pm
0.44$. The reduced $\chi^{2}$ for the fits are 1.1 (50 degrees of freedom) and
0.2 (49 degrees of freedom) for Poisson and Weibull, respectively, indicating
that the burst rate is Poissonian during the burst storm. Furthermore, the
large uncertainties on the Weibull shape parameter are also consistent with a
Poissonian distribution (the special case of $k=1$). This supports the use of
Poissonian error bars on the rate in Figure 8.

The fits to the cumulative wait time distribution reflect only the statistics
during the burst storm, and do not account for the $\sim 4700$ s leading up to
the burst storm where no bursts were detected (Figure 8). Following Oppermann
et al. (2018), and the analysis presented in Kirsten et al.
(2021)444https://github.com/MJastro95/weibull_analysis, we calculated the
posterior distribution of the 2022 January 14 observation (Figure 10, left)
and the combined posterior distribution of the observations on January 17,
February 21, February 23 and March 17 (Figure 10, right). The likelihood
function is computed using the burst ToAs reported in Table
LABEL:tab:burst_properties relative to the beginning of the observation, and
incorporates any gaps between the beginning of the observation and the first
burst, and the final burst to the end of the scan. We do not include the non-
detection observations, since we are specifically interested in exploring
whether the difference between 2022 January 14 and other detection days is
solely the burst rate. To combine observations we are assuming that the scans
are independent and calculate the likelihood of the data as the product of the
likelihoods of the individual observations. The prior ($f(k,R_{W})$) is
defined as uniform, and the posterior distribution is calculated as

${\rm Post}(k,R_{W}|d)\propto\mathcal{L}(d|k,R_{W})f(k,R_{W}),$ (3)

for the likelihood of the data $d$, $\mathcal{L}(d|k,R_{W})$.

Figure 10: Posterior distributions of the Weibull shape parameter $k$ and rate
$R_{W}$ for the 2022 January 14 observation (left) and the combination of 2022
January 17, February 21, 23 and March 17 observations (right). In each sub-
figure the contour plot represents the 2-dimensional distribution, where the
contours are 68%, 95% and 99% confidence intervals. The red lines highlight
the maximum probability density of the distribution (i.e., the most likely
values). The black dashed line highlights $k=1$, which is where the Weibull
distribution is equivalent to a Poisson distribution. The top and right panels
show the marginal distribution for $k$ and $R_{W}$, respectively. The orange
shaded regions represent the 68%, 95% and 99% confidence intervals.

We find that for the 2022 January 14 observation, the most likely values of
$k$ and $R_{W}$ are $0.50^{+0.04}_{-0.05}$ and $1079^{+377}_{-242}$ day-1,
respectively, where the uncertainties reflect the 68% confidence interval.
This indicates that the bursts are highly clustered (since $k<1$), which is
evident already from Figure 8. In contrast, the combined observations of
January 17, February 21, 23 and March 17 result in most likely values of
$k=0.69^{+0.20}_{-0.17}$ and $R_{W}=24^{+22}_{-7}$ day-1, showing no strong
evidence for clustering, and consistent with $k=1$ within the 95% confidence
interval (Figure 10).

###  4.4 Periodicity searches

In this work we have a relatively large burst sample, mostly concentrated in a
short time interval on 2022 January 14. We, therefore, used various methods to
search for a periodic arrival time of the bursts during the 2022 January 14
observation, as well as a periodicity in the activity of bursts over the $>1$
yr span of observations. Note that we only include the bursts presented in
this work and in Kirsten et al. (2022) for the periodicity analysis since they
were all detected with Effelsberg (observations with comparable sensitivity)
at the same observing frequency (frequency-dependent activity is seen in FRB
20180916B; Pleunis et al. 2021a; Pastor-Marazuela et al. 2021).

####  4.4.1 Burst arrival times

Using PRESTO (Ransom, 2001), we created dedispersed time series (DM$=87.7527$
pc cm-3; Nimmo et al. 2022a) of the entire 2-hr observation, the last $\sim
40$ minutes, and the $\sim 15$ minutes around the peak burst rate of 2022
January 14, after masking the RFI using rfifind. The reason for segmenting the
data in this manner is to increase sensitivity to the scenario where the
periodic emission has ‘turned on’ (e.g., nulling pulsars; Backer 1970). The
time series were created from the 40.96 $\upmu$s pulsar backend data since
there are roughly a few minutes of missing data from the raw voltages (see
Section 3.1.1). These time series were Fourier transformed (using a Fast
Fourier Transform, FFT) and then searched for periodic signals using PRESTO’s
accelsearch. We first use a maximum Fourier frequency derivative of $8$ bins
and $8$ maximum number of harmonics, and second a maximum Fourier frequency
derivative of $200$ bins and $16$ maximum number of harmonics. The only
periodic candidates above a S/N threshold of $7$ and coherent power of $100$
are confined to a small spectral range, and therefore are attributed to RFI.

We then performed a brute force search of an integer divisor of the burst ToAs
commonly used for period searches of rotating radio transients (RRATs;
McLaughlin et al. 2006)555Using rrat_period in the PRESTO psr_utils package..
We performed this test twice: once on all bursts excluding the first two which
are separated in time from the main outburst of FRBs, and second a subset of
those bursts which have a wait time from the previous burst $>2.5$ s. For the
latter, we are using only bursts in the long wait time log-normal (Figure 9),
which we attribute to the burst rate, and exclude bursts in the shorter wait
time log-normal which we attribute to a typical ‘event duration’ (see Section
5.5). Folding at the best-fit period from each search returns bursts across
all burst phases (Figure A4, bottom sub-figure). Therefore, we conclude that
there is no strict period in the arrival times of the bursts during the FRB
20200120E burst storm. We note that this method is insensitive to the arrival
of bursts at various rotational phases of the progenitor.

To increase our sensitivity to the situation where the bursts arrive at a
wider range of phases, or at multiple distinct rotational phases, we folded
the observation using a range of trial periods from 1 ms to 25 s. We made step
sizes of (1/$n_{\rm bins}$)/(2442.5 s) in frequency space, where 2442.5 s is
the time separation between the first and last burst on 2022 January 14, and
$n_{\rm bins}$ are the number of bins the period is divided into: we choose
$25$ bins which corresponds to a minimum duty cycle of 4%. In the folded
observation, we count the number of burst ToAs that fall into each phase bin,
and use the $\chi^{2}$ statistic to compare with a uniform distribution.
During the 2022 January 14 observation we have even exposure to all phase
bins, but when considering a longer period in the activity of FRB 20200120E
(see Section 4.4.2), the uneven exposure must be accounted for. This analysis
is described in detail in Chime/Frb Collaboration et al. (2020). The reduced
$\chi^{2}$ as a function of period for $n_{\rm bins}=25$ is shown in Figure
A4. We computed a significance from the $\chi^{2}$ survival function, and find
$4$ periods with significance $\sim 3\sigma$. For those 4 period candidates,
we fold the burst ToAs using those periods and find that in all cases the
burst ToAs appear across $>90$% of the phase. In Figure A4 we plot reduced
$\chi^{2}$ for a small range of periods around the highest significance
candidate (period $P=3.40$ ms), and also plot the histogram of phases after
folding the burst ToAs using this period. Since there are no periods that
confine the burst ToAs in phase in a statistically significant way, we
conclude that we find no evidence for periodicity in the arrival times.

####  4.4.2 Burst activity

The repeating FRB 20180916B has a confirmed $16.33\pm 0.12$ day periodicity in
its bursting activity (Chime/Frb Collaboration et al., 2020; Pleunis et al.,
2021a). Additionally, FRB 20121102A has a tentative $\sim 160$ day period in
its activity (Rajwade et al., 2020; Cruces et al., 2021). With the $>1$ yr
span of Effelsberg observations, as well as multi-epoch detections, we aim to
search for a similar periodic activity from FRB 20200120E. It may be that the
PRECISE detections of 2021 February–April (Kirsten et al., 2022), are one
activity cycle, and the 2022 January–March detections presented in this work
are a second cycle, giving a period of $\sim 11$ months, and an activity
window of $\sim 3$ months (Figure 1). In this case, however, having only $2$
cycles, and a deficit of observations from June 2021 to December 2021, means
this is impossible to confirm. Perhaps, however, there is a shorter period in
the activity ($<11$ months). We used two methods to search for periods between
1.5 days and 80 days: we constrain the lower search limit to $1.5$ days to
minimise the effect of the sidereal day and above $80$ days there are too few
cycles to constrain any period meaningfully with the current data.

Since our observations of FRB 20200120E are not evenly sampled in time, we
created a Lomb-Scargle periodogram (Lomb, 1976; Scargle, 1982), from 1.5 days
to 80 days in 50000 linear steps. We created a list of observation epochs
(using the time stamp of the observations beginning), paired with a list of
$1$s and $0$s: $1$ when the observation contained at least 1 burst, and $0$
when the observation resulted in a non-detection. Following VanderPlas (2018),
we then subtracted the mean of this time series, since the Lomb-Scargle model
assumes the time series is centred around the mean. The periodogram is shown
in Figure A4 (top left sub-figure, bottom panel), with a $\sim$12.5-day
candidate highlighted. Note that Lomb-Scargle periodograms have a complicated
window function due to the uneven sampling of the data. We produced this
window function by making a Lomb-Scargle periodogram of a time series
reflecting our observing cadence: the time series is $1$ for days where we had
observations, and $0$ for every other day. We confirm that this $\sim$12.5-day
candidate is not present in the window function, and is therefore present in
the data itself. To determine the 1 $\sigma$ significance level, we randomly
selected 8 days out of our list of observing epochs as ‘detection days’ and
compute the maximum value of the Lomb-Scargle periodogram. We repeated this
exercise 1000 times and from the distribution of maximum values compute the 1
$\sigma$ significance level. The 12.5-day candidate is $<1\sigma$ in
significance when following this approach.

Additionally, we fold the $>1$ yr span of observations using periods between
1.5 days to 80 days. We step in frequency by 0.1/(390 days) – or (1/(10
bins))/(separation of first detection and last detection) – and bin the data
into $3$, $5$, and $10$ bins. We compare detections per bin with a uniform
distribution, similar to the analysis we conducted on the single 2022 January
14 observation described above, calibrating for the uneven exposure per bin
(Chime/Frb Collaboration et al., 2020). In Figure A4 (top left sub-figure, top
panel) we show the reduced $\chi^{2}$ as a function of period using a binning
of $3$ bins per period. The 12.5-day candidate is also evident in this
analysis, but with similarly low significance. We bootstrap the significance
by randomly selecting 8 detection days from our observing epochs and computing
the largest reduced $\chi^{2}$ value, repeating this exercise 100 times, and
from the distribution of maximum reduced $\chi^{2}$ we compute the 1 $\sigma$
significance level.

Although there is again a candidate at a period of 12.5 days, it is not
statistically significant. Continued monitoring of FRB 20200120E at 1.4 GHz is
required to confirm whether FRB 20200120E’s activity is periodic similar to
the behaviour of FRB 20180916B (Chime/Frb Collaboration et al., 2020) and the
tentative activity period detected for FRB 20121102A (Rajwade et al., 2020;
Cruces et al., 2021).

###  4.5 Energetics

The cumulative distribution of burst fluences appears to turn-over towards low
fluences (Figure 11). This is likely the result of our inability to detect all
bursts close to the sensitivity limit of our observations. We must determine a
completeness threshold, above which the fluence distribution accurately
reflects the source’s behaviour. Selecting the completeness threshold, though,
is somewhat ambiguous, and can heavily influence the inferred fluence
distribution properties. We used the method of maximum-likelihood to measure
the optimal fluence threshold resulting in the best power law fit (Clauset et
al., 2007), under the assumption that the bursts follow a power-law energy
distribution above some threshold. This method returns a limit of $0.16$ Jy
ms, which is chosen as the completeness limit since it lines up with where the
distribution begins to turn-over by eye, and agrees with the limit derived
using the radiometer equation (Cordes & McLaughlin, 2003) and assuming a
minimum S/N of $10$, a burst width of $300\upmu$s and a burst bandwidth of
$150$ MHz. This threshold is also consistent with where the power law index,
$\alpha$ ($R\propto Fl^{-\alpha}$, for burst rate $R$ above some fluence
$Fl$), flattens out as a function of fluence threshold (Figure 11, right),
estimated using a Maximum-likelihood method, described in Crawford et al.
(1970) and James et al. (2019).

We fitted the cumulative distribution of burst fluences on 2022 January 14
above a completeness threshold of $0.16$ Jy ms, using a power-law and a least-
squares fit method (Figure 11). The fluences are considered to have 20%
uncertainty, arising due to the uncertainty in the system values for
Effelsberg. The best-fit power law has index $\alpha=2.39\pm 0.12$. The
uncertainties are the quadratic sum of the statistical fit uncertainties,
combined with systematic uncertainties derived by sampling 15 fluences above
the completeness threshold, performing the same least-squares fit to the
distribution and repeating this process 500 times to measure the standard
deviation of the power law indices measured.

Figure 11: Left: Distribution of burst fluences. Different coloured markers,
as shown in the legend, represent bursts detected on different observing days.
The black solid line represents the best fit power-law to the 2022 January 14
bursts above the fluence threshold. Right: The slope of the power-law
$\alpha$, determined by Maximum-likelihood estimation (Crawford et al., 1970;
James et al., 2019) as a function of fluence. The best fit $\alpha$ from the
least-squares fit to the distribution is shown by the horizontal line. In both
panels, the dashed vertical line represents the completeness limit of $0.16$
Jy ms.

In Figure 11, in addition to the fluence distribution of the bursts on 2022
January 14, we also plot the fluences of bursts detected at our other
observing epochs. Due to the different burst rates between observations, and
having only 1 or 2 bursts per observation outside of the burst storm on 2022
January 14, it is difficult to constrain how the energy distribution changes
from epoch-to-epoch, as is seen in other FRBs (e.g., Jahns et al., 2023). To
test whether the fluences measured on days other than 2022 January 14 are
drawn from a different energy distribution, we performed a Kolmogorov-Smirnov
(KS) test using the Python scipy.stats package tool
ks_2samp666https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ks_2samp.html.
The critical value for the KS-test is
$D=c(p)\sqrt{\left(\frac{N_{1}+N_{2}}{N_{1}N_{2}}\right)}=0.66$, where
$c(p)=1.63$ corresponding to a significance level of $0.01$, and $N_{1}$,
$N_{2}$ are the sizes of the two distributions we are comparing. We find a KS
statistic of $0.51<0.66$, and therefore we cannot reject the null hypothesis
that the 2022 January 14 fluences and the fluences of the other epochs are
drawn from the same distribution. We repeated this exercise adding the first
$2$ bursts from 2022 January 14 to the fluences at other epochs, motivated by
the fact that these bursts occur $\sim 15$ minutes before the burst storm,
seemingly less related to the high activity (see, e.g., Figure 8). In this
case the critical value is $D=0.59$ and the measured test statistic is
$0.34<0.59$, which still cannot rule out all fluences being drawn from the
same distribution.

##  5 Discussion

FRB 20200120E is a singular source: it provides a valuable bridge between the
populations of known pulsars and bursting magnetars in the Milky Way and
Magellanic clouds, and the much more distant FRBs in extragalactic space
(Nimmo et al., 2022a). Here we discuss FRB 20200120E in the context of other
fast radio transient sources. We show that FRB 20200120E presents many
similarities to the phenomena seen from radio-emitting magnetars and repeating
FRBs, but its range of luminosities, burst durations, and wait times also
distinguish it from these other known sources. It may be possible to reconcile
these quantitative differences by invoking an evolutionary sequence, or
spectrum of neutron stars, with a range of rotational rates and magnetic field
strengths. Alternatively, FRB 20200120E may originate from a qualitatively
different source class.

###  5.1 Lack of DM variations

Comparing our most recent bursts with those detected $>10$ months earlier
(Nimmo et al., 2022a; Kirsten et al., 2022), we constrain DM variations
towards FRB 20200120E to $<0.15$ pc cm-3. This is a strong constraint compared
to, e.g., the $>1$ pc cm-3 variations seen from FRB 20121102A on timescales of
months to years (Hessels et al., 2019; Li et al., 2021). The strong constraint
on DM variation is consistent with the conclusion that FRB 20200120E is in a
relatively ‘clean’ local environment compared to the extreme magneto-ionic
environments of FRB 20121102A (Michilli et al., 2018b) and FRB 20190520B
(e.g., Niu et al., 2022). Furthermore, this motivates continued searches for
FRB 20200120E bursts at low radio frequencies ($<400$ MHz) since such
detections can measure more subtle variations in the local medium (Pleunis et
al., 2021a). Likewise, the lack of DM variation is also consistent with the
hypothesis that FRB 20200120E was formed via accretion-induced collapse, or
compact binary merger, in its dense globular cluster environment (Kirsten et
al., 2022; Lu et al., 2022; Kremer et al., 2021). Note, however, that the Crab
pulsar, which is likely the product of a core-collapse supernova, also shows
only small DM variations ($\lesssim 0.02$ pc cm-3; Driessen et al. 2019).
Whereas some repeating FRBs are noisy probes of the intervening magneto-
ionised medium, because of their extreme local plasma environments (e.g. Niu
et al. 2022), FRB 20200120E demonstrates that some repeaters will serve as
accurate probes of the intervening magneto-ionised medium.

###  5.2 Burst storm & time dependent burst rate

The burst rate of FRB 20200120E varies significantly between observing epochs
(Table 1), with a peak rate of $26.5^{+6.2}_{-5.1}$ bursts/hr averaged over
the 2022 January 14 observation. The burst rate is also observed to be highly
time variable during the 2022 January 14 observation, with no bursts detected
until 1.3 hr into the 2 hr observation, and the rate (computed in 200 s time
intervals) ramping up to a maximum $252^{+17}_{-16}$ bursts/hr, before falling
back down towards the end of the observation (Figure 8). Due to this rapid
rise and decay in burst rate, we refer to this as the first observed ‘burst
storm’ from FRB 20200120E.

The first-discovered repeating FRB, FRB 20121102A (Spitler et al., 2016), is
one of the few repeating FRBs whose long-term activity has been studied in
detail. The burst rate varies significantly between observing epochs (Li et
al., 2021; Hewitt et al., 2022; Jahns et al., 2023) similar to the behaviour
we observe here: the peak rate in $\sim$1-hr observations has been observed to
be as high as 218$\pm$16 bursts/hr, which is less than a factor of 2 higher
than the 131$\pm$1 bursts/hr Poisson rate for FRB 20200120E (Figure 9).
Evidence of burst clustering has been observed for FRB 20121102A (Oppermann et
al., 2018; Oostrum et al., 2020). At least some of this burst clustering is
related to the apparently periodic activity cycle that FRB 20121102A follows
($\sim$160 days; Rajwade et al. 2020; Caleb et al. 2020). During these active
windows, however, the burst wait times are Poisson distributed, but the rate
changes from day-to-day (Cruces et al., 2021; Jahns et al., 2023). Although
there is only a hint of an activity period for FRB 20200120E, given our
observations, we find a similar behaviour: during the burst storm the bursts
are consistent with being Poisson distributed (Figure 9), and the observations
on other days with detections (excluding the storm) are consistent with being
Poisson distributed as well (Figure 10). The observation of 2022 January 14,
however, shows clustering on $<1$ hr timescales (Figures 8,10). This rapid
rise in burst rate, before quickly decreasing in rate has been seen before for
FRB 20121102A, although at much higher observing frequencies (Gajjar et al.,
2018; Zhang, 2018). For comparison, we plot the burst rate as a function of
time in $200$ s intervals for both the FRB 20200120E burst storm, and that of
FRB 20121102A (Figure 12). We, unfortunately, do not see the rate drop
completely to zero before the end of our observation, and the FRB 20121102A
storm had presumably begun before the beginning of the Gajjar et al. (2018)
observation. We do, however, find the durations of the two storms, with rate
above 80 bursts/hr, to be comparable ($\sim 20$ minutes).

Figure 12: Comparison between the burst rate as a function of time for the FRB
20200120E burst storm presented in this work, and that of an observation of
FRB 20121102A (Gajjar et al., 2018; Zhang, 2018). The rates are computed in
200 s time intervals. For the FRB 20200120E observations the time axis is the
lower x-axis (in black) from the beginning of the 2022 January 14 observation,
while the upper x-axis (in red) is the time axis for FRB 20121102A from the
beginning of the Gajjar et al. (2018) observation. The plots have been
arbitrarily aligned in time by eye to highlight the comparable temporal
extents. The shaded blue region highlights the extent plotted in the zoom-in
panel below. The horizontal dashed line represents a burst rate of 80
bursts/hr, above which the duration of the storm for both FRB 20200120E and
FRB 20121102A are comparable ($\sim$20 min).

Significant change of burst rate over month-to-year timescales has been
observed for the highly active repeating FRB 20201124A (Lanman et al., 2022).
Since CHIME is a transit telescope, it has almost daily exposure to FRB
20201124A. This provides strong constraints on the burst rate of FRB 20201124A
in the years prior to discovery in 2020, and how the burst rate slowly evolved
into an outburst in 2021 (Lanman et al., 2022). The burst rate through the
outburst varies on day-to-day timescales, rising sharply to the peak reaching
a plateau and rapidly turning off (Xu et al., 2022). Perhaps this is a similar
phenomenon to what has been observed from FRB 20200120E in this work (Figure
1). Xu et al. (2022) also observe day-to-day changes in the Weibull $k$
parameter, varying from Poissonian ($k=1$) to clustered ($k<1$) between
observations. The peak burst rate per observation at 1.5 GHz (similar central
frequency as the observations presented in this work) is
45.8${}^{+7.8}_{-8.3}$ hr-1 (Xu et al., 2022), consistent with our measured
burst rate from the 2022 January 14 observation (Table 1).

Magnetars are observed to go into outburst, producing tens to hundreds of
X-ray bursts per hour (Gavriil et al., 2004; Israel et al., 2008; van der
Horst et al., 2012). The Galactic magnetar SGR 1935$+$2154, is currently the
only known Galactic object that has produced a millisecond-duration radio
transient with luminosity comparable to that of the extragalactic FRBs (albeit
still 1–2 orders of magnitude weaker than the least luminous FRBs; CHIME/FRB
Collaboration et al. 2020; Bochenek et al. 2020). SGR 1935$+$2154 went into
outburst in 2020, hours before the FRB-like transient was discovered, with a
burst rate of $\sim 720$ bursts/hr (Fletcher & Fermi GBM Team, 2020; Palmer,
2020; Younes et al., 2020). This outburst was observed to have a consistently
high rate for at least $20$ minutes, before rapidly dropping in rate to $\sim
29$ bursts/hr in only 3 hours.

In the case of giant pulse emitters, variations in giant pulse rate have been
observed between observing epochs: e.g., the Crab pulsar (PSR B0531+21), where
the rate of high fluence ($>130$ Jy ms) giant pulses vary by up to a factor of
5 between observing days (Bera & Chengalur, 2019), and the ‘Crab twin’ PSR
B0540$-$69 in the Large Magellanic Cloud, which has giant pulse rate
variations of 65 /hr to 221 /hr between epochs separated by $\sim$ months
(Geyer et al., 2021).

###  5.3 Energetics

The spectral luminosities of FRB 20200120E bursts are at least two orders of
magnitude lower compared to other known repeating FRBs (Nimmo et al., 2022a),
and even $\sim 10\times$ lower than the exceptionally bright event seen from
SGR 1935+2154 on April 28 2020 (Bochenek et al., 2020; CHIME/FRB Collaboration
et al., 2020). In our unprecedentedly large sample of FRB 20200120E bursts we
also see a relatively narrow range of burst fluences, spanning only about an
order-of-magnitude from 0.04 Jy ms to 0.6 Jy ms. This limited range is partly
due to being strongly sensitivity limited, despite the large aperture of the
Effelsberg telescope. Furthermore, many of the bursts we detect are below our
nominal completeness threshold of 0.16 Jy ms and only detectable because of
their bright, narrow-band scintles. Larger on-sky time ($>100$ hr) may still
reveal FRB 20200120E bursts that are more comparable in their energetics to
other repeaters, but nonetheless FRB 20200120E appears to be, at least on
average, an anomalously weak source that is only detectable because of its
exceptional proximity to Earth (Bhardwaj et al., 2021; Kirsten et al., 2022).

Furthermore, we measure a steep power-law ($\alpha=2.39\pm 0.12$, see Section
4.5) burst energy distribution above our fluence threshold of 0.16 Jy ms.
Unless FRB 20200120E is found to have a bi-modal and/or time-variable energy
distribution, with a flatter tail at high fluences, then it is unlikely that
ongoing observing campaigns will detect bursts that are much above a fluence
of 2 Jy ms at 1.4 GHz (corresponding to an isotropic-equivalent spectral
luminosity of $\sim 2.4\times 10^{29}$ erg s-1 Hz-1). For comparison, Bhardwaj
et al. (2021) find fluences of $\sim 2$ Jy ms in the $400-800$ MHz range.
Given that the bursts we detect at 1.4 GHz are typically $\sim 0.2$ Jy ms,
this suggests an average spectral index, $S\propto\nu^{-\beta}$ of $\beta\sim
2-3$. If this were to continue to low radio frequencies, then the expected
average fluence at 150 MHz is $\sim 30-130$ Jy ms, easily detectable by LOFAR
or uGMRT. The caveat to this statement is that the higher fluences detected by
Bhardwaj et al. (2021) might reflect the lower sensitivity of CHIME compared
with Effelsberg, implying the power law is more shallow than determined here.

The burst energy distribution of FRB 20200120E is comparable to that of the
Crab pulsar (Karuppusamy et al., 2010). It is significantly steeper than the
energy distribution seen from FRB 20121102A (Li et al., 2021; Hewitt et al.,
2022), but conversely much flatter compared to what has been observed from FRB
20201124A (Lanman et al., 2022). We caution, however, that FRB 20121102A has
shown a bi-modal and time-variable burst energy distribution (Li et al., 2021;
Hewitt et al., 2022). This bi-modality could indicate that the source produces
multiple types of bursts, or that some bursts are apparently boosted in energy
due to local propagation effects like plasma lensing (Cordes et al., 2017).
Our burst energy distribution for FRB 20200120E is based on a single burst
storm and may not be representative of its average behaviour. Future
detections of burst storms from FRB 20200120E can test this. The pulse energy
distributions of the Crab and other pulsars appear to be stable with time
(Bera & Chengalur, 2019). If the burst energy distributions of repeating FRBs
are found to be time variable then models of the emission process need to
explain this behaviour.

###  5.4 Burst durations and morphology

The $\sim 100$ $\upmu$s bursts from FRB 20200120E are on average $>10\times$
shorter-duration compared to other known repeaters (Nimmo et al., 2022a;
Pleunis et al., 2021b; Li et al., 2021; Xu et al., 2022). Previous studies
have also detected (sub-)microsecond burst structure from FRB 20200120E (Nimmo
et al., 2022a; Majid et al., 2021). Coupled with the much lower burst
luminosities from FRB 20200120E compared to other repeaters, this suggests
that future studies using large burst samples should investigate whether there
is a correlation between burst duration and luminosity. Multi-frequency
observations of FRB 20121102A have demonstrated that its bursts are on average
narrower and less luminous at high radio frequencies (Michilli et al., 2018b;
Gajjar et al., 2018; Josephy et al., 2019). Future observations should aim to
establish such a trend for FRB 20200120E as well.

The voltage data we have collected here has also allowed us to constrain how
often FRB 20200120E produces ultra-short bursts, on timescales of microseconds
or less. The lack of interstellar or intergalactic scattering towards FRB
20200120E, along with its stable DM, also make it a prime target to explore
ultra-short timescales. We find no evidence for microstructure in our sample
of FRB 20200120E bursts, nor do we identify any additional bursts in a
separate search of the 2022 January 14 data at a time resolution of $1$
$\upmu$s. While some FRB 20200120E bursts do present structure on
(sub-)microsecond timescales (Nimmo et al., 2022a; Majid et al., 2021), we
conclude that such timescales are relatively rare777It is, of course, possible
that micro-bursts are common but that they typically overlap in time,
therefore our results indicate that isolated micro-bursts are rare. and that
most bursts have minimum timescales of variation on the order of $>10$
$\upmu$s.

Nonetheless, we find that the rise times of FRB 20200120E bursts are typically
very short: $50-200$ $\upmu$s. This constrains the size of the emission region
to tens of kilometres or less, though relativistic effects may also be
relevant. The decay times we measure are typically twice as long, and this
asymmetry should be explained in emission models. We note that magnetar X-ray
bursts are often also well modelled by a faster rise and slower decay
(Huppenkothen et al., 2015).

In any case, the intrinsic asymmetry of the bursts, along with the potential
for time-frequency drifts (Hessels et al., 2019), demonstrates that caution is
needed when inferring scattering times from FRBs. Burst B33 from 2022 January
14 is the best example of a ‘sad trombone’ drift in our new burst sample (see
Figure 2). This effect is also clearly visible in the baseband data from the
discovery of FRB 20200120E (Bhardwaj et al., 2021, see their Figure 1), and
provides an important phenomenological link with the rest of the known
repeater population. In addition, we find that the FRB 20200120E bursts are
sometimes narrow band ($\Delta\nu\sim 200$ MHz), as has been seen in other
repeaters (Hessels et al., 2019; Gourdji et al., 2019; Kumar et al., 2021).
The average burst spectrum from the burst storm shows two $\sim 100$ MHz
features (Figure 5), reminiscent of the spectral structure in the Majid et al.
(2021) FRB 20200120E burst, and unlike typical repeater spectra. However, it
has been shown that narrow-band FRB 20121102A bursts exhibit preferred
frequencies, consistent on timescales of days (Gourdji et al., 2019; Hewitt et
al., 2022).

###  5.5 Burst wait times

We find 3 peaks in the wait time distribution of bursts from FRB 20200120E
(Figure 9). The main peak at $\sim 25$ s simply reflects the overall burst
rate, where on relatively short timescales of $<1$ hr we find the wait times
to be reasonably well modelled by a Poissonian process.

We also find a secondary peak in the burst wait times of FRB 20200120E at
$\sim 1$ s. This is reminiscent of the secondary, shorter-timescale wait time
peaks seen for FRB 20121102A (Gourdji et al., 2019; Li et al., 2021; Hewitt et
al., 2022; Jahns et al., 2023) and FRB 20201124A (Xu et al., 2022), though
those sources both show such a peak at $\sim 30$ ms, roughly a 50$\times$
shorter timescale. These secondary wait-time peaks demonstrate that once a
burst has occurred, it is more likely to detect a second or third burst in
short succession. This deviates from the general Poisson wait-time
distribution. We suggest that these secondary wait-time peaks represent a
timescale on which repeated burst emission can occur, and that this could be
related to the overall physical size in which burst emission can be generated
around the central engine as well as the timescale on which perturbations
traverse this region. If so, then the much longer $\sim 1$ s timescale of FRB
20200120E could indicate a much larger overall emission region, or slower
propagation of disturbances, compared to the $\sim 30$ ms timescales that are
observed for FRB 20121102A and FRB 20201124A. While the secondary wait-time
peak of FRB 20200120E is $\sim 50\times$ longer in duration compared to FRB
20121102A and FRB 20201124A, its bursts are typically $\sim 30\times$ shorter.
It is worth considering whether these timescales are related.

Lastly, two of the bursts we detect from FRB 20200120E show sub-millisecond
separations between sub-bursts, and this suggests that there may also be a
tertiary wait-time peak on this timescale. Other repeaters have also shown a
characteristic spacing of wait-times between sub-bursts on timescales of
roughly milliseconds (e.g., Hessels et al. 2019). This timescale may reflect
the microphysics related to the coherent emission process: e.g., the interplay
between charge bunching and radiative feedback (Lyutikov, 2021). Some authors
have also interpreted the quasi-periodic spacing of FRB sub-bursts in the
context of outward propagating plasma oscillations (Sobacchi et al., 2021).

###  5.6 Periodicity constraints

We searched for a strict periodicity in the arrival times of the bursts,
focusing on the relatively large sample of 53 bursts from the 2022 January 14
storm. Given the short burst durations of typically $\sim 100$ $\upmu$s, our
analysis should be sensitive to rotational periods of $\sim 1$ ms or longer,
if the bursts are clustered in rotational phase. Note that the methods we used
are sensitive to bursts occurring in multiple rotational phase windows, as is
sometimes seen from pulsars and radio-emitting magnetars (Camilo et al.,
2006). The sample of 53 bursts from the 2022 January 14 observation shows no
statistically significant evidence for a short-duration period in the burst
arrival times, and hence we conclude that — if FRB 20200120E is a rotating
object with a period between 1 ms and $25$ s — the bursts are roughly evenly
distributed in rotational phase. This is consistent with the lack of
detectable periodicity in other repeaters (Gourdji et al., 2019; Li et al.,
2021; Hewitt et al., 2022).

Nonetheless, we caution that a larger burst sample may reveal a more subtle
clustering of bursts in rotational phase, and that clustering could
potentially be time-variable: e.g., radio-emitting magnetars show evolving
pulse profiles that can be stable on timescales of days to weeks or longer
(Camilo et al., 2006). The lack of observable periodicity distinguishes FRB
20200120E from known giant pulse emitters and suggests that the emission
region changes chaotically between the bursts.

We also searched the collection of known bursts from all our observations to
see if there is evidence for periodicity in FRB 20200120E’s activity rate.
Such searches are motivated by the well-established 16.3-day periodicity of
FRB 20180916B (Chime/Frb Collaboration et al., 2020) and the candidate 160-day
periodicity of FRB 20121102A (Rajwade et al., 2020; Cruces et al., 2021).
Though we find a hint for a 12.5-day period, a factor of a few more cycles are
needed to ascertain if this will become statistically significant, or not.

##  6 Conclusions & future work

We have presented the first-known ‘burst storm’ from FRB 20200120E, in which
53 bursts were detected in $<1$ hr of observation with the 100-m Effelsberg
telescope on 2022 January 14. We characterise this event as a burst storm
because of the high and rapidly varying burst rate, which is reminiscent of
the X-ray burst storms seen from magnetars. The energy distribution of the
burst storm is a steep power law ($\alpha=2.39\pm 0.12$ above a fluence
threshold of 0.16 Jy ms). We used these closely spaced bursts to search for a
strict periodicity in the arrival times, but find no such signal, consistent
with other known repeating FRBs. The burst wait times do, however, show a
secondary peak at $\sim 1$ s. This is reminiscent of the secondary wait-time
peaks seen for two other repeating FRBs on significantly shorter timescales of
$\sim 30$ ms. The secondary wait time peak may represent a characteristic
timescale related to the overall size of the system.

We note that a survey with a factor of 2 or 4 lower sensitivity than the
Effelsberg observations presented here would have detected approximately 42
and 19 of the 53 bursts, respectively, and therefore also would have
classified this event as a burst storm. Considering the instrumental
sensitivity dependence on classifying burst storm events will be important in
the future for determining the rate of such events from FRB 20200120E or from
other repeating FRBs.

We also present an additional 7 bursts, which were detected in 4 other
observing sessions in 2022 January through March. During these observations,
the lower and more stable burst rate suggests that the source was in a
different state compared to the 2022 January 14 storm. We used these and other
observations, including those with non-detections, to search for periodic
activity but find only tentative evidence for a 12.5-day period.

The observational record to date demonstrates that the DM of FRB 20200120E is
highly stable, unlike some other repeaters, and that its bursts are
characteristically $\sim 30\times$ shorter in duration and $\sim 100\times$
less luminous compared to other known repeaters. Nonetheless, the narrow-band
emission and time-frequency drift (‘sad trombone’ effect) seen from FRB
20200120E provide important observational links to other repeaters. By
comparing our $1.2-1.6$-GHz burst sample to that detected from $400-800$ MHz
by CHIME/FRB (Bhardwaj et al., 2021), we find that the average spectral index
is quite steep: $\beta=2-3$ (note the caveat to this statement discussed in
Section 5.3), indicating that there are good prospects for detecting FRB
20200120E at very low frequencies ($<400$ MHz).

We show that FRB 20200120E bursts typically have fast rise ($\sim 100$
$\upmu$s) and slower decay ($\sim 200$ $\upmu$s), but that this asymmetry is
not due to scattering. Whereas previous observations have demonstrated
(sub-)microsecond structure in the bursts from FRB 20200120E, we find that
such short timescales occur rarely (or that the microstructure is typically
bunched in time, as opposed to being resolvable). Additionally, searches of
our voltage data using coherent dedispersion and a time resolution of $1.28$
$\upmu$s led to the discovery of only one additional, low-S/N burst compared
to our initial searches at $40.96$ $\upmu$s time resolution. This burst is the
narrowest in the sample presented here, with a temporal scale of $\sim 14$
$\upmu$s. We find no bursts with durations $<10$ $\upmu$s.

Given the observations to date, we suggest that the most urgent avenues for
future observational investigation are:

  * •

Detect the source both below 400 MHz and above 3 GHz to establish whether the
burst widths are frequency-dependent.

  * •

Continue the observational timeline in order to establish or rule out periodic
variations in the source’s activity.

  * •

Use future detections to further constrain subtle DM and RM variations.

From the point-of-view of understanding the nature of FRB 20200120E, we
encourage theorists to focus on a self-consistent picture that explains the:
i. low burst luminosities, ii. short burst durations, iii. $\sim 1$-s
secondary wait-time peak and iv. steep average burst spectrum. Each of these
quantities deviates quite significantly from other known repeaters, and it may
be possible to link these burst properties to those of the central engine
(e.g., its rotation rate, magnetic field strength, age, etc.).

## Acknowledgements

K. N. would like to thank P. Chawla and K. Rajwade for helpful discussions
about the analysis presented in this work.

This paper is based on observations with the 100-m telescope of the MPIfR
(Max-Planck-Institut f’́ur Radioastronomie) at Effelsberg.

Research by the AstroFlash group at University of Amsterdam, ASTRON and JIVE
is supported in part by an NWO Vici grant (PI Hessels; VI.C.192.045).

This project has received funding from the European Union’s Horizon 2020
research and innovation programme under grant agreements No 730562 (RadioNet)
and 101004719 (OPTICON-RadioNet Pilot).

B. M. acknowledges support from the Spanish Ministerio de Economía y
Competitividad (MINECO) under grants AYA2016-76012-C3-1-P,
FPA2017-82729-C6-2-R, and MDM-2014-0369 of ICCUB (Unidad de Excelencia “María
de Maeztu”)

## Data Availability

The filterbank data containing the FRBs presented in this work are available
via Zenodo, at https://doi.org/10.5281/zenodo.7555187. Requests for other
materials should be addressed to the lead author.

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##  Appendix A Additional figures

Figure A1: (a) Frequency-averaged burst profiles, dynamic spectra and time-
averaged spectra for all of the FRB 20200120E bursts presented in this work,
ordered according to their arrival time. The filterbank data plotted is
created by channelising the raw voltages to a resolution of 5.12 $\upmu$s and
0.1953 MHz in time and frequency, respectively. The exception to this is B15,
which was discovered in the microsecond search and the filterbank data is
created with a resolution of 1.28 $\upmu$s and 0.7813 MHz (see Figure 2 for a
zoom-in panel of burst B15). Both the time and frequency have been downsampled
by various factors for plotting, with the resolutions being shown on the burst
profile and dynamic spectra, respectively. The data are coherently (within
frequency channels) and incoherently (between channels) corrected for
dispersion using a DM of 87.7527 pc cm-3 (Nimmo et al., 2022a). The coloured
bars highlight the 1-$\sigma$ (dark) and 2-$\sigma$ (light) error regions on
the burst extent in both frequency and time, where the different colours
represent different observing epochs: 2022 January 14 (purple), 2022 January
17 (blue), 2022 February 21 (grey), 2022 February 23 (green) and 2022 March 17
(yellow). Time $=0$ represents the burst centroid in time, and the horizontal
coloured line in the burst spectrum represents the frequency centroid.
Frequency channels that have been masked due to RFI have been omitted from the
dynamic spectra (horizontal white lines). The burst profile is created by
averaging the dynamic spectrum within the 2-$\sigma$ burst extent in
frequency, and similarly the burst spectrum is created by averaging the
dynamic spectrum within the 2-$\sigma$ burst extent in time.

Figure A1: (b) Continuation of Figure A1(a). Figure A2: Top sub-figure: Burst
widths in time (top panel), bandwidths (middle panel) and fluences (bottom
panel), as a function of time relative to the beginning of the observing
epoch. As shown in the legend, the colours represent the different observing
epochs. The vertical black line represents the start of the observations, and
the coloured vertical dashed lines indicate the end of each observation. The
horizontal purple line represents the mean value for the 2022 January 14
observation (burst storm). Bottom sub-figure: The ratio of burst fluences of
consecutive bursts on 2022 January 14 as a function of their time separation,
with a histogram shown on the right. The black dashed line represents the
divide between the fluence of the first burst (Fl1) being lower than the
fluence of the second burst (Fl2), and vice versa.  Figure A3: Burst time
duration versus frequency extent for bursts during the 2022 January 14
observation. The error bars are the $1\sigma$ fit errors from the
2-dimensional autocorrelation analysis described in the text, and reported in
Table LABEL:tab:burst_properties. The colour scale represents the burst
fluence.  Figure A4:  Periodicity search results. Top-left sub-figure: The
reduced $\chi^{2}$ for a uniform distribution of burst times as a function of
trial activity period (top panel, using 3 bins) and the Lomb-Scargle
periodogram (bottom panel) for the entire $>1$ yr span of FRB 20200120E
observations. The $1-\sigma$ significance level is indicated by the dashed
horizontal black line, calculated by bootstrapping 100 and 1000 trials for the
reduced $\chi^{2}$ and Lomb-Scargle, respectively. The red vertical line
highlights a candidate at 12.5 days (although continuous monitoring of FRB
20200120E is required to test the significance of this period). Top-right sub-
figure: The reduced $\chi^{2}$ for a uniform distribution of burst times
around the highest significance candidate for bursts detected during the 2022
January 14 observation (top panel, using 25 bins). The horizontal red line
shows the 3$-\sigma$ significance, calculated from the $\chi^{2}$ survival
function. The highest significance candidate (period 3.40 ms) is barely
$3\sigma$. Folding the burst ToAs using this period results in bursts arriving
across all phases (bottom panel). Bottom sub-figure: The distribution of burst
phases assuming the period measured from the brute-force search of an integer
divisor of the burst ToAs. See Section 4.4 for details of the analysis
resulting in this figure.