PASA 2024

# Murchison Widefield Array rapid-response observations of the short GRB
180805A

A. P. Beardsley1 B. Crosse2 D. Emrich3 T. M. O. Franzen2 B. M. Gaensler4,11,5
L. Horsley3 M. Johnston-Hollitt2 D. L. Kaplan7 D. Kenney2 M. F. Morales8 D.
Pallot9 K. Steele3 S. J. Tingay2,11,10 C. M. Trott2,11 M. Walker3 R. B.
Wayth2,11 A. Williams3 C. Wu9
1School of Earth and Space Exploration  Arizona State University  Tempe  AZ
85287  USA
2International Centre for Radio Astronomy Research  Curtin University  Bentley
WA 6102  Australia
3Curtin Institute of Radio Astronomy  Curtin University  GPO Box U1987  Perth
WA 6845
4Sydney Institute for Astronomy  School of Physics  The University of Sydney
NSW 2006  Australia
5Dunlap Institute for Astronomy and Astrophysics  University of Toronto  ON
M5S 3H4  Canada
6School of Chemical & Physical Sciences  Victoria University of Wellington
Wellington 6140  New Zealand
7Department of Physics  University of Wisconsin–Milwaukee  Milwaukee  WI 53201
USA
8Department of Physics  University of Washington  Seattle  WA 98195  USA
9International Centre for Radio Astronomy Research  University of Western
Australia  Crawley 6009  Australia
10Istituto Nazionale di Astrofisica (INAF) – Istituto di Radio Astronomia  Via
Piero Gobetti  Bologna  40129  Italy
11ARC Centre of Excellence for All-sky Astrophysics (CAASTRO)
G. E. Anderson1 E-mail<EMAIL_ADDRESS>P. J. Hancock1 A.
Rowlinson2,3 M. Sokolowski1 A. Williams1 J. Tian1 J. C. A. Miller-Jones1 N.
Hurley-Walker1 K. W. Bannister4 M. E. Bell5 C. W. James1 D. L. Kaplan6 Tara
Murphy7 S. J. Tingay1 B. W. Meyers1,8 M. Johnston-Hollitt1 R. B. Wayth1
1International Centre for Radio Astronomy Research, Curtin University, GPO Box
U1987, Perth, WA 6845, Australia  2Anton Pannekoek Institute, University of
Amsterdam, Postbus 94249, 1090 GE, Amsterdam, The Netherlands  3Netherlands
Institute for Radio Astronomy (ASTRON), PO Box 2, 7990 AA Dwingeloo, The
Netherlands  4Australia Telescope National Facility, CSIRO Astronomy and Space
Science, PO Box 76, Epping, NSW 1710, Australia  5University of Technology
Sydney, 15 Broadway, Ultimo NSW 2007, Australia  6Department of Physics,
University of Wisconsin-Milwaukee, 1900 E. Kenwood Boulevard, Milwaukee, WI
53211, USA  7Sydney Institute for Astronomy, School of Physics, The University
of Sydney, NSW 2006, Australia  8Department of Physics & Astronomy, University
of British Columbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada

###### Abstract

Here we present stringent low-frequency (185 MHz) limits on coherent radio
emission associated with a short-duration gamma-ray burst (SGRB). Our
observations of the short gamma-ray burst (GRB) 180805A were taken with the
upgraded Murchison Widefield Array (MWA) rapid-response system, which
triggered within 20 s of receiving the transient alert from the Swift Burst
Alert Telescope, corresponding to 83.7 s post-burst. The SGRB was observed for
a total of 30 min, resulting in a $3\sigma$ persistent flux density upper-
limit of 40.2 mJy beam-1. Transient searches were conducted at the Swift
position of this GRB on 0.5 s, 5 s, 30 s and 2 min timescales, resulting in
$3\sigma$ limits of $570-1830$, $270-630$, $200-420$, and $100-200$ mJy
beam-1, respectively. We also performed a dedispersion search for prompt
signals at the position of the SGRB with a temporal and spectral resolution of
0.5 s and 1.28 MHz, respectively, resulting in a $6\sigma$ fluence upper-limit
range from 570 Jy ms at DM$=3000$ pc cm-3 ($z\sim 2.5$) to 1750 Jy ms at
DM$=200$ pc cm-3 ($z\sim 0.1)$, corresponding to the known redshift range of
SGRBs. We compare the fluence prompt emission limit and the persistent upper-
limit to SGRB coherent emission models assuming the merger resulted in a
stable magnetar remnant. Our observations were not sensitive enough to detect
prompt emission associated with the alignment of magnetic fields of a binary
neutron star just prior to the merger, from the interaction between the
relativistic jet and the interstellar medium (ISM) or persistent pulsar-like
emission from the spin-down of the magnetar. However, in the case of a more
powerful SGRB (a gamma-ray fluence an order of magnitude higher than GRB
180805A and/or a brighter X-ray counterpart), our MWA observations may be
sensitive enough to detect coherent radio emission from the jet-ISM
interaction and/or the magnetar remnant. Finally, we demonstrate that of all
current low frequency radio telescopes, only the MWA has the sensitivity and
response times capable of probing prompt emission models associated with the
initial SGRB merger event.

###### doi:

10.1017/pas.2024.xxx

###### keywords:

gamma-ray bursts – gamma-ray bursts: individual: GRB 180805A – radio
continuum: transients – neutron star mergers.

##  1 Introduction

The detection of gravitational waves from the binary neutron star (BNS) merger
GW 170817, and its association with the short-duration gamma-ray burst (GRB)
170817A, heralds a new era of observational astrophysics (Abbott et al.,
2017a, b). This discovery demonstrated the importance of rapid multi-
wavelength follow-up, not only for providing complementary insight into the
central engine, the energy released, and the final merger remnant, but
primarily for localising the gravitational wave (GW) event. However, the
unconstrained localisation capability of the dedicated gravitational wave
detectors such as Advanced LIGO and Virgo (aLIGO/Virgo; up to thousands of
square degrees, eg Abbott et al., 2016) still limits the efficiency of even
the widest field-of-view instruments to identify the electromagnetic
counterpart.

In order to improve our understanding of the early-time (seconds to minutes)
electromagnetic counterparts to gravitational wave events involving BNS and
neutron star and black hole (NS-BH) mergers, we have devised a program to
exploit their association with short-duration GRBs (SGRBs). This is achieved
by using the upgraded Murchison Widefield Array (MWA, Tingay et al., 2013;
Wayth et al., 2018) rapid-response system (Hancock et al., 2019b), which
allows the MWA to respond to SGRB transient alerts, such as those broadcast by
the Neil Gehrels Swift Observatory (hereafter Swift; Gehrels et al., 2004)
Burst Alert Telescope (BAT) and the Fermi Gamma-ray Space Telescope (hereafter
Fermi) Gamma-ray Burst Monitor (GBM; Meegan et al., 2009). Using this system,
the MWA can automatically observe the event within seconds of its discovery
(e.g. GRB 150524A; Kaplan et al., 2015). As SGRBs are usually better localised
than GW events, performing triggered observations on SGRBs provides the
fastest and most efficient method for localising GW radio signatures,
bypassing the need for tiling large areas of sky (e.g. Kaplan et al., 2016) or
targeting a sample of nearby galaxies (e.g. Hallinan et al., 2017). Such
triggered observations will provide a template for the expected radio
brightness and timing properties of GW mergers, which will in-turn inform the
follow-up of future aLIGO/Virgo GW events by wide-field instruments like the
MWA, the Australian Square Kilometre Array Pathfinder (ASKAP; Hotan et al.,
2014) and the low frequency component of the Square Kilometre Array (SKA-Low).

On the very earliest timescales (seconds to minutes post-burst), merging BNS
and NS-BHs are expected to produce prompt, fast radio burst (FRB)-like
signals. The existence of repeating FRBs (Spitler et al., 2016; CHIME/FRB
Collaboration et al., 2019b; The CHIME/FRB Collaboration et al., 2019; Fonseca
et al., 2020) and a high volumetric rate ($\gtrsim 10^{4}$ Gpc-3 yr-1; Ravi et
al., 2019) argue against SGRBs being the sole progenitors of FRB. However, it
is entirely possible that observed FRBs are produced by two populations of
progenitors (Caleb et al., 2019), or that repeat bursts are produced by the
orbital interactions of compact objects which later merge in an SGRB (e.g.
Wang et al., 2016). Indeed, the volumetric rate of bright FRBs — only two of
which have been observed to repeat despite significant follow-up observations
(Kumar et al., 2019, 2020; James et al., 2020) — is remarkably consistent with
that of the SGRB population (James et al., 2019c).

Several models exist that predict coherent radio emission either just prior,
during, or shortly following a SGRB/BNS/NS-BH merger. For example, prompt FRB-
like emission is predicted to be produced just prior to the merger by magnetic
braking as the magnetic fields of the NSs are synchronised to the binary
rotation (Hansen & Lyutikov, 2001; Lyutikov, 2013). A low-frequency radio
burst could also be generated when the potential GRB jet first interacts with
the surrounding interstellar medium (ISM; see Usov & Katz, 2000). Following
the merger, a supramassive, rapidly rotating and highly magnetised NS, often
referred to as a magnetar, may be produced before either becoming stable or
further collapsing into a black hole within seconds to hours (Usov, 1992;
Rowlinson et al., 2013). The remnant magnetar may produce pulsar-like radio
pulses for its lifetime, which steadily fade as it spins down through the
release of dipole radiation. As it is expected that such emission will be
beamed along the magnetic axis (as is the case for standard pulsars), it can
be argued that this emission will be aligned with the relativistic jet axis
that produced the SGRB, meaning it may remain preferentially pointed towards
Earth and therefore observable as persistent radio emission (Totani, 2013). In
the event of an unstable magnetar, an FRB could be produced through the
ejection of its magnetosphere as it collapses into a black hole (Falcke &
Rezzolla, 2014; Zhang, 2014). This collapse could occur between 2 minutes to 3
hours post-merger depending on the mass, spin, and spin-down-rate of the
remnant and the nuclear equation-of-state (Ravi & Lasky, 2014). The detection
of such prompt radio emission from SGRBs would allow us to distinguish between
different binary merger models and scenarios, which would in-turn constrain
the equation-of-state of nuclear matter (Lasky et al., 2014). For a review of
the coherent radio emission mechanisms from compact binary mergers see
Rowlinson & Anderson (2019).

Radio signals are delayed as they propagate through astrophysical plasmas,
with low-frequency signals arriving later than those at high frequencies. This
delay gives low-frequency telescopes such as the MWA the potential to catch a
radio signal emitted simultaneously, or even before, the SGRB (Inoue, 2004),
provided they are capable of rapidly responding to transient alerts. The
rapid-response (triggering) mode on the MWA enables us to study the very
earliest low-frequency signatures from GRBs as it can be on target within
seconds of an alert (e.g. the MWA was on-target 23s following the Swift-
detected SGRB 150424A; Kaplan et al., 2015). Since the second half of 2018,
the MWA has been running an updated rapid-response mode that is capable of
performing triggered observations on VOEvents, which are the standard for
broadcasting alerts related to transient events (Seaman et al., 2011). Using
the ‘4 Pi Sky VOEvent Broker’ software (Staley & Fender, 2016) and the Comet
VOEvent client (Swinbank, 2014), we are able to monitor, parse and filter the
VOEvent streams from both Swift and Fermi, allowing for triggers to be
automatically pushed to the telescope for an observation override. Another
useful addition to the MWA rapid-response mode is the Sun suppression
subroutine in the MWA back-end scheduling web service, which places the Sun in
a primary beam null during daytime triggers while also optimising the
sensitivity of the target within the primary beam (for the full details on
this system and the GRB triggering strategy see Hancock et al., 2019b).

In the following we present the first rapid-response observations of a SGRB
(GRB 180508A) using the upgraded MWA rapid-response mode. In Section 2, we
describe the rapid-response observations and data analysis of GRB 180805A,
which pulls together different data processing and calibration techniques used
for MWA transient and continuum science. We then describe the transient and
variable search we performed using the Robbie workflow (Hancock et al.,
2019a), followed by the image dedispersion techniques we employed to perform a
dispersed transient search. In Section 3, we provide constraints on the prompt
emission from GRB 180508A over different timescales and dispersion measures
(DM), which is then followed by a discussion of the model remnant constraints
that can be placed on GRB 180508A given our upper limits in Section 4. We also
discuss the overall performance and potential of the MWA rapid-response mode
in comparison with other low-frequency facilities with programs designed to
probe for FRB-like emission associated with GRBs, and provide suggestions for
a similar transient mode-of-operation for SKA-Low.

##  2 MWA Observations and Data Analysis

The MWA rapid-response observations that we present in this paper are of GRB
180805A, which was detected by Swift-BAT at 09:04:49 UT on 2018 August 5
(trigger ID 851829; D’Avanzo et al., 2018). Refined analysis of the BAT light
curve determined the burst had a $T_{90}$111The time interval for which 5% to
95% of the event’s fluence was contained (Sakamoto et al., 2011) of $1.68\pm
0.41$ s (Palmer et al., 2018) placing this GRB within the short-duration class
($T_{90}\leq 2$ s; Kouveliotou et al., 1993), and showed no evidence for
extended emission. However, it is worth noting that the temporal and spectral
properties of this GRB lie within the parameter space for which there may be
contamination from long-duration GRBS (LGRBs, produced by core-collapse
supernovae; e.g. Galama et al., 1999; Stanek et al., 2003) so there is a small
chance this source could have a collapsar origin.

Its X-ray afterglow was subsequently detected by the Swift X-ray Telescope
(XRT) and localised to the position
$\alpha\mathrm{(J2000.0)}=11^{\mathrm{h}}10^{\mathrm{m}}15\overset{\mathrm{s}}{.}90$
and
$\delta(\mathrm{J2000.0})=-45^{\circ}19^{\prime}56\overset{{}^{\prime\prime}}{.}0~{}$
with a 90% confidence of $2\overset{{}^{\prime\prime}}{.}5$ (Beardmore et al.,
2018). The time-averaged spectrum from T+0.04 to T+1.90 sec is best fit by a
simple power-law model, with an index of $1.58\pm 0.32$ (Palmer et al., 2018).
No other follow-up was reported.

In the following, we describe the rapid-response MWA observations of GRB
180805A, and outline the data processing pipeline and the software we employed
to carry out transient searches for associated short-duration radio emission.

###  2.1 MWA rapid-response observations of GRB 180805A

The triggered Murchison Widefield Array (MWA; Tingay et al., 2013)
observations of GRB 180805A were taken in the Phase II extended baseline
configuration (Wayth et al., 2018) at a central frequency of 185 MHz
(bandwidth of 30.72 MHz) using the standard correlator mode, which has a
temporal and spectral resolution of 0.5 s and 10 kHz, respectively. The
position of GRB 180805A was observed for a total of 30 min (15 $\times$ 2 min
snapshots).

Each of the 15 MWA snapshot observations of GRB 180805A are summarised in
Table 1, which includes the observation identification number (ObsID), start
time, and pointing position. As a result of the Sun avoidance code, the
source’s right ascension and declination were not tracked in a standard way,
which meant the GRB was in a different position with respect to the primary
beam for each snapshot. This was particularly the case between ObsIDs
1217495544 and 1217495664, where the pointing centre changed by nearly 3 deg.
This large shift also resulted in the serendipitous placement of the bright
radio source Centaurus A (Cen A) in a 10% primary beam sidelobe for the
remainder of the observation.

Table 1: MWA 2-minute snapshot observations of GRB 180805A

ObsID | Start Time | Time | Pointing | Offset | RMS${}^{\mathrm{~{}c}}$
---|---|---|---|---|---
| 2018-08-05 | post-burst | RA | Dec |  |
| (UT) | (min) | (deg) | (deg) | (deg) | (mJy)
1217495184 | 9:06:06 | $1.32$ | $166.58$ | $-42.715$ | 2.71 | 35
1217495304 | 9:08:06 | $3.32$ | $167.08$ | $-42.715$ | 2.64 | 35
1217495424 | 9:10:06 | $5.32$ | $167.581$ | $-42.715$ | 2.62 | 36
1217495544 | 9:12:06 | $7.32$ | $168.081$ | $-42.714$ | 2.64 | 34
1217495664 | 9:14:06 | $9.32$ | $158.201$ | $-39.878$ | 8.78 | 63
1217495784 | 9:16:06 | $11.32$ | $158.702$ | $-39.878$ | 8.49 | 61
1217495904 | 9:18:06 | $13.32$ | $159.202$ | $-39.877$ | 8.22 | 61
1217496024 | 9:20:06 | $15.32$ | $159.703$ | $-39.877$ | 7.95 | 60
1217496144 | 9:22:06 | $17.32$ | $160.204$ | $-39.877$ | 7.68 | 59
1217496264 | 9:24:06 | $19.32$ | $160.704$ | $-39.876$ | 7.43 | 58
1217496384 | 9:26:06 | $21.32$ | $161.205$ | $-39.876$ | 7.19 | 55
1217496504 | 9:28:06 | $23.32$ | $161.706$ | $-39.876$ | 6.95 | 53
1217496624 | 9:30:06 | $25.32$ | $162.206$ | $-39.876$ | 6.73 | 56
1217496744 | 9:32:06 | $27.32$ | $162.707$ | $-39.875$ | 6.52 | 56
1217496864 | 9:34:06 | $29.32$ | $163.207$ | $-39.875$ | 6.33 | 57

All raw data corresponding to the listed ObsIDs are public and can be accessed
via the the MWA All-sky Virtual Observatory (https://asvo.mwatelescope.org/)
under project code D0009.
${}^{\mathrm{~{}c}}$ The RMS at the Swift-XRT position of GRB 180805A as
output by Robbie (see Section 2.2.2).

While each snapshot lasts 2 min, the first 4 s and last 5.5 s of each
observation are flagged. This means that only 110.5 s of data are collected
per snapshot, which results in a loss of 9.5 s of data between each
observation (142.5 s over the total 30 min integration). However, as we expect
SGRBs to be at cosmological redshifts, any coherent radio signal will be
highly dispersed and take tens of seconds to cross the 30.72 MHz bandwidth at
185 MHz (see Section 2.1.1). Therefore the missing data cannot entirely
obscure a dispersed signal, it will merely result in some loss in signal-to-
noise following image-based dedispersion (technique described in Section
2.2.3).

####  2.1.1 Latencies associated with the MWA trigger of GRB 180805A

The VOEvent associated with the Swift-BAT detection of GRB 180805A was
circulated 64 s post-burst (approx 18 m before the corresponding GCN Circular
was published online222https://gcn.gsfc.nasa.gov/gcn3/23074.gcn3). The MWA
rapid-response front-end web service received the VOEvent via the Comet client
1 s later, at which point the event was added to a queue that ensures incoming
events are sent to the Swift-Fermi VOEvent handler in chronological order. The
handler parses all incoming VOEvents for events of interest, and in this case
captured the event associated with GRB 180805A, identifying it as a real GRB
and triggering MWA observations. The MWA was on-target and observing GRB
180805A within 20 s of the Swift broadcast of the VOEvent. A time-line of the
detection, alert, and response is summarised in Table 2. The code that queues
incoming VOEvents and passes them to the various VOEvent handlers (event 3 in
Table 2) resulted in a delay of 2.8 s for GRB 180805A. At this point, the
front end VOEvent parser sent a request to the back-end web-service on the
telescope requesting an immediate observation. It took 1.8 s for the back-end
to calculate a pointing direction that placed the Sun in a primary beam null
for the first observation (since this was a day-time observation), calculate
the best calibrator to observe following the 30 min GRB observation, and then
schedule the observations.

The MWA was on target at 09:06:06 UT (77 s post-burst), however, the
correlated data recording started 2.7 s later (this delay is related to
internal MWA correlator setting changes) and the next 4 s of data were
automatically flagged by the AOFlagger algorithm (Offringa et al., 2010, 2012)
in order to remove bad data from the first scan integration boundary. However,
it is possible that a subset of this 4 s may still contain good data if using
the MWA Phase II correlator, so future GRB data processing may be able to
retrieve additional seconds of good data at the start of the observation. For
GRB 180805A, the very first non-flagged timestep was therefore collected by
the MWA at 09:06:12.7 UT, just 83.7 s following the Swift detection.

Table 2: Timeline for MWA triggered observations of GRB 180805A UT Time | Latency | Event
---|---|---
(2018-08-05) | (s) | # | Description
09:04:49 | $0$ | 1 |  Swift-BAT detects GRB 180805A
09:05:53 | $64$ | 2 |  Swift VOEvent alert notice circulated
09:05:54 | $65$ | 3 | MWA front-end receives VOEvent via Comet and is queued for processing
09:05:56.8 | $67.8$ | 4 | VOEvent handler processes VOEvent
09:05:57.1 | $68.1$ | 5 | VOEvent handler sends trigger to back-end to schedule observations
09:05:58.9 | $69.9$ | 6 | MWA schedule is updated
09:06:06 | $77$ | 7 | MWA is on target
09:06:12.7 | $83.7$ | 8 | MWA begins observations of SGRB 180805A

###  2.2 MWA data processing

In the following we describe the semi-automated transient reduction pipeline
used to process the triggered MWA observations of GRB 180805A (Section 2.2.1).
The final images output by this transient reduction pipeline are then
processed using the batch processing work-flow for detection of radio
transients and variables using Robbie (Hancock et al., 2019a, see Section
2.2.2). We then provide a description of the dedispersion technique we employ
to search for prompt, dispersed signals (e.g. Tingay et al., 2015; Sokolowski
et al., 2018, see Section 2.2.3).

In order to search for coherent low-frequency radio emission associated with
GRB 180805A, it is necessary to search over a wide range of cadences. The
choice of transient timescales must reflect the expected dispersion delay of
the prompt radio signals for the observing frequency and bandwidth. Taking
into account both extragalactic and Galactic ($DM=90$ cm-3 pc) contributions
to the dispersion measure, Hancock et al. (2019b, see their Figure 1)
determined that at 185 MHz, the arrival time of the signal could be delayed
between $28-277$ s for the observed SGRB redshift range of $0.1<z<2.5$
(Rowlinson et al., 2013) for a line-of-sight through a Galactic latitude of
$b=13.97^{\circ}$. In addition, they also determined it could take between
$9-91$ s for that same signal to cross the 30.72 MHz MWA observing band at 185
MHz. In most cases, the MWA will likely be on target fast enough, and will
integrate for long enough (usually 30 min), to catch any prompt signal emitted
during and/or several minutes following the merger (i.e. from a remnant
magnetar) for most SGRBs. For this particular experiment, we therefore chose
to create images on 5 s, 30 s, and 2 min timescale for transient searches,
which accommodate the length of time we might expect an associated prompt
radio signal to traverse the 30.72 MHz bandwidth for the lowest ($z\approx
0.1$), average ($z\approx 0.7$) and highest ($z\approx 2.5$) redshifts known
for SGRBs (Rowlinson et al., 2013). We also create images on 0.5 s timescales,
which is the native temporal resolution of the MWA Phase II correlator. Note
that while we expect the prompt radio signal from a GRB to take more than 0.5
s to cross the MWA band, we search for transients on these short timescales as
a demonstration of the MWA’s capability to create quality images on its native
temporal resolution due to its excellent instantaneous $(u,v)$ coverage and
moderate sensitivity. Imaging on these short timescales is extremely useful
for much closer transients, such as the related project to follow-up
aLIGO/Virgo-detected BNS and NS-BH mergers (Kaplan et al., 2016). A mean image
of the 2 min snapshots is also created and used to search for associated
persistent emission (e.g. Totani, 2013). We also generate 24 coarse channel
images (corresponding to a bandwidth of 1.28 MHz) on each 0.5 s timescale to
facilitate a more sensitive search for dispersed, prompt, coherent signals
over a wide range of dispersion measures (see Section 2.2.3).

####  2.2.1 MWA transient reduction pipeline

The MWA triggered observation of GRB 180805A was processed using a semi-
automated pipeline called MWA-fast-image-
transients,333https://github.com/PaulHancock/MWA-fast-image-transients which
is specifically designed for the reduction of transient MWA imaging data in
preparation for transient analysis. It is therefore capable of creating images
over a wide variety of timescales to match the coherent radio transient
timescales expected from GRBs. This workflow is heavily based on the
processing techniques employed for the GaLactic and Extragalactic All-sky
Murchison Widefield Array (GLEAM) survey (Hurley-Walker et al., 2017),
GLEAM-X444https://github.com/nhurleywalker/GLEAM-X-pipeline/, as well as the
MWA image-plane FRB search (Rowlinson et al., 2016).

All observations of GRB 180805A were calibrated using the in-field calibration
technique developed for the GLEAM-X pipeline. The in-field calibration scheme
uses the GLEAM catalogue as a sky model (Hurley-Walker et al., 2017), rather
than the more traditional single bright source model. This reduces the
positional shifts induced by differing ionospheric refraction in different sky
locations. Rather than deriving in-field calibration solutions for each
individual snap-shot observation of a GRB, we choose to apply a single
solution derived from a snap-shot close to the centre of the 30 minute
integration, which will likely have the median ionospheric shift compared to
the observations on either side. The advantage of a single solution is that
each calibrated observation will have a fairly consistent absolute flux
calibration. For GRB 180805A, we instead chose to use the in-field calibration
solutions derived from the observation 1217495544 as the nearby bright source
Cen A was in a primary beam null (the final calibration solution applied to
all ObsIDs can be accessed via Anderson, 2021). The change in the
observational pointing centre that occurred between this and the following
observation 1217495664 (due to the Sun suppression subroutine) resulted in Cen
A sitting in a $\sim 10\%$ primary beam sidelobe in all the following
snapshots. At the time of processing, the sky-model used for in-field
calibration did not include Cen A so if any later observations were used for
the in-field calibration, the resulting solutions would include unmodelled
flux.

The calibration and imaging was conducted in the following manner using
scripts from the MWA-fast-image-transients workflow (names of scripts are
indicated for reproducibility).

  1. 1.

We use obs_asvo.sh to fetch all target observations from the MWA All-Sky
Virtual Observatory (ASVO) service555https://asvo.mwatelescope.org/. The ASVO
service converts the MWA specific data format into a measurement set
format,666https://casa.nrao.edu/casadocs/casa-5.1.0/reference-
material/measurement-set/ applies phase calibration based on cable lengths and
antenna/tile positions, and flags known bad tiles and channels.

  2. 2.

We use an in-field calibration scheme (obs_infield_cal.sh) on one of the
target observations. Provided the ionosphere is reasonably stable, this would
usually be the central 2 min snapshot of the total 30 min observation. For GRB
180805A, we used ObsID 1217495544 (see explanation above). During the
calibration stage for GRB 180805A, we identified that tile 84 was not
producing good data, so it was flagged from all observations using
obs_flag_tiles.sh.

  3. 3.

The derived calibration solution is then applied to all of the target
observations using obs_applycal.sh.

  4. 4.

All imaging was carried out with wsclean (Offringa et al., 2014), with which
we generate multi-frequency synthesis images on a range of timescales (2min,
30s, 5s, and 0.5s) using a pixel scale of 16 arcsec and an image size of 4096
pixels ($18.2\deg$) on a side (these scales are appropriate for the Phase II
extended configuration). The 2min and 30s timescale images were cleaned such
that all peaks above $3\sigma$ were cleaned to $1\sigma$ (obs_image.sh and
obs_im28s), and the restored images were created using a 80 arcsec restoring
beam for all observations. The 5s and 0.5s images were created using
obs_im5s.sh and obs_im05s.sh but were not cleaned. All imaging scripts create
instrumental Stokes XX and YY polarisation images, which are primary beam
corrected and converted into Stokes I images. On 0.5s timescales, we also
produce a set of images that are divided into 24 coarse channels of bandwidth
1.28 MHz using obs_im05s_24c.sh.

All the output images are then prepared for transient and variable analysis
using Robbie (see Section 2.2.2) as this work-flow requires that all images
have the same shape and sky coverage. As each of the 15 snapshot observations
has a different pointing centre, all images were re-gridded to a template
image that represents the largest region of overlap between snapshots (a
nearly square region $\sim 140$ deg2 in size centred at
$\alpha\mathrm{(J2000.0)}=10^{\mathrm{h}}48^{\mathrm{m}}55\overset{\mathrm{s}}{.}7$
and
$\delta(\mathrm{J2000.0})=-40^{\circ}27^{\prime}50\overset{{}^{\prime\prime}}{.}4$)
using the Miriad (Sault et al., 1995) task regrid.

####  2.2.2 Transient and variable search

We used Robbie to search for transient and variable sources on all full-
bandwidth (30.72 MHz) images, grouped by cadence (2 min, 30 s, 5 s, and 0.5
s). The scale of data being processed for this project was beyond the
capability of Robbie as described by Hancock et al. (‘V1.0’ 2019a). The main
limitation was the use of Make (Feldman, 1979) as a workflow manager in an HPC
environment, as it does not integrate with queue scheduling systems such as
SLURM (Yoo et al., 2003). Additionally, V1.0 was developed and tested with 25
epochs of data, however when scaling out to the 3315 epochs required for the
0.5 s images in this project, it became clear that the processing and storage
choices were inappropriate. In particular,
FITS777https://fits.gsfc.nasa.gov/fits_standard.html tables are limited to
1000 columns. To counter these limitations, we ported Robbie to use NextFlow
(Tommaso et al., 2017) as the workflow manager, containerised the entire
software stack using Docker888https://www.docker.com/ and Singularity (Kurtzer
et al., 2017), and used
VOTables999https://www.ivoa.net/documents/VOTable/20191021/ instead of FITS
files to store tabulated data. This updated version of Robbie is now more
portable, can be run on desktop or HPC systems, and can scale to surveys with
thousands of epochs of observations. The logical flow and operation of Robbie
is unchanged and we summarise its operation below.

Robbie first derives and then applies an astrometric correction to each image
that corrects for any ionosphere distortion. This is conducted using the
algorithm fits_warp (Hurley-Walker & Hancock, 2018), and uses the GLEAM
catalogue as a template for the source positions (note that due to the minimal
signal detected in the coarse channel images, the ionospheric distortions
calculated for the full-bandwidth 0.5 s images were applied to the 24 coarse
channel images of the corresponding timestep, which were used in the analysis
described in Section 2.2.3). Once the ionospheric corrections are applied,
Robbie proceeds with a transient and variable search as follows:

  * •

Stack all epochs to form a cube;

  * •

Create a mean and noise image from the cube;

  * •

Use Aegean blind source finding to identify persistent sources in the mean
image;

  * •

Use Aegean priorized fitting to create a light curve for each persistent
source;

  * •

Mask persistent sources from each individual epoch; and

  * •

Use Aegean blind source finding on the masked single epoch images to identify
transient candidates (which may appear in one or more epochs).

Robbie was modified to allow positions of interest to be added to the
persistent source catalogue, causing light curves to be generated for these
locations via priorized fitting. This functionality was used to calculate a
light curve at the Swift-XRT position of GRB 180805A (see Section 3.1).

Corrections to the absolute flux scale were calculated using the software tool
flux_warp (Duchesne et al., 2020), which compares the source fluxes measured
by Aegean to the GLEAM catalogue. We assumed a mean offset in flux for each of
the 2 min snapshot images and applied this mean correction to all quoted flux
densities and limits in Table 1, Table 3, and Section 3. Deriving reliable
absolute flux-scale corrections on shorter timescales was not feasible due to
fewer sources being detected, and the source flux density uncertainties being
larger. We therefore assumed that the flux calibration did not change within a
2 min snapshot and applied the same correction to the shorter timescales (30
s, 5 s and 0.5 s). The flux scale corrected light curves at each timescale are
shown in Figure 7. Following the mean correction on the 2 min snapshot images,
we measured a $1\sigma$ scatter on the final flux values of $\leq 15$%.

####  2.2.3 Image de-dispersion and dispersed transient search

Searching for dispersed transient signals via image de-dispersion techniques
is potentially far more sensitive to these likely narrow (ms timescales) FRB-
like signals when compared to image searches for which the integration time is
equivalent to how long we expect the signal to traverse the full 30.72 MHz
bandwidth for a given DM (e.g. Law et al., 2018). For example, if the FRB has
an intrinsic duration of 100 ms at a redshift of 0.7, then it will take 30 s
to cross the MWA bandwidth so a snapshot of this duration would result in a
signal-to-noise loss of a factor of 300. The final stage of our data
processing for GRB 180805A is to perform a search for dispersed, prompt
signals on the native MWA correlator temporal resolution of 0.5 s and the
coarse channel resolution of 1.28 MHz. The recent detection of FRB 191001,
which was detected in an ASKAP snapshot image with a 10 s integration time and
later processed with a DM search, demonstrates the utility of a dual
processing approach (Bhandari et al., 2020). This search was conducted over
the full 30 min observation for a DM range of $200-3000$ pc cm-3, which
corresponds to the known SGRB redshift range of $\sim 0.1<z<2.5$. We compute
the dispersive delay of a pulse sweep between the upper ($\nu_{h}$) and lower
($\nu_{l}$) ends of a band for a given DM as:

$\displaystyle\delta t(DM,\nu_{l},\nu_{h})$ $\displaystyle=$ $\displaystyle
4.15~{}{\rm
DM}\,\left(\frac{1}{\nu^{2}_{l}}-\frac{1}{\nu^{2}_{h}}\right)~{}[{\rm ms}],$
(1)

where frequencies $\nu_{l}$ and $\nu_{h}$ are expressed in GHz. The MWA band
for the observations of GRB 180805A is between $\nu_{l}=0.175$ GHz and
$\nu_{h}=0.200$ GHz.

This analysis was performed on the 0.5 s duration coarse channel images that
were output by the MWA-fast-image-transients pipeline (see Section 2.2 point
iv). The ionospheric correction that Robbie calculated for each 0.5 s image
(see Section 2.2.2) was applied to each set of coarse channel images (of which
there are 24) for the corresponding timestep. It was not possible to calculate
the ionospheric correction on individual 0.5 s coarse channel images due to
their low sensitivity preventing the detection of individual field sources.
Ionospheric induced position shifts are frequency dependent ($\propto
1/\nu^{2}$), with larger offset distortions expected at lower frequencies. The
expected difference in position shifts between the upper and lower end of the
observing band are just $(\Delta\nu/\nu)^{2}\sim 3\%$ for a 30.72 MHz
bandwidth at 185 MHz. We did not apply a chromatic correction to the
ionospheric offsets calculated from the 0.5 s images over the full 30.72 MHz
bandwidth before applying them to the coarse channel images.

The 0.5 s coarse channel images were first used to create a $n_{t}\times
n_{ch}$ dynamic spectrum at the position of the GRB over the full 30 minute
observation. As the Swift-XRT $3\sigma$ positional uncertainty for GRB 180805A
was 4.7 arcsec, which is far less than the MWA Phase II synthesised beam of
$\sim 80$ arcsec at 185 MHz, it was therefore sufficient to perform our signal
search analysis on a single pixel (sized 16 arcsec square) at the nominal
position of the GRB. A small section of this dynamic spectrum showing the
first 100 s of the MWA follow-up observation at the pixel location of GRB
180805A is shown in Figure 1. Note that the first timestep (when the MWA was
on-target) began at $t=$76.98 s post-burst, but the first 2 s are not recorded
and a further 4 s are always flagged due to instrumental reasons. Therefore,
the first non-flagged integration started at 09:06:12.7 UTC ($83.68$ s post-
burst). The total number of time-steps is $n_{t}=3434$ including the 9.5 s
gaps between each 2 min snapshot.

Figure 1: The first 100 s of the dynamic spectrum measured at the pixel
location of GRB 180805A at a 1.28 MHz frequency and 0.5 s time resolution. The
full MWA follow-up observation covered approximately 30 min. The first 4 s and
last 5.5 s of each individual observation are flagged due to instrumental
reasons. While the first timestep begins at $t=$79.68 s post-burst, the first
4 s are flagged so the first non-flagged integration starts at 09:06:12.7 UTC
($83.68$ s post-burst). The full dynamic spectrum can be downloaded from
Anderson (2021).

In order to determine the noise in the dynamic spectrum in the direction of
the GRB, we first chose independent directions on the sky and created
additional dynamic spectra, the spectrum at the GRB location is labelled as
the ‘signal’ while the remainder are labeled as ‘noise’. In order to remove
instrumental effects and persistent astrophysical sources from each dynamic
spectrum, we measured a time-averaged spectral energy distribution (SED), and
subtracted this from each time step. This SED subtraction was done
independently for all pointing directions. The dynamic spectral plots for the
‘noise’ directions were combined into a cube, which were then used to compute
a mean ($\mu$) map. Finally, we computed a final GRB dynamic spectrum (DS) by
subtracting the mean from the signal:

$\mathrm{DS}=\mathrm{signal}-\mu$ (2)

Using the noise subtracted GRB dynamic spectrum, a de-dispersed time series
(DTS) was calculated for each DM in the range [$D_{min},D_{max}]$ and
potential pulse start time ($T_{s}$) in the range ($[-\tau_{max},T_{last}]$),
where $D_{min}$ is the minimum trialed DM (200 $\mathrm{pc\,cm^{-3}}$), $T=0$
s is the start time of the first recorded MWA timestep, $\tau_{max}\approx
122.4$ s is the maximum sweep time over the MWA band ($30.72$ MHz)
corresponding to the maximum DM ($D_{max}=3000$ pc cm-3), and $T_{last}$ is
the time of the last recorded MWA timestep ($3434\times 0.5$ s in this case).
Some of the FRBs show significant temporal pulse broadening due to scattering
(Qiu et al., 2020). These scattering times at GHz frequencies correspond to a
few seconds at the MWA frequency assuming frequency scaling proportional to
$\sim\nu^{-4}$ (Bhat et al., 2004). Therefore, we have also performed
averaging of dynamic spectrum along the time axis on timescales between 1 to
10 s and then formed DTS using the time averaged dynamic spectra. Similarly,
no statistically significant candidates were found.

An SGRB with a high DM could potentially allow observations at MWA observing
frequencies to detect prompt radio signals that are predicted to be emitted
prior to the merger (see Section 4.2). The GRB was detected by Swift-BAT just
83.7 s before the first MWA data were collected. Based on Equation 1, this
means that for a prompt radio signal emitted at the time of the SGRB (which we
assume corresponds to the first detection of $\gamma$-ray emission) to be
detectable in our MWA observing band (170–200 MHz) we required a $DM\gtrsim
800$ pc cm-3.

Therefore, for the higher DM trial values (in the range $800-3000$ pc cm-3) we
can use the full observing band sensitivity to probe the parameter space in
which radio prompt signals were emitted from the SGRB up to about 350 s before
the merger (first detection of $\gamma$-rays). For the DM range $580-800$ pc
cm-3, we can use part of the observing band to search for dispersed signals
emitted at the time of the SGRB as according to Equation 1, $DM=580$ pc cm-3
corresponds to a 83 s dispersive delay between the first $\gamma$-ray
detection and the lower end of the MWA observing band (170 MHz).

The resulting DTS is a two dimensional image with the horizontal axis
corresponding to the tested pulse start time ($T_{s}$) with a 0.1 s resolution
and the vertical axis corresponding to the DM in steps of 1 pc cm-3. The
sampling of pulse arrival times (0.1 s) was chosen to be smaller than the
actual temporal resolution of the images to ensure no signal was missed due to
rounding errors caused when calculating the positions of the pixels along the
dispersion sweeps. Following equation 1, we calculated the value in each pixel
at ($T_{s}$,DM) as the mean of all pixel values (in ${\rm Jy\,beam^{-1}}{}$)
along the corresponding tested path swept out by a pulse across the dynamic
spectrum between 170 and 200 MHz. The central time region of the DTS image
calculated for the central pixel (nominal position of GRB 180805A) is shown in
the left panel of Figure 2.

Figure 2: Left: The central region of the de-dispersed time series showing the
mean flux density for the path swept across the dynamic spectrum (Figure 1)
for every DM trial ranging from 100 to 3000 $\mathrm{pc\,cm^{-3}}$ at 1.0
$\mathrm{pc\,cm^{-3}}$ intervals, covering approximately $700-1300$ s at a
resolution of 0.1 s following the GRB detection. Right: The peak SNR over all
de-dispersed time series as a function of DM trial. The highest SNR values
detected in the de-dispersed time series (up to $\approx 10$) correspond to
low DMs ($<$140 $\mathrm{pc/cm^{3}}$), where the number of averaged pixels in
the dispersion sweep is low and a single channel RFI can increase the de-
dispersed value. Therefore, we have excluded these low DMs from our analysis.
Also note that we do not expect SGRBs to have a
$\mathrm{DM}<200\mathrm{pc\,cm^{-3}}$ (shaded areas) if we assume a minimum
SGRB redshift of $z\sim 0.1$. The full de-dispersed time series can be
downloaded from Anderson (2021).

The standard deviation of the DTS is not constant across the image as it
depends on the number of pixels averaged together for a given DM sweep, which
increases with increasing DM as the dispersion sweep across the dynamic
spectrum becomes longer before it reaches the lower frequency end. We
therefore generated a corresponding map of the number of pixels ($n_{d}$) used
to calculate each image pixel in the DTS image shown in the left panel of
Figure 2. This resulting map was used to derive the dependence of the DTS
standard deviation ($\sigma_{dts}$) as a function of $n_{d}$, such that
$\sigma_{dts}(n_{d})=\sigma_{dts}(0)/\sqrt{n_{d}}$, which was divided through
the DTS image to create a DTS image in units of SNR. Each pixel ($T_{s}$,DM)
of the final SNR DTS image with a DM between 200-3000 pc cm-3 was then
searched for any dispersed signals above the specified thresholds of
$\sigma_{dts}>5$ and $\sigma_{dts}>6$, for which Gaussian statistics predict
there to be approximately 2.76 and 0.01 random events (when only different
dispersion sweep paths through the dynamic spectrum are taken into account),
respectively, based on the number of DM and time trials. We verified that
values in the DTS images have a Gaussian distribution but we also note that
those dispersion sweeps with 1 or 2 pixels in common are not fully
statistically independent. However, this is only a few percent effect given
that even the lowest trail $\mathrm{DM}=200\mathrm{pc\,cm^{-3}}$ has $\gtrsim
50$ pixels.

We used the DTS SNR image of the GRB to further explore how the summed number
of pixels effects the final SNR measurements for a given DM by plotting the
peak SNR in each de-dispersed time series as a function of DM trial (i.e. the
maximum SNR value for each DM over all possible signal start times; see the
right panel of Figure 2). We found that the high SNR ($\lesssim 10$) dispersed
transient candidates for GRB 180805A were grouped at $\mathrm{DMs}\leq 140$ pc
cm-3. For this low DM region, the signals were calculated by averaging a low
number of dynamic spectrum pixels ($n_{d}$) due to the short dispersion sweep,
with the pixel count often being further reduced due to the sweep encountering
9.5 s gaps in the data between two MWA observations. In the case of a single
high value pixel in the dynamic spectrum (e.g. caused by RFI), this could
significantly increase the mean value of a small number of pixels averaged
over a short dispersion sweep, therefore boosting the final de-dispersed SNR
for the corresponding trial. However, such an anomaly does not impact our
analysis as we expect SGRBs to lie within the DM range of 200–3000 pc cm-3.
Indeed, assuming an extra-galactic origin for GRB 180805A, we may expect a
Galactic DM contribution of $\approx 178$ pc cm-3 estimated from Yao et al.
(2019) ($\approx$ 135 pc cm-3 from the NE2001 model from Cordes & Lazio, 2002)
along this line of sight. Additionally, contributions from the MW halo and
host galaxy to the DMs of localized FRBs have been found to be on average $75$
pc cm-3 (Macquart et al., 2020), which is consistent with the lowest DMs of
observed FRBs: 180729.J1316+55 (CHIME/FRB Collaboration et al., 2019a) and FRB
171020 (Shannon et al., 2018), with excess DMs of 78.4 pc cm-3 and 75.7 pc
cm-3, respectively. We could therefore expect a minimum DM of $210$ pc cm-3
for GRB 180805A.

This de-dispersed transient search procedure was verified by simulating
dispersed pulses and adding their fluxes to the appropriate pixels of a
dynamic spectrum based on the dispersion sweep calculated using equation 1. We
randomly simulated 100 pulses per DM and fluence pair (DM,$\mathcal{F}$) for
twelve DM values (200, 350, 500, 1000, 1250, 1500, 1750, 2000, 2250, 2500,
2750 and 3000 $\mathrm{pc\,cm^{-3}}$) and twenty one $\mathcal{F}$ values (50,
100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1500, 2000,
3000, 4000, 5000, 6000, 7000 and 10000 [Jy ms]). Currently, the algorithm only
simulates narrow pulses, such that the entire fluence is contained within a
single 0.5 s time bin. However, simulating temporally broadened pulses due to
scattering will be implemented in a future version. The arrival times of the
simulated pulses at the upper end of the MWA observing band were randomised
within the 30 min of the MWA observations. An example of an injected pulse is
shown in Figure 3. The dynamic spectra with injected pulses were processed
using the same analysis as was used to search for pulsed signals in the GRB
DTS (Figure 2). The efficiency ($\epsilon$) of the search was calculated as
$\epsilon=N_{det}/N_{gen}$, where $N_{det}$ is the number of simulated pulses
identified by the algorithm and $N_{gen}$ (100 in this simulation) is the
total number of generated pulses for a given (DM,$\mathcal{F}$) pair. Figure 4
shows the pulse detection efficiency (at $\geq 6\sigma_{dts}$) for each tested
DM and fluence pair. This demonstrates that for a threshold of
$\sigma_{dts}>6$, the 90% fluence detection efficiency limit varies as a
function of DM within the tested range, which ranges between 570 Jy ms at
DM$=3000$ pc cm-3 and 1750 Jy ms at DM=$200$ pc cm-3, with likely zero false
positives due to noise events. To illustrate this dependence, we performed
polynomial fits to the DM curves in Figure 4 to find the 90% fluence detection
efficiency for each tested DM, which are plotted in Figure 5. The variation in
efficiency is mainly due to the noise in the dynamic spectrum.

Figure 3: Left: An example of a simulated dispersed pulse with fluence 10000
Jy ms and DM = 1000 $\mathrm{pc\,cm^{-3}}$ added to the dynamic spectrum of an
image pixel used for this efficiency test. Again, the dynamic spectrum begins
at the first MWA timestamp of 79.68 s but the first 4 s are flagged as shown
in Figure 1. Right: The corresponding de-dispersed time series (DTS) around
the start time and DM of the injected pulse. The horizonal axis start time in
this DTS image corresponds to the Swift detection time of GRB 180805A, which
was 83.7 s before the MWA began observing the event. This algorithm therefore
probes possible pulse start times that began before the start of the MWA
follow-up observations if emitted at a high enough DM for the signal to be
dispersed by $>83.7$ s. The “green-hatched triangle” in the bottom-left corner
corresponds to negative pulse start times (radio signals arriving at the upper
end of the frequency band before the MWA started observations) and DM sweep
times too short to be captured at the lower frequency end ($T_{s}+\delta
t(DM,0.170,0.200)<0$), hence covering the DM/pulse start time parameter space
inaccessible to the analysis. As 100 pulses were generated for each pair of DM
(12 values) and fluence (21 values), a total of 25200 simulated pulses were
processed through the transient search pipeline used to search for signals in
the GRB DTS described in Section 2.2.3, allowing us to determine the
efficiency of this technique (see also Figure 4).  Figure 4: The measured
efficiency for detecting pulses with $\sigma_{dts}>6$ as a function of fluence
at twelve tested DMs (values indicated on the colour bar). The fluence where
detection efficiency exceeds a threshold of 90% varies as a function of DM
from $\approx$1750 Jy ms at DM=$200$ $\mathrm{pc\,cm^{-3}}$ to $\approx$570 Jy
ms at DM=$3000$ $\mathrm{pc\,cm^{-3}}$. Hence, any dispersed radio signal from
the GRB 180805A brighter than 1750 Jy ms in the trialled DM range $200-3000$
$\mathrm{pc\,cm^{-3}}$ should be detected with 90% probability by the search
procedure described in Section 2.2.3.  Figure 5: The 90% fluence detection
efficiency as a function of DM. A 6-order polynomial has been fitted in order
to interpolate the 90% fluence detection efficiency for any DM value within
the tested range of $200-3000$ pc cm-3.

##  3 Results

###  3.1 Light curve analysis

The Robbie workflow pipeline was used to perform a blind search for transients
within the field of GRB 180805A over multiple timescales (2 min, 30 s, 5 s,
and 0.5 s), however, none were detected. A summary of the RMS at the position
of GRB 180805A can be found in Table 1 for each of the 2 min snapshots, and
the full range in RMS at the position of GRB 180805A on the four different
timescales are also summarised in Table 3. The mean image output by Robbie
that was created from the 2 min snapshots (equivalent to the 30 min
integration) is shown in Figure 6, where the Swift-XRT position of GRB 180805A
is indicated. No associated persistent radio source was detected with a
$3\sigma$ upper limit of 40.2 mJy.

In order to better evaluate any potential variability properties of GRB
180805A, we use Aegean priorized (forced beam) fitting in the Robbie workflow
to measure the flux density at the Swift-XRT position over all four
timescales, producing light curves that are shown in Figure 7 (these light
curve data can be accessed via Anderson, 2021). The RMS (and three times the
RMS) at the GRB position are also shown. The jump in the RMS noise at $\sim
600$ s post-burst (ObsID 1217495664) is due to the large shift in the
observational pointing centre caused by the Sun avoidance algorithm, which
means GRB 180805A was sitting in a less sensitive part of the primary beam
from this ObsID onward. Another contribution to the noise may also be caused
by Cen A, which is not included in the GLEAM model and was sitting in a 10%
primary beam sidelobe for the same ObsID range.

####  3.1.1 Variability analysis

The Robbie workflow calculates variability statistics for each light curve it
generates. In Table 3, we quote the modulation index ($m=\frac{\sigma}{\mu}$),
the de-biased modulation index ($m_{d}$; which takes into account the errors
on each data-point, see Hancock et al., 2019a), and the probability of
observing such variability in a non-variable (steady) source (p_val).
Initially Robbie was designed with the assumption that a light curve would
have fairly consistent uncertainties on all observations such that the p_val
parameter could be computed from a $\chi^{2}$ statistic and an effective
number of degrees of freedom. However, when the telescope repoints part way
through the observation, the instrumental sensitivity changes (see Figure 7).
For GRB 180805A, the light curve of a non-variable source is therefore no
longer drawn from a normal distribution, but a population that is the sum of
two normal distributions with a common mean but different variance. We have
therefore modified the p_val calculation performed by Robbie so that it will
first normalise the light curve to a zero mean and unit variance via:

$Z_{i}=\frac{x_{i}-\mu}{\sigma_{i}}$ (3)

where $x_{i}$ and $\sigma_{i}$ are the measurement and associated uncertainty,
and $\mu$ is the mean flux. The modified p_val is now computed by performing a
Kolmogorov-Smirnov test (Smirnov, 1939) of $Z$ against a normal distribution
using the scipy.stats.kstest python function. The resulting p_val quoted in
Table 3 show there is no significant variability on any of the four timescales
at the position of GRB 180805A. For details on how Robbie calculates the
remaining statistics, see Hancock et al. (2019a).

Table 3: Light curve variability statistics and range in the RMS at the position of GRB 180805A for different monitoring timescales. Quantities reported are the modulation index ($m$), the debiased modulation index ($m_{d}$), and the probability that the this variability will be observed in a non-variable source (p_val). See §3.1.1 for a description of these metrics.  Timescale | Variability statistics | RMS
---|---|---
(s) | $m$ | $m_{d}$ | p_val | (mJy beam-1)
$0.5$ | $18.44$ | $6.34$ | $0.19$ | $190-610$
$5$ | $8.54$ | $3.59$ | $0.85$ | $90-210$
$30$ | $4.74$ | $1.03$ | $0.4$ | $65-140$
$120$ | $1.84$ | $-2.59$ | $0.86$ | $35-65$
Figure 6: Mean (averaged) image of the MWA 30 min integration (2 min $\times$
15 snapshot observations) of GRB 180805A, beginning 83.7 s post-burst. The
image size is $2^{\circ}\times 2^{\circ}$ centered on the XRT position of GRB
180805A ($2\overset{{}^{\prime\prime}}{.}5$ 90% confidence), which is also
indicated by two white lines that point to within $3^{\prime}$ of this
position. The image RMS at the position of GRB 180805A is 13.4 mJy. Figure 7:
Monitoring light curves at the position of GRB 180805A over four different
timescales (2 min, 30 s, 5 s, and 0.5 s) as a function of time following the
Swift-BAT detection. The plotted flux densities (blue data points) were
measured via performing priorized fitting at the Swift-XRT position of the GRB
using Robbie. All flux densities are plotted at the centre of each time-bin.
The vertical errorbars correspond to the flux density error output by Robbie
and the horizontal errorbars indicate the duration of the time-bin. The solid
black line shows the RMS for each time-bin at the position of the GRB, with
the $3\sigma$ level (3 $\times$ RMS) indicated by the dashed black line.
Statistics quoted in Table 3 indicate no significant variability was observed
at the position of GRB 180805A on any of the four timescales. The csv files
listing the resulting flux density as a function of time for these four
timescales can be downloaded from Anderson (2021).

###  3.2 Image de-dispersion analysis

As described in Section 2.2.3, the final DTS SNR image of the pixel position
of GRB 180805A was searched for trials ($T_{s}$,DM) for signals exceeding
thresholds of $5\sigma_{dts}$ and $6\sigma_{dts}$. No ($T_{s}$,DM) trials with
$\sigma_{dts}\geq 6$ were identified for the DM range
$200-3000\,\mathrm{pc\,cm^{-3}}$, while two $\sigma_{dts}\geq 5$ trials were
identified, which is in agreement with the statistical expectations of the
false-alarm-rate (see Section 2.2.3). As a sanity check, all the SNR$>5$
candidates were “eye-balled” and none of them had a corresponding FRB-like
signal dispersion sweep in the dynamic spectrum. We conclude that we did not
detect any SNR$>6$ prompt radio signals associated with the short GRB 180805A
in the de-dispersed MWA data in the DM range corresponding to the observed
SGRB redshift range, with fluence upper-limits ranging between 570 Jy ms at
DM$=3000$ pc cm-3 and 1750 Jy ms at DM=$200$ pc cm-3. The dynamic spectrum at
the pixel position of GRB 180805A and the final DTS can be accessed via
Anderson (2021).

##  4 Discussion

The MWA rapid-response follow-up observations of GRB 180805A have allowed us
to probe for prompt, coherent, dispersed radio signals that may have been
emitted either just prior to or shortly following the merger event. No
transient signals were detected at the position of GRB 180805A over a variety
of timescales that cover the spread of dispersion measures expected for the
minimum, average and maximum redshift range of SGRBs. However, we have
obtained some of the most stringent limits on short timescales (0.5 s, 5 s, 30
s and 2 mins starting just 83.7 s post-burst) at low radio frequencies ($<300$
MHz) for an SGRB (see Table 3).

Our image plane dedispersion analysis demonstrated that the rapid-response MWA
observation of GRB 180805A was sensitive to dispersed, prompt radio signals
over a range of fluences as a function of DM (570 Jy ms at DM$=3000$ pc cm-3
up to 1750 Jy ms for DM$=200$ pc cm-3; see Figures 4 and 5). The more
stringent fluence limits at higher DMs are due to the signal search being
conducted over many more dynamic spectrum pixels than at lower DMs. The range
of fluence limits derived in our analysis are high in comparison to the
(higher frequency) Parkes and ASKAP FRB population (Petroff et al.,
2016)101010http://www.frbcat.org/, with the brightest known event being FRB
180110 at $420\pm 20$ Jy ms (Shannon et al., 2018). James et al. (2019b)
assumed a power-law distribution for the rate $(R)$ of FRBs with a fluence
threshold of $(\cal F)$ according to

$R({\cal F})=R_{0}\left(\frac{\cal F}{{\cal
F}_{0}}\right)^{\alpha}\mathrm{sky^{-1}\,d^{-1}}$ (4)

where $R_{0}$ is the rate at the fluence threshold of ${\cal F}_{0}$, and used
Parkes and ASKAP FRB samples to calculate a power law index consistent with a
non-evolving Euclidean distribution $(\alpha=-1.5)$. If we take $R_{0}=12.7$
sky-1 d-1 and ${\cal F}_{0}=56.6$ Jy ms, which was derived from the ASKAP FRB
sample (James et al., 2019a), and scale the fluence from 1.3 GHz to MWA
frequencies using an assumed spectral index of -1.5 (Macquart et al., 2019),
then this value of $R_{0}$ corresponds to a fluence of 1054.3 Jy ms at 185
MHz. Therefore using Equation 4, we estimate a rate of $R=5.9-31.9$ sky-1 d-1
for FRBs with a fluence ranging from $>1750$ Jy ms down to $>570$ Jy ms (as a
function of increasing DM between $200-3000$ pc cm-3) at 185 MHz. However,
James et al. (2019b) also determined that there may be a steepening in the
source-count distribution to $\alpha=-2.2$ in the fluence range of
$R=4.2-49.1$ sky-1 d-1 for FRBs with a fluence ranging from $>1750$ Jy ms down
to $>570$ Jy ms at MWA frequencies.

These source counts do suggest that there could be FRBs at such a high
fluence, and if that is the case then the MWA could potentially detect them
using image dedispersion. However, this analysis is an over simplification
since such bright events have yet to be detected at $\sim 1$ GHz, and to apply
these statistics at 185 MHz we are assuming that the FRB emission is
broadband, extending down to MWA frequencies. Currently, we have have little
information about the behaviour of FRBs at MWA frequencies other than there
might be a spectral turn-over of ASKAP-detected FRBs above 200 MHz (Sokolowski
et al., 2018). The observation of FRBs down to 400 MHz by CHIME/FRB
Collaboration et al. (2019a) does indicate that some FRBs will be visible at
the MWA frequency range.

The triggered MWA observations of SGRBs are also specifically designed to
target several SGRB coherent emission models that predict signals within the
first 30 min post-burst (Rowlinson & Anderson, 2019). Many of these models
depend on the formation of a stable or unstable magentar, which is evidenced
by ongoing energy injection in the Swift X-ray light curves of many SGRB
events (Rowlinson et al., 2013). In the following, we use the X-ray light
curve to model the parameters of the magnetar formed following GRB 180805A,
which are then used in conjunction with our fluence and flux density upper-
limits to constrain the coherent radio emission from this merger.

###  4.1 Central engine activity

In order to constrain the central engine activity of GRB 180805A, we obtained
the 0.3–10 keV energy band light curve from the Swift Burst Analyser (Evans et
al., 2010). This light curve comprises the gamma-ray data obtained by the
Swift-BAT and the unabsorbed X-ray data from Swift-XRT. Using the average
short GRB redshift ($z=0.7$), a k-correction (Bloom et al., 2001), and
assuming the spectrum can be described as a single power law, we create a rest
frame 1–10,000 keV luminosity light curve as plotted in Figure 8. The light
curve of GRB 180805A shows energy injection up to at least $10^{3}$ s
following the merger as evidenced by the late-time plateau phase beginning at
$\sim 30$ s post-burst.

The rest frame light curve was fitted with the magnetar central engine model
(Zhang & Mészáros, 2001), following the method outlined in Rowlinson et al.
(2013). The fitted model suggests that a stable magnetar might have formed
with a magnetic field strength of $B=2.68f^{+1.62}_{-1.25}\times 10^{15}$ G
and a spin-period of $P=5.16f^{+1.22}_{-1.25}$ ms, where
$f=\left(\frac{\epsilon}{1-\cos\theta}\right)^{0.5}$ encompasses the
uncertainties in the efficiency, $\epsilon$, and the beaming angle, $\theta$,
of the emission. These magnetar properties are used to constrain the expected
coherent radio emission that may have been produced by GRB 180805A in Section
4.2.

Figure 8: Stable magnetar model fit to the Swift-BAT and Swift-XRT light curve
of GRB 180805A following formalism by Rowlinson et al. (2013).

###  4.2 Coherent emission models

If the X-ray light curve of GRB 180805A suggests that a stable magnetar may
have been formed following the SGRB event, then we expect that coherent radio
emission could have been produced by this source either just prior, during or
shortly following the merger. Using these magnetar parameters, we are able to
make predictions about the expected flux density of any associated coherent
radio emission following the prescription outlined in Rowlinson & Anderson
(2019, note that these models still remain highly uncertain). Given the rest
frame X-ray light curve, there are three key models that we are able to test:

  1. a.

Magnetic field alignment of merging neutron stars (e.g Lyutikov, 2013).
Following Rowlinson & Anderson (2019), the flux density, $F_{\nu}$, is
predicted to be

$F_{\nu}\sim 2\times 10^{8}(1+z)\frac{B_{15}^{2}M_{1.4}^{3}}{R_{6}\nu_{9,{\rm
obs}}D^{2}}\epsilon_{r}~{}{\rm Jy}$ (5)

where $B_{15}=\frac{B}{10^{15}~{}{\rm G}}$ is the magnetic field of one of the
merging neutron stars, $M_{1.4}=\frac{M}{1.4M_{\odot}}$ is the mass of one of
the merging neutron stars, $R_{6}=\frac{R}{10^{6}~{}{\rm cm}}$ is the radius
of one of the merging neutron stars, $\nu_{9,obs}$ is the observing frequency
in GHz, $D$ is the distance to the binary system in Gpc and $\epsilon_{r}$ is
the fraction of the wind luminosity that is converted into radio emission.
Here we assume that the two neutron stars are of standard mass and size
($M_{1.4}=R_{6}=1$), the magnetic field is $B_{15}=10^{-3}$ and either the
typical pulsar value of $\epsilon_{r}=10^{-4}$ (Taylor & Cordes, 1993) or a
much lower efficiency of $\epsilon_{r}=10^{-6}$ (Faucher-Giguère & Kaspi,
2006).

  2. b.

Interaction between the relativistic jet and the surrounding medium (Usov &
Katz, 2000). Usov & Katz (2000) suggest that the jet may be dominated by a
Poynting flux wind and that its properties are directly linked to that of the
newly formed magnetar that is powering the GRB, and therefore linked to the
luminosity of the coherent radio pulse at low frequencies (see prescription
and assumptions in section 2.4 of Rowlinson & Anderson, 2019). The fluence of
the coherent radio emission at frequency $\nu$ is

$\Phi_{\nu}\simeq\frac{0.1\epsilon_{B}(\beta-1)}{\nu_{\rm
max}}\left(\frac{\nu_{\rm obs}}{\nu_{\rm
max}}\right)^{-\beta}\Phi_{\gamma}~{}{\rm erg~{}cm}^{-2}{\rm Hz}^{-1}$ (6)

for $\nu>\nu_{\rm max}$ (this is the expected regime at MWA frequencies),
where $\nu_{\rm max}$ is the peak frequency of the coherent radio emission,
$\epsilon_{B}$ is the fraction of the wind energy contained in the magnetic
field (assumed to be $10^{-3}$), $\beta\simeq 1.6$ is the spectral index of
the emission, and $\Phi_{\gamma}$ is the observed fluence in gamma-rays in erg
cm-2 ($1.1\pm 0.3\times 10^{-7}$ erg cm-2 in the $0.3-10$ keV energy band for
GRB 180805A; Palmer et al., 2018). $\nu_{\rm max}$ is dependent on the
magnetic field at the shock front, and therefore the spin period and magnetic
field strength of the magnetar remnant (Usov & Katz, 2000). As the magnetar
remnant properties are derived from the X-ray luminosity and light curve in
the rest-frame (see Section 4.1), these values will change with redshift
causing the overall radio fluence prediction to also change in brightness over
redshift (Rowlinson & Anderson, 2019).

  3. c.

Persistent pulsar-like (dipole spin-down) emission from a magnetar remnant
(e.g. Totani, 2013). Shortly following the merger, the magnetic field and
rotational axes of the magnetar are likely to be aligned, and are therefore
along the same axis as the GRB jet, which is our line-of-sight (see discussion
by Rowlinson & Anderson, 2019, and references therein). The predicted pulsar-
like emission for this model is given by

$F_{\nu}\simeq 8\times 10^{7}\nu_{\rm
obs}^{-1}\epsilon_{r}D^{-2}B_{15}^{2}R_{6}^{6}P_{-3}^{-4}~{}{\rm Jy}$ (7)

where $P_{-3}$ is the spin period in milliseconds and $B_{15}$ in 1015 G is
the magnetic field of the newly formed magnetar, which were calculated for GRB
180805A in Section 4.1. Again, we assume either a typical pulsar value of
$\epsilon_{r}=10^{-4}$ or a much lower efficiency of $\epsilon_{r}=10^{-6}$.

As with figure 7 in Rowlinson & Anderson (2019), we can scale these predicted
fluence and flux density values to a range of redshifts, which are plotted in
Figure 9. Each plot panel is labelled a) to c), which corresponds to the three
models described above. For panels a) and b), we plot the fluence of the
predicted emission as we expect these signals to be prompt (FRB-like). For
model a) the prompt signals are assumed to have a duration of 10 ms so we
multiply the flux density prediction in Equation 5 by this pulse width to
obtain the predicted fluence. The fluence sensitivity limit as a function of
DM (and therefore redshift) calculated from the de-dispersed 0.5 s images at
the position of GRB 180805A are also plotted in panels a) and b) to illustrate
the constraints placed by this experiment. The fluence limit attained in the
images is simply the limiting flux density multiplied by the integration time
of the image in milliseconds. Similarly, the $3\sigma$ upper-limit at the
position of GRB 180805A calculated from the mean RMS of the the full 30 min
MWA triggered observation is plotted in panel c).

Due to the rapid response of the MWA observations of GRB 180805A, we were on-
target to constrain the expected signals from the alignment of the NS magnetic
fields prior to the merger (model proposed by Hansen & Lyutikov, 2001;
Lyutikov, 2013), where the emission is pulsar-like, with the peak luminosity
being dependent on typical neutron star parameters (see Section 2.3.1 of
Rowlinson & Anderson, 2019). Assuming a typical pulsar efficiency of
$\epsilon_{r}=10^{-4}$ (Taylor & Cordes, 1993), we would not expect to have
detected such a signal even if this event was at a low redshift of z < 0.2
(see solid blue curve in Figure 9a). However, for a lower efficiency, this
signal would certainly go undetected for reasonable SGRB redshifts (e.g.
$\epsilon_{r}=10^{-6}$; dashed curve in Figure 9a). The cause of the expected
non-detection is due to the relatively long integration time (0.5 seconds)
compared to the expected signal duration of order a few milliseconds. Thus
such a signal would be diluted over the 0.5 second integration and bandwidth
of the MWA. In order to detect this signal, we likely need to perform
observations at a much higher temporal resolution (this is possible using the
MWA Voltage Capture System or VCS; Tremblay et al., 2015). High time
resolution data processing from the VCS would allow for coherent beamforming
at the GRB location (or a range of locations if the GRB localisation covers a
larger area).

Similarly, the rapid follow-up allows us to probe for emission from the jet-
ISM interaction. The timescale of this pulse is expected to be equal to or
less than the duration of the prompt gamma-ray emission phase (which is 1.68 s
for GRB 180805A). Our fluence limit for GRB 180805A is not constraining for
any of the redshift range. However, many Swift SGRBs have been detected with
gamma-ray fluences $>10^{-6}$ erg cm-2 (an order of magnitude greater than GRB
180805A, for example see D’Avanzo et al., 2014) and given that the radio
fluence linearly scales with the gamma-ray fluence (see Equation 6 and Usov &
Katz, 2000), a more powerful event could be detectable in our MWA
observations, particularly if it is at a low redshift. Note that for this
prediction, we assume that the fraction of the energy available in the
magnetic fields is $\epsilon_{B}=10^{-3}$ and this factor is currently very
poorly constrained for GRBs, with values ranging from $10^{-6}$ – $10^{-3}$
(e.g. Santana et al., 2014), with lower values of $\epsilon_{B}$ further
reducing the radio fluence predictions. This value, and the properties of the
newly formed magnetar, are expected to vary between SGRBs and hence further
rapid response observations of multiple GRBs may lead to future detections.

Finally, if a magnetar was formed, we would expect pulsar-like dipole
radiation to be produced during its lifetime (Totani, 2013). We would expect
such emission to be beamed in a similar way to pulsars, and therefore most
likely along the direction of the SGRB jet. If the jet axis remains pointed
towards the Earth, the radio emission would likely be persistent, yet rapidly
fading as the magnetar spins down. Once again, the predicted radio flux
density is dependent on the magnetar parameters derived in Section 4.1. If the
jet-axis became slightly misaligned with the spin axis of the magnetar, it
could possibly form a repeating FRB (Metzger et al., 2017). Following the
prescription in section 2.5.1. of Rowlinson & Anderson (2019), and for a
typical pulsar efficiency of $\epsilon_{r}=10^{-4}$ (solid blue line in Figure
9c), this persistent emission is expected to be just below the detection
threshold of the deep MWA Phase II 30 min observation of GRB 180805A (black
dotted line in Figure 9c). For lower pulsar efficiencies, the 40.2 mJy
threshold for GRB 180805A is extremely unconstraining (dashed blue line in
Figure 9c). We note that these predictions are highly dependent upon the
magnetar spin period and the magnetic field strength (c.f. Equation 7). The
magnetar fitted to the X-ray data of GRB 180805A has a relatively low magnetic
field and a long spin period, which makes the predicted coherent radio
emission fainter. The majority of magnetars fitted to the population of SGRBs
have higher magnetic fields and faster spin periods (Rowlinson et al., 2013),
hence future events are more likely to produce detectable emission (see the
predictions in figure 9c of Rowlinson & Anderson, 2019).

Since the modelling of the X-ray light curve shown in Section 4.1 indicates
that a stable magnetar may have formed following GRB 180805A, this rules out
the possibility of a coherent radio pulse being emitted by the collapse of an
unstable magnetar into a black hole (Falcke & Rezzolla, 2014; Zhang, 2014). In
addition, as the triggered MWA observations of GRBs are usually 30 minutes in
duration, this coherent emission may be missed in future GRB triggers as the
total integration time may be shorter than the magnetar collapse timescale.

Given that no prompt or coherent radio emission was detected from GRB 180805A
over the DM range of $200-3000$ pc cm-3 using a light curve transient analysis
or via image dedispersion, we can infer from Figures 9a, 9b and 9c that the
predicted coherent radio emission for this GRB, even in the most optimistic
scenarios, lie below the MWA detection threshold. Therefore these models are
poorly constrained by this GRB, as a detection would only be possible if the
efficiency of producing the coherent radio emission is significantly larger
than that of normal pulsars. It is also worth mentioning that propagation
effects that absorb or scatter coherent radio emission may also hinder the
detectability of a signal (see e.g. Rowlinson & Anderson, 2019, for a
discussion of these propagation effects). However, we note that for future
SGRBs, a higher flux X-ray plateau phase will lead to correspondingly brighter
coherent radio emission for all three explored models that could be detectable
by our MWA rapid-response observations (see analysis by Rowlinson & Anderson,
2019).

Figure 9: GRB 180805A constraints on the predicted fluence and flux density of
three coherent radio emission models as a function of redshift. a) Coherent
signal emitted prior to the merger from the alignment of magnetic fields for a
standard pulsar efficiency of $\epsilon_{r}=10^{-4}$ (solid blue curve) or an
efficiency of $10^{-6}$ (dashed blue curve). The dashed black line labelled
(i) shows the MWA fluence limit ($6\sigma$) as a function of redshift based on
the dedispersion analysis of GRB 180805A (see Section 2.2.3). b) The
relativistic jet interaction with the ISM. The radio fluence predicted using
the magnetar parameters derived from the X-ray light curve in Section 4.1 and
the gamma-ray fluence of GRB 180805A (solid blue curve). Here, we assume the
fraction of wind energy in the magnetic field to be $\epsilon_{B}=10^{-3}$.
The black dashed line is the same as for a). c) Persistent pulsar-like
emission where the solid and dashed blue lines are the same as for a). The
black dotted line labelled (ii) shows the MWA 40.2 mJy 3$\sigma$ flux density
limit from the full 30 min observation of GRB 180805A.

###  4.3 Comparison to other facilities

The majority of new-generation low-frequency facilities are searching for
coherent radio emission associated with GRBs (both short and long) and
gravitational wave (GW) events. In the following, we compare the sensitivities
and follow-up response times of these different facilities and observing modes
to the MWA triggered observations of GRB 180805A, as well as the other
published MWA triggered SGRB (GRB 150424A; Kaplan et al., 2015), and discuss
their strengths and limitations for the study of prompt emission associated
with GRBs and GW events.

In Figure 10, we show the $3\sigma$ upper-limits of low-frequency telescopes
that perform continuous monitoring programs or rapid-response follow-up
observations of GRBs. The plotted points give the $3\sigma$ sensitivity for
each instrument as a function of the telescope rapid-response-time post-burst
(we assume that the Swift-BAT detection time of the GRB is its start time at
post-burst=0) on different timescales (represented by the black horizontal
error bars). The data points are colour-coded based on the central observing
frequency (see the colour-bar in Figure 10). We plot the sensitivities for GRB
180805A at 185 MHz on the 0.5 s, 5 s, 30 s, and 2 m timescales, which
correspond to 3 times the average RMS values over the first 2 min snapshot
(ObsID 1217495184). The 30 min sensitivity was measured from the mean image of
all 15 snapshot observations as output by Robbie. The sensitivities plotted
for GRB 150424A are at the central observing frequency of 132.5 MHz,
correspond to 4 s, 2 m and 30 m timescales (Kaplan et al., 2015). The dotted
vertical lines indicate the arrival time of the Swift-BAT VOEvents associated
with GRB 180805A (yellow) and GRB 150424A (dark green; the colours correspond
to the observing frequency of each GRB). The MWA sensitivity limits for GRB
180805A are more constraining as they were taken over a bandwidth of 30.72 MHz
as compared to a 2.56 MHz bandwidth for GRB 150424A, which was observed in a
“picket-fence” (sub-band) mode.

Other low frequency radio telescopes running rapid-response systems include
the recently commissioned LOFAR Responsive Telescope (RT), which uses a
similar VOEvent triggering protocol to the MWA through the utilisation of the
4 Pi Sky tools (Rowlinson et al., 2019, 2020). On receiving a transient alert,
the LOFAR RT triggers the LOFAR High Band Array (HBA; 120–168 MHz), which has
a temporal resolution of 1 s, and is capable of being on-target within 4-5 m
(Rowlinson et al., 2019, 2020). In Figure 10, we plot the $3\sigma$ upper-
limits from the LOFAR-RT triggered observation of the long GRB 180706A, which
began 4.5 m post-burst, searching for coherent emission on 30 s, 2 m, 5 m, 10
m and 2 h timescales (Rowlinson et al., 2019). We also include the LOFAR RT
results for the short GRB 181123B, which began 4.4 m post-burst, plotting the
$3\sigma$ upper-limits for the 8 s, 138 s and 2 hr timescales. For both GRBs,
we plot the arrival time of the Swift-BAT VOEvents in light green (based on
the central observing frequency of 144 MHz) as a dotted (GRB 180706A) and dot-
dashed (GRB 181123B) vertical line. The LWA1 also has a rapid-response mode
called the Heuristic Automation for LWA1 (HAL), which can form up to four
steerable beams that can be on-target as fast as two-minutes post-trigger,
which can be tuned to 25.85 and 45.45 MHz (Yancey et al., 2015). For LWA1 HAL,
we assume an approximate sensitivity of 5 Jy ($3\sigma$; Taylor et al., 2012;
Ellingson et al., 2013) for a 1 s integration at 45.45 MHz.

In order to compare the abilities of these three low-frequency triggering
instruments, we also depict the expected dispersion-delayed arrival times of a
prompt/coherent radio signal at four different observing frequencies (chosen
to be relevant for triggered observations with the MWA, LOFAR RT and LWA1 HAL)
as vertical dashed lines in Figure 10, assuming they were emitted at the time
of the GRB for an average SGRB redshift of $z=0.7$. The dispersion-delayed
arrival times also assume a typical Galactic DM of 90 pc cm-3 (185 MHz -
yellow, 144 MHz - light green, 132.5 MHz - dark green, and 45.45 MHz - indigo,
see equation 2 in James et al., 2019c). This clearly demonstrates that both
the MWA and LWA1 HAL are capable of being on-target before the arrival of any
prompt radio signals emitted at the time of the GRB at this average redshift
for the specified observing bands. Given the LOFAR RT trigger delay is between
$\sim 4$ to $5$ m, it will not be on-target in time to detect such a signal
emitted during or just prior to the GRB at 144 MHz. The advantage of LOFAR RT
is its sensitivity, which makes it more relevant for probing persistent,
coherent radio emission that could be emitted for up to several hours
following the GRB event by its magnetar remnant. However, note that in the
case of short GRB 181123B, LOFAR showed similar sensitivities on short
timescales (between 8 and 140 s) to the MWA triggered observations of GRB
180505A (Rowlinson et al., 2020). LOFAR RT triggers also observe for up to 2 h
(as opposed to the 30 m observation obtained by the MWA) so is more likely to
detect any prompt emission emitted by the collapse of said magnetar (if
unstable) into a black hole (see discussions in Rowlinson & Anderson, 2019).

There are also several low frequency facilities with all-sky and/or continuous
monitoring capabilities that rely on serendipitous observations of cataclysmic
and merger events. These include the the LOFAR all-sky monitor called the
Amsterdam ASTRON Radio Transient Facility and Analysis Centre (AARTFAAC;
Prasad et al., 2014; Prasad et al., 2016), which operates when the LOFAR Low
Band Array (LBA; 10-90 MHz) is observing. The Owens Valley Radio Observatory
Long Wavelength Array (OVRO-LWA; e.g. Eastwood et al., 2018) is another
example of an all-sky monitor. Its transient buffer can buffer up to 24 h of
data with a temporal and spectral resolution of 13 s and 24 kHz, respectively,
between 24-84 MHz. Using this transient buffer, both Anderson et al. (2018)
and Callister et al. (2019) have placed similar limits on coherent emission
from the short GRB 170112A and the binary black hole merger GW170104,
respectively. The first station of the Long Wavelength Array (LWA1, 10-88 MHz;
Taylor et al., 2012; Ellingson et al., 2013) also operates two all-sky
transient observing modes, one of which is equipped with the Prototype All Sky
Imager (PASI; Obenberger et al., 2015) backend, which images in near-real-time
at the native temporal resolution of 5 s. LWA1-PASI has already
serendipitously observed GRBs, placing limits at 37.9, 52.0 and 74 MHz
(Obenberger et al., 2014). The sensitivities and corresponding temporal
resolution of these monitoring, all-sky instruments are included in Figure 10
at time 1 s post-burst. While by definition these three programs will be on-
target in-time to receive associated prompt, coherent radio emission
associated with a GRB, they are unlikely to reach the sensitivities required
to detect them (Rowlinson & Anderson, 2019). The biggest limitation is their
temporal resolution, diluting any prompt signals, which are predicted to last
for only milliseconds in most cases. Note there are already plans for the
OVRO-LWA buffer to be upgraded to record at a much finer temporal resolution,
which will make them more sensitive to prompt radio transients (Callister et
al., 2019).

Overall, the MWA is the most competitive low frequency radio telescope for
detecting prompt signals emitted by a GRB just prior-to or during the merger.
This is due to its rapid-response triggering mode, combined with its
competitive instantaneous $(u,v)$ coverage and sensitivity ($0.5$ s) when
compared to all other facilities that are capable of being on-target either
during or rapidly following the GRB alert.

Figure 10: Comparison between the sensitivity and response time for different
low-frequency telescopes. The plotted points give the sensitivity for
different integration times, which are represented by the black bars, and are
colour coded based on the central observing frequency. Different symbols are
used to represent the different telescopes. Those plotted at 1 s post-burst
are continuous monitoring programs (the majority all-sky) that obtain
simultaneous observations of GRBs. The MWA, LOFAR-RT, LWA1 PASI, and OVRO-LWA
limits are from the follow-up of real GRBs. The dotted and dot-dashed vertical
lines show the arrival time post-burst of the Swift-BAT GRB alerts for the MWA
(GRB 150424A: dark green and GRB 180805A: yellow) and LOFAR (GRB 180706A and
GRB 181123B: light green dotted and dot-dashed, respectively) triggered events
with their colours matching the frequency of the observation. The dashed
vertical lines show the expected dispersion-delayed arrival time of a prompt
(FRB-like) signal emitted at the time of the GRB event located at a redshift
of $z=0.7$ for the four different central observing frequencies for the rapid-
response low-frequency telescopes (185, 144, 132.5 and 45.45 MHz), assuming a
typical Galactic DM contribution of 90 pc cm-3. The black horizontal dashed
and dotted lines show the predicted best case 2 hr $3\sigma$ thermal noise
limit for the MWA at 185 MHz (Wayth et al., 2015) and the 2 hr integration
sensitivity ($3\sigma$) for LOFAR at 150 MHz (using the LOFAR Image noise
calculator, assuming a frequency coverage between 120–168 MHz and that all
core, remote and international stations participated in the observation).
Figure 11: As for Figure 10 but the dashed vertical lines show the expected
arrival time of prompt emission associated with a BNS merger at the distance
of GW170817 (40 Mpc; Abbott et al., 2017b) for four different central
observing frequencies (185, 144, 132.5 and 45.45 MHz), assuming a typical
Galactic DM contribution of 90 pc cm-3.

####  4.3.1 Implications for rapid GW follow-up

One source class for which the standard MWA triggered observations are limited
is for nearby merger events. The aLIGO/Virgo O3 observing run had a BNS
horizon limit of $\sim 170$ Mpc, which is far closer than the redshift range
of Swift-detected SGRBs. While associated FRB-like emission will be brighter
due to the event’s proximity, an emitted prompt radio signal will be far less
dispersion delayed. Taking into account the delays associated with
transmitting the alert (best case for aLIGO/Virgo is $\sim 10-20$ s) and the
rapid-response repointing time of the MWA ($4-16$ s), the telescope is
unlikely to be on-target fast enough for observing frequencies $\gtrsim 136$
MHz (assuming a typical Galactic DM of 90 pc cm-3; James et al., 2019c). This
is demonstrated in Figure 11, which shows the response times and sensitivities
of the low frequency rapid-response telescopes (MWA, LOFAR RT and LWA1 HAL,
similar to Figure 10) but with the expected arrival time of a coherent, prompt
signal emitted at the moment of a BNS merger event located at the distance of
GW170817 (40 Mpc; Abbott et al., 2017b). Again, we assume a typical Galactic
DM of 90 pc cm-3 when calculating the signal dispersion delay, however, this
value can vary greatly with the Galactic latitude of the event (see figure 1
of Hancock et al., 2019b) and may therefore have a much shorter dispersion
delay. In Figure 11, it can be seen that rapid-response observations taken at
the lower end of the MWA observing band ($\lesssim 130$ MHz) and observations
within the LWA1 HAL observing band may be on-target in-time to detect
associated prompt signals. However, with the exception of the recent LOFAR
110-188 MHz detections of the repeating FRB 180916B (Pleunis et al., 2021),
prompt, coherent radio signals (aka FRBs) have not been detected below 400 MHz
(e.g. see Tingay et al., 2015; Rowlinson et al., 2016; Sokolowski et al.,
2018; Houben et al., 2019; ter Veen et al., 2019), which motivates searches at
frequencies $>130$ MHz.

Despite the shorter dispersion delays, the MWA still provides the best chance
of detecting prompt, coherent emission associated with aLIGO/Virgo-detected
BNS mergers due to its superior instantaneous sensitivity and rapid repointing
capabilities. James et al. (2019c) therefore devised a strategy for using the
MWA to trigger on ‘negative latency’ aLIGO/Virgo alerts of BNS mergers, which
involves a trigger being generated via the detection of gravitational waves
associated with the inspiral of the compact objects rather than waiting for
the signal produced by the merger. This necessarily shrinks our BNS merger
aLIGO/Virgo horizon with negative latency as inspiral GWs are fainter compared
to the merger. However, the precious seconds gained can be enough time for the
MWA to begin observing the event before the arrival of any prompt, coherent
radio emission. For further details on the proposed observing mode, see James
et al. (2019c).

Given the field of view of the MWA is $\sim 1000\,\mathrm{deg}^{2}$ for the
most commonly used observing frequencies ($120-200$ MHz) there is also a small
($\sim 2-3\%$) chance that any GW/SGRB that occurs during an MWA observation
will be captured by the MWA without any need for triggering or re-pointing of
the instrument.

###  4.4 Prospects for improvement

Since the automated triggered observations were performed for this GRB, we
have continued to improve the response time of the MWA triggering system. We
have optimised the front end processing of the VOEvents to reduce the latency
between receiving an event and requesting an observation from 2.8s (event 3 in
Table 2) to just 4 ms. For this work, all the GRB observations were queued at
once, and were therefore not queued until the Sun avoidance calculation was
performed (see Section 3.1.2 of Hancock et al., 2019b). By computing the Sun
avoidance for only the first observation, queuing that observation
immediately, and then computing and queuing the remainder of the 14
observations, it is possible to further reduce the time between the initial
trigger and the time of the first observation by an additional 1.7 s.

An overall improvement to this experiment is to use the Voltage Capture System
(VCS; Tremblay et al., 2015) when triggering rapid-response observations with
the MWA due to its high temporal and spectral resolution of $100\,\mu$s and
$10$ kHz, respectively. Such a temporal resolution will improve our
sensitivity to prompt (likely millisecond timescale) coherent emission, rather
than the signals being smeared by the standard correlator temporal resolution
of 0.5 s. The higher frequency resolution will also make us more sensitive to
determining the lower DM of nearby events, which is particularly relevant for
GW triggers as aLIGO/Virgo sensitivities only allow for searches of neutron
star mergers out to $<200$ Mpc (Buikema et al., 2020). In fact, Rowlinson &
Anderson (2019) made predictions about prompt coherent emission from SGRBs
over a wide range of redshifts, and compared the capabilities of many of the
low frequency radio telescopes that are actively targeting these events (e.g.
see Figure 10) to detecting such signals. They demonstrated that at early
times (seconds to minutes post-burst/merger) the MWA VCS is the most
competitive instrument for making such detections. VCS triggering on transient
alerts in the form of VOEvents have also recently been commissioned for the
MWA (see Hancock et al., 2019b).

Another suggested improvement will likely come with the MWA Phase III, when we
anticipate that all 256 MWA tiles will be capable of observing simultaneously
(currently only 128 can be run at any one time). Observing with all 256 tiles
will improve the instantaneous sensitivity of MWA and therefore make it more
sensitive to short timescale emission. Expanding the Sun avoidance component
of the rapid-response code to allow for other known bright sources (e.g. the
A-team sources) to be placed in a primary beam null would also improve the
sensitivity of the triggered observations. This would have been advantageous
for our rapid-response observations of GRB 180805A as Cen A was moving into
the primary beam sidelobe within the first 10 min of the observation. Having a
more complete sky model that includes good solutions to the brighter sources
would also help with providing a better calibration, and therefore better
sensitivity. Such a sky model is being developed as part of the GLEAM-X
processing pipeline.111111https://github.com/nhurleywalker/GLEAM-X-pipeline

##  5 Summary and Conclusions

We present the first triggered observation of a SGRB using the upgraded MWA
rapid-response mode. The MWA was observing GRB 180805A 83.7 s post-burst and
was therefore on-target to probe several models (see Section 4.2) that predict
prompt, coherent radio signals to be emitted either just before or for several
minutes following a merger event. We searched for such signals using three
different methods, including:

  1. 1.

A transient search at the Swift-XRT position of GRB 180805A over 0.5 s, 5 s,
30 s and 2 min timescales (resulting in $3\sigma$ flux density limit ranges of
$570-1830$, $270-630$, $200-420$, and $100-200$ mJy beam-1, respectively),
which cover the dispersion delay expected across the MWA observing band for a
range of known SGRB redshifts.

  2. 2.

A search for persistent coherent emission at the Swift-XRT position of GRB
180805A from a (quasi-) stable magnetar remnant over the full 30 min MWA
observation ($3\sigma$ flux density upper-limit of 40.2 mJy beam-1).

  3. 3.

A search for dispersed radio transients at the Swift-XRT position of GRB
180805A in the image domain using 0.5 s coarse channel (24 times 1.28 MHz)
images, which tested for pulse start times and DMs in steps of 0.1 s and 1 pc
cm-3, respectively, over the DM range of 200-3000 pc cm-3. This resulted in a
$6\sigma$ fluence upper-limit range from 570 Jy ms at DM$=3000$ pc cm-3 to
1750 Jy ms at DM$=200$ pc cm-3. Given how rapidly the MWA was on target and
the dispersion delay of such signals at MWA observing frequencies, we were
sensitive to any prompt emission emitted at the time of the GRB 180805A (i.e.
when the first gamma-rays were emitted) for DM trial values $\gtrsim 800$ pc
cm-3, and therefore up to 350 s before the merger for DMs between 800-3000 pc
cm-3.

No transients were detected at the position of GRB 180805A using any of the
above methods, yet we place some of the most stringent constraints on prompt,
dispersed, coherent radio emission on an SGRB to-date on short timescales and
using image dedispersion techniques. Results using these transient analysis
techniques to search for coherent radio signals from a larger sample of SGRBs
that were triggered between 2017 and 2020 using the MWA rapid-response system
will appear in the companion paper Tian et al., in prep.

Despite the deep limits obtained for this GRB, we were unable to place
meaningful constraints on three models that predict coherent radio emission
from SGRBs. Specifically, we cannot constrain the models predicting emission
from the magnetic field alignment of the merging neutron stars (Lyutikov,
2013), from the interaction between the gamma-ray jet and the ISM (Usov &
Katz, 2000) or from persistent pulsar-like emission from the magnetar remnant
(Totani, 2013). However, future events hold significant promise as with a more
powerful GRB with a gamma-ray fluence an order of magnitude higher than GRB
180805A and/or a brighter X-ray counterpart we would expect a brighter prompt
radio signal from the jet-ISM interaction and potentially a detectable pulsar-
like radio counterpart. In addition, these models could be more tightly
constrained for a GRB with a known redshift (Usov & Katz, 2000). Finally, if
such an event were then at a low redshift ($z\lesssim 0.5$) then according to
these models our MWA observations may be sensitive enough to detect this
coherent emission using the image dedispersion technique presented in this
paper.

Due to its extremely rapid transient response time, the MWA is therefore
currently the most competitive low frequency instrument for probing prompt and
coherent radio emission models that predict the production of such signals
just prior, during or shortly following a merger event (see Section 4.3).
While the MWA has the sensitivity to constrain some models, particularly at
low redshifts, better instantaneous sensitivity on shorter timescales, such as
will be possible with SKA-Low, are required to truly probe many of these
coherent emission models. This illustrates the importance of ensuring that the
SKA-Low has a rapid-response mode of operation that is capable of being
triggered and on-target within seconds of receiving a transient alert.

## Acknowledgements

Facilities: This scientific work makes use of the Murchison Radio-astronomy
Observatory, operated by CSIRO. We acknowledge the Wajarri Yamatji people as
the traditional owners of the Observatory site. Support for the operation of
the MWA is provided by the Australian Government (NCRIS), under a contract to
Curtin University administered by Astronomy Australia Limited.

This work made use of data supplied by the UK Swift Science Data Centre at the
University of Leicester and the Swift satellite. Swift, launched in November
2004, is a NASA mission in partnership with the Italian Space Agency and the
UK Space Agency. Swift is managed by NASA Goddard. Penn State University
controls science and flight operations from the Mission Operations Center in
University Park, Pennsylvania. Los Alamos National Laboratory provides gamma-
ray imaging analysis.

This work was supported by resources provided by the Pawsey Supercomputing
Centre with funding from the Australian Government and the Government of
Western Australia.

Funding: GEA is the recipient of an Australian Research Council Discovery
Early Career Researcher Award (project number DE180100346), and JCAM-J, NH-W,
and TM are the recipients of the Australian Research Council Future Fellowship
(project numbers FT140101082, FT190100231, and FT150100099) funded by the
Australian Government.

People: We thank the referee for their careful reading of the manuscript and
recommendations. The authors wish to thank Marco De La Pierre, Paolo Di
Tommaso, and Evan Floden, for the well timed Nextflow workshop that enabled
the authors to port Robbie to Nextflow.

Software: The following software and packages were used to support this work:
mwa_trigger (Hancock et al.,
2019b)121212https://github.com/MWATelescope/mwa_trigger/, GLEAM-X
pipeline131313https://github.com/nhurleywalker/GLEAM-X-pipeline, MWA-fast-
image-transients141414https://github.com/PaulHancock/MWA-fast-image-
transients, flux_warp (Duchesne et al.,
2020)151515https://gitlab.com/Sunmish/flux_warp/, comet (Swinbank, 2014),
voevent-parse (Staley & Fender, 2016), Robbie (Hancock et al.,
2019a)161616https://github.com/PaulHancock/Robbie, AegeanTools (Hancock et
al., 2018)171717https://github.com/PaulHancock/Aegean, fits_warp (Hurley-
Walker & Hancock, 2018)181818https://github.com/nhurleywalker/fits_warp,
TOPCAT/stilts (Taylor, 2005), Astropy (The Astropy Collaboration et al., 2013;
Astropy Collaboration et al., 2018), numpy (van der Walt et al., 2011), scipy
(Jones et al., 2001), matplotlib (Hunter, 2007),
docker191919https://www.docker.com/, singularity (Kurtzer et al., 2017). This
research has made use of NASA’s Astrophysics Data System. This research has
made use of SAOImage DS9, developed by Smithsonian Astrophysical Observatory.
This research has made use of the VizieR catalogue access tool (Ochsenbein et
al., 2000) and the SIMBAD database (Wenger et al., 2000), operated at CDS,
Strasbourg, France.

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