# Perovskite-type YRh3B with multiple types of nodal point and nodal line
states

Feng Zhou  School of Physical Science and Technology, Southwest University,
Chongqing 400715, China  Chaoxi Cui  Key Lab of Advanced Optoelectronic
Quantum Architecture and Measurement (MOE), Beijing Key Lab of Nanophotonics
$\&$ Ultrafine Optoelectronic Systems, and School of Physics, Beijing
Institute of Technology, Beijing 100081, China  Jianhua Wang  School of
Physical Science and Technology, Southwest University, Chongqing 400715, China
Minquan Kuang  School of Physical Science and Technology, Southwest
University, Chongqing 400715, China  Tie Yang  School of Physical Science and
Technology, Southwest University, Chongqing 400715, China  Zhi-Ming Yu  Key
Lab of Advanced Optoelectronic Quantum Architecture and Measurement (MOE),
Beijing Key Lab of Nanophotonics $\&$ Ultrafine Optoelectronic Systems, and
School of Physics, Beijing Institute of Technology, Beijing 100081, China
Xiaotian Wang<EMAIL_ADDRESS>School of Physical Science and
Technology, Southwest University, Chongqing 400715, China  Gang Zhang
<EMAIL_ADDRESS>Institute of High Performance Computing, Agency for
Science, Technology and Research (A*STAR), 138632, Singapore  Zhenxiang Cheng
<EMAIL_ADDRESS>Institute for Superconducting and Electronic Materials
(ISEM), University of Wollongong, Wollongong 2500, Australia

(December 27, 2020)

###### Abstract

Experimentally synthesized perovskite-type YRh3B with a $Pm\bar{3}m$ type
structure was proposed as a novel topological material (TM) via first-
principles calculations and the low-energy $k\cdot p$ effective Hamiltonian,
which has a quadratic contact triple point (QCTP) at point $\Gamma$ and six
pairs of open nodal lines (NLs) of the hybrid type. Clear surface states
observed in the surface spectrum confirmed the topological states. When spin-
orbit coupling was considered, the QCTP at $\Gamma$ transferred to the
quadratic-type Dirac nodal point (NP). Under 1$\%$ tetragonal strained lattice
constants, YRh3B hosted richer topological states, including a quadratic-type
two-fold degenerate NP, six pairs of open NLs of the hybrid type, and two
closed NLs of type I and hybrid type. Moreover, it was proved that the NLs of
YRh3B at its strained lattice constants contain all types of band-crossing
points (BCPs) (i.e., type I, type II, and critical type). Such rich types of
NP and NL states in one compound make it potentially applicable for
multifunctional electronic devices as well as an appropriate platform to study
entanglement among topological states.

###### pacs:

Valid PACS appear here

##  I Introduction

Topological semimetals/metals add1 ; add2 ; add3 ; add4 ; add5 , have
attracted tremendous research attention due to the nontrivial band-crossings
in their low-energy states, which give rise to novel fermionic excitations.
Basically, topological semimetals/metals include three types: nodal-point add6
; add7 ; add8 ; add9 ; add10 , nodal-line add11 ; add12 ; add13 ; add14 ;
add15 , and nodal-surface topological semimetals/metals add16 ; add17 ; add18
. Regarding nodal-surface topological materials (TMs), their classification,
electronic structures, and material realization were studied preliminarily by
Liang et al. add17  and Wu et al. add18 . However, related research is still
in its infancy, and much in-depth physical research needs to be conducted.

Nodal-point materials can be classified in at least the following methods: (i)
The degeneracy of the point. For example, recently, significant efforts have
been made to propose nodal point (NP) materials with 2-, 3-, 4-, 6-, and
8-fold degenerated band crossings add4 ; add7 ; add19 ; add20 ; add21 ; add22
; add23 ; add24 . Among them, NP materials with 2-, 3-, and 4-fold degenerated
band crossings—i.e., Weyl, triply degenerated, and Dirac NP materials—are of
significant importance due to their novel physical properties; (ii) The band
dispersion near the points. Besides the most common linear dispersion, in
principle, a quadratic and a cubic dispersion may also be found around NPs in
the low-energy regions add25 ; add26 ; add27 ; add28 ; add29 . Moreover, the
linear dispersion around the NPs can also be classified into three types
according to the tilting degree of the fermion cone: type I add30 ; add31 ;
add32 , type II add33 ; add34 ; add35 , and critical-type add14 . In type I
(type II) NPs, the two bands, which form the NP, have opposite (equal)
velocities; meanwhile, critical-type NPs are formed by one flat band and one
dispersive band add14 .

For nodal line (NL) materials, the BCPs can form NL states in the momentum
space of solids. If all the BCPs in the NL belong to one type, the NL is of
the corresponding type add36 ; add37 ; meanwhile, if the NL contains one more
type of BCP, the NL is hybrid-type add38 . Additionally, Yu et al. add39
found that higher-order NLs can also be found in nonmagnetic systems. More
interestingly, NL states in momentum space can form many sub-types. For
example, NLs can be classified into two types—closed NLs and open NLs—based on
whether the NLs are expanded to the edge of the first Brillouin zone (BZ)
add40 ; add41 .

In this work, we report an interesting TM with rich types of NL and NP states
under equilibrium and strained lattice constants. First, we show that monoxide
perovskite-type compound YRh3B is a dynamically stable material with a triply
degenerate NP with higher-order quadratic dispersion at $\Gamma$ and six pairs
of hybrid open NLs. Second, with spin-orbit coupling (SOC), we demonstrate
that the quadratic contact triple point (QCTP) - quadratic contact Dirac point
(QCDP) transition occurs at point $\Gamma$. Third, under 1$\%$ tetragonal
strain, a quadratic-type two-fold NP, six pairs of open NLs, and two closed
NLs appeared in the momentum space of YRh3B. Then, we reveal that BCPs of type
I, type II, and critical type can be observed at strained lattice constants.

Figure 1: (a) The crystal structure of YRh3B. (b) The three-dimensional (3D)
bulk Brillouin zone (BZ) and the surface BZ of the [101] surface (shown in
yellow). (c) The calculated phonon dispersion of YRh3B at its equilibrium
lattice constant along M-$\Gamma$-X-M-$\Gamma$-R-X paths.

##  II  MATERIALS AND COMPUTATIONAL METHODS

In this work, a first-principles method, as implemented in the Vienna ab
initio Simulation Package add42 , was selected to calculate the electronic
structure and the topological properties of YRh3B at equilibrium and strained
lattice constants. We adopted the generalized gradient approximation (GGA)
add43  of the Perdew–Burke–Ernzerhof (PBE) add44  function as the exchange-
correlation potential. Moreover, we set the cutoff energy as 600 eV and
sampled the BZ via a Monkhorst–Pack $\mathit{k}$-mesh with a size of 10
$\times$ 10 $\times$ 10\. We set the energy/force convergence criteria as 10-6
eV/ -0.0005 eV/Å. To achieve the phonon dispersions of YRh3B systems, a 2
$\times$ 2 $\times$ 2 supercell was selected and the phonon spectra were
calculated via the force-constants method as implemented in Phonopy code add45
. The surface states are calculated by using Wannier functions add46 . The
intensity is calculated by Green’s function method for the [101] surface add47
; add48 .

YRh3B sample was prepared via the arc-melting method in a titanium-gettered
argon atmosphere before add49 . In this work, the lattice constants of YRh3B
were totally relaxed via first-principles calculation, and the obtained values
were a = b = c = 4.1996 Å, which are in good agreement with the experimental
values add49 , namely a = b = c = 4.22 Å. The optimized crystal structure of
YRh3B at its equilibrium lattice constants is shown in Fig. 1(a). This
primitive cell has five atoms, namely one B atom, one Y atom, and three Rh
atoms, which are located at the 1b (0.5, 0.5, 0.5), 1a (0.0, 0.0, 0.0), and 3c
(0.5, 0.0, 0.5) Wyckoff sites, respectively.

Figure 2: (a) The band structure and the (total and partial) DOSs of YRh3B at
its equilibrium lattice constant along M-$\Gamma$-X-M-$\Gamma$-R-X paths. (b)
The enlarged band structure of YRh3B along M-$\Gamma$-R paths; point A is a
triply degenerated NP with a quadratic manner.

To evaluate the mechanical stability of YRh3B, the elastic constants were
obtained. For cubic-system YRh3B, there are three independent elastic
constants, namely, $C_{11},$ $C_{12}$ and $C_{44}.$ The values of $C_{11},$
$C_{12}$ and $C_{44}$, are 333.59 GPa, 102.78 GPa and 68.16 GPa, respectively.
The elastic stability criteria are as follows:

$C_{11}-C_{12}>0,$ (1) $C_{11}+2C_{12}>0,$ (2) $C_{44}>0.$ (3)

The elastic constants of YRh3B satisfy all of the above criteria add50 , and
therefore the material is mechanically stable.

The Bulk modulus ($\mathit{B}$) is calculated based on the following formula:

$B_{cal.}=\frac{\left(C_{11}+2C_{12}\right)}{3}.$ (4)

The calculated value of $\mathit{B_{cal.}}$ is 181.72 GPa, which is very close
to the experimental value ($\mathit{B_{exp.}}$ = 177.4 GPa) add49 .

Figure 3: (a) A schematic diagram of one pair of open nodal lines (NLs) (red
lines) in the [101] plane. (b) The 3D band dispersion of the [101] plane
around point R. The white dotted lines represent the NL states in the [101]
plane. (c) and (d) The shapes of the topological NLs (TNLs) (white dotted
lines) of the [101] and [110] planes.  Figure 4: (a) Selected $k$-paths in the
[101] plane; points B, C, D, E (F, G, H, I) are equally spaced between R (X)
and A ($\Gamma$). (b) Calculated band structures along the $\Gamma$-A, A-I,
I-B, B-H, H-C, C-G, G-D, D-F, F-E, E-X, and X-R paths, respectively. (c)–(e)
An illustration of NPs with type I, type II, and critical-type band crossings.

The phonon spectrum is widely used to study the stability of the system add51
; add52  and the occurrence of imaginary eigenfrequencies generally indicates
a structural instability add53 ; add54 . Hence, we will use this property to
study the the dynamically stability of YRh3B. The calculated phonon dispersion
of YRh3B at its equilibrium lattice constants is exhibited in Fig. 1(c). No
imaginary frequency mode in phonon dispersion indicates that this compound is
dynamically stable.

##  III ELECTRONIC AND TOPOLOGICAL SIGNATURES AT EQUILIBRIUM LATTICE CONSTANTS

Fig. 2(a) shows the calculated band structure and the (total and partial) DOSs
of YRh3B at its equilibrium lattice constant without SOC. Based on the band
structure, it can be seen that this compound is metallic and has several
remarkable crossings around the Fermi level, which are labeled as A, B and C.
We first consider point A. The enlarged band structure around A is presented
in Fig. 2(b), which shows that this point is triply degenerated add55 ; add56
and that the three bands completely split along the $\Gamma$-M path and become
a doubly degenerate NL and a single band along the $\Gamma$-R path. The triple
point at A ($\Gamma$) is a quadratic contact triple point (QCTP) as its band
representation is $T_{1g}$ of the $O_{h}$ point group. Specifically, the
little group of point $\Gamma$ is the $O_{h}$ point group, and its generating
elements can be chosen as $C_{4z}$, $M_{110}$, $C_{3,111}$, ${\cal P}$ and
time-reversal ${\cal T}$. With these symmetries constrained, the low-energy
$k\cdot p$ effective Hamiltonian of point A can be calculated as follows:

$\displaystyle{\cal H}_{\text{QCTP}}=c_{1}+$ $\displaystyle
c_{2}k^{2}+c_{3}\left(\begin{array}[]{ccc}k_{z}^{2}&0&0\\\ 0&k_{y}^{2}&0\\\
0&0&k_{x}^{2}\end{array}\right)$ (5)
$\displaystyle+c_{4}\left(\begin{array}[]{ccc}0&k_{y}k_{z}&-k_{x}k_{z}\\\
k_{y}k_{z}&0&k_{x}k_{y}\\\ -k_{x}k_{z}&k_{x}k_{y}&0\end{array}\right),$

where $c$’s are real parameters. One can check that the effective Hamiltonian
(Eq. 5) recovers the electronic band structure in Fig. 2. Moreover, from the
effective Hamiltonian, one can find that point A has quadratic dispersion
along any direction in the BZ; hence, this point is termed a QCTP. In
particular, along the three momentum axes (e.g., along the $k_{x}$ direction),
the energy dispersion of QCTP is as follows:

$\varepsilon_{1,2}=c_{1}+c_{2}k_{x}^{2},\ \
\varepsilon_{3}=c_{1}+(c_{2}+c_{3})k_{x}^{2}.$ (6)

Then, we find $c_{2}\simeq-c_{3}$ in YRh3B, leading to the appearance of an
almost flat band along the $k_{x,y,z}$ direction (see the example of
[$\Gamma$-X path] in Fig. 2).

Figure 5: (a) The [101] surface states of YRh3B along the surface Brillouin
zone $\bar{\Gamma}-\bar{\rm{R}}-\bar{\rm{X}}$; the positions of points A, B, C
(as shown in Fig. 2) are marked by black dots and the surface sates arising
from these points are marked by arrows. The colorscale represents intensity on
a log scale. (b) and (c) The calculated band structures of YRh3B along the
$\Gamma$-R-X and M-$\Gamma$-R directions, respectively, with the spin-orbit
coupling (SOC) effect.

We then consider points B and C, which are accidental band crossings appearing
at high-symmetry lines $\Gamma$-R and R-X, respectively. Since the YRh3B
material has ${\cal P}$ and ${\cal T}$ symmetries, points B and C should not
be isolated according to the arguments by Weng et al add36 ; add57 . As both
the $\Gamma$-R and R-X paths occur at the [101] mirror plane, we studied the
band structure of YRh3B in the [101] plane in detail by plotting a 3D band
structure around R (see Fig. 3), which directly shows that points B and C are
not isolated but reside on an open NL crossing the BZ around the R-A path, as
shown in Fig. 3(a). Due to the ${\cal P}$ symmetry of the YRh3B material,
there exists one pair of NLs rather than one open NL around the R-A path (see
Fig. 3). For clarity, a more detailed calculation was performed for the YRh3B
material at its equilibrium lattice constant. As shown in Fig. 4(a), we
selected 11 other $\mathit{k}$-paths throughout the NL states to perform the
calculations of band structures. The selected $\mathit{k}$-paths are the
$\Gamma$-A, A-I, I-B, B-H, H-C, C-G, G-D, D-F, F-E, E-X, and X-R paths,
respectively. The band structures of the above-mentioned $\mathit{k}$-paths
are given in Fig. 4(b). From the figure, it can be seen that the linear BCPs
appear along all of the 11 selected $\mathit{k}$-paths. Additionally, based on
the tilting degree of the band dispersion around the points in Fig. 4(c)–(e),
the point on open NL transfers from type I to type II from path $\Gamma$-A to
path X-R. Moreover, since YRh3B has an $O_{h}$ point group, there are five
more pairs of such open NL states in [110], [011], [$\bar{1}$10],
[01$\bar{1}$],[10$\bar{1}$], which are all connected to the [101] mirror by
symmetry. As an example, in Fig. 3(d), one pair of open NL states are
exhibited in [110] plane.

Since the low-energy part of the open NL is mainly located around point R, we
establish a $k\cdot p$ effective Hamiltonian at point R to capture the low-
energy feature of the open NL. From the electronic bands of YRh3B (see Fig.
2), it can be found that the formation of the open nodal ring involves six
entangled bands, which are degenerated into one pair of triply degenerate
points. As YRh3B only has symmorphic symmetries, the little group of point R
also is the $O_{h}$ point group, and the irreducible representations of the
two triply degenerate points at point R around the Fermi level are $T_{1g}$
and $T_{1u}$, respectively, as shown in Fig. 2. Using $T_{1g}$ and $T_{1u}$
representations as a basis, the $k\cdot p$ model (up to second-order) can be
expressed as follows:

${\cal H}_{R}=\left[\begin{array}[]{cc}h_{11}&h_{12}\\\
h_{12}^{\dagger}&h_{22}\end{array}\right],$ (7)

where each block is a $3\times 3$ submatrix with

$\displaystyle h_{11}=M_{1}+$ $\displaystyle
E_{1}k^{2}+D_{1}\left(\begin{array}[]{ccc}k_{z}^{2}&0&0\\\ 0&k_{y}^{2}&0\\\
0&0&k_{x}^{2}\end{array}\right)$ (8)
$\displaystyle+A_{1}\left(\begin{array}[]{ccc}0&k_{y}k_{z}&-k_{x}k_{z}\\\
k_{y}k_{z}&0&k_{x}k_{y}\\\ -k_{x}k_{z}&k_{x}k_{y}&0\end{array}\right),$

$\displaystyle h_{22}=M_{2}+$ $\displaystyle
E_{2}k^{2}+D_{2}\left(\begin{array}[]{ccc}k_{x}^{2}&0&0\\\ 0&k_{y}^{2}&0\\\
0&0&k_{z}^{2}\end{array}\right)$ (9)
$\displaystyle+A_{2}\left(\begin{array}[]{ccc}0&k_{y}k_{x}&k_{x}k_{z}\\\
k_{y}k_{x}&0&k_{z}k_{y}\\\ k_{x}k_{z}&k_{z}k_{y}&0\end{array}\right),$

and

$h_{12}=iB\left(\begin{array}[]{ccc}-k_{y}&k_{x}&0\\\ -k_{z}&0&k_{x}\\\
0&-k_{z}&k_{y}\end{array}\right),$ (10)

where the wave vector $\bm{k}$ is measured from point R point $M_{i}$,
$D_{i}$, $E_{i}$, $A_{i}$ with ($i=1,2$) and $B$ are the real coefficients
related to the specific material. Both $h_{11}$ and $h_{22}$ describe a QCTP,
and the crossings between them around the Fermi level form the open NL. Note
that, due to the three-fold rotation along the $\Gamma$-R direction, point B
(see Fig. 2(a)) actually resides at the intersection point of three symmetry-
related open NL.

Figure 6: (a) The band structure and the (total and partial) DOSs of YRh3B
with 1$\%$ tetragonal strain and without SOC; the bands around point 1 are
with a quadratic manner at point $\Gamma$. For the other numbered linear BCPs,
their types and positions are marked. (b) The phonon dispersion of YRh3B with
1$\%$ tetragonal strain along M-$\Gamma$-X-M-$\Gamma$-R-X directions.

The [101] surface spectrum for the NP and NLs is shown in Fig. 5(a). In the
figure, the positions of the NP A and the BCPs, B and C, are marked by black
dots, and the surface states originating from these points are shown by black
arrows. To reflect the quality of the wannierization of the DFT band
structure, the band structures obtained by Wannier along the $\Gamma$-R-X and
M-$\Gamma$-R directions, respectively, are shown in Fig. S1(a) and S1(c).
Obviously, the band structures around the band-crossing points (A, B, C)
obtained by Wannier are in good agreements with those obtained by DFT (see
Fig. S1(b) and S1(d)).

Figure 7: (a) The 3D band dispersion of the [101] plane around point R in R1.
(b) and (c): The $\Gamma$-centered 3D band dispersion of the $k_{z}$ = 0 plane
in R2 and R3, respectively. (d) The shapes of the open TNLs of the [101]
plane. (e) and (f): The shapes of the closed TNLs of the $k_{z}$ = 0 plane in
R2 and R3, respectively. The white dashed and solid lines represent the NL
states.

It should be noted that the topological NL (TNL) states of most predicted NL
materials will be opened by the inducing of the SOC effect. Fig. 5(b)
indicates that YRh3B is an ideal NL material and its TNL states are very
robust to the SOC effect. The SOC-induced gaps for the BCPs B and C along
$\Gamma$-R-X paths are up to 10 meV. Furthermore, a more advanced method,
modified Becke-Johnson GGA (mBJGGA) functional is also used to calculate the
band structures of YRh3B with SOC effect. Note that the mBJGGA functional
possesses similar accuracy with more expensive functionals, such as HSE06 and
GW, in predicting the band gap, and has been widely used in previous studies
add6 ; add58 . The results are shown in Fig. S2, one can see that the SOC-
induced gaps for the BCPs B and C along $\Gamma$-R-X paths are up to 20 meV.
It is much smaller than those of well-known NL materials such as ZrSiSe (25-35
meV) add59 ; add60 , Hg3As2 ($\sim$34 meV) add61 , FeSi2 (20-30 meV) add62 ,
and BaSn2 (50-160 meV) add63 . Fig. 5(c) shows the enlarged band structure of
YRh3B at point $\Gamma$ when SOC is taken into consideration. From the figure,
it can be seen that the QCTP A at point $\Gamma$ is gapped under SOC; however,
two higher bands at point $\Gamma$, now contacted with each other at 0.16 eV
above the Fermi level. As each band has two-fold degeneracy under SOC, this
point is a QCDP. It should be noted that similar triply degenerated NP to
Dirac point transition under SOC is also proposed in other TMs with linear-
contacted NPs, such as ErAs add64 , Li2NaN add65 , and TiB2 add55 .

##  IV  TOPOLOGICAL ELEMENTS AT STRAINED LATTICE CONSTANT

In this section, we study the electronic structures and the related
topological elements of YRh3B with 1$\%$ tetragonal strained lattice
constants. Now, the space group of YRh3B has been transferred from
$Pm\bar{3}m$ to $P_{4}/mmm$ and the lattice constants are a = b = 4.24 Å and c
= 4.11 Å, respectively. The phonon dispersion of YRh3B at 1$\%$ tetragonal
strained lattice constants is shown in Fig. 6(b) to demonstrate the material’s
dynamical stability. The band structure and the (total and partial) DOSs
without SOC along M-$\Gamma$-X-M-$\Gamma$-R-X directions is shown in Fig.
6(a). From the figure, it can be seen that the physical nature of this
compound is still metallic under 1$\%$ tetragonal strain, and seven points can
be found around the Fermi level. It should be noted that the two bands touch
in a quadratic manner at point $\Gamma$ (see point 1) with two-fold
degeneracy. Meanwhile, the bands around BCPs 2–7 are with a linear manner in
low-energy regions. We divided these BCPs into three regions, which are
labeled as R1, R2, and R3, respectively.

Figure 8: (a) Selected $k$-paths in the $k_{z}$ = 0 plane; points a, b, c, d
are equally spaced between M and X. (b) The calculated band structures along
the $\Gamma$-M, $\Gamma$-a, $\Gamma$-b, $\Gamma$-c, $\Gamma$-d, and $\Gamma$-X
paths, respectively. (c) The calculated band structure of YRh3B with 1$\%$
tetragonal strain along the M-$\Gamma$-X-M-$\Gamma$-R-X directions. SOC is
considered.

For BCPs 2 and 3 in R1, they belong to the open NLs in the [101] plane, as
shown in Fig. 7(a) and Fig. 7(d). Similar to the discussion in Section III, it
can be seen that the YRh3B compound at 1$\%$ tetragonal strained lattice
constants still hosts six pairs of open NL states in the [101], [110], [011],
[$\bar{1}$10], [01$\bar{1}$], and [10$\bar{1}$] planes.

Besides the above-mentioned topological elements, there are four other BCPs in
R2 and R3—two along the M-$\Gamma$ path and two along the $\Gamma$-X path.
These BCPs should belong to some nodal structures since the ${\cal P}$ and
${\cal T}$ symmetries are still maintained in this system. Very interestingly,
the BCPs in Fig. 6(a) are of three parts: point 3 is of type II; points 2, 4,
6, and 7 are of type I; and point 5 is of the critical type add14 . Note that,
some previous works reported that the existence of both type I and type II
BCPs in realistic materials add66 ; add67 . However, all-round types (type I,
type II and critical type) of BCPs in one compound have rarely been reported
before. Hence, this system at 1$\%$ tetragonal strained lattice constants can
be regarded as a perfect platform to investigate the relationship among BCPs
with different tilting degrees.

Based on the band dispersion around point $\Gamma$ in the $k_{z}$ = 0 plane,
as shown in Fig. 7(b) and Fig. 7(c), it can be seen that BCPs 4–7 are not
isolated and belong to two nodal rings in the $k_{z}$ = 0 plane. The shape of
the two nodal rings in the $k_{z}$ = 0 plane is given in Fig. 7(e) and Fig.
7(f). From these figures, it can be observed that these two nodal rings are
closed TNLs. Furthermore, a more detailed band structure calculation was
performed for the YRh3B compound with 1$\%$ tetragonal strain along selected
$k$-paths ($\Gamma$-M, $\Gamma$-a, $\Gamma$-b, $\Gamma$-c, $\Gamma$-d, and
$\Gamma$-X; see Fig. 8(a)). The calculated results, as shown in Fig. 8(b),
indicate that the BCPs were still maintained in the selected $k$-paths.
Moreover, from Fig. 8(b), it can be noted that the $\Gamma$-nodal ring in R1
is type I and the $\Gamma$-nodal ring in R2 is a hybrid type add68 ; add69 . A
critical-type BCP to type I BCP transition can be observed from paths
$\Gamma$-X to $\Gamma$-M in R2. The critical NP along $\Gamma$-X in R2 is
formed by one flat band (see Fig. 7(b)) and one dispersive band and leads to a
new fermionic state. As shown in Fig. 8(a), the $\Gamma$-nodal ring in R2 has
a larger radius than the $\Gamma$-nodal ring in R1.

Hence, it is concluded that YRh3B at 1$\%$ tetragonal strained lattice
constants is a topological metal with a quadratic type two-fold point at point
$\Gamma$, six pairs of open NLs, and two closed nodal rings when SOC is
ignored. Then, we come to study the effect of SOC on the band structure and
associated topological signatures. The results of band structure with the
consideration of SOC are exhibited in Fig. 8(c). From the figure, it can be
seen that the SOC-induced gaps for the BCPs in R1–R3 are very small and the
values of these gaps are up to 6 meV. That is, the NL states (including open
and closed NLs) in YRh3B at 1$\%$ tetragonal strained lattice constants show
strong robustness to the SOC effect. However, for the quadratic contacted
nodal point at point $\Gamma$, it is broken when the SOC is induced.

##  V  REMARKS AND SUMMARY

In this paper, we propose the realistic material YRh3B as a new topological
metal. The electronic structures and the topological signatures of YRh3B at
equilibrium and 1$\%$ tetragonal strained lattice constants are fully
investigated based on first-principles calculation. We show that YRh3B at
equilibrium and 1$\%$ tetragonal strained lattice constants is a topological
metallic material with various types of topological signatures. At equilibrium
lattice constants, it hosts a triply degenerated NP at point $\Gamma$ with a
quadratic manner, and six pairs of open NLs when SOC is ignored. When SOC is
considered, a QCTP-to-QCDP transition occurred at point $\Gamma$. At 1$\%$
tetragonal strained lattice constants, there are two bands that touch at point
$\Gamma$ near the Fermi level, resulting in a two-fold degenerated NP with a
quadratic manner. Besides the two-fold NP, YRh3B co-exhibits six open NLs and
two closed NLs. Moreover, type I, type II, and critical-type BCPs can be
observed in the NLs of YRh3B with 1$\%$ tetragonal strain. Our work identifies
a novel candidate material to study multiple kinds of NL and NP states in bulk
realistic materials. It is hoped that the topological elements proposed in
this work can be confirmed in follow-up experimental studies.

##  VI  ACKNOWLEDGMENTS

F. Zhou and C. Cui contributed equally to this work. X.T. Wang is grateful for
the support from the National Natural Science Foundation of China (No.
51801163) and the Natural Science Foundation of Chongqing (No.
cstc2018jcyjA0765).

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# A comprehensive search for the radio counterpart of GW190814 with the
Australian Square Kilometre Array Pathfinder

D. Dobie1,2, A. Stewart3, K. Hotokezaka4, Tara Murphy3,2, D. L. Kaplan5,
D.A.H. Buckley6,7,8, J. Cooke1,2, A. Y. Q. Ho9,10, E. Lenc11, J. K.
Leung3,11,2 M. Gromadzki12 A. O’Brien5, S. Pintaldi13, J. Pritchard3,11,2 Y.
Wang3,11,2 Z. Wang3,11,2
1Centre for Astrophysics and Supercomputing, Swinburne University of
Technology, Hawthorn, Victoria, Australia
2ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav), Hawthorn,
VIC 3122, Australia
3Sydney Institute for Astronomy, School of Physics, The University of Sydney,
NSW 2006, Australia
4Research Center for the Early Universe, Graduate School of Science,
University of Tokyo, Bunkyo, Tokyo 113-0033, Japan
5Department of Physics, University of Wisconsin-Milwaukee, P.O. Box 413,
Milwaukee, WI 53201, USA
6South African Astronomical Observatory, PO Box 9, Observatory Road,
Observatory 7935, Cape Town, South Africa
7Department of Astronomy, University of Cape Town, Private Bag X3, Rondebosch
7701, South Africa
8Department of Physics, University of the Free State, PO Box 339, Bloemfontein
9300, South Africa
9Department of Astronomy, University of California, Berkeley, 501 Campbell
Hall, Berkeley, CA, 94720, USA
10Miller Institute for Basic Research in Science, 468 Donner Lab, Berkeley, CA
94720, USA
11CSIRO, Space and Astronomy, PO Box 76, Epping, NSW 1710, Australia
12Astronomical Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-478
Warszawa, Poland
13Sydney Informatics Hub, The University of Sydney, NSW 2008, Australia

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

###### Abstract

We present results from a search for the radio counterpart to the possible
neutron star–black hole merger GW190814 with the Australian Square Kilometre
Array Pathfinder. We have carried out 10 epochs of observation spanning 2–655
days post-merger at a frequency of 944 MHz. Each observation covered 30 deg2,
equivalent to 87% of the event localisation. We conducted an untargeted search
for radio transients in the field, as well as a targeted search for transients
associated with known galaxies. We find one radio transient, ASKAP
J005022.3$-$230349, but conclude that it is unlikely to be associated with the
merger. We use our observations to place constraints on the inclination angle
of the merger and the density of the surrounding environment by comparing our
non-detection to model predictions for radio emission from compact binary
coalescences. This survey is also the most comprehensive widefield search (in
terms of sensitivity and both areal and temporal coverage) for radio
transients to-date and we calculate the radio transient surface density at 944
MHz.

###### keywords:

radio continuum: transients – gravitational waves – black hole - neutron star
mergers

††pubyear: 2021††pagerange: A comprehensive search for the radio counterpart
of GW190814 with the Australian Square Kilometre Array Pathfinder–References

##  1 Introduction

The detection of light and gravitational waves from a neutron star merger,
GW170817, had profound implications for astrophysics (Abbott et al., 2017a,
b). While there were significant results from the thermal (“kilonova”)
emission seen in the optical and near-infrared (Tanvir et al., 2017; Pian et
al., 2017; Cowperthwaite et al., 2017; Kasen et al., 2017; Kasliwal et al.,
2017, e.g.) observations of the synchrotron after were uniquely able to shed
light on the nature of the jet launched by the merger and allowed measurements
of the total energy released, the circum-merger density and the merger’s
inclination angle (e.g. Mooley et al., 2018; Ghirlanda et al., 2019; Hajela et
al., 2021; Makhathini et al., 2020; Troja et al., 2020). While the radio
counterpart to GW170817 was only discovered as part of targeted observations
of the optical counterpart (Hallinan et al., 2017), it would have been
possible to discover it (albeit at a much later time) as part of a radio-only
search (Dobie et al., 2021). Similarly, we expect that some future mergers
will be detectable with radio observations alone, although this is dependent
on the typical properties of these afterglows including the jet structure,
energetics and microphysics parameters. Here we illustrate future capabilities
by presenting a case study of the search for radio emission from the potential
neutron star-black hole merger GW190814.

GW190814 (Abbott et al., 2020) is a compact binary coalescence detected during
the third LIGO/Virgo observing run (O3) at a distance of $241^{+41}_{-45}$
Mpc. The primary component is a black hole with mass $23.2^{+1.1}_{-1.0}$ M☉,
and the secondary component has mass $2.59^{+0.08}_{-0.09}$ M☉. While current
understanding suggests that this component was a black hole (e.g. Essick &
Landry, 2020; Nathanail et al., 2021; Tews et al., 2021), a neutron star
cannot be completely ruled out (e.g. Biswas et al., 2021; Godzieba et al.,
2021; Roupas, 2021; Zhou et al., 2021b).

Despite a comprehensive multi-wavelength follow-up effort, no counterparts
have been detected in optical/near-IR (Gomez et al., 2019; Ackley et al.,
2020; Andreoni et al., 2020; Antier et al., 2020; Gompertz et al., 2020;
Morgan et al., 2020; Thakur et al., 2020; Vieira et al., 2020; Watson et al.,
2020; de Wet et al., 2021; Kilpatrick et al., 2021), radio (Dobie et al.,
2019b; Alexander et al., 2021) or X-ray (Page et al., 2020, Cenko et al. in
prep.) observations. Even if the secondary component is a neutron star it is
unclear whether this event would be expected to produce an electromagnetic
counterpart as current neutron star–black hole (NSBH) models make a large
range of predictions spanning no counterpart at any wavelength, to kilonovae
that are an order of magnitude brighter than neutron star mergers (e.g.
Hotokezaka et al., 2016; Kasen et al., 2017; Rosswog et al., 2017; Zhu et al.,
2021). However, for GW190814 in particular, the extreme mass ratio
($0.112_{-0.009}^{+0.008}$; Abbott et al., 2020) suggests that the merger
likely immediately formed a black hole, ruling out the presence of any
counterparts associated with the collapse of a supramassive neutron star into
a black hole, although this does not preclude the presence of radio emission
produced by relativistic tidal debris (e.g. Nakar & Piran, 2011).

Several events detected during O3 had southern localisations with at least one
plausible neutron star component, making follow-up with the Australian Square
Kilometre Array Pathfinder (Hotan et al., 2021) feasible. However, most were
localised to hundreds of square degrees and while ASKAP is capable of
following up these events (Dobie et al., 2019a), we instead focused on events
that could be followed up with a single pointing. GW190814 was initially
localised to 23 $\deg^{2}$, which has since improved to 18.5 $\deg^{2}$, and
was the the only event suitable for single-pointing ASKAP follow-up111We also
performed observations of the candidate binary neutron star merger S190510g,
but this event was later reclassified as having a terrestrial origin.. Our
observations covered 89% of the initial localisation area within a single
pointing, centered on the skymap posterior maximum.

In Dobie et al. (2019b) we reported an initial search for a counterpart
spanning 2–33 days post-merger. While no counterpart was detected, these
observations allowed us to rule out the presence of an on-axis relativistic
jet which would have been detectable at the early times we observed. However,
the final gravitational wave parameter estimates for this event later
suggested the inclination angle was $\theta_{\rm obs}=46^{+17}_{-11}\,\deg$
meaning that the radio lightcurve would be expected to peak at much later
times. The potential delay between the merger, the optical emission and the
radio afterglow is not unexpected and has been observed previously in gamma-
ray bursts and other transient classes, where the GHz-frequency radio emission
may not peak until months post-event (Horesh et al., 2021; Leung et al.,
2021).

In this paper we report the results of our continued monitoring with ASKAP out
to 655 days post-merger. In Section 2 we outline the observations that were
carried out and describe the details of our search for transient and variable
sources. In Section 3 we discuss the candidate counterparts found in our
search and ultimately rule them all out as related to GW190814 based on their
lightcurve morphology, archival radio data from the Karl G. Jansky Very Large
Array (VLA) and other multi-wavelength observations. We also discuss the
constraints that our observations place on the properties of any jet launched
by the merger, the implications of this search for the field of radio
transient astronomy and evaluate the various follow-up strategies that have
been applied to this event.

Epoch | SBID | Start Time |  $\Delta$T | Int. Time | $\sigma_{\rm RMS}$
---|---|---|---|---|---
|  | (UTC) | (days) | (hours) | ($\mu$Jy)
1 | 9602 | 2019-08-16 14:11:27 | 2.6 | 10.7 | 35
2 | 9649 | 2019-08-23 13:42:59 | 9.6 | 10.7 | 39
3 | 9910 | 2019-09-16 12:08:34 | 33.5 | 10.6 | 39
4 | 10463 | 2019-11-07 08:44:10 | 85.4 | 10.6 | 39
5 | 12704 | 2020-04-03 23:00:00 | 234 | 15.3 | 28
6 | 13570 | 2020-04-29 21:41:11 | 260 | 10.0 | 38
7 | 15191 | 2020-07-03 17:01:21 | 325 | 10.5 | 31
8 | 18925 | 2020-11-28 09:18:30 | 472 | 9.0 | 35
9 | 18912 | 2020-11-29 07:15:31 | 473 | 7.1 | 46
10 | 27379 | 2021-05-29 19:23:44 | 655 | 10.6 | 31
Table 1: ASKAP follow-up observations of GW190814 centered on $\alpha=00^{\rm
h}50^{\rm m}37\aas@@fstack{s}5$, $\delta=-25\degr 16\arcmin
57\aas@@fstack{s}37$ (J2000). All observations were carried out with 288 MHz
of bandwidth centered on 943 MHz. Epoch 6 was rotated by 67.5 degrees with
respect to the other observations and centered on $\alpha=00^{\rm h}58^{\rm
m}00$, $\delta=-23\degr 45\arcmin 00$. Data products from all observations are
publicly available from the CSIRO ASKAP Science Data Archive under project
code AS111 with the Schedulude Block ID (SBID) given in column 2. Figure 1:
ASKAP imaging of the localisation region of GW190814 at 234 (bottom right) and
260 (top left, rotated as discussed in Section 2) days post-merger with both
footprints outlined in grey. The 50% (dashed) and 90% (solid) contours for the
initial and final skymaps are shown in red and blue respectively.

##  2 Data and Analysis

###  2.1 Observations and Data Reduction

Table 1 provides the details of our ASKAP observations, which were carried out
at 944 MHz and span 2 to 655 days post-merger. We used the closepack36222See
Hotan et al. (2021) footprint with a beam spacing of 0.9$\degr$ for all
observations, centered on $\alpha=00^{\rm h}50^{\rm m}37\aas@@fstack{s}5$,
$\delta=-25\degr 16\arcmin 57\aas@@fstack{s}37$ (J2000) corresponding to the
posterior maximum of the initial skymap as seen in Figure 1. This footprint
covers 89% and 87% of the initial and final gravitational wave localisations
respectively, with large extraneous coverage. Each observation was
approximately 10 hours, achieving full u-v coverage along with a typical
sensitivity of 35–40 $\mu$Jy. However, there are three exceptions to the above
specifications:

  1. 1.

Epoch 5 consists of two observations separated by 1 day, as a result of
technical difficulties encountered five hours into the initial observation. We
have combined the good data from each observation into a single image
consisting of $\sim 15$ hours on-source, resulting in better sensitivity.

  2. 2.

Epoch 6 was centered on $\alpha=00^{\rm h}58^{\rm m}00$, $\delta=-23\degr
45\arcmin 00$ (offset by $\sim 2\degr$) and rotated with respect to the other
pointings by 67.5$\degr$ in order to rule out instrumental effects as the
origin of six rapid scintillators discovered in the field (Wang et al., 2021).
The footprint of this pointing has a 74% overlap with the primary footprint
and also covers 89/87% of the initial/final localisation333Both pointings have
similar total coverage due to the large extraneous area covered by each. The
shifted pointing covers the entirety of the 50% credible interval for this
lobe, and the majority of the 90% credible interval..

  3. 3.

Epoch 9 consists of two $\sim 3.5$ hour observations with a 3.5 hour gap
between them. We have combined the data from each observation into a single
image consisting of $\sim 7$ hours on source.

Each observation was reduced using the ASKAPsoft pipeline (Whiting et al.,
2017) with standard parameters, as described by Dobie et al. (2019b). To
assess the data quality we selected all bright (SNR>7), isolated (no sources
within 150 arcsec) compact sources, where we following the definition of
compactness by Hale et al. (2021) of an integrated to peak flux ratio of
$S_{I}/S_{P}<1.024+0.69\times\textrm{SNR}^{-0.62}$, and compared their
position and flux density in the first epoch to all subsequent observations.
We find a median peak flux density ratio of $0.99\pm 0.11$ and median
positional offsets of $0.01\pm 0.70$ and $-0.03\pm 0.61$ arcsec in Right
Ascension and Declination respectively.

###  2.2 Transient Search

We have used all 10 epochs to undertake a search for all intrinsically
transient radio sources in the field. These observations are the most
sensitive radio imaging of this field to-date, so no pre-merger reference
image exists. We therefore cannot exclude the possibility that the radio
counterpart to GW190814 was detected in our first observation and as such we,
do not require a constraining non-detection of a source for it to be
considered a candidate counterpart, or have a transient origin. This
definition also ensures that our search is sensitive to all transient sources
in the field, independent of our observing strategy. However, it does mean
that our search will initially be contaminated with variable sources (either
intrinsic variables like pulsars and AGN, or steady sources that are varying
due to scintilation). In addition, we distinguish between intrinsic transients
(those originating from a one-off, cataclysmic event) and observational
transients (variable sources that appear transient due to our observing
sensitivity and cadence). We refer to the former simply as “transients”
throughout the rest of the text.

####  2.2.1 Untargeted radio variability search

We carried out a transient search of the field using the VAST transient
detection pipeline444https://vast-survey.org/vast-pipeline/ (Murphy et al.,
2021; Pintaldi et al., 2021) using the standard ASKAPSoft data products. We
used a de Ruiter radius of 5.68 (Scheers, 2011) to associate sources between
epochs and recalculated the uncertainty estimates produced by the ASKAPSoft
source finder, selavy, using the equations of Condon (1997).

We applied the following criteria to build our variability search source
sample:

  * •

A ratio of integrated to peak flux density $<1.5$

  * •

Maximum signal-to-noise ratio in a single epoch larger than 5

  * •

2 selavy detections

  * •

No relations555See https://vast-survey.org/vast-
pipeline/design/association/##relations

  * •

Distance to nearest source $>1\,$′

which reduced our sample size from 66 117 to 10 254. We note that the final
two criteria mean that this search is not sensitive to mergers ocurring in
radio-loud hosts. While this scenario is unlikely (Hotokezaka et al., 2016),
for completeness we have carried out a galaxy-targeted search independent of
the above criteria which we describe in Section 2.2.2.

Figure 2: Variability metrics ($V$ and $\eta$) for all sources in our sample,
coloured by kernel density estimate. Grey lines show the cutoffs used for each
metric, while the shaded quadrant (top right) shows the sources that are
considered to be statistically variable. These sources were manually vetted to
search for transient candidates, which are denoted by red stars.

We calculated the standard $\eta$ and $V$ variability metrics for the peak
flux density of the remaining sources in our sample, defined as

$V=\frac{1}{\overline{S}}\sqrt{\frac{N}{N-1}(\overline{S^{2}}-\overline{S}^{2})},$
(1)
$\eta=\frac{N}{N-1}\left(\overline{wS^{2}}-\frac{\overline{wS}^{2}}{\overline{w}}\right),$
(2)

where $N$ is the number of observations, $S_{i}$ and $\sigma_{i}$ are the flux
density and uncertainty in the $i$th epoch and overbars denote means (i.e.,
$\overline{S}\equiv\frac{1}{N}\sum_{i}S_{i}$). We then fit a Gaussian to the
distribution of the logarithm of each metric to calculate the mean, $\mu$, and
standard deviation, $\sigma$ (see Figure 2). Based on Rowlinson et al. (2019)
we consider sources with $\eta>\mu_{\eta}+1.5\sigma_{\eta}$ and
$V>\mu_{V}+1.0\sigma_{V}$ to be significantly variable, corresponding to
$\eta>2.1$ and $V>0.24$ for this dataset. This resulted in 186 candidate
variable sources.

We then manually classified all sources via inspection of their lightcurves
and images. We found that 81 candidates were clearly artefacts. These sources
are either sidelobes of bright sources, noise spikes incorrectly classified as
sources, or sources that are at the near the edge of the epoch 6 footprint and
do not pass the variability threshold after removing that measurement. We
classified an additional 84 candidates as either potential artefacts or
variable sources detected at low significance. Finally, we found that 10
candidates with lightcurves that are consistent with persistent radio sources
exhibiting variability. Of these, one is a known pulsar (PSR J0038$-$2501),
while the remaining nine have infrared counterparts in the Wide-field Infrared
Survey explorer All-sky data release (WISE; Cutri & et al., 2012). This leaves
11 sources with lightcurves that exhibit a rise and fall consistent with
expectations for a radio transient. We discuss these in detail in Section 3.1

####  2.2.2 Galaxy-targeted search

We also carried out an independent galaxy-targeted search using version 2.4 of
the GLADE catalogue (Dálya et al., 2018). We searched for GLADE sources within
20″of all 66 117 sources found by the VAST pipeline. This crossmatch radius
corresponds to a physical distance of 23 kpc at the estimated distance to the
merger (241 Mpc), larger than the host galaxy offset of >90% of known short
GRBs (Fong & Berger, 2013). We then removed all GLADE sources with distance
estimates that are outside of the 90% credible interval of the distance to the
merger, leaving 662 unique galaxies, of which 325 have no distance estimate.
This corresponds to a sample of 799 VAST pipeline sources. Since we are using
Stokes I total intensity images, any real source must have a positive flux
density, and therefore must have a positive variability index. After applying
this constraint we were left with 589 sources.

We manually inspected the lightcurves and images of all 589 sources with the
goal of searching for counterparts that may have been missed by the search
described in Section 2.2.1 due to having small offsets from a radio-loud host
galaxy. We found two sources that are not artefacts and have lightcurves that
are qualitatively consistent with the rise and fall expected of an
extragalactic radio transient, one of which (ASKAP J003537.3$-$271844) was
already discovered in the search described in Section 2.2.1.

##  3 Discussion

Figure 3: Lightcurves for the 12 candidate afterglows found in our initial
search. Source-finder measurements are denoted by solid circles, while open
diamond markers show forced photometry on images with no detection.

###  3.1 Candidates

Figure 3 shows the lightcurves of the 12 candidate sources found in our search
(11 from our untargeted search, plus one additional source from the galaxy-
targeted search). We have used a number of archival surveys to help classify
each candidate. The first epoch of the Rapid ASKAP Continuum Survey (RACS;
McConnell et al., 2020) was at an observing frequency of 888 MHz and covers
the sky south of $+41\,\degr$ to a sensitivity of $\sim 250\,\mu$Jy. The
fields of interest for our work were observed on 2019-04-27 and 2019-04-28
(before the gravitational wave event) and there are no crossmatches with our
candidates. The VLA Sky Survey (VLASS; Lacy et al., 2020) is an ongoing survey
at 3 GHz covering the sky north of $-40\,\degr$ to a sensitivity of 120
$\mu$Jy in each epoch. The fields of interest for our work were observed in
epochs 1.1, 1.2 and 2.1 on 2018-02-18, 2019-07-09, and 2020-10-27 respectively
(with the first two observed prior to GW190814). Parts of this field were also
covered by the GW190814 follow-up reported by Alexander et al. (2021) and one
candidate (ASKAP J005022.3$-$230349) is within the primary beam of any
pointing.

To compare the variability of the source to the expected extrinsic variability
caused by scintillation we use NE2001 (Cordes & Lazio, 2002) to calculate the
Galactic contribution to the electron distribution along the line of sight and
the equations of Walker (1998) to calculate the expected variability due to
scintillation. We find that compact sources in this field at our observing
frequency will exhibit $\sim 30\%$ variability on timescales of $\sim 10$
days.

We use Data Release 8 of the Dark Energy Spectroscopic Instrument Legacy
Imaging Surveys (Dey et al., 2019), specifically data from the Dark Energy
Camera Legacy Survey (DECaLS), to search for optical emission associated with
our candidates or their potential hosts, along with the photometric redshift
estimates from Zhou et al. (2021a). We have also used the WISE All-sky data
release to search for infrared emission associated with our candidates and
calculated the standard WISE colours, shown in Figure 4. However, no sources
have a detection in the WISE 12 $\mu$m band and therefore any decisive
classification from colours alone is not possible.

Figure 4: Colour-colour diagram of the WISE sources associated with the
candidate variables and transients discussed in Section 3.1. We have also
included the classification regions from (Wright et al., 2010) for context,
although we note that any classification of these sources from WISE colours
alone is limited by a lack of any detection in the 12$\mu$m band.

####  3.1.1 ASKAP J004114.7$-$235714

ASKAP J004114.7$-$235714 is within the 90% credible interval for the
localisation of GW190814 and doubles in flux density between the first and
fourth epochs before remaining relatively stable in the remaining
observations. The coordinates are covered by VLASS 1.2, but no radio emission
is detected. The source has a counterpart in both WISE and DECaLS, with a
photometric redshift of $1.0\pm 0.1$. The source has a variability index of
$V=0.26$, consistent with expectations for refractive scintillation along this
line of sight. We therefore suggest that this source is an unrelated variable
and rule it out as a counterpart.

####  3.1.2 ASKAP J005043.9$-$241602

ASKAP J005043.9$-$241602 is within the 30% credible interval for the
localisation of GW190814. The source was observed by VLASS 1.2, but no radio
emission is detected. The closest DECaLS source is offset by $14\arcsec$, with
a photometric redshift of $z=1.4\pm 0.5$ (corresponding to a physical offset
of $\sim 120$ kpc) and is therefore unrelated to the radio source. While we
cannot classify this source using existing archival data, it is unlikely to be
a transient due to the low variability index ($V=0.26$) that is consistent
with refractive scintillation. However, we cannot comprehensively rule it out.

####  3.1.3 ASKAP J004108.5$-$255607

ASKAP J004108.5$-$255607 is outside of the 99% credible interval for the
localisation of GW190814 and we therefore rule it out as a counterpart. It is
spatially coincident with sources in WISE and DECaLS, with a photometric
redshift of $z=0.88\pm 0.05$. The source was observed in VLASS 1.2, but no
radio emission was detected. The source has a variability index of $V=0.29$,
consistent with expectations for refractive scintillation along this line of
sight. We therefore suggest that this source is likely an unrelated variable.

####  3.1.4 ASKAP J003712.3$-$274029

ASKAP J003712.3$-$274029 is outside of the 99% credible interval for the
localisation of GW190814 and we therefore rule it out as a counterpart. It is
spatially coincident with sources in WISE and DECaLS, with a photometric
redshift of $1.7\pm 0.5$. The source has a variability index of $V=0.28$,
consistent with expectations for refractive scintillation along this line of
sight. There is a flux excess of $\sim 800\,\mu$Jy at the source location in
VLASS 1.2, implying that the source was significantly brighter prior to our
first epoch, unless it has an optically thin spectrum. We therefore
comprehensively rule this source out as a transient and classify it as an
unrelated variable.

####  3.1.5 ASKAP J005022.3$-$230349

ASKAP J005022.3$-$230349 tripled in luminosity between epochs 5 and 6 before
slowly declining. While the final epoch shows a slight rise compared to the
trend of the previous data points, this deviation from the trend is consistent
with the expected variability due to scintillation along this line of sight.

The candidate position is covered by the publicly available VLA observations
reported by Alexander et al. (2021) on 2019-09-22 and 2020-02-29, which have
independently analysed. Data were calibrated using the automated pipeline
available in the Common Astronomy Software Applications (CASA; McMullin et al.
2007), with additional flagging performed manually, and imaged666Cell size was
1/10 of the synthesized beamwidth, field size was the smallest magic number
($10\times 2^{n}$) larger than the number of cells needed to cover the primary
beam. using the CLEAN algorithm (Högbom, 1974). Because the source is offset
from the phase centre we also performed a primary beam correction with pbcorr.
We find no radio emission to a $3\sigma$ limit of 36$\,\mu$Jy at 6 GHz in
either epoch.

The candidate is offset by 1.9″ from an optical source that has been observed
by DECaLS and Gaia (Gaia Collaboration et al., 2016). The catalogued
photometric redshift based on DECaLS data is $z=0.3$ (95% confidence interval
0.09-0.7; Zhou et al., 2021a), which is consistent with the redshift of the
merger, and the source has no significant parallax measurement in the second
Gaia Data Release (Gaia Collaboration et al., 2018). We obtained spectroscopy
of the optical source on 2020-12-08 with the Robert Stobie Spectrograph (RSS;
Burgh et al., 2003) on the 10m-class Southern African Large Telescope (SALT).
We find no evidence for any host galaxy emission lines. Instead, the spectrum
is consistent with that of an M-dwarf star. We have since queried the Gaia
early DR3 (released after our SALT observations had been carried out; Gaia
Collaboration et al., 2021) and find a parallax consistent with a distance of
$\sim$400 pc. We therefore rule out the optical source as the host galaxy of
the candidate. We also note that the M dwarf is not the source of the radio
emission based on the the spatial offset and the variability timescale (radio
flare stars are generally variable on timescales of minutes–hours, see e.g.
Zic et al., 2020).

We find that even the most extreme assumption of a highly energetic ($E_{\rm
iso}=10^{53}$ erg) top-hat jet (i.e. a jet with uniform velocity profile, as
opposed to structured jets) propagating into a dense ($n=2\,$cm-3) circum-
merger medium cannot reproduce the observed steep rise (see Figure 5). We
conclude that this source is not a viable counterpart to GW190814, but do
consider it to be a real (but unrelated) radio transient that likely occurred
months after the merger. Detailed study and classification of this source is
beyond the scope of this work and will be presented in a separate manuscript
(Dobie et al. in prep.).

####  3.1.6 ASKAP J010242.7$-$251021

ASKAP J010242.7$-$251021 is outside of the 99% credible interval for the
localisation of GW190814 and we therefore rule it out as a counterpart. It is
spatially consistent with a DECaLS source with photometric redshift $z=0.3\pm
0.1$. The source has constraining non-detections in our first four epochs,
although manual inspection of the images suggests marginal evidence for a
detection in the fourth epoch. The source has a variability metrics of
$V=0.74$ and $\eta=25$. However, it is detected in VLASS 1.2 with a flux
density of $\sim 700\,\mu$Jy, 270 days before it is detected in our
observations. Extrapolating the observed trend in the 944 MHz lightcurve, we
find that the source would have been a few $\mu$Jy at the time of the VLASS
observation, corresponding to a spectral index of $\alpha\gtrsim 5$. We
therefore rule this out as a transient and instead classify it as an
intrinsically variable source.

####  3.1.7 ASKAP J003537.3$-$271844

ASKAP J003537.3$-$271844 was found in both our untargeted variability search
and our galaxy targeted search. However, it is outside the 99% credible
interval for the localisation GW190814 and we therefore rule it out as a
counterpart. It is offset by 1.1″ from a known galaxy with a spectroscopic
redshift of $z=0.22436$ observed as part of the 2-degree Field Lensing Survey
(Blake et al., 2016). This galaxy also has an infrared counterpart detected by
WISE. There is marginal evidence for emission at the radio source location in
VLASS at $\sim 480\,\mu$Jy although we caution that this is only three times
the local noise level and there are multiple pixels within a 30″ radius with
comparable flux density measurements. While the positions of the radio source
and the galaxy are marginally discrepant ($\gtrsim 1\sigma$), the inferred
radio luminosity of the radio source if it is at the distance of the galaxy is
$\sim 10^{30}$ erg s-1 Hz-1, consistent with the population of AGN (Brown et
al., 2011). We therefore conclude that this source is likely an AGN.

####  3.1.8 ASKAP J003809.2$-$231751

ASKAP J003809.2$-$231751 is outside the 98% credible region for the
localisation of GW190814 and is therefore unlikely to be a counterpart. There
is no evidence for radio emission in either VLASS 1.1 or 2.1. The radio
lightcurve consists of a continual rise, with the flux density almost tripling
across 10 epochs and a variability index of $V=0.27$. The source is offset
from two sources in DECaLS with separations of 2.9″ and 3.8″ and photometric
redshifts of $z=0.2\pm 0.1$ and $z=0.8\pm 0.2$. These angular separations at
those redshifts correspond to physical offsets of 10″ and 30″ respectively,
meaning that either optical source could plausibly be the host galaxy if the
radio source is a transient.

However, we note that the source exhibits no significant variability between
epochs 2 and 9. Applying the two-epoch variability metrics of Mooley et al.
(2016), only epochs 1 and 10 show significant variability when compared to
other epochs. Removing either epoch from our analysis results in a variability
metric, $V$, lower than the cutoff in Section 2.2.1. Based on this and the
fact that the variability metric of the full radio lightcurve is comparable to
expectations for refractive scintillation, we suggest that it is unlikely that
this source is a transient. However, we are unable to classify it with
archival data, nor comprehensively rule it out.

####  3.1.9 ASKAP J004150.8$-$255512

ASKAP J004150.8$-$255512 is outside of the 99% credible interval for the
localisation of GW190814 and we therefore rule it out as a counterpart. It is
spatially coincident with a source in both WISE and DECaLS, with photometric
redshift $z=1.1\pm 0.1$. There is no counterpart in epoch 1.2 of VLASS,
observed on 2019-07-06. The variability index of this source is $V=0.25$,
consistent with expectations for refractive scintillation. We therefore
suggest that this source is likely an unrelated variable.

####  3.1.10 ASKAP J004033.2$-$274119

ASKAP J004033.2$-$274119 is outside of the 99% credible interval for the
localisation of GW190814 and we therefore rule it out as a counterpart. It is
spatially coincident with sources in WISE and DECaLS, with photometric
redshift $z=0.7\pm 0.05$. There is marginal ($\sim 3\sigma$) evidence for
radio emission of $\sim 400\,\mu$Jy in VLASS 1.2, observed on 2019-07-06.
While the variability index ($V=0.4$) of this source is higher than
expectations for refractive scintillation, the spatial coincidence with a
known optical and IR source suggests that it is likely an AGN exhibiting some
combination of intrinsic and extrinsic variability.

####  3.1.11 ASKAP J004545.5$-$265643

ASKAP J004545.5$-$265643 is outside of the 99% credible interval for the
localisation of GW190814 and we therefore rule it out as a counterpart. There
is no coincident optical source in DECaLS, and the closest has a photometric
redshift of $1.7\pm 0.7$. However, the optical source is offset by 12″ and is
therefore unlikely to be related to the radio source. The source has a likely
counterpart in VLASS 1.2 with flux density $\sim 500\,\mu$Jy suggesting that
it was brighter prior to our observations and is therefore not a transient.
The variability index of $V=0.3$ is consistent with expectations for a compact
source exihbiting refractive scintilation.

####  3.1.12 ASKAP J010019.1$-$234315

ASKAP J010019.1$-$234315 was found in our galaxy targeting search and is
outside of the 99% credible interval for the localisation of GW190814 so we
rule it out as a counterpart. It is offset from PGC 3195680, which has no
distance estimate in GLADE, by 17″. After querying WISE and DECaLS we find
that there is a closer source offset by only 1.3″ with a photometric redshift
of $z=1.2\pm 0.25$. The source is covered by VLASS 1.1 and 2.1 but no radio
emission is detected in either epoch, which is not unexpected given its low
flux density. Similar to ASKAP J003537.3$-$271844, the offset between the
radio and optical sources is small, but statistically significant and the
inferred radio luminosity ($\sim 10^{30}$ erg s-1 Hz-1) is broadly consistent
with expectations for an AGN. We therefore suggest that this source is also an
AGN, but note that the classification is less certain in this instance due to
the larger spatial offset, alongside the larger uncertainty of the photometric
redshift.

Figure 5: Detctions of ASKAP J005022-230348 in our GW190814 follow-up
observations. The lightcurve of a tophat jet with with an isotropic equivalent
energy of $E_{\rm iso}=10^{53}$ erg propagating into a medium with density
$n=2\,$cm-3 viewed at an angle of 67 ° off-axis is shown in blue. Even this
extreme assumption cannot reproduce the rapid rise observed for this source.
Figure 6: Radio lightcurve of the candidate near ESO 474-035 reported by
Alexander et al. (2021). ASKAP observations at 944 MHz are denoted by solid
markers, while open markers show VLA observations at 6 GHz and triangle
correspond to 3$\sigma$ upper limits. The blue line shows the mean flux
density in our observations, while the maximum expected variability due to
scintillation at 944 MHz ($\sim$30%) is denoted by the blue shaded region.

###  3.2 Candidate counterpart associated with ESO 474-035

Alexander et al. (2021) reported the discovery of a candidate radio
counterpart near ESO 474-035 in their galaxy-targeted follow-up observations.
The observed lightcurve and spectral energy distribution is consistent with a
highly energetic ($E_{\rm iso}\sim 8\times 10^{53}$) tophat jet propagating
through a dense medium ($n\sim 0.5\,$cm-3), or high velocity ($\beta_{0}\sim
0.8c$) kilonova ejecta. The authors suggest that the candidate is unrelated to
GW190814 as the required energies and velocities are high compared to the
population of known short GRBs and compact object mergers.

The source is detected in all nine ASKAP observations with an average peak
flux density of 1.85 mJy, in good agreement with the spectral energy
distribution reported by Alexander et al. (2021). The lightcurve (Fig. 6) is
consistent with a relatively steady source and we measured $V_{s}=0.03$,
$\eta=3.04$. We can therefore comprehensively rule it out as a counterpart to
GW190814, independent of any physical arguments.

Figure 7: Parameter space ruled out by our radio non-detections for a merger
with isotropic equivalent energy $10^{51}$ erg, an initial jet opening angle
of $10\degr$ and microphysics parameters $\epsilon_{e}=0.1$,
$\epsilon_{B}=0.01$ and $p=2.2$. Shaded regions correspond to the ruled out
parameter space for a range of distances corresponding to $1\sigma$ either
side of the median as determined by gravitational wave measurements.

###  3.3 Constraints on the properties of a relativistic jet associated with
GW190814

Based on a continued non-detection of a radio afterglow from GW190814 we can
constrain the physical properties of any potential outflow from the merger. We
do this using two approaches.

In Dobie et al. (2019b) we constrained the inclination angle and circum-merger
density of the merger using afterglow lightcurves from an off-axis tophat jet
with isotropic equivalent energy $E_{\rm iso}=10^{51}$ erg, a jet opening
angle of $10\degr$ and microphysics parameters $\epsilon_{e}=0.1$,
$\epsilon_{B}=0.01$ and $p=2.2$. Figure 7 shows the same procedure applied to
our more recent results along with the updated gravitational wave distance
estimate. We find a significant improvement over our previous results, and are
able to rule out an additional $\sim$10 ° of parameter space across all values
of circum-merger density. Comparing our results to the merger inclination
angle estimated from the gravitational wave signal (45 °; Abbott et al., 2020)
we find that our results are only constraining for the lower end of the
distance estimate, where we are able to constrain $n\lesssim 0.5$ cm-3.

Figure 8: Parameter space ruled out by our radio non-detections to date for a
15$\degr$ tophat (left) and Gaussian (right) jet. Shaded regions show
constraints from Alexander et al. (2021), while hatched regions show the
constraints from this work, with the areas to the upper left of the region
ruled out. The width of the region corresponds to the uncertainty in the
distance to the merger. The inclination angle and associated $1\sigma$
uncertainties from the gravitational wave signal are shown in the solid and
dashed vertical lines respectively.

Alexander et al. (2021) follow a similar logic using afterglowpy (Ryan et al.,
2020) for tophat and Gaussian jet models and two 6 GHz non-detections at 38
and 208 days post-merger. Both models assume the same microphysics parameters
as above with a jet opening angle of $15\degr$ and are computed for a range of
isotropic equivalent energies ($E_{\rm iso}=2\times 10^{51}$, $5\times
10^{51}$, $5\times 10^{52}$ erg). The Gaussian jet model consists of a core
with wings extending to $90\degr$. We have applied the same process to our
observations and Figure 8 shows our limits which are comparable to Alexander
et al. (2021), albeit with slightly better constraints for higher energies. We
note that our limits are more comprehensive due to the substantially higher
fraction of the localisation area covered by our observations.

###  3.4 Radio Transient Rates

In Dobie et al. (2019b) we noted that our initial three epochs of follow-up
comprise the best widefield GHz-frequency transient survey to-date,
superseding previous surveys by an order of magnitude in both area and depth.
The observations presented in this work has more than tripled the number of
epochs, although we note that epoch 6 only has a 74% overlap with the other
pointings. The total areal coverage for this search is $262\,\deg^{2}$, over
four times larger than the initial search which covered 60 $\deg^{2}$
(excluding the initial reference epoch in both cases). Anderson et al. (2020)
report a search for transients with a total areal coverage of $\sim
540\,\deg^{2}$, but with a detection threshold of $500\,\mu$Jy. Assuming the
extragalactic radio transient source count obeys $N\propto S^{-1.5}$ as would
be expected in a Euclidean Universe, this makes our observations over twice as
sensitive to radio transients those reported by Anderson et al. (2020),
although the difference is statistically negligible at such low detection
rates777This estimate ignores the different choices of observing frequency
(943 MHz vs 3 GHz). However, the spectral index of most radio transients at
late times (i.e. typical of their long-term evolution) is generally expected
to be negative, making our observations even more sensitive.

We have detected one radio transient (excluding variable sources such as
scintillating AGN) that is likely unrelated to GW190814, ASKAP
J005022.3$-$230349, and therefore measure the surface density of radio
transients above $170\,\mu$Jy at 944 MHz to be
$0.0038^{+0.02}_{-0.0037}\,\deg^{-2}$ with uncertainties corresponding to a
double-sided 95% confidence interval (Gehrels, 1986). However, if ASKAP
J005022.3$-$230349 is related to GW190814 then we have detected no transients
in our untargeted search and place an upper limit of $0.013\,\deg^{2}$ on the
radio transient surface density for transients above 170 $\mu$Jy at 95%
confidence. This measurement is in good agreement with theoretical estimates
for the surface density of off-axis long GRBs (Metzger et al., 2015), and is
also consistent with estimates for tidal disruption events and neutron star
mergers.

###  3.5 Evaluating follow-up strategies

While our constraints on the properties of any relativistic afterglow produced
by GW190814 are comparable to those of Alexander et al. (2021), the observing
strategies and resources used to achieve them differ significantly.

By targeting potential host galaxies within the localisation volume, Alexander
et al. (2021) minimise the total area required to be observed and thereby the
total time per-epoch. The smaller, more targeted, areal coverage results in
fewer false-positives in general while any transients that are detected are
likely associated with the targeted galaxy and therefore fall within the
localisation volume of the event. In comparison, our widefield unbiased
follow-up predisposes our search to a larger number of false-positives. Some
of these can be ruled out via comparison to galaxy catalogues that either
classify them as variable AGN or as being associated with galaxies outside of
the localisation volume, as we have done in this work. However, many of these
require further observations to determine their nature, which could take the
form of dedicated follow-up (which is not feasible for tens–hundreds of
candidates) or continued widefield monitoring. To ensure that we are left with
a manageable number of candidates for human vetting we therefore require
either a larger number of observations that will intrinsically decrease the
number of false-positives in our sample, or more stringent variability
cutoffs. While the latter option may be suitable for widefield untargeted
transient searches (e.g. Mooley et al., 2016), it is not ideal for
gravitational wave follow-up where we know the radio counterparts will likely
be faint.

While our widefield many-epoch strategy is more resource intensive, it has a
number of advantages to a targeted approach with fewer epochs. The lack of
deep all-sky galaxy catalogues means that any galaxy-targeted approach is only
feasible for the closest events and simultaneously, the interpretation of any
results is always limited by the completeness of the galaxy catalogue. As we
move toward the 2030s, galaxy targeting will become a less effective strategy
as gravitational wave detector horizons expand, and next-generation radio
facilities with higher survey speeds come online (Dobie et al., 2021).

Observing a small number of epochs necessitates the targeting of the expected
peak timescale to maximise the chance of a detection. However, compact object
mergers (even when including the population of known short GRBs) are not yet
well-understood and therefore this strategy risks limiting the detectable
sample to events that fit canonical models. Additionally, observations
targeting the peak of the lightcurve may detect radio emission from a merger
that does not pass the relevant transient detection thresholds. For example,
if the observations occur either side of the lightcurve peak and measure
similar flux densities, or occur with insufficient time between them to detect
any source evolution.

Future widefield gravitational follow-up observations with next-generation
facilities will provide a unique opportunity for serendipitous discoveries. In
Section 3.4 we demonstrated that the observations reported in this work
comprise an unparalleled dataset in terms of sensitivity, areal coverage and
number of repetitions. Wang et al. (2021) discovered a Galactic plasma
filament in a search for short timescale variability in these observations,
while Koribalski et al. (2021) have combined the first eight epochs of this
search to form the deepest ASKAP observation to-date and found a new
extragalactic circular radio source. While the utility of follow-up
observations for unrelated science goals is short-lived as they will
eventually be superseded by large-scale dedicated surveys, they will still
produce useful data in the meantime.

##  4 Conclusions

We have carried out further follow-up observations of the possible neutron
star–black hole merger GW190814 with the Australian Square Kilometre Array
Pathfinder, building upon the work originally reported by Dobie et al.
(2019b). Our ten epochs of observation were carried out on an approximately
logarithmic cadence out to 655 days post-merger and cover 30 $\deg^{2}$,
comprising 87% of the merger localisation.

We used two techniques to search for a radio counterpart to the merger. We
carried out a widefield transient search of the entire field, which found 187
initial candidates that passed our initial search criteria and variability
metrics. A qualitative analysis of the images and lightcurve morphology of all
187 sources found that only 12 were real sources with lightcurves resembling
those expected from extragalactic synchrotron transients. After a more
detailed analysis including comparison to archival multiwavelength data we
find that only one candidate is likely to be an intrinsically transient
source. However, we are able to rule it out as a counterpart to GW190814 based
on its steep, late-time, rise which is incompatible with even the most extreme
radio afterglow models. We also carried out a targeted search around known
galaxies and found no viable counterparts. In addition, we have also used our
observations to comprehensively rule out the candidate counterpart found by
Alexander et al. (2021).

These observations comprise the most sensitive widefield radio transient
survey to-date, and based on our detection of a single transient (likely
unrelated to GW190814) we estimate the surface density of radio transients
above 170 $\mu$Jy at 944 MHz to be $0.0043^{+0.02}_{-0.0042}\,\deg^{-2}$. This
survey has helped set expectations for searches for radio transients that are
in their early stages (Murphy et al., 2021; Fender et al., 2016; Lacy et al.,
2020), as well as those that will be performed with next-generation telescopes
like the Square Kilometre Array (Fender et al., 2015).

The continued non-detection of a radio counterpart to GW190814 allows us to
improve our previous constraints on the circum-merger density, $n$ and merger
inclination, $\theta_{\rm obs}$. However, our limits are not sufficiently
constraining to confirm that this merger did not produce a radio counterpart.

The fourth gravitational wave observing run (O4) is expected to begin in
mid-2022 after upgrades to Virgo and both LIGO detectors and the Kamioka
Gravitational Wave Detector (KAGRA), is also expected to join the run. The
improved detector network sensitivity will result in a higher merger detection
rate and better localisation capabilities, both of which will lead to a larger
number of events for which electromagnetic follow-up is feasible. We expect
ASKAP to take a leading role in this effort with a focus on localising events
that do not produce a kilonova, or those that are not possible to follow up
with optical facilities due to observing constraints.

## Acknowledgements

We thank Kate Alexander and Andrew Zic for useful discussions.

TM acknowledges the support of the Australian Research Council through grant
DP190100561. DK and AO are supported by NSF grant AST-1816492. JL and JP are
supported by the Australian Government Research Training Program Scholarship.
Parts of this research were conducted by the Australian Research Council
Centre of Excellence for Gravitational Wave Discovery (OzGrav), project number
CE170100004.

The Australian SKA Pathfinder is part of the Australia Telescope National
Facility which is managed by CSIRO. Operation of ASKAP is funded by the
Australian Government with support from the National Collaborative Research
Infrastructure Strategy. ASKAP uses the resources of the Pawsey Supercomputing
Centre. Establishment of ASKAP, the Murchison Radio-astronomy Observatory and
the Pawsey Supercomputing Centre are initiatives of the Australian Government,
with support from the Government of Western Australia and the Science and
Industry Endowment Fund. We acknowledge the Wajarri Yamatji people as the
traditional owners of the Observatory site.

This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

This publication makes use of data products from the Wide-field Infrared
Survey Explorer(Wright et al., 2010), which is a joint project of the
University of California, Los Angeles, and the Jet Propulsion
Laboratory/California Institute of Technology, funded by the National
Aeronautics and Space Administration.

The SALT observations were obtained under the SALT Large Science Programme on
transients (2018-2-LSP-001; PI: DAHB) which is also supported by Poland under
grant no. MNiSW DIR/WK/2016/07. DAHB acknowledges research support from the
National Research Foundation. MG is supported by the EU Horizon 2020 research
and innovation programme under grant agreement No 101004719.

This research has made use of the CIRADA cutout service at URL
cutouts.cirada.ca, operated by the Canadian Initiative for Radio Astronomy
Data Analysis (CIRADA). CIRADA is funded by a grant from the Canada Foundation
for Innovation 2017 Innovation Fund (Project 35999), as well as by the
Provinces of Ontario, British Columbia, Alberta, Manitoba and Quebec, in
collaboration with the National Research Council of Canada, the US National
Radio Astronomy Observatory and Australia’s Commonwealth Scientific and
Industrial Research Organisation.

This research has made use of NASA’s Astrophysics Data System Bibliographic
Services.

This research has made use of the NASA/IPAC Extragalactic Database (NED) which
is operated by the Jet Propulsion Laboratory, California Institute of
Technology, under contract with the National Aeronautics and Space
Administration. This paper made use of WebPlotDigitizer
(http://arohatgi.info/WebPlotDigitizer/) by Ankit Rohatgi The acknowledgements
were compiled using the Astronomy Acknowledgement Generator. This research
made use of matplotlib, a Python library for publication quality graphics
(Hunter, 2007) This research made use of SciPy (Virtanen et al., 2020) This
research made use of Astropy, a community-developed core Python package for
Astronomy (Astropy Collaboration et al., 2018, 2013) This research made use of
NumPy (Harris et al., 2020) This research made use of pandas (McKinney, 2010,
2011)

## Data Availability

The ASKAP data used in this paper can be accessed through the CSIRO ASKAP
Science Data Archive
(CASDA888https://data.csiro.au/dap/public/casda/casdaSearch.zul) under project
code AS111.

The SALT spectrum of the optical counterpart candidate for ASKAP
J005022.3-230349 can be obtained from the SAAO cloud sever at this address:
https://cloudcape.saao.ac.za/index.php/s/XzuMSDVZtzLpnBo

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