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# A fast radio burst localized at detection to a galactic disk using very long
baseline interferometry

Tomas Cassanelli1,2,3, Calvin Leung4,5,6, Pranav Sanghavi7,8, Juan Mena-
Parra2,1, Savannah Cary4,9, Ryan Mckinven10,11, Mohit Bhardwaj10,11, Kiyoshi
W. Masui4,5, Daniele Michilli4,5, Kevin Bandura7,8, Shami Chatterjee12,
Jeffrey B. Peterson13, Jane Kaczmarek14,15,16, Chitrang Patel2,10, Mubdi
Rahman17, Kaitlyn Shin4,5, Keith Vanderlinde1,2, Sabrina Berger10,11,
Charanjot Brar10,11, P. J. Boyle10,11, Daniela Breitman18, Pragya Chawla19,
Alice P. Curtin20,10, Matt Dobbs10,11, Fengqiu Adam Dong21, Emmanuel
Fonseca8,22, B. M. Gaensler1,2,23, Adaeze Ibik1,2, Victoria M. Kaspi10,11,
khairy kholoud7,8, Adam E. Lanman10,11, Mattias Lazda10, Hsiu-Hsien Lin24,25,
Jing Luo26, Bradley W. Meyers21, Nikola Milutinovic21, Cherry Ng2, Gavin
Noble1,2, Aaron B. Pearlman10,11,27,28,29, Ue-Li Pen2,24,25,30,31, Emily
Petroff10,11,19, Ziggy Pleunis2, Brendan Quine32,33, Masoud Rafiei-
Ravandi10,11, Andre Renard2, Ketan R Sand10,20, Eve Schoen4, Paul Scholz2,
Kendrick M. Smith31, Ingrid Stairs21, Shriharsh P. Tendulkar34,35

00footnotetext:  $\ast$ Corresponding author: Calvin Leung. E-mail:
<EMAIL_ADDRESS>$\dagger$: These authors contributed equally to this
work. David A. Dunlap Department of Astronomy & Astrophysics, University of
Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada Dunlap Institute
for Astronomy & Astrophysics, University of Toronto, 50 St. George Street,
Toronto, ON M5S 3H4, Canada Department of Electrical Engineering, Universidad
de Chile, Av. Tupper 2007, Santiago 8370451, Chile 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 NHFP Einstein Fellow Lane Department of Computer Science and
Electrical Engineering, 1220 Evansdale Drive, PO Box 6109 Morgantown, WV
26506, USA Center for Gravitational Waves and Cosmology, West Virginia
University, Chestnut Ridge Research Building, Morgantown, WV 26505, USA
Department of Astronomy, Wellesley College, 106 Central Street, Wellesley, MA
02481, USA 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 Cornell Center for Astrophysics
and Planetary Science, Ithaca, NY 14853, USA McWilliams Center for Cosmology,
Department of Physics, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh
PA 15213 USA Dominion Radio Astrophysical Observatory, Herzberg Research
Centre for Astronomy and Astrophysics, National Research Council Canada, PO
Box 248, Penticton, BC V2A 6J9, Canada Department of Computer Science, Math,
Physics, & Statistics, University of British Columbia, Kelowna, BC V1V 1V7,
Canada CSIRO Space & Astronomy, Parkes Observatory, P.O. Box 276, Parkes NSW
2870, Australia Sidrat Research, 124 Merton Street, Suite 507, Toronto, ON M4S
2Z2, Canada Scuola Normale Superiore, 56126 Pisa, PI, Italy Anton Pannekoek
Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH
Amsterdam, The Netherlands Trottier Space Institute, McGill University, 3550
rue University, Montréal, QC H3A 2A7, Canada Department of Physics and
Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver,
BC V6T 1Z1 Canada Department of Physics and Astronomy, West Virginia
University, P.O. Box 6315, Morgantown, WV 26506, USA Department of Astronomy
and Astrophysics, University of California Santa Cruz, 1156 High Street, Santa
Cruz, CA 95064, USA Institute of Astronomy and Astrophysics, Academia Sinica,
Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei 10617,
Taiwan Canadian Institute for Theoretical Astrophysics, 60 St. George Street,
Toronto, ON M5S 3H8, Canada Deceased Banting Fellow McGill Space Institute
Fellow FRQNT Postdoctoral Fellow Canadian Institute for Advanced Research, 661
University Ave, Toronto, ON M5G 1M1 Perimeter Institute for Theoretical
Physics, 31 Caroline Street N, Waterloo, ON N25 2YL, Canada Thoth Technology
Inc. 33387 Highway 17, Deep River, Ontario K0J 1P0, Canada Department of
Physics and Astronomy, York University, 4700 Keele Street, Toronto, ON M3J
1P3, Canada 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

Fast radio bursts (FRBs) are millisecond-duration, luminous radio transients
of extragalactic origin. Precise localization within the host galaxy can
discriminate between progenitor models, a major goal of the field. Here we
demonstrate the direct localization of FRB 20210603A with very long baseline
interferometry (VLBI) on two baselines, following its blind detection in a
$200$ deg2 field of view of the Canadian Hydrogen Intensity Mapping
Experiment. We use full-array baseband data from the CHIME core to first
narrow down the position to the arcminute level, and add VLBI outriggers to
localize the burst to a final ellipse whose radius is 0.2” x 2”. The host
galaxy, SDSS J004105.82+211331.9 shows recent star formation in the $\sim 10$
kiloparsec-scale vicinity of the burst. Its edge-on inclination allows for a
unique comparison between the line of sight towards the FRB and lines of sight
towards known pulsars. The DM, rotation measure, and scattering suggest a
progenitor coincident with the host galactic plane, strengthening the link
between the local environment of FRB 20210603A and the disk of its host
galaxy. Single-pulse VLBI localizations of FRBs to within their host galaxies,
following the one presented here, will further constrain the origins of one-
off FRBs.

FRB 20210603A, shown in Fig. 1, was first detected by the Canadian Hydrogen
Intensity Mapping Experiment (CHIME), located at the Dominion Radio
Astrophysical Observatory. The CHIME/FRB instrument [1] searches for dispersed
single pulses within CHIME’s wide field of view (FoV). The detection of FRB
20210603A triggered the recording of voltage data at CHIME [2], as well as at
a 10-m dish at Algonquin Radio Observatory (referred to as ARO10 hereafter)
[3], and TONE, a compact array of eight, 6-m dishes at Green Bank Observatory
(GBO)[4]. These three stations (Fig. 2) were operating in tandem as a
triggered very-long baseline interferometric (VLBI) array observing between
$400800\text{\,}\mathrm{MHz}$, and localized the burst to the host galaxy in
Fig. 3.

Figure 1: The Stokes-$I$ dynamic spectrum of FRB 20210603A. We detect the
single pulse in autocorrelation at CHIME/FRB with a signal-to-noise ratio
exceeding $100$. The data are shown at a time resolution of
$25.6\text{\,}\mathrm{\SIUnitSymbolMicro s}$ with pixel colours scaled to
their $199$ percentile values. To remove dispersion, we use a DM derived by
lining up three closely-overlapping sub-burst components within the main pulse
using fitburst [5, 6]. In addition to the main burst, fainter emission
components occurring $\sim 12\text{\,}\mathrm{ms}$ and $\sim
18\text{\,}\mathrm{ms}$ afterwards are visible in CHIME/FRB baseband data, but
are neglected for VLBI localization. The faint dispersed sweeps left and right
of the main pulse are known instrumental artifacts from spectral leakage. The
red streaks to the left highlight the frequency channels that are masked out
due to RFI. Most RFI come from cellular communication and television
transmission bands between $700750\text{\,}\mathrm{MHz}$ and
$600650\text{\,}\mathrm{MHz}$, respectively. Figure 2: Map of baselines formed
between CHIME and ARO10 (CA) and TONE (CT). The baselines span from Penticton,
BC to Algonquin, ON, and Green Bank, WV with lengths
$b_{\mathrm{CA}}=$3074\text{\,}\mathrm{km}$$ and
$b_{\mathrm{CT}}=$3332\text{\,}\mathrm{km}$$. For our localization analysis,
we omit the $848\text{\,}\mathrm{km}$ baseline between ARO10 and TONE because
the FRB was not sufficiently bright to be detected on that baseline.

This ad-hoc VLBI array is dominated by east-west separations and has a maximum
baseline length of $\sim 3300\text{\,}\mathrm{km}$ (CHIME-TONE). Of the three
stations, only ARO10 is a traditional single-dish telescope. CHIME and TONE
are compact interferometric arrays consisting of $1024$ and $8$ dual-
polarisation antennas, respectively. All three stations observe the sky in
drift-scan mode. The primary beam of CHIME at $600\text{\,}\mathrm{MHz}$ is
approximately a $\sim 110\text{\,}\mathrm{\SIUnitSymbolDegree}$-long strip of
width $\sim 2\text{\,}\mathrm{\SIUnitSymbolDegree}$ oriented along the local
meridian [1]. Simultaneously, ARO10 and TONE are pointed to shadow a portion
of the CHIME primary beam at a fixed declination
($\sim+22\text{\,}\mathrm{\SIUnitSymbolDegree}$). This common FoV is chosen
because it contains the Crab pulsar (PSR B0531+21), which we use as an
astrometric calibrator. Upon detection of a single dispersed pulse such as an
FRB or a giant pulse (GP) from the Crab pulsar, CHIME/FRB forwards low-latency
alerts over the internet to the TONE and ARO10 systems, triggering a recording
of buffered data to disk (see Methods: Instrumentation and Observations,
CHIME/FRB). The current network and triggered observing strategy serve as a
pathfinder for CHIME/FRB Outriggers: three CHIME-like telescopes located
across the North America whose primary purpose will be to perform triggered
VLBI on FRBs [26, 3, 27].

Figure 3: VLBI Localization of FRB 20210603A. Left: The $1\sigma$ and
$2\sigma$ localization contours, defined by an empirical estimate of our
localization errors using Crab measurements, are overlaid on a CFHT MegaCAM
$gri$-band image of its host galaxy SDSS J004105.82+211331.9. The nearly edge-
on geometry of the host galaxy is apparent. We allow the pixel colours to
saturate within $\approx 1$ half-light radius, to accentuate the faint
structure on the outskirts of the galaxy. The localization and burst
properties point towards a progenitor living deep in the ionized disk of the
galaxy. Right: H$\alpha$ flux observed at varying distances from the galactic
center along the major axis of the galaxy, calculated from the spectra in
Extended Data Fig. 9. Positive/negative coordinates refer to H$\alpha$ fluxes
northward/southward of the galactic center respectively. Blue circles and
upside-down triangles represent detections and $2\sigma$ upper limits on the
local H$\alpha$ flux, with flux uncertainties estimated using the detrended
spectrum (SD; $N=3199$). Horizontal bars denote the size of the spectral
aperture ($1\text{\,}\mathrm{arcsec}$). The half light radius of the galaxy is
indicated by a gray shaded area.

Since CHIME and TONE are interferometers, we use beamforming to combine the
multiple antennas within a single station into an effective single dish. We
calibrate relative cable delays for the antennas within CHIME and TONE and
phase them up towards the most precise estimate of the FRB’s position
available from CHIME alone, computed with the baseband localization pipeline
(see Methods: Local calibration and beamforming and [7, 4]). This initial
estimate of the position is denoted as $\widehat{\mathbf{n}}_{0}$. We
subsequently perform 3-station VLBI correlation (taking beamformed CHIME,
beamformed TONE, and the ARO as inputs), generating long-baseline visibilities
which are then used for precision localisation of the FRB. We apply
appropriate geometric delays and phase rotations to each of the $1024$
frequency channels. This compensates for large, time-varying geometric delays
according to the Consensus model [9], but not any clock delays (which vary in
time) or ionospheric delays (which vary over time and between different
sightlines), since the latter two are smaller contributions which we calibrate
after correlation. Then, we correlate the delay-compensated baseband data on
the CHIME-ARO10 and CHIME-TONE baselines. We use a custom VLBI correlator to
coherently dedisperse the FRB to a fiducial DM, and form on- and off-pulse
visibilities (see Methods: VLBI Correlation and [8]). FRB 20210603A is
detected in CHIME autocorrelation, but not in autocorrelation at the other
stations (see Methods: Instrumentation and Observations). In cross-
correlation, we detect the burst on both the CHIME-ARO10 and CHIME-TONE
baselines with a signal-to-noise ratio (S/N) of $\sim 35$ after coherently
combining all frequency channels. Without CHIME, the third ARO10-TONE baseline
is much less sensitive, having a effective collecting area of $\sim 1/10$ of
other two. As expected, it was not sensitive enough to detect the burst and we
omit it from the localization analysis.

After the burst is detected in cross-correlation, ionosphere and clock
corrections remain to be applied. Typically, these calibration solutions are
straightforward to determine using VLBI observations of continuum sources with
precisely-known positions in the same observing session. However, with our ad-
hoc array, such observations are difficult due to the unknown availability of
VLBI calibrators at $600\text{\,}\mathrm{MHz}$, the fixed pointings and low
sensitivity of ARO10 and TONE, and the limited internet connectivity of the
ARO10 station. Our calibration strategy instead relies on observing bright
Crab giant pulses, once per day, resulting in calibration measurements which
are much sparser than typically achievable with a mature, steerable VLBI
array. Nevertheless, with each baseline individually, we conduct monitoring
campaigns of the Crab, where we observed and delay-calibrated 10 Crab GP
datasets on the CHIME-ARO10 baseline and 11 on the CHIME-TONE baseline to
empirically estimate our $1\sigma$ localization uncertainties. Since the Crab
emits giant pulses unpredictably, we observe them in our system with a range
of fluences, spectral properties, and sky locations: in both the CHIME-ARO10
and the CHIME-TONE monitoring campaigns, the pulses spanned a range of
$\approx 1.1$ degrees in hour angle. Because our drift-scan telescopes do not
track any particular RA, the sky rotation and pulse-to-pulse variability
mimics the observation of astrophysical sources with distinct source
properties at distinct RAs. The delay uncertainties correspond to a systematic
uncertainty ellipse of
$$0.2\text{\,}\mathrm{arcsec}$\times$2\text{\,}\mathrm{arcsec}$$ in the east-
west and north-south directions respectively (see Methods: VLBI Calibration
and Empirical Localization Error Budget).

In the science run, both the CHIME-ARO10 and the CHIME-TONE baselines operated
simultaneously. During this science run we observed FRB 20210603A, and several
Crab GP before and after its detection, which we refer to as C1-C4. These GPs
allow us to derive a set of phase, delay, and delay-rate calibration
solutions, which we used to localize the FRB (Methods: FRB Localization).
However, before performing the localization, we validate the calibration
solutions by using them to localize a Crab GP (referred to as C3), which we
detected one day after the FRB and omitted from our calibration solutions,
making it an independent check of our calibration. The discrepancy between the
Crab’s true position and our Crab localization falls well within the
systematic uncertainty ellipse from the monitoring campaigns. Finally, we
apply the exact same calibration solutions to localize the FRB. The target-
calibrator separation is 1.5 degrees in hour angle, 0.8 degrees in
declination, and 4 hours in time. The derived coordinates of FRB 20210603A in
the International Celestial Reference Frame (ICRF) are $(\upalpha)=$
$0\text{h}41\text{m}05.774\text{s}\pm 0.0192\text{s}$ and $(\updelta)=$
+$21\text{d}13\text{m}34.573\text{s}\pm 1.08\text{s}$ (Table 1). These
coordinates coincide with SDSS J004105.82+211331.9 [10], a disk galaxy with a
nearly edge-on orientation (see Figure 3).

We observed SDSS J004105.82+211331.9 with the Canada-France Hawaii-Telescope
(CFHT) MegaCam on 2021 September 10 using the wideband gri filter [11]. Figure
3 shows the location of the FRB within the host galaxy. In contrast to other
FRB host galaxies that have been robustly identified so far, this galaxy is
viewed nearly edge-on; it has an inclination of $83\pm
3\text{\,}\mathrm{\SIUnitSymbolDegree}$ (InclinationZoo, [12]). We determine
the r-band half-light radius and Galactic extinction-corrected apparent
magnitude to be $8.2\pm 0.9\text{\,}\mathrm{kpc}$ and $17.90\pm 0.01$,
respectively, using photometric data provided by the Sloan Digital Sky Survey
(SDSS [10]), see Methods: Host Galaxy Analysis.

Additionally, we acquired long-slit spectra with the Gemini Multi-Object
Spectrograph (GMOS [13]) on 2021 August 1 with the combination of a R400
grating and a GG455 low-pass filter configured with a
$1.5\text{\,}\mathrm{arcsec}$ slit, covering the wavelength range from
$46508900\text{\,}\mathrm{\SIUnitSymbolAngstrom}$. A total of two
$1200\text{\,}\mathrm{s}$ exposures were taken on the same night but at two
different central frequencies, $6650\text{\,}\mathrm{\SIUnitSymbolAngstrom}$
and $6750\text{\,}\mathrm{\SIUnitSymbolAngstrom}$, to have coverage in the
GMOS-N detector chip gap, with $2\times 2$ binning, providing a spatial scale
of $0.002\,92\text{\,}{\mathrm{pix}}^{-1}$ and an instrumental resolution of
$4.66\text{\,}\mathrm{\SIUnitSymbolAngstrom}$, sampled at
$1.48\text{\,}\mathrm{\SIUnitSymbolAngstrom}\text{\,}{\mathrm{pix}}^{-1}$. The
seeing condition was very good during the observation night, with a mean
airmass of $1.007$. Fitting Gaussian line profiles to the H$\alpha$ and N II
lines (rest wavelengths of $6564.6\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ and
$6585.2\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) yields a redshift of
$z=$0.1772\pm 0.0001$$. Assuming the Planck 2018 cosmology [14], this redshift
implies a Galactic extinction- and k-corrected absolute $r$-band magnitude of
$-22.03\pm 0.02$.

The measured redshift of the galaxy implies an angular diameter distance of
$639\text{\,}\mathrm{Mpc}$ and a transverse angular distance scale of
$3.1\text{\,}\mathrm{kpc}\text{\,}{\mathrm{arcsec}}^{-1}$. Using these values,
we measure a projected spatial offset for the FRB of
$7.2\text{\,}\mathrm{kpc}$ from the host galactic centre along the host
galactic plane. This offset is consistent with the distribution of projected
offsets measured from a sample of both repeating and non-repeating FRBs
localized by the Australian SKA Pathfinder (ASKAP, see e.g., Figure 9 in
[15]), with the caveat that our localization ellipse is too large to draw any
meaningful conclusion about the host offset.

To characterize the host galaxy, we combined Gemini spectroscopy data with
archival photometry from the Two Micron All Sky Survey (2MASS) [16] and the
Wide-Field Infrared Space Explorer (WISE) [17] to extend our wavelength
coverage upwards to
$1\text{\times}{10}^{5}\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ (see Methods:
Host Galaxy Analysis).

We fit a spectral energy distribution (SED) model to the combined spectral and
photometric data using the Bayesian SED-fitting package Prospector [18]. We
estimate best-fit values and uncertainties for the present-day stellar mass,
mass-weighted age, V-band dust extinction, and metallicity of our host galaxy
using Markov-Chain Monte Carlo (MCMC) posterior sampling [19]. The parameters
determined by Prospector and the star formation rate (SFR) are shown in Table
1. From the H$\alpha$ luminosity measured with Gemini data, we determine the
galaxy’s overall SFR ($0.24\pm 0.06\leavevmode\nobreak\
\text{M}_{\odot}\text{\,}{\mathrm{yr}}^{-1}$) and detect star formation in the
$\sim 10$ kiloparsec-scale vicinity of the FRB. The detection of H$\alpha$
emission is potentially a sign of recent ($\sim 10\text{\,}\mathrm{Myr}$) star
formation and young stellar populations. However, as with the case of other
FRBs, spatially-resolved spectroscopic studies of this galaxy are needed to
further constrain the age and nature of the FRB progenitor.

In addition to the host galaxy properties, the burst itself can provide
insight into the sightline toward the FRB progenitor and the progenitor
itself. For instance, if the FRB is located in the inner disk, it would
experience enhanced dispersion and scattering due to the long line-of-sight
path out of the host galaxy’s ionized disk towards the observer, similar to
pulsars at low Galactic latitudes in the Milky Way. FRB 20210603A therefore
allows for a detailed accounting of host-galactic contributions to the
observed DM, RM, and scattering (i.e., pulse broadening). To check this
possibility, we calculated the DM excess by subtracting estimated DM
contributions from the Milky Way, the Milky Way halo, and the intergalactic
medium (IGM) from the measured DM. We obtain a large DM excess of
$\text{DM}^{\text{r}}_{\text{host}}=$302\pm
109\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$$, where the superscript
denotes that $\text{DM}^{\text{r}}_{\text{host}}$ is defined in the host
galaxy’s rest frame.

One interpretation of this excess is that of a dense environment local to the
FRB progenitor [20], which may add significant contributions to the DM, RM,
and/or scattering timescale. Another interpretation is that the host galaxy
itself contributes a significant portion of the DM excess, with subdominant
circumburst contributions to the other properties. Our estimate of the DM
budget of the host galaxy is $\sim$264\pm
97\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$$ (see Methods: Dispersion
and Scattering Analysis) and is consistent with the latter hypothesis. While
both interpretations are compatible with the data in hand, Occam’s razor leads
us to favor the interpretation that the excess DM of this FRB is dominated by
the host galaxy’s disk.

This is consistent with our measurements of the pulse broadening timescale,
which we determine by fitting a pulse model to the FRB’s dynamic spectrum. The
complex time-frequency structure of the bright main burst requires three sub-
pulse components, temporally broadened by the same characteristic timescale,
to obtain a robust fit to the data (see Methods: Burst Morphology and [5]).
This places an upper limit on the scattering timescale of
$\tau_{\text{$600\text{\,}\mathrm{MHz}$}}\lesssim$165\pm
3\text{\,}\mathrm{\SIUnitSymbolMicro s}$$ at a reference frequency of
$600\text{\,}\mathrm{MHz}$. Since the scattering from the Milky Way is
expected to be subdominant ($\sim$$1.0\pm
0.5\text{\,}\mathrm{\SIUnitSymbolMicro s}$) [21, 22], we conclude that the
observed pulse broadening is dominated by unresolved substructure in the burst
profile or extragalactic scattering, likely in the host rather than the Milky
Way [23]. If the measured broadening timescale is attributed entirely to
scattering and scaled to the rest frame and scattering geometry of the host
galaxy, the implied scattering efficiency of the host galactic gas is similar
to a typical sight-line toward a pulsar through a galactic disk with Milky
Way-like density fluctuations (see Methods: Dispersion and Scattering
Analysis).

In addition, the interpretation of a dominant host galactic contribution is
consistent with our measurement of the burst RM (see Methods: Polarization
Analysis). After subtracting Galactic and terrestrial contributions
($\mathrm{RM_{MW},RM_{iono}}$; see Table 1), the excess is
$\mathrm{RM_{excess}}=$(+198\pm
3)\text{\,}\mathrm{rad}\text{\,}{\mathrm{m}}^{-2}$$. Since no intervening
systems (e.g., galaxy groups/clusters) have yet been observed along this
sight-line, the RM contribution from the IGM is likely negligible [24]. The
magnitude of the RM excess is unremarkable and easily be explained by
contributions from the host galaxy’s ISM. These properties suggest that the
source of FRB 20210603A is located close to its galactic plane, consistent
with our localization ellipse.

In conclusion, we have commissioned a VLBI array to demonstrate the first VLBI
localization of a non-repeating FRB. The limitations of our ad-hoc VLBI array,
however, leads to a final localization uncertainty on par with connected-
element interferometers like ASKAP, DSA-110, and MeerKAT. Nevertheless, this
paves the way towards precisely localizing a large sample of one-off bursts
using VLBI. The FRB 20210603A sightline has implications for galactic
astrophysics and the progenitors of FRBs. It demonstrates the potential for
using edge-on FRB host galaxies as probes of the ionized gas of other
galaxies. In addition the H$\alpha$ emission in the neighbourhood of the FRB
suggests recent star formation activity. This highlights the need for high-
resolution follow-up to discriminate among progenitor models by assessing
whether FRBs are spatially coincident with star-forming regions [25]. The
instruments and methods used here constitute pathfinders for the CHIME/FRB
Outriggers project, which will enable VLBI localizations of large numbers of
both repeating and non-repeating sources [26, 3, 27]. Thus, a more complete
picture of the diverse host environments of FRBs, and how the environments
correlate with other burst properties, will soon be available.

Table 1: Measured and Derived Parameters associated with FRB 20210603A and its host galaxy. Properties derived from radio and optical follow-up data are listed in the top and bottom halves of the table respectively. Parameters which are derived from external models or measurements are indicated with daggers. ($z_{\text{phot}}$, DM, $\uptau$, and RM${}_{\text{iono}}$ predictions [21, 22, 28, 29, 30, 31]).  Parameter | Value
---|---
Right ascension $\upalpha$ (ICRS) | $10.274\,058\pm 0.000\,08\text{\,}\mathrm{\SIUnitSymbolDegree}$
Declination $\updelta$ (ICRS) | $21.226\,270\pm 0.0003\text{\,}\mathrm{\SIUnitSymbolDegree}$
CHIME arrival time at ($400\text{\,}\mathrm{MHz}$) | 2021-06-03 15:51:34.431652 UTC
Dispersion measure (DM) | $500.147\pm 0.004\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$
$\text{DM}_{\text{MW-NE2001}}^{\dagger}$ | $40\pm 8\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$
$\text{DM}_{\text{MW-halo}}^{\dagger}$ | $30\pm 20\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$
$\text{DM}_{\text{cosmic}}$ | $172\pm 90\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$
$(\text{DM}_{\text{host}})/(1+z)=(\text{DM}_{\text{host-disk}}+\text{DM}_{\text{host-halo}})/(1+z)$ | $257\pm 93\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$
RM | $-219.00\pm 0.01\text{\,}\mathrm{rad}\text{\,}{\mathrm{m}}^{-2}$
$\text{RM}_{\text{MW}}^{\dagger}$ | $-22.4\pm 0.3\text{\,}\mathrm{rad}\text{\,}{\mathrm{m}}^{-2}$
$\text{RM}_{\text{iono}}^{\dagger}$ | +$1.4\text{\,}\mathrm{rad}\text{\,}{\mathrm{m}}^{-2}$
$\Pi_{\text{L-$800\text{\,}\mathrm{MHz}$}}$ | $\gtrsim$96\text{\,}\mathrm{\char 37\relax}$$
$\Pi_{\text{L-$400\text{\,}\mathrm{MHz}$}}$ | $\gtrsim$87\text{\,}\mathrm{\char 37\relax}$$
$\tau_{\text{$600\text{\,}\mathrm{MHz}$}}$ | $165\pm 3\text{\,}\mathrm{\SIUnitSymbolMicro s}$
$\tau_{\text{$600\text{\,}\mathrm{MHz}$-NE2001}}^{\dagger}$ | $1.02\text{\,}\mathrm{\SIUnitSymbolMicro s}$
Fluence | $64.4\pm 6.5\text{\,}\mathrm{Jy}\text{\,}\mathrm{ms}$
Peak flux density | $64.9\pm 6.5\text{\,}\mathrm{Jy}$
Specific energy | $5.7\text{\times}{10}^{31}\text{\,}\mathrm{erg}\mathrm{/}\mathrm{Hz}$
Specific luminosity | $5.8\text{\times}{10}^{34}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{Hz}}^{-1}$
Band-averaged pulse FWHM | $740\text{\,}\mathrm{\SIUnitSymbolMicro s}$
Spectroscopic redshift, $z$ | $0.1772\pm 0.0001$
Photometric redshift, $z_{\text{phot}}^{\dagger}$ | $0.175\pm 0.0133$
Inclination angle | $83\pm 3\text{\,}\mathrm{\SIUnitSymbolDegree}$
Present-day stellar mass, $\log(\text{M}_{\text{host}}^{\star}/\text{M}_{\odot})$ | $$10.93$^{+0.04}_{-0.04}$
Metallicity, $\log\mathinner{\left(\text{Z}/\text{Z}_{\odot}\right)}$ | $$-0.22$^{+0.05}_{-0.04}$
Mass-weighted age |  $$4.32$^{+0.73}_{-0.75}$ $\mathrm{Gyr}$
Total star formation rate (SFR) | $\gtrsim 0.24\pm 0.06M_{\odot}\text{yr}^{-1}$
Projected offset | $7.2\text{\,}\mathrm{kpc}$
$r$-band half-light radius | $8.2\pm 0.9\text{\,}\mathrm{kpc}$
Absolute $r$-band magnitude | $-22.03\pm 0.02$
E(B-V) | $0.28$

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## Methods

### Instrumentation and Observations

We use a VLBI network consisting of three stations: the Canadian Hydrogen
Intensity Mapping Experiment (CHIME) at the Dominion Radio Astrophysical
Observatory (DRAO) [1], ARO10, a 10-m single dish at Algonquin Radio
Observatory (ARO) [3], and TONE, a compact array of eight 6-m dishes at Green
Bank Observatory (GBO) [4]. CHIME/FRB detected FRB 20210603A at 2021-06-03
15:51 UTC. In Fig. 1 we show the Stokes-I dynamic spectrum of the beamformed
data from FRB 20210603A as observed at CHIME. Between August 2018 and May
2021, $35.6\text{\,}\mathrm{h}$ of exposure were accumulated in the direction
of FRB 20210603A; however only the burst reported here was detected. For VLBI
calibration and testing our localization procedure, we used several Crab GPs
captured at a cadence of one per day, which we refer to as C1–C4 respectively
(see Extended Data Fig. 1).

#### CHIME/FRB

CHIME consists of four $$20\text{\,}\mathrm{m}$\times$100\text{\,}\mathrm{m}$$
cylindrical paraboloid reflectors oriented with the cylinder axis in the
North-South direction [2]. Each cylinder is fitted with
$256\text{\,}\mathrm{d}$ual-linear-polarisation antennas that are sensitive in
the frequency range of $400800\text{\,}\mathrm{MHz}$. The $2048$ analog
signals from the antennas are amplified and digitized using an array of $128$
field programmable gate array (FPGA) driven motherboards with mezzanine
analog-to-digital converters (ADCs) called ICE boards [32]. At each ICE board,
raw voltages are channelized with a polyphase filterbank (PFB) producing
$1024$ complex channels with $2.56\text{\,}\mathrm{\SIUnitSymbolMicro s}$ time
resolution. We refer to the channelized and time-tagged voltage data as raw
baseband data (as opposed to beamformed baseband data, see Methods: Local
Calibration and Beamforming). These data are sent to $256$ GPU-based compute
nodes comprising the X-Engine correlator driven by the open-source kotekan
software repository [33, 34]. Here, the spatial correlation is computed and
polarisations are summed, forming $1024$ ($256\text{-NS}\times 4\text{-EW}$)
independent beams within the North-South primary beam [35]. These beams are
searched for FRBs in real-time using detection pipelines designed for
discovering radio transients. The real-time pipeline and the baseband system
collectively make up the CHIME/FRB instrument [1, 7]. The baseband system uses
a memory ring buffer system to record (or ‘dump’) baseband data to disk. The
ring buffer holds $\sim 35.5\text{\,}\mathrm{s}$ of baseband data for
subsequent capture by a detection trigger. On successful detection of an FRB
candidate by the real-time pipeline above an S/N of $12$, a trigger from the
real-time pipeline saves a $\sim 100\text{\,}\mathrm{ms}$ snapshot of data
centred around the pulse at each frequency channel of the baseband buffer. The
latency between the time of arrival of a signal and the triggered baseband
recording is typically $\sim 14\text{\,}\mathrm{s}$. The buffer can record the
full band’s worth of data when the dispersive sweep of the FRB does not exceed
$\sim 20\text{\,}\mathrm{s}$ (corresponding to a maximum DM of $\sim
1000\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$).

The outrigger triggering system involves asynchronous servers running at ARO10
and TONE. Each station sends a “heartbeat” to the CHIME/FRB backend. The
CHIME/FRB backend then registers each outrigger with a heartbeat as an active
outrigger. Upon detection by the real-time pipeline of an FRB or a Crab pulsar
GP [36] in the FoV of TONE and ARO10, a trigger is sent to the active
outriggers. To prevent GP triggers overwhelming the baseband readout system
with thousands of events, we record only triggers with a detection S/N greater
than $40$ (near CHIME’s zenith) having a duty cycle of
$1\text{\,}\mathrm{\char 37\relax}$. This results in a Crab GP dump rate of
about once per day.

#### Algonquin Radio Observatory 10-m telescope

ARO10, a 10-m single dish, is located at the Algonquin Radio Observatory in
Algonquin Provincial Park, Ontario. The CHIME-ARO10 baseline is over
$b_{CA}\gtrsim$3000\text{\,}\mathrm{km}$$ (see Figure 2). The two analog
signals from the polarizations of the single CHIME cloverleaf feed [37] are
digitized and acquired with a digital infrastructure identical to that of
CHIME and TONE except that the large ($\sim 24\text{\,}\mathrm{h}$ long) ring
buffer is stored on hard disks. A complete description of the radio frequency
(RF) chain and the digital system is provided elsewhere [3]. The data at ARO10
exhibit a delay drift relative to DRAO amounting to $\sim
0.1\text{\,}\mathrm{\SIUnitSymbolMicro s}\text{\,}{\mathrm{day}}^{-1}$. This
extra shift in addition to the $\sim 2\text{\,}\mathrm{ms}$ geometrical delay
is predictable and is corrected (see Figure 15 of [3]).

#### TONE

TONE is located at GBO near the Green Bank Interferometer Control Building.
The CHIME-TONE baseline is $b_{\mathrm{CT}}\approx$3332\text{\,}\mathrm{km}$$
long (see Figure 2). TONE is an array of 6-m dishes placed in a regular
$4\times 3$ grid with 9.1-m spacing with the shorter side aligned
$60\text{\,}\mathrm{\SIUnitSymbolDegree}$ off true north. Each dish is
oriented to observe the Crab pulsar at the same time as CHIME. Eight dishes
are deployed with feeds instrumented with active-balun dual-polarised
cloverleaf antennas [37, 38]. The $16$ analog signals are each transmitted
over a radio-frequency-over-fiber (RFoF) system [39]. For this work, $7$
signals from one polarisation and $6$ signals from the other were used to
synthesize a single beam for VLBI. The signals from the RFoF receiver are
digitized and channelized by an ICE board (in the same way that was previously
described for CHIME and ARO10). A TM-4 GPS clock module [40] provides a
$10\text{\,}\mathrm{MHz}$ clock and absolute time. Additionally, a
$10\text{\,}\mathrm{MHz}$ maser signal is fed into the ICE board replacing one
of the analog inputs for post-hoc clock delay characterization [27, 41]. The
digitized and channelized voltages are sent via two $40\text{\,}\mathrm{Gbit}$
ethernet network links over to the recording computer node. The recording node
uses kotekan, as it does at CHIME and ARO10, to create a $\sim
40\text{\,}\mathrm{s}$ buffer of the baseband data [26]. The length of the
buffer must accommodate both the latency of the CHIME/FRB detection pipeline
and the network in addition to the science data. The baseband readout saves a
$\sim 0.5\text{\,}\mathrm{s}$ slice of the buffer around the pulse on the
arrival of a trigger to disk for offline VLBI analysis. Taurus A is used as a
calibrator to phase the antennas within TONE for beamforming (see Methods:
Local Calibration and Beamforming). See [4, 42] for a detailed description of
the system and its performance.

We have summarized in Extended Data Table 1 the three sites and their
properties.

Table 1: A summary of the properties of the CHIME, ARO10, and TONE stations. System equivalent flux density (SEFD) at ARO10 was calculated with a set of Crab GPs [3]. The SEFD and FoV of TONE have been computed from a drift scan observation of Taurus-A [42]. CHIME SEFD at Dec $+22\text{\,}\mathrm{\SIUnitSymbolDegree}$ has not been calculated, but its system temperature has been extensively studied in [2]. Property | CHIME | ARO10 | TONE
---|---|---|---
SEFDs $S_{\mathrm{sys}}$ at Dec $+22\text{\,}\mathrm{\SIUnitSymbolDegree}$ | – | $\sim 1.7\text{\,}\mathrm{kJy}$ | $\sim 2040\text{\,}\mathrm{kJy}$
Field of view (at $600\text{\,}\mathrm{MHz}$) |  $\sim 110\text{\,}\mathrm{\SIUnitSymbolDegree}$ N-S, $1.74\text{\,}\mathrm{\SIUnitSymbolDegree}$ E-W | $3.59\text{\,}\mathrm{\SIUnitSymbolDegree}$ | $\sim 611\text{\,}\mathrm{\SIUnitSymbolDegree}$
Processed frequency channels | $916$ | $1024$ | $1024$
Baseline length | – | $b_{\mathrm{CA}}=$3074\text{\,}\mathrm{km}$$ | $b_{\mathrm{CT}}=$3332\text{\,}\mathrm{km}$$
Longitude ($\deg$) | $-119.6237$ | $-78.0701$ | $-79.8452$
Latitude ($\deg$) | $49.3207$ | $45.9556$ | $38.4293$

### Clock Calibration

There exist timing errors intrinsic to the digital backends at each station,
which are locked to different clocks with varying degrees of stability. The
severity of timing errors depends on the type of clock used at each station
and varies from unit to unit. Timing errors are characterized in terms of the
Allan deviation ($\sigma(\Delta t)$) as a function of timescale $\Delta t$,
e.g. between successive clock calibrations [27]. The CHIME digital system is
locked to a single $10\text{\,}\mathrm{MHz}$ clock signal provided by a GPS-
disciplined, oven-controlled crystal oscillator. While sufficient for the
operations of CHIME as a stand-alone telescope, this clock does not meet the
stringent stability requirements for VLBI with CHIME/FRB Outriggers. To
overcome this limitation, we sample the more stable passive hydrogen maser
(located at the DRAO site) during FRB VLBI observations [27] on a regular
cadence. This minimally-invasive clocking system was developed as part of the
effort to expand CHIME’s capabilities to include VLBI with CHIME/FRB
Outriggers. It works by digitizing the signal from an external maser using one
of the inputs of the GPS-clock-driven ICE board. We read out a
$2.56\text{\,}\mathrm{\SIUnitSymbolMicro s}$ snapshot of maser data at a
cadence of once every $\Delta t_{\text{GPS,C}}=$30\text{\,}\mathrm{s}$$ at
CHIME. The data readout from the maser are processed offline to measure the
drift of the GPS clock between calibrator observations. A similar readout
system records a $10\text{\,}\mathrm{MHz}$ clock at TONE at a cadence of
$\Delta t_{\text{GPS,T}}=$1\text{\,}\mathrm{s}$$. In contrast, the digital
system of ARO10 is directly clocked by an actively-stabilized hydrogen maser,
removing the need for station-based clock corrections.

Once clock corrections are applied to the observations, the expected delay
error between two observations separated by $\Delta t_{sep}$ in time is given
by the quadrature sum of the jitter at each station. Assuming that the jitter
is characterized by the Allan deviation of the maser alone, this is given by
$\sigma_{\text{maser}}(\Delta t_{sep})\Delta t_{sep}$. On 24-hour timescales,
this corresponds to a delay error of $\approx$0.35\text{\,}\mathrm{ns}$$ for
the CHIME-ARO10 baseline (one passive, one active maser), and
$\approx$0.48\text{\,}\mathrm{ns}$$ for the CHIME-TONE baseline (two passive
masers) [27]. In addition, on the CHIME-TONE baseline, observations are
referenced to the maser by interpolating between the maser readouts directly
before and after the observation. The slow cadence of maser readout at these
stations induces an additional interpolation error of size
$\sigma_{\text{GPS}}(\Delta t_{\text{sync}})\times\Delta t_{\text{sync}}$
[41], for a total of $0.52\text{\,}\mathrm{ns}$.

### Local Calibration and Beamforming

CHIME has $1024$ antennas, and TONE has $8$ antennas. It is infeasible to
correlate such a large number of antennas as independent VLBI stations. To
reduce the computational burden of correlating such a large array, we
coherently add, or beamform, the raw baseband data from the antennas within
each station to combine the multiple low-sensitivity antennas from a single
station into a high-sensitivity equivalent single dish using beamforming.

Beamforming requires independent measurements of the individual sensitivities
and delays for each antenna, i.e., complex-valued gains which contain both
amplitude and phase information. At CHIME, the infrastructure to calculate
these so-called “$N^{2}$-gains” and a tied-array beamformer have already been
developed [2]. We generalized several of CHIME’s software frameworks [43, 44,
7], to use the same basic $N^{2}$-gain calibration algorithms [45] at TONE.
First, the visibility matrix from all $N^{2}$ pairs of antennas at the
correlator is calculated when a bright point source (Taurus A for TONE)
dominates the FoV. In the single-source limit, the visibility matrix has a
rank-$1$ eigendecomposition; the non-singular eigenvector and eigenvalue
encode a combination of geometric delays and instrumental gains and delays.
Once the gains are characterized, they are used to beamform the raw baseband
data from CHIME and TONE towards the best-known positions of the Crab and the
FRB provided by the baseband pipeline ($\widehat{\mathbf{n}}_{0}$). The
synthesized beam at CHIME is $\sim 1\text{\,}\mathrm{arcmin}$ wide, and the
synthesized beam at TONE is $\sim 0.5\text{\,}\mathrm{\SIUnitSymbolDegree}$
wide. Since the FRB’s true position is well within a synthesized-beam width
away from $\widehat{\mathbf{n}}_{0}$, our final sensitivity only depends
weakly on $\widehat{\mathbf{n}}_{0}$.

### VLBI Correlation

After beamforming is completed at each station, the beamformed baseband data
are correlated with a custom Python-based VLBI correlator [8]. We use the
standalone delay model implemented in difxcalc[46] to calculate geometric
delays towards the fiducial sky location $\widehat{\mathbf{n}}_{0}$ of each
source. For the Crab pulses, we use the VLBI position of the Crab pulsar [47]
extrapolated using its proper motion to the epoch of our observations:

$\widehat{\mathbf{n}}_{0}=\mathinner{\left($83.633\,037\,9\text{\,}\mathrm{\SIUnitSymbolDegree}$,$22.014\,501\text{\,}\mathrm{\SIUnitSymbolDegree}$\right)},$
(1)

with RA and Dec components reported in decimal degrees. Including the pulsar
position error ($\sigma_{\widehat{\mathbf{n}}}$) and the proper motion
($\boldsymbol{\mu}$) error ($\sigma_{\boldsymbol{\mu}}$) extrapolated over
$\approx$10\text{\,}\mathrm{yr}$$ from recent Crab pulsar astrometry [47], we
sum the absolute position error at the archival observing epoch and the
uncertainty in the proper motion, scaled by the time between our observations
($\sim 10\text{\,}\mathrm{yr}$), in quadrature for the RA and Dec components
individually. The uncertainties in the Crab position propagate into equally-
sized positional uncertainties of the FRB; however these are subdominant
compared to our systematics, so we do not quote them above. For the FRB, we
use the best-fit position derived from a CHIME-only baseband localization
($\widehat{\mathbf{n}}_{0}=($10.2717\text{\,}\mathrm{\SIUnitSymbolDegree}$,$21.226\text{\,}\mathrm{\SIUnitSymbolDegree}$)$).
This is precise to within an arcminute; nevertheless, we find strong fringes
on the FRB pointing towards this position.

In our correlator, we break the total delay into an integer number of
$2.56\text{\,}\mathrm{\SIUnitSymbolMicro s}$ frames and a sub-frame (or sub-
integer) component whose value is in the range
$-1.281.28\text{\,}\mathrm{\SIUnitSymbolMicro s}$. The integer shift is
applied to the data via an array shift, and the sub-integer shift is applied
by a phase rotation to each $2.56\text{\,}\mathrm{\SIUnitSymbolMicro s}$
frame. While this time resolution is lower than that of more conventional VLBI
backends, doing delay compensation on this timescale does not appreciably
increase phase errors, even at the top of the band where these would be most
noticeable. We estimate an upper limit on the phase error at the top of our
band to be $\sim\epsilon\times$2.56\text{\,}\mathrm{\SIUnitSymbolMicro
s}$\times$800\text{\,}\mathrm{MHz}$$, where $\epsilon$ is the maximum delay
rate encountered during our observations. For the most extreme scenario of two
antipodal VLBI stations located on the equator, $\epsilon\approx 3\times
10^{-6}$ gives a phase error of $2.2^{\circ}$: an acceptably small amount of
decorrelation.

After delay compensation, each of the $1024$ frequency channels of data is de-
smeared by a coherent dedispersion kernel [48]. While several conventions may
be used (see e.g., Eq. 5.17 in [49]), we use the following kernel in our VLBI
correlator:

$H(\nu)=\exp\left(2\pi\mathrm{i}k_{\mathrm{DM}}{\mathrm{DM}}\dfrac{\nu^{2}}{2\nu_{k}^{2}(\nu_{k}+\nu)}\right).$
(2)

In Eq. (2), we take $k_{\text{DM}}=$1$/($2.41\text{\times}{10}^{-4}$)$
$\mathrm{s}\text{\,}{\mathrm{MHz}}^{2}\text{\,}{\mathrm{pc}}^{-1}\text{\,}{\mathrm{cm}}^{3}$
(for consistency with previous conventions in the pulsar community [49, 50]),
and the fiducial DM of the FRB is taken to be $500.147\pm
0.004\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$. We choose this
dedispersion kernel in order to avoid introducing delays into each frequency
channel (i.e. it preserves times of arrival at the central frequency of each
channel). The chosen DM de-smears the pulse within each frequency channel.
This concentrates the signal into a narrow temporal duration and increases the
correlation power. The argument
$\nu\in\mathinner{\left[-$195.3125\text{\,}\mathrm{kHz}$,+$195.3125\text{\,}\mathrm{kHz}$\right]}$
indicates the offset from the reference $\nu_{k}$, chosen to be the centre of
each frequency channel:
$\nu_{k}\in\mathinner{\left[$800.0$,$799.609\,375$,...,$400.390\,625$\right]}$
${\mathrm{M}\mathrm{Hz}}$.

After the delay compensation towards the fiducial sky position
$\widehat{\mathbf{n}}_{0}=\mathinner{\left(\upalpha_{0},\updelta_{0}\right)}$
and coherent dedispersion, we form visibilities for each frequency channel
(indexed by $k$) independently on both long baselines involving CHIME
($b_{\mathrm{CA}}$ and $b_{\mathrm{CT}}$, hereafter indexed by $i$) by
multiplying and integrating the complex baseband data. To reject noise, we
integrate only $\sim 100\text{\,}\mathrm{\SIUnitSymbolMicro s}$ of data on
either side of the pulse in each of $1024$ frequency channels. In addition, we
rejected RFI channels (see Extended Data Fig. 1) within each site. This
produces $\sim 900$ complex visibilities per baseline which are used for
localization (hereafter referred to as $V\mathinner{\left[i,k\right]}$). We
integrate $13$ other windows of the same duration in the same dataset but
shifted to off-pulse times to estimate the statistical uncertainties on the
visibilities. The statistical uncertainties are hereafter referred to as
$\sigma\mathinner{\left[i,k\right]}$.

### VLBI Calibration and Empirical Localization Error Budget

The complex visibilities $V\mathinner{\left[i,k\right]}$ must be phase-
calibrated prior to the localization analysis. We calibrate the visibilities
with phase, delay, and rate corrections derived from our Crab GPs before
performing our final localization analysis. In an ideal setup, we would
systematically characterize localization errors in the CHIME-ARO10-TONE array
as a function of sky pointing and time separation and perform end-to-end
localization of known pulsars as a checks of our localization. However, our
ability to do so is limited due to logistical factors at each station. Perhaps
most logistically difficult is the extremely limited internet access to the
ARO10 site, which fundamentally limits the data that can practically be read
out from the ARO10 site [3]. At TONE, frequent misalignment of the dishes due
to high wind conditions requires manual repointing and recalibration of the
array, which frequently interrupts observations. Therefore, the only data
available for characterizing the full CHIME-ARO10-TONE array around the time
the FRB was observed are a sequence of triggered baseband dumps from the Crab
pulsar collected in May–June 2021, simultaneous with CHIME, occurring at a
cadence of about $1$ per day, at each station. We enumerate these Crab pulses
as C1–C4. Waterfall plots of these pulses, in addition to the FRB, are shown
in Extended Data Fig. 1.

List of extdatafigures 1 Dynamic spectra of all observations. At each VLBI
station we recorded five single pulses (including the FRB): Crab GPs which we
refer to as C1–C4 in the several days surrounding FRB 20210603A. Each row
corresponds to a different VLBI station (CHIME at the Dominion Radio
Astrophysical Observatory, ARO10 at the Algonquin Radio Observatory, and TONE
at the Green Bank Observatory). Timestamps show site-local clocks aligned to
within $2.56\text{\,}\mathrm{\SIUnitSymbolMicro s}$ at a reference frequency
of $800.0\text{\,}\mathrm{MHz}$. Though the FRB is too faint to be detected at
the testbeds alone, it is robustly detected in cross-correlation with CHIME at
both stations. The intensity was adjusted by normalizing its standard
deviation and setting the colour scale limits to the $1$ and $99$ percentile
values of the data. Waterfall plots are shown downsampled to a frequency
resolution of $390.625\text{\,}\mathrm{kHz}$ and a time resolution of
$25.6\text{\,}\mathrm{\SIUnitSymbolMicro s}$. The noisy radio frequency
interference (RFI) channels in $700750\text{\,}\mathrm{MHz}$ correspond to the
cellular communications bands and the RFI channels at
$\approx$600\text{\,}\mathrm{MHz}$$ frequencies correspond to television
transmission bands. These RFI channels were removed in our analysis and are
highlighted with red strikes to the left of each waterfall plot. Symbols next
to the telescope label in each waterfall plot indicate what each Crab pulse
was used for. We use C2 on all baselines as a phase/delay calibrator, and C1
and C4 as rate calibrators for the CHIME-ARO10 and CHIME-TONE baselines
respectively. We localized C3 as an end-to-end cross-check of our calibration
solutions.

Within the constraints of these limited data, we perform the following steps
for VLBI calibration. We use C2, the closest Crab pulse in time to the FRB, as
a delay and phase calibrator, i.e. we calculate instrumental phase and delay
solutions for all baselines, and apply them to all observations on all
baselines. The phase and delay solutions remove static instrumental cable
delays and frequency-dependent beam phases, and suppress unwanted astrometric
shifts related to baseline offsets towards the elevation angle of the Crab,
which is less than a degree away from the FRB in alt-azimuth coordinates. In
addition to the phase and delay calibration, a large delay rate correction
($\sim 0.1\text{\,}\mathrm{\SIUnitSymbolMicro s}\text{\,}{\mathrm{day}}^{-1}$)
is needed for the CHIME-ARO10 baseline [3]. Upon removal of the CHIME-ARO10
clock rate, our delay residuals are small (see Extended Data Fig. 2). In that
Figure we also include all of the delay residuals from historical data
available on each baseline individually, calibrated similarly (i.e., with a
clock rate correction for CHIME-ARO10 and with no significant clock rate
correction detected for the CHIME-TONE).

List of extdatafigures 2 Delay residuals measured from the two separate
baselines CHIME-ARO10 and CHIME-TONE baselines. The graph shows the empirical
uncertainty obtained by analysing earlier data sets [3, 4], with CHIME-ARO10
data shown in the top row and CHIME-TONE data showed in the bottom row. Each
point corresponds to the residual delay after applying delay and phase
corrections (CHIME-ARO10 is calibrated to 2020-10-22, and TONE is calibrated
to 2021-02-18). The extracted delays have all been compensated for clock
errors and for a clock rate error on the CHIME-ARO10 baseline.

In the absence of commissioning data available when all three stations were
operating, we characterize each baseline individually. For CHIME-ARO10, we
show a previously-published dataset of $10$ correlated Crab pulses from
October 2020. For CHIME-TONE data, we use $11$ Crab GPs from the
February–March 2021 period during which the instrument was commissioned [4].
From these data, we establish $1\sigma$ systematic localization uncertainties
by calculating the RMS delay errors on each baseline using most of the data
plotted in Extended Data Fig. 2. The RMS delay error on the CHIME-ARO10 and
the CHIME-TONE baselines are $8.5\text{\,}\mathrm{ns}$ and
$6.0\text{\,}\mathrm{ns}$ respectively, calculated from 10 and 11 Crab single-
baseline measurements respectively. These RMS values have been calculated
excluding the pulses used for delay/rate calibration (whose delay residuals
are zero by definition) and faint pulses (CHIME-TONE data from March 2021)
whose fringe detections are marginal, due to a windstorm at Green Bank which
blew several TONE dishes off-axis before they were manually repointed.

### Crab Localisation

In addition to quantifying delay errors on each baseline individually using
Crab pulses, we perform an independent, end-to-end cross-check of the delay
and rate solutions derived for the FRB using C3. This is the only Crab GP
remaining which is detected at all stations and baselines which we have not
used to obtain delay and rate solutions; we use it here as an independent
check of our delay and rate solutions and of our localization procedure, which
combines data from both baselines.

To localize C3, we calibrate C3 visibilities for both baselines using the
aforementioned delay and phase solutions from C2. In addition, on the CHIME-
ARO10 baseline we apply the clock rate measured from C1 and C2. The calibrated
residual delay when the C3 data are correlated towards the true Crab position
is $2.8\text{\,}\mathrm{ns}$ for the CHIME ARO10 baseline and
$2.1\text{\,}\mathrm{ns}$ for the CHIME TONE baseline. To further model the
short-term trend seen in the CHIME-TONE delay residuals, we attempted to apply
a clock rate correction to CHIME-TONE data measured from C2 and C4 (since the
TONE correlator restarted between C1 and C2). Doing so only changes the CHIME-
TONE delay by $\sim 1\text{\,}\mathrm{ns}$. The residual delays, as well as
the final delay rate correction, are subdominant to our $1\sigma$ systematic
error budget of 8.5 and $6.0\text{\,}\mathrm{ns}$ for the CHIME-ARO10 and
CHIME-TONE baselines.

We refer to the visibilities calibrated this way as
$\mathcal{V}\mathinner{\left[i,k\right]}$ (not to be confused with the un-
calibrated visibilities $V\mathinner{\left[i,k\right]}$), where $i$ denotes
the baseline (either CA or CT) and $k$ denotes our $1024$ independent
frequency channels. They are plotted with residual delays removed in Extended
Data Fig. 3. In addition to the correlation start times in each channel
$t_{0}\mathinner{\left[i,k\right]}$, and the baseline vectors
$\mathbf{b}_{\mathrm{CA}}$, $\mathbf{b}_{\mathrm{CT}}$, we use
$\mathcal{V}\mathinner{\left[i,k\right]}$ to localize C3 to an inferred
position $\widehat{\mathbf{n}}$ relative to the fiducial sky position
($\widehat{\mathbf{n}}_{0}$) used to correlate C3.

List of extdatafigures 3 Calibrated visibilities from the Crab pulsar giant
pulse (C3) used to validate our calibration solutions. We plot visibilities
from the CHIME-ARO10 (left) and CHIME-TONE (right) baselines respectively. In
each top panel, we plot the absolute value of the Fourier transform of the
visibilities (i.e. the time-lag cross-correlation function
$\rho\mathinner{\left(\tau\right)}$ as a function of the delay referenced to
the correlator pointing center. This shows a detection S/N exceeding $50$ on
each baseline. In each bottom panel we plot the phase of the calibrated
visibilities $\mathcal{V}\mathinner{\left[i,k\right]}$, binned to
$1.6\text{\,}\mathrm{MHz}$ resolution, with $1\sigma$ phase errors estimated
from off-pulse scans ($N=10$) plotted as
$\sigma\mathinner{\left[i,k\right]}/\mathcal{V}\mathinner{\left[i,k\right]}$
(blue points). In the bottom panels we overlay the phase model (Eq. 4)
evaluated at the parameters which maximize $\mathcal{L}_{\varphi}$, where we
have fit for the ionosphere and the positions simultaneously (green “full fit”
curve), as well as the phase model evaluated at the $\mathcal{L}_{\tau}$
position at zero ionosphere (yellow “delay only” curve). Since our correlator
pointing is the $\mathcal{L}_{\tau}$ position, we would then expect the yellow
“delay only” curve to be flat; note that our plotting code automatically
unwraps all of the phases in each bottom panel by some amount automatically
chosen to reduce phase wrapping, explaining the very small deviation from zero
delay. List of extdatafigures 4 The localization posterior of the Crab pulse
(C3) as a function of RA, Dec, and $\Delta\mathrm{DM_{CA}}$, and
$\Delta\mathrm{DM_{CT}}$. Due to the extremely sparse sampling of the
$uv$-plane, we bypass traditional methods of VLBI imaging, and directly fit
the visibilities $\mathcal{V}\mathinner{\left[i,k\right]}$. Owing to our wide
bandwidth, we see that the ionosphere parameters $\Delta\mathrm{DM}$ are well-
constrained even in the absence of external information (e.g., TEC maps or
ionosphere priors). In the same spirit as a MCMC corner plot, each 2D plot
shows the posterior marginalized over all except two axes. Calling these
projections $P$, we colour evenly-spaced contours between $\log P=0$ (the
maximum value of each $P$ is normalized to $1$) and $\log P=-16$. List of
extdatafigures 5 Localization of C3 as an independent, end-to-end cross check
of our VLBI calibration solution used to localize the FRB. Due to the
extremely sparse sampling of the $uv$-plane, we avoid traditional imaging. We
compare two localization methods: a delay-space $\chi^{2}$-minimization of the
residual delays left after calibration ($+$), and a visibility-space fitting
of the phases ($\times$). Both methods agree to within the true position of
the Crab (star) within systematic uncertainties (ellipses).

List of extdatafigures 6 Calibrated VLBI fringes on FRB 20210603A from the
CHIME-ARO10 and CHIME-TONE baselines respectively. We plot visibilities from
the CHIME-ARO10 (left) and CHIME-TONE (right) baselines respectively. In each
top panel, we plot the absolute value of the Fourier transform of the
visibilities (i.e. the time-lag cross-correlation function
$\rho\mathinner{\left(\tau\right)}$ as a function of the delay referenced to
the correlator pointing center. This shows a detection S/N exceeding $50$ on
each baseline. In each bottom panel we plot the phase of the calibrated
visibilities $\mathcal{V}\mathinner{\left[i,k\right]}$, binned to
$1.6\text{\,}\mathrm{MHz}$ resolution, with $1\sigma$ phase errors estimated
from off-pulse scans ($N=10$) plotted as
$\sigma\mathinner{\left[i,k\right]}/\mathcal{V}\mathinner{\left[i,k\right]}$
(blue points). In the bottom panels we overlay the phase model (Eq. 4)
evaluated at the parameters which maximize $\mathcal{L}_{\varphi}$, where we
have fit for the ionosphere and the positions simultaneously (green “full fit”
curve), as well as the phase model evaluated at the $\mathcal{L}_{\tau}$
position at zero ionosphere (yellow “delay only” curve). Since our correlator
pointing is the $\mathcal{L}_{\tau}$ position, we would then expect the yellow
“delay only” curve to be flat; note that our plotting code automatically
unwraps all of the phases in each bottom panel by some amount automatically
chosen to reduce phase wrapping, explaining the very small deviation from zero
delay.

Several approaches to localizing single pulses been taken in the literature
[26, 3, 51], reflecting the significant challenge of astrometry with sparse
$uv$-coverage. For example, the traditional method of making a dirty map of a
small field and using traditional aperture synthesis algorithms to de-convolve
the PSF is not well-suited to the present VLBI network because of the sparse
$uv$-coverage. We have found that one robust method is to take the delay
estimated from the peak of the Fourier transform of the visibilities, and use
that delay measurement to localize the FRB by maximizing Eq. 3. This method is
robust is the sense that Eq. 3 only has one global maximum, so it works well
even when the true position is arcminutes away from the pointing center.

$\log\mathcal{L}_{\tau}=\sum_{i=\text{CA,CT}}\dfrac{\mathinner{\left(\tau_{i}^{\mathrm{max}}-\tau_{i}\mathinner{\left(\widehat{\mathbf{n}}\right)}\right)}^{2}}{2\sigma_{\tau,i}^{2}}$
(3)

The drawback of this simple method is that it only is sensitive to the
information contained in the linear part of the phase model
($\operatorname{d\\!}\phi/\operatorname{d\\!}\nu_{k}$), which means it mixes
the ionosphere and geometric delays and therefore is only accurate at the
arcsecond level. Working in visibility space is a straightforward way to break
this degeneracy, since we can fit higher-order contributions to the phase as a
function of frequency. We fit Eq. 4 to our data to disentangle the ionosphere
from the geometric delays:

$\phi\mathinner{\left[i,k\right]}=2\pi\mathinner{\left(\nu_{k}\tau_{i}+k_{\mathrm{DM}}\Delta\mathrm{DM}_{i}\frac{1}{\nu_{k}}\right)}.$
(4)

We obtain the best fit solution by maximizing the visibility-space likelihood
function (Eq. 6). Practically, it is difficult to do this because the
posterior is highly multimodal as seen in our final contours, which are shown
in Extended Data Figure 4. We resort to using a box centred on a good initial
guess. For the R.A. and declination, the initial guess is taken from the
$\mathcal{L}_{\tau}$ localization. The initial guesses for Delta DM on each
baseline were determined by independently optimizing the signal to noise (Eq.
5) over a range of Delta DM and delay values on each baseline.

$\rho_{\mathrm{sf}}(\tau,\Delta\mathrm{DM})=\mathinner{\\!\left\lVert\sum_{k}\frac{\mathcal{V}\mathinner{\left[i,k\right]}\exp\mathinner{\left(-\mathrm{i}\phi\mathinner{\left[i,k\right]}\right)}}{\sigma\mathinner{\left[i,k\right]}}\right\rVert}$
(5)

With these initial guesses we evaluate Eq. 6 on a 4D grid to simultaneously
solve for the source position and the ionosphere parameters. Eq. 6 uses a
signal-to-noise weighting scheme, weighting the real part of the phase-rotated
visibilities by $|V|/\sigma^{2}$. The denominator of this weighting
corresponds to inverse noise weighting; $\sigma\mathinner{\left[i,k\right]}$
refers to the statistical uncertainties in the visibilities. The numerator
corresponds to an upweighting by the visibility amplitude. Since the FRB is
detected in each channel with a signal-to-noise of $\sim 5-10$, and since it
is the single dominant source of correlated flux in the correlated data, we
use the visibility amplitude $|V\mathinner{\left[i,k\right]}|$ as a convenient
approximation to the statistically-optimal upweighting, which is the true
signal power in each channel after applying appropriate bandpass and beam
corrections to each baseline. Note that the band-integrated signal-to-noise
reported elsewhere (e.g. Extended Data Fig. 3) is an underestimate of the true
signal-to-noise, since the flux from the FRB contributes significantly to the
RMS noise level of the FFT.

$\log\mathcal{L}_{\varphi}\propto\sum_{i=\text{CA,CT}}\sum_{k=0}^{1023}\dfrac{\mathinner{\\!\left\lVert\mathcal{V}[i,k]\right\rVert}\mathrm{Re}\mathinner{\left[\mathcal{V}\mathinner{\left[i,k\right]}\exp\mathinner{\left(-\mathrm{i}\phi\mathinner{\left[i,k\right]}\right)}\right]}}{\sigma\mathinner{\left[i,k\right]}^{2}.}$
(6)

The posterior as a function of our four parameters
$(\alpha,\delta,\Delta\mathrm{DM_{CA}},\Delta\mathrm{DM_{CT}})$ is shown in
Extended Data Fig. 4. We take the parameter set that maximizes the likelihood
on the grid as the best-fit model. The model phases corresponding to these
parameters, as well as the model phases corresponding to the parameters which
maximize $\mathcal{L}_{\tau}$ are plotted in Extended Data Fig. 3. The
maximum-$\mathcal{L}_{\varphi}$ position of C3 is
$\widehat{\mathbf{n}}=\mathinner{\left($83.633\,053\text{\,}\mathrm{\SIUnitSymbolDegree}$,$22.014\,539\text{\,}\mathrm{\SIUnitSymbolDegree}$\right)}$.
Finally, we draw systematic error contours around this best-fit position using
$\sigma_{\tau,i}=8.6,$6.0\text{\,}\mathrm{ns}$$ respectively in Extended Data
Fig. 5. The 1-sigma systematic error contour drawn around the best fit
position easily encloses the Crab’s true position and the delay-only best-fit
position Extended Data Fig. 5 which does not separate out the ionospheric
delay, showing that the ionosphere is not the dominant source of systematic
error in our localization.

### FRB Localization

We apply the exact same calibration solutions used to localize C3 to the FRB
visibilities. Following the same procedure, we use the coarse localization
with $\mathcal{L}_{\tau}$ to coarsely localize the FRB. The
$\mathcal{L}_{\tau}$ position is
$\widehat{\mathbf{n}}=($10.274\,056\text{\,}\mathrm{\SIUnitSymbolDegree}$,$21.226\,24\text{\,}\mathrm{\SIUnitSymbolDegree}$)$,
and is offset from the baseband localization by $8\text{\,}\mathrm{arcsec}$ in
the RA direction and $\approx$-1.3\text{\,}\mathrm{arcsec}$$ in the
declination direction. To recover some sensitivity, we re-point the correlator
towards this refined position before fringe fitting the calibrated
visibilities (Extended Data Fig. 6) for the ionosphere using
$\mathcal{L}_{\varphi}$. The initial guesses for the ionosphere are estimated
as done previously for C3, and the fringe fit yields the maximum-likelihood
position $\widehat{\mathbf{n}}=\mathinner{\left($10.274\,058\pm
0.000\,08\text{\,}\mathrm{\SIUnitSymbolDegree}$,$21.226\,270\pm
0.0003\text{\,}\mathrm{\SIUnitSymbolDegree}$\right)}$ (Table 1). The
posteriors are shown in Extended Data Fig. 7.

List of extdatafigures 7 The posterior localization contour of FRB 20210603A
as a function of RA, Dec, and $\Delta\mathrm{DM_{CA}}$, and
$\Delta\mathrm{DM_{CT}}$. The ionosphere parameters $\Delta\mathrm{DM}$ are
well-constrained even in the absence of external information (e.g., TEC maps
or ionosphere priors). In the same spirit as a MCMC corner plot, each 2D plot
shows the posterior marginalized over all except two axes. Calling these
projections $P$, we colour evenly-spaced contours between $\log P=$0$$ (the
maximum value of each $P$ is normalized to $1$) and $\log P=$-16$$.

#### Possible Error Sources

We summarize some known contributions to our systematic error, which we find
cannot account for the empirically measured delay errors (8.5 and
$6.0\text{\,}\mathrm{ns}$ at $1\sigma$). We have seen that this corresponds to
a $0.2^{\prime\prime}\times 2^{\prime\prime}$ ellipse on the sky, and that
relative to this ellipse, the effect of including the ionosphere is small. We
estimate our station positioning errors to be $21\text{\,}\mathrm{marcsec}$
assuming a conservative $\approx$10\text{\,}\mathrm{m}$$ baseline uncertainty.
Time variations in the phasing of the antennas may also arise at CHIME or
TONE, since relative cable lengths fluctuate on weeklong timescales by around
$0.1\text{\,}\mathrm{ns}$ at these stations, but they are also re-calibrated
every day. Uncertainties in the proper-motion extrapolated position of the
Crab pulsar at its current epoch ($2\text{\,}\mathrm{marcsec}$) are also
subdominant. Another systematic uncertainty is the astrometric frame tie
between our VLBI localization (ICRF) and optical follow-up observations, which
are performed relative to the FK5/ICRS reference frame. The discrepancy
between the frames is on the order of $\sim$1\text{\,}\mathrm{mas}$$ [52, 53,
54, 55].

Since none of these explain the magnitude of our systematic error, we have to
consider alternate sources of delay fluctuations. One-day timescale variations
in the masers’ relative oscillation frequencies or the signal chains carrying
the maser signals to the digitizers in the F-engine may add delay noise on
timescales relevant for our sparse calibration. Regardless, our empirical
measurement of the RMS delay residuals (see Extended Data Fig. 2) to quantify
our localization uncertainty encompasses all of the known and unknown sources
of systematic astrometric uncertainties, putting our scientific conclusions on
firm footing. In the future, dedicated lab tests could verify this. To avoid
the issue completely, the time between VLBI calibrations could also be
shortened to minutes or hours. With future outrigger stations having
significantly more collecting area than ARO10 and TONE, this will be readily
achievable.

### Burst Morphology

FRB 20210603A was detected with a signal-to-noise ratio of $\sim 136$ in the
CHIME/FRB real-time detection pipeline. Afterwards, we characterized its burst
morphology and estimated its brightness using high-resolution baseband data;
the peak flux, fluence, specific energy, and specific luminosity of the burst
are listed in Table 1. Viewed in baseband data, the FRB has a broadband main
pulse with a total full-width half maximum of
$740\text{\,}\mathrm{\SIUnitSymbolMicro s}$. In addition, two trailing
components are visible in the baseband dump (Fig. 1). Using the DM_phase
algorithm [56], we line up substructures in the main pulse, yielding a DM of
$500.147\pm 0.004\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$. The DM and
the baseband data are inputted to fitburst [6], which simultaneously fits the
main burst with three closely-spaced sub-bursts with full-width half maximum
widths of 310, 450, and $834\text{\,}\mathrm{\SIUnitSymbolMicro s}$, all
broadened by $165\text{\,}\mathrm{\SIUnitSymbolMicro s}$ at 600 MHz.

### Dispersion and Scattering Analysis

In general the observed DM of an FRB can be split into four components as,

$\mathrm{{DM}_{FRB}}=\mathrm{{DM}_{\text{MW-disk}}}+\mathrm{{DM}_{\text{MW-
halo}}}+\mathrm{{DM}_{cosmic}}+\mathrm{{DM}_{host}},$ (7)

where $\text{DM}_{\text{MW-disk}}$ is the contribution of the disk of the
Milky Way, $\text{DM}_{\text{MW-halo}}$ is that from the extended hot Galactic
halo and $\text{DM}_{\text{cosmic}}$ is from the intergalactic medium. The DM
contribution of the host, $\text{DM}_{\text{host}}$, is a combination of the
contributions from the interstellar medium (ISM) of the host galaxy
$\text{DM}_{\text{host-disk}}$, the halo of the host galaxy
$\text{DM}_{\text{host-halo}}$ and the contributions from the source
environment $\text{DM}_{\text{host-env}}$.

To interpret unknown contributions to the total DM, we subtract known
contributions from the total. To estimate the contribution from the Milky Way
disk we default to the NE2001 model [21, 22] obtaining $\text{DM}_{\text{MW-
disk,NE2001}}=$40\pm 8\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$$,
noting that the YMW16 model[57] yields similar results. We estimate the
contribution of the Galactic halo to be $\text{DM}_{\text{MW-halo}}=$30\pm
20\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$$ using the model described
in [29]. We can treat this estimate as conservative, and it can be as low as
$6\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$[58]. This is also
consistent with CHIME/FRB constraints on the halo DM[59]. The IGM contribution
is estimated to be $\text{DM}_{\text{cosmic}}=$172\pm
90\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$$ [60], where the range is
due to cosmic variance in the Macquart relation out to $z\approx$0.18$$ [30].
This leaves the contribution to the DM from the host galaxy halo, disk, and
the FRB local environment as $\text{DM}_{\text{host}}$ = $257\pm
93\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$.

The large value of $\text{DM}_{\text{host}}$ is consistent with a long line-
of-sight traveled through the host galaxy disk, resulting from the galaxy
inclination angle. We can estimate the DM contributions of the host galaxy
disk and halo by scaling the Milky Way’s properties using the stellar mass of
the host galaxy (see Methods: Host Galaxy Analysis). We assume the disk size
($R$) scales with the galaxy stellar mass $\rm{M}_{\text{host}}^{\star}$ as a
power law
$R\propto\mathinner{\left(\rm{M}_{\text{host}}^{\star}\right)}^{\beta}$ where
for simplicity we choose $\beta\sim 1/3$. This value of $\beta$ is close to
the measured value in the literature for galaxies with
$\text{M}^{\star}=$1\text{\times}{10}^{7}1\text{\times}{10}^{11}$\leavevmode\nobreak\
\text{M}_{\odot}$ [61]. Thus the galaxy size scales as
$\mathinner{\left(\text{M}_{\text{host}}^{\star}/\text{M}^{\star}_{\text{MW}}\right)}^{1/3}=($1.4\pm
0.3$)^{1/3}=$1.12\pm 0.08$$, where $\text{M}_{\text{host}}^{\star}=($8.5\pm
0.8$)\times 10^{10}\leavevmode\nobreak\ \text{M}_{\odot}$ and
$\text{M}^{\star}_{\text{MW}}=($6.1\pm 1.1$)\times 10^{10}\leavevmode\nobreak\
\text{M}_{\odot}$ are the present-day stellar masses of the Milky Way [62] and
the host galaxy respectively,. Assuming the halo size also scales as
$\mathinner{\left(\text{M}_{\text{host}}^{\star}/\text{M}^{\star}_{\text{MW}}\right)}^{1/3}$,
the average Milky Way halo DM contribution $43\pm
20\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$ [29] can be scaled to
estimate $\text{DM}^{\text{r}}_{\text{host-halo}}=\text{DM}_{\text{MW-
halo}}\times(\text{M}_{\text{host}}^{\star}/\text{M}^{\star}_{\text{MW}})^{1/3}=$48\pm
23\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$$ in the host galaxy’s rest
frame. Similarly, we can conservatively estimate the rest frame DM due to the
disk of the host galaxy, $\text{DM}^{\text{r}}_{\text{host-disk}}$. A first
approximation is to assume that the FRB originates from close to the midplane
of the disk, and scale the DM contribution of the half-thickness of the Milky
Way ($N_{\perp}(\infty)\approx$24\pm
3\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$$ [63]) by a factor of
$\csc\mathinner{\left($7\pm
3\text{\,}\mathrm{\SIUnitSymbolDegree}$\right)}=$8\pm 3$$ to account for the
viewing geometry. We assume the electron density stays equivalent to that of
the Milky Way and scale for the host galaxy size. This yields an estimate of
$\text{DM}^{\text{r}}_{\text{host-
disk}}=N_{\perp}(\infty)\times\csc\mathinner{\left($7\pm
3\text{\,}\mathrm{\SIUnitSymbolDegree}$\right)}\times\mathinner{\left(\text{M}_{\text{host}}^{\star}/\text{M}^{\star}_{\text{MW}}\right)}^{1/3}=$193\pm
82\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$$ in the host galaxy rest
frame. We can sum these estimates of the $\text{DM}^{\text{r}}_{\text{host-
disk}}$ and $\text{DM}^{\text{r}}_{\text{host-halo}}$ to give the DM in the
observer’s frame as
$\text{DM}_{\text{host}}=(\text{DM}^{\text{r}}_{\text{host-
disk}}+\text{DM}^{\text{r}}_{\text{host-halo}})/(1+z)=$224\pm
82\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$$ which is consistent with
the observed $\text{DM}_{\text{host}}$. If the FRB is behind the galaxy, the
expected contribution from the host galactic disk could be increased by up to
a factor of $2$ yielding $448\pm
164\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$; however, this possibility
is inconsistent with the observed DM excess.

In addition to the DM of the host galaxy, we can also measure gas fluctuations
in the host galaxy using pulse broadening. The measured pulse broadening
timescale from fitburst is
$\tau_{\text{scatt-$600\text{\,}\mathrm{MHz}$}}=$165\pm
3\text{\,}\mathrm{\SIUnitSymbolMicro s}$$. However on visual inspection of the
dynamic spectrum, we cannot rule out the possibility that this timescale
originates from unresolved downward-drifting substructure. We treat this
timescale as an upper limit on the true scattering timescale, and consider the
implications for the FRB progenitors and the host galactic gas by comparing
the dispersion and scattering to Galactic pulsars at similar Galactic
latitudes. To place these measurements on equal footing, we scale
$\tau_{\text{scatt-$600\text{\,}\mathrm{MHz}$}}$ to $1\text{\,}\mathrm{GHz}$,
and multiply by $(1+z)^{3}$ to account for time dilation and the un-redshifted
frequency at which the pulse is scattered. This gives
$\tau_{\text{proper,$1\text{\,}\mathrm{GHz}$}}=$45\text{\,}\mathrm{\SIUnitSymbolMicro
s}$$ in the rest frame of the host galaxy. Further dividing this by $3$
converts the geometric weighting from that of extragalactic (plane-wave)
scattering to Galactic (spherical-wave) scattering [64]. Finally, subtracting
$\mathrm{DM}_{\text{host-halo}}$ from the observed DM excess in the host
galaxy rest frame yields $\mathrm{DM}^{\text{r}}_{\text{host-disk}}=$254\pm
111\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$$. We then calculate the
ratio of observables

$\frac{\tau_{\mathrm{proper},$1\text{\,}\mathrm{GHz}$}}{3(\mathrm{DM}^{\text{r}}_{\mathrm{host-
disk}})^{2}}\lesssim$(4\pm
3)\text{\times}{10}^{-7}\text{\,}\mathrm{ms}\text{\,}{\mathrm{pc}}^{-2}\text{\,}{\mathrm{cm}}^{6}$\propto\widetilde{F}G.$

This ratio characterizes the efficiency of the scattering along the line of
sight. It is proportional to the product of the fluctuation parameter
$\widetilde{F}$ and an order-unity geometric factor $G$. The proportionality
constant is $\Gamma(7/6)r_{e}^{2}c^{3}\nu^{-4}$, where
$\Gamma(7/6)\approx$0.9277$$, $c$ is the speed of light,
$r_{e}=$2.8\text{\,}\mathrm{fm}$$ is the classical electron radius, and $\nu$
is the frequency at which the scattering is observed [65]. This
proportionality constant captures the microphysics and the frequency
dependence of the scattering and relates it to the ratio of observables. The
bulk properties of the gas are captured by $\widetilde{F}$, which depends on
the volume filling factor of gas cloudlets, the size distribution of cloudlets
doing the scattering, the size of the density variations within a cloudlet,
and the inner/outer scales of the turbulence [64]. For the Milky Way’s disk,
typical values of $\widetilde{F}$ range from
$0.0011\text{\,}{\mathrm{pc}}^{-2/3}\text{\,}{\mathrm{km}}^{-1/3}$ for low-
latitude sightlines, roughly corresponding to scattering-$\text{DM}^{2}$
ratios of
$1\text{\times}{10}^{-8}1\text{\times}{10}^{-5}\text{\,}\mathrm{ms}\text{\,}{\mathrm{pc}}^{-2}\text{\,}{\mathrm{cm}}^{6}$
[64]. $G$ can vary by an order of magnitude because it depends on the relative
position of the scattering media to the source and observer, which is poorly
constrained for extragalactic sources of scattering. For example, for the
geometry of a homogeneous scattering medium between the FRB and the edge of
the host galaxy and a distant observer at infinity, $G=1$. However, for a
spiral arm of thickness $L\approx$1\text{\,}\mathrm{kpc}$$ at a distance
$d\approx$10\text{\,}\mathrm{kpc}$$ in front of the FRB, $G=L/d\approx$0.1$$.
In conclusion, the host DM and scattering upper limit are consistent with
expectations from a host-galactic disk with Milky Way-like density
fluctuations. These properties are suggestive of a source close to the host
galaxy’s plane as opposed to an FRB progenitor significantly displaced from
the host galaxy’s disk.

Another interpretation is that the DM excess is partially contributed by the
source’s local environment. The DM excess observed is not extreme: it is only
a factor of two greater than the median measured in population studies
($\text{DM}_{\text{host}}\approx$145\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$$
[66]). Furthermore, the upper limit on the scattering timescale and low RM are
not outliers within the diverse population of FRBs. In this scenario, the FRB
could be produced by a progenitor significantly displaced from the host
galactic plane relative to the electron scale height ($1.57\pm
0.15\text{\,}\mathrm{kpc}$), reducing the host disk contribution to a fraction
of our estimate ($224\pm 82\text{\,}\mathrm{pc}\text{\,}{\mathrm{cm}}^{-3}$).
This displacement would imply an old progenitor since young progenitors
typically have low scale heights, $\sim 30\text{\,}\mathrm{pc}$ and
$100\text{\,}\mathrm{pc}$, for young magnetars and massive stars respectively
[67, 68]).

### Polarisation Analysis

The polarisation analysis follows a similar procedure to that previously
applied to other FRBs detected by CHIME/FRB [69, 70]. In particular, an
initial RM estimate is made by applying RM-synthesis [71, 72] to the Stokes
$Q$ and $U$ data of the burst. This initial estimate is then further refined
through a judicious selection of time and frequency limits that optimize the
S/N of the polarised signal. We then apply a Stokes $QU$-fitting routine that
directly fits for the modulation between Stokes $Q$ and $U$ from Faraday
rotation but is further extended to capture additional features in the Stokes
spectrum.

We analyse FRB 20210603A using the CHIME/FRB polarization pipeline, identical
to that recently employed on FRB 20191219F [73]. We determine an
$\text{RM}=$-219.00\pm 0.01\text{\,}\mathrm{rad}\text{\,}{\mathrm{m}}^{-2}$$
and find the lower limit of the linear polarised fraction ($\Pi_{\text{L}}$)
differs between the top ($\gtrsim$$96\text{\,}\mathrm{\char 37\relax}$ at
$800\text{\,}\mathrm{MHz}$) and the bottom of the CHIME band
($\gtrsim$$87\text{\,}\mathrm{\char 37\relax}$ at $400\text{\,}\mathrm{MHz}$).
This is counteracted by a very small but changing circular polarised fraction
that becomes more significant at the bottom of the band. While this result may
reflect the intrinsic properties of the burst at the source or be an imprint
of some unknown propagation effect [74, 75, 76], it is also not possible to
rule out instrumental effects such as cross-polarisation between CHIME’s
orthogonal feeds. For this reason, we do not report on the circular
polarisation and conservatively set our $\Pi_{\text{L}}$ measurements as lower
bounds (see Table 1).

The Galactic $\text{RM}_{\text{MW}}=$-22.4\pm
0.3\text{\,}\mathrm{rad}\text{\,}{\mathrm{m}}^{-2}$$ contribution can be
estimated from recent all-sky Faraday Sky maps [31]. The RM contribution of
Earth’s ionosphere,
$\text{RM}_{\text{iono}}=+$1.4\text{\,}\mathrm{rad}\text{\,}{\mathrm{m}}^{-2}$$,
is determined from the RMextract package[28]. The uncertainty on this value is
not provided, however, the variability in $\text{RM}_{\text{iono}}$ is
expected to be $\lesssim+$1\text{\,}\mathrm{rad}\text{\,}{\mathrm{m}}^{-2}$$
based on observations of pulsars and repeating FRB sources.

Given that the Galactic pulsar population preferentially occupies the Milky
Way disk, this similarity, while not ruling out alternative scenarios, is
consistent with the notion that FRB 20210603A resides in or near the disk
component of its host galaxy. Extended Data Fig. 8 further explores this
analysis by locating our $\text{DM}_{\text{host}}$,
$\mathinner{\\!\left\lvert\text{RM}_{\text{host}}\right\rvert}$ and
$\tau_{\text{scatt}}$ estimates of FRB 20210603A within the equivalent phase
space of the Galactic pulsar sample. Galactic pulsar data are obtained from
the latest Australia Telescope National Facility (ATNF) pulsar catalogue [77]
using the psrqpy package [78]. FRB 20210603A occupies a well sampled region of
this phase space, however, the distribution is also seen to be highly
dependent on the Galactic latitude. We estimate a quasi-latitude value for FRB
20210603A, determined from a simple transformation of the inclination angle of
the host galaxy (i.e.,
$$4\text{\,}\mathrm{\SIUnitSymbolDegree}$\leq$90\text{\,}\mathrm{\SIUnitSymbolDegree}$-\rm{inclination\,angle}\leq$10\text{\,}\mathrm{\SIUnitSymbolDegree}$$),
and find that the average pulsar properties of DM,
$\mathinner{\\!\left\lvert\text{RM}\right\rvert}$ and $\tau_{\text{scatt}}$ at
this equivalent latitude agree well with what is observed from FRB 20210603A.
The agreement is further improved by rescaling DM,
$\mathinner{\\!\left\lvert\text{RM}\right\rvert}$ to account for the larger
disk mass of the host galaxy relative to the Milky Way. This scaling factor
corresponds to the ratio of the disk mass of the host galaxy and Milky Way and
is found to be
$\mathinner{\left(\text{M}_{\text{host}}^{\star}/\text{M}^{\star}_{\text{MW}}\right)}^{1/3}=$$1.12\pm
0.08$ (See Dispersion and Scattering analysis). Such a result suggests that
most of the observed $\text{DM}_{\text{host}}$,
$\mathinner{\\!\left\lvert\text{RM}_{\text{host}}\right\rvert}$ and
$\tau_{\text{scatt}}$ observed from FRB 20210603A can be supplied by the host
galaxy ISM with little additional contribution needed from the source’s local
environment.

List of extdatafigures 8 A visualization of propagation effects due to the
Milky Way’s disk, as measured via the ATNF Pulsar Catalogue. We plot joint
distributions of DM, $\mathinner{\\!\left\lvert\text{RM}\right\rvert}$ and
$\tau_{\text{scatt}}$ for Galactic pulsars for two different latitude ranges:
$$4\text{\,}\mathrm{\SIUnitSymbolDegree}$\leq\mathinner{\\!\left\lvert
b\right\rvert}\leq$10\text{\,}\mathrm{\SIUnitSymbolDegree}$$ (blue) and
$\mathinner{\\!\left\lvert
b\right\rvert}\geq$20\text{\,}\mathrm{\SIUnitSymbolDegree}$$ (orange) taken
from the ATNF Pulsar Catalogue [77]. Contour lines indicate $1$, $2$ and
$3$$\sigma$ regions of this parameter space. Green regions/lines indicate
estimates of equivalent quantities determined for the host galaxy of FRB
20210603A, namely: $\text{DM}_{\text{host}}$,
$\mathinner{\\!\left\lvert\text{RM}_{\text{host}}\right\rvert}$ and our upper
limit on $\tau_{\text{scatt}}$. $\text{DM}_{\text{host}}$,
$\mathinner{\\!\left\lvert\text{RM}_{\text{host}}\right\rvert}$ and
$\tau_{\text{scatt}}$ estimates are in the source frame with
$\tau_{\text{scatt}}$ referenced at $1\text{\,}\mathrm{GHz}$ assuming a
$\tau_{\text{scatt}}\propto\nu^{-4.4}$ relation used by ATNF. This shows that
the burst properties of FRB 20210603A ($\text{DM}_{\text{host}}$,
$\mathinner{\\!\left\lvert\text{RM}_{\text{host}}\right\rvert}$ and
$\tau_{\text{scatt-$1\text{\,}\mathrm{GHz}$}}$), once corrected for
extragalactic contributions, are similar to that of low-latitude
($$4\text{\,}\mathrm{\SIUnitSymbolDegree}$\leq\mathinner{\\!\left\lvert
b\right\rvert}\leq$10\text{\,}\mathrm{\SIUnitSymbolDegree}$$) Galactic
pulsars.

### Host Galaxy Analysis

Optical images of SDSS J004105.82+211331.9 were taken with the CFHT MegaCam
using the wide-band gri filter. The data were reduced using the standard bias,
dark, and flat corrections using the Elixir pipeline [79, 80]. Several
exposures were combined using this filter to create an image with a total
exposure of $2500\text{\,}\mathrm{s}$.

The half-light radius of the host galaxy was determined using the given
Petrosian radii fluxes provided by SDSS Data Release 12 [10] and Eq. 7 of
[81]. The half-light radius in the $r$-band using these values was found to be
$8.2\pm 0.9\text{\,}\mathrm{kpc}$. Furthermore, the SDSS-provided apparent
magnitude in the $r$-band was corrected for Milky Way extinction using the
model from Fitzpatrick & Massa 2007 [82]; this gave us an absolute magnitude
of $-22.03\pm 0.02$ after k-corrections [83].

In addition to imaging, we conducted Gemini spectroscopic observations
consisting of two $1000\text{\,}\mathrm{s}$ exposures, one centred at
$6750\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ and the other centred at
$6650\text{\,}\mathrm{\SIUnitSymbolAngstrom}$. This wavelength offset was to
account for the gap between the detectors. The images were reduced using
standard bias and flat corrections, and combined using the Gemini IRAF/PyRAF
package tools [84, 85]. Using the same package, we also wavelength- and flux-
calibrated the spectrum, and accounted for skylines and cosmic rays in the
data. We extract spectra with various aperture sizes along the galaxy. The
redshift was determined by extracting a spectrum from a
$1\text{\,}\mathrm{arcsec}$ wide aperture centred at the central coordinates
of the host galaxy. Due to the edge-on orientation of the galaxy, almost all
of the galaxy’s light falls within the slit, and the effect of slit
corrections on the measured fluxes are negligible (see Extended Data Fig. 9).

The H$\alpha$ and the redwards line of the N II doublet (rest wavelengths of
$6564.6\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ and
$6585.2\text{\,}\mathrm{\SIUnitSymbolAngstrom}$) are some of the most
detectable lines (Extended Data Fig. 9). Other prominent lines are from Na and
Mg absorption (rest wavelengths of
$5895.6\text{\,}\mathrm{\SIUnitSymbolAngstrom}$ and
$5176.7\text{\,}\mathrm{\SIUnitSymbolAngstrom}$). Fitting a linear combination
of Gaussian line profiles to the H$\alpha$ and N II lines yields a redshift of
$z=$0.1772\pm 0.0001$$. The uncertainty in the spectroscopic redshift is
dominated by the statistical uncertainties in the measured spectrum, which are
normalized such that the reduced-$\chi^{2}$ of the residuals is $1$.

To further characterize the galaxy, we combine our Gemini spectra with
archival 2MASS[16] and WISE photometry[17]. We use the spectral-energy
distribution (SED) fitting code Prospector to determine the stellar mass,
metallicity, and star formation history of the galaxy [18]. Our modelling and
analysis of this host galaxy closely follows a similar effort for FRB
20181030A [86]. However, because the galaxy is nearly edge-on, dust extinction
in the host-galactic centre reddens the observed emission. Therefore, we first
correct the spectrum for extinction (see Eqs. 10 and 13 of [87]) due to its
inclination of $83\pm 3\text{\,}\mathrm{\SIUnitSymbolDegree}$ [12].

Our best-fit model is overlaid on the spectral and photometric data in
Extended Data Fig. 10. It assumes a delay-$\uptau$ star formation history
$\propto t\exp\mathinner{\left(-{t}/\uptau\right)}$, where $\uptau$ is the
characteristic decay time and $t$ is the time since the formation epoch of the
galaxy. We set five free parameters: present-day stellar mass, metallicity,
$\uptau$, $t$, and the diffuse dust V-band optical depth (referred to as
“dust2” in Prospector), which accounts for the attenuation of old stellar
light. We use $\uptau$ and $t$ as determined by Prospector to calculate the
mass-weighted age of the galaxy. Additionally, we used a standard dust
attenuation model [88], and enabled nebular emission and dust emission [89,
90].

Before sampling the likelihood, we choose reasonable priors for each free
parameter (Extended Data Table 2). We use Eq. (6) of [91] to obtain an initial
estimate of the galaxy’s mass, and to set a weak prior on the mass range.

$\log_{10}(\text{M}_{\text{host}}^{\star}/\text{M}_{\odot})=$1.097$(g-r)-$4.06$-$0.4$(M_{r}-$4.97$)-$0.19$z,$
(8)

where $g$ and $r$ are the apparent magnitudes in the $g$-band and $r$-band
filters, $M_{r}$ is the absolute magnitude in the $r$-band, and $z$ is the
redshift. The prior on $t$ was cut off at $12\text{\,}\mathrm{Gyr}$ because
the age of the Universe at $z=$0.1772\pm 0.0001$$ is only $\sim
12\text{\,}\mathrm{Gyr}$. The prior on $\text{Z}/\text{Z}_{\odot}$ and
$\uptau$ were set according to recommendations in Prospector [18]. Using these
priors, we obtain the fit plotted in Extended Data Fig. 10 and list the
results in Table 1.

Table 2: Priors set for SED modeling. The parameters here are used for modeling the host galaxy with a delayed-$\tau$ model as implemented in Prospector. Parameter |  | Prior $\mathinner{\left[\text{min},\text{max}\right]}$
---|---|---
$\log(M^{\star}/M_{\odot})$ | Present-day Stellar Mass | Log Uniform $\mathinner{\left[$10$,$12$\right]}$
$\log\mathinner{\left(Z/Z_{\odot}\right)}$ | Metallicity | Top Hat $\mathinner{\left[-2,0.19\right]}$
$t$ | Time since formation (Gyr) | Top Hat $[0.1,12]$
$\uptau$ | Star formation characteristic decay rate (Gyr) | Log Uniform $\mathinner{\left[0.3,15\right]}$
dust2 | Diffuse dust V-band optical depth | Top Hat $\mathinner{\left[0,3\right]}$

Finally, to determine the galaxy-integrated SFR, we extract a spectrum with an
aperture of $10\text{\,}\mathrm{arcsec}$ in diameter, encompassing all of the
galaxy’s light within our half-light radius of $\sim
2.5\text{\,}\mathrm{arcsec}$. We calculate the total SFR of the host galaxy
using the intensity and line width of the H$\alpha$ line [92]:

$\text{SFR}=$7.9\text{\times}{10}^{-42}$\mathinner{\left(\frac{\text{L}_{\text{H}\alpha}}{$\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}$}\right)}\frac{\text{M}_{\odot}}{$\mathrm{yr}$},$
(9)

where $\text{L}_{\text{H}\alpha}$ is the flux-derived luminosity of the
$\text{H}\alpha$ emission from our Gemini data. To correct our luminosity
measurement for extinction we apply the inclination-angle dependent correction
as well as the inclination-independent correction, parameterized as dust2 in
Prospector. The latter quantifies the amount of V-band extinction of old
stellar light in the host galaxy. Optical reddening is characterized by using
$\textrm{R}_{\text{V}}$ = $\textrm{A}_{\text{V}}$/E(B-V), where E(B-V) is the
colour index of the galaxy and $\textrm{A}_{\text{V}}$ is the extinction in
the V-band; this equation is thus the ratio of total to selective extinction
in the V-band [93]. The dust extinction is taken to be
$\textrm{A}_{\text{V}}=$1.086$\times\text{dust2}$ [18, 94], where we take
dust2 to be the best-fit value of $0.79$. With an $\textrm{R}_{\text{V}}$
value of $3.1$ [93], we calculated E(B-V) to be $0.28$. The H$\alpha$
extinction coefficient can be calculated using
$\textrm{A}_{\text{H}\alpha}=\textrm{R}_{\text{H}\alpha}\times$ E(B-V) where
we take $\textrm{R}_{\text{H}\alpha}=$2.45$$; this value is within the range
of values predicted by several different extinction models [95, 88, 82, 96].
The inclination-independent attenuation results in the H$\alpha$ flux being
attenuated by a factor of
$\exp\mathinner{\left(\textrm{A}_{\text{H}\alpha}\right)}=1.97$. Correcting
the galaxy-integrated H$\alpha$ flux for extinction yielded a total SFR of
$$0.24\pm 0.06$\,\leavevmode\nobreak\ \text{M}_{\odot}${\mathrm{yr}}^{-1}$$.

List of extdatafigures 9 Spatially resolved spectroscopy of the host galaxy.
Optical image and spatially-resolved spectra of the host galaxy of FRB
20210603A acquired using CFHT MegaCAM and Gemini long-slit spectroscopy
respectively. Pixel intensities are scaled linearly and normalized to reduce
the saturation evident in Figure 3. All spectra are given offsets in
increments of
$1\text{\times}{10}^{-17}\text{\,}\mathrm{erg}\text{\,}{\mathrm{s}}^{-1}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{-1}$.
One spectrum is extracted from the bulge of the galaxy (spectrum b, centered
at 0). There are additional eleven spectra extracted from the FRB side of the
galaxy (shown as positive offsets), and from the opposite side of the galaxy
(shown as negative offsets), with offsets from the center of the galaxy in
increments of $1\text{\,}\mathrm{arcsec}$. All spectra are extracted using an
aperture size of
$$1.5\text{\,}\mathrm{arcsec}$\times$1\text{\,}\mathrm{arcsec}$$, as
represented on the galaxy image. Spectrum a is extracted within the vicinity
of the FRB and represented by the shaded box a in the galaxy image. The twelve
spectra and Gaussian fits to the H$\alpha$ and one of the NII emission lines,
are plotted here after correcting for Milky-Way extinction.  List of
extdatafigures 10 Spectral energy distribution of host galaxy: Gemini long-
slit spectrum, integrated over the galaxy, with archival infrared photometry
from 2MASS and WISE, plotted after correcting for extinction due to the host
galaxy’s inclination angle. Plotted alongside the observations (red) are the
best-fit model (blue) from Prospector, and the relative passbands for the
2MASS J, H, and Ks and WISE W1-W3 filters. Flux uncertainties are plotted by
converting $1\sigma$ photometric errors reported by each catalogue.

### Disk Chance Coincidence Probability

While FRB 20210603A was ostensibly localized to the disk of its host galaxy,
it is possible that the progenitor is actually a halo object (as in the case
of the globular cluster host of FRB 20200120E [97]) coincidentally aligned
with the disk in projection. The probability that this occurs by a chance
coincidence is small: we estimate this as the ratio of the solid angles
subtended by the disk and halo, that is
$P_{cc}\approx\Omega_{\mathrm{disk}}/\Omega_{\mathrm{halo}}\approx 10^{-3}$.
The angular area of the nearly edge-on disk can be approximated as an ellipse
with major and minor axes of 15 and $2.7\text{\,}\mathrm{arcsec}$
respectively, while the area of the halo can be approximated as a circle of
radius
$r_{\mathrm{vir}}\approx\text{M}_{\text{host}}^{\star}/\text{M}^{\star}_{\text{MW}}r_{\mathrm{vir,MW}}\approx$\sim
280\text{\,}\mathrm{kpc}$$ estimated by scaling up the Milky Way’s virial
radius $r_{\mathrm{vir,MW}}\approx$200\text{\,}\mathrm{kpc}$$ [98]. This low
chance coincidence probability of $10^{-3}$ implies a robust association with
the disk and favours progenitor models involving disk populations over halo
populations.

##### Data Availability

Calibrated visibilities, dynamic spectra for producing figures, and MCMC
chains for the localization analysis are available upon request and will be
hosted by the time of publication as downloadable HDF5 files on the CHIME/FRB
CANFAR repository
https://www.canfar.net/storage/list/AstroDataCitationDOI/CISTI.CANFAR/24.0086/data).
Optical images, spectra, and photometric data are immediately available as
fits files at https://github.com/tcassanelli/frb-vlbi-loc.

##### Code Availability

The code used for beamforming, VLBI localization, and polarisation analysis
are available on Github: https://github.com/CHIMEFRB/baseband-analysis. The
scattering timescale has been measured using fitburst [6], available at
https://github.com/CHIMEFRB/fitburst. Code for interpreting burst properties,
and producing the figures and tables in this manuscript from the results of
our analyses is available at https://github.com/tcassanelli/frb-vlbi-loc. In
our analyses, we also make use of open-source software including astropy [99],
baseband [100], difxcalc11 [46], matplotlib [101], numpy [102], scipy [103] ,
h5py [104], emcee [19], and corner [105], cartopy [106], IRAF [84, 85], and
prospector [18].

##### Acknowledgments

We would like to dedicate this work to our colleague Dr. Jing Luo, who passed
away on February 15, 2022. Jing worked for several years on the commissioning
and maintenance of the 10-m telescope at the Algonquin Radio Observatory. His
expertise in radio pulsars, radio observations, and hardware were
indispensable in accomplishing this scientific milestone.

We acknowledge that CHIME is located on the traditional, ancestral, and
unceded territory of the Syilx/Okanagan people. We are grateful to the staff
of the Dominion Radio Astrophysical Observatory, which is operated by the
National Research Council of Canada. 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 thanks to 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.

We would like to thank the staff of Dominion Radio Astrophysical Observatory,
operated by the National Research Council of Canada, for gracious hospitality,
support, and expertise. The ARO 10-m telescope operated by the University of
Toronto. TONE is located at Green Bank Observatory, the Green Bank Observatory
facility, which is supported by the National Science Foundation, and is
operated by Associated Universities, Inc. under a cooperative agreement. We
would like to thank the staff at Green Bank Observatory for logistical support
during the construction and operations of TONE.

This work is based on observations obtained at the international Gemini
Observatory, a program of NSF’s NOIRLab, which is managed by the Association
of Universities for Research in Astronomy (AURA) under a cooperative agreement
with the National IRAF was distributed by the National Optical Astronomy
Observatory, which was managed by the Association of Universities for Research
in Astronomy (AURA) under a cooperative agreement with the National Science
Foundation. PyRAF is a product of the Space Telescope Science Institute, which
is operated by AURA for NASA.Science Foundation. on behalf of the Gemini
Observatory partnership: the National Science Foundation (United States),
National Research Council (Canada), Agencia Nacional de Investigación y
Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación
(Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações
(Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea).

This work is also based on observations obtained with MegaPrime/MegaCam, a
joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope
(CFHT) which is operated by the National Research Council (NRC) of Canada, the
Institut National des Science de l’Univers of the Centre National de la
Recherche Scientifique (CNRS) of France, and the University of Hawaii. The
observations at the Canada-France-Hawaii Telescope were performed with care
and respect from the summit of Maunakea which is a significant cultural and
historic site.

IRAF was distributed by the National Optical Astronomy Observatory, which was
managed by the Association of Universities for Research in Astronomy (AURA)
under a cooperative agreement with the National Science Foundation. PyRAF is a
product of the Space Telescope Science Institute, which is operated by AURA
for NASA.

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.
A.P.C. is a Vanier Canada Graduate Schola B.M.G. acknowledges the support of
the Natural Sciences and Engineering Research Council of Canada (NSERC)
through grant RGPIN-2015-05948, and of the Canada Research Chairs program.
C.L. was supported by the U.S. Department of Defense (DoD) through the
National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.
E.P. acknowledges funding from an NWO Veni Fellowship. F.A.D is funded by the
UBC Four Year Doctoral Fellowship. FRB research at UBC is funded by an NSERC
Discovery Grant and by the Canadian Institute for Advance Research. The CHIME
baseband system was funded in part by a CFI JELF award to IHS. FRB research at
WVU is supported by an NSF grant (2006548, 2018490) J.B.P. is support by the
NSF MRI grant (2018490) 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. M.D. is supported by a Canada
Research Chair, Killam Fellowship, NSERC Discovery Grant, CIFAR, and by the
FRQNT Centre de Recherche en Astrophysique du Québec (CRAQ) P.S. is a Dunlap
Fellow. S. Cary would like to thank Prof. Kim McLeod from Wellesley College
for her supervision and feedback, which was essential for the host galaxy
analysis. S.C. is a member of the NANOGrav Physics Frontiers Center, which is
supported by NSF award PHY-1430284. U.P. is supported by the Natural Sciences
and Engineering Research Council of Canada (NSERC), [funding reference number
RGPIN-2019-067, CRD 523638-201, 555585-20], Ontario Research Fund—research
Excellence Program (ORF-RE), Canadian Institute for Advanced Research (CIFAR),
Simons Foundation, Thoth Technology Inc, and Alexander von Humboldt
Foundation. This research is supported by the MOST grant
110-2112-M-001-071-MY3 from the Ministry of Science and Technology of Taiwan.
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. Z.P. is a Dunlap Fellow.

##### Author Contributions

Author contributions T.C. led the full instrument adaptation, triggering
system, and data management of the ARO10 telescope, wrote in the main text,
methods sections, and prepared several figures and tables. C.L. wrote the VLBI
software correlator and analysis pipeline used to localize the FRB, designed
and built the digital backend of the TONE array, and led the data analysis,
scientific interpretation, and writing of the manuscript. P.S. led the design,
construction, commissioning, and data acquisition of all aspects of the TONE
telescope, and contributed significantly to the scientific interpretation and
writing of the manuscript. J. M. P. designed and installed the maser hardware,
characterized the clock stabilization system, and made foundational
contributions to the array calibration pipelines used at TONE and CHIME. S.C.
led the calibration, reduction, and analysis of optical follow-up data. All
authors from the CHIME/FRB collaboration played either leadership or
significant supporting roles in one or more of: the management, development,
construction, commissioning, and maintenance of CHIME, the CHIME/FRB
instrument, the ARO10 instrument, the TONE instrument, their respective
software data pipelines, and/or the data analysis and preparation of this
manuscript.

##### Competing Interests

The authors declare that they have no competing financial interests.

##### Correspondence and requests for materials

should be addressed to Calvin Leung at<EMAIL_ADDRESS>
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