# Rapid-response radio observations of short GRB 181123B with the Australia
Telescope Compact Array

G. E. Anderson1 M. E. Bell,2 J. Stevens,3 M. D. Aksulu,4 J. C. A. Miller-
Jones,1 A. J. van der Horst,5,6 R. A. M. J. Wijers,4 A. Rowlinson,4,7 A.
Bahramian,1 P. J. Hancock,1 J.-P. Macquart,1 S. D. Ryder,8,9 R. M. Plotkin10
1International Centre for Radio Astronomy Research, Curtin University, GPO Box
U1987, Perth, WA 6845, Australia
2University of Technology Sydney, 15 Broadway, Ultimo NSW 2007, Australia
3CSIRO Astronomy and Space Science, Australia Telescope National Facility, Box
76, Epping, NSW 1710, Australia
4Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science
Park 904, NL-1098 XH Amsterdam, The Netherlands
5 Department of Physics, The George Washington University, 725 21st Street NW,
Washington, DC 20052, USA
6 Astronomy, Physics, and Statistics Institute of Sciences (APSIS), 725 21st
Street NW, Washington, DC 20052, USA
7 ASTRON, the Netherlands Institute for Radio Astronomy, Postbus 2, NL-7990 AA
Dwingeloo, The Netherlands
8 Department of Physics and Astronomy, Macquarie University, Sydney NSW 2109,
Australia
9 Macquarie University Research Centre for Astronomy, Astrophysics &
Astrophotonics, Sydney, NSW 2109, Australia
10 Department of Physics, University of Nevada, Reno, NV 89557, USA Contact
e-mail<EMAIL_ADDRESS>address: International Centre for
Radio Astronomy Research, Curtin University, GPO Box U1987, Perth, WA 6845,
Australia

(Last updated 2021 Mar 3; in original form 2020 Apr 29)

###### Abstract

We introduce the Australia Telescope Compact Array (ATCA) rapid-response mode
by presenting the first successful trigger on the short-duration gamma-ray
burst (GRB) 181123B. Early-time radio observations of short GRBs may provide
vital insights into the radio afterglow properties of Advanced LIGO- and
Virgo-detected gravitational wave events, which will in turn inform follow-up
strategies to search for counterparts within their large positional
uncertainties. The ATCA was on target within 12.6 hr post-burst, when the
source had risen above the horizon. While no radio afterglow was detected
during the 8.3 hr observation, we obtained force-fitted flux densities of
$7\pm 12$ and $15\pm 11\mu$Jy at 5.5 and 9 GHz, respectively. Afterglow
modelling of GRB 181123B showed that the addition of the ATCA force-fitted
radio flux densities to the Swift X-ray Telescope detections provided more
stringent constraints on the fraction of thermal energy in the electrons (log
$\epsilon_{e}=-0.75^{+0.39}_{-0.40}$ rather than log
$\epsilon_{e}=-1.13^{+0.82}_{-1.2}$ derived without the inclusion of the ATCA
values), which is consistent with the range of typical $\epsilon_{e}$ derived
from GRB afterglow modelling. This allowed us to predict that the forward
shock may have peaked in the radio band $\sim 10$ days post-burst, producing
detectable radio emission $\gtrsim 3-4$ days post-burst. Overall, we
demonstrate the potential for extremely rapid radio follow-up of transients
and the importance of triggered radio observations for constraining GRB blast
wave properties, regardless of whether there is a detection, via the inclusion
of force-fitted radio flux densities in afterglow modelling efforts.

###### keywords:

transients: gamma-ray bursts – gamma-ray burst: individual: GRB 181123B –
radio continuum: transients – transients: neutron star mergers – gamma-ray
burst: general

††pubyear: 2021††pagerange: Rapid-response radio observations of short GRB
181123B with the Australia Telescope Compact Array–7

##  1 Introduction

The first gravitational wave (GW) detection of a binary neutron star (BNS)
merger, GW170817, by the Advanced LIGO and Virgo (aLIGO/Virgo) facilities, was
an eagerly awaited event (Abbott et al., 2017a). Such a merger was predicted
to produce a multi-wavelength electromagnetic afterglow radiating from radio
to gamma-rays, and GW170817 did not disappoint (Abbott et al., 2017b; Andreoni
et al., 2017). The most conspicuous predicted counterpart was the prompt
ejection of collimated, short-lived gamma-ray emitting jets, similar to the
observed short gamma-ray burst (SGRB, gamma-ray durations $<2$ s; Narayan et
al., 1992) phenomenon, which is one of the two main classes of gamma-ray burst
(GRB; Norris et al., 1984; Dezalay et al., 1992; Kouveliotou et al., 1993)
detected 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). The
other dominant population known as long GRBs (LGRBs) typically have durations
$>2$ s and are attributed to core collapse supernovae (e.g. Galama et al.,
1998a; Bloom et al., 1998). It was therefore the near-simultaneous detection
of GW170817 and GRB 170817A (the latter of which was a SGRB detected by Fermi;
Abbott et al., 2017b) and the late-time radio and X-ray follow-up confirming
the presence of an off-axis jet (e.g. Mooley et al., 2018; Ghirlanda et al.,
2019; Troja et al., 2019a) that strongly supported the link between BNS
mergers and SGRBs.

The detection of the electromagnetic counterpart to a aLIGO/Virgo-detected BNS
merger is of great importance as it enables the localisation of the source,
along with providing complementary information such as an independent distance
measurement, insight into the central engine, the energy released, and the
final merger remnant. However, the initial localisation of a GW event by
aLIGO/Virgo is tens to hundreds of square degrees, making it difficult to
search for counterparts. We therefore introduce a method designed to exploit
the established link between GW-detected BNS mergers and SGRBs by using the
Australia Telescope Compact Array (ATCA) rapid-response mode to trigger on
Swift-detected SGRBs.

While the radio emission from SGRBs is usually short-lived ($\lesssim 2$ days;
Fong et al., 2015), the ATCA rapid-response mode is capable of being on-source
within $10$ minutes. By rapidly responding to Swift SGRB triggers, ATCA can
become a new diagnostic tool for uncovering the range of radio behaviour shown
by SGRBs to help interpret what to look for from GW events that have off-axis
gamma-ray jets. As targeted observations can usually reach deeper
sensitivities than wide-field surveys, ATCA observations can provide a
template of the radio brightness and timing properties of BNS mergers, which
will in-turn inform the follow-up strategies of the next era of aLIGO/Virgo GW
events by wide-field radio telescopes, such as Australian instruments like the
Murchison Widefield Array (MWA; Tingay et al., 2013) and the Australian Square
Kilometre Array Pathfinder (ASKAP; Johnston et al., 2008).

The jet launched during an SGRB is expected to produce a radio afterglow as
predicted by the fireball model (Cavallo & Rees, 1978; Rees & Meszaros, 1992).
In this model, the relativistic ejecta interact with the circumstellar medium
(CSM) producing a forward shock that accelerates electrons and generates
synchrotron emission. Reverse shock synchrotron emission, produced by the
shock that propagates back into the post-shock ejecta, may also be observed
depending on the density of the CSM and the ejecta. The broadband spectrum
produced by the jet interactions in the GRB afterglow is described by the peak
flux and 3 characteristic frequencies ($\nu_{m}$, the minimum electron energy
frequency; $\nu_{sa}$, the synchrotron self-absorption frequency; and
$\nu_{c}$, the electron cooling frequency), which evolve over time (Sari et
al., 1998; Wijers & Galama, 1999; Granot et al., 1999). Only early-time radio
observations are able to properly constrain 2 of these 3 frequencies
($\nu_{m}$ and $\nu_{sa}$), and also disentangle the reverse and forward shock
components. By combining ATCA observations with multi-wavelength observations
to perform SED modelling, these parameters can be derived, thus providing
information about the blast wave kinetic energy, the CSM density, the magnetic
field energy density and the power law electron energy distribution (Sari et
al., 1998; Wijers & Galama, 1999; Granot et al., 1999). Limits on the linear
polarisation of the reverse shock can also provide information on the jet
magnetic field structure (Granot & van der Horst, 2014). Early-time radio
observations of SGRBs are also sensitive to temporal steepening from the jet-
break (Sari et al., 1999), which constrains the jet opening-angle used to
calculate the true energy released (and therefore merger BNS/GW event rates,
e.g. Fong et al., 2014, 2015; de Ugarte Postigo et al., 2014). Even early-time
non-detections in the radio band can allow us to make predictions about when
the forward-shock emission may peak, which can inform the cadence and duration
of follow-up radio observations, potentially optimising the success of a late-
time detection as we demonstrate in this paper. In addition, sensitive, multi-
frequency, high-cadence radio observations may allow us to distinguish between
more exotic emission models caused by the ejection of neutron star material or
the propagation of shocks caused by the merger event, which may produce non-
to ultra-relativistic omnidirectional radio emission (e.g. Nakar & Piran,
2011; Kyutoku et al., 2014). It is therefore crucial to obtain early-time
radio observations (within minutes to days) of a larger sample of SGRBs to
better characterise the timescales and frequencies necessary for understanding
the range of behaviours we might expect from GW radio counterparts.

There are also several BNS merger models that suggest a short-lived,
supramassive and highly magnetised neutron star (NS) or “magnetar”, supported
by rotation, can exist for a short time ($<10^{4}$ s) before finally forming a
stable magnetar or further collapsing into a black hole (BH, e.g. Usov, 1992;
Zhang & Mészáros, 2001; Falcke & Rezzolla, 2014; Zhang, 2014). Evidence for
such merger products comes from the detection of a “plateau phase” in some
SGRB X-ray light curves between $\sim 10^{2}-10^{4}$ s post-burst, where this
departure from power-law decay indicates ongoing energy injection (Rowlinson
et al., 2013). Such merger remnant scenarios may be sources of prompt,
coherent radio emission (see Rowlinson et al., 2016, for a review). However,
no continuous monitoring of the radio behaviour has yet been performed at GHz
frequencies during the plateau phase. Such detections or upper limits could
constrain different central engine models as has been done at late-times (e.g.
Fong et al., 2016).

Only eight SGRBs have published detections in the radio band to date: GRB
050724A, 051221A, 130603B, 140903A, 141212A, 150424A, 160821B and 200522A
(Berger et al., 2005; Soderberg et al., 2006; Fong et al., 2014, 2015, 2017;
Troja et al., 2016; Zhang et al., 2017; Troja et al., 2019b; Lamb et al.,
2019; Fong et al., 2021). Note that this does not include GW170817 as it had a
far more off-axis outflow than standard cosmological SGRBs so the
corresponding radio afterglow was detected much later when the ejecta had
moved into our line-of-sight (Mooley et al., 2018). Out of a sample of $>70$
radio-observed SGRBs, only $\sim 10$% have been detected in the radio band at
GHz frequencies (Fong et al., 2021). This low detection rate may be due to an
observed fast rise in radio emission with a potentially short radio afterglow
lifetime. For example, 7 of the 8 radio-detected SGRBs were detected within 1
day post-burst, at least half of which faded below detectability within $\sim
2$ days (see Figure 1). Given these short timescales, it is possible the radio
emission is frequently dominated by the reverse-shock (as was the case for GRB
051221A; Soderberg et al., 2006) since simulations of BNS mergers demonstrate
forward shock radio emission may evolve over days to weeks (Hotokezaka et al.,
2016) as is also the case for many LGRBs (e.g. van der Horst et al., 2008,
2014). If we instead compare the radio-detected sample to those SGRBs that
were initially observed at radio wavelengths $<1$ day post-burst, this gives a
much higher radio detection rate of $\sim 30$% (Fong et al., 2015). However,
while the first four radio-detected SGRBs showed initial flux densities of
$>0.1$ mJy/beam at GHz frequencies, few of the other $<1$ day post-burst
pre-2016 observations had sufficient sensitivity to detect a predicted peak
flux density of $\sim 40\mu$ Jy/beam at 10 GHz for an SGRB at an average
redshfit of $z=0.5$ with an expected CSM density of $n_{0}\sim 0.1$ cm-3
(Berger, 2014). In fact, the four most recent radio-detected SGRBs peak at
$\lesssim 40\mu$ Jy/beam.

The small sample of radio detected SGRBs therefore provides limited knowledge
of their radio afterglow brightnesses and timescales, and is insufficient for
deriving the energy outputs and environmental properties of the population
through multi-wavelength modelling. It is therefore vital to perform both
rapid and sensitive radio follow-up observations of SGRBs to capture these
short-lived and faint events. The key to achieving this is through the use of
rapid-response (also known as triggering) systems, where a telescope has the
ability to automatically respond to a transient alert, and either repoint at
the event or update its observing schedule to begin observations when the
source has risen above the horizon. Rapid-response radio telescopes have been
in use since the 1990’s (for example see Green et al., 1995; Dessenne et al.,
1996; Bannister et al., 2012; Palaniswamy et al., 2014; Kaplan et al., 2015)
but predominantly at low radio frequencies (100 MHz to 2.3 GHz), with the
majority of experiments being designed to search for prompt, coherent radio
emission. However, until recently, the only high frequency ($>5$ GHz) rapid-
response program designed to target incoherent (synchrotron) radio emission
from GRBs has been run on the Arcminute Microkelvin Imager (AMI) Large Array
(LA), known as ALARRM (the AMI-LA Rapid Response Mode), which has been active
since 2012 (Staley et al., 2013; Anderson et al., 2018a). It was only through
ALARRM that it was possible to be on-source fast enough to detect the rise and
peak in the reverse-shock radio emission at 15 GHz from GRB 130427A within 1
day post-burst, which also represents one of the earliest radio detections of
a GRB to date (Anderson et al., 2014). In addition, the radio catalogue of AMI
observations of 139 GRBs (12 were short GRBs but non-detections), the majority
of which were automatically triggered on using the rapid-response mode within
$1$ day post-burst, was the first representative sample of GRB radio
properties that was unbiased by multi-wavelength selection criteria (Anderson
et al., 2018a). This work revealed that possibly up to $\sim 44-56$% of Swift-
detected LGRBs have a radio counterpart (down to $\sim 0.1-0.15$ mJy/beam),
with the increase in detection rate from previous studies ($\sim 30$%; Chandra
& Frail, 2012) likely being due to the AMI rapid-response mode, which allows
observations to begin while the reverse-shock is contributing to the radio
afterglow. This program has motivated the installation of a rapid-response
mode on the ATCA.

Here we present the first triggered observation of a SGRB using the new ATCA
rapid-response mode. ATCA is an ideal instrument for performing triggered
radio follow-up of Swift SGRBs due to its high sensitivity and broadband
receivers that provide simultaneous multi-frequency coverage. The ATCA
response times (which can be as short as minutes) have the potential to be
much faster than the current median SGRB response of the Karl G. Jansky Very
Large Array (VLA; $\sim 24.7$ hrs), which rely on manually scheduling target-
of-opportunity observations (Fong et al., 2015). In Section 2, we describe the
ATCA rapid-response system from the observer interaction (front-end) level and
the observatory (back-end) level. In Section 3, we describe the triggered ATCA
observation and data reduction of GRB 181123B, and corresponding results. This
is followed by a comparison of our radio limits for GRB 181123B to the sample
of radio-detected SGRBs and a discussion of the parameter space that the
triggered ATCA observations are probing in Section 4. Finally, we perform
modelling of the GRB 181123B afterglow and thus demonstrate the usefulness of
obtaining early-time (within 1 day) radio observations of an SGRB (regardless
of whether or not there is a detection) to place constraints on the GRB
physics.

##  2 ATCA rapid-response mode

ATCA is a six element, 22 m dish, East-West interferometer based in New South
Wales in Australia. Its maximum baseline length is 6 km and it is capable of
observing in multiple, broad frequency bands with full polarisation, and in a
variety of array configurations. ATCA is currently equipped with the Compact
Array Broadband Backend (CABB; Wilson et al., 2011), which has a 2 GHz
bandwidth that is capable of observing in two frequency bands simultaneously
with tunable receivers that operate between 1.1-105 GHz.

Since 2017 April 18, ATCA has been capable of rapidly responding to transient
alerts. The rapid-response mode can trigger using the 16 cm, 4 cm and 15 mm
receivers, corresponding to a usable frequency range of $1.1-25$ GHz, and can
observe in any CABB mode. In the following, we describe both the observer
front-end and the observatory back-end of this new triggering system.

###  2.1 VOEvent parsing/front-end

The front-end software we use to interface with the ATCA rapid-response system
(vo_atca)111https://github.com/mebell/vo_atca is designed to trigger on
Virtual Observatory Events (VOEvent; Seaman et al. 2011), which are the
standard format for broadcasting machine readable astronomical alerts related
to transient events. A VOEvent package contains all the required data (in xml
format) that allow automated decisions to be made in real-time given certain
keywords and parameters. VOEvents are brokered via the 4 Pi Sky VOEvent Broker
(Staley & Fender, 2016) and the comet VOEvent client (Swinbank, 2014). These
packages allow us to listen to multiple VOEvent streams, including those
broadcast by Swift. We use the Python package vovent-parse (Staley, 2014) as
the main tool to read the VOEvents and to extract the required information to
be assessed by the triggering algorithm.

Upon receiving a Swift VOEvent, the ATCA VOEvent parser uses the keyword
grb_identified = true to initially identify a GRB packet. Packets containing
startrack_lost_lock=true are ignored as it means that Swift has lost its
celestial position-lock so such an alert is unlikely to be from a real
transient. While the observatory back-end prevents the telescope from
overriding for sources that are too far north (see Section 2.2), we impose an
additional declination cut-off for all SGRBs north of +15∘ to ensure the
potential for $>8$ hr integrations for the triggered observations.

On passing these stages, the parser then assesses the duration of the trigger
so that SGRB candidates can be identified. However, on the short timescales
following the alert, and with growing uncertainty as the GRB burst duration
increases, it is difficult to classify Swift GRBs as short or long in an
automated way. A rigorous classification of the GRB requires human inspection
of the data, which is only published online on the Gamma-ray Coordinates
Network Circulars (GCN) Archive,222https://gcn.gsfc.nasa.gov/gcn3_archive.html
usually between 10 mins and 1 hr post-burst and therefore not via a VOEvent.
To account for this, we implemented a three-tiered system to flexibly respond
to different GRB durations and therefore filter for those events more likely
to be SGRBs. The keyword integ_time (the length of time for the transient
signal to reach a significant threshold) parameter is used as an estimator of
the incoming GRB’s true duration.

  * •

GRBs with integ_time$<$0.257 s have a high probability of being SGRBs so the
VOEvent parser will automatically submit these triggers to the observatory and
alert team members via text and email of the override observation.

  * •

With durations $0.257$ s $<$integ_time $<1.025$ s, we have implemented a
"wait-to-proceed" algorithm as the probability of the GRB being a SGRB
decreases with increasing integ_time. In this case, we issue email and text
alerts so that team members can check the GCN Archive for adequate
verification of the GRB classification. If the GRB is confirmed to be short,
then the duty team member responds "YES" to the detection email, and this
email reply is read by an algorithm (via the Google email Application
Programming Interface333https://developers.google.com/gmail/api) that then
proceeds with submitting the trigger to ATCA, resulting in an override
observation. This provides an easy interface to assess and submit triggers via
a mobile phone, which can receive SMS alerts and allow responding to emails
away from a computer.

  * •

If integ_time$>$1.025 s then we presume that the GRB is long and we do not
proceed with submitting a trigger to override the telescope.

After the parser (or duty team member) has successfully identified the event
as an SGRB, our algorithm then searches the ATCA calibrator database for a
nearby and suitable phase calibrator. It then automatically builds a schedule
file (we use the ATCA scheduler software cabb-schedule-
api)444https://github.com/ste616/cabb-schedule-api for a 12-hour observation
of the GRB in the requested frequency band (for GRB triggering we currently
use the 4 cm receiver), which has interleaved phase calibrator observations
every 20 minutes. Note that the total exposure time is also limited by how far
the GRB is above the horizon at the time of the trigger. The schedule file and
override request is then submitted to the observatory where it is assessed for
submission to the observing queue by the ATCA back-end.

###  2.2 Observatory back-end

Time on the ATCA is scheduled into two 6-month long semesters, and the order
of observations in each semester is set months in advance. This is done to
allow the project investigators, who are also responsible for conducting the
observations, to plan their activities. A rapid-response system is not easily
compatible with this mode of operation.

Nevertheless, demand for the telescope to quickly respond to events has been
steadily rising. In 2016, roughly 10% of telescope time was given to NAPA (Non
A-priori Assignable) or ToO (Target of Opportunity) projects, while in 2019
this figure had risen to 19%. For a NAPA project, a science case is given to
the time assignment committee (TAC), which ranks its significance against the
other projects for that semester. Provided the science is considered
compelling, these projects are allowed to displace time from other projects
during the semester, with the philosophy being that were we to know during the
scheduling process when an event would happen, a compelling project would have
been scheduled to observe it.

Rapid-response NAPAs operate in the same way. A scientific justification must
be supplied to the TAC, who must agree that rapid response is warranted. The
observatory then supplies an authentication Javascript Web Token (JWT) to the
project, and assists the investigators to test their automatic triggering
system.

A web service is provided so that the trigger to start observations can be
sent from any internet-connected device. A Python library (atca-rapid-resonse-
api) is also available to make it easier to send requests to this
service.555https://github.com/ste616/atca-rapid-response-api All requests must
contain a valid schedule file, and must nominate the target coordinates and a
nearby phase calibrator.

Upon receipt of a trigger, the web service tries to schedule the observation
as soon as possible. If the source is above the horizon and the user-nominated
minimum useful observing time can be obtained before the source sets, the
current and subsequent observations can be displaced and the system can start
the observations within 2 seconds of the trigger’s arrival. Within that time,
emails are sent to the projects that will be displaced, and to the triggering
team, describing the new order of the scheduling. The schedule is also altered
as necessary to add a scan on a flux density calibrator at an opportune time,
and potentially to shorten the observations to fit the available time. At all
times, the emphasis is to move the telescope to the target coordinates as
quickly as possible.

The service can also provide an immediate rejection should no suitable time be
found for the observation. For example, if no available time can be found up
to 100 hours in the future (generally because the request was made during a
time when the array is shutdown for maintenance or participating in VLBI
observing), the observations are rejected and the proposal team are notified.
While no explicit limit is set for the source declination, sources too far
north may not be available for the user-nominated minimum useful observing
time, and will thus be rejected.

If the web service can schedule the observations, a separate service then
takes over, and takes control of the observing control software. Some more
checks are made to see if the array can be used for observing, and will delay
the start of the observations if the weather conditions are unsuitable. This
service also monitors the observations for interruptions due to weather,
equipment failure and human intervention. Rudimentary responses are pre-
programmed for any such eventuality. The service stops once the observations
have finished, the target sets, or the observations are cancelled, whichever
comes first. Control of the telescope then goes to the investigators whose
project was scheduled to be running at this end time.

A more complete guide to the operation of the rapid-response system is
provided in the ATCA Users
Guide.666https://www.narrabri.atnf.csiro.au/observing/users_guide/html/atug.html

###  2.3 Triggering performance

Since the commencement of the program, we have worked with the observatory to
improve the success of SGRB triggered observations with ATCA, which involved
extensive system and software debugging. Many SGRBs were missed due to the
telescope being in uninterruptible modes such as maintenance, reconfiguration,
participating in VLBI or operating in an incompatible correlator mode (the
latter has since been resolved).

Our original override strategy involved triggering on all Swift GRBs with
integ_time$<1.025$ s as SGRBs have been detected with integ_time up to $1.024$
s. However, as mentioned in Section 2.1, the majority of events within this
timescale are LGRBs. Swift data requires a human in the loop to classify the
event as long or short, which is usually based on the duration and the
hardness of the event (note that SGRBs often produce higher energy prompt
emission than LGRBs) and are only published on the GCN Archive up to an hour
post-burst (also note that the distinction between events with durations
between $1-2$ s can be tenuous and has led to discussions regarding
intermediate GRB classes; e.g. Mukherjee et al., 1998; Horváth, 1998; Huja et
al., 2009; de Ugarte Postigo et al., 2011). This original strategy therefore
resulted in several false ATCA triggers, most of which were identified and
cancelled before the telescope was overridden as there was additional lead
time before the event in question had risen above the horizon. However, there
were a few instances where some data was collected on LGRBs. Recent edits to
the VOEvent parsing of event timescales using the keyword integ_time, which
are described in Section 2.1 have resulted in a significant reduction in ATCA
triggers of LGRB contaminants.

When ATCA receives a trigger of an event that is above the horizon, the main
limitation to the response time is the telescope slew speed. On receiving the
VOEvent via the parsing code, it takes $2-3$ s for the observation to be
queued and the subsequent maximum observing time calculated. Following a Swift
alert on the long GRB 190519A (Ukwatta et al., 2019), ATCA was on target and
observing the event in 2 min and 39 s. Other response times range between
$3-6$ min post-burst, which make the ATCA rapid-response system competitive
with other triggering facilities such as AMI (e.g. Anderson et al., 2018a) yet
is also based in the Southern Hemisphere, has more collecting area, a larger
number of frequency bands, polarisation capabilities, and (in some
configurations) better angular resolution.

###  2.4 Short GRB experimental design

The majority of GRBs detected by Swift-BAT are LGRBs, with SGRBs (in this case
events with $T_{90}\leq 2$ s including those found in ground analysis) only
accounting for $\sim 7-8$% (this is based on event numbers between 2017 and
2019 using the Swift GRB Look-up
Table,777https://swift.gsfc.nasa.gov/archive/grb_table/ where $T_{90}$ is the
time between 5 and 95% of the fluence being emitted). We therefore expect
$\sim 5-10$ SGRBs to be detected by Swift per year, and therefore predict
$\lesssim 2$ will be observable with ATCA (below a Declination cut-off of +15
deg) during an observing semester.

Our rapid-response observations are performed using the $4$ cm receiver, which
has dual 2 GHz windows that are usually centered at 5.5 and 9 GHz, which is
the most sensitive ATCA band. This choice is based on several factors: the
full-width half-maximum of the primary beam encompasses the initial Swift-BAT
positional uncertainty of newly detected GRBs (1-4 arcmin; Barthelmy et al.,
2005), it is largely immune to atmospheric instabilities, and is less
disrupted by RFI than other ATCA bands. In addition, as synchrotron emission
from GRB reverse and forward shocks peaks earlier and brighter with increasing
frequency, the 4 cm band (5.5/9 GHz) is optimal for ensuring the source will
be bright but not peaking before the telescope is on-target.

As mentioned in Section 1, the radio afterglows from SGRBs are usually
detected within 1 day post-burst (e.g. Fong et al., 2015), which strongly
motivates our need for the ATCA rapid-response mode. The triggered
observations are designed to observe between $2-12$ h (depending on how long
the source is above the horizon following the trigger). As previous SGRB radio
studies have shown that the radio afterglow has already switched-on within
$4-16$ h post-burst (e.g. Anderson et al., 2018a), a $\leq 12$ hr observation
allows us to track the rapid rise in emission with a sensitivity of $\sim
60\,\mu$Jy ($3\sigma$) on one hour
timescales.888https://www.narrabri.atnf.csiro.au/myatca/interactive_senscalc.html
This means that any delays of $\leq 1$ hr related to waiting for the GRB
classification does not affect the rapid-response science goal (see Section
2.1). A $\leq 12$ hr track also ensures some periods of simultaneous Swift
X-ray Telescope (XRT, observing band between $0.3-10$ keV; Lien et al., 2018)
observations, which is essential for modelling the spectral energy
distribution (SED), and for exploring the radio properties associated with the
plateau phase (e.g. see our modelling in Section 4.1).

Following the triggered, rapid-response observation, we also request three
$\sim 4$ hr follow-up observations in the $4$ cm band to occur between $1-3$,
$4-6$, and $8-12$ days post-burst, which can reach a sensitivity of
$30\,\mu$Jy ($3\sigma$). While 3 of the previous radio-detected SGRBs faded
below detectability within 2 days post-burst, the other 2 were detected up to
10 days post-burst (see Figure 1), thus motivating this more long-term
monitoring of any triggered candidate.

Figure 1: Radio light curves of SGRB radio detections ($1\sigma$ error bars)
and $3\sigma$ upper-limits observed at frequencies between 6 and 10 GHz. Left:
Radio flux density vs days post-burst and Right: $k$-corrected spectral
luminosity vs days post-burst in the rest-frame. The 9 GHz upper-limit of GRB
181123B is depicted as a large white triangle. For those GRBs without a known
redshift we assume $z=0.5$. The $3\sigma$ upper limits of those SGRBs that
were observed but not detected in the radio band are depicted as grey
triangles. References for all radio flux densities and redshifts for radio-
detected SGRBs: Berger et al. (2005), Fox et al. (2005), Prochaska et al.
(2005), Soderberg et al. (2006), Cucchiara et al. (2013), de Ugarte Postigo et
al. (2014), Cucchiara et al. (2014), Chornock et al. (2014), Fong et al.
(2014), Fong et al. (2015), Troja et al. (2019b), Lamb et al. (2019), Paterson
et al. (2020), Fong et al. (2021). All radio upper limits shown in grey were
taken from Fong et al. (2015, see references therein).

##  3 ATCA observations of GRB 181123B

Swift-BAT detected the short GRB 181123B at 05:33:03 UT (trigger=873186),
which was rapidly detected in the X-rays by the Swift-XRT and localised to the
position
$\alpha\mathrm{(J2000.0)}=12^{\mathrm{h}}17^{\mathrm{m}}28\overset{\mathrm{s}}{.}05$
and
$\delta(\mathrm{J2000.0})=+14^{\circ}35^{\prime}52\overset{{}^{\prime\prime}}{.}4~{}$
with a 90% confidence of $1\overset{{}^{\prime\prime}}{.}8$ (Osborne et al.,
2018). Further optical and near-infrared follow-up detected a source
coincident with the Swift-XRT position (Fong et al., 2018; Paterson & Fong,
2018; Paterson et al., 2018), resulting in the identification of the host
galaxy at redshift $z=1.754$ and the detection of the optical afterglow to GRB
181123B ($i=25.1$ mag at $9.1$ h post-burst; Paterson et al., 2020). This
makes GRB 181123B one of only three SGRBs at $z>1.5$ (Paterson et al., 2020).

On receiving the VOEvent trigger, ATCA was automatically scheduled to begin
observations on 2018 Nov 23 at 18:07:24.9 UT (12.6 h post-burst) for 8.3 h
(Anderson et al., 2018b), when the GRB had risen above the horizon (minimum
elevation of 12 deg). On this date, ATCA was in the 6B array configuration,
and the triggered observations were taken in the 4 cm band, with the dual 2
GHz bandwidth windows centered at 5.5 and 9 GHz. The observation pointing was
at the initial BAT position, which was $1.2$ arcmin offset from the final
Swift-XRT position of GRB 181123B. Note that we requested no follow-up ATCA
observations due to the imminent reconfiguration and correlator reprogramming,
with many subsequent programmes having priority.

The ATCA rapid-response observation was reduced and analysed with the radio
reduction software MIRIAD (Sault et al., 1995) using standard techniques. Flux
and bandpass calibration were conducted using PKS 1934-638 and phase
calibration with PKS 1222+216. Several rounds of phase and amplitude self
calibration were also applied (this was possible due to the nearby bright
field source FIRST J121731.7+143953; Helfand et al., 2015). In order to obtain
the most robust flux density upper limits at the position of the GRB, we used
mfclean to create a clean model of the sources in the field (manually drawing
clean boxes) and subtracted this model from the visibilities. A primary beam
correction was then applied due to the 1.2 arcmin offset between the pointing
centre and the best known GRB position from the Swift-XRT. GRB 181123B was not
detected, and the final $3\sigma$ upper-limits can be found in Table 1.

As we know the precise location of GRB 181123B to within the ATCA beam, we
also report the peak force-fitted flux density at both 5.5 and 9 GHz in Table
1. These were calculated using the task imfit to force-fit a Gaussian to the
beam that was fixed at the Swift-XRT position of the GRB (errors are the
$1\sigma$ rms). The advantage of quoting the force-fitted flux density over an
upper-limit is that such a measurement also accounts for the presence of
nearby sources, as well as variations in the noise across the image. The data
were also divided into 3 h and 1 h timescales and then re-imaged to search for
evidence of emission that may have switched on nearer the end of the
observation; however none was detected.

Table 1: ATCA observations of GRB 181123B at 5.5 and 9 GHz, which began on 2018 Nov 23 at 18:07:24.9 UT (12.6 h post-burst) for 8.3 h. Frequency |  $3\sigma$ Upper-limit | Forced-fit flux density
---|---|---
(GHz) | ($\mu$Jy/beam) | ($\mu$Jy/beam)
5.5 | 34 | $7\pm 12$
9.0 | 32 | $15\pm 11$

##  4 Discussion

In this section, we first demonstrate that our radio flux density limits for
GRB 181123B are consistent and competitive with previous studies of the radio-
detected SGRB population. This is followed by afterglow modelling to
demonstrate the importance of obtaining early-time radio observations
(regardless of whether there is a detection) to better constrain the
properties of the blast wave.

In Figure 1, we show the light curves of SGRBs observed in the radio band
between 6 and 10 GHz. The 8 radio-detected SGRBs are colour-coded with
$3\sigma$ upper-limits represented by triangles. The $3\sigma$ upper limits of
those SGRBs observed but not detected in the radio band have been plotted as
grey triangles. The ATCA 9 GHz $3\sigma$ upper-limit of GRB 181123B is shown
as a large white triangle. In the left panel of Figure 1, we have plotted the
observed radio flux density vs days post-burst, whereas in the right panel we
have plotted the spectral luminosity vs days post-burst in the rest frame,
assuming a redshift of $z=0.5$ (Berger, 2014) for those events with no known
redshift. When converting the flux ($F$) to luminosity ($L$), a $k$-correction
was also applied such that $L=4\pi Fd_{L}^{2}(1+z)^{\alpha-\beta-1}$ erg s-1
Hz-1, where $d_{L}$ is the luminosity distance for the redshift $z$ (assuming
$\Lambda$CDM cosmology with $H_{0}=68$ km s-1 Mpc-1 and $\Omega_{m}=0.3$;
Planck Collaboration et al., 2016), and $\alpha$ and $\beta$ are the temporal
and spectral indices defined as $F\propto t^{\alpha}\,\nu^{\beta}$ (Bloom et
al., 2001). We assume $\alpha=0$ and $\beta=1/3$, which are appropriate for an
optically thin, post-jet-break light curve (see Chandra & Frail, 2012).

From Figure 1 we can see that the ATCA flux limit for GRB 181123B is extremely
competitive and consistent with the most constraining lower-limits. Using
formalism by Granot & Sari (2002), Berger (2014) showed that if we assume
fiducial parameters for SGRBs, along with typical microphysical parameters for
LGRBs, the expected peak flux density at a redshift of $z=0.5$ is $F_{\nu}\sim
40\mu$ Jy at $\sim 10$ GHz for an ambient medium density of $n_{0}=0.1$ cm-3.
Our $3\sigma$ sensitivity at 9 GHz was 32$\mu$ Jy, and therefore sensitive
enough to detect emission from a GRB with the above properties, however, it is
important to note that some GRB microphysical and macrophysical parameters
like the kinetic energy and the CSM density can vary by several orders of
magnitude (Granot & van der Horst, 2014).

The luminosity light curves in Figure 1 show the $3\sigma$ upper-limit for GRB
181123B at $\sim 1$ day post-burst (in the rest frame). Given the very high
redshift of GRB 181123B, even these sensitive ATCA observations would not have
detected the radio counterpart to the seven SGRBs detected at early times
(within a day post-burst in the rest frame) if they were placed at $z=1.754$.
We therefore cannot draw any further comparisons between the physical
properties of the radio-detected GRB sample and GRB 181123B based on
luminosity alone and require more detailed multi-wavelength light curve
modelling (see Section 4.1).

###  4.1 Modelling constraints

In this section, we model the afterglow of GRB 181123B in order to explore how
early-time ($<1$ day) radio observations of SGRBs can help to constrain the
dynamical and microphysical parameters of such blast waves in the context of
the fireball model. Using the redshift derived from the identification of the
host galaxy of GRB 181123B ($z=1.754$; Paterson et al., 2020), we model the
force-fitted flux density values at the Swift-XRT position of the GRB from our
ATCA observations together with the Swift-XRT light curve (Evans et al., 2009,
2010). We have chosen to use the force-fitted flux measurements plus errors in
our modelling as it allows us to assign a likelihood to a predicted model flux
for a set of model parameters, which is not possible with an upper limit (for
some examples of where radio force-fitted flux measurements are quoted and
used in afterglow modelling see Galama et al., 1998b; Kulkarni et al., 1999;
van der Horst et al., 2011, 2015).

For this modelling, we have chosen to only consider the forward-shock
component to minimise complexity, particularly as we are dealing with a small
number of data points. As previously mentioned, the reverse-shock could be
dominant at early times ($\lesssim 1$ day) in the radio band as has been
observed for some SGRBs (e.g. Soderberg et al., 2006; Lamb et al., 2019; Troja
et al., 2019b). Given that the reverse-shock evolves to lower frequencies more
rapidly than the forward-shock and we have no radio detection, our modelling
depends primarily on the X-ray detections, which are always dominated by the
forward-shock, thus motivating our model choice. Our afterglow fitting also
does not rule out a reverse shock contribution. We therefore assume a
spherical, relativistic, blast wave interacting with the circumburst medium
and generating synchrotron emission. Since SGRBs are known to occur in
homogeneous, low density environments (median densities of
$n_{0}\approx(3-15)\times 10^{-3}$ cm-3 with $\approx 80-95\%$ of events being
situated in environments of $n_{0}<1$ cm-3; Fong et al., 2015), we assume a
constant density circumburst medium.

We use the boxfit code to model the afterglow emission (van Eerten et al.,
2012). boxfit makes use of pre-calculated hydrodynamics data to calculate the
dynamics of the blast wave, and solves radiative transfer equations on the go.
Since in this work we assume a spherical blast wave, we fix the opening angle
($\theta_{0}$) to $\pi/2$. We then use the C++ implementation of the MultiNest
nested sampling algorithm, which is a Bayesian inference tool, to determine
the posterior distributions of the free parameters (Feroz et al., 2009). The
free parameters of our model are defined as:

  * •

$E_{K,\mathrm{iso}}$: Isotropic equivalent kinetic energy in units of erg.

  * •

$n_{0}$: Circumburst medium number density in units of $\mathrm{cm}^{-3}$.

  * •

$p$: Power-law index of the accelerated electron distribution, such that
$N(\gamma)\propto\gamma^{-p}$, with some minimum Lorentz factor $\gamma_{m}$
(Wijers & Galama, 1999).

  * •

$\epsilon_{B}$: Fraction of thermal energy in the magnetic fields.

  * •

$\epsilon_{e}$: Fraction of thermal energy in the electrons.

In order to demonstrate how the inclusion of early-time radio data helps to
further constrain the dynamical and microphysical parameters (when combined
with Swift-XRT observations and regardless of whether or not there is a radio
detection), we model the afterglow of GRB 181123B with and without the ATCA
force-fitted fluxes and compare the posterior distributions of the free
parameters. In both fits, we use the same prior for the free parameters (Table
2) and the resulting best fit values in Table 3 are set with the lowest chi-
squared value in the posterior.

Light curves for the posterior predictive distribution when the ATCA force-
fitted flux density values are included in the modelling, together with the
best fit, can be found in Figure 2. Given that the modelling of the X-ray
detections of GRB 181123B alone suggests an energetic solution, the inclusion
of radio information aids to pull down the overall fit so that at both 5.5 and
9 GHz, the best fit light curves are clustered around the ATCA force-fitted
flux densities. While the resulting model is consistent with the Swift
Ultraviolet/Optical Telescope (UVOT; Roming et al., 2005) upper-limits (Oates
& Lien, 2018), it over-predicts the Galactic extinction corrected $i$-band
flux reported by (Paterson et al., 2020) by a factor of $\sim 3$ or 1.2
magnitudes. At this high redshift, an $i$-band detection indicates the
afterglow emission was produced at ultraviolet wavelengths in the rest frame,
and would therefore be quite prone to extinction by dust. Given our model does
not consider extinction, intrinsic or otherwise, this over-prediction may
therefore not be unreasonable. However, our $i$-band prediction is much higher
than the host optical extinction calculated by Paterson et al. (2020) from
photometric observations ($A_{V}$=0.23) or calculated from their observed
excess hydrogen column density ($N_{H}$; derived from X-ray afterglow spectral
modelling), which is known to scale to optical extinction (Güver & Özel,
2009), predicting $A_{V}$=0.38. There are also other potential sources of
optical and infrared emission from SGRBs such as a kilonova from r-process
radiative decay (e.g. Metzger et al., 2010), which our model does not include.
However, such emission usually does not dominate over the afterglow until $>1$
d post-burst (e.g. Tanvir et al., 2013).

As can be seen in Table 3, the inclusion of the ATCA force-fitted fluxes in
our modelling allows for much better constraints to be placed on
$\epsilon_{e}$ (see also Figure 5, which shows a comparison between the
marginal distributions of the parameters for both cases - modelling with and
without the ATCA data). The rest of the parameters are consistent between both
modelling experiments but the $E_{K,\mathrm{iso}}$ is on the brighter end of
known SGRBs (Fong et al., 2015). Our findings are consistent with those by
Beniamini & van der Horst (2017), who have shown that the flux density and
time of the GRB radio light curve peak can be used to particularly constrain
$\epsilon_{e}$. We also note that our constraint on $\epsilon_{e}$ is also
consistent (within the 95% credible interval) with the distribution of
$\epsilon_{e}$ ($0.13-0.15$) found through the analysis of 36 GRB radio
afterglows performed by Beniamini & van der Horst (2017). The predicted radio
peak also suggests that at later times ($\gtrsim 3-4$ days post-burst), the
forward shock radio emission from GRB 181123B may have been detectable at 5.5
and 9 GHz with $\geq 4$ hr ATCA integrations (see Figure 2). Therefore, the
inclusion of early-time radio data in GRB afterglow modelling (regardless of
whether or not there is a detection), together with an X-ray light curve,
allows us to predict the forward shock peak radio flux density, thus
constraining the fraction of shock energy in the relativistic electrons
($\epsilon_{e}$). Paterson et al. (2020) also derived these same afterglow
parameters for GRB 181123B but assumed fixed values of $\epsilon_{e}=0.1$ and
$\epsilon_{B}=0.1$ or 0.01. While our parameters are far less constrained, our
values for $E_{K,iso}$ and $n_{0}$ (as well as $\epsilon_{e}$ and
$\epsilon_{B}$) are consistent with Paterson et al. (2020) within the 95%
credible intervals. However, our value range for $p$ was higher and did not
overlap with the range derived by Paterson et al. (2020). Note that our value
range for $p$ is more consistent with those calculated for radio-detected
SGRBs (see Section 4.2).

Table 2: Assumed priors for the free parameters for all modelling efforts. Parameter range | Prior distribution
---|---
$10^{49}<E_{K,\mathrm{iso}}~{}\mathrm{(erg)}<10^{54}$ | log-uniform
$10^{-4}<n_{0}~{}\mathrm{(cm^{-3})}<10$ | log-uniform
$2.0<p<3.5$ | uniform
$10^{-7}<\epsilon_{B}<0.50$ | log-uniform
$10^{-4}<\epsilon_{e}<0.50$ | log-uniform
Figure 2: Fit result for the afterglow light curves of GRB 181123B at ATCA observing frequencies 5.5 GHz (top panel) and 9.0 GHz (middle panel), and with the Swift-XRT ($0.3-10$ keV; bottom panel) when the ATCA data are included (in this case the force-fitted flux densities; red data point and error bar plotted on the 5.5 and 9.0 GHz light curves). The plotted values in the Swift-XRT light curve (also red data points) were downloaded via the Swift Burst Analyser (Evans et al., 2010). For each of the three frequency bands, 200 light curves are drawn by sampling the inferred posterior distribution of the parameters. The solid line represents the best fit model. The horizontal dashed lines show the 3-$\sigma$ detection limit for various ATCA integration times.  Table 3: Fit results for GRB 181123B for when the ATCA force-fitted data are excluded, included or the ATCA force-fitted mean is lowered by an order of magnitude. The errors on the parameters represent the 95% credible interval. It can be seen that when the ATCA data are included, $\epsilon_{e}$ is better constrained.  Parameter name | ATCA data excluded | ATCA data included | Lower ATCA forced fit
---|---|---|---
$\log_{10}E_{K,\mathrm{iso}}$ | $52.4^{+1.4}_{-1.6}$ | $52.0^{+1.5}_{-1.2}$ | $51.5^{+1.1}_{-0.85}$
$\log_{10}n_{0}$ | $-0.4^{+1.4}_{-1.5}$ | $-0.5^{+1.4}_{-1.4}$ | $-1.1^{+1.4}_{-1.3}$
$p$ | $2.92^{+0.42}_{-0.37}$ | $2.90^{+0.42}_{-0.38}$ | $2.97^{+0.38}_{-0.39}$
$\log_{10}\epsilon_{B}$ | $-2.9^{+2.5}_{-3.2}$ | $-3.0^{+2.7}_{-3.5}$ | $-2.5^{+2.1}_{-2.3}$
$\log_{10}\epsilon_{e}$ | $-1.13^{+0.82}_{-1.2}$ | $-0.75^{+0.39}_{-0.40}$ | $-0.60^{+0.30}_{-0.35}$

####  4.1.1 Robustness of the results for more complicated models

The aim of the modelling analysis presented in Section 4.1 is to demonstrate
how early-time radio data (even a non-detection) can help to constrain
physical parameters in the framework of the fireball model. However, the
presence of a plateau feature in many GRB X-ray light curves indicates that
energy injection and more complex emission mechanisms are at play beyond a
simple forward and reverse shock. One of the main interpretations of X-ray
plateaus observed from SGRBs is likely an energy injection signature from a
potentially short-lived, supramassive, highly magnetised, rapidly rotating
neutron star remnant, often referred to as a ‘magnetar’ (e.g. Zhang &
Mészáros, 2001; Yu & Huang, 2007; Rowlinson et al., 2013). In fact, Gompertz
et al. (2015) has performed broad-band modelling of SGRBs that includes energy
injection from the spin-down of such a magnetar. Alternatively, Leventis et
al. (2014) were able to demonstrate that X-ray plateaus could be explained by
the combined emission from the reverse and forward shock, provided that the
blast wave is in the thick shell regime, and such a reverse shock would also
lead to an additional emission component in radio and optical wavelengths. In
the case of GRB 181123B, the X-ray light curve of the afterglow shows evidence
of a plateau phase at early times that Rowlinson et al. (2020) have
interpreted as energy injection from an unstable magnetar that collapsed a few
hundred seconds following its formation. While many models have been proposed
in the literature to describe the X-ray light curve behaviour of GRBs, our
limited radio data-set means that an exhaustive analysis of these complex
models is beyond the scope of this paper. Nonetheless, it is worth exploring
whether the constraints we have derived from our simple forward shock model
are still meaningful if we introduce additional free parameters.

In the following we investigate how the inclusion of the ATCA data affects the
posterior of modelling efforts that also include energy injection. We
therefore incorporate energy injection into boxfit, which is modelled by
varying the isotropic equivalent kinetic energy ($E_{K,\mathrm{iso}}$) as a
power-law in time. In this case, $E_{K,\mathrm{iso}}$ is described as:

$E=\begin{cases}E_{0}&t\leq t_{\mathrm{inj}}\\\
E_{0}(t/t_{\mathrm{inj}})^{\alpha}&t_{\mathrm{inj}}<t\leq
t_{\mathrm{inj}}+dt_{\mathrm{inj}}\\\
E_{0}(1+dt_{\mathrm{inj}}/t_{\mathrm{inj}})^{\alpha}&t_{\mathrm{inj}}+dt_{\mathrm{inj}}<t\end{cases}$
(1)

where the three additional parameters are defined as:

  * •

$t_{\mathrm{inj}}$: Start time of the energy injection in seconds (s).

  * •

$dt_{\mathrm{inj}}$: Duration of energy injection in seconds (s).

  * •

$\alpha$: Power-law index of the energy injection.

The assumed prior distributions for the energy injection parameters can be
seen in Table 4. We use the same priors as before for all other burst
parameters (Table 2).

The resulting best-fit parameters for the afterglow modelling of GRB 181123B
that includes energy injection for the cases when the ATCA force-fitted flux
densities are included and excluded can be found in Table 5, with the
resulting light curves for the posterior predictive distribution, together
with the best fit model plotted in Figure 3. Due to the limited multi-
wavelength coverage of the afterglow, we are not able to place tight
constraints on the energy injection parameters. However, note that
$\epsilon_{e}$ continues to be well constrained when ATCA data are included,
even with a more complex model with additional parameters (see Figure 6, which
shows the marginal distributions of the parameters for the energy injection
cases when ATCA data are included and excluded). In addition, Figure 7
compares the obtained marginalized distribution for the GRB parameters
(omitting the energy injection parameters) for the two modelling cases that
include the ATCA data: with and without including energy injection. It can be
seen that the resulting parameter values common between both fits are
consistent within the 95% credible intervals despite different model
complexities. However, while the model is consistent with the Swift-UVOT
upper-limits, it over-predicts the $i$-band detection (Paterson et al., 2020),
which demonstrates the limitations of our modelling.

The modelling of GRB 181123B shows that early-time radio observations,
regardless of whether they are detections or non-detections, are able to
constrain the fraction of thermal energy in the accelerated electrons,
$\epsilon_{e}$, beyond what is possible with just the Swift-XRT X-ray light
curve data. Our modelling also predicted that observations at later times
(1-10 days) may have resulted in a detection of the forward shock, which would
further constrain the GRB parameters.

Table 4: Assumed priors for the energy injection parameters for all modelling efforts. Parameter range | Prior distribution
---|---
$8.64<t_{\mathrm{inj}}~{}\mathrm{(s)}<4.32\times 10^{5}$ | log-uniform
$8.64<dt_{\mathrm{inj}}~{}\mathrm{(s)}<4.32\times 10^{5}$ | log-uniform
$0.0<\alpha<2.0$ | uniform
Table 5: Fit results for GRB 181123B for when the ATCA force-fitted data are excluded and included, with energy injection also included in our modelling. The errors on the parameters represent the 95% credible interval. It can be seen that when the ATCA data are included, $\epsilon_{e}$ is better constrained.  Parameter name | ATCA data excluded | ATCA data included
---|---|---
$\log_{10}E_{K,\mathrm{iso}}$ | $51.8^{+1.9}_{-1.3}$ | $51.4^{+1.7}_{-0.91}$
$\log_{10}n_{0}$ | $-0.7^{+1.6}_{-1.7}$ | $-0.9^{+1.7}_{-1.8}$
$p$ | $3.08^{+0.42}_{-0.47}$ | $3.16^{+0.35}_{-0.50}$
$\log_{10}\epsilon_{B}$ | $-1.9^{+1.6}_{-3.5}$ | $-2.1^{+1.9}_{-4.0}$
$\log_{10}\epsilon_{e}$ | $-1.01^{+0.70}_{-1.2}$ | $-0.66^{+0.35}_{-0.39}$
$\log_{10}t_{\mathrm{inj}}$ (days) | $-1.23^{+1.7}_{-0.91}$ | $-1.32^{+1.8}_{-0.84}$
$\log_{10}dt_{\mathrm{inj}}$ (days) | $-1.2^{+1.8}_{-2.3}$ | $-1.1^{+1.8}_{-2.3}$
$\alpha$ | $0.86^{+0.94}_{-0.77}$ | $0.88^{+0.92}_{-0.76}$
Figure 3: As for Figure 2 but with energy injection incorporated into our
modelling.

To test how the dependencies between the parameters in our model are affected
by the mean of the forced fitted values, we ran an additional fit using boxfit
(without energy injection) where we lowered the mean of the ATCA force-fitted
flux density values by an order of magnitude. Table 3 shows the resulting
inferred parameters with the best fit light curves shown in Figure 4. The main
effect of lowering the mean value of the force-fitted ATCA flux densities on
the parameters was to decrease the mean value of the circumburst medium
density ($n_{0}$) and increase the fraction of thermal energy in the magnetic
fields ($\epsilon_{B}$) by a similar amount (factor of $\sim 3-4$) when
compared to the results from fitting the original force-fitted ATCA flux
densities. However, note that all parameters presented in Table 3 that were
derived from including ATCA force-fitted flux densities in our modelling still
agree within the 95% credible intervals of the modelling performed without the
ATCA information. The reduction in the ATCA force-fitted mean flux densities
also indicate that the predicted peak forward shock emission in the radio band
would be delayed and also drop below the ATCA $3\sigma$ detection limits (see
Figure 4) when compared to the fit performed with the measured force-fitted
flux densities shown in Figure 2.

Figure 4: As for Figure 2 but with the ATCA forced-fitted flux densities
lowered by an order of magnitude.

Overall, our analysis demonstrates the importance of quoting force-fitted flux
density values for radio transients over just reporting $3\sigma$ upper-
limits, which is traditional in most fields of astrophysics. If only upper-
limits are reported then it is not always possible to incorporate this
information into some modelling analyses (e.g. like our GRB afterglow
modelling), which means we are throwing away important data that could further
constrain the physics of an event or source. Finally, the inclusion of early-
time radio force-fitted flux densities allows us to make predictions about the
time and brightness of the forward shock peak in the radio band, which can
inform late-time radio follow-up strategies.

###  4.2 Comparisons of GRB 181123B to radio-detected SGRBs

We now compare our parameter constraints on the micro- and macro-physical
properties of GRB 181123B resulting from our modelling to those obtained for
other radio-detected GRBs. For this comparison, we only focus on the
parameters derived from our forward-shock modelling using boxfit with the
inclusion of the ATCA data (see Table 3). Six of the eight radio-detected
SGRBs have constraints on the same parameters (e.g. Table 2) through afterglow
modelling (GRB 050724A, 051221A, 130603B, 140903A, 160821B, GRB 200522A;
Berger et al., 2005; Soderberg et al., 2006; Fong et al., 2014; Pandey et al.,
2019; Troja et al., 2016; Zhang et al., 2017; Troja et al., 2019b; Lamb et
al., 2019; Fong et al., 2021). The advantage of these modelling efforts was
that these events had extensive multi-wavelength data (radio, infrared,
optical, X-ray) so the afterglow analysis led to stringent constraints on
these parameters and in many cases, an estimate of the gamma-ray jet opening
angle, which has important implications for rate calculations. While the
parameters we derived for GRB 181123B were far less constrained, our 95%
credible intervals agree with those values derived for the six SGRBs mentioned
above, but the upper limits in our prediction for both $n_{0}$ and $p$ are
much higher overall. In fact, our derived accelerated electron distribution is
steeper than that usually expected for GRBs ($p=2.90^{+0.42}_{-0.38}$) but not
unreasonably so. Overall, as previously mentioned, the inclusion of ATCA
force-fitted flux densities within 1 day post-burst have allowed us to place
reasonable constraints on $\epsilon_{e}$.

##  5 Conclusions

In this paper, we introduce the ATCA rapid-response observing mode by
presenting results from the first successful SGRB trigger on GRB 181123B. This
new mode of operations allows the telescope to automatically and rapidly
respond to transient alerts broadcast via VOEvents, causing the active
observing programme to be interrupted to allow for time-critical observations
of transient phenomena. Successful triggers on LGRBs (see Section 2.3) have
demonstrated that if the source is above the horizon, the ATCA can be on
target and observing the event as fast as 3 minutes post-burst, allowing us to
probe this early-time radio regime over a wide range of frequencies ($1.1-25$
GHz) with full polarisation, and in a variety of array configurations.

The ATCA rapid-response observations of GRB 181123B began 12.6 hr post-burst,
as soon as the target had risen above the horizon, collecting 8.3 h of data at
5.5 and 9 GHz. While no radio emission was detected from GRB 181123B, we quote
force-fitted flux densities, which enabled more constraining GRB afterglow
modelling to be performed then would usually be possible with just X-ray data
from Swift-XRT. The addition of early-time radio data in the modelling allowed
us to obtain more stringent constraints on the fraction of thermal energy in
the electrons behind the shock wave ($\epsilon_{e}$), which in turn allowed us
to predict the peak in the forward shock radio afterglow emission around $\sim
10$ days post-burst. This modelling indicates that $\gtrsim 3-4$ days post-
burst, the radio afterglow of GRB 181123B may have been detectable with a
$\geq 4$ hr ATCA integration.

Our results demonstrate the importance of including early-time radio
observations in afterglow modelling efforts for constraining GRB blast wave
properties and predicting the late-time peak in the radio forward shock,
regardless of whether or not there is a detection, provided that force-fitted
flux densities are quoted rather than upper-limits in the case of a non-
detection.

This project also demonstrates the importance of implementing rapid-response
observing systems on radio telescopes to probe a new parameter space in
transient science. Early-time radio observations of SGRBs can allow us to
distinguish between different sources of early-time synchrotron afterglow
emission (e.g. Kyutoku et al., 2014) and even detect prompt and persistent
coherent signals predicted to be produced during the compact merger and from
the merger remnant (e.g. Rowlinson & Anderson, 2019). Detections from rapid-
response radio observations will provide crucial insight into the radio
brightness and timescales we might expect from aLIGO/Virgo-detected merging
BNSs or NS-BH systems, which will aid in our search for electromagnetic
counterparts in the large GW positional error regions. Other science cases
include LGRBs, which may show bright, early-time radio emission from the
reverse shock (e.g. Anderson et al., 2014) and flare stars, which have shown
simultaneous high-energy and radio flaring behaviour (e.g. Fender et al.,
2015).

Finally, our efforts running rapid-response programs on ATCA act as an
excellent test for transient observing strategies with the SKA. It is only
through the utilisation of a rapid-response system that we can exploit the SKA
to study early-time BNS and BH-NS merger physics down to sub-micro-Jansky
levels.

## acknowledgements

We thank the referee for their careful reading of the manuscript and
recommendations. GEA is the recipient of an Australian Research Council
Discovery Early Career Researcher Award (project number DE180100346) and
JCAM-J is the recipient of Australian Research Council Future Fellowship
(project number FT140101082) funded by the Australian Government.

The Australia Telescope Compact Array (ATCA) is part of the Australia
Telescope National Facility, which is funded by the Australian Government for
operation as a National Facility managed by CSIRO. 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.

The ATCA rapid-response front-end software makes use of comet (Swinbank, 2014)
and voevent-parse (Staley & Fender, 2016) to process the incoming VOEvents.
Both the front-end (vo_atca)999https://github.com/mebell/vo_atca and back-end
(atca-rapid-resonse-api)101010https://github.com/ste616/atca-rapid-response-
api software for ATCA rapid-response triggering rely on the Astropy, a
community-developed core Python package for Astronomy (The Astropy
Collaboration et al., 2013; Astropy Collaboration et al., 2018), numpy (van
der Walt et al., 2011) and scipy (Jones et al., 2001) python modules. This
research also makes use of matplotlib (Hunter, 2007). 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.

## Data Availability Statement

The unprocessed ATCA visibility datasets are public and can be accessed via
the ATCA online archive (https://atoa.atnf.csiro.au/) under project code C3204
and PI G Anderson. The reduced images of these observations have been uploaded
to Zenodo (Anderson, 2021).

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##  Appendix A Marginalised parameter distributions for different model fits

The following Figures 5, 6 and 7 show the marginalised parameter distributions
for different modelling tests performed in Section 4.1.

Figure 5: The corner plot for the marginalized parameter distributions
resulting from forward-shock modelling of the GRB 181123B afterglow using
boxfit. The red distributions show the modelling results when the ATCA force-
fitted flux densities are not included in the data set and the blue
distributions show the results for when the ATCA data are included.  Figure 6:
As for Figure 5 but with energy injection included in the model.  Figure 7: As
for Figure 5, however, in this case both presented parameter distributions
include the ATCA data. The red distributions show the modelling results when
energy injection is included in the model and the blue distributions show the
results without the inclusion of energy injection. Although including energy
injection increases the complexity of the model, it can be seen that
$\epsilon_{e}$ is well constrained in either case when ATCA data are included.
The additional parameters for the energy injection case ($t_{\mathrm{inj}}$,
$dt_{\mathrm{inj}}$ and $\alpha$) are omitted in this plot for clarity.