# Morphologies of Bright Complex Fast Radio Bursts with CHIME/FRB Voltage Data

Jakob T. Faber Department of Physics, McGill University, 3600 rue University,
Montréal, QC H3A 2T8, Canada  Trottier Space Institute, McGill University,
3550 rue University, Montréal, QC H3A 2A7, Canada  Cahill Center for Astronomy
and Astrophysics, MC 249-17 California Institute of Technology, Pasadena CA
91125, USA  Daniele Michilli 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  Ryan Mckinven
Department of Physics, McGill University, 3600 rue University, Montréal, QC
H3A 2T8, Canada  Trottier Space Institute, McGill University, 3550 rue
University, Montréal, QC H3A 2A7, Canada  Jianing Su Department of Physics,
McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada  Dunlap
Institute for Astronomy & Astrophysics, University of Toronto, 50 St. George
Street, Toronto, ON M5S 3H4, Canada  Aaron B. Pearlman Department of Physics,
McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada  Trottier
Space Institute, McGill University, 3550 rue University, Montréal, QC H3A 2A7,
Canada  Kenzie Nimmo 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  Robert A. Main Department of
Physics, McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada
Trottier Space Institute, McGill University, 3550 rue University, Montréal, QC
H3A 2A7, Canada  Victoria Kaspi Department of Physics, McGill University, 3600
rue University, Montréal, QC H3A 2T8, Canada  Trottier Space Institute, McGill
University, 3550 rue University, Montréal, QC H3A 2A7, Canada  Mohit Bhardwaj
Department of Physics, McGill University, 3600 rue University, Montréal, QC
H3A 2T8, Canada  Trottier Space Institute, McGill University, 3550 rue
University, Montréal, QC H3A 2A7, Canada  Department of Physics, Carnegie
Mellon University, 5000 Forbes Avenue, Pittsburgh, 15213, PA, USA  Shami
Chatterjee Department of Astronomy and Cornell Center for Astrophysics and
Planetary Science, Cornell University, Ithaca NY 14853, USA  Alice P. Curtin
Department of Physics, McGill University, 3600 rue University, Montréal, QC
H3A 2T8, Canada  Trottier Space Institute, McGill University, 3550 rue
University, Montréal, QC H3A 2A7, Canada  Matt Dobbs Department of Physics,
McGill University, 3600 rue University, Montréal, QC H3A 2T8, Canada  Trottier
Space Institute, McGill University, 3550 rue University, Montréal, QC H3A 2A7,
Canada  Gwendolyn Eadie Dunlap Institute for Astronomy & Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada
Department of Statistical Sciences, University of Toronto, 700 University
Ave., Toronto, ON M5G 1Z5, Canada  B. M. Gaensler 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  Present address: Division of Physical and Biological Sciences,
University of California Santa Cruz, Santa Cruz, CA 95064, USA  Zarif Kader
Department of Physics, McGill University, 3600 rue University, Montréal, QC
H3A 2T8, Canada  Trottier Space Institute, McGill University, 3550 rue
University, Montréal, QC H3A 2A7, Canada  Calvin 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  Kiyoshi 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  Ayush Pandhi
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  Emily Petroff Perimeter Institute for Theoretical
Physics, 31 Caroline Street N, Waterloo, ON N25 2YL, Canada  Ziggy Pleunis
Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St.
George Street, Toronto, ON M5S 3H4, Canada  Masoud Rafiei-Ravandi Department
of Physics, McGill University, 3600 rue University, Montréal, QC H3A 2T8,
Canada  Trottier Space Institute, McGill University, 3550 rue University,
Montréal, QC H3A 2A7, Canada  Ketan R. Sand Department of Physics, McGill
University, 3600 rue University, Montréal, QC H3A 2T8, Canada  Trottier Space
Institute, McGill University, 3550 rue University, Montréal, QC H3A 2A7,
Canada  Paul Scholz Dunlap Institute for Astronomy & Astrophysics, University
of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada  Department of
Physics & Astronomy, York University  Kaitlyn 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  Kendrick Smith Perimeter Institute for Theoretical Physics, 31
Caroline Street N, Waterloo, ON N25 2YL, Canada  Ingrid Stairs Department of
Physics and Astronomy, University of British Columbia, 6224 Agricultural Road,
Vancouver, BC V6T 1Z1 Canada Jakob T. Faber<EMAIL_ADDRESS>
###### Abstract

We present the discovery of twelve thus far non-repeating fast radio burst
(FRB) sources, detected by the Canadian Hydrogen Intensity Mapping Experiment
(CHIME) telescope. These sources were selected from a database comprising
$\mathcal{O}(10^{3})$ CHIME/FRB full-array raw voltage data recordings, based
on their exceptionally high brightness and complex morphology. Our study
examines the time-frequency characteristics of these bursts, including
drifting, microstructure, and periodicities. The events in this sample display
a variety of unique drifting phenomenologies that deviate from the linear
negative drifting phenomenon seen in many repeating FRBs, and motivate a
possible new framework for classifying drifting archetypes. Additionally, we
detect microstructure features of duration $\lesssim$ 50 $\mu s$ in seven
events, with some as narrow as $\approx$ 7 $\mu s$. We find no evidence of
significant periodicities. Furthermore, we report the polarization
characteristics of seven events, including their polarization fractions and
Faraday rotation measures (RMs). The observed $|\mathrm{RM}|$ values span a
wide range of $17.24(2)$ \- $328.06(2)\mathrm{~{}rad~{}m}^{-2}$, with linear
polarization fractions between $0.340(1)$ \- $0.946(3)$. The morphological
properties of the bursts in our sample appear broadly consistent with
predictions from both relativistic shock and magnetospheric models of FRB
emission, as well as propagation through discrete ionized plasma structures.
We address these models and discuss how they can be tested using our improved
understanding of morphological archetypes.

Radio transient sources (2008), High energy astrophysics (739), Compact
objects (288)

††facilities: CHIME/FRB††software: astropy (Price-Whelan et al., 2018); scipy
(Virtanen et al., 2020), bilby (Ashton et al., 2019), dynesty (Speagle, 2020)

##  1 Introduction

Fast radio bursts (FRBs; Lorimer et al., 2007) are a class of highly luminous,
predominantly extragalactic radio transients with durations of a few
nanoseconds to seconds (Petroff et al., 2019; Cordes & Chatterjee, 2019; Majid
et al., 2021; Nimmo et al., 2022; CHIME/FRB Collaboration et al., 2022a). The
origin of FRBs is unknown. The Canadian Hydrogen Intensity Mapping Experiment
Fast Radio Burst (CHIME/FRB) Project (CHIME/FRB Collaboration et al., 2021)
has detected $\mathcal{O}(10^{3})$ FRB sources of a variety of signal
strengths, morphologies and durations, of which approximately 3% show
repeating behavior (CHIME/FRB Collaboration et al., 2018, 2019; Fonseca et
al., 2020; CHIME/FRB Collaboration et al., 2020a; Pleunis et al., 2021;
CHIME/FRB Collaboration et al., 2023a).

Many models have been proposed to explain the origin of FRBs. While initially
one-off FRBs appeared to suggest cataclysmic progenitor channels such as
compact object mergers (Kashiyama et al., 2013; Mingarelli et al., 2015; Keane
et al., 2016), or collapsing neutron stars (Falcke & Rezzolla, 2014), the
discovery of repeating FRBs argued for longer-lived progenitors, such as
magnetars (e.g. Lyubarsky, 2014; Beloborodov, 2017; Margalit et al., 2020) or
giant pulses from conventional radio pulsars (Lyutikov et al., 2016). More
exotic source models that have been proposed include cosmic strings and
primordial black holes (see Platts et al., 2018, for a comprehensive review of
FRB source models). While the aforementioned models succeed in accounting for
some observed FRB properties, none explain them all, and coincident multi-
wavelength (e.g., gamma and X-ray bursts; Scholz et al., 2017, 2020; Pearlman
et al., 2023) or multi-messenger emissions (e.g., neutrinos; Aartsen et al.,
2020) that could in principle constrain such models remain elusive.

Magnetars have shown great promise as source candidates for FRBs. Young
magnetars embedded in their birth supernova remnants or wind nebulae can, for
instance, possess the plasma environments for synchrotron maser emission via
relativistic shocks (Lyubarsky, 2014; Beloborodov, 2017; Metzger et al.,
2019). These models generally account for some of the observed features in
repeating FRBs, such as their luminosities, time scales and spectra
(Lyubarsky, 2014; Masui et al., 2015; Margalit & Metzger, 2018; Beloborodov,
2019; Wadiasingh & Timokhin, 2019; Margalit et al., 2020; Lyubarsky, 2020).
Moreover, the detection of $\sim$MJy radio bursts from the Galactic magnetar
SGR 1935+2154 (CHIME/FRB Collaboration et al., 2020a; Bochenek et al., 2020;
Kirsten et al., 2020) lends strong supporting evidence for the magnetar model.
The detection of periodic activity windows in some repeating FRBs has been
used to claim that FRBs may originate from rotating or precessing magnetars
(e.g. CHIME/FRB Collaboration et al., 2020b; Rajwade et al., 2020; Cruces et
al., 2020; Levin et al., 2020; Zanazzi & Lai, 2020), sparking numerous multi-
wavelength observational campaigns (Scholz et al., 2016, 2020; Pearlman et
al., 2023). CHIME/FRB detected a sub-second periodicity in a single event,
which favors models that invoke magnetospheric emission from a neutron star
(CHIME/FRB Collaboration et al., 2022a).

Another major advancement in the field is the publication of the first large
sample of FRBs observed in a single survey with uniform selection effects by
CHIME/FRB (CHIME/FRB Collaboration et al., 2021). The catalog contains 536
FRBs detected between 2018 July 25 and 2019 July 1, including 62 bursts from
18 previously reported repeating sources, enabling detailed studies of the FRB
population and its properties. Differences in morphology and spectra between
repeating FRBs and apparent non-repeaters, previously hinted at in more
limited samples (Scholz et al., 2016; CHIME/FRB Collaboration et al., 2019;
Hashimoto et al., 2020), were made clear by the large numbers of events in the
catalog (Pleunis et al., 2021), suggesting potentially distinct emission
mechanisms or circumburst environments.

With the advent of high-time resolution surveys like CRAFT (Macquart et al.,
2010; Cho et al., 2020), and the baseband raw-voltage storing capabilities of
radio telescopes including CHIME/FRB, FRBs have been successfully resolved
down to micro- and even nanosecond timescales (Majid et al., 2021; Nimmo et
al., 2021, 2022; Snelders et al., 2023). Detections of FRB substructure at and
below the microsecond scale enable powerful constraints on both emission and
propagation physics by resolving subtle time-frequency variations. Time-
frequency variations have been characterized in detail for a variety of
repeating sources, including FRB 20121102A (Hessels et al., 2019; Platts et
al., 2021), FRB 20180916B (Sand et al., 2022, 2023), FRB 20180301A (Kumar et
al., 2023), and others. When such variations are bright, it may be possible to
distinguish between “propagation” effects imposed by intervening plasmas along
the line of sight (e.g., time delays due to lensing, or scattering tails) and
“intrinsic” effects that arise from the emission mechanism itself (e.g.,
nanosecond-duration bursts from magnetic reconnection or beam-driven
instabilities).

In this paper, we present a high-time resolution analysis of the time-
frequency properties of twelve thus far non-repeating FRBs detected by
CHIME/FRB, one of which appears in the first CHIME/FRB catalog (FRB 20190425A;
see CHIME/FRB Collaboration et al., 2021). We also report their polarization
properties. The FRBs in our sample exhibit morphologies of compelling
complexity on $\mu$s timescales with high signal-to-noise (S/N). We leverage
the diversity of these morphological characteristics to evaluate a number of
FRB source models, with an emphasis on magnetospheric and relativistic shock
emission scenarios from magnetars. We also discuss the role that propagation
effects from interstellar plasma structures may have in shaping their
morphologies.

In §2 we describe the CHIME/FRB baseband analysis system and present the full
burst sample. In §3 we describe several morphological archetypes present in
the sample, particularly as they relate to time-frequency drifting. We also
present a new series of fitting techniques to characterize both drifting and
microstructure in complex FRBs (also described in §A and §B), and search for
periodicities. In §4, we explore the implications of these possible new
archetypes with respect to FRB emission models and propagation effects,
highlighting the relevance to relativistic shock and magnetospheric scenarios,
as well as plasma lensing. Finally, we summarize and draw conclusions in §5,
and discuss how our sample affects our understanding of non-repeating FRBs.
Polarization measurements are reported in §C.

##  2 Observations & Burst Sample

###  2.1 The CHIME/FRB Real-Time Detection Pipeline and Baseband Analysis
System

Investigations into the underlying physics of FRB emission and propagation
have historically been limited by the unavailability of baseband raw voltage
data. CHIME/FRB overcomes this limitation by way of a real-time detection and
analysis pipeline that records coherent electric field data measured by the
full array (baseband raw voltages) upon a detection trigger (Michilli et al.,
2021). Combined with the high detection rate of CHIME/FRB, this provides a
wealth of high-resolution data (spectral and temporal) with full-Stokes
parameters.

Located at the Dominion Radio Astrophysical Observatory near Penticton, BC,
the CHIME111See www.chime-experiment.ca telescope consists of four 100-m
$\times$ 20-m cylindrical reflectors with North-South orientations, each
bearing 256 dual-polarization feeds along the focal line that operate between
400 and 800 MHz.

The raw voltages measured by the telescope are amplified, digitized, and
channelized by an FPGA-based F-engine. Data from the F-engine are sent to the
GPU-based X-engine where 1024 digital sky beams are formed (Ng et al., 2017),
the data from which are sampled at 0.983 ms time resolution with 16k frequency
channels. See CHIME/FRB Collaboration et al. (2022b) for details.

The CHIME/FRB detection and analysis pipeline operates in two stages:

  1. I.

Real-time Detection: The first stage is the real-time detection pipeline,
which runs on a dedicated cluster of 128 nodes and searches for short-
duration, dispersed peaks in a total intensity data stream across 1024
independently formed beams. Upon detection of an FRB, the data are buffered
and stored.

The F-engine uses a 4-tap polyphase filter bank (PFB) to produce a spectrum
with 1024 channels (each 390 kHz wide) at a time resolution of 2.56 $\mu$s.
The baseband data are quantized with 8-bit accuracy, resulting in a data rate
of 6.5 Tb/s. A memory buffer allows the storage of 35.5 seconds of baseband
data at a given time. From the moment a signal arrives at the telescope, the
real-time pipeline can process the event and trigger a baseband dump in about
14 seconds, leaving a usable data buffer of about 20 seconds. For a detailed
overview of this first stage, refer to CHIME/FRB Collaboration et al. (2018).

  2. II.

Baseband Processing: The second stage is the baseband processing pipeline,
which is designed to be highly scalable. The pipeline can run automatically on
new events that are identified by the real-time detection pipeline, or be
manually triggered to process specific events.

The baseband system is configured to store approximately 100 ms of data around
an FRB detection. This allows time-frequency features and propagation effects
such as scattering and scintillation to be resolved. A grid of overlapping
beams is formed around the initial position of the FRB candidate (i.e.,
beamforming), and the signal intensity is mapped and fitted against the
telescope response to obtain a refined position with subarcminute precision.
For a complete description of this second stage, refer to Michilli et al.
(2021).

Finally, coherent dedispersion is performed to remove the dispersive effects
induced by free electrons along the line of sight. This is done by applying
frequency-dependent phase correction to each frequency channel, removing
intrachannel smearing and preserving the temporal resolution of the signal.
The phase-preserving nature of coherent dedispersion also enables the
reconstruction of the polarization state of the signal. By combining the two
orthogonal linear polarizations measured by each antenna, we can quantify the
rotation of the polarization angle due to the interaction of the
electromagnetic wave with a magnetized plasma along the line of sight, or
Faraday rotation measure (RM), defined as:

$\mathrm{RM}=8.1\times
10^{5}\int_{0}^{s}\left(\frac{n_{e}\left(s\right)}{\mathrm{cm}^{-3}}\right)\left(\frac{B_{\|}\left(s\right)}{\mathrm{G}}\right)\left(\frac{ds}{\mathrm{pc}}\right)=\frac{d\psi}{d\lambda^{2}}\quad\left[\mathrm{rad}~{}\mathrm{m}^{-2}\right]$
(1)

where $B_{\|}$ and $n_{e}$ are the parallel component of the magnetic field
with respect to the electromagnetic field and free electron number density
along a line of sight element $ds$, $\psi$ is the polarization angle, and
$\lambda$ is the observing wavelength. Once de-rotated, the intrinsic
polarization angle (PA) of the source can be obtained. Since CHIME/FRB does
not calibrate for polarization, however, we can only measure zero-mean-
relative deviations in the PA. We can also measure the polarization fractions,
which are the ratios of the linearly and circularly polarized intensities to
the total intensity of the signal. For a more detailed description of the
CHIME/FRB polarization pipeline, see Mckinven et al. (2021).

###  2.2 Burst Sample

The bursts in our sample are shown in Figure 1. These bursts were selected
based on their brightness (S/N $\gtrsim$ 30 in baseband) and unusual
morphological characteristics that differ noticeably from those currently
observed in most FRBs — including, but not limited to atypical time-frequency
drifting, large numbers of sub-bursts, and time-variable properties. Figure 1
shows both dynamic spectra as well as full polarimetric data for select
bursts, as described in detail in §3.

Table 1:  Burst properties, including: baseband localizations; signal-to-noise ratios (S/N), coherent power-maximizing dispersion measures (DM) obtained using DM_phase; excess dispersion measures ($\langle\mathrm{DM}_{\mathrm{excess}}\rangle$) inferred from the NE2001 Galactic electron density model (Cordes & Lazio, 2002); and full burst durations ($\Delta t$). TNS Name | MJD | RA (J2000) | $\sigma_{\text{RA}}(\arcsec)$ | Dec (J2000) | $\sigma_{\text{Dec}}(\arcsec)$ | S/N |  DM (pc cm-3) |  $\mathrm{DM}_{\mathrm{ex}}$ (pc cm-3) |  $\Delta t$ (ms)
---|---|---|---|---|---|---|---|---|---
FRB 20190425A | 58598.44993 |  17h02m41s | 11 | +21°34′34″ | 11 | 57.6 | 128.1279(3) | 79.4 | 0.65(1)
FRB 20191225A | 58842.69064 |  15h28m37s | 11 | +85°29′32″ | 11 | 65.1 | 683.9113(1) | 634.5 | 14.24(5)
FRB 20200603B | 59003.05128 |  10h09m37s | 24 | +71°34′48″ | 13 | 31.8 | 295.0828(4) | 253.9 | 10.23(4)
FRB 20200711F | 59041.03444 |  12h10m41s | 11 | +48°23′48″ | 11 | 175.1 | 527.6773(3) | 500.7 | 1.25(2)
FRB 20201230B | 59213.84582 |  19h00m44s | 23 | +26°01′15″ | 12 | 101.1 | 256.1293(4) | 95.0 | 2.93(3)
FRB 20210406E | 59310.09213 |  19h08m26s | 23 | +71°20′16″ | 12 | 100.7 | 355.2626(3) | 297.1 | 3.64(2)
FRB 20210427A | 59331.58050 |  20h30m33s | 23 | +79°15′54″ | 11 | 88.8 | 268.4785(4) | 204.0 | 2.13(1)
FRB 20210627A | 59392.57575 |  00h13m28s | 23 | +00°24′43″ | 11 | 85.7 | 299.158(4) | 267.5 | 2.32(2)
FRB 20210813A | 59439.63073 |  04h31m15s | 24 | +39°55′57″ | 12 | 61.9 | 399.264(7) | 237.0 | 2.95(9)
FRB 20210819A | 59445.91005 |  11h44m03s | 23 | +30°00′40″ | 12 | 124.9 | 362.142(2) | 342.0 | 3.46(3)
FRB 20211005A | 59492.94871 |  15h44m01s | 23 | +20°43′26″ | 12 | 73.7 | 226.1078(3) | 198.4 | 1.85(7)
FRB 20220413B | 59682.48227 |  16h49m03s | 23 | +66°58′56″ | 11 | 29.0 | 115.723(2) | 74.4 | 7.54(8)

Figure 1: Dynamic spectra for the 12 bursts reported on in this work. In each
panel, the bottom sub-panel shows signal intensity as a function of time and
frequency. The second sub-panel from the bottom shows the frequency-integrated
burst profile (timeseries). Each burst has been coherently dedispersed to a DM
measured by DM_phase. 4-paneled figures: the upper two sub-panels show the
cumulative polarization position angle (PA) in degrees relative to a zero-mean
$(\mathrm{PA}-\langle$PA$\rangle)$ and the fractional linear (L) and circular
(V) degrees of polarization, respectively (see §C). We omit polarization data
for FRBs 20200603B, 20200711F, 20210427A, 20210813A, and 20220413B, as we were
unable to confidently constrain rotation measures (RMs) due to spurious
$QU$-fits. The bursts show a variety of complex morphologies, discussed in §3.

##  3 Analysis & Results

Here we present various properties of the twelve bursts shown in Figure 1.
Figure 2 shows the dramatic difference in the appearance of a burst at the
nominal time- and frequency-resolution of the CHIME/FRB search pipeline versus
that available via baseband raw voltage data.

All DM measurements quoted in this work were obtained using
DM_phase222https://github.com/danielemichilli/DM_phase, which searches for the
DM that maximizes the coherent power of the signal across the observing band
in time. In addition to being dispersed by cold plasma along the line of
sight, many of the bursts in this sample exhibit additional frequency
“drifting” behavior, where the flux densities of either individual sub-bursts
or burst envelopes show unique variations in arrival time across the band,
after the full burst has been coherently dedispersed to a nominal DM. We
attempt to characterize and measure the various forms of drifting present in
the sample in §3.1. Additionally, we search for and measure microstructure in
select events with distinctly narrow features in §3.2 and §B. We also search
for periodicities in §3.3. Polarimetry performed on a sub-set of the bursts
for which reasonable RM fits could be achieved is outlined in §C.

Figure 2: A comparison of the full $2.56~{}\mu s$-resolution dynamic spectrum
of FRB 20210427A with the same dynamic spectrum downsampled to 1 ms (the
resolution of intensity data stored by the CHIME/FRB backend, see CHIME/FRB
Collaboration et al., 2021), reducing the resolvable sub-bursts to a simple
component.

###  3.1 Time-Frequency Drifting Archetypes

The events shown in Figure 1 suggest several possible categories or
“archetypes” of drift phenomenology: linear negative drifting, linear positive
drifting, power-law negative drifting, and power-law positive drifting. We
illustrate these archetypes by simulating idealized burst spectra for each
drifting scenario in Figure 3. We report our measurements of both linear drift
rates and power-law drift indices, as outlined below, in Table 2. Next, we
discuss our bursts with these archetypes in mind.

Figure 3: Simulated (idealized) representations of dynamic spectra for the four morphological archetypes outlined in §3.1 and §4.1. From left to right we show examples of linear negative, linear positive, power-law negative, and power-law positive drifting. Each of the sub-bursts in these representations are modeled as 2D Gaussians for simplicity. Table 2: Drifting properties for three events that offer the most salient examples of both linear and power-law drifting. The power-law drift indices are measured in two ways: $(1)$ assuming a relativistic shock emission mechanism (fitting for $\beta$; Metzger et al., 2022) as described in §3.1.2, and $(2)$ via a heuristic, incoherent alignment algorithm (fitting for $\gamma$) described in §3.1.4. TNS Name | Drift Rate (MHz ms-1) | Drift Index ($\beta$) | Drift Index ($\gamma$)
---|---|---|---
FRB 20201230B | +285(50) | … | …
FRB 20210813A | … |  $+0.76^{+0.07}_{-0.06}$, $+0.77^{+0.05}_{-0.07}$ |  $+$1.2(1)
FRB 20211005A | … | … |  $+$3.9(5)

####  3.1.1 Linear Negative Drifting

The “linear negative drifting” archetype describes the case where a burst
envelope or series of sub-bursts drift downwards in frequency along a single
negative slope in time (also referred to as the “sad trombone” effect). First
observed by Gajjar et al. (2018) in FRB 20121102A, it has become the most
common drifting archetype in FRBs, having since been observed in events from a
variety of other sources as well (Hessels et al., 2019; Rajwade et al., 2020;
Platts et al., 2021; Sand et al., 2022; Hewitt et al., 2023). Despite being
the most common, however, it is not obviously present in our sample. This is a
selection effect, in part, as we intended to select for events with uncommon
morphologies. It is also the case that the most salient instances of linear
negative drifting typically occur in repeating sources, whereas the sources
present here are thus far non-repeating. The only event that appears to be
drifting linearly with a negative slope, is FRB 20210819A. By eye, this
appears to be only subtly present in the lower half of the band, though it
does not clearly match the archetype as seen in other FRB sources. For this
reason, we do not focus on this particular archetype in detail here.

####  3.1.2 Power-Law Negative Drifting

The “power-law negative drifting” archetype describes the case where an
individual sub-burst, or entire burst envelope, drifts downwards in frequency
as a power-law in time after it has been dedispersed to a nominal DM. The
events in our sample that exhibit this behavior are FRB 20210813A, FRB
20200603B, FRB 20210427A, FRB 20210627A, and FRB 20211005A.

The most common example of power-law negative drifting is cold-plasma
dispersion, which follows the well-understood frequency-dependent time-delay
$t_{d}\propto\nu^{-2}$. The only cases where this would appear noticeable
after coherent dedispersion has been performed are when events contain sub-
bursts with unique DM values. The only event that clearly exhibits non-
dispersive power-law negative drifting, however, is FRB 20210813A. As such, we
will focus on this event here and reserve a study of DM variability for
§3.1.4.

We assume a nominal DM of 399.264(7) pc cm-3 for FRB 20210813A, based on the
coherent power-maximizing DM measured for the narrowest leading feature in the
spectrum, again using DM_phase. In §3.2, we measure the width of this feature
to be only $\Delta t=22.3(5)~{}\mu s$ (see Table 4), hence it provides good
constraining power for the DM. We find that the drifting behavior observed in
this burst after coherent dedispersion is not a consequence of cold plasma
dispersion, which would show a frequency-dependent time-delay in agreement
with $t_{d}\propto\nu^{-2}$. To confirm this, we perform a modified form of
incoherent dedispersion on the burst spectrum for a range of power-law
indices, and search for the index that best aligns the intensity across the
full band in time, effectively maximizing S/N in the timeseries. With this
method, we find a frequency-dependent time-delay relation closer to
$t_{d}\propto\nu^{-1.2(1)}$. This procedure is described in more detail in
§3.1.4.

Metzger et al. (2022) have proposed a toy model for FRB time-frequency
structure to explain precisely this phenomenon, with the primary intention of
resolving the morphological dichotomy between one-off and repeating FRBs
observed by CHIME/FRB (Pleunis et al., 2021; CHIME/FRB Collaboration et al.,
2021). According to the model, an FRB is generated by a release of energy from
a stellar-mass compact object, triggering a relativistic shock that, upon
expansion into a magnetized upstream medium described by a power-law density
profile, produces synchrotron maser emission. However, the model can also
accommodate coherent magnetospheric emission mechanisms that lead to a similar
power-law evolution of the SED over time, including magnetic reconnection
(Philippov et al., 2019; Lyubarsky, 2020), and curvature radiation
(Beloborodov, 2017; Ghisellini & Locatelli, 2018).

The model defines the flux density of a burst with multiple components as a
function of frequency and time as:

$F_{\nu}(t)=\sum_{i}F_{i}(t)\exp\left[-\frac{\left(\nu-\nu_{\mathrm{c},i}(t)\right)^{2}}{\Delta\nu_{\mathrm{c},i}(t)^{2}}\right]$
(2)

where $F_{i}(t)$ is the frequency-integrated flux density of the $i$-th
spectral component (or sub-burst), $\nu_{\mathrm{c},i}(t)$ is the central
frequency of the $i$-th component, and $\Delta\nu_{\mathrm{c},i}(t)$ is the
spectral width of the $i$-th component. The evolution of the central frequency
in time $\nu_{\mathrm{c}}(t)$ is defined:

$\nu_{\mathrm{c}}(t)=\nu_{0}\left(1+\frac{t}{t_{0}}\right)^{-\beta}$ (3)

where $\nu_{0}$ is the central frequency of the SED at a characteristic
timescale $t_{0}$, and $\beta$ is the power-law index that determines the rate
at which the SED drifts across the band. The frequency-integrated flux (see
Eq. 6 in Metzger et al., 2022) is defined:

$\displaystyle F_{i}(t)$
$\displaystyle\approx\frac{2}{\sqrt{\pi}}\frac{F_{0}}{\chi\nu_{0}}\left(1+\frac{t}{t_{0}}\right)^{(\beta+\mu-\alpha)}=\frac{2}{\sqrt{\pi}}\frac{F_{0}}{\chi\nu_{0}}\left(\frac{\nu_{\mathrm{c},i}(t)}{\nu_{0}}\right)^{(\alpha-\mu-\beta)/\beta}$
(4)

where $F_{0}$ is the initial peak flux density, $\alpha$ is the decay in time
of the frequency-integrated flux, $\mu$ describes how $\Delta\nu_{\mathrm{c}}$
evolves with $\nu_{\mathrm{c}}$ within the emission envelope, and $\chi$ is a
dimensionless parameter that controls the intrinsic bandwidth of the burst. In
total, this model is described by seven free parameters per component ($i$):
$\nu_{0}$, $F_{0}$, $t_{0}$, $\alpha$, $\mu$, $\beta$, and $\chi$.

Figure 4: Left: The dynamic spectrum of FRB 20210813A. Middle: The fitted two-
component flux density model, defined in Eq. 2, in accordance with the toy
model proposed by Metzger et al. (2022). Right: The real data are multiplied
by the model and smoothed to reveal “hot spots,” where, if the structure is
indeed produced by propagation effects, we would expect the greatest phase
gradients in the lensing structure to appear, producing caustic patterns
within the emission envelope.

We fit the 2D flux density model defined in Eq. 2 by Metzger et al. (2022) to
event FRB 20210813A, as it exhibits the most salient instance of power-law
negative drifting in our sample, as well as complex temporal substructure. We
use the dynesty (Speagle, 2020) nested sampler as implemented in the
bilby333https://pypi.org/project/bilby/ Python package (Ashton et al., 2019)
to estimate the best-fit parameters of Eq. 2 for FRB 20210813A, assuming
uniform priors. Since we are mainly concerned with the drifting index $\beta$
and not the full SED, however, we can reduce the degrees of freedom by fixing
values for $F_{0}=[1,1]$, $\alpha=[1,1]$, $\mu=[0,0]$, (consistent with
prototypical values used by Metzger et al., 2022). We find that the best-fit
values for the remaining burst parameters are
$\nu_{0}=[1.21^{+0.09}_{-0.08},1.41^{+0.09}_{-0.09}]$ GHz,
$t_{0}=[1.35^{+0.35}_{-0.25},1.39^{+0.35}_{-0.27}]$ ms,
$\chi=[0.05^{+0.01}_{-0.01},0.06^{+0.01}_{-0.01}]$,
$\beta=[+0.76^{+0.07}_{-0.06},+0.77^{+0.05}_{-0.07}]$, where $\beta$ is
defined as a positive quantity for negative drifting, as per Eq. 3. Note that
each parameter has two best-fit values, as the fits were performed for each
sub-burst. The leading, narrowest sub-burst is also omitted in the fit, as it
is quite faint and does not appear to drift, making it relatively
uninformative in the context of this model. We show the fitted model, and the
data multiplied by the fitted model in Figure 4. By multiplying the modeled
burst with the original data, we are able to better highlight increases in
flux density not explicitly accounted for in the toy model, which we will
henceforth refer to as “hot spots”. Variations of this kind could point to the
influence of propagation effects like lensing, or other intrinsic effects that
induce variability in the burst profile (Beniamini & Kumar, 2020; Lu et al.,
2021). Our results suggest that the power-law negative drifting observed in
FRB 20210813A could be reasonably explained by a relativistic shock
propagating into an expanding upstream medium, for which Metzger et al. (2022)
predict $\beta\approx 0.2$-$0.7$, though we note that magnetospheric scenarios
(e.g., radius-to-frequency mapping; Lyutikov, 2020) have suggested
$\beta\simeq 1$.

####  3.1.3 Linear Positive Drifting

The “linear positive drifting” archetype describes the case where a series of
sub-bursts or burst envelope drifts upwards in frequency along a single
positive slope in time (also referred to as the “happy trombone” effect). We
find only one event in the sample, FRB 20201230B, that exhibits this
morphology, showing a series of three bright sub-bursts with centroids
(regions of maximum flux density) that appear to increase in frequency over
time in a linear (or near-linear) fashion. This morphological archetype has
been observed in only a handful of FRBs to date (CHIME/FRB Collaboration et
al., 2020a, b; Marthi et al., 2020; Main et al., 2021; Zhou et al., 2022;
CHIME/FRB Collaboration et al., 2023b, further discussed in §4.1.2). We
measure the drift rate of FRB 20201230B by performing a least-squares fit of a
2D Gaussian function to the 2D autocorrelation function (ACF) of the dynamic
spectrum, and calculate the tilt in its semi-major axis, a standard technique
for measuring linear negative drifting behavior (Hessels et al., 2019; Pleunis
et al., 2021). To best characterize the 2D ACF, we use a modified 2D Gaussian
function $G(x,y)$, defined as:

$\displaystyle G(x,y)=$ $\displaystyle
A\exp\left\\{-\frac{1}{2}\left[x^{2}\left(\frac{\cos^{2}\theta}{\sigma_{x}^{2}}+\frac{\sin^{2}\theta}{\sigma_{y}^{2}}\right)\right.\right.\left.\left.+2xy\sin\theta\cos\theta\left(\frac{1}{\sigma_{x}^{2}}-\frac{1}{\sigma_{y}^{2}}\right)+y^{2}\left(\frac{\sin^{2}\theta}{\sigma_{x}^{2}}+\frac{\cos^{2}\theta}{\sigma_{y}^{2}}\right)\right]\right\\},$
(5)

where ($x,y$) are the time and frequency lag coordinates, $A$ is the
amplitude, $\sigma_{x}$ and $\sigma_{y}$ are the standard deviations along the
$x$ and $y$ axes, respectively, and $\theta$ is the rotation angle in radians.

The 2D Gaussian fit is shown in Figure 5, plotted as contours over the 2D ACF
of FRB 20201230B. We also show the best-fit drift rate plotted over the full
burst dynamic spectrum. To calculate this drift rate, we simply take the
cotangent of the best-fit rotation angle $\mathrm{cot}(\theta)$, and obtain a
rate of $+285(50)$ MHz ms-1.

Figure 5: Left: A 2D Gaussian fit to the 2D ACF of event FRB 20201230B; the 1,
2, and 3 $\sigma$ regions of the fitted Gaussian are plotted over the ACF as
white solid lines, and the semi-major axis is plotted as a white dashed line.
Right: The fitted drift rate, represented by the white dashed line, is plotted
over a downsampled dynamic spectrum of FRB 20201230B, which better highlights
some of the dimmer features.

####  3.1.4 Power-Law Positive Drifting and DM Variability

Perhaps the most remarkable morphological archetype present in our sample is
“power-law positive drifting,” which describes the case where an individual
sub-burst, or entire burst envelope, drifts upwards in frequency as a power-
law in time, again after it has been dedispersed to a nominal DM. The clearest
example of this phenomenon is exhibited by FRB 20220413B, as shown in Figure
6, and will serve as the primary case study for this archetype. Other FRBs in
this sample that appear to show power-law positive drifting are FRB 20200711F,
FRB 20210427A, FRB 20210627A, and FRB 20211005A (see Figure 7, as well as §A).

Assuming a nominal DM of 115.723(2) pc cm-3 for FRB 20220413B, which we
measure for the apparently non-drifting upper half (600-800 MHz) of the band
using DM_phase, we proceed to measure the drifting using two techniques.

The first technique is heuristic and makes no assumption about the power-law
index of the drifting. Instead we aim to measure the index by iteratively
performing a modified form of incoherent dedispersion on burst spectrum across
the full band (also performed in §3.1.2 on FRB 20210813A) as:

$t_{d}\simeq
10^{6}\mathrm{~{}ms}\times\left(\nu_{1}^{-\gamma}-\nu_{2}^{-\gamma}\right)\times\mathrm{DM_{Effective}}$
(6)

where we sample over a range of drifting indices $\gamma$,
$0\lesssim\gamma\lesssim 6$, with a dimensionless multiplicative prefactor
DMEffective, and $\nu_{1}$, $\nu_{2}$ that span 400-800 MHz. Through this
iterative process, we search for the index that maximizes the S/N in the time
series. We find that the best-fit drifting index $\gamma$ for the full band is
inconsistent with $\nu^{-2}$, and instead follows a $\nu^{-\gamma}$ where
$\gamma=3.9(5)$, as shown in Figure 6.

The second technique we use to quantify power-law positive (and negative)
drifting assumes that the drifting is dispersive (in agreement with
$t_{d}\propto\nu^{-2}$), and occurs due to interactions with compact cold
plasma structures of non-uniform density along the line of sight, as might be
expected from a plasma lens (Cordes et al., 2017). Given this assumption, we
iteratively coherently dedisperse the dynamic spectrum for time-limited
regions across the burst for a range of trial DM offsets ($\Delta$DM) between
[$-$0.15 pc cm-3, 0.15 pc cm-3] from the nominal value calculated previously,
again using DM_phase, to search for the DM value that maximizes coherent power
in the time-limited region of the spectrum. The ranges in time over which
these maximizations are performed are determined by judiciously isolating sub-
bursts or sub-burst clusters in time. For certain bursts with narrower band
occupations, we limit the frequency range over which we perform dedispersion
as well.

By inspection of the dynamic spectrum of FRB 20220413B, there appears to be a
bifurcation in the first sub-burst (a separation into two distinct sub-bursts)
that occurs at $\nu_{l}\approx$ 545 MHz (possibly the “focal frequency”, as
described by Cordes et al., 2017). Below this frequency, the drifting appears
to be reasonably consistent with cold plasma dispersion. To show this, we plot
DM curves adjacent to the drifting features in accordance with the estimated
$\Delta$DM offsets from the nominal value calculated for FRB 20220413B, as
shown in Figure 6. Under the assumption that this bifurcation arises due to
multiple-imaging (a consequence of plasma lensing), we limit the frequency
range of the dynamic spectrum to 400-545 MHz and calculate the respective DM
values for which the coherent power of the leading sub-burst and trailing sub-
bursts is maximized.

We perform the same iterative coherent dedispersion procedure for bursts FRB
20200711F, FRB 20210427A, FRB 20210627A and FRB 20211005A, all of which show
both positive and negative power-law drifting. Respective $\Delta$DM values
measured for each event are recorded in Table 3. In Figure 7, we again plot DM
curves adjacent to the drifting features to show the respective deviations in
DM from the nominal values. Note that, similar to FRB 20220413B, FRB 20210627A
also shows possible focal frequencies at $\nu_{l,1}\approx 650$ MHz,
$\nu_{l,2}\approx 480$ MHz, above which no drifting is observed. The
coherently dedispersed dynamic spectra for these events at each
$\mathrm{DM}_{\mathrm{nominal}}+\Delta\mathrm{DM}$ value recorded in Table 3
are shown in §A (see Figures 10, 11, 12, and 13). This method illustrates that
DM variability on microsecond timescales is likely present in a substantial
fraction of FRBs in our sample. These data highlight the worthwhile endeavor
of characterizing plasma lensing in FRBs through more robust, raw voltage
searches of phase coherence between sub-bursts—a smoking gun for lensing
phenomena (Kader et al., in prep.).

Figure 6: The upper left panel shows the dynamic spectrum of event FRB
20220413B, dedispersed to its nominal DM calculated using DM_phase, where the
measured frequency-dependent drift over-plotted as a white solid line. The
upper right panel shows the dynamic spectrum of FRB 20220413B, re-aligned
(“dedispersed”) for a frequency index of $\nu^{-3.9(5)}$. The middle left
panel shows the dynamic spectrum of FRB 20220413B with DM curves over-plotted
as white solid lines and the approximate focal frequency $\nu_{l}\approx$ 545
MHz as a white dotted line. The panels following show dynamic spectra of the
same event dedispersed to the coherent power-maximizing $\Delta$DM offsets
from the nominal burst DM for respective sub-bursts, highlighted in purple in
the timeseries. The lowest panel shows the averaged pulse profile between
400-545 MHz of the band as a function of time and DM, showing clear
“bowtie”-like features that arise from the differential DMs between sub-
bursts. The DMs present in the burst are indicated by white dotted lines,
whereas the DMs corresponding to respective sub-bursts are specified by white
dotted circles. The shaded circle indicates a region where the coherent power-
maximizing DM measurement disagrees with the most intense region in the right-
most bowtie feature. This feature contains two centroids, the centroid of
lowest DM (also highlighted by a white dotted circle) corresponds to the
coherent power-maximizing DM of the sub-burst. Figures 7, 10, 11, 12, and 13
show the $\Delta$DM values for the other events in our sample exhibiting
seemingly dispersive drifting, for which values are reported in Table 3.

Figure 7: Dynamic spectra for events FRB 20200603B, FRB 20210427A, FRB 20210627A and FRB 20211005A, with DM curves over-plotted as white lines, highlighting potential DM variability present in each burst. For FRB 20210627A, we also plot the frequencies at which drifting starts to occur (the so-called “focal frequencies”; $\nu_{l,1}\approx 650$ MHz, $\nu_{l,2}\approx 480$ MHz) as white dotted lines. The color scale of the spectra is more constrained in comparison to those in Figure 1 to better show fainter features. The dispersion measure variations with respect to the nominal DM values of each burst are reported in Table 3. Table 3: The nominal DM values and measured offsets ($\Delta\mathrm{DM}$) for five of the twelve events in the sample, all of which show drifting features that appear consistent with dispersive smearing. FRB 20220413B is shown in Figure 6, while the others are shown in the §A. The $\Delta\mathrm{DM}$ values (all in pc cm-3) are listed as they appear across each burst from left to right, and are measured to within errors of $\pm 10\%$. TNS Name | $\mathrm{DM}\left(\mathrm{pc~{}}\mathrm{cm}^{-3}\right)$ | $\Delta\mathrm{DM}_{1}$ | $\Delta\mathrm{DM}_{2}$ | $\Delta\mathrm{DM}_{3}$ | $\Delta\mathrm{DM}_{4}$ | $\Delta\mathrm{DM}_{5}$ | $\Delta\mathrm{DM}_{6}$
---|---|---|---|---|---|---|---
FRB 20200603B | $295.0828(4)$ | 0.0 | +0.002 | +0.02 | … | … | …
FRB 20210427A | $268.4785(4)$ |  $-$0.018 |  $-$0.006 |  $-$0.002 | 0.0 | +0.005 | …
FRB 20210627A | $299.158(4)$ |  $-$0.015 | 0.0 |  $-$0.01 | +0.01 | +0.04 | …
FRB 20211005A | $226.1078(3)$ |  $-$0.005 | 0.0 | +0.002 | +0.004 |  $-$0.008 | +0.05
FRB 20220413B | $115.723(2)$ |  $-$0.05 | 0.0 |  $-$0.11 | … | … | …

###  3.2 Microstructure

The majority of the bursts in our sample contain narrow $\mu$s features that
rival some of the narrowest features seen to date in both repeating (Nimmo et
al., 2021, 2022; Majid et al., 2021; Snelders et al., 2023; Hewitt et al.,
2023) and non-repeating (Farah et al., 2018, 2019; Day et al., 2020) sources.
While complex microstructure appears to be relatively common in repeaters, its
prevalence in non-repeaters is not well studied. As many of the bursts in our
sample are quite narrow across the full burst profile, we set a limit of
$\lesssim 50~{}\mu s$ for the sub-bursts that we consider to be
“microstructure”. In turn, we take all sub-bursts with widths $\gtrsim 50\;\mu
s$ to collectively describe the broader flux distribution or “envelope” across
the burst. Due to the numerous sub-bursts present in many of the events in
this sample, we set this admittedly arbitrary limit to highlight the most
strikingly narrow features. We identify microstructure in seven of the twelve
bursts in this sample by performing multi-Gaussian fits to the timeseries and
ACF measurements for sub-divided regions surrounding individual sub-bursts and
sub-burst clusters. For most bursts, we fit the timeseries for the integrated
upper half (600-800 MHz) of the observing band rather than the full band, to
enhance the S/N of narrow features. We report the measured Gaussian widths of
$\lesssim 50~{}\mu s$ features in Table 4. The fits themselves are shown
Figure 8.

The microstructure is measured in three steps, which in short reduce to: (1)
isolating the upper half of the band if the sub-structure is sufficiently
broadband and if broadening (either due to scattering or some other mechanism)
is present in the lower half of the band, (2) performing a multi-Gaussian fit
to the timeseries using the minimum number of Gaussians that sufficiently
characterize the envelope and sub-structure (such that the residuals contain
no apparent signal), (3) isolating the identified sub-structures in time,
calculating the autocorrelation functions for the specified regions (ACF), and
fitting a 1D Lorentzian to the ACF to the validate the previous Gaussian fit.

To ensure that we do not fit for noise spikes, we implement two tests. First,
we calculate a 5-$\mu s$ window rolling mean across the burst profile to
search for signals that exceed $3\sigma$ in amplitude with respect to the
noise statistics measured in the off-pulse region, which we assume to be
Gaussian. Second, we measure the maximum width and prominences of noise spikes
in the off-pulse region to ensure that the features fit for in the multi-
Gaussian profile exceed these values. While these tests do not fully take into
account the effects of amplitude-modulated noise, which is expected to be
boosted by the signal itself, we assume that these effects are sufficiently
ignored by the widths measured from the ACFs. The ACF measurement methods are
discussed in B and fits are reported in Table 5.

Table 4: The measured widths (FWHM) of $\lesssim 50\mu s$ sub-bursts detected in seven events in the sample using a multi-Gaussian fit, as shown in Figure 8. The methods used to perform the multi-Gaussian fits are outlined in §3.2. TNS Name | $\Delta\mathrm{t}_{1}$ | $\Delta\mathrm{t}_{2}$ | $\Delta\mathrm{t}_{3}$ | $\Delta\mathrm{t}_{4}$ | $\Delta\mathrm{t}_{5}$ | $\Delta\mathrm{t}_{6}$ | $\Delta\mathrm{t}_{7}$ | $\Delta\mathrm{t}_{8}$
---|---|---|---|---|---|---|---|---
FRB 20190425A | 9.2(4) | 22(1) | 14.5(1) | 16.6(2) | 8.3(1) | 17.2(4) | 23.3(3) | …
FRB 20200603B | 7.10(2) | 29(1) | 42.5(3) | 16.5(9) | … | … | … | …
FRB 20210406E | 11.1(1) | 6.3(1) | 23.8(2) | 14.3(3) | 15.0(3) | 26.4(5) | 24.0(2) | 15.0(3)
FRB 20210427A | 38.5(8) | 19.1(5) | … | … | … | … | … |
FRB 20210627A | 44.6(3) | 31.5(5) | … | … | … | … | … | …
FRB 20210813A | 22.3(5) | 38(1) | … | … | … | … | … | …
FRB 20211005A | 36.8(9) | … | … | … | … | … | … | …

Figure 8: A microstructure analysis of seven of the twelve bursts the sample.
The purple curve plotted over the burst timeseries in each panel shows a
multi-Gaussian fit to all features in the burst. Microstructure in five of the
seven are significantly masked by flux envelopes in the lower half of the
band, the origin of which is not well understood. The magenta curves show the
isolated Gaussians from the fit with FWHM $\lesssim 50~{}\mu s$ (i.e.,
“microstructure”) while the grey curves show the isolated Gaussian fits with
FWHM $\gtrsim 50~{}\mu s$ (i.e., “envelope”), together forming the full multi-
Gaussian fit. The blue curve shows the residuals of the fit. The methods of
this analysis are described in §3.2, and the intrinsic widths of $\lesssim
50$-$\mu s$ sub-bursts for each event are reported in Table 4.

###  3.3 Quasi-Periodicites

As many of these bursts contain multiple sub-components, we search for
periodic or quasi-periodic substructure using the Rayleigh significance test
outlined in detail by CHIME/FRB Collaboration et al. (2021). To identify
candidates in our sample that exhibit plausible quasi-periodic structure, we
first calculate the power spectra of the timeseries of each burst and search
for prominent peaks in the power spectra. The only event in our sample that
appears to show encouraging evidence for a periodicity in its power spectrum
is FRB 20210819A, as shown in Figure 9. As this burst exhibits more complex
features below 600 MHz, we choose to isolate the upper-half (600-800 MHz) of
the band for the purposes of this analysis, so as to better resolve each
individual sub-burst. To evaluate the significance of the periodicity
indicated by the most prominent peak in the power spectrum, we use the
Rayleigh significance statistic ($Z_{1}^{2}$), which has been used previously
by CHIME/FRB Collaboration et al. (2022a) to identify the first sub-second
periodicity in an FRB, and is commonly used to search for periodicities in
high-energy pulsar emission (Buccheri et al., 1983; de Jager, 1994). The
Rayleigh statistic is a significance measure for periodicities in irregularly
sampled data, defined in general form ($Z_{n}^{2}$) as:

$Z_{n}^{2}=\frac{2}{N}\sum_{k=1}^{n}\left[\left(\sum_{j=1}^{N}\cos
k\phi_{j}\right)^{2}+\left(\sum_{j=1}^{N}\sin k\phi_{j}\right)^{2}\right]$ (7)

where $N$ is the number of pulses, $n$ is the number of harmonics (for which
we choose $n=1$, in accordance with the Rayleigh test), and $\phi_{j}$
represents the pulse phases. We perform a blind periodicity search using Eq. 7
by randomly generating time-of-arrival (ToA) differences, drawn from a uniform
probability distribution (see CHIME/FRB Collaboration et al., 2022a, for
details; the same exclusion parameters are applied). We generate $10^{3}$
random ToA distributions with the same number of components and duration as
FRB 20210819A, sufficient to uncover a notable statistical significance, and
apply the Rayleigh test to each distribution, shown in Figure 9. Finally, we
compare the $Z_{1}^{2}$ values obtained for each simulation to that obtained
for the ToAs measured for FRB 20210819A. The most significant (quasi-)period
indicated by the power spectrum of FRB 20210819A is measured to be
$448(40)~{}\mu$s ($2232(230)$ Hz), also shown in Figure 9. When we apply the
Rayleigh significance test, we find that the significance of this periodicity
is only 1.1(2)$\sigma$, insufficient to indicate a detection.

We further note that the quasi-periodicity likely exceeds the maximum
estimated rotation frequency possible for a neutron star under currently known
equations of state, suggesting it is unlikely to be attributed to neutron star
rotation (Lattimer & Prakash, 2016).

Figure 9: A diagnostic plot of the power spectrum burst analysis for FRB
20210819A. The left panel shows the burst dynamic spectrum for the upper half
of the band (600-800 MHz) with a putative period corresponding to the highest
peak in the power spectrum, plotted in white dotted lines. The burst
timeseries is also shown, with the measured ToAs (solid grey lines) and
putative spin period again (dotted grey lines) to highlight the respective ToA
offsets. The middle panel shows the burst power spectrum, where the peak
indicates the best estimate of the period of the burst. The right panel shows
the results of the Rayleigh significance test, which indicates a statistical
significance of 1.1(2)$\sigma$ for the measured period of the burst. The
vertical purple line marks the $Z_{1}^{2}$ value of the measured period.

##  4 Discussion

###  4.1 Revisions to Time-Frequency Drifting Archetypes

The events in our sample offer an opportunity to revisit our current
understanding of the FRB morphologies, and possible archetypes, first proposed
by Pleunis et al. (2021). These include “simple broadband,” “simple
narrowband,” “temporally complex,” and “downward drifting”. As seen in
previous investigations of high-resolution FRB data (Farah et al., 2018, 2019;
Hessels et al., 2019), bursts previously considered “simple” may only be
simple by virtue of the resolution at which the data are stored. On $\mu$s
timescales, many FRBs are seen to be complex. Based on the bursts in our
sample, it is clear that “drifting” in FRBs can deviate from the linear
negative drifting, or “downward drifting” archetype, thus motivating us to
suggest new categories of drifting archetypes, as described in §3.1 above. We
discuss possible physical origins for each archetype below.

####  4.1.1 Power-Law Negative Drifting and the Nebula Toy Model

Of the twelve events in our sample, three show clear indications of power-law
negative drifting: FRB 20210813A, FRB 20210627A, and FRB 20210427A, as
described in §3.1.4. Only FRB 20210813A, however, appears to disagree with
dispersive smearing, suggesting that the Metzger et al. (2022) toy model may
be relevant.

Metzger et al. (2022) provide a useful tool to compare the observed burst
properties with theoretical predictions from other FRB models that invoke both
relativistic shock and magnetospheric emission mechanisms (e.g. Lyutikov,
2020; Sridhar et al., 2021). While the overall shape of the flux density
envelope is explained by the model, it does not obviously account for sub-
structure. Metzger et al. (2022) suggest that sub-structure may originate from
propagation effects such as plasma lensing. We entertain this possibility by
multiplying the model from the data and plotting the result in the right-most
panel of Figure 4 to highlight the “hot spots” in flux density that may arise
due to amplifications by an intervening plasma lens (i.e., caustics). While we
cannot conclusively extract the lens position or geometry, it motivates
extending this model to include such effects.

Evaluated in the context of the Metzger et al. (2022) model, the best-fit
values for the drifting index
$\beta=[+0.76^{+0.07}_{-0.06},+0.77^{+0.05}_{-0.07}]$ for the two spectral
components in FRB 20210813A seem to imply emission by a decelerating
relativistic shock propagating into an expanding upstream medium. For this
scenario, Metzger et al. (2022) estimate an index range of $\beta\simeq
0.2-0.7$. The precise range of drifting indices depends, however, on the
density gradient $n(r)\propto r^{-k}$ of the upstream medium in the radial
direction, which is unknown in this case, but is thought to lie in the range
of $0\lesssim k\lesssim 2$.

####  4.1.2 Linear Positive Drifting

While FRB 20201230B is not the first FRB to show linear positive drifting, it
is the first to show linear positive drifting between sub-bursts separated by
$\lesssim 1$ ms. Linear positive drifting is not nearly as common as linear
negative drifting in FRBs, and certainly not often seen in non-repeater
events, but it has been detected in bursts from six other FRBs of which the
authors are aware444The number of FRBs showing linear positive drifting may be
higher, but as this feature is not widely reported, it is challenging to gauge
its prevalence in the literature., two of which were seen by CHIME/FRB. The
first detection was in a burst emitted by FRB 20180916B, which contained two
components separated in time by $\sim$60 ms, exhibiting a drift rate of
$\sim+$1.6 MHz ms-1 (CHIME/FRB Collaboration et al., 2020b). The second was
seen in the detection of two bursts emitted by SGR 1935+2154 (CHIME/FRB
Collaboration et al., 2020a), separated in time by $\sim$29 ms. The drift rate
of the latter is more challenging to measure as the bursts extend beyond the
CHIME/FRB band, but if the centroids were taken to be the lower and upper band
limits (400 and 800 MHz, respectively), the drift rate would be close to
$\sim$13 MHz/ms. The third instance of drifting, though not explicitly
reported by the authors, was again observed in a burst from FRB 20180916B by
Marthi et al. (2020) with the uGMRT array, showing a sub-burst separation of
order $\sim$ 20 ms between $\sim 600$-$650$ MHz, hence a drift rate of
$\sim+2.5$ MHz ms-1. The fourth instance of drifting, again not explicitly
reported, can be seen in a burst from FRB 20201124A observed with the
Effelsberg telescope by Main et al. (2021), which shows a sub-burst separation
of order $\sim 8$ ms between $\sim 1300$-$1425$ MHz, indicating a drift rate
of $\sim+15$ MHz ms-1. The fifth instance of linear positive drifting was seen
in three separate events, again of FRB 20201124A, by Zhou et al. (2022) with
the FAST telescope during an extremely active period. The specific drift rates
were not measured, the dynamic spectra suggest that the drifting sub-burst
centroids span $\gtrsim 10$ ms in time and $\sim 1100$-$1400$ MHz in
frequency, giving a rough upper limit of $\sim+30$ MHz ms-1. Finally, the most
recent instance of linear positive drifting was observed in FRB 20190630D by
CHIME/FRB Collaboration et al. (2023b). While the drift rate has not yet been
carefully measured, the dynamic spectrum appears to suggest a frequency span
of $\sim 200$ MHz, and a time span of $\sim 2$-$3$ ms, resulting in an
estimated drift rate of $\sim+66$-$100$ MHz ms-1.

Overall, the drift rates of these events are notably less dramatic than that
seen in FRB 20201230B, which we measured to be $+285(50)$ MHz/ms. This
difference is due to the sub-millisecond separations of each sub-burst in FRB
20201230B.

Notably, linear positive drifting has already been seen in some radio pulsars
(e.g. Bilous et al., 2022). One possible mechanism by which linear positive
drifting can occur is via radius-to-frequency mapping in the magnetospheres of
neutron stars, both pulsars and magnetars (Ruderman & Sutherland, 1975;
Manchester & Taylor, 1977; Beloborodov, 2017; Lyutikov, 2020; Bilous et al.,
2022). This occurs when charged particle bunches move along curved magnetic
field lines in the magnetosphere, which rotate around the magnetic axis,
allowing different bunches to cross the line of sight at different times,
producing a series of sub-bursts that drift upward or downward in frequency,
the direction dependent on the geometry of the dipolar field and the viewing
angle (Bilous et al., 2022). The rate of the drifting is thought to depend on
the rotation rate of the loop and the curvature radius of the magnetic field
lines. The assumption is that the plasma in the magnetosphere produces
coherent emission with frequencies that depend on the height of the emitting
region (higher frequencies originating at lower heights). The fact that FRB
20201230B also exhibits a moderate PA swing of approximately 80 degrees,
favors the hypothesis that emission originates from within the magnetosphere.
However, there are major challenges with FRBs emerging from neutron star
magnetospheres. Beloborodov (2021, 2023) argue that such luminous radio waves
get damped in the magnetosphere, interacting with plasma particles,
accelerating them to high energies at the expense of the wave energy. If so,
FRBs could not escape a magnetosphere. On the other hand, Qu et al. (2022)
argue that in the open field line region, the likely high outward plasma speed
and the alignment of the field with the radio wave propagation direction mean
the expected interaction between them is reduced, such that full damping is
avoided.

####  4.1.3 Power-Law Positive Drifting and DM Variability

There are several possible explanations for power-law positive drifting
observed in FRB 20200711F, FRB 20210427A, FRB 20210627A, FRB 20211005A, and
FRB 20220413B. Notably, this phenomenon bears some similarity to a subclass of
Type III solar radio bursts (Alvarez & Haddock, 1973; Lyutikov & Rafat, 2019;
Vedantham, 2020) which are generated by stimulated electron beams propagating
along open magnetic field lines toward the stellar surface rather than away,
the latter of which would lead to power-law negative drifting, as we see in
the model proposed Metzger et al. (2022). Comparisons between FRBs and solar
radio bursts have been discussed previously by Hewitt et al. (2023).

The frequency dependence of the power-law positive drifting features exhibited
by events in this sample seems to agree with $t_{d}\propto\nu^{-2}$, and may
therefore be explainable by propagation through a dispersive medium, such as a
discrete plasma structure (or lens) with varying electron column densities.
Plasma lensing occurs when electron over- or under-densities in a plasma
structure along the line of sight magnify or de-magnify the radio signal from
a distant source. In addition to magnification, lensing can lead to multiple-
imaging. This occurs when radio waves propagate through a region of plasma
with a density gradient, such as a clump or sheet, which leads to the
formation of caustics (images) below a specific focal frequency. Below this
frequency, images are expected to experience differential delays in time,
dependent on the region of the lens that is being probed. These delays ought
to be both dispersive, reflecting the DM depth of the region, and geometric,
due to the differential path lengths traversed by each image. Hence, we expect
multiply imaged FRBs to exhibit multiple burst components of different DM
values.

Plasma lensing can occur in local magneto-ionic environments, where some FRBs
are known to reside (such as FRB 20121102A; Michilli et al., 2018), or at
larger distances from the source. It has been suggested as a dominant agent in
shaping the morphologies of radio pulses from certain Galactic pulsars in
binary systems (Main et al., 2018; Li et al., 2023; Lin et al., 2023), as well
as the Galactic Center magnetar, PSR J1745$-$2900 (Pearlman et al., 2018),
which is believed to be embedded in a highly magneto-ionic environment as
well.

Currently, plasma lensing has yet to be unambiguously demonstrated in FRBs,
partially due to the still limited sample of well-localized FRBs measured at
high time resolution. Plasma lensing has been suggested, however, as a
possible contributor to the morphologies of some FRBs, such as FRB 20121102
(Gajjar et al., 2018; Michilli et al., 2018; Hessels et al., 2019; Platts et
al., 2021). The persistence of downward drifting morphologies in bursts from
FRB 20121102 without a comparable occurrence of upward drifting, however,
calls this claim into question. Lensing has also been suggested as a possible
cause for quasi-periodic temporal modulations seen in select bursts from FRB
20180916B (Nimmo et al., 2021), though these features could also be explained
by self-modulation (Sobacchi et al., 2020).

The disparate degrees of seemingly dispersive drifting between multiple sub-
bursts observed in FRB 20220413B, FRB 20200603B, FRB 20210427A, FRB 20210627A
and FRB 20211005A, as highlighted by the DM curves plotted over drifting
features in their respective spectra (see Figure 6, 7 and Table 3), seem to
suggest that plasma lensing may play an important roll in shaping the
morphologies of these bursts. Dispersive drifting of this kind would be
expected in the case of multiple imaging. The simplest lens model that
explains the upward drifting morphology of FRB 20220413B by plasma lensing, is
one that invokes a convergent (i.e. underdense) Gaussian lens, and assumes
that the emission is probing different transverse regions of the lens,
provided the lens has a non-zero effectively velocity with respect to the
source. If this scenario is valid, the varying electron densities in each
region of the lens would cause the multiple images to drift upward in
accordance with the specific DM depth ($\Delta$DMł) of that region. Such
scenarios have been modeled previously by Platts et al. (2021). We measure
these $\Delta$DMł values in §3.1.3 and report them in Table 3.

As FRB 20220413B shows the clearest example of apparently dispersive delays
below a visually apparent focal frequency, we will explore explore the
possibility of plasma lensing being the dominant agent in shaping the
morphology using conventional lensing theory outlined in Cordes et al. (2017).

The condition that must be satisfied in order to produce multiple images below
a focal frequency $\nu_{l}$ can be defined using Eq. 8 from Cordes et al.
(2017):

$\nu_{l}\approx
39.1~{}\mathrm{GHz}\times\frac{|\Delta\mathrm{DM}_{l}|^{1/2}}{a}\left(\frac{d_{\mathrm{sl}}d_{\mathrm{lo}}/d_{\mathrm{so}}}{1\mathrm{kpc}}\right)^{1/2},$
(8)

where $|\Delta\mathrm{DM}_{l}|$ is the DM depth of the lens at a specific
region (in pc cm-3), $\nu_{l}$ is focal frequency (i.e., the frequency at
which multiple-imaging, or drifting is observed in GHz), $d_{\mathrm{sl}}$ is
the distance from the source to the lens (in pc), $d_{\mathrm{so}}$ is the
distance from the source to the observer (in Gpc), and $a$ is the
characteristic lens scale (in AU). We assume a conservative geometry in this
relation, placing the lens close to the source, such that $d_{\mathrm{sl}}=1$
kpc and $d_{\mathrm{so}}/d_{\mathrm{sl}}\sim 10^{6}$. Of course, these values
describe just one of many possible lensing geometries.

Under these assumptions, we can estimate the lower-limit of $a_{\mathrm{AU}}$
required for multiple-imaging to occur at $\nu_{l}\approx 545$ MHz (the focal
frequency), where $|\Delta\mathrm{DM}_{l}|\approx 0.05$ pc cm-3 (measured
between the first and second sub-burst, see Figure 6) to be

$\displaystyle a\approx
16~{}\mathrm{AU}\times\Biggl{(}\frac{|\Delta\mathrm{DM}_{l}|}{0.05~{}\mathrm{pc~{}cm^{-3}}}\Biggr{)}^{1/2}\Biggl{(}\frac{0.545~{}\mathrm{GHz}}{\nu_{l}}\Biggr{)}\Biggl{(}\frac{d_{\mathrm{sl}}d_{\mathrm{lo}}/d_{\mathrm{so}}}{1\mathrm{kpc}}\Biggr{)}^{1/2},$
(9)

a reasonable estimate for the characteristic scale of the lens, as plasma
lenses in the Milky Way are typically only a few AU across (Bannister et al.,
2016).

To evaluate if the effects present in FRB 20220413B and other events truly
originate from lensing, however, we can look for phase-coherence between the
sub-bursts to assess whether these are in fact multiply imaged. This is
possible given the phase-preserving nature of baseband raw voltages and is
currently under study (Kader et al., in prep.).

###  4.2 Microstructure

In the magnetospheric reconnection model, FRBs are generated via coherent
curvature radiation or inverse Compton scattering by charged bunches moving
along curved magnetic field lines. In this model, the burst duration is
determined by the light-crossing time of the emission region, which is
typically of order $\sim 10~{}\mu s$ for a neutron star radius of order $\sim
10$ km. The burst morphology can be influenced by the plasma density
distribution and the magnetic field configuration in the magnetosphere, as
well as by propagation effects in the magnetosphere and the interstellar
medium (Cordes et al., 2017).

In the outflow model, however, FRBs are produced by synchrotron maser emission
from relativistic shocks driven by magnetar flares (Metzger et al., 2019;
Beloborodov, 2019). The burst duration, in turn, is determined by the shock
crossing time of the outflow shell, which must be much longer than the light-
crossing time of the central neutron star. The morphology may then be
influenced by some combination of the shock dynamics, the outflow geometry,
and the ambient medium. These models involve coherent emission mechanisms. As
estimated by Metzger et al. (2019), bursts emitted via relativistic shocks can
span roughly $0.01$-$10$ ms in duration—values extending past the light
crossing time of the neutron star by the propagation of the shock. Hence
narrower features favor magnetospheric emission, if the burst durations are
indeed intrinsic (Beniamini & Kumar, 2020).

The narrowest sub-burst measured in our sample appears in FRB 20210406E with a
width $\Delta t=6.3(1)$ $\mu s$ (consistent to within $\sim 1~{}\mu s$ as
measured by the fitting the ACF; see §B and Tables 4, 5). Assuming
$d_{e}\lesssim c\Delta t$, the upper limit on the diameter of the emission
region, $d_{e}$, inferred from this would be $\approx$ 1.9 km. All of the
narrowest sub-structures in the bursts that we measured suggest emission
regions of order kilometers in size. This estimate neglects relativistic
effects such as aberration and retardation (e.g. Blaskiewicz et al., 1991).

Alternatively, plasma lensing (Cordes et al., 2017) and self-modulation
(Sobacchi et al., 2020) can also produce microstructure due to propagation
through a turbulent, possibly magnetized plasma along the line of sight. This
plasma can either reside in the interstellar medium (ISM) of the host galaxy
or in the circumburst environment surrounding the FRB source (such as a
supernova remnant or a companion star; Main et al., 2018).

##  5 Conclusion

In this work, we have shown that thus far non-repeating FRBs can exhibit
complex time-frequency structure, opening up a possible bridge between the
morphological characteristics of both repeating and non-repeating FRBs. We
have used this sample of events to further inform and refine our understanding
of such characteristics, particularly as they relate to drifting. Furthermore,
we suggest a new framework for classifying and interpreting drifting
phenomenologies that goes beyond the linear negative drifting behavior
observed in many repeating FRBs. We divide this framework into four
morphological classes or “archetypes,” and consider both intrinsic emission
mechanisms and extrinsic propagation effects that may be responsible for them.
The most promising emission mechanisms considered in this paper include the
synchrotron maser process and magnetospheric modulations of curvature
radiation, expected to originate from compact objects such as magnetars. We
further highlight events that show apparent frequency-dependent magnifications
and dispersion measure variablity over time, which favor extrinsic propagation
effects like plasma lensing. While this study includes just twelve newly
discovered FRBs, the recent expansion in publicly available baseband raw
voltage data for both apparent non-repeaters and repeaters by CHIME/FRB
(CHIME/FRB Collaboration et al., 2023b) will allow for more detailed
explorations of the proposed archetype classification framework, and enable
more rigorous tests and constraints of the models outlined in this paper, as
well as others.

##  6 Acknowledgements

We acknowledge that CHIME is located on the traditional, ancestral, and
unceded territory of the sylix (Okanagan) people. We thank the Dominion Radio
Astrophysical Observatory, operated by the National Research Council Canada,
for gracious hospitality and expertise. CHIME is funded by a grant from the
Canada Foundation for Innovation (CFI) 2012 Leading Edge Fund (Project 31170)
and by contributions from the provinces of British Columbia, Québec and
Ontario. The CHIME/FRB Project is funded by a grant from the CFI 2015
Innovation Fund (Project 33213) and by contributions from the provinces of
British Columbia and Québec, and by the Dunlap Institute for Astronomy and
Astrophysics at the University of Toronto. Additional support was provided by
the Canadian Institute for Advanced Research (CIFAR), McGill University and
the McGill Space Institute via the Trottier Family Foundation, and the
University of British Columbia. The Dunlap Institute is funded through an
endowment established by the David Dunlap family and the University of
Toronto. Research at Perimeter Institute is supported by the Government of
Canada through Industry Canada and by the Province of Ontario through the
Ministry of Research & Innovation. The National Radio Astronomy Observatory is
a facility of the National Science Foundation (NSF) operated under cooperative
agreement by Associated Universities, Inc. FRB research at UBC is supported by
an NSERC Discovery Grant and by the Canadian Institute for Advanced Research.
The baseband instrument for CHIME/FRB is funded in part by a CFI John R. Evans
Leaders Fund grant to IHS. This research used the Canadian Advanced Network
For Astronomy Research (CANFAR) operated in partnership by the Canadian
Astronomy Data Centre and The Digital Research Alliance of Canada with support
from the National Research Council of Canada the Canadian Space Agency,
CANARIE and the Canadian Foundation for Innovation. JTF would like to thank
the Fulbright Canada Foundation for funding this work and all members of the
CHIME/FRB Collaboration at the Trottier Space Institute at McGill
(tsi.mcgill.ca) for their gracious mentorship. FRB research at WVU is
supported by an NSF grant (2006548, 2018490). FRB research at UBC is supported
by an NSERC Discovery Grant and by the Canadian Institute for Advanced
Research. The CHIME/FRB baseband system is funded in part by a Canada
Foundation for Innovation John R. Evans Leaders Fund award to IHS. The Dunlap
Institute is funded through an endowment established by the David Dunlap
family and the University of Toronto. B.M.G. acknowledges the support of the
Natural Sciences and Engineering Research Council of Canada (NSERC) through
grant RGPIN-2022-03163, and of the Canada Research Chairs program. M.B is a
McWilliams fellow and an International Astronomical Union Gruber fellow. M.B.
also receives support from the McWilliams seed grant. A.M.C. is supported by
an NSERC Doctoral Postgraduate Scholarship. M.D. is supported by a CRC Chair,
NSERC Discovery Grant, CIFAR, and by the FRQNT Centre de Recherche en
Astrophysique du Québec (CRAQ). G.M.E. is supported by an NSERC Discovery
Grant RGPIN-2020-04554, and a Canadian Statistical Sciences Institute (CANSSI)
Collaborative Research Team Grant. B.M.G. acknowledges the support of the
Natural Sciences and Engineering Research Council of Canada (NSERC) through
grant RGPIN-2022-03163, and of the Canada Research Chairs program. V.M.K.
holds the Lorne Trottier Chair in Astrophysics & Cosmology, a Distinguished
James McGill Professorship, and receives support from an NSERC Discovery grant
(RGPIN 228738-13), from an R. Howard Webster Foundation Fellowship from CIFAR,
and from the FRQNT CRAQ. C.L. is supported by NASA through the NASA Hubble
Fellowship grant HST-HF2-51536.001-A awarded by the Space Telescope Science
Institute, which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS5-26555. K.W.M. holds the Adam J.
Burgasser Chair in Astrophysics and is supported by an NSF Grant (2008031,
2018490). A.P. is funded by the NSERC Canada Graduate Scholarships – Doctoral
program. A.B.P. is a Banting Fellow, a McGill Space Institute (MSI) Fellow,
and a Fonds de Recherche du Quebec – Nature et Technologies (FRQNT)
postdoctoral fellow. Z.P. is a Dunlap Fellow. P.S. was a Dunlap Fellow. K.S.
is supported by the NSF Graduate Research Fellowship Program. A.P.C is a
Vanier Canada Graduate Scholar.

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##  Appendix A Additional DM Variability Measurements

Repeating the analysis in §3.1.4, we estimate dispersion measure variations in
the dynamic spectra of FRB 20200603, FRB 20210427A, FRB 20210627, and FRB
20211005A for event-specific time-limited regions across the burst. With the
exception of FRB 20210627A, we assume a focal frequency of 800 MHz, as the
drifting in all other bursts appears to set in at or beyond this frequency.
For FRB 20210627A, however, there appear to be two potential focal frequencies
within the observing band, manifesting at $\nu_{l,2}\approx$ 480 MHz for the
first burst cluster and $\nu_{l,1}\approx$ 650 MHz for the second. Hence we
limit the frequency range over which we perform dedispersion to a range
between 400 MHz and the focal frequency, as we did for FRB 20220413B. Below
the focal frequency, drifting appears consistent with cold plasma dispersion.
To highlight this, we plot DM curves adjacent to the drifting features in
accordance with the estimated $\Delta$DM offsets from the nominal value, as
shown in Figures 10, 11, 12, and 13, respectively. $\Delta$DM values measured
for each event are recorded in Table 3.

Figure 10: The upper left panel shows the dynamic spectrum of FRB 20200603B
with DM curves over-plotted as white solid lines. The panels following show
dynamic spectra of the same event dedispersed to the coherent power-maximizing
$\Delta$DM offsets from the nominal DM for respective sub-bursts, highlighted
in purple in the timeseries. The DMs to which the full burst is dedispersed
are ordered by sub-burst ToA.

Figure 11: The upper left panel shows the dynamic spectrum of FRB 20210427A
with DM curves over-plotted as white solid lines. The following panels show
dynamic spectra of the same event dedispersed to the coherent power-maximizing
$\Delta$DM offsets from the nominal DM for respective sub-bursts, highlighted
in purple in the timeseries. The DMs to which the full burst is dedispersed
are ordered by sub-burst ToA.

Figure 12: The upper left panel shows the dynamic spectrum of FRB 20210627A
with DM curves over-plotted as white solid lines. The following panels show
dynamic spectra of the same event dedispersed to the coherent power-maximizing
$\Delta$DM offsets from the nominal DM for respective sub-bursts, highlighted
in purple in the timeseries. The DMs to which the full burst is dedispersed
are ordered by sub-burst ToA. Note that in measuring $\Delta\mathrm{DM}_{1}$,
the coherent power has been maximized for the sub-band below a focal frequency
of $\nu_{l,2}\approx 480$ MHz, at which point drifting away from the nominal
DM is visible, and that $\Delta\mathrm{DM}_{5}$ is measured similarly below a
focal frequency of $\nu_{l,1}\approx 650$ MHz.

Figure 13: The upper left panel shows the dynamic spectrum of FRB 20211005A
with DM curves over-plotted as white solid lines. The following panels show
dynamic spectra of the same event dedispersed to the coherent power-maximizing
$\Delta$DM offsets from the nominal DM for respective sub-bursts, highlighted
in purple in the timeseries. The DMs to which the full burst is dedispersed
are ordered by sub-burst ToA.

##  Appendix B Measuring Microstructure with Autocorrelation Functions

Building on the analysis in §3.2, we re-measure the widths (FWHM) of $\lesssim
50~{}\mu s$ features (i.e., “microstructure”) in seven of the twelve bursts in
this sample. We now estimate sub-burst widths by calculating the ACF of each
sub-burst or sub-burst cluster within a time-limited region of the full burst
profile, and fitting a 1D Lorentzian function to the ACF. Prior to fitting, we
mask the zero-lag spike in the ACF. Sub-burst clusters are defined as regions
in the burst timeseries where peaks in intensity are not well-separated in
time, but still show $\gtrsim 3\sigma$ variability across an underlying
envelope of intensity with respect to noise in the off-pulse region.

The measured widths for each sub-burst or sub-burst cluster are presented in
Table 5. Figure 14 shows an example of the respective timeseries and
Lorentzian fits to the ACFs of sub-bursts and sub-burst clusters in the burst
profile of FRB 20190425A. Certain width measurements obtained using this
method are slightly broader than those measured in §3.2 (see Table 4),
primarily due to the inability to completely isolate sub-bursts in clustered
regions while still ensuring a reasonable fit to the ACF. The widths do,
however, agree to well within an order of magnitude of those measured by a
multi-Gaussian fit, validating the measurement technique outlined in §3.2, and
confirming the intrinsically narrow ($\lesssim 50~{}\mu s$) timescales of
these features.

Table 5: The intrinsic widths (FWHM) of $\lesssim 50$-$\mu s$ sub-bursts observed in seven events in the sample. The widths are derived from 1D Lorentzian fits to ACFs calculated for individual sub-bursts and sub-burst clusters in time. An example of the time-limits placed on both isolated and clustered sub-bursts is shown in Figure 14. Due to the clustering of sub-bursts in certain events, there are fewer $\Delta t$ measurements per event than in Table 4, as the multi-Gaussian fits performed in §3.2 are better-suited to disentangle clusters into their individual components. TNS Name | $\Delta\mathrm{t}_{1}$ | $\Delta\mathrm{t}_{2}$ | $\Delta\mathrm{t}_{3}$ | $\Delta\mathrm{t}_{4}$ | $\Delta\mathrm{t}_{5}$ | $\Delta\mathrm{t}_{6}$ |
---|---|---|---|---|---|---|---
FRB 20190425A | 10.8(7) | 15(2) | 10.1(2) | 9.0(6) | … | … |
FRB 20200603B | 9.7(2) | 29(1) | 49.2(7) | 17(7) | … | … |
FRB 20210406E | 7.4(9) | 19(4) | 12.9(4) | 24.9(8) | 24.7(4) | 14.9(6) |
FRB 20210427A | 33(2) | … | … | … | … | … |
FRB 20210627A | 44.7(2) | 43.7(5) | … | … | … | … |
FRB 20210813A | 18(2) | 20(3) | … | … | … | … |
FRB 20211005A | 29(1) | … | … | … | … | … |

Figure 14: Time-limited regions across the FRB 20190425A timeseries, isolating
four regions containing either a sub-burst (in the three left-most panels) or
sub-burst cluster (in the right-most panel). The ACFs are calculated and
fitted with 1D Lorentzian functions to confirm that the widths are comparably
narrow to those quoted in Table 4.

##  Appendix C Polarimetry

The CHIME/FRB polarization pipeline is part of the analysis stage of the
CHIME/FRB baseband system, described in §2. Since baseband data retain full
Stokes parameters and phase information, we are able to measure Faraday
Rotation Measure (RM) using both RM synthesis and $QU$-fitting (see methods
outlined in Mckinven et al., 2021). RM synthesis is a non-parametric Fourier-
like transformation method that gives an initial estimate of the RM.
$QU$-fitting is a parametric technique that fits the modulations of Stokes $Q$
and $U$ using a nested sampling algorithm, which offers more flexibility than
RM synthesis by the inclusion of parameters characterizing instrumental
polarization.

The model described by Mckinven et al. (2021) has 4 parameters: linear
polarization fraction ($p$), polarization angle at zero wavelength
($\phi_{0}$), RM, and cable delay between the two linear polarizations
($\tau$; due to the relative path length differences between the two linear
feeds of each antenna). However, this model was found to not entirely describe
the instrumental phase between the X and Y polarizations. When unaccounted
for, this differential phase can result in sign ambiguities in the RM as
detailed in Mckinven et al. (2021). The residual instrumental polarization can
be adequately fit by including additional wavelength-independent parameters
that account for the phase offset between the $X$ and $Y$ polarizations at
zero frequency, $\phi_{\rm{lag}}$. Thus, in the polarization analysis shown
here, we include 5 additional parameters on top of the original model to help
constrain the RM sign. This more complex model considers the variation of
linear and circular polarization fractions across bands. We include (1) a
wavelength-independent parameter that acts as a constant offset
($\phi_{\rm{lag}}$), (2) a non-zero circular polarization fraction that
follows a power law ($p_{\nu}$), (3) an exponent for the power law of $p$
($\gamma_{L}$), (4) an exponent for $p_{\nu}$ ($\gamma_{L}$), and (5) a gain
difference that considers the leakage from Stokes $I$ to $Q$. Furthermore, we
limit the bounds of the cable delay and $\phi_{\rm{lag}}$ by constraining them
to ranges of values they normally fall into. This method allowed us to
confidently determine the RMs and linear polarization fractions of seven FRBs
in our sample (see Table 6), all of which have $QU$-fitting results that are
consistent with the signs obtained from RM synthesis.

Table 6: Polarization properties for selected bursts, including: measured RM ($\mathrm{RM}_{\text{obs }}$), the RM contribution expected from the Milky Way ($\mathrm{RM}_{\mathrm{MW}}$), and linear polarization ($\mathrm{L/I}$). The RM reported here is corrected for an ionospheric contribution of $+0.1$ rad m-2. Estimates of the Galactic contribution to RM are drawn from the Faraday Sky map of Hutschenreuter et al. (2022), which infers $\mathrm{RM}_{\mathrm{MW}}$ values based on measurements of polarized extragalactic sources. TNS Name | $\mathrm{RM}_{\mathrm{obs}}\left(\mathrm{rad}~{}\mathrm{m}^{-2}\right)$ | RM${}_{\textrm{MW}}$ (rad m-2) | $\langle L/I\rangle$ |
---|---|---|---|---
FRB 20190425A | +57.30${}_{-0.01}^{+0.01}$ | +48.6 $\pm$ 14.2 | 0.946${}_{-0.003}^{+0.003}$ |
FRB 20191225A |  $-$328.06${}_{-0.02}^{+0.02}$ |  $-$26.7(8.7) | 0.577${}_{-0.002}^{+0.002}$ |
FRB 20200603B | … |  $-$18.7 $\pm$ 5.6 | … |
FRB 20200711F | … | +9.0 $\pm$ 1.7 | … |
FRB 20201230B | +80.63${}_{-0.04}^{+0.04}$ | +92.1 $\pm$ 17.4 | 0.354${}_{-0.002}^{+0.002}$ |
FRB 20210406E | +77.609${}_{-0.01}^{+0.01}$ | +17.7 $\pm$ 22.5 | 0.887${}_{-0.002}^{+0.002}$ |
FRB 20210427A | … | +5.3 $\pm$ 8.4 | … |
FRB 20210627A |  $-$28.327${}_{-0.01}^{+0.01}$ |  $-$4.9 $\pm$ 3.5 | 0.82${}_{-0.01}^{+0.01}$ |
FRB 20210813A | … |  $-$25.4 $\pm$ 30.4 | … |
FRB 20210819A | +32.23${}_{-0.04}^{+0.04}$ |  $-$7.2 $\pm$ 2.8 | 0.340${}_{-0.001}^{+0.001}$ |
FRB 20211005A | +17.24${}_{-0.02}^{+0.02}$ | 17.0 $\pm$ 5.5 | 0.887${}_{-0.002}^{+0.002}$ |
FRB 20220413B | … | +36.4 $\pm$ 7.2 | … |