# Image plane detection of FRB121102 with the MeerKAT radio telescope

J. C. Andrianjafy,1 N. Heeralall-Issur,1 A. A. Deshpande$,^{2,3,4}$ K. Golap,5
P. Woudt,6 M. Caleb,7,8 E. D. Barr,9 W. Chen,9 F. Jankowski,10 M. Kramer,9,10
B. W. Stappers,10 and J. Wu9
1Department of Physics, University of Mauritius, Réduit 80837, Mauritius
2Raman Research Institute, Bangalore 560080 , India
3Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
4Indian Institute of Technology, Kanpur 208016, India
5National Radio Astronomy Observatory, PO Box O, Socorro, NM 87801, USA
6Department of Astronomy, University of Cape Town, Private Bag X3, Rondebosch,
7701, South Africa
7Sydney Institute for Astronomy, School of Physics, The University of Sydney,
Sydney, 2006, NSW, Australia
8ASTRO3D: ARC Centre of Excellence for All-sky Astrophysics in 3D, Canberra,
2601, ACT, Australia
9Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn,
Germany
10Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy,
The University of Manchester, Manchester M13 9PL, UK
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present the analysis of radio interferometric 2-s images from a MeerKAT
observation of the repeating fast radio burst FRB121102 on September 2019,
during which 11 distinct pulses have been previously detected using high time
and frequency resolution data cubes. In this work, we detected 6 out of the 11
bursts in the image plane at 1.48 GHz with a minimum peak signal-to-noise
ratio (S/N) of 5 $\sigma$ and a fluence detection limit of $\sim$ 0.512 Jy ms.
These constitute the first detections of a fast radio burst (FRB) or a radio
transient using 2-s timescale images with MeerKAT data. Analysis of the fitted
burst properties revealed a weighted average precision of $\sim$ 1 arcsec in
the localization of the bursts. The accurate knowledge of FRB positions is
essential for identifying their host galaxy and understanding their mysterious
nature which is still unresolved to this day. We also produced 2-s images at
1.09 GHz but yielded no detection which we attributed to the spectral
structure of the pulses that are mostly higher in strength in the upper
frequencies. We also explore a new approach to difference imaging analysis
(DIA) to search for transients and find that our technique has the potential
to reduce the number of candidates and could be used to automate the detection
of FRBs in the image plane for future MeerKAT observations.

###### keywords:

radio continuum: transients – instrumentation: interferometers – techniques:
image processing

††pubyear: 2022††pagerange: Image plane detection of FRB121102 with the
MeerKAT radio telescope–LABEL:lastpage

##  1 Introduction

Fast radio bursts (FRBs) are the newly discovered bright $\sim$ 1 Jy $\sim$
millisecond duration radio transients (Lorimer et al., 2007). The source of
FRBs emission is yet of unknown origin but the foremost leading theory
suggests magnetars as their progenitors (Li et al., 2021; Scholz et al., 2020;
Bochenek et al., 2020; Mereghetti et al., 2020). The mysterious nature of FRBs
aroused tremendous consideration from the astronomy community and there have
been several advancements made during the past decade to understand these
phenomenon (for reviews, see Caleb & Keane, 2021; Petroff et al., 2019).

Given their high range of dispersion measure values, FRBs are potentially
invaluable tools to probe the cosmological unverse such as the study of
intergalactic turbulence (Zhu & Feng, 2021), the determination of the cosmic
baryon density in the intergalactic medium (Macquart et al., 2020), as well as
an estimation of the Hubble constant, being suggested by Wei et al. (2019).
However, these studies can only be operated with an accurate knowledge of the
position of the FRB source and its host galaxy.

One of the major findings in FRB field is the first detection of the repeating
source FRB121102 (Spitler et al., 2016; Scholz et al., 2016) with the single
dish Arecibo telescope. The repetition of the bursts allowed targeted follow-
up observations with radio interferometers to measure its position up to
$\sim$ milliarcsecond precision using high resolution fast timescale imaging
(with coordinates
$\alpha=05^{\textrm{h}}31^{\textrm{m}}58.698^{\textrm{s}},\delta=33^{\circ}08^{\prime}52.586^{\prime\prime}$;
Marcote et al., 2017; Chatterjee et al., 2017). As a result, Tendulkar et al.
(2017) found that FRB121102 is localized in a low-mass and low-metallicity
dwarf galaxy by matching the measured position with optical observations from
the Gemini North telescope. Among the few hundreds distinct FRBs reported in
the literature (Amiri et al., 2021; Petroff et al., 2016), more than 10 of
them have been localized to their host galaxies by combining the
interferometric image plane location of the bursts and its matched position
with telescopes operating at other wavelengths. For instance, Ravi et al.
(2019) localized FRB190523 with the use of $\sim$0.5-s radio images from the
Deep Synoptic Array (DSA) and the low resolution imaging spectrometer of the
Keck I telescope. Similarly, the position of FRB190711 were obtained with
3.1-s radio images from the Australian Square Kilometre Array Pathfinder
(ASKAP) and deep images of the Very Large Telescope (Macquart et al., 2020).

In general, detecting FRB and fast transient type sources through
interferometric imaging can be achieved by correlating the signals from each
pair of antennas in the array and averaging the correlated output, known as
visibilities, in short integration time that is adequate to the science
requirements. However, searching for fast radio transients in the image plane
can encounter different challenges. The sparse (u,v) sample over the short
period of time could give rise to lower sensitivity and poor quality images.
The duration of the transient pulses is often much shorter than the
integration time, causing loss of signals into the noisy visibility data. The
other challenging factor is also the high rate at which data is recorded that
makes computing heavily expensive, and often preventing real time imaging
detection.

In 2019, observations of the repeating source FRB121102 have been performed
with the MeerKAT radio telescope in South Africa. From this observation, 11
bursts from FRB121102 have been detected using high time and frequency
resolution data cubes (Caleb et al., 2020) by the The Meer(more) TRAnsients
and Pulsars (MeerTRAP) team (Stappers, 2016). Knowing the position and arrival
times of these pulses, these detections are of crucial importance in
investigating and testing the capability of the MeerKAT telescope to detect
FRBs in the image plane using fast dump visibility data, which will be the
main focus of this paper.

The paper is organized as follows, the observations are described in Section
2.1, followed by the description of our methodology including data flagging,
calibration and imaging in Section 2.2 and 2.3. The results are presented in
Section 3 and their properties will be discussed in Section 4 as well as its
implications towards MeerKAT surveys before we conclude in Section 5.

##  2 Methods

###  2.1 Data observations

As part of a Director’s Discretionary Time (DDT) proposal, MeerKAT (Mauch et
al., 2020; Jonas, 2016) carried out 3 hour observations towards the position
of FRB121102 on the 6th September 2019, 10th September 2019, 6th October 2019,
and 8th October 2019. The 4 sessions were conducted in slightly different
telescope configurations (number of antennas, integration time, frequency
channel resolution), therefore we will only describe the 10th September
observation during which FRB121102 pulses have been previously detected and
for which we performed our analysis. In our data, the observations were
conducted using 58 out of the 64 MeerKAT dishes at a frequency center of 1.28
GHz and a total bandwidth of 856 MHz that is divided into 4096 frequency
channels. Although the data was initially recorded with a native resolution of
4.785 $\mu$s, the visibility data was dumped at 2 s integration time for the
imaging purposes. The observations of the target were separated into 12 scans
of 15 minutes each. A primary calibrator, J0408-6545, was observed for 5
minutes at the beginning of the observation, as well as a complex gain
calibrator J0534+1927, which was observed in two sessions of 1 minute duration
before and after the 3 hour observation of the target. To accelerate the data
processing in this work (see Section 2.2 and 2.3), we only carried out our
analysis on a set of 5 minutes data around the reported arrival times of the
11 bursts (Caleb et al., 2020).

###  2.2 Data editing

Firstly, we corrected for the observed shift in the time stamps of the
visibility data which was offset by 2 s to their true values. This offset
error has been fixed for the latest MeerKAT raw data as discussed in Mauch et
al. (2020).

We have decided to unflag all the data flagged by the MeerKAT online flagger
111https://skaafrica.atlassian.net/wiki/spaces/ESDKB/pages/305332225/Radio+Frequency+Interference+RFI.
This procedure was applied because the effect of the online flagger to
transient detection is not well studied and transient emissions could be
mistaken as radio frequency interference (RFI). Due to the weak response of
the receiver at the edges (Mauch et al., 2020), we trimmed 210 and 186
frequency channels at the lower and higher edges of the frequency band. These
values were chosen based on manual inspection of the visibility data. Our
final bandwith for processing is then ranging from 900 to 1673 MHz.

To mitigate RFI, frequencies that are known to be corrupted for MeerKAT L-band
were flagged for short baselines ($<$1km). Given the large amount of data,
automated flagging algorithms are required to remove residual RFI. To this
end, we adopted different strategies to flag the calibrators and target data.
In the case of calibrators, we run a combination of automated algorithms
including, sumthreshold in AOFlagger (version 3.0.0; Offringa et al., 2012),
tfcrop and rflag from the Common Astronomy Software Applications, CASA(version
6.0.0; McMullin et al., 2007). The aggresive flagging applied to the
calibrators is necessary to obtain good calibration solutions. However, for
the target data, we decided to avoid algorithms that flag data based on
thresholding in the time direction in order to minimize removal of potential
transient candidates that only appear for a short period of time (Cendes et
al., 2018). We instead chose to use the threshold_channel_rms function in
AOFlagger which averages data of a given segment length in time and flag
frequency channels in which the rms of their amplitude values exceed a user
based threshold (3$\sigma$ level in our case). This step was repeated three
times during which we vary the segment length in a decreasing time intervals
(5 minutes, 1 minute and 10 seconds) to identify channels containing both
steady and intermittent RFI. After these procedures, about 40 $\%$ of our
target data was removed.

###  2.3 Data calibration and imaging

####  2.3.1 Initial calibration

Following data flagging, we performed standard data calibration method using
CASA tools. With a known absolute flux density ($\sim$ 17 Jy at 1.28 GHz and a
spectral index of
-1.179222https://github.com/IanHeywood/oxkat/blob/master/oxkat/1GC_04_casa_setjy.py),
we used the primary calibrator to derive the frequency-dependent complex gain
factors. We then bootstrapped its flux density to the secondary calibrator,
from which time-dependent gain solutions were determined. The solutions were
then applied to all datasets.

Afterwards, we divided the data into 7 subbands and performed 2 rounds of
phase-only self calibration in each of the subbands independently. The sky-
models to perform self calibration was generated with the fast generic
widefield imager WSCLEAN (version 2.9.0; Offringa & Smirnov, 2017; Offringa et
al., 2014). The sky-models from each 5 minute dataset contain sources with
high signal-to-noise ratio (S/N $>450$) that is sufficient for our self
calibration process to succeed.

The observations did not contain a polarized calibrator to perform an accurate
polarimetric calibration. The other alternative is to use the averaged
polarization calibration of the antennas obtained from other MeerKAT data,
which was calibrated using a polarized calibrator and apply them to our
measurement sets. The latter method, as described in Plavin et al. (2020), was
not feasible in our case because it requires the two datasets to have the same
reference antenna and there were no available MeerKAT datasets that had
polarization calibration using our preferred reference antenna
(${}^{\prime\prime}m007^{\prime\prime}$), which was chosen based on the S/N of
the parallel-hand calibration solutions.

####  2.3.2 Peeling

We identified two bright sources ($>100$ mJy/beam) dominating the FRB121102
field, that exhibit direction-dependent effects towards the center, especially
with the 2-s images. Such effects are undesirable as residual undeconvolved
sidelobes from those sources can potentially mimic transients in the image
plane (Frail et al., 2012; Bower et al., 2007).

Hence, we chose to remove these sources with the technique known as peeling
(Noordam, 2004). There are many existing approaches (Kazemi et al., 2011;
Smirnov, 2011; Intema et al., 2009) to perform peeling but we adopted similar
strategy to the one described in Williams et al. (2019). In this method, the
calibration terms $G_{bs}$ specific to the bright source to be peeled is
determined and it can be subtracted by replacing the model column with:

$MC_{cor}=\frac{1}{G_{bs}}M_{bs}(u,v),$ (1)

where $MC_{cor}$ is the corrected model column and $M_{bs}(u,v)$ an
approximated model of the bright source in (u,v) space.

In our case, we performed a phase-only followed by a bandpass self calibration
towards the source and the inverse of the gains $G_{bs}$ was calculated by
dividing the data with the corrected column. $M_{bs}(u,v)$ was generated by
predicting the model image of the bright source during self calibration. The
bright sources were peeled independently in each 7 subbands to capture the
variations of $G_{bs}$ across the frequency band. We implemented these
procedures using CASA and WSCLEAN tasks wrapped into customized python
scripts. Figure 1 shows a comparison of the 2-s images at 1.09 GHz (see
Section 2.3.3 for imaging method) before and after peeling where the rms value
at the position of the target went from $533$ to $410$ $\mu$Jy/beam.

\begin{overpic}[scale={0.49}]{Fig1_nopeel.png}
\put(9.0,12.0){\includegraphics[scale={0.15}]{Fig1_nopeel_zoom.png}}
\end{overpic}

\begin{overpic}[scale={0.49}]{Fig1_peel.png}
\put(9.0,12.0){\includegraphics[scale={0.15}]{Fig1_peel_zoom.png}}
\end{overpic}

Figure 1: Comparison of MeerKAT 2-s images of the FRB121102 field at 1.09 GHz
before (top panel) and after (bottom panel) peeling two bright sources (blue
circles) using the method described in section 2.3.2. The blue squares
indicate an area of $18^{\prime}\times 18^{\prime}$ around the position of
FRB121102. A zoom in of this region is shown in the bottom left corner of each
panel. The improvement in the image quality is clearly seen as the ripples
caused by the bright sources was mitigated after peeling, along with the
appearance of faint emission from real sources.

####  2.3.3 Imaging

Table 1: WSCLEAN main parameters during 2-s imaging. The other parameters were set to their default values. Parameter | Values
---|---
size | 6000
scale | 1.5 arcsec
auto-mask | 4
auto-threshold | 0.1
weight | Briggs 1
super-weight | 10
minuv-l | 100
taper-inner-tukey | 400
mgain | 0.85

To search for the bursts, we only divided the data into two frequency bands
centered around 1.09 GHz and 1.48 GHz. We review briefly the effect of this
spectral window setup in Section 4.5.5. We produced stokes I images of each
integration for each 5 minutes data set with WSCLEAN using the imaging
parameters in Table 1. These parameters were tuned to obtain reliable images
without decreasing drastically the sensitivity. The automatic masking scheme
is suitable to our science goal as it allows deep cleaning close to the
thermal noise value, but only constrained towards peaks with high S/N. A
circular taper was applied to the inner edges of the (u,v) samples as this
form of tapering was observed to decrease slightly the level of sidelobes. We
did not apply primary beam correction because our target is situated at the
phase center. Figure 2 illustrates typical examples of the 2-s images of the
two subbands when the bursts are not present.

The rms thermal noise of the images were evaluated within a $7^{\prime}\times
7^{\prime}$ square around FRB121102 position, using the method described in
(Swinbank et al., 2015) from which pixel values that are more than 4 standard
deviations away from the median are masked. Overall, the mean rms is 403
$\mu$Jy/beam and 259 $\mu$Jy/beam at 1.09 and 1.48 GHz with similar
elliptically restored beam size of $42^{\prime\prime}\times
13^{\prime\prime}$. For each sequence of images, we evaluated the peak
fluctuation over the same local region and estimated that only pixels with
peak S/N $>$5$\sigma$ can be considered as potential transient emission.

\begin{overpic}[scale={0.49}]{Fig2_1090MHz.png}
\put(58.0,10.0){\includegraphics[scale={0.21}]{Fig2_1090MHz_zoom.png}}
\end{overpic}

\begin{overpic}[scale={0.49}]{Fig2_1480MHz.png}
\put(58.0,10.0){\includegraphics[scale={0.21}]{Fig2_1480MHz_zoom.png}}
\end{overpic}

Figure 2: MeerKAT 2-s images of FRB121102 field at 1.09 GHz (Top) and 1.48 GHz
(Bottom) when the bursts are off. The blue squares indicate a
$7^{\prime}\times 7^{\prime}$ area centered around the position of the FRB and
the corresponding zoomed-in view is shown in the bottom right corner of each
image. For each zoom-in image, the grey ellipse in the bottom left corner
indicates the synthesized beam size and the white cross in the center
indicates the reported position of FRB121102. A known $\sim$ 3 mJy compact
source, J053153+3310
($\alpha=05^{\textrm{h}}31^{\textrm{m}}53.92^{\textrm{s}},\delta=33^{\circ}10^{\prime}20.07^{\prime\prime}$),
is also observed which we used for astrometry in Section 4.2 and Section 4.3

###  2.4 FRB limits

Among the main factors deciding the detection of FRB in our image plane is the
intrinsic width of the bursts. Considering that the pulse width of the 11 FRBs
are much shorter than our integration time, we would expect their peak flux
density to decrease due to averaging of the FRB signal in the visibility.
Based on the framework described in Trott et al. (2013) and Rowlinson et al.
(2016), the minimum FRB flux density that our 2-s image is sensitive to can be
estimated by:

$S_{min}=S_{snap,2s}(\frac{\Delta t}{w}),$ (2)

where $S_{snap,2s}$ is the rms in one snapshot 2-s image, $\Delta t$ is 2 s
and $w$ the duration of the FRB pulses. From equation (2), we can then define
the minimum detectable fluence as:

$F_{min}=S_{min}w=S_{snap,2s}\Delta t,$ (3)

By taking into account the rms values measured in Section 2.3.3, and using the
equation (3), we calculated that the theoretical fluence limit values in our
images are 0.80 and 0.51 Jy ms at 1.09 GHz and 1.48 GHz. Using the fluence
values reported in Table 1 of Caleb et al. (2020), we could then set
constraints on which burst we would expect to detect as illustrated in Figure
3, and from which we show that 5 bursts are detectable at 1.09 GHz, while 6 of
them lay above the detection limit at 1.48 GHz.

Figure 3: Theoretical fluence limits of detectable FRBs in the MeerKAT 2-s
snapshot images produced in this work. The detection limits were calculated
using the equation (3) derived from the frameworks in Trott et al. (2013) and
Rowlinson et al. (2016). The blue triangles are the bursts that we detected at
1.48 GHz while the red points were not observed. These bursts represents all
pulses detected in the dynamic spectrum by Caleb et al. (2020) and referred
with the same indices. ie. B01 refers to burst number 01.

##  3 Results

###  3.1 Burst detection

After inspecting the images, we have detected 6 bursts at the arrival times of
B02, B03, B05, B07, B08 and B11 (Labelled with the same indices as in Caleb et
al. (2020)) at the position of FRB121102 at 1.48 GHz with a peak S/N above
5$\sigma$. These constitute the first detections of FRBs or any transient
sources in 2 seconds radio images with the MeerKAT telescope. Figure 4
illustrates the 2-s images during the appearance of all the detected bursts.
To estimate the integrated flux density, we fitted a gaussian component with
the task imfit in CASA in a circular regions that enclose the burst structure.
The measured properties of each fitted burst are shown in Table 2. None of
these bursts were observed at 1.09 GHz above our peak detection threshold.
None of the bursts situated below our detection limits (see Figure 3) were
detected in the two subbands as expected.

###  3.2 Burst Positions

The fitted centroid location of the bursts are scattered within $\lesssim
2.70^{\prime\prime}$ of the milliarcsecond localization from the simultaneous
observations of European VLBI network and the Arecibo telescopes (Marcote et
al., 2017). Given that the position uncertainties (see Table 2) are inversely
proportional to the source S/N, we estimated that the strongest burst, B11,
which is offset by $\sim 1.07^{\prime\prime}$, gives the highest confidence in
our measured positions. Nevertheless, to account for all the 6 detected
bursts, we calculated the weighted average position of the burst emission
peaks by using as weights the inverse of the uncertainties from CASA. As a
result, we found a weighted average position of
$\alpha=05^{\textrm{h}}31^{\textrm{m}}58.68^{\textrm{s}}\pm
0.31^{\prime\prime},\delta=33^{\circ}08^{\prime}53.61^{\prime\prime}\pm
0.69^{\prime\prime}$ and a combined offset of $\sim 1.03^{\prime\prime}$. The
position offsets measured for the individual bursts is shown in Figure 5.

(a) Burst 02

(b) Burst 03

(c) Burst 05

(d) Burst 07

(e) Burst 08

(f) Burst 11

Figure 4: MeerKAT 2-s images of the detected bursts (White circles) at 1.48
GHz. The grey ellipse in the bottom left corner indicates the synthesized beam
size. Table 2: Properties of the bursts detected in the image plane at 1.48
GHz. The quoted arrival times are the time center of the 2-s visibility data
at the moment of detection on 10 September 2019. The peak $P_{\nu}$,
integrated flux density $S_{\nu}$ and position values were measured with the
CASA task imfit. The peak S/N is based on the rms value of the image during
detection. The systematic offsets are obtained with the procedure described in
Section 4.2

.  Burst Arrival time Peak flux density $P_{\nu}$ Flux density $S_{\nu}$ Peak
S/N Centroid position [J2000] Systematic offsets (UTC) (mJy) (mJy) RA (h:m:s)
DEC (∘:′:′′) RA (′′) DEC (′′) 02 03:58:31.4 1.85 $\pm$ 0.21 2.22 $\pm 0.46$
7.2 05:31:58.70 $\pm 0.67^{\prime\prime}$ 33:08:55.37 $\pm
2.87^{\prime\prime}$ $+0.51\pm 0.36$ $-0.09\pm 2.27$ 03 03:58:33.4 1.41 $\pm$
0.15 1.93 $\pm 0.14$ 5.4 05:31:58.61 $\pm 0.60^{\prime\prime}$ 33:08:54.75
$\pm 3.86^{\prime\prime}$ $-0.71\pm 0.26$ $-1.08\pm 2.37$ 05 04:26:10.7 1.58
$\pm$ 0.15 1.32 $\pm 0.30$ 6.1 05:31:58.80 $\pm 0.30^{\prime\prime}$
33:08:54.76 $\pm 2.70^{\prime\prime}$ $+0.58\pm 0.14$ $+2.07\pm 1.43$ 07
05:04:37.8 1.51 $\pm$ 0.22 1.66 $\pm 0.48$ 5.4 05:31:58.69 $\pm
1.03^{\prime\prime}$ 33:08:52.49 $\pm 4.12^{\prime\prime}$ $-0.19\pm 0.42$
$-1.62\pm 2.22$ 08 05:38:38.9 1.67 $\pm$ 0.17 1.60 $\pm 0.48$ 6.4 05:31:58.53
$\pm 0.74^{\prime\prime}$ 33:08:53.54 $\pm 2.78^{\prime\prime}$ $-0.08\pm
0.49$ $+0.91\pm 1.91$ 11 06:06:04.2 2.90 $\pm$ 0.16 2.83 $\pm 0.35$ 11.1
05:31:58.64 $\pm 0.75^{\prime\prime}$ 33:08:51.81 $\pm 1.96^{\prime\prime}$
$+0.03\pm 0.58$ $-0.47\pm 1.62$

Figure 5: Offsets of the fitted centroid position of the FRB121102 bursts
detected in this work (Blue points) to the milliarcsecond localization with
EVN (Marcote et al., 2017). The orange point indicates the weighted average
position based on the fitted position uncertainties with CASA. The horizontal
lines indicate the position errors for each point.

##  4 Discussion

###  4.1 Bursts S/N

In comparison to our detection limit in Section 2.4, B03 and B11 have the
lowest and highest S/N as expected. However, we could notice that the fitted
peak S/N for B07 in the 2-s image is among the lowest despite its high fluence
value of $\sim$ 2.23 Jy ms (see Figure 3). Similarly, we measured a high S/N
of B02 ($>$ 7.2) although it is among the bursts with the lowest fluence. The
discrepancies between the observed and expected S/N could arise from the
variation of rms between the images. At the arrival time of B07 for example,
the rms is slightly higher than the average value ($\sim 274\;\mu$Jy),
inducing imfit to decrease the fitted peak to $\sim 1.51$ mJy although the
peak directly extracted from the image pixel values is $1.94$ mJy. Further
discussion of flux density accuracy is discussed in the next section.

###  4.2 Flux density and position uncertainty

Due to the sparse (u,v) coverage of the 2 s data, the measured flux density
and position from the gaussian fitting can be affected by systematic errors
due to residual calibration effects or by the fluctuations of thermal noise in
the images. We use the observed compact source, J053153+3310 (with coordinates
$\alpha=05^{\textrm{h}}31^{\textrm{m}}53.92^{\textrm{s}},\delta=33^{\circ}10^{\prime}20.07^{\prime\prime}$
from Marcote et al. (2017)), with a flux density range comparable to our
bursts ($\sim 3$ mJy, $\sim 11\sigma$), to evaluate the flux density and
position uncertainties. Given the short angular separation of the compact
source from the target (offset by $\sim 100^{\prime\prime}$ which is about
three synthesized beam widths away), we estimated that both sources are
affected to the same variation of noises and share relatively the same
systematic uncertainties in their fitted values.

Hence, with the 2-s snapshot images in each 5 minute data, we fitted the
compact source with imfit the same way as the bursts. We defined its
fractional flux density error as the ratio of the root mean square of the flux
density variation errors with the mean flux density in each 5 minutes epoch.
As a result, we obtained an average fractional error of 12 $\%$ in flux
density values. Furthermore, we did not observe any significant increase in
flux density greater than the fractional error in the compact source during
the appearances of the bursts. However, the S/N of the compact source in the
B07 image decreased by 1, which indicates that the fitted properties of B07
could be under estimated.

We evaluated the systematic offsets in our position by comparing the MeerKAT
position of the compact source to the VLBI observations. The magnitude of the
offsets has a median of $0.45^{\prime\prime}$ in RA and $1.28^{\prime\prime}$
in Dec, with interquartile ranges of $0.57^{\prime\prime}$ and $1.62$
respectively. The systematic offsets measured at the arrival time of each
burst is shown in Table 2.

###  4.3 Astrometry

The early MeerKAT data suffered from few instrumental issues that could cause
systemic inaccuracies of the astrometry (Heywood et al., 2022; Knowles et al.,
2022; Mauch et al., 2020). We investigated if the discrepancies in our burst
positions were the results of these bugs or due to the limited dynamic range
of the 2-s images. To this end, we merged all the 5 minute chunks of data in
our analysis and imaged the concatenated measurement set ($\sim$ 50 minute
observations) to assess the position of J053153+3310 in a higher dynamic range
image. We obtained a noise level of 42 $\mu$Jy, yielding a S/N of $\sim$70 for
this compact source. With this deeper image, the fitted position of
J053153+3310 now deviates by $0.07^{\prime\prime}\pm 0.03$ in RA and
$0.46^{\prime\prime}\pm 0.13$ in DEC from its catalogue position, which is
smaller compared to the median offsets observed in the 2-s images, and
suggesting that the large position uncertainties are mainly from statistical
origin.

Further testing were applied based on cross-correlation operation between the
2-s images to probe if the peak of the cross-correlated image exhibit a
relative shift from the origin, which would indicate the presence of
astrometric errors of all the sources in the field resulting from calibration
or related to beam shape differences. Therefore, we chose one reference image
at the beginning of the observation and cross-correlate it with the 2-s images
prior to all the burst appearances. As a consequence, we did not observe a
shift in the output peaks with pre-burst images near (in time) the reference
image. However, a 1-pixel shift in the declination axis was always noticed for
images separated by more than $\sim 1$ hour to the reference image. Given that
the point spread function (PSF) major axis in our images is elongated along
the declination axis, these analysis suggest an astrometric uncertainty of
1.5” (size of one pixel) due to beam shape in our DEC position.

By taking into account the S/N and beam width, we estimated that the spread of
the FRBs and their position uncertainties in our 2-s images is fairly
comparable to the expectation and astrometry correction is not required for
the purpose of the present work. The low fractional error and position
uncertainty that we obtained decrease the probability that the bursts that we
have detected could be produced from imaging artefacts.

###  4.4 Non detection at 1.09 GHz

Despite the high range values in the rms of the images at 1.09 GHz ($\sim
400\mu$Jy), some of the bursts that we have detected are still above the
detection limit at this frequency but yielded no detection. The produced
residual images at the burst arrival times were verified visually but revealed
no significant peaks above the 5$\sigma$ detection threshold. Considering that
FRB121102 pulses showed some spectral variations, we suspect that the non
detection could be explained by the fact that these bursts peak at the higher
frequencies as can be seen with their dynamic spectra in Figure 1 of Caleb et
al. (2020). Spectral index measurements could further support this explanation
but the quality of the images declined rapidly in images produced with shorter
frequency resolution, making high level of uncertainty in flux density
estimation.

###  4.5 Review methods for future MeerKAT observations

In the next few subsections, we will briefly review and discuss the
methodology that we performed in Section 2 and discuss their practical
implication in searching for FRBs in future MeerKAT surveys or archival data.

####  4.5.1 Flagging

The flagging approach that we described in Section 2.2 efficiently removed all
suspected RFI without negatively affecting the detection of the bursts. Manual
inspection of the visibility data at the moment of appearance was still
checked and we flagged small residual RFI and the bursts were still observed
in the images. To investigate the efficiency of our method, we decided to
apply to our data the automated flagging algorithm
Tricolour333https://github.com/ratt-ru/tricolour, which is widely incorporated
into some of the latest MeerKAT data reduction pipelines such as
MeerKATHI444https://meerkathi.readthedocs.io/en/latest/ (Józsa et al., 2020)
or oxkat555https://ascl.net/code/v/2627(Heywood, 2020). As a results, the S/N
for B05, B08, and B07 decreased by $\sim 10\%$ and B02 was not detected.
Although, we tested Tricolour in its default mode and a customized strategy
might be required to optimize the algorithm, these tests show how an automated
flagging technique using thresholding following the time axis can affect the
detection of short transient emissions.

####  4.5.2 Bright source peeling

The removal of bright sources in Section 2.3.2 to minimize the sidelobe
effects is a computationally intensive process. In order to assess its
efficiency, we made 2-s images at the moment of the burst appearance without
peeling any sources. At 1.09 GHz where the bright sources are the most
dominant due to the steep slope of their spectral index, it became practically
unfeasible to differentiate genuine astronomical sources, such as the compact
source, from sidelobes in the forms of horizontal stripes (see Figure 1),
which could increase false detection rate. Furthermore, we also observed a
decrease of $\leavevmode\nobreak\ 10\%$ in S/N of the bursts at 1.48 GHz
without applying the peeling.

####  4.5.3 Weighting scheme

Further testing of the weight values during imaging shows that the bursts
remain detected above our detection threshold mainly from natural to the 0.8
value of the Briggs robust parameter (Briggs, 1995). We decided to use robust
1 because it provides more resolution gain without much degradation in S/N
from natural weighting mode. Given that a considerable number of MeerKAT
dishes ($\sim 40\;\text{antennas}$) is located around the $\sim$ 1 km inner
core, briggs values that come close to uniformly weighted scheme deteriorate
drastically the sensitivity due to the sparse distribution of the 2 s $(u,v)$
coverage.

####  4.5.4 Integration time

The majority of MeerKAT visibility measurement sets are dumped at 8 s
integration time. In order to understand the detectability of similar bursts
and fast transients in the MeerKAT archival data, we performed 8-s imaging
using the same parameters as in Table 1. The overall resulting rms image is
$150\;\mu$Jy, yelding a fluence detection limit of $1.2$ Jy ms using the
equation 3. In this case, B07 and B11 are the bursts that remain above the
detection limit but we only detected B11 with a reduced peak S/N ($\sim 6.8$)
compared to the 2-s image values. Figure 6 displays the detection of B11 in
the 8-s image. These findings show the importance of fast imaging and we
recommend future MeerKAT observations of FRBs to be operated using the 2
second dump rate. The computational expenses of the short timescale imaging is
discussed in Section 4.6.3.

Figure 6: MeerKAT image of B11 using 8s integration time. The rms in this
image is 150 $\mu$Jy.

####  4.5.5 Bandwidth

Instead of using the full band, we decided to split the data into two spectral
windows to avoid similar averaging issue as discussed in Section 4.5.4.
Indeed, since the bursts does not appear in all the band, their signals are
expected to be averaged out with larger bandwidths. Nonetheless, we produced
2-s images at the arrival times of the 11 bursts by combining all the
available frequencies. As a results, we did not observe improvement of the
image quality (rms $\sim 260\mu$Jy ), and only B02, B03 and B11 were detected.

###  4.6 Image subtraction

####  4.6.1 Reference image

Since we already know the location of our target source and the arrival times
of the bursts, it was straightforward to make the search towards a specific
region of the sky. However, in a given survey of an unknown field, it is often
challenging to identify a real transient source, especially at short
integration time, where imaging artefacts can occasionally appear and
increases the number of potential candidates. One of the most well known
techniques used in transient search surveys is difference image analysis (DIA)
(Tomaney & Crotts, 1996; Bond et al., 2001), in which a reference image which
is a model of the sky containing all steady-state sources, is subtracted from
a new image. This section is not intended to derive a generalized image
subtraction method for MeerKAT data, which can be a complex topic that could
be explored in future studies, but rather a tentative framework to show its
capability. Advanced discussions of the subject from previous works could be
found in Sánchez et al. (2019), Zackay et al. (2016), Bramich (2008) or Alard
(2000).

In contrast to existing methods, where the reference image is constructed only
from the preceding images of a sequence, we propose a new method where the
subsequent images are also considered. Such procedure is inspired by the
moving average technique widely known in economics (Chou, ). Given an image
sequence of $N$ samples $\\{I\\}=\\{I_{1},I_{2},I_{3}..,I_{N}\\}$, the
reference image $R_{i}$ of the $i-$th image, $I_{i}$, to be subtracted is
defined as:

$\centering R_{i}=\frac{1}{2n}\sum_{\begin{subarray}{c}j=i-n\\\ j\neq
i\end{subarray}}^{i+n}I_{j},\@add@centering$ (4)

where $n$ is a tunable parameter that indicates the number of images in both
sides of the $i-$th image to include in the summation. We tested our method
with different values of $n$ and observed that the overall bursts S/N in the
subtracted images increase by $20\%$ typically for $n=1$ to $5$ and tend to
follow a flat curve afterwards. Figure 4 illustrates the evolution of S/N for
B11 in the generated difference images for $n=1$ to $n=20$. For B11 only, we
noticed a brief up and down trend after $n=5$ that was not seen in the S/N
curve of the other bursts. Based on Figure 4, it is tempting to claim that
$n=7$, which provided the maximum S/N is the optimal value, but we verified
from manual inspection that it is simply due to small decrease of thermal
noise from the added images at that period. Moreover, keeping the value of $n$
as small as possible is essential to preserve images with similar PSF that are
produced from visibility with nearly the same (u,v) sampling distribution.

Figure 9 demonstrates our difference imaging procedures and its effect in a
$38^{\prime}\times 38^{\prime}$ region around the burst position. The mean rms
values of the subtracted images are about $3$ to $5\%$ lower than the original
images and the bursts were still observed above $5\sigma$ except for B03 with
$3\sigma$ level. The non detection of B03 is due to the presence of B02 when
constructing the reference image at that moment, given that the appearance of
the two bursts are only separated by 2 s. This shows that our proposed method
is mainly limited to one-off events like most FRBs, or to repeating sources
that emit pulses within sufficiently large time interval ($\geqslant 20$ s for
$n=5$). Additionally, constant sources in the $38^{\prime}\times 38^{\prime}$
area were almost completely removed and the occasional low level remaining
artefacts are unclean subtraction from extended or bright sources. We show in
Figure 9 the subtracted images for all 6 bursts.

Figure 7: Signal-to-noise ratio (S/N) of B11 in the subtracted images for
different values of $n$ (see equation 4), to build the reference image.

(a)

(b)

(c)

Figure 8:  Illustration of an image subtraction procedure as described in
Section 4.6 for an area of $38^{\prime}\times 38^{\prime}$ around FRB121102.
The figures are showing the reference image (a), B11 field before (b) and
after (c) subtraction of the reference image. The subtracted image shows that
most sources except B11 (White circle in the center) were removed.

(a) Burst 02

(b) Burst 03

(c) Burst 05

(d) Burst 07

(e) Burst 08

(f) Burst 11

Figure 9: MeerKAT 2-s image around an area of $7^{\prime}\times 7^{\prime}$ of
the detected bursts after applying image subtraction (see Section 4.6).

####  4.6.2 Blind search mode

In order to show the potential advantages of our method in a blind search
mode, we apply the procedure described in Section 4.6.1 to all 2-s images
produced from each 5 minute data and use the automated source finder
PySE666https://tkp.readthedocs.io/en/release4.0/tools/pyse.html?highlight=pyse
from the TraP pipeline (Swinbank et al., 2015) to identify the remaining point
sources in the subtracted images. We set the detection threshold to 6$\sigma$
to decrease the number of candidates and mask the bright source positions to
exclude eventual residual effects. We constrained the search to half of the
images (about $1.25{{}^{\circ}}$ around the center) where 80$\%$ of the total
flux density of the image resides and where the PSF is similar. As a results,
only B07,B08 and B11 were detected and there were 23 false detections observed
in a total of 1380 images, from which we calculated the fraction of false
detection per synthesized beam element to be around $1.34\times 10^{-6}$. In a
blind search mode, automatic searches through the difference images are often
performed with the use of machine learning techniques to classify real
transients from artefacts (Goldstein et al., 2015; Wright et al., 2015), but
in our case, the remaining candidates can also be reduced by searching for
dispersed pulses in the dynamic spectrum of the raw voltage. Furthermore, more
than $60\%$ of FRBs detected and published to date (Spanakis-Misirlis, 2022)
have a fluence comparable or even stronger ($\sim$ 4 Jy ms to 3500 Jy ms) than
B11 and we would expect to detect them with our method.

####  4.6.3 Computational expenses

Since our technique requires to perform imaging for each integration, it is
important to assess the computational cost to run this approach. In terms of
data storage, we are only considering to keep the 2-s dump rate around the
time intervals where serious candidates are triggered and the data could be
averaged to the standard integration time of 8 second otherwise. The data rate
of the 2-s visibilities is 0.55 TB per hour for
MeerKAT777https://skaafrica.atlassian.net/wiki/spaces/ESDKB/pages/277315585/MeerKAT+specifications#Visibility-
integration-times, hence if we only keep for instance a 1 minute dataset due
to an eventual candidates, only 9 GB of memory is needed.

With regards to imaging, the gridding step, which is the main operation that
requires heavy processing, is often implemented with the use of a convolution
kernel of $5\times 5$ pixel wide, which means that 25 additions and
multiplications will be operated for each visibility. One complex
multiplication is a 7 float operations, whereas the addition involves 2 float
operations, from which we can estimate that the convolution of one visibility
requires $9\times 50$ float operations. The number of visibility points
involved in a stokes I 2-s imaging for the full MeerKAT array is given by
$n_{polarization}\times n_{channels}\times{n_{baseline}}=2\times 4096\times
2016$, thus the computation of gridding need about $\sim 7.5$ GB float
operations, which could be achieved in less than 1 second with a GPU or a
multicore CPU implementation (Veenboer & Romein, 2020).

##  5 Conclusions

The detection of 11 bursts from FRB121102 was reported by Caleb et al. (2020)
with the MeerKAT radio telescope using high time and frequency resolution
filterbank data. In this work, we investigated the ability of MeerKAT to
detect these bursts in 2-s snapshot images produced with visibility data.

We detected 6 out of the 11 bursts in the images above a detection threshold
of $5\sigma$ at 1.48 GHz. These represent the first detections of FRBs and
radio transients in MeerKAT image produced with 2 seconds timescale. The 6
bursts were detected in accordance to our expectation with a fluence detection
limit of $\sim 0.512$ Jy ms at the corresponding frequency. Additionally, the
analysis of their properties revealed an $\sim$ arcsec precision of their
localization in the images which is highly required to tie the FRB position
with their potential host galaxy.

We estimated from further investigation that the detection is strongly limited
by the integration time and we recommend future MeerKAT observations of FRBs
to be operated using the 2 second dump rate, which is the fastest supported
integration period for this telescope.

We explored a new approach to the difference imaging analysis from which each
image to be subtracted has their own reference image generated from their
respective neighbor images. Such method takes advantage of the similarity of
the $(u,v)$ distribution in the 2-s visibility data and could be adequately
suitable to detect FRB-like transients in fast images.

## Acknowledgements

This paper employs a MeerKAT data resulted from a Director’s Discretionary
Time (DDT) proposal (Project ID: DDT-20190905-MC-01). 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 authors acknowledge the contribution of all those
who designed and built the MeerKAT instrument.

Research reported in this paper is supported by the Newton Fund project, DARA
(Development in Africa with Radio Astronomy), and awarded by the UK’s Science
and Technology Facilities Council (STFC) \- grant reference ST/R001103/1.

J.C.A. acknowledges the MeerTRAP team in collaboration with the ThunderKAT
programme for allowing the access to the data in achieving this work. MeerTRAP
is a project to continuously use the MeerKAT radio telescope to search the
radio sky for pulsars and fast radio transients and to rapidly and accurately
locate them. ThunderKAT is the MeerKAT Large Survey Projects (LSPs) for image-
domain (explosive) radio transients.

M.C. acknowledges support of an Australian Research Council Discovery Early
Career Research Award (project number DE220100819) funded by the Australian
Government and the Australian Research Council Centre of Excellence for All
Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number
CE170100013.

M.C, F.J and B.W.S acknowledge funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation pro-
gramme (grant agreement No 694745).

We acknowledge the use of the ilifu cloud computing facility -
www.ilifu.ac.za, a partnership between the University of Cape Town, the
University of the Western Cape, the University of Stellenbosch, Sol Plaatje
University, the Cape Peninsula University of Technology and the South African
Radio Astronomy Observatory. The ilifu facility is supported by contributions
from the Inter-University Institute for Data Intensive Astronomy (IDIA - a
partnership between the University of Cape Town, the University of Pretoria
and the University of the Western Cape), the Computational Biology division at
UCT and the Data Intensive Research Initiative of South Africa (DIRISA).

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding authors.

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