# Burst timescales and luminosities link young pulsars and fast radio bursts

K. Nimmo ASTRON, Netherlands Institute for Radio Astronomy, Oude
Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands.  Anton Pannekoek
Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH,
Amsterdam, The Netherlands  J. W. T. Hessels Anton Pannekoek Institute for
Astronomy, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The
Netherlands  ASTRON, Netherlands Institute for Radio Astronomy, Oude
Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands.  F. Kirsten Department
of Space, Earth and Environment, Chalmers University of Technology, Onsala
Space Observatory, 439 92, Onsala, Sweden  A. Keimpema Joint Institute for
VLBI ERIC, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands  J. M.
Cordes Department of Astronomy and Cornell Center for Astrophysics and
Planetary Science, Cornell University, Ithaca, New York, 14853, USA  M. P.
Snelders Anton Pannekoek Institute for Astronomy, University of Amsterdam,
Science Park 904, 1098 XH, Amsterdam, The Netherlands  D. M. Hewitt Anton
Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904,
1098 XH, Amsterdam, The Netherlands  R. Karuppusamy Max Planck Institute for
Radio Astronomy, Auf dem Heugel 69 53121 Bonn, Germany  A. M. Archibald School
of Mathematics, Statistics and Physics, Herschel Building, Newcastle
University, Newcastle upon Tyne, NE1 7RU, UK  V. Bezukovs Engineering Research
Institute Ventspils International Radio Astronomy Centre (ERI VIRAC) of
Ventspils University of Applied Sciences (VUAS), Inzenieru street 101,
Ventspils, LV-3601, Latvia  M. Bhardwaj Department of Physics, McGill
University, 3600 rue University, Montréal, QC H3A 2T8, Canada  McGill Space
Institute, McGill University, 3550 rue University, Montréal, QC H3A 2A7,
Canada  R. Blaauw ASTRON, Netherlands Institute for Radio Astronomy, Oude
Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands.  S. T. Buttaccio
Istituto Nazionale di Astrofisica, Istituto di Radioastronomia Radiotelescopio
di Noto, C.da Renna Bassa Loc. Case di Mezzo C.P. 161, 96017, Noto (SR), Italy
T. Cassanelli Dunlap Institute for Astronomy & Astrophysics, University of
Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada  David A. Dunlap
Department of Astronomy & Astrophysics, University of Toronto, 50 St. George
Street, Toronto, ON M5S 3H4, Canada  J. E. Conway Department of Space, Earth
and Environment, Chalmers University of Technology, Onsala Space Observatory,
439 92, Onsala, Sweden  A. Corongiu Istituto Nazionale di Astrofisica,
Osservatorio Astronomico di Cagliari, Via della Scienza 5, I-09047, Selargius,
Italy  R. Feiler Institute of Astronomy, Faculty of Physics, Astronomy and
Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń,
Poland  E. Fonseca Department of Physics, McGill University, 3600 rue
University, Montréal, QC H3A 2T8, Canada  McGill Space Institute, McGill
University, 3550 rue University, Montréal, QC H3A 2A7, Canada  Department of
Physics and Astronomy, West Virginia University, P.O. Box 6315, Morgantown, WV
26506, USA  Center for Gravitational Waves and Cosmology, West Virginia
University, Chestnut Ridge Research Building, Morgantown, WV 26505, USA  O.
Forssén Department of Space, Earth and Environment, Chalmers University of
Technology, Onsala Space Observatory, 439 92, Onsala, Sweden  M. Gawroński
Institute of Astronomy, Faculty of Physics, Astronomy and Informatics,
Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland  M.
Giroletti Istituto Nazionale di Astrofisica, Istituto di Radioastronomia, via
Gobetti 101, I-40129 Bologna, Italy  M. A. Kharinov Institute of Applied
Astronomy of the Russian Academy of Sciences, Kutuzova Embankment 10, St.
Petersburg, 191187, Russia  C. Leung MIT Kavli Institute for Astrophysics and
Space Research, Massachusetts Institute of Technology, 77 Massachusetts Ave,
Cambridge, MA 02139, USA  Department of Physics, Massachusetts Institute of
Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA  M. Lindqvist
Department of Space, Earth and Environment, Chalmers University of Technology,
Onsala Space Observatory, 439 92, Onsala, Sweden  G. Maccaferri Istituto
Nazionale di Astrofisica, Istituto di Radioastronomia, via Gobetti 101,
I-40129 Bologna, Italy  B. Marcote Joint Institute for VLBI ERIC, Oude
Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands  K. W. Masui MIT Kavli
Institute for Astrophysics and Space Research, Massachusetts Institute of
Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA  Department of
Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave,
Cambridge, MA 02139, USA  R. Mckinven Dunlap Institute for Astronomy &
Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S
3H4, Canada  David A. Dunlap Department of Astronomy & Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada  A.
Melnikov Institute of Applied Astronomy of the Russian Academy of Sciences,
Kutuzova Embankment 10, St. Petersburg, 191187, Russia  D. Michilli Department
of Physics, McGill University, 3600 rue University, Montréal, QC H3A 2T8,
Canada  McGill Space Institute, McGill University, 3550 rue University,
Montréal, QC H3A 2A7, Canada  A. Mikhailov Institute of Applied Astronomy of
the Russian Academy of Sciences, Kutuzova Embankment 10, St. Petersburg,
191187, Russia  C. Ng Dunlap Institute for Astronomy & Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada  A.
Orbidans  Engineering Research Institute Ventspils International Radio
Astronomy Centre (ERI VIRAC) of Ventspils University of Applied Sciences
(VUAS), Inzenieru street 101, Ventspils, LV-3601, Latvia  O. S. Ould-
Boukattine Anton Pannekoek Institute for Astronomy, University of Amsterdam,
Science Park 904, 1098 XH, Amsterdam, The Netherlands  Z. Paragi Joint
Institute for VLBI ERIC, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The
Netherlands  A. B. Pearlman Department of Physics, McGill University, 3600 rue
University, Montréal, QC H3A 2T8, Canada  McGill Space Institute, McGill
University, 3550 rue University, Montréal, QC H3A 2A7, Canada  Division of
Physics, Mathematics, and Astronomy, California Institute of Technology,
Pasadena, CA 91125, USA  McGill Space Institute (MSI) Fellow  FRQNT
Postdoctoral Fellow  E. Petroff Anton Pannekoek Institute for Astronomy,
University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands
Department of Physics, McGill University, 3600 rue University, Montréal, QC
H3A 2T8, Canada  McGill Space Institute, McGill University, 3550 rue
University, Montréal, QC H3A 2A7, Canada  Veni Fellow  M. Rahman Sidrat
Research, PO Box 73527 RPO Wychwood, Toronto, ON M6C 4A7, Canada  P. Scholz
Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St.
George Street, Toronto, ON M5S 3H4, Canada  K. Shin MIT Kavli Institute for
Astrophysics and Space Research, Massachusetts Institute of Technology, 77
Massachusetts Ave, Cambridge, MA 02139, USA  Department of Physics,
Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA
02139, USA  K. M. Smith Perimeter Institute for Theoretical Physics, 31
Caroline Street North, Waterloo, ON, N2L 2Y5, Canada  I. H. Stairs Dept. of
Physics and Astronomy, University of British Columbia, 6224 Agricultural Road,
Vancouver, BC V6T 1Z1  G. Surcis Istituto Nazionale di Astrofisica,
Osservatorio Astronomico di Cagliari, Via della Scienza 5, I-09047, Selargius,
Italy  S. P. Tendulkar Department of Astronomy and Astrophysics, Tata
Institute of Fundamental Research, Mumbai, 400005, India  National Centre for
Radio Astrophysics, Post Bag 3, Ganeshkhind, Pune, 411007, India  W. Vlemmings
Department of Space, Earth and Environment, Chalmers University of Technology,
Onsala Space Observatory, 439 92, Onsala, Sweden  N. Wang Xinjiang
Astronomical Observatory, 150 Science 1-Street, Urumqi, Xinjiang 830011, China
J. Yang Department of Space, Earth and Environment, Chalmers University of
Technology, Onsala Space Observatory, 439 92, Onsala, Sweden  J. Yuan
Xinjiang Astronomical Observatory, 150 Science 1-Street, Urumqi, Xinjiang
830011, China K. Nimmo<EMAIL_ADDRESS>
###### Abstract

Fast radio bursts (FRBs) are extragalactic radio flashes of unknown physical
origin (Petroff et al., 2019; Cordes & Chatterjee, 2019). Their high
luminosities and short durations require extreme energy densities, like those
found in the vicinity of neutron stars and black holes. Studying the burst
intensities and polarimetric properties on a wide range of timescales, from
milliseconds down to nanoseconds, is key to understanding the emission
mechanism. However, high-time-resolution studies of FRBs are limited by their
unpredictable activity levels, available instrumentation and temporal
broadening in the intervening ionised medium. Here we show that the repeating
FRB 20200120E (Bhardwaj et al., 2021) can produce isolated shots of emission
as short as about $60$ nanoseconds in duration, with brightness temperatures
as high as $3\times 10^{41}$ K (excluding relativistic effects), comparable to
‘nano-shots’ from the Crab pulsar. Comparing both the range of timescales and
luminosities, we find that FRB 20200120E bridges the gap between known
Galactic young pulsars and magnetars, and the much more distant extragalactic
FRBs. This suggests a common emission mechanism spanning many orders of
magnitude in timescale and luminosity. While the burst timescales and
luminosities can be explained by magnetic reconnection in the vicinity of an
isolated, young, highly magnetised neutron star, the localisation of FRB
20200120E to a globular cluster (Kirsten et al. submitted) also opens the
possibility of magnetic reconnection in an older binary system featuring
compact stars or a black hole.

Fast Radio Bursts

##  1 Introduction

In the late 1960s, the discovery of radio pulsars was enabled by observations
using an unprecedented time resolution of $50-100$ ms (Hewish et al., 1968).
The subsequent discovery of the Crab pulsar (Staelin & Reifenstein, 1968, also
known as PSR B0531+21) eventually led to the insight that its giant pulses
(Heiles & Campbell, 1970; Staelin, 1970) show structure on timescales as short
as 0.4 nanosecond (Hankins et al., 2003). These ‘nano-shots’ have
exceptionally high brightness temperatures of $\sim 10^{40}$ K (Hankins &
Eilek, 2007). The more recent discovery of the fast radio burst (FRB)
phenomenon (Lorimer et al., 2007; Thornton et al., 2013) has shown us that
nature produces $\sim$ millisecond duration radio flashes that are $10^{9-12}$
times more luminous than those of average pulsars (for reviews, see Petroff et
al., 2019; Cordes & Chatterjee, 2019).

As with pulsars, the recording of raw voltage data can allow us to study FRB
signals on timescales of microseconds ($\upmu$s) down to nanoseconds (ns).
Thus far, such observations have demonstrated that FRB signals can show
temporal structure on timescales of tens of microseconds down to even just a
few microseconds (Farah et al., 2018; Michilli et al., 2018a; Cho et al.,
2020; Nimmo et al., 2021). Nimmo et al. (2021) also discuss how individual
FRBs can display a dynamic range of temporal structure of 500, from a few
microseconds up to milliseconds. The temporal behaviour of FRBs — along with
their polarimetric properties (Michilli et al., 2018a; Day et al., 2020) and
time-frequency structure (Hessels et al., 2019) — provide key inputs for
distinguishing between the dozens of proposed source models and emission
mechanisms (see Platts et al., 2019, for a living catalogue of FRB theories).
These burst properties can also help to observationally distinguish the
populations of repeating and apparently one-off FRBs, and to thereby
strengthen the case that they have physically distinct origins (e.g. CHIME/FRB
Collaboration et al., 2019; Fonseca et al., 2020)

Kirsten et al. (submitted) recently associated the repeating FRB 20200120E
(Bhardwaj et al., 2021) with [PR95] 30244, a globular cluster that is part of
the M81 galactic system. At a distance of 3.63 Mpc, FRB 20200120E is the
closest-known extragalactic FRB, bridging the gap between the putative
Galactic FRB source SGR 1935$+$2154 (a known magnetar at a distance of $\sim
3-10$ kpc; CHIME/FRB Collaboration et al., 2020a; Bochenek et al., 2020; Zhong
et al., 2020) and FRB 20180916B at a luminosity distance of 149 Mpc (Marcote
et al., 2020). Given its remarkable proximity, FRB 20200120E is a promising
source for multi-wavelength follow-up studies. At the same time, its burst
‘envelopes’ (which we define as the total temporal extent of all sub-burst
components) have been found to be atypically narrow ($100-300$ $\upmu$s)
compared to other repeating FRBs (Kirsten et al. submitted; Bhardwaj et al.,
2021; CHIME/FRB Collaboration et al., 2019; Fonseca et al., 2020). This
suggests that FRB 20200120E could be an excellent source to study at the
highest-possible temporal resolutions.

Here we present a spectro-polarimetric study of 4 FRB 20200120E bursts
detected with the Effelsberg 100-m telescope during a broader localisation
campaign using _ad hoc_ interferometric observations with dishes from the
European Very-long-baseline Interferometry (VLBI) Network (EVN). In §2 we
describe the observations and data; in §3 we present the analysis and results;
in §4 we discuss the implications of our findings for understanding the origin
and emission mechanism of repeating FRBs; and finally we summarize our results
in §5.

##  2 Observations & Data

We observed FRB 20200120E (Bhardwaj et al., 2021) with an ad hoc EVN array at
1.4 GHz, on 2021 February 20 UT 1700 – 2200, and 2021 March 7 UT 1545 – 2045.
For details on the interferometric array configuration and localisation
results, see Kirsten et al. (submitted). Since this was an interferometric
campaign, we regularly observed a phase calibrator source (5.5 minutes on
target, 2.0 minutes on the calibrator). The total time on target was 2.93 hr
per observation.

With the 100-m Effelsberg telescope, we recorded dual circular polarization
raw voltages (R and L) using 32 MS/s real sampling per 16-MHz subband and
2-bit samples written in VDIF format (Whitney et al., 2010). The total
bandwidth of the data is 256 MHz. In parallel, we also recorded total
intensity filterbanks using the PSRIX pulsar backend (Lazarus et al., 2016).
The PSRIX data were recorded with a time and frequency resolution of 102.4
$\upmu$s and 0.49 MHz, respectively, and a total bandwidth of 250 MHz. Both
data sets were searched for bursts (§3.1).

For further analysis of the burst properties — using full polarimetric
information at a range of time and frequency resolutions — we generated
filterbank data from the raw voltages using both SFXC (Keimpema et al., 2015)
and digifil (van Straten & Bailes, 2011).

###  2.1 SFXC

Using SFXC (phased array branch111https://github.com/aardk/sfxc/tree/phased-
array), we produced low time resolution filterbank data (8 $\upmu$s), in order
to have sufficient frequency resolution (125 kHz) to study frequency structure
due to scintillation, and to determine the rotation measure (RM). The data are
coherently dedispersed within the 16-MHz subbands, and incoherently
dedispersed between the subbands. Using dspsr (van Straten & Bailes, 2011) we
created archive files containing each burst at the resolution of the
filterbank data, and remove frequency channels from the data that are
contaminated by radio frequency interference using the psrchive tool pazi
(Hotan et al., 2004).

The real-sampled VDIF data with 16-MHz subbands allow for up to 31.25 ns time
resolution. Due to the Fast Fourier Transform-based (FFT-based) correlation
and delay corrections implemented in SFXC (phased array), the practical time
resolution limit is 125 ns. In this case, the data have 4 channels per
subband. Since SFXC does not window the data before the FFT, potential
spectral leakage artefacts are a concern, especially in the case of a low
number of channels per subband. This data is used to study the polarimetry at
high time resolution.

Additionally, we output coherently dedispersed total intensity (Stokes I) at
the original data sampling rate (i.e. no channelization within subbands) using
the SFXC bolometer branch222https://github.com/aardk/sfxc/tree/bolometer. Here
we have no concerns of spectral leakage or any other artefacts that may be
introduced at the channelization stage of the processing.

###  2.2 digifil

We also used digifil to produce data at the highest-possible time resolution,
in order to verify the results presented in this work. digifil utilises a
convolving filterbank, which reduces spectral leakage effects (van Straten &
Bailes, 2011). However, digifil converts to complex-sampled data internally,
resulting in a factor of 2 decrease in the time resolution for a given number
of channels (for the Nyquist limit). Thus, the best time resolution we can
achieve with our 16-MHz subbands is 62.5 ns. digifil produces one filterbank
file per subband, and the subbands are combined with incoherent dedispersion.

In both the digifil and SFXC data, the incoherent dedispersion between
subbands is performed with integer sample shifts.

##  3 Analysis

Here we first discuss the burst search, and then the spectro-polarimetric
analysis of the bursts at low (8 $\upmu$s) and high (down to 31.25 ns) time
resolution, respectively.

###  3.1 Burst search

We performed two independent analyses on the single-dish Effelsberg data to
search for bursts from FRB 20200120E. The voltage data were converted to
total-intensity filterbanks using digifil with time and frequency resolutions
of 64 $\upmu$s and 125 kHz, respectively. These data were searched using a
Heimdall-based pipeline and burst candidates were classified using the machine
learning classifier, FETCH (Agarwal et al., 2020). A more detailed description
of this pipeline was presented in Kirsten et al. (2021). The PSRIX pulsar
backend data were analysed using a PRESTO-based pipeline (Ransom, 2001), and
single pulse candidates were classified using an automated classifier based on
Michilli et al. (2018b). We recorded a test pulsar scan of PSR B0355+54 to
inspect the data quality.

Four bursts from FRB 20200120E were discovered in the search of the raw
voltages using the Heimdall-based search (B1 and B2 on 2021 February 20; B3
and B4 on 2021 March 7). Only three of the four bursts were found in the PSRIX
data because burst B1 occurred during the $\sim$ 40 s latency between the
start of the VLBI recording and the pulsar backend recording. Initially, B2
was flagged as radio frequency interference in the PSRIX data by the automated
classifier (Michilli et al., 2018b) due to strong scintillation structure.
Throughout this work we label the bursts B$n$, ordered according to their
arrival time, and matching the nomenclature used in Kirsten et al.
(submitted).

###  3.2 Lower-time-resolution data

As described in §2, we produce 8 $\upmu$s time resolution data using the
software correlator SFXC. The data are coherently (within subbands) and
incoherently (between subbands) dedispersed to $87.75$ pc cm-3, which is
within $\sim 0.003$ pc cm-3 of the value we measured using higher time
resolution data (see §3.3). This $0.003$ pc cm-3 offset corresponds to a
dispersive delay, across the burst extent in frequency, that is less than the
time resolution.

####  3.2.1 Stokes I

In Figure 3, we show the dynamic spectra and full polarization profiles of the
four bursts (Stokes I is shown by the black line).

We performed a 2-dimensional Gaussian fit to the burst dynamic spectra, to
determine the burst extents in time and frequency. The measured widths were
clearly underestimated compared with what can be seen by eye in the dynamic
spectra, likely since the bursts are not well-modelled by a 2-dimensional
Gaussian function. In the case of B1, B3 and B4, we use the Gaussian mean in
time as the Time$=$0 reference in Figure 3, and use this to calculate the
burst time of arrival corrected to the Solar System Barycenter at infinite
frequency, reported in Table 1. For B2, since there are two clear burst
components, we fit a 2-dimensional Gaussian to each and determined the
Time$=$0 reference as the center of the means of those Gaussians. Note that we
do not fit pulse broadening functions to estimate the scattering timescale
since the estimated scattering timescale from the Milky Way interstellar
medium is $\sim$ 50 ns ($\ll 8$ $\upmu$s) at 1.4 GHz (Cordes & Lazio, 2002),
and is consistent with the frequency structure we attribute to scintillation
(see § 4).

To more accurately determine the burst widths, we performed a 2-dimensional
autocorrelation of the dynamic spectra, and fit these with 2-dimensional
Gaussian functions (Figure 4). Note the zero-lag noise spike is removed from
this autocorrelation function (ACF). We convert the standard deviation of this
Gaussian fit (in both time and frequency) to a full-width at half-maximum
(FWHM) by multiplying the standard deviation by the factor
$2\sqrt{2\mathrm{ln}(2)}$. We report the burst time width ($1/\sqrt{2}\
\times$ FWHM) and frequency extent (FWHM) in Table 1. In Figure 3, the colored
bars below each burst profile indicate the $\pm$ 2$\sigma$ width used for
calculations of the fluence and polarization fractions.

In addition to the frequency extent measured with the 2-dimensional ACF, there
is another, narrower frequency scale evident in the one-dimensional frequency
ACF (or simply by eye in the dynamic spectra of the bright bursts). Shown in
Figure 5 is the frequency ACF after subtracting the larger frequency scale
Gaussian. We perform a least-squares fit of a Lorentzian function to the
center of this ACF (defined by eye using the clearly visible central feature
in the ACF; Figure 5). A Lorentzian frequency ACF is expected for
scintillation (Rickett, 1990). The fit function is of the form

$\frac{a}{x^{2}+\nu_{\text{scale}}^{2}}+b,$ (1)

where $a$ is the amplitude, $b$ is a vertical offset, and $\nu_{\text{scale}}$
is the scintillation bandwidth (defined as the half-width at half-maximum of
the ACF; Rickett 1990). The scintillation bandwidth measurements are reported
in Table 1, and are compared with Galactic electron density models in §4.

Each burst profile, in signal-to-noise ratio (S/N) units, is then converted to
physical units (flux density, Jy) using the radiometer equation (Cordes &
McLaughlin, 2003), using typical values for Effelsberg’s 1.4 GHz receiver
temperature (20 K) and gain (1.54 Jy K-1). We expect these system values to be
accurate to within 20%, which dominates the errors on the peak flux density
and fluence. We additionally consider a sky background temperature of 0.8 K,
by extrapolating from the 408 MHz map (Remazeilles et al., 2015), using a
spectral index of $-$2.7 (Reich & Reich, 1988), and 3 K from the cosmic
microwave background (Mather et al., 1994). We report the peak S/N, peak flux
density and fluence (measured in the $\pm$ 2$\sigma$ width region) in Table 1.
We also report the isotropic-equivalent spectral luminosity of the bursts,
taking the distance to FRB 20200120E as 3.63 $\pm$ 0.34 Mpc (Kirsten et al.
submitted).

####  3.2.2 Polarization

To study the polarization properties of the bursts, we must first calibrate
the data. In these observations, we did not record a noise diode scan to use
for delay calibration; instead, we use the test pulsar data, also taken to
inspect the general data quality, to calibrate the polarimetric data. This
analysis strategy has been used successfully in previous work to determine the
polarimetric properties of radio bursts from the Galactic magnetar SGR
1935+2154, detected using voltage data of the Westerbork RT1 VLBI backend
(Kirsten et al., 2021), and also in a study of the repeating FRB 20180916B,
using data from the Effelsberg telescope as part of an EVN campaign (Nimmo et
al., 2021). Since we detected bursts at two separate epochs, we calibrate the
data using the test pulsar scan closest in time to the bursts. B1 and B2 are
$<\,1$ hr from the PSR B0355+54 calibration scan, and B3 and B4 are $\sim 4$
hr and $<\,2$ hr from the PSR B0355+54 scan, respectively.

The data could exhibit leakage between the polarization signals, which we
assume only significantly affects Stokes V (defined as V=LL$-$RR using the
PSR/IEEE convention; van Straten et al. 2010). In the pulsar data, without
calibrating the leakage, we reproduce the circular polarization fraction to
within 3% and 1% of the published values (Gould & Lyne, 1998), for the Feb 20
and Mar 7 epochs, respectively. We, therefore, apply no leakage calibration.

A delay between the polarization hands is more crucial to correct for since it
can significantly impact our interpretation of the linear polarization
fraction and RM. Using the known RM of PSR B0355+54, 79 rad m-2 (Taylor et
al., 1993), we performed a brute-force search for the delay between
polarization hands, $D$, that maximises the linear polarization, by rotating
the data using the factor

$\mathrm{e}^{-2i\mathrm{RM}({c^{2}}/{\nu^{2}})}\mathrm{e}^{-2i\nu\pi D},$ (2)

where $c$ is the speed of light and $\nu$ is the frequency in Hz. We searched
for delays between $-15$ and $15$ ns, in steps of 0.01 ns. Note that previous
work with the VLBI recorder at Effelsberg showed an instrumental delay of 5.4
ns (Nimmo et al., 2021). The estimated delays are $-0.18$ ns and $-4.11$ ns
for the Feb 20 and Mar 7 observations, respectively.

After removing the effect of the estimated delays, we performed RM synthesis
(Brentjens & de Bruyn, 2005) on the burst data to estimate the RMs of the
bursts. The Faraday spectra for each burst are shown in the top panel of
Figure 6.

To refine the RM and delay measurements further, we performed a joint least
squares fit of Stokes Q and U spectra normalised by the linear polarization
L$=\sqrt{\mathrm{Q}^{2}+\mathrm{U}^{2}}$, using the following equations

$Q/L=\cos(2(c^{2}\mathrm{RM}/\nu^{2}+\nu\pi D+\phi)),$ (3)
$U/L=\sin(2(c^{2}\mathrm{RM}/\nu^{2}+\nu\pi D+\phi)),$ (4)

where $\phi$ is a linear combination of the absolute angle of polarisation on
the sky (referenced to infinite frequency) and the phase difference between
the R and L polarisation channels. The estimates of the delay and RM are given
as initial guesses to the fit, and we simultaneously fit the pulsar and the
two bursts from the same observational epoch. We force the delay to be the
same between the pulsar and FRB data, fix to the known RM of the pulsar (79
rad m-2), and initially we allow for a different RM per burst. The measured
delays are $-0.22$ $\pm$ 0.02 ns and $-4.16$ $\pm$ 0.03 ns, for the Feb 20 and
Mar 7 observations, respectively, and the measured RMs are presented in Table
2. The QU-fits are shown in Figure 6. The measured RMs have large
uncertainties due to covariances between the fit parameters, which is
difficult to alleviate due to the low number of rotations (due to either RM or
delay) across the burst frequency extent. We conclude that the bursts in this
work have consistent RM values (B2’s RM is slightly over $3\sigma$ from B3,
but this apparent difference should be verified in future observations of this
source using an independent delay calibrator), which is also in agreement with
the previously reported RM ($-29.8$ rad m-2; Bhardwaj et al. 2021).

The data for each burst were then corrected for the measured delay and RM. The
polarization position angle (PPA) was calculated using the following equation:

$\mathrm{PPA}=0.5\,\mathrm{arctan}\left(\frac{U}{Q}\right),$ (5)

and, to correct for the parallactic angle, this is rotated by

$\theta=2\tan^{-1}\left({\frac{\sin({\rm HA})\cos(\phi_{\rm
lat})}{(\sin(\phi_{\rm lat})\cos(\delta)-\cos(\phi_{\rm
lat})\sin(\delta)\cos({\rm HA})}}\right),$ (6)

where ${\rm HA}$ is the hour angle of the burst, $\phi_{\rm lat}$ is the
latitude of the Effelsberg telescope, and $\delta$ is the declination of FRB
20200120E. Due to the fact that our observations did not feature an
independent polarization calibrator scan, there remains an uncalibrated
absolute phase offset in the data. Therefore, we cannot compare the PPAs
between our two observational epochs, or with other PPA measurements of FRB
20200120E. By allowing for individual RM values per burst, we find that B1 and
B2 exhibit a $\Delta$PPA of 28.5∘, and the $\Delta$PPA between B3 and B4 is
21.7∘. The unbiased linear polarization is computed following Everett &
Weisberg (2001), where

$L_{\rm unbias}=\begin{cases}\sigma_{I}\sqrt{\left(\frac{L_{\rm
meas}}{\sigma_{I}}\right)^{2}-1},&{\text{if}~{}\frac{L_{\rm
meas}}{\sigma_{I}}\geq 1.57}\\\ 0,&\text{otherwise}\end{cases}$ (7)

where $L_{\rm meas}=\sqrt{Q^{2}+U^{2}}$, and $\sigma_{I}$ is the standard
deviation in the off-burst Stokes I data.

The bursts are highly linearly polarized ($>90$%), and exhibit little-to-no
evidence for circular polarization. The linear and circular fractions, as well
as the PPA offset from a weighted mean PPA of bursts from a single epoch, are
presented in Table 2, and the polarization profile and PPA for each burst is
shown in Figure 3.

It has been seen in the literature that some repeating FRBs exhibit a constant
PPA ($\mathrm{\Delta(PPA)<\,10^{\circ}}$) and RM per observing epoch (e.g.
Michilli et al. 2018a, Nimmo et al. 2021). Therefore, in addition to the
individual burst RM measurements, we fit for a global RM per observing epoch.
In this global fit, we find that the PPA of B1 and B2 differ by 68.3∘ (Table
2). This large $\Delta$PPA may result from the low S/N of burst B1. The
$\Delta$PPA between B3 and B4 in this global fit is 23.6∘, comparable to the
difference we measured in the independent-RM fit above, owing to the very
similar RM values in the independent fits.

###  3.3 High-time-resolution data

At sufficient time resolution, the bursts detected from FRB 20200120E at 1.4
GHz are extremely narrow in duration (FWHM on the order of $10-100$ $\upmu$s;
Table 1, Figure 3). In the case of burst B3, there is a sharp unresolved spike
in the 8 $\upmu$s resolution profile (Figure 3), motivating us to study these
data at even higher time resolution. Galactic electron density models predict
pulse broadening due to scattering in this line-of-sight of only $\sim$ 50 ns
at 1.4 GHz (Cordes & Lazio 2002; see also Figure 5), further motivating a
study at the highest-possible time resolution.

####  3.3.1 Dispersion Measure

As explained in §2, the raw voltages were stored, giving us a limiting
resolution of 31.25 ns. At this time resolution, the DM must be correct to
$<0.0005$ pc cm-3 to avoid DM smearing across the 256 MHz bandwidth larger
than the time bin width.

To limit potential spectral leakage artefacts in the SFXC data (see §2), we
produced 500 ns time resolution filterbank files, with 16 channels per subband
(1 MHz channels), at a range of DM values around the expected DM (determined
by eye in the dynamic spectrum of burst B3). These data are both coherently
and incoherently dedispersed to limit DM smearing within each channel, and
across the band. These data were then downsampled in time to 1 $\upmu$s (i.e.
a downsampling factor of 2). The reason for producing the data products in
this way, as opposed to creating 1 $\upmu$s resolution data with higher
frequency resolution, is to minimise smearing due to incoherent dedispersion
between subbands (integer bin shift). In Figure 7, we plot the peak S/N of the
burst profile as a function of DM, and fit a Gaussian function to determine
the best DM. We search for a DM in the range $87.74-87.765$ pc cm-3 in steps
of 0.001 pc cm-3 and find that the best DM is DM$=87.7527\,\pm\,0.0003$ pc
cm-3, where the uncertainty is determined by $\sigma/\mathrm{A}$, where
$\sigma$ and $A$ are the standard deviation and amplitude of the Gaussian fit.
This DM is close to, but still $>9\sigma$ lower than the previously reported
measurement of 87.782 $\pm$ 0.003 pc cm-3 (Bhardwaj et al., 2021, where the
quoted value is based on the average of 3 bursts). We note that the range of
DMs searched do not include the previously measured DM (Bhardwaj et al.,
2021), since the dynamic spectrum of burst B3 is visibly over-corrected when
dedispersed to this value. Both measurements of the DM use the same dispersion
constant of 1/(2.41$\times 10^{-4}$) MHz2 pc-1 cm3 s. The observed difference
in DM could be due to unresolved time-frequency structure in the Bhardwaj et
al. (2021) results, often seen in FRBs (Hessels et al., 2019). Future
measurements of the DM will be crucial to determine if there is a frequency or
time dependence on the DM.

In the right panel of Figure 7 we plot the burst profile and dynamic spectrum
coherently (within channels) and incoherently (between subbands) dedispersed
to this best-fit DM. This analysis was repeated on digifil filterbank data
products generated with 62.5 ns time and 16 MHz frequency resolution,
coherently and incoherently dedispersed, and then downsampled to 1 $\upmu$s
time resolution. We find a consistent DM value from digifil and SFXC data
(noting also that both softwares use the same dispersion constant of
1/(2.41$\times 10^{-4}$) MHz2 pc-1 cm3 s).

####  3.3.2 Full polarisation

We use SFXC to generate a 125 ns time resolution full polarization filterbank
containing burst B3, where each channel is 4 MHz. The polarization data were
calibrated and Faraday de-rotated using the delay and RM, respectively,
measured from the lower-time-resolution data (see §3.2.2). In Figure 8, we
show the frequency-averaged polarization profile of burst B3 (where we summed
over the frequency range 1254 – 1430 MHz), and the PPA across the burst
profile. The $\sim$100 ns – 1 $\upmu$s structures are highly linearly
polarized, consistent with the polarization properties at lower time
resolution. The PPA varies between each shot of emission by up to a few 10s of
degrees. In these data we have 22 degrees of freedom, since 125 ns $\times$ 4
MHz $=$ 0.5, and we average over a total of 44 channels. In this regime it is
possible that some of the scatter in the PPA arises due to the fact that the
Stokes parameters are only physically meaningful with sufficient averaging
(van Straten, 2009). Although we note that the scatter is not completely
random (the PPAs are somewhat contained), and thus suggest the PPA is varying
on timescales of $\sim 100$ ns.

####  3.3.3 Total intensity at 31.25 ns time resolution

As is clear in the dynamic spectrum of B3 presented in both Figure 3 and
Figure 7, there is an exceptionally bright scintle where the majority of the
flux falls within one subband ($1318-1334$ MHz). With SFXC, we generated 31.25
ns time resolution data (16 MHz channels, i.e. one channel per subband),
coherently dedispersed to the best-fit DM = 87.7527 pc cm-3. By studying only
the bright subband, the accuracy of the incoherent dedispersion between
subbands is not a concern (sub-bin shifts are not implemented here, since such
corrections can also introduce artefacts). We present the bright scintle of B3
at 31.25 ns time resolution in Figure 1. In the uncertainty principle limit
$\delta t\delta\nu\sim 1$, where $\delta t$ and $\delta\nu$ are the time and
frequency resolution (respectively) of individual samples, the off-burst noise
is $\chi^{2}$-distributed with 2 degrees of freedom. Both the right- and left-
hand polarizations are individually Gaussian distributed, but when converting
from voltage to intensity, the noise becomes positive-biased (note that the
noise again approaches a Gaussian distribution when averaging many samples
together). It is clear that there is barely resolved burst structure in these
data implying shots of emission with a duration as short as $\sim 60$ ns.

In Figure 9, we present each coherently dedispersed subband of burst B3
(covering the frequency extent of the burst, i.e. 1254 – 1430 MHz) at 31.25 ns
resolution. This is essentially the burst dynamic spectrum with poor frequency
resolution. Out of the 11 subbands plotted, we selected the four brightest
subbands that contain the most burst structure, and computed the ACF of the
time profile. These ACFs were averaged together and shown in the lower right
sub-figure of Figure 9. The reason for computing the ACF in this manner, as
opposed to creating a frequency-averaged profile and computing the ACF, is to
limit the smearing due to inaccuracies in the incoherent dedispersion (the
subbands are shifted by an integer number of bins). There are three clear
timescales in this ACF, measured by fitting a Lorentzian function for each
timescale to the ACF (out to a time lag that is chosen by eye, to help the
fitting distinguish between multiple timescales). We measure a 35.6 $\upmu$s
timescale, which is the same scale we are seeing in the 1$\sigma$ burst width
measured in the lower time resolution data. In addition, there is a clear 1.11
$\upmu$s timescale measured in the ACF, and even a shorter timescale (40 ns)
consistent with temporal structure on the few-bin level.

The burst power spectrum is presented in the upper right sub-figure of Figure
9. We perform a Bayesian maximum likelihood fit of a power law (red noise)
plus constant (white noise) of the form

$f(\nu)=A\nu^{-\alpha}+C,$ (8)

where A is the amplitude, $\alpha$ is the slope of the power law, and $C$ is a
white noise component, to the power spectrum, using the Stingray modelling
interface (Huppenkothen et al., 2019). Additionally, we fit a red noise plus
white noise plus Lorentzian model to the data, to search for the presence of a
quasi-periodic oscillation (QPO). This search was motivated by the hint of
structure in the ACF of bursts from FRB 20180916B (Nimmo et al., 2021), and
additionally, the low amplitude, wide frequency bumps seen by eye in the
downsampled power spectrum (Figure 9). First, we compute the Bayesian
Information Criterion for each model fit, defined as

${\rm BIC}=-2{\rm ln}(L)+k{\rm ln}(n),$ (9)

where $L$ is the maximum likelihood of the fit, $k$ is the number of
parameters in the model, and $n$ is the number of data points. A lower BIC
implies the data is better represented by that model, although it does not
mean that the preferred model is a good fit to the data. Since the number of
model parameters $k$ is included in the BIC, models with more parameters are
penalized to avoid overfitting the data. Here we computed the $\Delta$ BIC =
BIC${}_{PL}-$BICPL+lor, where BICPL is the BIC of the red noise model, and
BICPL+lor is the BIC of the red noise plus QPO model. For B3, we measure a
$\Delta$ BIC $=-12.1$, which is significantly in favor of the red noise model.
We then measure the goodness-of-fit p-value of the red noise model, which is
the fraction of 100 simulations (using the MCMC package emcee; Foreman-Mackey
et al. 2013) with a maximum likelihood lower than the likelihood of our fit.
This p-value is 0.53, implying the fit to the data is good. Finally, we test
the significance of the highest outlier in the residuals of our best-fit
model. The residuals are defined as

$R(\nu)=\frac{2P(\nu)}{M(\nu)},$ (10)

for the power spectrum $P(\nu)$ and best-fit model $M(\nu)$. By simulating 100
power spectra from the posterior distribution (using emcee) and computing the
highest outlier for each simulation, we can compute a p-value (the fraction of
simulated outliers that are higher than our measured outlier). We find no
significant outliers in the residuals, implying we have no evidence of a QPO
in the data.

For comparison, we repeated the analysis for burst B2 and B4 (the other bursts
in our sample with sufficient S/N), and show that they too exhibit a timescale
on the order of 10 $\upmu$s, likely the same scale we measure in the lower
time resolution data (Figures 10 & 11). For B4, we additionally measure a
short-temporal scale suggesting that there is temporal structure of a few-bins
in the B4 31.25 ns profile (Figure 11). Although, it is worth noting that the
height of this narrow ACF feature relative to the wider ACF feature (height of
the cyan Lorentzian relative to the green Lorentzian in Figures 9 and 11) is
smaller for B4 than B3, implying either that the S/N of these temporal
fluctuations are lower, or that there are fewer temporal features on this
timescale. In B2, we see no evidence for power on shorter timescales in the
ACF (Figure 10). Bursts B2, B3 and B4 are all consistent with red noise, with
B2 and B4 exhibiting a steeper power law ($\alpha=1.85\pm 0.04$ and $2.04\pm
0.05$, respectively) than B3 ($\alpha=1.46\pm 0.05$). The results of the ACF
and power spectra analyses are reported in Table 3.

####  3.3.4 Isolated shots or Amplitude Modulated Noise?

Due to strong spectral dips near the subband edges, even higher frequency
resolution is needed in order to robustly correct the bandpass and compare
individual bin spectra with each other. We therefore created a 1 $\upmu$s, 500
kHz filterbank using SFXC. Shown in Figure 12 is the correlation coefficient
between individual 1 $\upmu$s time bins above a S/N threshold of 9 in burst
B3, as a function of their time separation. We find that the correlation
coefficients have a geometric mean S/N weighted average of 0.31. The
scintillation frequency structure is expected to be perfectly correlated
within the duration of the burst (we observe that the B1 and B2 spectra,
separated by 4.3 minutes, are correlated; Figure 13), while the Amplitude
Modulated Polarized Shot Noise frequency structure will change depending on
the degree of polarisation (the Scintillating Amplitude Modulated Polarized
Shot Noise model (SAMPSN); Cordes et al. 2004). SAMPSN predicts a correlation
coefficient of

$\rho=\frac{1}{2+p_{\rm frac}^{2}},$ (11)

where $p_{\rm frac}$ is the total polarization fraction. Our measured
$\rho=0.31$ implies that the signal is 100 % polarized, consistent with the
high linear polarization fraction we measure in the frequency-averaged burst
profiles (Figure 8). Additionally, we find that the shot energy distribution
of B3 (shown in the top right panel of Figure 1) is $\chi^{2}$-distributed
with $2$ degrees of freedom, again consistent with 100 % polarized SAMPSN
(Cordes, 1976). As is clear in the B3 burst profile at 31.25 ns resolution
(Figure 1), the burst temporal structure is made up of individual sub-
microsecond shots of emission.

The question remains whether the short timescale structures we observe are
isolated shots of emission or noise fluctuations consistent with the
$\chi^{2}$-distribution (with $2$ degrees of freedom). In the latter case,
this still implies short-temporal structure in the burst profile, but without
the ability to distinguish individual shots, and instead we see the
superposition of many shots. In the case of B3, most of the structure at the
highest possible time resolution is at least 2 bins wide ($2\times 31.25$ ns;
see Figure 1), supporting that these structures are isolated shots. To measure
the significance of the maximum S/N structure at Time $=$ 0 in the third panel
of Figure 1 relative to the local distribution, we fit a
$\chi^{2}$-distribution with 2 degrees of freedom to the distribution of S/N
values within $\pm 1.5625\,\upmu$s ($\pm 50$ bins) of the maximum value,
excluding the feature we wish to calculate the significance of. We take this
range of bins, to ensure that we are including enough samples to measure the
local distribution, and to ensure we are not taking too many samples such that
we lose the information of the burst envelope locally (since there are
temporal fluctuations on the few $\upmu$s level in the 1 $\upmu$s resolution
data; see Figure 12). Note that since we cannot distinguish (by eye) between
temporal spikes that are due to amplitude-modulated noise versus individual
emission spikes, we include all time bins (within the range mentioned),
excluding the central feature, in the distribution; therefore, the
probabilities measured are lower-limits. We find that the probability of
drawing this high-S/N, two-bin-wide structure from the distribution is p
$=4\times 10^{-8}\times 100\,{\rm bins}/2=2\times 10^{-6}$. Therefore, we
conclude that this structure is a real isolated shot, as opposed to noise
fluctuations consistent with the $\chi^{2}$-distribution of the amplitude-
modulated noise.

We repeated the same analysis on B2 and B4 in this burst sample. For B2 we
created the temporal profile at 31.25 ns using the subband 1302–1318 MHz, and
for B4 we use subband 1398–1414 MHz: in both cases this is the subband
containing the brightest scintillation feature. In the case of B3, at the
highest time resolution there are temporal fluctuations that are multiple bins
wide. In contrast, the only bright structure in both B2 and B4 at the highest
time resolution are unresolved single-bin spikes. Given that the frequency
extent of the bright scintle is less than the subband width of 16 MHz, this
results in an effective time resolution lower than the sampling resolution.
Single bin spikes in this case are therefore more likely to be consistent with
the noise process. We tested the significance of the brightest unresolved
structure using the same method as described for B3, where in these cases we
take the range $\pm 3.125$ $\upmu$s ($\pm$100 bins) since the 1 $\upmu$s
profiles do not show as clear variations as for B3. The probability of the
highest unresolved spike in B2 and B4 is p $=1\times 10^{-4}\times 200\,{\rm
bins}=0.02$ and p $=4\times 10^{-4}\times 200\,{\rm bins}=0.08$, respectively.
Given the effective resolution argument above, combined with the relatively
high probabilities, there is not strong evidence supporting that these
structures are isolated, unresolved shots of emission. Instead, we conclude
that these features are consistent with the $\chi^{2}$ amplitude-modulated
noise distribution. Additionally, we find a weighted average correlation
coefficient of the individual 1 $\upmu$s time bin spectra (above a S/N of 9)
of 0.19 $\pm$ 0.001 and 0.16 $\pm$ 0.001, significantly offset from the $0.33$
expectation in SAMPSN (Cordes et al., 2004), and the $0.31$ measured from B3,
but also significantly offset from $0$. This is consistent with highly
polarized SAMPSN (similar to B3), where potentially the lower correlation
coefficient can be attributed to one or a combination of low S/N and/or
sparseness of shot pulses.

In Figure 2, we compare the luminosity of the three highest significance shots
of emission in the B3 31.25 ns profile with other short-duration transients,
including the luminosity of the bright $<10\,\upmu$s component of B3 seen in
the 1 $\upmu$s resolution data (Figure 12), and the wider burst envelopes seen
in B1, B2 and B4.

##  4 Discussion

The most striking result of our observations and analysis is the discovery of
a ‘forest’ of sub-microsecond structures in one of the four bursts (B3). In
the case of B3, it appears that the minimum time of variation is around 62.5
ns. For comparison, the Galactic interstellar medium is expected to introduce
a broadening due to scattering of $\sim 50$ ns (at 1.4 GHz) along this line-
of-sight (Cordes & Lazio, 2002), in rough agreement with our measured
scintillation bandwidth ($1/(2\pi\Delta\nu_{\rm scint})\sim 27$ ns). Hence,
multi-path propagation due to the Milky Way foreground may ultimately limit
the effective time resolution at 1.4 GHz and motivates observations at higher
radio frequencies. The sub-microsecond forest of shots in B3 is similar to
what is sometimes seen at higher radio frequencies ($\sim 10$ GHz) in the
giant pulses of the Crab pulsar (e.g. Jessner et al., 2010, see their Figures
$2-5$). Temporal structure down to sub-nanosecond timescales has been observed
in Crab pulsar giant pulses, often referred to as ‘nano-shots’ (Hankins et
al., 2003). Crab nano-shots are known to be extremely energetic, with
brightness temperatures reported up to $10^{41}$ K (ignoring relativistic
effects; Hankins & Eilek, 2007). The sub-microsecond shots in B3 exhibit a
comparable, extremely high, brightness temperature (again, ignoring
relativistic effects; Figure 2). This is at least four orders of magnitude
higher than typically seen from the FRB population ($10^{32}$–$10^{37}$ K;
Petroff et al., 2019). We show also that bursts B2, B3 and B4 are consistent
with the Scintillating Amplitude Modulated Polarized Shot Noise model, which
has been used to describe many aspects of pulsar emission, including giant
pulses from the Crab pulsar (Cordes et al., 2004; Karuppusamy et al., 2010).
However, only B3 is observed to resolve down to sub-microsecond individual
shots of emission. This is similar to observations of the Crab pulsar, where
not all Crab pulsar giant main pulses resolve down to individual nano-shots
(Hankins & Eilek, 2007; Jessner et al., 2010). Furthermore, most Crab giant
main pulses consist of at least one broadband ‘micro-burst’, with a
characteristic time of a few microseconds (Hankins & Eilek, 2007; Hankins et
al., 2016), similar to the structure that can be seen in burst B3 at 1
$\upmu$s time resolution and consistent with the measured 1.11 $\upmu$s
timescale in the temporal ACF (Figures 12 & 9). Sometimes the micro-bursts are
seen to resolve down to individual narrowband nano-shots, completely
consistent with the features seen at 31.25 ns in burst B3, which also appear
to be narrowband (see Figure 9).

Previously, Hessels et al. (2019) have also discussed how the high linear
polarization fraction, low circular polarization fraction, and flat PPA of
bursts from the repeater FRB 20121102A are similar in phenomenology to the
high-frequency Crab giant inter-pulses (Hankins et al., 2016) — but dissimilar
to the giant pulses associated with the main pulse of the Crab pulsar. In the
case of the Crab pulsar, PPA variations between nano-shots/micro-bursts are
also detected (Hankins et al., 2016, see their Figures $4-6$ and 8). In fact,
sometimes the PPA appears randomly scattered during forests of nano-shots,
though part of this could be due to $\delta{\nu}\delta{t}\sim 1$ (van Straten,
2009). In our study of the polarimetry of B3 at high time resolution, we may
still remain in the regime of insufficient averaging, which is required to
have physically meaningful polarization information (van Straten, 2009).
However, it is clear in Figure 8 that the PPA is not completely random,
indicating that there are real variations in the PPA on sub-$\upmu$s
timescales.

The other high S/N bursts in our sample (B2 and B4) show wider characteristic
timescales of tens to about 100 $\upmu$s. These wider components have a
luminosity on the order of $10^{27-28}$ erg s-1 Hz-1, which is 1–2 orders of
magnitude weaker than the bright FRB-like radio burst from the Galactic
magnetar SGR 1935+2154 (Bochenek et al., 2020; CHIME/FRB Collaboration et al.,
2020a). The observed luminosities are much lower than the proposed low-energy
cutoff at $\sim$1037 erg for the low-twist magnetar model (Wadiasingh et al.,
2020), implying that the FRB luminosity function does not abruptly end at
$\sim$1037 erg. The brightness temperatures of these wider components are
$\sim 10^{32}$ K, comparable to the possible Galactic FRB (Bochenek et al.,
2020; CHIME/FRB Collaboration et al., 2020a), and also consistent with the
lower end of the observed FRB brightness temperatures (Figure 2).

FRB 20200120E burst components display a wide range of timescales, roughly a
factor of 1000, which is comparable to what has been found in a similar
analysis of FRB 20180916B (Nimmo et al., 2021). In the case of FRB 20180916B,
Nimmo et al. (2021) were limited by a larger scatter-broadening of 2.7
$\upmu$s (Marcote et al., 2020, note that this source is at a Galactic
latitude of only $3.7^{\circ}$, see also Figure 5), and could not rule out the
possibility that the wider sub-bursts are composed of closely spaced
microsecond structures. One burst in our sample of FRB 20200120E bursts (B3)
has clear isolated shots of duration tens of nanoseconds, and also evidence
that the sub-microsecond shots are clustered on microsecond timescales (from
the characteristic timescales measured in the ACF; Figure 9). For B2 and B4,
there is no clear evidence for isolated shots in the 31.25 ns burst profile,
but it is possible that the S/N is too low to detect these individual shots,
consistent with the lower $<$0.33 measured correlation coefficient (Figure
12).

The polarimetric properties of FRB 20200120E are consistent with those of most
other well-studied repeaters (Michilli et al., 2018a; Nimmo et al., 2021; Day
et al., 2020). As is often observed, we find a very high ($\sim 100$%) linear
and low ($\sim 0$%) circular polarization fraction as well as a polarization
position angle (PPA) that is roughly constant during bursts. As with FRB
20180916B (Nimmo et al., 2021), we find that FRB 20200120E shows small PPA
variations ($\Delta$PPA) on timescales $<10$ $\upmu$s. Between bursts,
however, we see variations in the PPA of a few 10s of degrees, in contrast to
the $<10^{\circ}$ $\Delta$PPA from bursts detected on the same observing
epoch, seen in other repeaters (Michilli et al., 2018a; Nimmo et al., 2021).
The polarimetric similarities strengthen the physical connection between FRB
20200120E and the general population of repeating FRBs, but we note that at
least one source (FRB 20180301A) has shown lower linear polarization fractions
($40-80$%) and significant PPA swings in some bursts (Luo et al., 2020).

The spectrum of FRB 20200120E shows at least two scales of variation. We find
narrow-band brightness variations on the scale of $\sim 5$ MHz, which we
ascribe to scintillation in the interstellar medium of our own Milky Way
galaxy. This interpretation is supported by the stronger correlation in the
spectrum of two bursts (B1 and B2) separated by 4.3 minutes, compared to the
lack of correlation between bursts B3 and B4, which are separated by 2.5 hrs
(Figure 13). The expected scintillation time is $\sim 10$ minutes (at 1.4 GHz)
at high Galactic latitudes, which is dependent on an effective velocity (the
assumption for Galactic sources is 100 km s-1; Cordes & Lazio 1991, 2002).
This effective velocity is likely smaller for an extragalactic source than for
a Galactic pulsar in the same line of sight, since the effective velocity is
usually dominated by the velocity of the pulsar. Assuming an effective
velocity of $\sim 30$ km s-1, the expected scintillation time will be $\sim
30$ minutes (at 1.4 GHz), consistent with the decorrelation timescale
constraints using FRB 20200120E. The other spectral variation we observe is on
the scale of $\sim 100$ MHz, and may be intrinsic to the source emission
mechanism or imparted by local propagation effects. This wider-frequency
spectral envelope is similar to what is seen from other repeaters (Hessels et
al., 2019; Gourdji et al., 2019).

Constraints on the shortest timescale variations in FRB light-curves are
extremely important for understanding the physical mechanism producing the
bursts, and can ultimately lead to clues about the progenitor. The
observational connection to the Crab pulsar, the Galactic magnetar SGR
1935+2154, and repeating FRBs, supports a common magnetically powered emission
mechanism (with potentially a different radiation mechanism creating the
coherent emission, e.g. curvature radiation; Lu & Kumar 2018) spanning many
orders of magnitude in timescales and luminosity. The 62.5 ns to 1 $\upmu$s
timescales observed in B3 correspond to a light-travel size of 20–300 m,
ignoring relativistic effects. The sub-microsecond timescales observed in FRB
20200120E are too short to be naturally explainable via emission from a
synchrotron maser in a relativistic shock (Metzger et al., 2019), since it
would require a very small instantaneous region to be emitting at any given
time. Nimmo et al. (2021) previously argued that the short timescales observed
in FRB 20180916B are more naturally explainable in the context of a neutron
star magnetospheric origin. The results presented here further support a
magnetospheric origin of the FRB emission. Additionally, Lyutikov (2017) argue
that the extragalactic distances of FRBs support magnetic energy being the
fundamental power source for the bursts, as opposed to rotational energy.

Magnetic reconnection is one possible way to harness the magnetic energy to
power a coherent radiation mechanism that produces the radio emission. This
has been proposed to explain Crab nano-shots (Philippov et al., 2019), the
FRB-like radio burst from SGR 1935$+$2154 (Yuan et al., 2020), and FRBs
(Lyubarsky, 2020; Lyutikov, 2021). Philippov et al. (2019) use particle in
cell simulations to consider the origin of Crab pulsar nano-shots, and argue
that they are the low-frequency afterglows of relativistic magnetic
reconnections occurring from plasmoids in the current sheet beyond the light
cylinder. They find a power-law distribution of individual spike and pulse
durations that is related to the range of sizes of these plasmoids. Similarly,
Yuan et al. (2020) simulate magnetar flares which create plasmoids within the
magnetosphere. These plasmoids interact with the magnetic field structure
causing magnetic reconnections to occur and emitting energy that we detect as
short-duration radio flashes. These simulations explain the observed FRB-like
event from SGR 1935+2154, and simultaneous X-ray detection (Mereghetti et al.,
2020). A large range of magnetic energy releases can be expected from this
same mechanism, which is consistent with the large range of FRB luminosities;
from the weaker possible FRBs emitted by the relatively old magnetar SGR
1935+2154, and the bursts from FRB 20200120E, to the more energetic FRBs
potentially coming from extragalactic young, active magnetars.

The observed timescales and luminosities of bursts from FRB 20200120E can be
explained by magnetic reconnection events in the close vicinity of a young,
isolated, highly magnetised neutron star. The association of FRB 20200120E
with an old globular cluster strongly implies that the source must have been
produced via accretion-induced collapse of a white dwarf or merger of compact
objects, as opposed to the more common prompt progenitor formation channel
(e.g. core-collapse supernova; Kirsten et al. submitted). Tendulkar et al.
(2021) and Pleunis et al. (2021) recently discussed a neutron star high-mass
binary model to explain the periodic activity of the repeating FRB 20180916B
(CHIME/FRB Collaboration et al., 2020b), as well as its time-variable rotation
measure and offset from the nearest region of active star formation in the
host galaxy (Marcote et al., 2020). Such a massive binary system is unlikely
to be found in a globular cluster, and hence is strongly disfavoured to
explain FRB 20200120E. Rather, globular clusters typically form compact, low-
mass binary systems with a neutron star or black hole primary — at a higher
rate (by orders of magnitude) per unit stellar mass compared to the galactic
field (Katz, 1975). If FRB 20200120E were such a system, then one possibility
is that its radio bursts are created through magnetic reconnections in an
accretion-induced relativistic jet that is (sometimes) pointed towards Earth
(see also Sridhar et al., 2021, who discuss a model in which repeating FRBs
are associated with precessing relativistic jets formed in ultra-luminous
X-ray sources). The wide range of temporal scales we resolve in our study
could then be associated with magnetic reconnections occurring on a variety of
physical scales within such a jet. However, the lack of a persistent X-ray
counterpart to FRB 20200120E places limits on such scenarios (Kirsten et al.,
submitted).

##  5 Summary and conclusions

In this work we observed the closest precisely localized FRB to date, FRB
20200120E (Bhardwaj et al., 2021, Kirsten et al. submitted) and discovered
that FRB 20200120E emission fills the gap in the luminosity-duration phase
space between young neutron star giant pulses, FRBs, and Galactic magnetars.
We studied temporal variations down to 31.25 ns, where in this case the
limitation was the sub-band widths of 16 MHz, but likely scatter broadening
from the Milky Way interstellar medium (we estimate to be $\sim$27 ns from the
scintillation bandwidth) will limit future observations of FRB 20200120E at
1.4 GHz. This is the shortest timescale measured in any FRB, to date, owing to
the high Galactic latitude and low scatter broadening from the interstellar
medium. One burst in our sample resolves down to isolated shots of emission
with widths of $\sim$ 60 ns, and also has evidence of a microsecond timescale
in the ACF, similar to the nano-shot and microburst phenomenology seen in Crab
pulsar giant pulses. Additionally, the brightness temperature of the isolated
shots in this work are comparable to Crab nano-shots ($\sim 10^{41}$ K). The
other bursts in our sample do not appear to resolve down to isolated shots,
which could be related to the S/N. This, however, is also seen in Crab pulsar
main pulses, where most actually do not resolve down to individual emission
shots. The wider burst temporal structures observed in this work have a
luminosity 1–2 orders of magnitude lower than the FRB-like radio burst from
SGR 1935$+$2154\. The short timescales measured further support a
magnetospheric origin of the emission (Nimmo et al., 2021), while the observed
similarity of FRB 20200120E bursts with the Crab pulsar giant pulses and SGR
1935$+$2154 in terms of timescales and luminosities supports that all are
magnetically powered. Recording raw voltages with a receiver bandwidth of
$>$200 MHz, at a higher radio frequency (where the scatter broadening will be
lower) is needed to explore even shorter timescales. Continued observations of
FRB 20200120E will provide statistics on the distribution of emission
timescales and whether the burst activity is periodic, like FRB 20180916B
(CHIME/FRB Collaboration et al., 2020b). Such data will also help determine
whether, e.g., there are quasi-periodic fluctuations in the burst lightcurves
(hinted at, in the case of FRB 20180916B; Nimmo et al., 2021) or a secular
variation in the widths of burst envelopes. We also highlight that the short
timescales measured from FRB 20200120E in this work, motivate searches for a
population of ultra-fast radio bursts (especially at extremely high and low
Galactic latitudes, where the expected scattering time is low).

## Acknowledgements

We thank W. van Straten for help with digifil. The European VLBI Network is a
joint facility of independent European, African, Asian, and North American
radio astronomy institutes. Scientific results from data presented in this
publication are derived from the following EVN project code: EK048. A.B.P is a
McGill Space Institute (MSI) Fellow and a Fonds de Recherche du Quebec -
Nature et Technologies (FRQNT) postdoctoral fellow. B.M. acknowledges support
from the Spanish Ministerio de Economía y Competitividad (MINECO) under grant
AYA2016-76012-C3-1-P and from the Spanish Ministerio de Ciencia e Innovación
under grants PID2019-105510GB-C31 and CEX2019-000918-M of ICCUB (Unidad de
Excelencia “María de Maeztu” 2020-2023). C.L. was supported by the U.S.
Department of Defense (DoD) through the National Defense Science & Engineering
Graduate Fellowship (NDSEG) Program. D.M. is a Banting Fellow. E.P.
acknowledges funding from an NWO Veni Fellowship. F.K. acknowledges support
from the Swedish Research Council. FRB research at UBC is supported by an
NSERC Discovery Grant and by the Canadian Institute for Advanced Research.
J.P.Y. is supported by the National Program on Key Research and Development
Project (2017YFA0402602). K.S. is supported by the NSF Graduate Research
Fellowship Program. K.W.M. is supported by an NSF Grant (2008031). M.B. is
supported by an FRQNT Doctoral Research Award. N.W. acknowledges support from
the National Natural Science Foundation of China (Grant 12041304 and
11873080). P.S. is a Dunlap Fellow and an NSERC Postdoctoral Fellow. The
Dunlap Institute is funded through an endowment established by the David
Dunlap family and the University of Toronto. V.B. acknowledges support from
the Engineering Research Institute Ventspils International Radio Astronomy
Centre (VIRAC). Work at UvA and ASTRON was funded by the NWO Vici grant
“AstroFlash” (PI: Hessels, VI.C.192.045).

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Table 1: Burst properties.

Burst | Time of Arrivala | Fluenceb | Peak S/N | Peak Flux Densityb | Spectral Luminosityb,c | Width d | Frequency Extent d | Scintillation bandwidthf
---|---|---|---|---|---|---|---|---
| [MJD] | [Jy ms] |  | [Jy] | [1028 erg s-1 Hz-1] | [$\upmu$s] | [MHz] | [MHz]
B1 | 59265.88304437179 | 0.13 $\pm$ 0.03 | 6.6 | 1.59 $\pm$ 0.32 | 0.56 $\pm$ 0.13 | 156 $\pm$ 1 | 197 $\pm$1 | 1.9 $\pm$ 0.7
B2 | 59265.88600912486 | 0.63 $\pm$ 0.13 | 36.1 | 8.71 $\pm$ 1.74 | 2.3 $\pm$ 0.6 | 62 $\pm$ 1, 93 $\pm$ 0.5 e | 146 $\pm$ 1, 126 $\pm$ 1 e | 3.4 $\pm$ 1.0
B3 | 59280.69618745651 | 0.53 $\pm$ 0.11 | 64.8 | 15.6 $\pm$ 3.12 | 8.0 $\pm$ 1.9 | 47 $\pm$ 0.1 | 133 $\pm$ 1 | 6.9 $\pm$ 1.1
B4 | 59280.80173397988 | 0.71 $\pm$ 0.14 | 29.3 | 7.07 $\pm$ 1.41 | 4.0 $\pm$ 1.0 | 117 $\pm$ 1 | 189 $\pm$1 | 6.8 $\pm$ 1.3
a Corrected to the Solar System Barycenter to infinite frequency assuming a
dispersion measure of $87.75$ pc cm-3,
reference frequency 1502 MHz and dispersion constant of 1/(2.41$\times
10^{-4}$) MHz2 pc-1 cm3 s
The times quoted are dynamical times (TDB).
b We take a conservative 20% error on these measurements, arising due to the
uncertainty in the System Equivalent Flux Density (SEFD) of Effelsberg.
c Using the distance to the globular cluster [PR95] 30244 as 3.63 $\pm$0.34
Mpc (Freedman et al., 1994).
d Defined as $1/\sqrt{2}$ multiplied by the FWHM
of the autocorrelation function (ACF).
e Width per burst component.
f The uncertainties are a combination of the 1-$\sigma$ fit uncertainty, and
1/$\sqrt{\rm N}$, where N $\approx$ 5 is the number of scintles.

Table 2: Burst polarization properties and polarization position angle fit
results.

Burst | RMa [rad m-2] | PPA offsetb [deg] | RM (global)a,c [rad m-2] | PPA offset (global)c [deg] | Lunbiased/Id [%] | V/Id [%] |  $\chi^{2}$ e | Degrees of freedome
---|---|---|---|---|---|---|---|---
B1 |  $-$21.9 $\pm$ 13.1 | 28.5 | -54.2 $\pm$ 4.8 | 68.3 | 94 $\pm$ 9 | 4 $\pm$ 9 | 18.9 | 7
B2 |  $-$57.2 $\pm$ 5.1 | 0 | -54.2 $\pm$ 4.8 | 0 | 103 $\pm$ 3 | -13 $\pm$ 3 | 59.6 | 27
B3 |  $-$37.1 $\pm$ 4.2 | -8.6 | -36.9 $\pm$ 3.8 |  $-$9.3 | 102 $\pm$ 2 | 1 $\pm$ 1 | 15.5 | 11
B4 |  $-$36.4 $\pm$ 8.0 | 13.1 | -36.9 $\pm$ 3.8 | 14.3 | 94 $\pm$ 2 | 6 $\pm$ 2 | 25.7 | 22
a The large fractional errors arise due to covariances between fit parameters in the QU-fitting, see text for more details. |
b Offset from a weighted mean of the bursts from a single epoch. |
c The global values are assuming all bursts detected on the same day have the same RM. |
d The quoted uncertainties are 1$\sigma$ uncertainties, and do not include uncertainties from the calibration. |
Note: we reproduce the published pulsar circular (linear) fractions within 3% (10%) and 1% (6%)) |
for the Feb 20 and March 7 observations, respectively. |
e Fit results of weighted least squares fitting of a straight line to the PPA. |

Table 3: High time resolution autocorrelation function and power spectra
results.

Burst | Characteristic timescales [$\upmu$s] | Red. $\chi^{2}$ a | Power law index b |  $\Delta$ Bayesian Information Criterionc | Goodness of fit p-valued | Outlier p-valuee
---|---|---|---|---|---|---
B2 | 28.5 $\pm$ 0.2 | 2.0 | $1.85\,\pm\,0.04$ |  $-$20.5 | 0.50 | 0.98
B3 | 0.04 $\pm$ 0.3, 1.1 $\pm$0.4, 35.6 $\pm$0.5 | 2.4, 1.64, 1.3 | $1.46\,\pm\,0.05$ | $-12.1$ | 0.53 | 0.99
B4 | 0.05 $\pm$ 0.02, 64.1 $\pm$ 1.5 | 2.7,1.9 | $2.04\,\pm\,0.05$ |  $-$15.4 | 0.66 | 0.97
a The reduced $\chi^{2}$ of the Lorenzian fit to the high time resolution ACF in Figures 9–11. |
b The power law index measured for the power spectra. |
c Metric for model comparison (BIC for power law red noise model $-$ BIC for power law plus Lorentzian). |
d Goodness of fit of the best fit model. |
e p-value of the highest outlier in the residuals of the power spectrum. |

Figure 1: Burst B3 from FRB 20200120E exhibits a ‘forest’ of 10 ns to 1
$\upmu$s shots of emission. Top panel: left shows the time profile of burst B3
at 31.25 ns time resolution (black) and downsampled to 1 $\upmu$s resolution
(green), and right shows a histogram of the S/N values in the 31.25 ns data,
also showing the $\chi^{2}$-distributed (2 degrees of freedom) noise
distribution (red) arising in the limiting case of $\delta t\delta\nu\sim 1$,
where $\delta t$ and $\delta\nu$ are the time and frequency resolutions of the
data, respectively. This plot contains time profiles computed for the bright
scintle only, i.e. the frequency range $1318-1334$ MHz. The data were
generated with SFXC and are coherently dedispersed to 87.7527 pc cm-3. The
second panel shows a zoom in of the top left panel, highlighting the temporal
regions plotted in the third (yellow) and fourth (blue) panels.

Figure 2: Nanosecond to millisecond transient phase space. The FRB 20200120E
burst temporal structures and their measured isotropic-equivalent spectral
luminosity are shown by the black stars. We plot the three highest
significance isolated shots from burst B3 (left-most black stars), the bright
$<10$ $\upmu$s structure evident in the 1 $\upmu$s time resolution data of
burst B3, as well as the wider burst structure seen in B1, B2 and B4 (right-
most black stars). The FRBs plotted are the published localized repeating
FRBs, with known distances: FRB 20121102A (Spitler et al., 2016; Scholz et
al., 2017; Law et al., 2017; Michilli et al., 2018a; Hessels et al., 2019;
Gourdji et al., 2019; Gajjar et al., 2018; Hardy et al., 2017; Houben et al.,
2019; Majid et al., 2020; Josephy et al., 2019; Rajwade et al., 2020; Caleb et
al., 2020), FRB 20180916B (CHIME/FRB Collaboration et al., 2019; Marcote et
al., 2020; Chawla et al., 2020; CHIME/FRB Collaboration et al., 2020b; Pleunis
et al., 2021; Nimmo et al., 2021), and FRB 20190711A (Macquart et al., 2020;
Kumar et al., 2021). In purple we plot the radio bursts from the Galactic
magnetar SGR 1935+2154 (CHIME/FRB Collaboration et al., 2020a; Bochenek et
al., 2020; Zhang et al., 2020; Kirsten et al., 2021; Good & Chime/Frb
Collaboration, 2020). Giant pulses from the Crab pulsar (GRPs) are shown in
orange (Karuppusamy et al., 2010), and the ‘nano-shots’ are represented by the
yellow crosses (Hankins et al., 2003; Hankins & Eilek, 2007; Jessner et al.,
2010). The pulsar and Rotating RAdio Transient (RRAT) population are shown in
pink (Keane, 2018). The grey lines represent lines of constant brightness
temperature.

Figure 3: The polarization profiles, dynamic spectra, time-averaged spectra
and polarization position angle (PPA) of the four bursts detected from FRB
20200120E. The data are plotted with 8 $\upmu$s and 1 MHz time and frequency
resolution, respectively (with the exception of B1 which is plotted with 4 MHz
frequency resolution). The data were generated with SFXC and are coherently
dedispersed within each 16 MHz subband to 87.75 pc cm-3(incoherently shifted
between subbands). For each sub-figure, the top panel is the PPA across the
burst profile, where the color gradient represents the linear polarization S/N
(black is high S/N and white is low S/N), and the colored horizontal line
represents the weighted best-fit line to the PPA. Only the PPAs above a linear
S/N threshold of 3 are plotted. The second panel shows the total intensity
(Stokes I; black), unbiased linear polarization (Everett & Weisberg 2001; red)
and circular polarization (blue) burst profiles. In the top left of the panel
is the burst name used throughout this work, and the time resolution used for
plotting. The colored bar at the bottom of the panel represents the
$\pm$2$\sigma$ burst width used to measure the polarization fractions and
burst fluence. The bottom panel is the dynamic spectrum (left) and time-
averaged frequency spectrum (right). The red marks on the dynamic spectrum
outline the edges of the subbands. Data that have been removed due to radio
frequency interference has not been plotted.

Figure 4: Low time resolution 2D autocorrelation functions (ACFs) of the
bursts detected from FRB 20200120E. Each sub-figure shows the 2D ACF (main
panel) with colored contours overplotted representing the 2D Gaussian fit
1,2,3 and 4 $\sigma$. The zero lag spike is not plotted. The ACF is computed
using filterbank data generated with SFXC (Keimpema et al., 2015), with time
and frequency resolution of 8 $\upmu$s and 125 kHz, respectively. The top
panels show the frequency-averaged time ACF, with the frequency-averaged
Gaussian fit overplotted, and similarly the right panels show the time-
averaged frequency ACF, with the time-averaged Gaussian fit overplotted. The
time and frequency scales characterised in this plot, arise from the burst
temporal width and frequency extent. The colored lines coordinate with other
figures in this work (e.g. Figures 3 and 6) to define B1, B2, B3 and B4.

Figure 5: Measurement of the scintillation bandwidth in the autocorrelation
function (ACF) of each of the four bursts from FRB 20200120E. The top sub-
figure shows the time-averaged frequency ACF from Figure 4, subtracted the
Gaussian fit shown in the same figure in black, with the Lorentzian fit to the
central component shown by the colored line. The burst name is shown in the
top left of each panel, and the measured scintillation bandwidth (defined as
the half-width at half-maximum of the Lorentzian; Rickett 1990) is shown in
the top left of each panel. The bottom sub-figure shows a colormap of the
expected scattering timescale at 1.4 GHz as a function of Galactic longitude
and latitude, from the NE2001 Galactic electron density model (Cordes & Lazio,
2002). The sky positions of both FRB 20200120E and FRB 20180916B are shown by
the black cross and white plus, respectively.

Figure 6: Rotation measure (RM) determination for the four bursts from FRB
20200120E. The top sub-figure shows the Faraday spectrum per burst (labelled),
determined using RM synthesis (Brentjens & de Bruyn, 2005), with the grey line
showing the previous RM measurement of this source (Bhardwaj et al., 2021).
The grey-scale scatter points in the bottom four sub-figures show the Stokes Q
(top panel) and Stokes U (bottom panel) spectra normalised by the linear
polarization L$=\sqrt{\mathrm{Q}^{2}+\mathrm{U}^{2}}$, where the darker color
represents a higher S/N. The colored lines show the best-fit QU-fitting
result, where we fit for both the RM and the delay between the polarization
hands (see text). The color of the line indicates which burst is being
plotted, using the legend in the top figure.

Figure 7: Constraining the dispersion measure (DM) using the short timescale
structure in burst B3 from FRB 20200120E. Using data products generated using
SFXC (Keimpema et al., 2015), with a time and frequency resolution of 500 ns
and 1 MHz, respectively, we coherently (within subbands) and incoherently
(between subbands) dedisperse to a range of DMs, downsample in time by a
factor of 2, and compute the peak S/N of the frequency-averaged profile (left
panel). Also plotted on the left is a Gaussian fit to the peak S/N as a
function of DM, with the best-fit DM (DM = 87.7527$\pm$0.0003 pc cm-3) shown
by the grey line. Right: we plot the burst profile (top) and dynamic spectrum
(bottom) coherently and incoherently dedispersed to the best-fit DM. The time
and frequency resolutions used for plotting in the left panels are 1 $\upmu$s
and 16 MHz, respectively. The red lines on the dynamic spectrum indicate the
frequency extent averaged over to determine the peak S/N per DM, and to
produce the profile in the top panel.

Figure 8: High time resolution polarimetric profile and polarization position
angle (PPA) for burst B3 from FRB 20200120E. The top panels show the PPA as a
function of time, with the orange line representing the weighted best-fit line
to the PPA. Only the PPAs above a linear S/N threshold of $5$ are plotted. The
bottom panels show the polarimetric profile of the burst sampled at 125 ns,
with Stokes I (black), unbiased linear polarization (Everett & Weisberg 2001;
red) and circular polarization (blue). The yellow and blue regions plotted on
the left panels represent the time ranges used for plotting the middle and
right panels, respectively. This data was generated with SFXC, with 4 MHz
channels and coherently (within subbands) and incoherently (between subbands)
dedispersed to 87.7527 pc cm-3. The frequency information was averaged for the
frequency range 1254 – 1430 MHz (visually, the extent of the burst in
frequency), which, in this data product, corresponds to averaging by a factor
of 44.

Figure 9: Burst B3 from FRB 20200120E dynamic spectrum with time resolution
31.25 ns, temporal autocorrelation function (ACF) and power spectrum (PS). The
left sub-figure shows the dynamic spectrum (bottom panel) in the form of
temporal profiles per subband. This data was generated with SFXC, and each
subband has been coherently dedispersed to 87.7527 pc cm-3. The top panel
shows the frequency-averaged burst profile. The top right sub-figure shows the
average power spectrum (PS) of the four subbands containing significant burst
structure in the top panel (grey), with a downsampled PS (factor 8)
overplotted in black. The purple and blue lines represent fits to the PS of a
red noise power law plus white noise model and a power law/white noise plus
lorentzian model, respectively. The panels below show the residuals ($2\times
D/M$, for data $D$ and model $M$) of both models, matching the colors in the
top panel. The dashed lines represent the perfect case of $D=M$. The bottom
right sub-figure shows the average temporal ACF of the same four subbands (top
panel, orange). For comparison the off burst ACF is also shown (grey). The
residual of the average ACF subtracted the noise ACF is shown in panel below,
with the green and purple Lorentzian fits to the ACF residuals highlighting
two distinct temporal scales in the data. The bottom panel shows a zoom in on
the ACF residuals highlighting a third temporal scale by the cyan Lorentzian
fit.

Figure 10: The same as Figure 9, for burst B2 from FRB 20200120E. Note the
average ACF only shows one temporal scale (unlike the three seen for burst
B3). Additionally, we only plot the red noise power law plus white noise model
since any wide Lorentzian features are less apparent in this power spectrum,
than the case of B3.

Figure 11: The same as Figures 9 and 10, for burst B4 from FRB 20200120E. Note
the average ACF shows two temporal scales (unlike the $3$ seen for burst B3).
Additionally, we only plot the red noise power law plus white noise model
since any wide Lorentzian features are less apparent in this power spectrum,
than the case of B3.

Figure 12: Bursts B2, B3 and B4 from FRB 20200120E plotted at 1 $\upmu$s
resolution (left column). The burst name and time resolution is shown in the
top left corner and the frequency range averaged over to produce the burst
profile in the top right corner of each panel. The right column shows the
correlation coefficient between single time bin spectra above a S/N threshold
of $9$ (left). The color gradient indicates the geometric mean of the two time
bins used to determine the correlation coefficient (darker color implying a
higher geometric mean). On the right of the right column is a histogram of the
correlation coefficients. The colored line represents the geometric mean S/N
weighted correlation coefficient.

Figure 13: Comparing the time-averaged spectra between bursts detected close
in time. The top panel shows the time-averaged spectra for B1 (black) and B2
(grey). The bottom panel shows the time-averaged spectra for B3 (grey) and B4
(black). In the top right of each panel, we quote the time between the two
bursts in the plot, $\delta t$, and the correlation coefficient of the burst
spectra, $R$.

Figure 14: Bursts B2, B3 and B4 from FRB 20200120E plotted at 31.25 ns
resolution (left column). The burst name and time resolution is shown in the
top left corner and the frequency range averaged over to produce the burst
profile in the top right corner of the panels containing the full burst
profile (grey), with off burst noise (black) shown for comparison. The off
burst noise is used to convert to S/N units on the y-axis. Underneath these
panels are zoomed-in profiles containing the highest S/N feature in the burst
profile. The colored region represent the local region (time span $\pm 1.5625$
$\upmu$s for B3 and $\pm 3.125$ $\upmu$s for B2 and B4) used to determine the
probability density function (pdf) and cumulative density function (cdf)
plotted in the right column. Note the feature at the center of the colored
region, is not added to the distribution, since this is the feature which we
want to determine the significance of relative to the local distribution. An
exponential distribution fit is overplotted (colored lines) on the pdf and
cdf. The highest S/N feature is represented by the vertical dashed line on the
cdf (where in the case of B3, there are two dashed lines since the feature is
2 bins wide), and the legend shows the probability (or 1-cdf) of these
features. The horizontal dashed lines on the zoomed in burst profiles
represent the 3 $\sigma$ levels for single bin features, using this local
distribution (also for 2-bin features in the case of B3).