# Probing the distant universe with a very luminous fast radio burst at
redshift $1$

Stuart D. Ryder1,2, Keith W. Bannister3, S. Bhandari4,5, A. T. Deller6, R. D.
Ekers3,7,
Marcin Glowacki7, Alexa C. Gordon8, Kelly Gourdji6, C. W. James7,
Charles D. Kilpatrick8, Wenbin Lu9, Lachlan Marnoch1,2,3,10, V. A. Moss3,
J. Xavier Prochaska11,12,13, Hao Qiu14, Elaine M. Sadler15,3, Sunil Simha11,
Mawson W. Sammons7, Danica R. Scott7, Nicolas Tejos16, R. M. Shannon6,∗
1School of Mathematical and Physical Sciences, Macquarie University, NSW 2109,
Australia
2Astronomy, Astrophysics and Astrophotonics Research Centre, Macquarie
University,Sydney, NSW 2109, Australia
3Australia Telescope National Facility, CSIRO, Space and Astronomy, PO Box 76,
Epping, NSW 1710, Australia
4ASTRON, Netherlands Institute for Radio Astronomy, Oude Hoogeveensedijk 4,
7991 PD Dwingeloo, The Netherlands
5Joint institute for VLBI ERIC, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The
Netherlands
6Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, Hawthorn,VIC 3122, Australia
7International Centre for Radio Astronomy Research, Curtin Institute of Radio
Astronomy,
Curtin University, Perth, Western Australia, Australia.
8Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA)
and Department of Physics and Astronomy,
Northwestern University, Evanston, IL 60208, USA
9Departments of Astronomy and Theoretical Astrophysics Center, UC Berkeley,
Berkeley, CA 94720, USA
10 ARC Centre of Excellence for All-Sky Astrophysics in 3 Dimensions (ASTRO
3D), Australia
11 Department of Astronomy and Astrophysics, University of California, Santa
Cruz, CA 95064, USA
12 Kavli Institute for the Physics and Mathematics of the Universe, 5-1-5
Kashiwanoha, Kashiwa, 277-8583, Japan
13Simons Pivot Fellow
14SKA Observatory, Jodrell Bank, Lower Withington, Macclesfield, SK11 9FT, UK
15Sydney Institute for Astronomy, School of Physics A28, University of Sydney,
NSW 2006, Australia
16Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla
4059, Valparaíso, Chile
∗To whom correspondence should be addressed; E-mail<EMAIL_ADDRESS>
> Fast radio bursts are millisecond-duration pulses of radio emission that
> have been found to originate at extragalactic distances. The bursts show
> dispersion imparted by intervening plasma, with the bulk attributed to the
> intergalactic medium. Here we report the discovery of a burst, FRB
> 20220610A, in a complex host galaxy system at a redshift of $z=1.016\pm
> 0.002$. The relationship between its redshift and dispersion confirm that
> the bulk of the baryonic matter was ionized and in the intergalactic medium
> when the universe was almost half its present age. The burst shows evidence
> for passage through a significant additional column of turbulent and
> magnetized high-redshift plasma. It extends the maximum observed burst
> energy by a factor of four, confirming the presence of an energetic burst
> population at high redshift.

Fast radio bursts (FRBs, (?, ?)) have emerged as an invaluable cosmological
tool. Free electrons along the propagation path from the FRB source to the
observer impart a frequency-dependent time delay (dispersion) on the impulsive
radio signal. This dispersion provides a direct measure of the total free
electron column (dispersion measure, DM) between the FRB source and observer.
FRBs localized to host galaxies at different redshifts exhibit a positive
correlation between total electron column and host redshift, referred to as
the “Macquart relation” (?). Analysis of FRBs on this relation yields an
independent measurement of the cosmic baryon fraction and the present-day
expansion rate of the universe (?). To date, this relation has been
demonstrated with securely identified host galaxies only to modest redshift
($z\lesssim 0.5$). Some unlocalized FRBs have DMs consistent with redshifts
$>1$ (?); conversely, a burst with large DM has been associated with a galaxy
at moderate redshift in at least one case (?). Consequently, it is unclear
whether high-DM FRBs commonly reside in relatively nearby hosts that impart a
significant dispersion contribution of their own.

We have been searching for (?) and localizing (?) FRBs using the Australian
Square Kilometre Array Pathfinder (ASKAP, (?)), a radio interferometer in
Western Australia comprising thirty-six 12-m antennas. Each antenna is
equipped with phased-array receiving systems, enabling 36 beams to be
digitally formed across the focal plane, covering approximately 30 square
degrees. We search for FRBs in real-time in the incoherent sum of the
intensities of each antenna in each beam. When an FRB is detected, voltage
buffers are downloaded, correlated, calibrated, and imaged, enabling the
position of the burst to be measured to an accuracy of typically a few tenths
of an arcsecond (?, ?). FRB 20220610A was detected in a field containing a
previously discovered burst (?), in observations centred at a frequency of
$1271.5$ MHz and a time resolution of 1.18 ms. FRB 20220610A is immediately
notable for having a high DM of $1457.624\pm 0.001$ pc cm-3; of the 54 bursts
detected by ASKAP, only one (FRB 20210407E, (?)) has a higher DM (?). A
dedispersed dynamic spectrum of the burst is shown in Figure 1, and properties
of the burst are listed in Table 1.

When the burst was detected, voltage buffers were downloaded, enabling a sub-
arcsecond localization. The 2 s dispersive sweep of the burst across the band
and 2.4 s latency in the detection system resulted in only the lowest $88$ MHz
of the burst being captured in the $3.1$ s-duration voltage buffer. This
nevertheless proved sufficient to localize the burst to a precision of 0.5
arcsec. We also used the voltage data to reconstruct the high time resolution
and polarimetric properties of the burst. After correcting for dispersive
smearing, the burst shows an exponentially decreasing tail consistent with
scatter broadening due to turbulence in intervening plasma (?). The pulse
broadening time is measured to be $0.511\pm 0.012$ ms at a reference frequency
of $1148$ MHz assuming a $\nu^{-4}$ frequency dependence. We find strong
evidence for Faraday rotation, with the rotation measure (RM) measured to be
$215\pm 2$ rad m-2. After correcting for Faraday rotation we observe the pulse
to have a linear polarization fraction of greater than 96%. The high
fractional linear polarization allows us to place a limit on Faraday
dispersion ($\sigma_{\rm RM}$) reported for other FRBs (?) and induced by
fluctuations in rotation measure in intervening turbulent plasma, constraining
$\sigma_{\rm RM}<$ $0.6$ rad m-2.

We undertook ground-based optical and infrared observations to identify and
characterize the burst host galaxy (?). The images show an extended, multi-
component morphology, where the burst position is coincident with one
component (see Figure 2). Based on a Bayesian framework for assessing the
chance of coincidence between transients and host galaxies (?), we find the
probability of correct association to be greater than $99.99\%$ and conclude
the association is robust. Simultaneous optical and infrared spectroscopy of
components A, B and C (Figure 2) with the Very Large Telescope (VLT) resulted
in the detection of multiple emission lines, which yield (?) a redshift for
the host system of $1.016\pm 0.002$. A complete summary of properties of the
host can be found in Table 1. While the complex has a total stellar mass and
star formation history comparable to that of nearby FRB hosts (?, ?), the
morphology is markedly different. The total mass is measured to be
approximately $10^{10}$ solar masses and we estimate the current star
formation rate to be $0.4$ solar masses per year (?).

The presence of two bright clumps A and C (separated by a distance of 16 kpc),
and the diffuse feature B between them, is suggestive of two galaxies
interacting or merging. It is also possible that the morphology is due to
structure within a single galaxy, since at these redshifts as many as half of
all galaxies show clumpy morphologies (?). However, this latter possibility is
less likely, given the large spatial separation between the components.
Additionally, component A appears brightest in the $K_{\rm s}$-band image
(most likely due to having an older stellar population), but is well displaced
from the overall centroid of the optical light in $g$\- and $R$-band, contrary
to what is expected for a single undisturbed galaxy at this redshift. Higher
spatial resolution should be able to discriminate between the components
forming via gravitational instabilities in gas-rich disks (?, ?), or if an
interaction or merger event is in progress (?).

The burst dispersion extends the Macquart relation to higher redshift. Figure
3 shows the relationship between dispersion measure and redshift for the ASKAP
FRB sample. Subtracting off a model for the Milky-Way contribution to the
observed DM (?), we estimate an extragalactic DM of $\approx 1376\,\rm
pc\,cm^{-3}$, requiring a high column density of ionized gas between the FRB
and Earth. This confirms the inference from other experiments (e.g. the
Ly$\alpha$ forest; (?)) that the gas of the cosmic web is highly ionized.
Furthermore, the detection of FRBs at $z>1$ enables additional opportunities
to study the nature of ionized plasma between, around, and within distant
galaxies. For example, one expects a sightline to $z=1$ to intersect several
halos of galaxies comparable to our own (?). Follow-up observations will
identify all such galaxies towards FRB 20220610A and permit studies of their
circumgalactic medium (?). Last, the extension of the Macquart relation to
$z\sim 1$ paves the way to yet higher redshifts and potential analysis of He
ii reionization.

We find significant excess DM of approximately $650$ pc cm-3 relative to the
median expectation from the Macquart relation — equivalent to $1300$ pc cm-3
in the host rest frame (?). The scatter broadening and Faraday rotation of FRB
20220610A provide a unique opportunity to investigate the properties of plasma
at high redshift. This observed dispersion excess could be due to any
combination of gas in the immediate vicinity of the source, the interstellar
medium of the host galaxy, or foreground intervening gas. The absence of
strong Faraday rotation or depolarization contrasts to other FRB sources which
show excess dispersion (?). This suggests the excess dispersion for FRB
20220610A originates in a less magnetoionically active plasma, such as in the
interstellar medium of the host galaxy, rather than primarily in the circum-
burst media hypothesized for other sources (?, ?, ?). Models imply that the DM
of a typical spiral galaxy is unlikely to exceed a few hundred
$\mathrm{pc~{}cm}^{-3}$ except in extreme edge-on systems, but higher DM
values can plausibly be produced by high-density clumps of gas within the host
galaxy (?), particularly given that galaxies at $z\sim 1$ have a substantially
higher fraction of their baryons in gas rather than stars. It is also possible
that the dispersion originates from structure in the foreground intergalactic
medium, or is the result of additional ionized material associated with a
putative galaxy merger.

The burst extends the maximum characteristic energy of FRBs and requires
revision of models of the population. The bandwidth-averaged fluence for this
event is $45\pm 5$ Jy ms, implying an energy of $(6.4\pm 0.7)\times 10^{32}$
erg Hz-1 (?). This exceeds the characteristic $E_{\rm max}$ derived from
previous FRB population models (?), suggesting FRBs to be even more extreme
phenomena than previously thought. Using previous methods (?), we re-estimate
the characteristic maximum FRB energy to be $E_{\rm max}=5^{+3}_{-2}\times
10^{32}$ erg Hz-1. This rules out the lower range of allowed maximum FRB
energies from previous estimates (?, ?, ?). The presence of further high-
redshift high-luminosity bursts would challenge the model and further extend
burst energetics.

The burst energy, $\sim 2\times 10^{42}\rm\,erg$, is the highest in all
unambiguously localized FRBs (Figure 3). Based on statistical analysis of the
FRB rate function, this is near the maximum energy that the entire FRB source
population can produce. This provides a stress test for the emission models of
FRBs. In one class of models, the emission is produced near the surface of a
neutron star. From the luminosity of the burst $\sim 3\times
10^{46}\rm\,erg\,s^{-1}$ in the host-galaxy’s rest frame, one infers an
electric field strength of $1.4\times 10^{12}(r/10\mathrm{\,km})^{-1}$
electrostatic units, for a linearly polarized wave. This is a few percent of
the Schwinger field strength for emission from near the neutron star surface
($r\sim 10\rm\,km$), and an electric field component of this strength parallel
to the local magnetic field would be quickly shielded by copious pair
production. This could cause a suppression of the FRB rate above this
luminosity. In the other class of models, FRBs are produced by a shock driven
by relativistic ejecta accompanied by a magnetar flare. In these models, the
radiative efficiency is very low ($\lesssim 10^{-5}$) and hence the required
ejecta energy would be $\gtrsim 10^{47}\rm\,erg$, while the total flare energy
may be much higher. It is possible that FRB 20220610A is produced by one of
the most energetic magnetic flares in the universe.

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## Acknowledgments

We thank K. Heintz for contributions to the FURBY project, and N. Förster-
Schreiber and K. Glazebrook for discussions. We thank ATNF staff for
supporting CRAFT observations with ASKAP. Based on observations collected at
the European Southern Observatory under ESO programmes 0105.A-0687 and
1108.A-0027. The Australian SKA Pathfinder is part of the Australia Telescope
National Facility (https://ror.org/05qajvd42) which is managed by CSIRO.
Operation of ASKAP is funded by the Australian Government with support from
the National Collaborative Research Infrastructure Strategy. ASKAP uses the
resources of the Pawsey Supercomputing Centre. Establishment of ASKAP, the
Murchison Radio-astronomy Observatory (MRO) and the Pawsey Supercomputing
Centre are initiatives of the Australian Government, with support from the
Government of Western Australia and the Science and Industry Endowment Fund.
Some of the data presented herein were obtained at the W. M. Keck Observatory,
which is operated as a scientific partnership among the California Institute
of Technology, the University of California, and the National Aeronautics and
Space Administration. The Observatory was made possible by the generous
financial support of the W. M. Keck Foundation. We acknowledge the Wajarri
Yamatji people as the traditional owners of the MRO site. We recognize and
acknowledge the very significant cultural role and reverence that the summit
of Maunakea has always had within the indigenous Hawaiian community. We are
most fortunate to have the opportunity to conduct observations from this
mountain. SB is supported by a Dutch Research Council (NWO) Veni Fellowship
(VI.Veni.212.058). ATD and KG acknowledge support through ARC Discovery
Project DP200102243. ATD and RMS acknowledge support through Australian
Research Council Discovery (ARC) Project DP220102305. CWJ and MG acknowledge
support through ARC DP DP210102103. RMS acknowledges support through ARC
Future Fellowship FT190100155. JXP, SS, CK, ACG, and NT, as members of the
Fast and Fortunate for FRB Follow-up team, acknowledge support from National
Science Foundation grants AST-1911140, AST-1910471 and AST-2206490.

|
---|---

Figure 1. FRB 20220610A. Left: FRB as observed in the incoherently summed data
stream. The pulse width is dominated by intra-channel dispersion smearing.
Panel A shows the integrated pulse profile, while panel B shows the
dedispersed burst dynamic spectrum, highlighting an unmodulated spectrum
unlike many lower DM ASKAP FRBs (?). Right: High time resolution data produced
from the downloaded voltages. Panel C shows linear polarization position angle
$\Psi$, while panel D shows the integrated pulse profile. We show total
intensity $I$, linear polarization $L_{\rm eff}$ (?), Stokes V, and the
maximum likelihood model for stokes I is labelled $M_{I}$. We show the
residuals $R_{I}$ between $I$ and $M_{I}$ offset from zero by $-20$ Jy.

---

---

Figure 2. Optical and infrared observations of the FRB 20220610A host. A:
$g$-band image, with the ellipses outlining the apertures used for each clump.
The unlabeled circle is the aperture used for the entire combined object. B:
$R$-band image, with the FRB localization and uncertainty (68% confidence)
indicated by the black ellipse. C: $K_{\rm s}$ band image. The scale bar shows
the angular scale and corresponding projected physical scale at the host
redshift. All three images are on the same scale. D: VLT/X-shooter detection
of [O ii] lines with rest wavelengths of 3726 and 3729 Å from the host galaxy
of FRB 20220610A at a slit position angle on the sky of $45^{\circ}$ covering
apertures A and B above. E: A 1D spectrum (black solid line) and its
uncertainty (red dashed line) extracted from the 2D image with an aperture
width of 1.8′′ full width at half maximum.

|
---|---

Figure 3. Left: Fast radio burst $z$–DMEG distribution for the ASKAP
incoherent sum (ICS) survey. Shown are localized FRBs (red circles showing
host galaxy redshifts) and un-localized FRBs (red dotted lines showing 99%
confidence interval for redshift). The color scale is proportional to the
detection likelihood per d$z$ and extragalactic dDMEG increment (?) with an
increased maximum energy $\log_{10}E_{\nu}\,[{\rm erg\,Hz^{-1}}]=32.7\pm 0.2$
found in this work. Dotted, dash-dot, and dashed white contours contain 50%,
90%, and 99% of the probability mass. FRB 20220610A is shown with the blue
star. Right: The fluence-redshift-luminosity properties of localized FRBs. FRB
localisation instruments are noted in the top right. The magenta star is FRB
20220610A. The curved solid and dashed contours show energy density in units
of erg Hz-1. The dash-dotted lines show the sensitivity of our detection
system (AK-ICS) and the more sensitive FAST and SKA telescopes. Repeating FRBs
are shown at multiple fluences.

Table. 1. Properties of FRB 20220610A and its host galaxy. The fluence is
derived from filterbank data recorded by the FRB detection system, which
includes the full ASKAP bandwidth. The Milky-Way disk DM component is
estimated from the NE2001 model (?).
Measured burst properties Dispersion Measure (DM) $1457.624\pm 0.001$ pc cm-3
Arrival time at 1271.5 MHz 2022-06-10 22:26:43.402 Fluence $45\pm 5$ Jy ms
Right Ascension (J2000) $23^{\rm h}24^{\rm m}17.569^{\rm s}\pm 0.040^{\rm s}$
Declination (J2000) $-33^{\circ}30^{\prime}49.37^{\prime\prime}\pm
0.50^{\prime\prime}$ Galactic Longitude $8.8^{\circ}$ Galactic Latitude
$-70.2^{\circ}$ Incoherent Detection S/N (1104 – 1440 MHz) 29.8 Image S/N
(1104-1152 MHz) 81 Rotation Measure $215\pm 2$ rad m-2 Host galaxy properties
Redshift $1.016\pm 0.002$ Mass-weighted age (Gyr) $1.02^{+1.64}_{-0.62}$
log(Total mass) (M⊙) $10.11^{+0.18}_{-0.07}$ log(Stellar mass) (M⊙)
$9.98^{+0.14}_{-0.07}$ 100 Myr SFR (M⊙/yr) $0.40$ log(Metallicity) (Z/Z⊙)
$-0.11^{+0.17}_{-1.68}$ $g$ (mag) $24.15\pm 0.07$ $V$ (mag) $23.89\pm 0.13$
$R$ (mag) $23.78\pm 0.06$ $I$ (mag) $22.17\pm 0.07$ $z$ (mag) $21.95\pm 0.12$
$J$ (mag) $21.97\pm 0.07$ $K_{\rm s}$ (mag) $22.08\pm 0.12$ Inferred burst
properties Intrinsic width (FWHM) $0.41\pm 0.01$ ms Implied FRB isotropic
energy density $6\times 10^{32}$ erg Hz-1 Milky-way disk DM contribution 31 pc
cm-3

Supplementary materials for Probing the distant universe with a very luminous
fast radio burst at redshift $1$

Authors: Stuart D. Ryder, Keith W. Bannister, S. Bhandari, A. T. Deller, R. D.
Ekers, Marcin Glowacki, Alexa C. Gordon, Kelly Gourdji, C. W. James, Charles
D. Kilpatrick, Wenbin Lu, Lachlan Marnoch, V. A. Moss, J. Xavier Prochaska,
Hao Qiu, Elaine M. Sadler, Sunil Simha, Mawson W. Sammons, Danica R. Scott,
Nicolas Tejos, & R. M. Shannon.

This PDF file includes
Materials and Methods
Supplementary Text
Figures S1 to S8
Tables S1 to S2
References 31-79

##  S1 Materials and Methods

###  S1.1 FRB detection

FRB 20220610A was detected as part of the Commensal Real-time ASKAP Fast
Transient survey science project (?), which uses the Australian Square
Kilometre Array Pathfinder (ASKAP (?)) to search for dispersed radio
transients such as FRBs. ASKAP is an interferometer comprising $36$ antennas,
each of $12$-m diameter. Each antenna is equipped with a phased array feed
(PAF) receiver. The PAF receivers enable $36$ beams to be digitally
synthesized across the focal plane of the antenna, generating a total field-
of-view of approximately $30$ deg2.

The current FRB detection system on ASKAP searches intensity data,
incoherently summed across telescopes, in real time. Due to constraints on
performance of the search system, only a subset of the $36$ antennas are
included in the real-time sum, with trade offs existing between the number of
antennas included and the time resolution of the data searched. In the case of
FRB 20220610A, the searches were conducted using $22$ of the antennas, with a
time resolution of $1.182$ ms. In all cases a total bandwidth of $336$ MHz is
searched with a spectral resolution of $1$ MHz. The search data streams are
recorded to disk in pulsar filterbank111http://sigproc.sourceforge.net format
for subsequent analysis in the case a burst is detected. Additional details of
the search system have previously been provided along with earlier ASKAP FRB
discoveries (?).

FRB searches with ASKAP are intended to be commensal with other observations.
However, some observations are also conducted in filler mode. These
observations occur during times where standard observations are not
scheduleable. The observations were conducted at a central frequency of
$1271.5$ MHz with the configurable beam configuration in a hexagonal close
pack configuration beam centers separated by $0.9$ degree. FRB 20220610A was
detected during filler observations, pointed towards FRB 220501C, an FRB
previously detected by ASKAP (?).

The burst was detected with a reported signal to noise ratio (S/N) of 29.8 in
primary beam. As the ASKAP beams oversample the focal plane, the burst was
detected with S/N$>5$ in four adjacent beams. The burst width, at full width
half maximum, as measured in the filterbank was $5.6\pm 0.4$ ms. This is
consistent with the 6.0 ms burst width expected from intrachannel dispersion
smearing.

###  S1.2 FRB localization

The localisation of FRB 20220610A made use of the 3.1 s of saved voltage data
from each ASKAP antenna triggered by the real-time detection described above.
Due to the dispersive sweep of 2.04 s across the 336 MHz-wide ASKAP band,
combined with the $2.4$ s latency of the detection system, much of the FRB had
already been lost from the voltage buffer before it was frozen and downloaded.
Below a frequency of 1192 MHz, the FRB signal remained present in the saved
data. Approximately $2.5\,$h after the FRB detection, a voltage download was
triggered while observing the bright source PKS 0407-658, to be used for
calibration purposes, followed shortly after by a voltage download on the Vela
pulsar (used as a polarization calibrator).

The localisation of FRB 20220610A made use of the ASKAP FRB astrometric
pipeline first described by (?), as extended by (?). Following the procedure
laid out in these works, we correlated a small time window matching the
dispersed FRB itself (forming the “gated” dataset), as well as the full 3.1s
time window from the FRB voltage download (the “field” dataset) and the
voltages downloaded while observing PKS 0407-658 (the “calibrator” dataset).
Finally, the voltages downloaded while observing the Vela pulsar were also
correlated (the “polcal” dataset).

The downloaded voltage data was processed using the “CELEBI” pipeline, which
is based on the procedures detailed in (?) and (?) and will be fully described
in a forthcoming publication (Scott et al., in prep). Voltage data was
correlated using the DiFX software correlator (?), producing the four
visibility datasets described above.

Calibration was derived from the calibrator dataset and applied to the gated,
field, and polcal datasets as described by (?). After calibration, each
dataset was imaged using CASA (?). Portions of the spectrum affected by radio
frequency interference (for the field and polcal datasets) and the lack of FRB
emission due to the limited voltage buffer size and FRB dispersion (for the
target dataset) were flagged prior to imaging. Positions and corresponding
uncertainties were measured in the image plane using the AIPS task JMFIT.

The target position was measured from the FRB image to be $23^{\rm h}24^{\rm
m}17.559^{\rm s}\pm 0.006^{\rm s}$
$-33^{\circ}30^{\prime}49.87^{\prime\prime}\pm 0.07^{\prime\prime}$. Following
the procedure detailed in (?), we used an ensemble of 7 background radio-
continuum sources from our 3.1 second field image to estimate any systematic
shift in the FRB position. These 7 sources were all the detections from this
field image that were unresolved in the NRAO VLA Sky Survey (NVSS) (?). All
sources were also present in the Rapid ASKAP Calibrator Survey (RACS) catalog
(?). Neither catalogue is, however, ideal as a point of comparison; RACS is at
lower frequency than our observations (and the initial data release is
affected by astrometric errors of up to $\lesssim$1 arcsecond) while NVSS is
at higher frequency and lower angular resolution. We measure a small
astrometric correction that is consistent at the 1$\sigma$ level from each
catalogue: $-0.16^{\prime\prime}\pm 0.5^{\prime\prime}$ and
$0.85^{\prime\prime}\pm 0.5^{\prime\prime}$ in right ascension and declination
respectively based on RACS catalogue positions, and $0.39^{\prime\prime}\pm
0.5^{\prime\prime}$ and $0.14^{\prime\prime}\pm 0.5^{\prime\prime}$ in right
ascension and declination respectively based on NVSS catalogue positions. As
we have no prior information to prefer one catalogue over the other, we take
an unweighted average of the two offsets as our final correction:
$0.12^{\prime\prime}$ and $0.50^{\prime\prime}$ in right ascension and
declination respectively, while conservatively maintaining the uncertainty on
the correction at $0.5^{\prime\prime}$ in each coordinate. This is equivalent
to using an unweighted average of the RACS and NVSS reference positions for
each source when performing the comparison to the field image positions,
without reducing the corresponding reference position uncertainty. We note
that should a more suitable reference catalogue be available (e.g., an
astrometrically robust RACS-mid catalogue at frequencies matching
observations) the uncertainty on our systematic position correction would
shrink by a factor of almost three; currently, it completely dominates the
final position uncertainty. After applying this astrometric correction, the
final FRB position is $23^{\rm h}24^{\rm m}17.569^{\rm s}\pm 0.040^{\rm s}$
$-33^{\circ}30^{\prime}49.37^{\prime\prime}\pm 0.50^{\prime\prime}$.

###  S1.3 Beamforming and spectral-temporal polarimetry

The voltage data was also used to reconstruct a complex-valued time series of
the electric field in two linear polarizations, and hence the I, Q, U, V
Stokes parameters and measurements of the polarization properties of FRB
20220610A at a time resolution of 3 ns. The beamforming process used to
achieve this has been previously outlined in (?) and is now incorporated into
the CELEBI pipeline (Scott et al., in prep) already referred to above. In this
pipeline, we apply per-antenna time delays to account for the difference in
signal arrival times and apply a polyphase filterbank (PFB) inversion to
obtain a single complex fine spectrum for each polarization per antenna.
Calibration solutions were then applied, before spectra were summed across all
antennas and derippled. Differential gain and phase between the two linearly
polarized feeds was derived using the “polcal” dataset of the Vela pulsar (PSR
J0835$-$4510). The FRB data was then coherently dedispersed (using the
S/N-maximising DM =$1457.624\pm 0.001$ pc cm-3) and a Fourier transform
inversion applied. Finally, the Stokes products are detected and the data
averaged in time and frequency to the desired resolution.

###  S1.4 Burst scatter broadening

Determining the scattering time requires modelling the intrinsic burst
profile. We model the intrinsic pulse as a Gaussian with a full width half
maximum, $w$ and amplitude $a$. The intrinsic pulse is then convolved with an
exponential scattering kernel characterized by scattering time $\tau$. We
initially assume no frequency evolution due to the narrow fractional bandwidth
of the pulse. This model is fit to the temporal profile of the burst
integrated over 88 MHz centred at 1149 MHz where the burst is present, and
hence our effective reference frequency for the scattering time $\tau$ is 1149
MHz. Each 1 MHz channel is normalized to mean zero and standard deviation one
to remove any radio frequency interference prior to summation in frequency.

We use a nested sampling approach (?), which implements the Bilby (?) python
library to determine the best model. Assuming uniform priors on $\tau$ and
$w$, the peak posterior parameters are $\tau=0.511\pm 0.012$ ms and
$w=0.407\pm 0.012$ ms, as shown in Figure S1. The best fit model is plotted in
Figure 1. Fitting to four 22 MHz sub-bands and assuming a
$\tau\propto\nu^{-4}$ scaling yields a consistent result for the scattering
time. We do not attempt to model the frequency behavior of the burst in detail
owing to the small bandwidth captured in voltage data.

Figure S1: Posterior probabilities for the scattered gaussian model. Shaded regions contain 0.39, 0.86 and 0.99 the total probability mass. Results are listed in $\mu s$, except for $a$ and error parameters which have arbitrary scale, where error is the standard deviation of the residuals to the fit. The full width at half maximum (FWHM), $w$, corresponds to $2\sqrt{2\ln 2}\sigma$. | FRB 20220610A | 20190520B (?)
---|---|---
$\tau$ (ms) | $0.511\pm 0.012$ | $10\pm 2$
$\nu_{\tau}$ (GHz) | 1.149 | 1.25
$z$ | $1.016\pm 0.002$ | $0.241\pm 0.001$
$\tau^{\prime}_{\rm 1.4\,GHz}$ (ms) | $1.88\pm 0.02$ | $12\pm 2$
Table S1: Observed scattering properties of FRBs observed with large excess
DM, including FRB 20190520B and (?). We scale scattering timescale $\tau$ to
1.4 GHz in the host galaxy rest frame, assuming $\tau\propto\nu^{-4}$, to give
$\tau^{\prime}_{\rm 1.4\,GHz}$.

Taking the measured redshift of 1.016 along with our reference frequency of
$1.149$ GHz, and assuming a scattering index of $\tau\propto\nu^{-4}$, we
scale to the host galaxy rest frame (indicated by ${}\prime$) to find
$\tau^{\prime}_{\rm 1.4\,GHz}=1.88\pm 0.02$ ms, and $w^{\prime}=0.202\pm
0.006$ ms. To compare with other FRBs with large excess DMs above the Macquart
relation, we also scale their observed scattering properties using the same
method, as given in Table S1.

###  S1.5 Burst rotation measure

After polarimetric calibration, it it was obvious that FRB 20220610A was
highly linearly polarized, and that the Stokes $Q$ and $U$ parameters showed
frequency dependent variation that we attribute to Faraday rotation in cold
plasma.

As the polarization of the burst is constant in time, it is simplest to
determine the rotation measure (RM) of the burst using a one-dimensional
spectrum. We formed the spectrum by integrating over a $1.9$ ms gate around
the peak of the pulse. We used a Bayesian methodology previously applied to
ASKAP detected FRBs (?). Briefly, we fitted for the expected frequency
dependent variations in Stokes Q and U, while marginalizing over potential
intensity variations in individual channels, finding a best-fit rotation
measure of 215 rad m-2. The pulse-averaged spectrum of the burst and the best
fit model for the rotation measure induced change in the polarization position
angle $\Psi$ are presented in Figure S2.

Figure S2: Pulse averaged spectrum of FRB 220610. Top: Spectra for Total
Intensity (black), Stokes $Q$ (red), Stokes $U$ (magenta), and Stokes $V$
(blue). The variation in flux density between $Q$ and $U$ is the result of
Faraday rotation. The absence of FRB emission above $\sim$1195 MHz is due to
the highly dispersed FRB not being captured in the buffered voltages above
this frequency. Bottom: Linear polarization position angle $\Psi$ (black
points). The maximum-likelihood model is shown as the red line.

The burst shows strong linear polarization with no evidence for polarization
position angle changing across the pulse. If plotted on a Poincare sphere, the
polarization vector would be constant and lie in the $Q-U$ plane. In Figure 1,
we show the linear polarization projected onto this point. The noise
statistics of this quantity are Gaussian, unlike the more general estimate of
linear polarization $L=\sqrt{Q^{2}+U^{2}}$ (?, ?).

###  S1.6 Optical and infrared imaging

Imaging of the location of FRB 20220610A was initially undertaken using the
FOcal Reducer and low dispersion Spectrograph 2 (FORS2) on UT1 of the European
Southern Observatory’s Very Large Telescope (VLT) on Cerro Paranal. On-chip
binning of 2$\times$2 yielded a pixel scale of 0.25′′ over the
6.8′$\times$6.8′ field of view. Five exposures of 400 sec in the R_SPECIAL
filter, with offsets of $\pm 10$′′ between each, were obtained on 2022 July 1
UT, while a total of 10 exposures of 600 sec in the $g$ filter were obtained
across 2022 Oct 2-4 UT, in seeing of 0.9–1.0′′. The FORS2 images were
processed in the same manner as described in (?), with the photometry
calibrated against DELVE (?) for the $g$-band images and using the ESO FORS2
QC1222http://archive.eso.org/bin/qc1_cgi?action=qc1_browse_table&table=fors2_photometry
database for $R$-band.

Supplemental imaging of the host of FRB 20220610A was obtained with the Deep
Imaging Multi-Object Spectrograph (DEIMOS) on the Keck-II 10m telescope on
Maunakea, Hawaii on 2022 September 24 UT in the $V$, $I$, and $z$ filters for
3$\times$350 s in each. Atmospheric conditions were near-photometric with an
average seeing of 0.9′′ and the field was observed at an average airmass of
1.7. All imaging was reduced following standard procedures in the python-based
package POTPyRI see e.g., (?). Zero points for the stacked frames were derived
using Landolt photometric standards (?) transformed into the DEIMOS
photometric bands.

Near-infrared imaging was carried out with the HAWK-I camera (?) in
combination with the GRAAL ground-layer adaptive optics system on UT4 of the
VLT, covering a 7.5′$\times$7.5′ field at 0.106′′/pixel. Observations in the
$K_{\rm s}$ filter were taken on 2022 July 24 UT, and in the $J$ filter on
2022 September 29 UT in clear conditions and delivered image quality of
0.4–0.5′′. For each filter 15 integrations of 10 sec were averaged at each of
16 random offset positions within a 20′′ box. Image mosaics were processed
using ESOReflex (?), with photometric calibration undertaken using the 2MASS
point source catalogue (?).

For the DEIMOS imaging, aperture photometry was performed using a 3′′ host
radius and a 4′′ to 7.5′′ background annulus (Table 1). For the VLT imaging
two approaches were used to measure photometry: first, a single circular
aperture with a radius of 3′′ encompassing the entire source (Table
Acknowledgments); and second, three ellipses defined by eye (as shown in
Figure 2a) from the $R$-band imaging, to individually measure clumps A, B and
C (Table S2). Both approaches, including background subtraction, were
undertaken using the SEP package (?, ?).

Clump: | A | B | C
---|---|---|---
$g$ | $25.36\pm 0.07$ | $25.13\pm 0.07$ | $26.01\pm 0.09$
$R$ | $24.98\pm 0.06$ | $25.69\pm 0.08$ | $24.82\pm 0.06$
$J$ | $23.07\pm 0.08$ | $23.84\pm 0.12$ | $23.40\pm 0.13$
$K_{\rm s}$ | $22.92\pm 0.09$ | $23.76\pm 0.15$ | $>23.66$
$(R-K_{\rm s})$ | $2.06\pm 0.15$ | $1.93\pm 0.23$ | $<1.16$
Table S2: Photometric measurements for each of the clumps in the host of FRB
20220610A as marked on Figure 2.

###  S1.7 Optical and infrared spectroscopy

Spectroscopy covering the entire ultraviolet through near-infrared wavelength
range of 0.3–2.48 $\mu$m was conducted with the X-shooter spectrograph (?) on
UT3 of the VLT. Slit widths of 1.0′′, 0.9′′, and 0.9′′ yielded spectral
resolutions of 5400, 8900, and 5600 in the UVB, VIS, and NIR arms,
respectively, with 2$\times$2 on-chip binning employed in the UVB and VIS
detectors due to the faintness of the target.

Observations of the target were made at 2 slit position angles: the first on
2022 July 29 UT at a position angle of 45∘ covering clumps A and B shown in
Fig. 2; and the second on 2022-September 23/24 UT at a position angle of 90∘
covering clumps A and C. At each position angle, a total of between 7200 and
7548 sec of integration time was accumulated in clear conditions and seeing
0.5–1.2′′, with frequent nodding of the target by $\pm$2.5′′ along the slit to
assist with sky subtraction. Observations of the B9 V stars HD 138940 and HD
168852 were obtained to enable removal of telluric features, and of the
spectrophotometric standard stars EG 21 and LTT 987 to allow relative flux
calibration. The spectra were reduced with the PypeIt data reduction pipeline
(?) using standard techniques for image processing and wavelength calibration.
The VIS science exposures were individually processed and the sky-subtracted
2D spectral images were co-added to maximize S/N.

From the spectroscopy of components A, B and C we were able to identify lines
at 7510 and 7515 Å associated with the [O ii] 3726 and 3729 Å forbidden
transitions of ionized oxygen (Figure 2), and at 13228 Å associated with the
6563 Å H$\alpha$ transition. Together these lines confirm the redshift of the
host to be $1.016\pm 0.002$.

Figure S3:  VLT/X-shooter spectra of the host galaxy of FRB 20220610A,
covering the region of the [O ii] lines with rest wavelengths 3726 and 3729 Å.
The peak of the [O ii] 3729 Å line in clump C is marked as a vertical dashed
line for references. The red dashed line shows the uncertainty in the
spectrum. The blue horizontal line shows zero relative flux.

##  S2 Supplementary Text

###  S2.1 Nature of the host galaxy

The spectra in Figure S3 indicate that components A and C are consistent in
redshift to 0.01%, while component B is blueshifted by an amount equivalent to
a velocity difference of just 150 km s-1. With a projected separation of 16
kpc between compact components A and C, it is conceivable that they represent
the two distinct nuclei of a merging or interacting system, while B is the
gaseous tail linking them and currently drawn out towards the observer.

The measured $(R-K_{\rm s})$ colors for the individual clumps, as well as for
the host system as a whole ($1.70\pm 0.18$) are unusually blue compared to
those for field galaxies at redshifts around 1 (?, ?, ?). At $z=1$ the
$(R-K_{\rm s})$ color approximates rest-frame $(U-J)$. Starburst models, e.g.
(?) only produce $(U-J)$ colors close to these values around 10 Myr after the
onset of the burst, or at least 600 Myr later.

To model the stellar population of the host in more detail, we use the stellar
population synthesis code Prospector (?) which performs Bayesian inference to
determine the most likely stellar population based on the data and prior
assumptions. We have used the integrated photometry from the entire complex to
make an estimate of the host properties as there is insufficient information
to characterize individual components. This effectively assumes that all
components have the same star formation history. We fit the photometry using
the stellar population synthesis library python-fsps (?, ?) and used the
dynamic nested sampling routine dynesty (?) to sample the posteriors.
Additional prior assumptions include a Chabrier IMF (?), Milky Way dust
attenuation law (?), mass-metallicity relationship (?), a ratio on dust
attenuation between old and young stars, and a continuity model non-parametric
star formation history (SFH, (?)) using 8 age bins.

The photometry is best described by a galaxy of $1.2\times 10^{10}$ solar
masses with an age of 1.02 Gyr. Additional parameters are reported in Table 1.
The posterior probability show bimodality in age, mass, dust, and metallicity.
This could be attributed to the known degeneracy in spectral energy
distribution modeling for these parameters. However, given the complex
morphology of the host, another interpretation of the bimodality is the
presence of multiple stellar populations corresponding to multiple galaxies.
Further imaging of the host with space-based facilities is required to
disentangle the complex morphology in order to better characterize the host
stellar population.

###  S2.2 Dispersion-measure analysis

Our DM analysis is based on the four-component model of (?),

$\displaystyle{\rm DM}_{\rm FRB\,20220610A}$ $\displaystyle=$
$\displaystyle{\rm DM}_{\rm MW}\ +{\rm DM}_{\rm halo}\ +{\rm DM}_{\rm
cosmic}+\frac{{\rm DM}_{\rm host}}{1+z},$ (S1)

where ${\rm DM}_{\rm MW}$ is the Milky-Way disk DM contribution, ${\rm
DM}_{\rm halo}$ is the Milky Way halo contribution, ${\rm DM}_{\rm cosmic}$ is
the cosmic DM contribution and ${\rm DM}_{\rm host}$ is the host DM
contribution.

We assume the contribution from the Milky-Way interstellar medium (ISM) to be
${\rm DM}_{\rm MW}$=31$\mathrm{pc~{}cm}^{-3}$ from (?), and the halo
contribution to be ${\rm DM}_{\rm halo}$=50$\mathrm{pc~{}cm}^{-3}$, which is
on the low side of predictions from (?), but consistent with the observation
of nearby, low-DM FRBs (?). The contribution from the intergalactic medium
(IGM), including filaments and intervening halos, is a probabilistic
distribution about the mean density of ionized gas in the universe (?). The
full model is developed in (?), and implemented in the ‘FRB’ python library
(?). We use cosmology from planck (?), in particular ${H_{0}}=67.4$ $\rm
km\,s^{-1}\,Mpc^{-1}$, and $\Omega_{b}h^{2}=0.0224$, and assume a ‘feedback’
parameter $F=0.32$, which governs the clumpiness of cosmic gas distributions,
and hence the variance of ${\rm DM}_{\rm cosmic}$ about its expectation value.
The remaining contribution is attributed to ${\rm DM}_{\rm host}$, which
includes the FRB host galaxy halo and ISM, and any plasma in the immediate
vicinity of the progenitor. This contribution is suppressed by a factor of
$1+z$ (here, $\sim 2$), since the dispersion is induced at higher frequencies
than those observed.

Figure S4: Probability distributions for the rest-frame host galaxy dispersion
measures of FRB 20220610A (blue solid line) and FRB 20190520B (orange dashed
line). The green dotted line shows the best-fit log-normal distribution for
DMhost derived by the population modelling of (?).

Using Eq. (S1), we estimate the probability distribution of ${\rm DM}_{\rm
host}$ for FRB 20220610A in Figure S4. Since ${\rm DM}_{\rm cosmic}$ is
upwardly skewed, with the most likely DM being below the cosmic mean, and a
small probability of very large excess DMs due to intersections with cosmic
structures, our estimate for ${\rm DM}_{\rm host}$ is left-skewed. The most
likely value is ${\rm DM}_{\rm host}=1304$ $\mathrm{pc~{}cm}^{-3}$, with a 68%
confidence interval of $(981,1475)$ $\mathrm{pc~{}cm}^{-3}$. However, we
cannot exclude the possibility of a negligible host contribution. We note that
observational biases against high DM are irrelevant for this calculation,
since we here only consider the relative contribution to DM from different
sources, while the observational bias is fixed at the total observed value.

We also calculate the equivalent distribution for FRB 20190520B. This FRB,
detected by the Five Hundred metre aperture Synthesis Telecope (FAST),
originates from $z=0.241$ (?). Its observed ${\rm DM}_{\rm 20190520B}=1204.7$
$\mathrm{pc~{}cm}^{-3}$ implies a host galaxy contribution in the observer
frame of $903^{+72}_{-111}$. Using our model for ${\rm DM}_{\rm cosmic}$,
${\rm DM}_{\rm halo}$, and the value ${\rm DM}_{\rm
MW}=60$$\mathrm{pc~{}cm}^{-3}$ from (?), we find a rest-frame DM of $1172$
$\mathrm{pc~{}cm}^{-3}$ with a 68% confidence limit of $(1104,1197)$
$\mathrm{pc~{}cm}^{-3}$. The predicted range is smaller due to the lower
redshift of FRB 20190520B, and hence lower absolute variance in ${\rm DM}_{\rm
cosmic}$.

Both values are much large than the median ${\rm DM}_{\rm host}$ of 186
$\mathrm{pc~{}cm}^{-3}$ derived from population models (?). The lognormal
distribution of ${\rm DM}_{\rm host}$ is also shown in Figure S4 — while very
high values of ${\rm DM}_{\rm host}$ are disfavoured, they are allowed within
the model.

It is likely therefore, but not certain, that FRB 20220610A has the highest
intrinsic host galaxy DM of any known FRB.

###  S2.3 Burst energetics

FRB 20220610A was measured with a peak signal-to-noise (S/N) of 29.8 (which by
definition has an uncertainty of $\pm 1$) in CRAFT incoherent sum (ICS) data
formed from 22 ASKAP antennas. The sensitivity in this configuration scales
with $\sqrt{N}_{\rm ant}$ compared to single-antenna searches (?), which have
noise level of ${N}_{\rm 1ms}=2.68\pm 0.02$ Jy ms for a 1 ms burst (?, ?).
Tests on pulsars comparing ICS to single-antenna mode have confirmed this
scaling to within $97.5\pm 2.5$%.

The effective width of a burst in ICS data is increased from its intrinsic
(after scatter-broadening) width by DM smearing over the 1 MHz channel
bandwidth and by the time resolution of 1.182 ms. Thus S/N was maximized when
the burst was integrated over four time samples. This corresponds to an
initial band-averaged fluence estimate of ${\rm S/N}N_{\rm ant}^{-0.5}(\Delta
t)^{0.5}{N}_{\rm 1ms}=37$ Jy ms. This is a strict lower limit on the fluence,
some of which will lie outside the 4-sample search window used by our real-
time detection pipeline. Offline fitting of a Gaussian profile to the data
produced a full-width half-maximum of 5.6 ms and integrated fluence of $43\pm
5$ Jy ms. Including the potential inefficiency of ICS observations, and
correcting for the offset from beam centre ($B=0.98$ at central frequency), we
estimate a band-averaged fluence of $F_{\nu}=45\pm 5$ Jy ms.

The isotropic-equivalent spectral energy of transients is related to the
observed fluence via

$E_{\nu}=\frac{4\pi D_{L}^{2}}{(1+z)^{2}}F_{\nu}.$ (S2)

The FRB host galaxy has a redshift of $1.016\pm 0.002$, corresponding to a
luminosity distance $D_{L}=6929\pm 2$ Mpc using Planck cosmology (?). We
therefore find a spectral energy of $E_{\nu=2.543\,{\rm GHz}}=6.4\pm
0.7\,10^{32}$ erg Hz-1 at the mean emission frequency of $2.543$ GHz.

The spectral behaviour of FRBs is complex, with some bursts showing broadband
structure, and others being isolated in frequency (?). On average, bursts
appear to be either brighter (?) or more common (?, ?) at lower frequencies.
In the former case, fluence scales as $F_{\nu}\propto\nu^{\alpha}$, with a
best-fit $\alpha=-1.5_{-0.3}^{+0.2}$ (?). If this is the correct behaviour,
then a k-correction of $(1+z)^{-\alpha}=2.85$ should be used to obtain
$E_{\nu=1271.5\,{\rm MHz}}=(1.8\pm 0.2)\times 10^{33}$ erg Hz-1; if not,
$E_{\nu=1271.5\,{\rm MHz}}=E_{\nu=2.543\,{\rm GHz}}$.

###  S2.4 Implications for maximum FRB energy

Accurately modelling the maximum energy of FRBs, $E_{\rm max}$, requires
either a sample of localized bursts, or accounting for variations in the
DM–$z$ (‘Macquart’) relation. Furthermore, several parameters — such as source
evolution, spectral behaviour, and the slope of the luminosity function — are
correlated with $E_{\rm max}$, and must be simultaneously fit to the data.
This approach has been taken by several authors (?, ?, ?), who yield mutually
consistent results. The most precise measurement — using a sample of 16 FRBs
with measured redshifts, and 60 without — is $\log_{10}E_{\rm
max}\,{\rm[erg]}=41.26^{+0.27}_{-0.22}$ at 68% confidence (?). This
calculation assumes an intrinsic emission bandwidth of 1 GHz, and does not
include a k-correction, i.e., it allows for the rate of FRBs to vary with
frequency, but not their energy. The burst energy function used is an upper
incomplete gamma (Schechter) function, with differential slope $\gamma-1$, and
exponential cut-off of the form $\exp-E/E_{\rm max})$. In this formalism, the
burst energy of FRB 20220610A becomes $6.4\pm 0.7\,10^{41}$ erg, 3.5 times the
cutoff energy — allowable, but unlikely, under this best-fit model.

Figure S5: Estimation of the characteristic maximum FRB energy, $E_{\rm max}$.
Shown are likelihoods $\mathcal{L}$ evaluated when adding FRB 20220610A to the
sample used by (?) and varying $E_{\rm max}$ only, and the posterior
probability distribution $p(E_{\rm max})$ assuming a log-uniform prior on
$E_{\rm max}$.

To test the influence of this observation on $E_{\rm max}$, we use the model
of (?) as implemented in (?, ?), add FRB 20220610A to the sample, and vary
$E_{\rm max}$ only. The obtained likelihoods are shown in Figure S5. The peak
likelihood is obtained for $\log_{10}E_{\rm max}\,{\rm[erg]}=41.7\pm 0.2$,
i.e. $\log_{10}E_{\nu}\,[{\rm erg\,Hz^{-1}}]=32.7\pm 0.2$, with error margins
set by assuming a log-uniform prior on $E_{\rm max}$ to produce a Bayesian
posterior $p(E_{\rm max})$. This is 2.7 times greater than the previous best
estimate, but still within the 90% confidence interval for $\log_{10}E_{\rm
max}\,{\rm[erg]}$ found by (?).

Nonetheless, FRB 20220610A is an unusually high-energy FRB. Given the
time/frequency resolutions of the FRB detection algorithm ($t_{\rm
samp}=1.182\,$ms and $\Delta\nu=1$ MHz respectively), the DM of $1457.624\pm
0.001$ pc cm-3 smears the signal over $w_{\rm DM}=5.8$ ms at band centre.
Including the scattering time $\tau$ and intrinsic width $w$, the total
effective width $w_{\rm eff}$ becomes

$w_{\rm eff}\approx\sqrt{w_{\rm DM}^{2}+t_{\rm
samp}^{2}+w^{2}+\tau^{2}}=5.9\,{\rm ms}.$ (S3)

Without the $w_{\rm DM}$, the width would be 1.35 ms. Since observed signal-
to-noise scales with $w_{\rm eff}^{-0.5}$, the greater width caused by the
high DM of the burst has decreased sensitivity by 52%.

Figure S6: Cumulative probability $p(z|FRB\,20220610A)$ for the redshift $z$
of FRB 20220610A given its properties, estimated with the previous best-fit
FRB population parameters of (?); population parameters varied within their
90% confidence limits; and with our new estimates of $E_{\rm max}$.

Using the observed properties of FRB 20220610A (DM, width, fluence), the
observation parameters at time of detection (location in beam, observation
frequency, sampling time, number of antennas), and estimates of the FRB
population parameters, allows us to estimate the probability of observing FRB
20220610A at a given redshift, $p(z|{\rm FRB\,20220610A})$. This is plotted in
Figure S6. We use the previous best-fit population parameters (maximum energy
$E_{\rm max}$, cumulative luminosity index $\gamma$, spectral rate scaling
index $\alpha$, scaling with the star-formation rate $n_{\rm sfr}$, and log-
mean and standard deviation of the host galaxy DM $\mu_{\rm host}$ and
$\sigma_{\rm host}$) for ${H_{0}}$=67.4 $\rm km\,s^{-1}\,Mpc^{-1}$ from (?),
and also set $E_{\rm max}$ to our new best-fit value. We also explore
parameter sets corresponding to these same parameters when at their upper and
lower 90% confidence limits. The resulting cumulative probability
distributions cdf$(z|{\rm FRB\,20220610A})$ are plotted in Figure S6.

###  S2.5 Limits on depolarization due to multi-path propagation

The depolarization $f$ due to a spatially variable rotation measure in a
foreground scattering screen can be modelled to be (?, ?)

$f=1-\exp\left(-2\lambda^{4}\sigma_{\rm RM}^{2}\right),$ (S4)

where $f$ is the observed polarization fraction, $\lambda$ is the observing
wavelength and $\sigma_{\rm RM}$ parameterizes the RM complexity.

We can thus use our lower limit on polarization to set an upper limit on
$\sigma_{\rm RM}$ using the relationship

$\sigma_{\rm RM}<\sqrt{-\frac{\log(1-f)}{2\lambda^{4}}}=0.57\,{\rm rad}\,{\rm
m}^{-2}.$ (S5)

assuming $f>0.96$. In the frame of the host galaxy this corresponds to
$\sigma_{\rm RM}<1.2$ rad m-2.

###  S2.6 The origin of the excess dispersion for FRB 20220610A

When considering possible origins for the excess dispersion seen for FRB
20220610A, we can make use of the additional information encoded by the
burst’s propagation on the observed temporal scattering and rotation measure.
In the rest frame of the host galaxy the pulse broadening is 1.88 ms, and the
rotation measure is $860\pm 8$ rad m-2. As the burst was detected at high
Galactic latitude, the Milky-Way contribution to both scattering and rotation
measure is small and can be neglected.

We first consider the possibility that the excess is associated with plasma
closely associated with the burst source (a “circumburst” medium). Such an
environment has been considered for some repeating FRB sources (?, ?). The
excess dispersion seen in FRB 20220610A and the active repeating FRB source
20190520B are similar, but the pulse broadening is a factor of $6$ higher for
FRB 20190520B, while the rotation measure of FRB 20190520B is highly variable
but reaches values over an order of magnitude above that of FRB 20220610A (?).
The frequency-dependent polarization seen in FRB 20190520B is consistent with
multi-path propagation through a highly magnetized and turbulent local medium
that could explain both the scattering and rotation measure; in this model,
the rest-frame Faraday dispersion for this source is $\sigma_{\rm RM}=337$ rad
m-2, over two orders of magnitude higher than the limit we derive for FRB
20220610A above. Thus, for the local environment to contribute the bulk of the
excess DM seen in FRB 20220610A, the medium would need to be less turbulent
and less highly magnetized than for FRB 20190520B.

Another possibility is that this excess arises in the interstellar medium
(ISM) of the host galaxy. For that, it s useful to compare the properties of
FRB 20220610A in the host galaxy rest frame to that of FRB 20190520B and
pulsars in the Galaxy. In Figure S7, we show the distribution of DM and pulse
broadening times for pulsars (?, ?) and localized FRBs. In the case of the
FRBs we show the expected host DM contribution. FRB 20220610A shows
significantly lower scattering than expected from Milky Way-like ISM. In
Figure S8, we show the distribution of DM and rotation measures for pulsars
(?) and the two FRBs. FRB 20220610A shows a rotation measure comparable to
most Milky Way pulsars at similar DM, but much lower than the RM associated
with pulsars close the Galactic Centre (?), some of which have DMs comparable
to the upper end of the allowable range for FRB 20220610A.

So, while the Faraday rotation of the burst is not inconsistent with the
relationship between dispersion and rotation measure observed in Galactic
pulsars, for a Milky Way-like sightline, the observed excess DM would imply
scatter broadening of $>100$ ms at 1.4 GHz (?). Accordingly, we disfavour the
host galaxy ISM as the sole source of the excess DM for FRB 20220610A.

A final possibility is that the excess DM is associated with plasma in an
intervening structure along the line of sight but outside of the host galaxy
complex. Identification would require detailed analysis of galaxies close to
the burst line of sight (?). However, plasma in the intergalactic medium is
not expected to harbour high levels of turbulence or magnetisation, so is not
expected to cause the observed rotation measure or pulse broadening, and so
this is (like the host galaxy ISM) disfavoured as the sole source of excess DM
for FRB 20220610A (unless an intervening galaxy halo, where density and
turbulence can be higher, contributed significantly).

Given the analysis above, it is not presently possible to definitively
identify a dominant location for the excess DM seen in FRB 20220610A, but the
observed properties can be plausibly reproduced by a combination of two (or,
indeed, all three) of the potential locations.

Figure S7: FRB and pulsar dispersion measure and scatter broadening times. We
have increased the pulse broadening times of the FRBs by a factor of two to
correct for their plane-wave scattering geometry. Figure S8: FRB and pulsar
dispersion measures and rotation measures.