# A study of two FRBs with low polarization fractions localized with the
MeerTRAP transient buffer system

K. M. Rajwade,1,2 L. N. Driessen,3 E. D. Barr,4 I. Pastor-Marazuela,5 M.
Berezina,4,16 F. Jankowski,7,5 A. Muller,6 L. Kahinga,8 B. W. Stappers,5 M. C.
Bezuidenhout,9,10 M. Caleb,3 A. Deller,11 W. Fong,12 A. Gordon,12 M. Kramer,4
M. Malenta,5 V. Morello,13 J. X. Prochaska,8 S. Sanidas,5 M. Surnis,14 N.
Tejos15 S. Wagner16
1 Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road ,
Oxford OX1 3RH, UK
2 ASTRON, 4 Oude Hoogeveensedijk, Dwingeloo 7991 PD, The Netherlands
3 Sydney Institute for Astrophysics, School of Physics, University of Sydney,
NSW, Sydney 2006, Australia
4 Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn,
Germany
5 Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford Road,
Manchester M13 9PL
6 Maria Mitchell Observatory, Nantucket, MA 02554, USA
7 LPC2E, Université d’Orléans, CNRS, 3A Avenue de la Recherche Scientifique,
45071 Orléans, France
8 University of California, Santa Cruz, 1156 High St., Santa Cruz, CA 95064,
USA
9 Department of Mathematical Sciences, University of South Africa, Cnr
Christiaan de Wet Rd and Pioneer Avenue, Florida Park, 1709, Roodepoort, South
Africa
10 Centre for Space Research, North-West University, Potchefstroom 2531, South
Africa
11 Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, Hawthorn, VIC 3122, Australia
12 Center for Interdisciplinary Exploration and Research in Astrophysics
(CIERA), Department of Physics and Astronomy,
Northwestern University, Evanston, IL 60208, USA
13 SKA Observatory, Jodrell Bank, Lower Withington, Macclesfield, SK119FT, UK
14 Department of Physics, IISER Bhopal, Bhauri Bypass Road, Bhopal, 462066,
India
15 Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla
4059, Valparaíso, Chile
16 Landessternwarte, Universität Heidelberg, Königstuhl 12, D-69117
Heidelberg, Germany
E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>authors contributed equally

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Localisation of fast radio bursts (FRBs) to arcsecond and sub-arcsecond
precision maximizes their potential as cosmological probes. To that end, FRB
detection instruments are deploying triggered complex-voltage capture systems
to localize FRBs, identify their host galaxy and measure a redshift. Here, we
report the discovery and localisation of two FRBs (20220717A and 20220905A)
that were captured by the transient buffer system deployed by the MeerTRAP
instrument at the MeerKAT telescope in South Africa. We were able to localize
the FRBs to precision of $\sim$1 arc-second that allowed us to unambiguously
identify the host galaxy for FRB 20220717A (posterior probability$\sim$0.97).
FRB 20220905A lies in a crowded region of the sky with a tentative
identification of a host galaxy but the faintness and the difficulty in
obtaining an optical spectrum preclude a conclusive association. The bursts
show low linear polarization fractions (10–17$\%$) that conform to the large
diversity in the polarization fraction observed in apparently non-repeating
FRBs akin to single pulses from neutron stars. We also show that the host
galaxy of FRB 20220717A contributes roughly 15$\%$ of the total dispersion
measure (DM), indicating that it is located in a plasma-rich part of the host
galaxy which can explain the large rotation measure. The scattering in FRB
20220717A can be mostly attributed to the host galaxy and the intervening
medium and is consistent with what is seen in the wider FRB population.

###### keywords:

radio continuum: transients – stars: neutron – techniques: interferometric

††pubyear: 2024††pagerange: A study of two FRBs with low polarization
fractions localized with the MeerTRAP transient buffer system–A

##  1 Introduction

Fast radio bursts (FRBs) are intense, millisecond-duration radio flashes that
originate from cosmological distances (Lorimer et al., 2007). They have
remained one of the most enigmatic astrophysical mysteries since their
discovery over a decade ago. Several theories have been proposed to explain
their origin but we still lack any definitive evidence to decipher their
nature. The detection of repeating FRBs allowed astronomers to regularly
monitor the sources and enable precise localisation to their host galaxies
(Tendulkar et al., 2017). These follow-up studies have been important to put
constraints on their progenitors. The discovery of FRB-like bursts from a
Galactic magnetar SGR J1935+2154 suggests that highly magnetized neutron stars
(magnetars) have the ability to produce luminous radio bursts (CHIME/FRB
Collaboration et al., 2020; Bochenek et al., 2020). This suggested that we
should expect FRBs in star forming regions of their host galaxies where most
of the magnetars are produced via core-collapse supernovae. This conjecture
was put to the test again when a repeating FRB was discovered and localised to
a globular cluster in a near-by galaxy M81 (Kirsten et al., 2022). One needs
to invoke exotic models for the creation of magnetars in an environment that
is dominated by an old stellar population. These results already show the
importance of precise localisations of FRBs and their environs that provide
important clues about their progenitors. Moreover, it also could help in
determining the distribution of FRBs across different galaxy types, probe the
intergalactic medium with extreme precision and count the ‘missing’ baryons
and their distribution (Macquart et al., 2020). All of these advancements can
lead to a deeper understanding of the physics behind these enigmatic signals.

Until a few years ago, precise localisation of the FRBs was only possible with
repeating FRBs as it allows for regular follow-up using radio interferometers.
However, recent advancements in instrumentation and observing strategies have
enabled arc-second localisations of one-off FRBs, opening up the field
entirely. The most significant breakthrough in localising single FRBs came
with the development of the commensal real-time ASKAP FAST Transients survey
(CRAFT; Bannister, 2018). CRAFT enabled ASKAP to detect and localise FRBs in
real-time, providing rapid follow-up optical observations and identification
of host galaxies. Since then, other radio telescopes have followed suit and
are now spear-heading the real-time localisation efforts of one-off FRBs
(CHIME/FRB Collaboration et al., 2018; Bannister, 2018; Ravi et al., 2023). In
this paper, we report two sub-arcsecond localisations of FRBs using the
transient buffer capture mode on MeerTRAP: A commensal, real-time FRB detector
at the MeerKAT telescope in South Africa. The paper is organized as follows;
in section 2, we describe the transient buffer capture system. In section 3,
we describe the discovery, localisation and optical follow-up of the first two
FRBs with this system. In section 4, we discuss the properties of the FRBs and
their host galaxies and in section 5, we summarize our results and
conclusions.

##  2 MeerTRAP Transient Buffer System

Figure 1: A flow chart showing the entire transient buffer trigger pipeline
(see text for details). Here the F-engine corresponds to where the poly-phase
filter is applied on the complex voltages streaming from the telescope. The
figure has been created using Lucid Chart.

###  2.1 The real-time search

The detailed description of the real-time FRB detection system has been
presented in Rajwade et al. (2020) and Rajwade et al. (2022). Figure 1 shows
the detailed flow diagram of the system. Raw data from each antenna are
channelized using a poly-phase filter (van der Byl et al., 2022) to create a
discretely channelized complex voltage datastream. This datastream is acquired
by the Filterbank BeamFomer User Supplied Equipment (FBFUSE) where these data
are detected and converted into total power beams across the FoV of MeerKAT.
MeerTRAP observations typically use only the inner 40 dishes of the MeerKAT
array for beamforming. This is a trade-off between sensitivity and achievable
field of view (FoV) given the finite compute resources available to FBFUSE
(Chen et al., 2021). Even when only beamforming a subset of the antennas,
FBFUSE ingests the full complement of channelised voltages from the MeerKAT
antennas. This is essential for the operation of the transient buffer. The
Transient User Supplied Equipment (TUSE) receives the coherent total power
beams from FBFUSE and runs a real-time search on the data for FRBs and other
transients.

###  2.2 Detection and trigger

In order to save complex voltages from the telescope, it is important to send
out prompt triggers to the beamformer immediately after the detection of an
FRB to initiate data extraction. Typically, the real-time system has to
process the data, classify the candidates and send a trigger within 45 seconds
of receiving the data from the beamformer. To that end, we decided to use low-
latency VOEvent alerts to communicate triggers. That is because VOEvents are
well established in the transient community, a software ecosystem exists, a
VOEvent standard for FRB alerts had already been proposed (Petroff et al.,
2017), and was subsequently adopted at several radio telescopes, most notably
CHIME. For MeerTRAP, we implemented a VOEvent-based software to trigger the
voltage buffer read-out on the FBFUSE cluster from the real-time transient
detection system running on the TUSE servers (Jankowski et al., 2022). VOEvent
messages are in XML format (Seaman et al., 2011) and contain the parameters of
the alert, e.g. a unique identifier, the author, the event time, its sky
position, and the instrumental setup. The event packets are distributed by
brokers, for which we employ the comet software (Swinbank, 2014), both locally
on the MeerTRAP head nodes and the central MeerKAT observatory-wide broker. A
containerised comet subscriber runs on the FBFUSE head node, waiting for
events. When an FRB, or any other transient, is detected by the MeerTRAP
pipeline, its parameters are written into a VOEvent message which is sent to
the local comet broker and forwarded to the observatory-wide one. The alert is
then received by the FBFUSE subscriber which parses the contents and converts
them into a request to write-out the corresponding complex voltage data from
the transient buffer. More details are presented in Jankowski et al. (2022)
and software are available online111https://github.com/fjankowsk/meertrig/.
Using VOEvents has the advantage that we can easily disseminate our triggers
to external collaborators in the future.

###  2.3 Extraction of complex voltage data and phase-up

Data from MeerKAT channelisers arrive on the the FBFUSE cluster as a 1.8 Tb/s
Ethernet stream, split over 256 multicast groups, with each group containing
1/256th of the full MeerKAT bandwidth for all the available antennas included
in the current observations. The groups are split such that each of the
32-servers that comprise the FBFUSE cluster ingests 8 groups, 4 per network
interface. Physically, the processing for each set of 4 multicast groups is
mapped to a single non-uniform memory architecture (NUMA) node, hosting a
network card, CPU, GPU and 192 GB of DDR4 RAM. The depth of the transient
buffer that can be accommodated on such a system is determined by $t_{\rm
tb}=8M/(2N_{\rm pol}N_{\rm ant}BN_{\rm bits})\,\mathrm{s}$, where $M$ is the
available memory in bytes, $N_{\rm pol}$ is the number of polarisations,
$N_{\rm ant}$ is the number of antennas being ingested, $B$ is the received
bandwidth per NUMA node in Hz and $N_{\rm b}$ is the bit depth per sample. For
MeerKAT, we have $N_{\rm pol}=2$, $N_{\rm bits}=8$, $N_{\rm ant}\leq 64$ and
$B=8.5$, $13.375$, or $13.671875$ MHz at UHF (816 MHz), L-band (1.4 GHz), and
S-band (2.2 GHz), respectively. Approximately 95 % of the RAM ($\sim$182 GB)
on each FBFUSE NUMA node is available for the transient buffer, hence we
achieve a buffer depth of $\sim$54, 56 and 88 s at L-band (1284 MHz), UHF (816
MHz) and S-band (2500 MHz) for the full array. The buffer depth may be
increased by moving to a lower bandwidth receiver or by specifying that only a
subset of the current sub-array be used (although it should be noted that the
subset used by the transient buffer defines the superset available for
beamforming). Depending on the number of frequency channels requested from the
MeerKAT correlator, the time resolution of the transient buffer data varies
from 1.9 to 36 $\mu$s.

Figure 2: Left: Shared memory ring buffer configuration for the FBFUSE
transient buffer. Each segment represents a block of memory in the ring
buffer, with blue showing a block that is being written to, green showing
blocks that are occupied and orange showing blocks that free and can be
written to. Shown are the positions of the write pointer for data coming from
the MeerKAT correlator network, the beamformer read pointer for data going
through the FBFUSE beamforming pipeline and the buffer extractor read pointer
for data being recorded upon receipt of a trigger. The write pointer
progresses though the buffer in a clock-wise direction. Right: The algorithm
that extracts the data corresponding to the DM of the detected FRB after
accounting for the dispersion delay. The dispersion delay has been shown here
as a linear trend for simplicity. The FRB data are spread accross several data
blocks due to the delay as shown by the dashed vertical lines. The coloured
regions shows the data that are extracted from each data block.

As illustrated in Figure 2, the FBFUSE transient buffer is implemented as a
PSRDADA222https://psrdada.sourceforge.net/ shared memory ring buffer (SMRB)
with one writer and two readers. The writing process captures data from the
MeerKAT correlator network, orders it by time, antenna and frequency and
writes it to the SMRB. The primary reading process is the beamformer itself,
which operates in real time, consuming and processing blocks from the SMRB as
they become available. The secondary reading process is the transient buffer
data extractor. This process does not immediately read blocks from the SMRB
but instead monitors the overall usage of the SMRB and holds open blocks in
the buffer, only releasing them when the overall occupancy of the buffer
reaches 95%. It thus guarantees that at least 95% of the buffer is maintained
in memory at all times. The remaining 5% of the buffer is required to be left
unoccupied to allow sufficient time for data extraction and processing on
receipt of a trigger event (see below) such that the writing process is not
blocked, resulting in data loss.

The triggers received by FBFUSE are propagated to the buffer data extractor
process via a UNIX socket. Each is formatted as a JSON message containing a
DM, reference frequency, start UTC, end UTC and trigger identifier. The start
and end UTC along with the reference frequency and DM define the section of
data to be extracted from the transient buffer. As noted above, extraction of
data from the SMRB must be sufficiently fast as to avoid blocking the writing
process. Several tests have shown that the instrument can safely write up to
300 ms of the buffer to disk at a time without affecting the capture of data
from the MeerKAT correlator network. As 300 ms may be shorter than duration of
the time delay of a highly dispersed FRB, the buffer data extractor
incoherently dedisperses the buffer data at the time of extraction. Upon
receipt of a trigger, the buffer data extractor re-references the start and
end UTCs of the trigger to the highest frequency in the currently processed
subband and scans through the buffer until it reaches the block containing the
start of the event. The frequency channels and times corresponding to the
event window are then extracted for all antennas and polarisations and written
to a temporary memory buffer in dedispersed order. This process continues over
subsequent blocks until the end of the event is reached, at which point the
temporary memory buffer is written to disk with a header containing
observation and trigger metadata. This process is illustrated in the right-
hand panel of Figure 2.

In order to aide in the downstream analysis of the extracted voltages, FBFUSE
records a snapshot of the current complex gain solutions as calculated by the
MeerKAT Science Data Processor (Jonas & MeerKAT Team, 2016). These are written
locally as Numpy arrays to be applied to the transient buffer data extracted
for any FRB.

###  2.4 Imaging and localisation

####  2.4.1 Producing measurement sets

The extracted transient buffer data are correlated using xGPU333xGPU:
https://github.com/GPU-correlators/xGPU (Clark et al., 2011). These data
already have the geometric delays applied and we apply the gain and phase
solutions to each antenna, time and frequency channel to phase-up the data to
the pointing centre of the observation using the solutions obtained during the
initial delay calibration. Each file produced contains one subband (1/64th of
the full bandwidth) and, due to dispersion correction, has a different start
time. In order to calibrate and image the correlated visibilities, they need
to be packaged with appropriate metadata (e.g., phase centre position,
baseline direction cosines etc.) in a recognised visibility file format such
as FITS-Interferometry Data Interchange (IDI) format
444https://lweb.cfa.harvard.edu/~jzhao/SMA-FITS-CASA/docs/AIPSMEMO102.pdf or a
Measurement Set (MS). We made use of the difx2fits application provided by
DiFX (Deller et al., 2007, 2011) to produce FITS-IDI files that could
subsequently be converted to an MS using CASA (McMullin et al., 2007), after
providing the necessary metadata in the format expected by the difx2fits
application.

First we use Sched555Sched: http://www.aoc.nrao.edu/software/sched/, a program
often used to schedule VLBI observations. Although scheduling is not
necessary, the software produces the output files describing the details of
the MeerKAT observation in a format that DiFX can read. Hence, we first
generate several files required to run Sched. This includes the station file
with the location of the MeerKAT antennas that were used, a frequency file
with the frequency setup, and the main KEY file with instructions for Sched.
At this stage, we also generate the V2D file with information on the observing
setup, Earth orientation and antenna clock offsets that will be used by DiFX.
Once these files are created, we run Sched, which produces the VEX files that
will be the input for DiFX.

We then run the DiFX functions vex2difx and calcif2 to produce a model of the
geometric delays. We now have the delay model and uvw-plane values required to
assign to the xGPU correlated visibilities. We next re-structure the xGPU
visibilites into a DiFX format, including the metadata required such as the
polarisation, band, and baseline. Finally, we use the DiFX function difx2fits
to convert the file into a FitsFile.

For every different number of baselines a new version of xGPU needs to be
compiled. We would ideally always be observing with and saving data from all
64 MeerKAT dishes, however this is not always the case. To avoid compiling
multiple versions of xGPU, we assume that we always have 64 dishes. To do
this, we create fake antenna files prior to the xGPU step that we can later
flag. For example, if we have only 60 dishes in an observations we create 4
copy antennas to pad to 64 dishes. Now that we have a DiFX fits file, we read
this in to CASA using importfitsidi. We then use CASA (The CASA Team et al.,
2022) to flag the copied/fake antennas and the auto-correlations. Finally, we
output the data as an MS that we can image.

####  2.4.2 Producing images and transient localisation

We now have one MS for each of the 64 frequency subbands. Since each MS
technically has a different start time, instead of performing a joint
deconvolution on all of the MSs together, we image each MS individually. We
first perform a simple, dirty clean on each MS using WSClean, and visually
inspect the resulting images. This allows us to manually exclude channels
dominated by RFI. This process will be automated in the future. We exclude
those parts of the band that are dominated by RFI by excluding those MSs. We
then produce a frequency and time average image by adding each dirty image
together and dividing by the number of images. We compare this frequency and
time averaged image to e.g. the ASKAP RACS-Mid (Duchesne et al., 2023) of the
same area of the sky to confirm that our image reflects reality.

In order to detect an FRB we need to re-image each MS to produce images with
shorter integration times. We expect the FRB to be close to the centre of the
300 ms due to the DM-slicing process, and therefore, we image in an odd number
of time bins. We image in 11 time bins and proceed to average each time bin in
frequency by adding the images in each bin together and dividing by the number
of images. We now have one frequency averaged image per time bin.

Each transient buffer dataset is 300 ms long, which means that the uv-plane
does not rotate significantly over the observation, and we do not expect the
noise to change substantially over the dataset, even when taking into account
the dispersion delay. This means that we can perform difference imaging to
find the FRB. We do this by subtracting our time and frequency averaged image
from each frequency averaged time bin image. We then visually inspect the
resulting difference images to find the FRB. If we find the burst we confirm
that it is the FRB by checking that it appears in the image corresponding to
the FRB arrival time.

Next we produce images with shorter integration times around the time bins
where the FRB was seen, so that we can accurately select all the time bins
where it was detected. We integrate these time bins to produce an “on” image,
and then produce an “off” image with the same integration time where the FRB
was not visible. We produce these images with more advanced cleaning
parameters in WSClean, which we also apply to the full integration time image.
The WSClean parameters we use for the stopping criteria are 100 iterations, or
a threshold of 0.01 (arbitrary units). We apply a Cotton-Schwab cleaning with
major iteration gain of 0.8, and auto-masking with $\sigma=3$. We apply a
Briggs weighting with a robustness parameter of -0.3, and a weighting rank
filter of 3. Finally, we use W-gridding on the data.

###  2.5 Astrometry

We corrected the absolute astrometry of the radio sources in the FoV of the
detected FRBs using the method described in Driessen et al. (2022) and
Driessen et al. (2024). We used the Python Blob Detector and Source
Finder666https://www.astron.nl/citt/pybdsf/ (PyBDSF) to determine the
positions of sources in the full integration time, “on” and “off” images,
which we used to determine and correct the accuracy of our absolute
astrometry.

For the astrometric corrections, where possible, we prioritised using
reference catalogues that use Very Long Baseline Inferferometry (VLBI) to
achieve milliarcsecond precision on the position, such as the Long Baseline
Array (LBA) Calibrator Survey (LCS1; Petrov et al., 2011). Alternatively, the
Australian Telescope Compact Array (ATCA) Parkes-MIT-NRAO (PMN) (ATPMN;
McConnell et al., 2012) has an astrometric accuracy of 0.4" in RA and DEC.
However, these catalogues do not always have sufficient sources in the FoV of
the images where the FRBs were localised. The Rapid ASKAP Continuum Survey
(RACS; Hale et al., 2021), on the other hand, usually contains tens to
hundreds of sources within the FoV, but the astrometric accuracy of the source
positions has systematic offsets of $\sim 1-2$ arcseconds due to the lack of
sufficient radio sources with VLBI positions in the Southern Hemisphere to
perform accurate astrometric corrections of the catalogue.

The Radio Fundamental Catalog (RFC777RFC: http://astrogeo.org/rfc/), which
provides positions with milliarcsecond accuracy, often contains more sources
in the FoV of interest than LCS1 or ATPMN, but not enough to use on its own.
When that was the case, we used RFC sources in a larger FoV than the image to
correct the positions of the RACS sources, and finally used these corrected
RACS positions to align the coordinates of the sources in the full integration
MeerKAT images, using the astroalign module (Beroiz et al., 2020) in Python.
We selected unresolved RACS sources with an uncertainty in both RA and Dec
<0.5" and a total flux >20 mJy.

Once we obtained the transformation matrix for the full integration time
image, we applied it to the “on” and “off” images and source positions to
obtain the corrected FRB coordinates. We computed the average separation
between the corrected and reference sources after each alignment, and added
them in quadrature to obtain the total astrometric error on the FRB position.
The details about the astrometric corrections we performed are given in
Appendix A.

###  2.6 Offline beamforming

Along with offline imaging, the channelized complex voltages saved to disk can
be used to form beams at the best known location of the transient that is
determined from the imaging and localisation. To do that, the corresponding
gain solutions saved by the beamformer are used to phase up the interferometer
to the phase centre of the observation. To form a phased beam at the location
of the transient, one needs to multiply the gain/phase solutions by
appropriate weights. In simple terms, this means adding an extra rotation
phase to the existing vector of beamformed weights at the phase centre of the
observation. To obtain these additional phase corrections, we use MOSAIC (Chen
et al., 2021) to compute the delay polynomials for each antenna i.e the
expected delays that need to be added to each antenna to align the phase of
the electric field from a given location in the sky. These are in-turn used to
generate the beam weights as function of antenna and frequency. Since we
extract the buffer data after compensating for the dispersion delay at each
frequency channel, we generate the delay polynomials for each frequency
separately based on the slightly different epoch of observation (corresponding
to the dispersion delay at that frequency) before computing the weights. We
note that these delays are similar to the delays computed during the imaging
of these data and the differences are negligible. These weights are finally
multiplied with the gain/phase solutions before they are applied to the
channelized voltage data from the transient buffer. This process produces a
phased up coherent beam at the location of the transient. Forming a coherent
beam at the location of the transient has significant advantages: 1) the
coherent beam contains all the antennas in the array unlike the core antennas
typically used in the real-time search which increases the S/N of the
detection 2) the coherent beams overlap at the 25$\%$ power point which means
that FRBs that fall between two coherent beams get a significant boost (factor
of $\sim$4) 3) the formed beam has the highest time-resolution possible with
the correlator configuration and 4) there is polarization information
available in the buffer data which can be used to study the polarization
properties of the transient. The scripts used for offline beamforming are
provided in an online repo 888https://gitlab.com/kmrajwade/tbeamformer.

Before any scientific utilisation of polarization data can be done, it is
important to take into account the effects of the primary beam on the
polarization properties of the instrument. For a coherent beam that is
pointing at a given location $x,y$ (where the origin is at the boresight of
the primary beam) within the primary FoV, the measured electric field vector
(for an elliptically polarized wave) for the electric field for each hand ($H$
and $V$) of polarization per antenna, per frequency channel,

$\epsilon^{{}^{\prime}}_{H,V}(x,y,i,\nu)=\mathcal{J}_{H,V}~{}\epsilon
0_{H,V}\,,$ (1)

where the Jones Matrix,

$\mathcal{J}_{H,V}=\begin{pmatrix}j_{HH}&j_{HV}\\\ j_{VH}&j_{VV}\end{pmatrix}$
(2)

and the electric field vector,

$\epsilon^{{}^{\prime}}_{H,V}(x,y,i,\nu)=\begin{pmatrix}E_{HH}\\\
E_{VV}\end{pmatrix}.$ (3)

We assume here that for narrow channel widths, the electromagnetic wave can be
considered to be monochromatic and thus, Jones algebra is applicable. Hence,
in order to get the true measurement of the electric field at the position of
the FRB, one has to correct for the primary beam Jones matrix. In order to
obtain $\mathcal{J}_{H,V}$, we used the measurements from de Villiers (2023)
obtained from holography experiments with the MeerKAT telescope. Assuming that
the Jones matrix for the primary beam does not change significantly with
elevation, we use Eq. 3 to obtain the calibrated electric field for both hands
of polarization. The resulting voltages are fully calibrated and can be
directly used to measure the polarization of the detected FRBs. We do note
that this is not the most accurate method of calibrating the data as there is
no measurement of the Jones matrix at the location of the FRB at the time of
the FRB. We caution the reader that the correction may not entirely account
for the leakage and we absorb these uncertainties with an additional $5\%$
uncertainty on the estimated polarization fraction.

Figure 3: Calibrated polarization emission profiles for FRB 20220717A and FRB
20220905A created from the transient buffer data. The data for FRB 20220717A
was dedispersed at the scattering-corrected DM while FRB 20220905A was
dedispersed at a DM that accounts for the intra-channel DM smearing at the
bottom of the band. The top panels show the absolute polarization position
angle and the bottom panels show the total intensity (black), linear
polarization (red) and circular polarization (blue).

##  3 Results

FRB parameter | Unit | FRB 20220717A | FRB 20220905A
---|---|---|---
MJD |  | 59777.8221507637 | 59827.7480359790
UTC |  | 2022-07-17T19:43:53.826 | 2022-09-05T17:57:10.309
RA (J2000) | (hms) | 19:33:13.0$\pm$0.9" | 16:54:19.8$\pm$0.7"
Dec (J2000) | (dms) | -19:17:15.8$\pm$0.9" | -20:04:16.9$\pm$0.7"
$l$ | (deg) | 19.83515767 | 0.78476176
$b$ | (deg) | -17.63203224 | 14.61426288
Detection frequency | (MHz) | 816 | 1284
S/N-maximising DM | (${\rm pc\,cm^{-3}}$) | $637.34\pm 3.52$ | $800.61\pm 0.60$
Scattering-corrected DM | (${\rm pc\,cm^{-3}}$) | $634.69\pm 0.10$ | –
Detection S/N |  | 15.3 | 14.4
Beamformed S/N |  | 101.1 | 141.9
$\tau_{s}$ 1 GHz | (ms) | $8.2\pm 0.3$ | –
Scattering index |  | $-3.7\pm 0.2$ | –
W${}_{\text{50p}}^{a}$ | (ms) | $8.4\pm 0.3$ | $1.1\pm 0.1$
W${}_{\text{10p}}^{a}$ | (ms) | $20.1\pm 0.6$ | –
W${}_{\text{eq}}^{a}$ | (ms) | $10.0\pm 0.3$ | –
RM | (rad m-2) | $385.7\pm 0.4$ | $-83.1\pm 1.9$
$S_{\text{peak}}$ | (Jy) | $0.34\pm 0.03$ | $6.40\pm 0.04$
$F$ | (Jy ms) |  $6.83\pm$0.03 |  $7.0\pm$0.6
${\rm DM}_{\rm NE2001}$ | (${\rm pc\,cm^{-3}}$) | 118 | 154
${\rm DM}_{\rm YMW16}$ | (${\rm pc\,cm^{-3}}$) | 83 | 104
${\rm DM}_{\rm halo}$ | (${\rm pc\,cm^{-3}}$) | 86 | 115
Table 1: Various observed and measured properties of FRB 20220717A and FRB
20220905A.
a Measured at 1020.3 MHz.

Figure 4: MeerKAT images of the localisation of FRB 20220717A and FRB
20220905A. Panel a shows a 43 ms integration of the region before the FRB
detection (OFF), while panel b shows a 43 ms integration where the FRB was
detected and localised (ON). The synthesised beam is shown on the lower left
corner of each image. Panels c and d show similar images for FRB 20220905A for
7.7 ms integration.

###  3.1 FRB 20220717A

FRB 20220717A was discovered during commensal observations with the MeerTime
project (Bailes et al., 2020) at a DM of 637 pc cm-3. It was discovered at the
UHF band (816 MHz) and shows clear evidence of scattering. The burst is
broadband across the entire 544 MHz of bandwidth with no visible structure
seen at smaller timescales. The burst shows a low linear polarization fraction
(30$\pm$2$\%$) that maximizes at a rotation measure of 385.7$\pm$0.4 rad m-2.
From the calibrated transient buffer data, we were able to localize the FRB to
RA (J2000): +19:33:13.0$\pm$0.9" and DEC (J2000): $-$19:17:15.8$\pm$0.9" after
performing an astrometric correction using the sources detailed in Table 2.
The errors on the position were obtained from summing in quadrature the
PyBDSFerror of the source position (0.4" RA, 0.4" Dec) and the error from the
astrometric correction (0.9").

###  3.2 FRB 20220905A

FRB 20220905A was discovered during a MeerTime (Bailes et al., 2020)
observation at UTC 17:01:04. The FRB was detected at L-Band (1284 MHz) in the
incoherent beam which triggered the storage of complex voltage data in the
transient buffer. The FRB was detected at a DM of 800.6 pc cm-3 and shows no
evidence of scattering or any emission at shorter timescales. Similar to FRB
20220717A, the FRB shows a low degree of linear polarization at a rotation
measure of $-$83.81$\pm$1.9 rad m-2. The FRB was localized to RA (J2000):
16:54:19.8$\pm$0.7" and DEC (J2000): $-$20:04:16.9$\pm$0.7" which led to the
immediate optical follow-up and identifying the the host galaxy as shown
below. The coordinates were obtained after performing an astrometric
correction with the sources listed in Table 1. The errors on the position were
obtained from summing in quadrature the PyBDSFerror of the source position
(0.09" in RA, 0.2" in Dec) and the error from the astrometric correction
(0.7"). The astrometric corrections are detailed in Appendix A.

###  3.3 Optical Observations

We obtained deep imaging of the field of FRB 20220905A with the Gemini Multi-
Object Spectrograph on the 8-m Gemini South Telescope (Gimeno et al., 2016) to
identify all possible host candidates (Program GS-2022B-Q-123, PI Gordon). We
obtained 20x120s in $r$-band on 11 October 2022 UTC and 25x100s in $z$-band on
12 October 2022 UTC. Both datasets were reduced using the
POTPyRI999https://github.com/CIERA-Transients/POTPyRI pipeline. Then, we
utilized the Probabilistic Association of Transients to its Host (PATH) method
to link the transient to a host galaxy, as outlined in Aggarwal et al. (2021).
We used photutils to perform photometry and found 15 candidates within 30
arcseconds of the FRB localization (see Figure 5). The prior that the host is
unseen was set to be $P(U)=0.05$, and the offset prior was set to 50% of the
half-light radius of the host. PATH output indicated that the host is unseen
(see 4). The PATH unseen posterior $P(U|x)\sim 1$. We also conducted a manual
inspection of the image, during which we noted a faint $\approx 3\sigma$
source offset 0.9 arcseconds from the FRB-localisation and with an angular
size of 1.1 arcseconds. If we include this source in the list of candidates,
it is assigned a very high PATH posterior ($P(O|x)\approx 0.98$). However,
this candidate is still a tentative source.

The FRB 20220717A localization is close (0.6") to a galaxy seen in PanSTARRS
DR1 archival data of the field (see Figure 5). A PATH analysis on the image
confirmed the source (PSO J293.3038-19.2876) as the host galaxy of FRB
20220717A with a high posterior probability ($P(O|x)\approx 0.97$). We
obtained spectroscopy of the host of FRB 20220717A on 28 October 2022 UTC with
the Goodman High Throughput Spectrograph on the 4-m Southern Astrophysical
Research Telescope (SOAR; Clemens et al. 2004) to determine its redshift,
totalling $2\times 1200$ s of science exposure (Program SOAR2022-007B, PI
Gordon). We used the M1 400 lines/mm grating covering a wavelength range of
3000–7050 Å in conjunction with the BlueCam and a 1.0 arcsecond slit. The
position angle was oriented to align the host with a nearby object for ease of
identification during reduction. The data were processed with PypeIt
(Prochaska et al., 2020), using a quicklook reduction to identify the host
redshift.

We obtained a second spectrum of the host of FRB 20220717A with Keck/DEIMOS on
27 October 2022 UTC by taking a single 900s exposure (Program U129, PI
Prochaska). We used the ZD 600 lines/mm grating for a wavelength coverage of
4550–9450 Å with a 1.0 arcsecond slit. The data were reduced fully using the
PypeIt reduction package (Prochaska et al., 2020) to produce a flux-calibrated
1D spectrum of the host galaxy. This spectrum shows substantial contamination
from skylines, likely due to a manufacturing issue during production of the
relevant slit mask, which we were unable to remove fully in the reduction
process. Nonetheless, we perform all further analysis on this DEIMOS spectrum.
These observations yield a spectroscopic redshift of $z=0.36295\pm 0.00018$
for the FRB host galaxy.

Figure 5: Left:Archival PanSTARRS DR1 image of the field surrounding the
FRB20220717A localization (see PATH results in table 5). The best known
1$\sigma$ position of the FRB is shown by the white ellipse and the red
ellipse shows the host galaxy. Right: GMOS image showing FRB20220905A
localisation field crowded with stars (PATH results in table 4), white ellipse
is 1 $\sigma$ localisation region, orange ellipse is the tentative host for
FRB20220905A.

In order to confirm the redshift and to measure H$\alpha$ emission, the DEIMOS
spectrum was fit using the pPXF spectral fitting package to fit both the
spectral continuum and emission features (Cappellari, 2023). Due to the
presence of poorly-subtracted skylines in the spectrum, we masked these
regions out of the pPXF fit. Masking was applied to any region with a flux
measurement error above
0.25$\times\mathrm{10^{-17}\;erg\;s^{-1}\;cm^{-2}}$Å-1, as well as any region
with a flux measurement <
0.2$\times\mathrm{10^{-17}\;erg\;s^{-1}\;cm^{-2}}$Å-1 as this is indicative of
over-subtraction. The resulting pPXF fit to the H$\alpha$ feature is shown in
Figure 6. Integrating this fit yields an H$\alpha$ flux of 17.08 $\pm$ 3.7
$\times\mathrm{10^{-17}\;erg\;s^{-1}\;cm^{-2}}$, uncorrected for Galactic
extinction.

Using the linear model to compute star formation rate (SFR) from H$\alpha$
emission given in Kennicutt et al. (1994), this galaxy is observed to have an
SFR of $0.65\pm 0.14$ M⊙ yr-1. Unfortunately this emission feature falls
directly on an observed skyline, which was masked out of the flux integration
measurements. Though we fit this feature using a Gaussian profile, the nearby
[NII]$\lambda$6584 line shows a double-peaked profile indicating rotational
broadening of the emission features. The limited data quality likely makes our
measurement on H$\alpha$ an underestimation, and therefore our result for SFR
computed therefrom should also be understood as a lower limit.

We estimate the host galaxy DM contribution using the H$\alpha$ emission
measure (EM) as described in Tendulkar et al. (2017):

$\textrm{DM}_{\textrm{host}}=387\ \textrm{pc\ cm}^{-3}\
L_{\textrm{kpc}}^{1/2}\left[\frac{4f_{\textrm{f}}}{\zeta(1+\epsilon^{2})}\right]^{1/2}\left(\frac{\textrm{EM}}{600\
\textrm{pc\ cm}^{-6}}\right)^{1/2},$ (4)

where $f_{\textrm{f}}$ is the volume filling factor of the ionized clouds,
$\zeta\geq 1$ specifies cloud-to-cloud density variations, $\epsilon\leq 1$ is
the fractional variation within discrete clouds, and $L_{\textrm{kpc}}$ is the
depth of the total ionized region in kpc. As in Tendulkar et al. (2017), we
assume that $\zeta=2$ (indicating 100% variation between clouds) and that
$\epsilon=1$ (indicating that the electron density within clouds is fully
modulated). We also assume that $f_{\textrm{f}}$ = 1.

We compute EM from the observed H$\alpha$ surface brightness as described in
Reynolds (1977). Because the PanSTARRS image of this host cannot be used to
constrain its morphology, we cannot place good constraints on
$L_{\textrm{kpc}}$. If we take $L_{\textrm{kpc}}$ to be 0.150, the expected
value for a Milky Way-like spiral galaxy with the FRB in its midplane, we can
thus estimate a $\textrm{DM}_{\textrm{host}}$ contribution of $\sim$ 100 pc
cm-3 (Kalberla & Kerp, 2009).

Figure 6: Keck/DEIMOS spectrum of the FRB20220717A host galaxy showing the Hα
emission line at 6563 Å and neighboring [NII] emission at 6548 Å and 6584 Å at
a common redshift $z=0.3633$. The black histogram shows the spectral data,
while the observed error is shown in red. Blue shows the pPXF model fit to the
data. Grey vertical regions indicate skylines that are masked in the spectral
fitting process.

##  4 Discussion

###  4.1 Benefits of complex voltage capture

The ability to save complex voltage data from each antenna at the native time
resolution allows MeerTRAP to overcome these limitations of post-detection
analysis. Along with the ability to localize the FRBs by creating images from
these data, we can also study FRBs at the finest possible time-resolution and
also obtain polarization information. We also note that the ability to
beamform the transient buffer data to the correct location of the FRB also
enables one to increase the sensitivity of the telescope towards these FRBs
significantly since the transient buffer data includes all the telescopes that
were used in the observations as opposed to the limit of 40 dishes that is
used in the real-time coherent searches for MeerTRAP. Furthermore, it also
accounts for the reduction in S/N in the search due to offset of the FRB from
the boresight of the coherent beam in which it was discovered. This is clearly
shown by the difference in the estimated S/N of the bursts in the real-time
search and the processed transient buffer data in Table 1. This ability
enables one to reveal fainter features in the emission across the dynamic
spectrum that may be washed out in the down-sampled data. The results
presented in this paper reiterate the power of saving complex voltage data for
FRBs.

###  4.2 Complex environments around FRB progenitors

Both the FRBs presented here show flat polarization position angles (PAs).
This is consistent with PAs observed for most one-off FRBs (Pandhi et al.,
2024). It is important to note that PAs are also flattened due to scattering
in the intervening medium based on observations of Galactic pulsars (Li & Han,
2003; Karastergiou, 2009). FRB 20220717A and FRB 20220905A show a very low
degree of linear polarization (10$\pm 2\%$ and 17.5$\pm 1.5\%$) which is
consistent with what has been recently seen for one-off FRBs (Sherman et al.,
2024; Pandhi et al., 2024). One of the possibilities of depolarization could
be instrumental but any residual phase and gain differential between the two
dipoles of the receiver will only increase the linear/circular polarization
fraction hence depolarization is unlikely to be due to calibration
inaccuracies. The calibration and leakage correction for circular polarisation
measurements with MeerKAT is not yet well understood. As such, we could not
reliably measure the circular polarization of these FRBs.

Recent studies of linear polarization of a large sample of FRBs (Sherman et
al., 2024; Pandhi et al., 2024) have shown that one-off FRBs seem to have a
large diversity in the degree of linear polarization. On the other hand,
linear polarization fractions with values ranging between 90–100% (Mckinven et
al., 2023) seems to be a distinct property of the repeating FRBs. These
observations suggest a possible dichotomy in the nature of FRB progenitors, a
key open question in the field. One argument for a small degree of linear
polarization for some of the one-off FRBs could be a complex environment in
the vicinity of the FRB source causing depolarization of radiation due to RM
scattering (Plavin et al., 2022). Such environments could explain the large
contribution by the host to the total DM in a number of apparently one-off
FRBs recently discovered by ASKAP and MeerKAT (Bhandari et al., 2023; Caleb et
al., 2019). This might be true for FRB 20220717A with a potentially
significant RM in the source frame but this conjecture is hard to reconcile
with FRB 202209095A. To investigate the source of RM contribution, we compute
the expected Galactic contribution to the RM along the line of sights of the
two FRBs presented in this paper. To do this we use the Galactic RM maps
created by Hutschenreuter et al. (2022) to obtain the mean RM contribution by
the Galaxy. The Galactic contribution along the line of sight to FRB
202209095A and FRB 20220717A is small (45 $\pm$ 17 and 0 $\pm$24 rad m-2),
suggesting that the majority of the RM can be attributed to the host galaxy
and any foreground, magnetized plasma.

###  4.3 Origin of Scattering in FRB 20220717A

Figure 7: Dispersion measure versus scattering timescale at 1 GHz. The grey
points show the measurement for Galactic Pulsars. The squares and triangles
show scattering timescale as a function of different DM components for all
ASKAP and MeerTRAP Localised FRBs. Here DMMW refers to the DM contribution
from the ISM of the Milky Way. Here we assume the MW halo contribution of 52.8
pc cm-3 (Cook et al., 2023).

The burst from FRB 20220717A exhibits a strong scattering feature. In order to
characterise it, we fit the profile with a combination of a Gaussian and a
scattering function of the intervening medium. The scattering function can be
approximated by an exponential quantified by the scattering timescale $\tau$.
We use the scatfit software (Jankowski, 2022; Jankowski et al., 2023) to fit
the scattering function as a function of frequency. We split the data into 4
subbands such that there was enough signal in each to obtain a robust fit to
the burst profile. Figure 8 shows the results of our analysis. We obtain
$\tau=8.2\pm 0.3$ ms at 1 GHz with the scattering timescale scaling with
frequency as a power-law with an exponent, $\alpha=-3.7\pm 0.2$. The analysis
also optimises for the DM while fitting the scattering function so as to
maximise the S/N which gives us the best-fit DM of 634.69 pc cm-3.

The total DM of any FRB is made of different components such that,

$\begin{split}\rm DM_{obs}={\rm DM}_{\rm ISM}+{\rm DM}_{\rm halo}+DM_{EG}\\\
\rm DM_{EG}={\rm DM}_{\rm cosmic}+\frac{DM_{host}}{1+z}\end{split}$ (5)

where ${\rm DM}_{\rm ISM}$ is the contribution from the MW’s ISM and ${\rm
DM}_{\rm halo}$ is the contribution from the MW halo. $\mathrm{DM_{EG}}$ is
the extragalactic DM contribution composed of ${\rm DM}_{\rm cosmic}$ which is
the contribution from the cosmic web (combined effects of the intergalactic
medium (IGM) and intervening galaxies), and $\frac{{\rm DM}_{\rm host}}{1+z}$
which is the redshifted contribution from the host galaxy’s ISM including its
halo and any gas in the immediate vicinity of the FRB source. An FRB with a
known redshift allows us to estimate ${\rm DM}_{\rm cosmic}$ and given that we
can estimate ${\rm DM}_{\rm ISM}$ and ${\rm DM}_{\rm halo}$, we can then infer
an estimate for $\frac{\rm DM_{host}}{1+z}$. An increasing sample of
accurately localized FRBs with identified host galaxies gives us an
opportunity to assess the component of DM that contributes most significantly
to the observed scattering in them.

To do this, we collated all the well localized, scattered FRBs from ASKAP and
MeerTRAP with measured redshifts (James et al., 2022; Baptista et al., 2023;
Caleb et al., 2023; Driessen et al., 2022) and where the DM contribution from
the host can be estimated based on the method presented in (James et al.,
2022). Then we looked for any correlations between the scattering timescale at
1 GHz and the DM contributions due to different components as shown in Figure
7. For majority of the FRBs, the expected scattering from the Milky Way for
these FRBs is a lot smaller compared to the measured scattering timescale. It
potentially hints at the fact that the measured scattering for FRBs cannot be
explained by the ISM in our own Galaxy. Therefore, the scattering should be
dominated by turbulence in the foreground galaxies and/or the host galaxy
itself. For the published MeerKAT FRBs, it is evident that ${\rm DM}_{\rm
host}$ can account for most of the scattering observed, further validating the
claim made in Chawla et al. (2022).

Figure 8: Top Panel: Scattered profile of FRB 20220717A shown in 4 subbands
with the corresponding best-fit model. Bottom Panel: Estimate of scattering
timescale and pulse width as a function of frequency along with the best-fit
linear fit. The two number at the top right show the scattering timescale at 1
GHz and scaling index of scattering.

###  4.4 Host Galaxy contribution to the DM of FRB 20220717A

As discussed in the previous section, the dispersion of FRBs makes them
excellent probes for unraveling the structure of the cosmic web. This was
initially shown by Macquart et al. (2020) who provided a relationship between
the expected DMEG and the redshift of the FRB host (assuming a typical DMhost
of 100 units). FRB 20220717A shows a host DM contribution that is consistent
with these predictions. We compute the expected DMcosmic for FRB 20220717A
using the Macquart relation with the same assumptions as presented in Caleb et
al. (2023). Assuming a DMhost of 100 pc cm-3 and a MW ISM and halo
contribution of 83 pc cm-3 (from the YMW16 model) and 52 pc cm-3 using the
model from Cook et al. (2023), we obtain DMcosmic of $\simeq$402 pc-cm-3. This
DM contribution from the IGM is within the scatter of the Macquart relation.
It is worth noting that if we assume that the RM is mostly dominated by the
host galaxy, the expected RM in the reference frame of the host, RMhostframe =
RM(1+z)${}^{2}\simeq$720 rad m-2. This is a large value of RM that is
typically measured in the dense star-forming regions of a Galaxy (Van Eck et
al., 2021). Furthermore, the high star-formation rate measured for the host
galaxy can explain the turbulent and dense regions in the galaxy. These
diagnostic measurements along with a large H$\alpha$ flux from the host galaxy
spectrum suggests that FRB 20220717A may lie in a dense region of its host
galaxy.

##  5 Conclusions

In summary, we present the discovery and the subsequent sub-arcsecond
localisation of two FRBs with the MeerTRAP instrument. The transient buffer
capture functionality has allowed us to localise and identify the host
galaxies and study the polarization of these bursts. Both, FRB 20220717A and
FRB 20220905A show a low degree of linear polarization with no conclusive
evidence on the presence or absence of circular polarization due to
calibration issues. This is consistent with what is observed for one-off FRBs
and may hint at the fact that linear polarization fraction could be a
distinguising property between the apparently repeating and non-repeating
population of FRBs. It also suggests that there is a distibution in the
polarization fraction in FRBs akin to single pulses seen from neutron stars
and could be attributed to depolarization near the source. The host DM
contribution for FRB 20220717A is estimated to be around 100 pc cm-3 which is
consistent with the measured H$\alpha$ flux. The high star-formation rate of
the host galaxy and the RM measurement suggests that the FRB may lie within a
dense region of the galaxy. FRB 20220717A also exhibits scattering which can
be mostly attributed to the host galaxy and the intervening medium, consistent
with scattering seen in the FRB population. The transient buffer mode is fully
operational on MeerTRAP with transient buffer data on more than 20 FRBs that
are currently being investigated. This study again demonstrates the power of
saving raw voltage data for accurately localising FRBs and further promotes
the deployment of such systems on all real-time FRB detection systems around
the world.

## Acknowledgements

The authors would like to thank the referee for their comments that
significantly improved the manuscript. The MeerKAT telescope is operated by
the South African Radio Astronomy Observatory, which is a facility of the
National Research Foundation, an agency of the Department of Science and
Innovation (DSI). The MeerTRAP collaboration would like to thank the MeerKAT
Large Survey Project teams for allowing MeerTRAP to observe commensally. The
MeerTRAP collaboration acknowledges funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation
programme (grant agreement No 694745). The authors also acknowledge the usage
of TRAPUM infrastructure funded and installed by the Max-Planck-Institut für
Radioastronomie and the Max-Planck-Gesellschaft. KMR would like to thank
Mattieu DeVilliers and Ludwig Schwarz for useful discussions regarding off-
boresight polarization calibration for MeerKAT. The authors would like to
thank the South African Radio Astronomy Observatory (SARAO) for immense
support during the commissioning of the transient buffer mode. KMR
acknowledges support from the Vici research programme “ARGO” with project
number 639.043.815, financed by the Dutch Research Council (NWO). AM
acknowledges support from the U.S. National Science Foundation through grant
AST-2206492 and from the Nantucket Maria Mitchell Association. MC acknowledges
support of an Australian Research Council Discovery Early Career Research
Award (project number DE220100819) funded by the Australian Government. MB
acknowledges support from the Bundesministerium für Bildung und
Forschung(BMBF) D-MeerKAT award 05A17VH3 (Verbundprojekt D-MeerKAT).

## Data Availability

The processed data products from the transient buffer corresponding to FRB
20220905A and FRB 20220717A and the corresponding scripts will be made
available to others upon reasonable request.

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##  Appendix A Astrometry sources

Tables 2 and 3 detail the sources that were used to perform the astrometric
correction for FRB 20220710A and FRB 20220905A respectively. In both cases. no
LCS1 or ATPMN sources were available, but several RFC sources laid in a 3.5°
radius from the images phase centre. We thus used the RFC sources to align the
positions of the matching RACS sources, and thus obtained the transformation
to correct the RACS source position. Next we used the RACS sources matching
the MeerTRAP sources obtained with PyBDSF to perform the final astrometric
transformation. The resulting mean offsets between RFC and RACS, and RACS and
MeerTRAP after each transformation, were added in quadrature to obtain the
astrometric uncertainty. For FRB 20220717A, this is
$\Delta\theta=(0.20^{2}+0.83^{2})^{1/2}=0.85"$, while for FRB 20220905A, we
get $\Delta\theta=(0.20^{2}+0.63^{2})^{1/2}=0.66"$.

RFC Source | RACS Source | Sep. before (") | Sep. after (")
---|---|---|---
J1924-1949 | J192441.4-194949 | 1.35 | 0.13
J1925-1813 | J192512.4-181303 | 1.44 | 0.36
J1928-2035 | J192809.1-203543 | 1.18 | 0.32
J1928-1707 | J192851.2-170758 | 1.71 | 0.20
J1930-2053 | J193010.3-205304 | 1.25 | 0.18
J1931-2025 | J193149.0-202537 | 1.11 | 0.19
J1935-1804 | J193509.3-180444 | 1.53 | 0.02
| Mean | 1.36 | 0.20
RACS Source |  | Sep. before (") | Sep. after (")
J192139.2-175408 |  | 1.75 | 1.23
J192113.6-174846 |  | 1.60 | 0.98
J192109.9-170507 |  | 1.54 | 1.57
J192047.2-174602 |  | 1.26 | 0.60
J192045.1-164410 |  | 0.84 | 0.47
J192043.7-202838 |  | 1.91 | 0.83
J192043.6-185557 |  | 0.77 | 0.36
J192036.7-172940 |  | 2.28 | 0.87
J192036.5-202954 |  | 1.29 | 0.78
J192030.7-170746 |  | 0.80 | 0.26
J192032.7-191010 |  | 0.50 | 0.11
J192029.1-163509 |  | 1.79 | 1.01
J192017.5-174030 |  | 1.10 | 0.78
J192017.1-195115 |  | 1.03 | 0.63
J192008.7-203228 |  | 1.60 | 0.67
J192015.6-181904 |  | 3.29 | 0.86
J191941.1-180128 |  | 2.06 | 1.81
J191937.9-195826 |  | 1.80 | 0.86
J191919.7-205020 |  | 1.82 | 1.05
| Mean | 1.53 | 0.83
Table 2: Sources used for the astrometric correction of FRB 20220717A. The first group were the RFC sources used to align RACS, while the second group are the corrected RACS sources used to align the MeerTRAP sources. RFC Source | RACS Source | Sep. before (") | Sep. after (")
---|---|---|---
J1644-2156 | J164443.3-215608 | 1.15 | 0.03
J1647-1926 | J164753.7-192618 | 0.65 | 0.24
J1650-2010 | J165010.5-201012 | 0.93 | 0.24
J1656-2010 | J165655.1-201056 | 0.55 | 0.13
J1657-2004 | J165733.2-200434 | 0.88 | 0.25
J1701-2007 | J170135.4-200759 | 0.63 | 0.29
J1703-2110 | J170327.4-211049 | 0.70 | 0.22
| Mean | 0.79 | 0.20
RACS Source |  | Sep. before (") | Sep. after (")
J165532.6-184546 |  | 2.45 | 0.33
J165204.9-212536 |  | 1.29 | 0.08
J165128.6-221213 |  | 0.99 | 0.49
J165118.8-231359 |  | 1.36 | 0.24
J165115.5-195629 |  | 1.30 | 0.12
J165059.1-230533 |  | 1.40 | 0.67
J165056.1-211911 |  | 0.28 | 0.58
J165054.4-232933 |  | 1.65 | 1.93
J165037.4-222326 |  | 1.26 | 0.57
J165033.9-201748 |  | 0.85 | 0.49
J164954.1-214558 |  | 0.07 | 0.26
J164953.0-220609 |  | 1.13 | 0.90
J164939.7-201149 |  | 1.01 | 0.85
J164910.4-183237 |  | 0.39 | 1.29
J164852.8-225423 |  | 2.11 | 2.19
J164846.4-214847 |  | 0.55 | 0.23
J164813.4-215206 |  | 1.74 | 0.83
J164753.7-192618 |  | 0.87 | 0.21
J164638.1-210942 |  | 1.64 | 0.11
J164528.9-195622 |  | 2.16 | 0.44
J164508.8-224833 |  | 1.40 | 0.89
J164438.8-184024 |  | 2.06 | 0.21
| Mean | 1.27 | 0.63
Table 3: Sources used for the astrometric correction of FRB 20220905A. The first group were the RFC sources used to align RACS, while the second group are the corrected RACS sources used to align the MeerTRAP sources. RA | DEC | Ang-size | Mag | Sep | P(O|x)
---|---|---|---|---|---
J2000 | J2000 | arc-sec | arc-sec |  |
16:54:20.31 | -20:04:17.13 | 0.2 | 24.4 | 7.3 |  $\ll$10-6
16:54:19.81 | -20:04:03.52 | 0.3 | 21.1 | 12.7 |  $\ll$10-6
16:54:20.02 | -20:04:07.41 | 0.2 | 23.6 | 9.4 |  $\ll$10-6
16:54:19.20 | -20:04:07.62 | 0.2 | 22.7 | 12.0 |  $\ll$10-6
16:54:19.30 | -20:04:27.19 | 0.2 | 21.8 | 13.0 |  $\ll$10-6
Table 4: PATH analysis results for FRB 20220905A showing the top 5 most probably host galaxy candidate. Here P(O|x) denotes the posterior probability of a galaxy being the host for the FRB. Most of the candidates have insignificant PATH posteriors. The value of 10-6 roughly corresponds to 0.001$\%$ interval for a Gaussian probability density function. RA | DEC | Ang-size | Mag | Sep | P(O|x)
---|---|---|---|---|---
J2000 | J2000 | arc-sec | arc-sec |  |
19:33:12.91 | -19:17:15.42 | 2.2 | 21.8 | 0.6 | $9.69\times 10^{-1}$
19:33:13.12 | -19:17:09.35 | 2.2 | 20.9 | 5.6 | $2.28\times 10^{-2}$
19:33:12.53 | -19:17:15.74 | 2.2 | 22.6 | 5.3 | $5.86\times 10^{-3}$
19:33:13.17 | -19:17:30.54 | 2.2 | 24.9 | 16.2 | $7.37\times 10^{-58}$
Table 5: PATH analysis results for FRB 20220717A showing the most probable
host galaxy candidates.