###### Abstract

A rapidly rotating and highly magnetized remnant neutron star (NS; magnetar)
could survive from a merger of double NSs and drive a powerful relativistic
wind. The early interaction of this wind with the previous merger ejecta can
lead to shock breakout (SBO) emission mainly in ultraviolet and soft X-ray
bands, which provides an observational signature for the existence of the
remnant magnetar. Here we investigate the effect of an anisotropic structure
of the merger ejecta on the SBO emission. It is found that bolometric light
curve of the SBO emission can be broadened, since the SBO can occur at
different times for different directions. In more detail, the profile of the
SBO light curve can be highly dependent on the ejecta sturcture and, thus, we
can in principle use the SBO light curves to probe the structure of the merger
ejecta in future.

###### keywords:

kilonova/mergernova; magnetar; shock breakout

1 1 0 https://doi.org/ Magnetar wind-driven shock breakout emission after
double neutron star mergers: The effect of the anisotropy of the merger ejecta
Title Guang-Lei Wu1, Yun-Wei Yu1,2* and Shao-Ze Li3 Firstname Lastname,
Firstname Lastname and Firstname Lastname Lastname, F.; Lastname, F.;
Lastname, F. Correspondence<EMAIL_ADDRESS>
##  1 Introduction

Kilonovae are optical transient emission originating from mergers of double
neutron stars (NSs) or NS-black hole (BH) binaries Li and Paczyński (1998);
Metzger et al. (2010); Roberts et al. (2011); Barnes and Kasen (2013); Kasen
et al. (2013); Tanaka and Hotokezaka (2013). The power source of the kilonova
emission is conventionally considered to be the radioactive decays of
$r$-process elements, as these elements can be synthesized effectively in the
neutron-rich merger ejecta. As an electromagnetic counterpart of the merger-
induced GW radiation, kilonova emission can play a very important role in
confirming the position, time, redshift, and even the progenitor properties of
the mergers. Such effects of kilonovae had been manifested completely in the
famous GW170817 event Abbott et al. (2017a), which was accompanied with a
kilonova AT2017gfo Abbott et al. (2017b); Arcavi et al. (2017); Coulter et al.
(2017); Cowperthwaite et al. (2017); Evans et al. (2017); Nicholl et al.
(2017); Smartt et al. (2017); Soares-Santos et al. (2017); Tanvir et al.
(2017). The detailed modeling of the observed kilonovae and as well as their
associated gamma-ray burst (GRB) afterglows could further give constraint on
the properties of the merger products, especially, when the traditional
kilonova model is challenged by the observations.

The nature of the remnant of double NS mergers is one of the most concerned
issues in current astrophysical studies. The answer to this mystery would help
to constrain the mass limit of NSs and thus the equation of state (EOS) of
nuclear matter, which is highly related to the unclear non-perturbative
quantum chromodynamics at low energies. However, the confirmation of the
nature of merger products is beyond the ability of the current GW detectors,
since the detector sensitivities are still higher than the potential GW
radiation from the merger products Abbott et al. (2017). Therefore,
alternatively, it is expected that the electromagnetic counterparts of the GW
events can provide other observational signatures for judging the nature of
the merger products. Following this consideration, Yu et al. (2013) (Yu et
al., 2013) and Metzger & Piro (2014) (Metzger and Piro, 2014) investigated the
influence of a post-merger NS on the kilonova emission, where the remnant NS
is considered to be rapidly rotating and highly magnetized, i.e., a
millisecond magnetar. As the most direct effect, the spin-down of the
millisecond magnetar can inject energy into the merger ejecta and then enhance
the kilonova emission and accelerate the ejecta significantly. Thus, a new
name of mergernova was suggested to replace the traditional kilonova, in order
to reflect the predicted wide range of the emission luminosity that depends on
the specific properties of the remnant NS Yu et al. (2013). Using this
magnetar-driven mergernova model, Yu et al. (2018) successfully accounted for
the relatively high luminosity of AT 2017gfo on the order of $\sim 10^{42}\rm
erg~{}s^{-1}$ Yu et al. (2018), whereas the radioactive kilonova model needs
to invoke a too high ejecta mass Li et al. (2018); Shibata et al. (2017);
Metzger et al. (2018) (cf., Reference Kawaguchi et al. (2018) showed this
difficulty could somewhat overcome by considering the 2D radiative transfer
elaborately).

Frankly speaking, in view of the complication of mergernova emission, only the
information of the luminosity and temperature of the emission is not enough
for confirming the existence of a post-merger magnetar. The detailed transfer
and transformation of the spin-down energy of the magnetar need to be
investigated further Metzger and Piro (2014); Li and Yu (2016); Gao et al.
(2015); Siegel and Ciolfi (2016a, b); Gao et al. (2017); Yu et al. (2018); Li
et al. (2018); Wollaeger et al. (2019); Yu et al. (2019); Ren et al. (2019);
Ren and Dai (2022); Wu et al. (2021); Ai et al. (2022), which could lead to
some extra independent observational signatures for the magnetar.
Specifically, the energy release from the spinning-down magnetar could be
initally in the form of a Poynting flux and gradually transform into a
relativistic wind consisting of electron/positron pairs. Once this magnetar
wind catches up and collides with the preceding merger ejecta, it will
generate a forward shock (FS) propagating into the ejecta and a termination
shock (TS) reversely into the continuously injected wind. After a short
period, the FS would break out from the ejecta, while the TS is long lasting.
So, the primary channel of the energy transfer is the absorption of the TS
emission (i.e., a pulsar wind nebula emission) by the merger ejecta. The TS
emission can finally leak from the merger ejecta as the ejecta becomes
transparent in the related electromagnetic band. As a rsult, a non-thermal
emission component can appear in the late phase of the mergernova emission,
which have been found in many mergernova candidates including AT2017gfo Gao et
al. (2015, 2017); Ren et al. (2019); Yu et al. (2019); Wu et al. (2021); Ren
and Dai (2022). Meanwhile, the breakout of the FS could also cause a rapid
soft X-ray flare prior to the primary mergernova emission Li and Yu (2016),
which is similar to the situation discovered in the supernovae that are
suggested to be driven by a magnetar too Kasen et al. (2016); Liu et al.
(2021); Zhang et al. (2022). Generally, this shock breakout (SBO) precursor
emission of a mergernova is likely to be outshone by more luminous afterglow
emission of the associated GRB. Neverthelss, the observation of GRB 170817A
indicates that the nearby GW events are very probably observed off-axis, which
can significantly suppress the early afterglow emission and then make the SBO
emission emerging.

Therefore, at present, it is necessary to investigate in advance more detailed
features of the observational signatures of the magnetar-driven mergernovae,
particularly, in expectation of the future discovery of the SBO emission. In
theory, the propagation of the FS into the merger ejecta is determined by the
radial structure of the merger ejecta. The description of the ejecta structure
requires detailed numerical simulations. The first simulation on this topic
was performed by Davies et al. (1994) with an analytical EOS of nuclear matter
and a Newtonian gravity Davies et al. (1994), which showed that $\sim 2\%$
mass of the system can be ejected around the equatorial plane as the dynamical
tail of the spiral tidal arms. This result was subsequently reproduced by more
simulations Ruffert et al. (1996); Rosswog et al. (1999, 2000); Ruffert and
Janka (2001); Korobkin et al. (2012), which further found that (i) the
neutrino-energy deposition in the cool outer regions of the tidal arms can
enhance the mass loss and (ii) the material at the contact interface between
the NSs can be squeezed out although the tidal ejecta could still be dominant.
Subsequently, the consideration of general relativity and more realistic EOSs
leads to some new understandings of the formation of the ejecta Piran et al.
(2013); Rosswog et al. (2013); Bauswein et al. (2013); Hotokezaka et al.
(2013); Sekiguchi et al. (2016); Foucart et al. (2016); Radice et al. (2016);
Dietrich et al. (2017a, b); Radice et al. (2018); Shibata et al. (2021). It is
showed that the squeezed component of the ejecta could become dominant over
the tidal component Oechslin et al. (2007); Bauswein et al. (2013); Hotokezaka
et al. (2013), as the squeezed material is effectively heated and accelerated
by a shock, spreading into a quasi-isotropic region and owning a velocity
higher than that of the tidal component. Then, the collision of the squeezed
component with the tidal component would lead to a more complex structure of
the ejecta. On the other hand, the simulations also showed that a thick disk
of a mass of $\sim 0.1M_{\odot}$ can surround the merger remnant and the
neutrino emission from both the disk and remnant can drive a hot wind into a
funnel shape region in the polar direction Dessart et al. (2009); Perego et
al. (2014); Martin et al. (2015); Fujibayashi et al. (2017). The disk wind
component can last for a relatively long timescale due to the viscous heating
in the disk, which is further dependent on the lifetime of the remnant NS and
the magnetic field configuration of the disk Siegel et al. (2014); Fujibayashi
et al. (2018); Siegel and Metzger (2018); Fujibayashi et al. (2018); Fernández
et al. (2019). As the accretion disk finally expands and becomes advection
dominated, the wind would become more isotropic and slower until the accretion
becomes inefficient Fernández and Metzger (2013); Just et al. (2015);
Fujibayashi et al. (2018); Fernández et al. (2019). In summary, the properties
of the merger ejecta can vary obviously with the angle relative to the
symmetric axis of the system, which may leave imprints in the SBO emission.
Therefore, in this paper, we revisit the SBO emission by taking into account
the anisotropic structure of the merger ejecta.

##  2 The model

###  2.1 Anisotropic merger ejecta

Figure 1: The density profile employed in our calculations.

As introduced, the material ejected during a merger of double NSs can have
different origins, which at least contain three channels including the tidal
and squeezed dynamical origins and the disk wind origin. These ejecta
components own different masses, velocities, electron fractions, and element
compositions, which leads the merger ejecta to be highly anisotropic. In this
paper, we adopt the empirical description of the ejecta structure suggested by
Kawaguchi et al. Kawaguchi et al. (2018, 2020). While the disk wind is
considered to be roughly isotropic, the mass distribution of the dynamical
ejecta can exhibit an angular dependence as follows: Kawaguchi et al. (2018,
2020)

$\eta\left(\theta\right)=\left[1-\Theta\left(\theta\right)\right]f_{\mathrm{}}+\Theta(\theta),$
(1)

where $f_{\mathrm{}}$ represents the density ratio of $\theta=0$ to $\pi/2$
and

$\Theta\left(\theta\right)=\frac{1}{1+\mathrm{exp}\left[-10\left(\theta-\pi/4\right)\right]}.$
(2)

The above expressions were summarized from the numerical simulations such as
those given by References Radice et al. (2016); Sekiguchi et al. (2016);
Kiuchi et al. (2017); Shibata et al. (2017), which describe the combination of
the tidal and squeezed components. The propagation of the magnetar wind-driven
FS in the ejecta is highly dependent on the radial distribution of the ejecta
mass. According to numerical simulations, we assume as usual that the radial
profile of the different ejecta components can be described by power laws as
follows Nagakura et al. (2014)

$\rho_{\mathrm{ej}}\left(r,\theta\right)\propto\begin{cases}r^{-3},&{\rm~{}for~{}the~{}wind~{}component,}\\\
\eta\left(\theta\right)r^{-4},&{\rm~{}for~{}the~{}dynamical~{}component,}\end{cases}$
(3)

which can be normalized by the masses of the disk wind ejecta
$M_{\mathrm{ej,w}}$ and the dynamical ejecta $M_{\mathrm{ej,d}}$,
respectively. This 2D distribution of the density of the merger ejecta in the
$v_{x}-v_{z}$ plane is shown in Fig. 1, for the parameter values of Model A
listed in Table 1. An axial symmetry around the $z-$axis is adopted. Here, the
maximum radii of the ejecta components are determiend by

$\displaystyle r_{\max,\rm w}(t)=r_{\max,\rm w}(0)+v_{\mathrm{max,w}}t,$ (4)
$\displaystyle r_{\max,\rm d}(t)=r_{\max,\rm d}(0)+v_{\mathrm{max,d}}t,$ (5)

where $v_{\mathrm{max,w}}$ and $v_{\mathrm{max,d}}$ are the corresponding
maximum velocities.

Model | A | B | C | D | E | F
---|---|---|---|---|---|---
$L_{\mathrm{w,i}}/\mathrm{erg\,s^{-1}}$ |  |  | $10^{48}$ |  |  |
$t_{\mathrm{md}}/\mathrm{s}$ |  |  | $5\times 10^{3}$ |  |  |
$\kappa_{\mathrm{w}}/\mathrm{cm^{2}\,g^{-1}}$ |  |  | 1 |  |  |
$\kappa_{\mathrm{d,p}}/\mathrm{cm^{2}\,g^{-1}}$ |  |  | 1 |  |  |
$\kappa_{\mathrm{d,e}}/\mathrm{cm^{2}\,g^{-1}}$ |  |  | 10 |  |  |
$\kappa_{\mathrm{x}}/\mathrm{cm^{2}\,g^{-1}}$ |  |  | $7\times 10^{3}$ |  |  |
$f$ | $0.01$ | $0.1$ | $0.01$ | $0.01$ | $0.01$ | $0.01$
$M_{\mathrm{ej,w}}/0.01M_{\odot}$ | $1$ | $1$ | $0.25$ | $1$ | $1$ | $1$
$M_{\mathrm{ej,d}}/0.01M_{\odot}$ | $1$ | $1$ | $0.1$ | $0.25$ | $1$ | $1$
$v_{\mathrm{max,d}}/c$ | $0.3$ | $0.3$ | $0.3$ | $0.3$ | $0.2$ | $0.4$
$v_{\mathrm{max,w}}/c$ |  |  | $0.1$ |  |  |
Table 1: Model parameters

###  2.2 Magnetar wind

The remnant NS of a merger event is very likely to be in differential rotation
initially, which can lead to the amplification of the magnetic fields of the
NS through dynamo mechanisms (e.g. Duncan and Thompson, 1992; Price and
Rosswog, 2006; Cheng and Yu, 2014). As the NS become a magnetar, a powerful
relativistic wind can be driven with a luminosity of

$L_{\mathrm{w,i}}=9.6\times
10^{48}B_{\mathrm{p,}15}^{2}R_{\mathrm{s,}6}^{6}P_{\rm i,-3}^{-4}\mathrm{erg\
s}^{-1},$ (6)

where $B_{\rm p}$, $R_{\mathrm{s,}}$ and $P_{\mathrm{i}}$ are the polar
magnetic filed strength, radius, and spin period of the magnetar. Here the
convention $Q_{x}/10^{x}$ is adopted in cgs units. The reference values of the
parameters in the above expression are adopted by according to the inference
from the shallow-decay and plateau afterglows of GRBs by ascribing these
afterglow features to the consequence of a magnetar engine Yu et al. (2010);
Lyons et al. (2010); Lü and Zhang (2014); Lü et al. (2015). Nevertheless, the
fitting of the mergernova AT2017gfo, which is in counterpart with the
GW170817/GRB 170817A event, indicates that the magnetic filed of the remnant
NS on a timescale of days could be not much higher than $10^{11}$ G (Yu et
al., 2018; Li et al., 2018), if such a NS indeed played a role in there as
supposed. By combining with these two different observational constraints, Yu
et al. (2018) suggested that the ultra-high magnetic field of the remnant
magnetar could be suppressed drastically by some unclear mechanisms (e.g.,
hidden by fallback material) at a time of a few hundreds to thousand of
seconds Yu et al. (2018). This assumption could also be supported by the
discovery of an extremely steep decay following a plateau in some GRB
afterglows. In any case, for simplicity, here we would not consider this
potential complex in our calculation and the temporal evolution of the wind
luminosity is adopted to be as usual as

$L_{\mathrm{w}}\left(t\right)=L_{\mathrm{w,i}}\left(1+\frac{t}{t_{\mathrm{md}}}\right)^{-2},$
(7)

where $t_{\mathrm{md}}=2\times
10^{3}R_{\mathrm{s,}6}^{-6}B_{\mathrm{p,}15}^{-2}P_{\mathrm{i,-3}}^{2}\,\mathrm{s}$
is the spin-down timescale.

###  2.3 Shock dynamics and breakout emission

As the powerful magnetar wind collides with the merger ejecta, the wind can be
shocked by the TS to generate high energy emission, which is absorbed in part
by the merger ejecta. Meanwhile, the FS propagates into and finally crosses
the ejecta and its the dynamical evolution can be determined by Li and Yu
(2016)

$\frac{dv_{\mathrm{sh}}}{dt}=\frac{1}{M_{\mathrm{sh}}v_{\mathrm{sh}}}\left[L_{\mathrm{w}}-L_{\mathrm{tot}}-\frac{1}{2}\left(v^{2}_{\mathrm{sh}}-v_{\mathrm{ej}}^{2}\right)\frac{dM_{\mathrm{sh}}}{dt}-\frac{dU}{dt}\right],$
(8)

where $v_{\mathrm{sh}}$ is the shock velocity of the shock front, $U$ is the
total internal energy of the shocked region, and $L_{\mathrm{tot}}$ is the
total luminosity of the thermal emission of merger ejecta. The increase of the
swept-up mass $M_{\mathrm{sh}}$ can be calculated by

$\frac{dM_{\mathrm{sh}}}{dt}=4\pi
r_{\mathrm{sh}}^{2}\rho_{\mathrm{ej}}\left(v_{\mathrm{sh}}-v_{\mathrm{ej}}\right),$
(9)

where $r_{\rm sh}$ is the radius of the shock front, $v_{\mathrm{ej}}$ is the
velocity of the ejecta material in front of the shock, and the mass density
$\rho_{\rm ej}$ is given by Eq. (3). Meanwhile, the thermal energy deposited
in the shocked material is given by

$H_{\mathrm{sh}}=\frac{1}{2}\left(v_{\mathrm{sh}}-v_{\mathrm{ej}}\right)^{2}\frac{dM_{\mathrm{sh}}}{dt}.$
(10)

Here, since the merger ejecta is anisotropic, the above equations should be
solved separately for different directions. After the determination of $H_{\rm
sh}(t)$, the evolution of the internal energy accumulated by the shock can be
derived from

$\frac{dU_{\mathrm{sh}}}{dt}=H_{\mathrm{sh}}-P_{\mathrm{sh}}\frac{dV_{\mathrm{sh}}}{dt}-L_{\mathrm{sh}},$
(11)

where $V_{\mathrm{sh}}$ and
$P_{\mathrm{sh}}=U_{\mathrm{sh}}/\left(3V_{\mathrm{sh}}\right)$ are the volume
and pressure of the shock heating region, respectively, and $L_{\rm sh}$ is
the bolometric luminosity of the SBO emission. Meanwhile, the evolution of the
internal energy excluding the shock-accumulated part,
$U_{\mathrm{ej}}=U-U_{\mathrm{sh}}$, can be written as (ignoring the
radioactivity energy)

$\frac{dU_{\mathrm{ej}}}{dt}=L_{\mathrm{w}}-P_{\mathrm{ej}}\frac{dV_{\mathrm{ej}}}{dt}-L_{\mathrm{mn}},$
(12)

where $V_{\mathrm{ej}}$ and
$P_{\mathrm{ej}}=U_{\mathrm{ej}}/\left(3V_{\mathrm{ej}}\right)$ are the volume
and the pressure of the ejecta behind the shock, respectively, and $L_{\rm
mn}$ is the bolometric luminosity of the mergernova emission.

Following the approximate one-zone diffusion model in Reference Kasen and
Bildsten (2010), the bolometric luminosity of the SBO emission can be
estimated by111Here the shocked energy is considered to distribute
approximately uniformly behind the shock, which is different from Li and Yu
(2016) where the shocked energy is assumed to be concentrated within a thin
shell immediately behind the shock front.

$L_{\mathrm{sh}}\approx\frac{r_{\mathrm{max,d}}^{2}U_{\mathrm{sh}}c}{r_{\mathrm{max,d}}^{3}-r_{\mathrm{sbo}}^{3}}\left[\frac{1-e^{-\tau_{\mathrm{sbo}}}}{\tau_{\mathrm{sbo}}}\right],$
(13)

where $r_{\mathrm{sbo}}$ is the radius at which SBO occurs and
$\tau_{\mathrm{sbo}}$ is the optical depth of the shell between the radii
$r_{\mathrm{sbo}}$ and $r_{\mathrm{max,d}}$. Above $r_{\mathrm{sbo}}$, photons
can escape from the merger ejecta, because the photon diffusion time in the
outside shell is equal to the dynamical time, i.e.,

$\tau_{\rm sbo}=\int_{r_{\rm sbo}}^{r_{\max,\rm d}}\kappa\rho dr={ct\over
r_{\max,\rm d}-r_{\rm sbo}},$ (14)

from which the radius $r_{\rm sbo}$ can be derived, where $\kappa$ is the
opacity. When $r_{\rm sbo}\ll r_{\max,\rm d}$, the above equation returns to
its usual form as $\tau_{\rm sbo}=c/v_{\rm max,d}$. Meanwhile, the bolometric
luminosity of the mergernova emission can be given by

$L_{\mathrm{mn}}\approx\frac{U_{\mathrm{ej}}c}{r_{\mathrm{max,d}}}\left[\frac{1-e^{-\left(\tau_{\mathrm{sh}}+\tau_{\mathrm{un}}\right)}}{\tau_{\mathrm{sh}}+\tau_{\mathrm{un}}}\right],$
(15)

where $\tau_{\mathrm{sh}}\approx\kappa M_{\mathrm{sh}}/4\pi
r_{\mathrm{sh}}^{2}$ and
$\tau_{\mathrm{un}}=\int_{r_{\mathrm{sh}}}^{r_{\mathrm{max,d}}}\kappa\rho dr$
are the optical depths of shocked and unshocked ejecta. In our calculations,
the opacity $\kappa$ is adopted to be Chen et al. (2021); Ren and Dai (2022)

$\kappa=\kappa_{\mathrm{x}}\left(\frac{3.92kT_{\mathrm{int}}}{1\mathrm{keV}}\right)^{-1}$
(16)

for $kT_{\mathrm{int}}\geq 0.3\mathrm{keV}$ and

$\kappa=\begin{cases}\kappa_{\mathrm{w}},&{\rm
for~{}the~{}wind~{}component},\\\ \kappa_{\mathrm{d,p}},&{\rm
for~{}the~{}dynamical~{}component~{}of~{}}\theta\leq\pi/4,\\\
\kappa_{\mathrm{d,e}},&{\rm
for~{}the~{}dynamical~{}component~{}of~{}}\theta>\pi/4,\end{cases}$ (17)

for $kT_{\mathrm{int}}<0.3\mathrm{keV}$, where
$T_{\mathrm{int}}\approx\left(cU/4V\sigma\right)^{1/4}$ is the average
internal temperature of the related region, $k$ is the Boltzmann constant,
$\sigma$ is the Stefan-Boltzmann constant, and the values of parameters
$\kappa_{\mathrm{x}}$, $\kappa_{\mathrm{w}}$, $\kappa_{\mathrm{d,p}}$ and
$\kappa_{\mathrm{d,e}}$ are listed in Table 1. Here, for the dynamical ejecta,
two different opacity values are simply taken for $\theta\leq\pi/4$ and
$\theta>\pi/4$, in order to reflect the angluar-dependence of the electron
faction, which is result of the anisotropic neutrino irradiation from the
remnant NS and the disk.

Finally, as photons diffuse and are thermalized continuously, a black-body
emission appears at a photosphere of radius $r_{\rm ph}$ with an effective
temperature of

$T_{\mathrm{eff}}=\left(\frac{L_{\mathrm{tot}}}{4\pi\sigma
r_{\mathrm{ph}}^{2}}\right)^{1/4},$ (18)

where $L_{\mathrm{tot}}=L_{\mathrm{sh}}+L_{\mathrm{mn}}$ and
$r_{\mathrm{ph}}\approx r_{\mathrm{max,d}}$ is taken in our calculation. Then,
the emergent net flux at a frequency $\nu$ can be given by using the black-
body spectrum as

$F_{\nu}=\frac{2\pi
h\nu^{3}}{c^{2}}\frac{1}{\mathrm{exp}\left(h\nu/kT_{\mathrm{eff}}\right)-1},$
(19)

where $h$ is the Planck constant.

###  2.4 Integration over the emission surface

Figure 2: The sketch of the coordinate system we use, the angles $\Theta$ and
$\Phi$ are the represent the direction of line of sight, the angles $\theta$
and $\phi$ represent the location of a point in local structure.

As illustrated in Fig. 2, we adopt coordinates with $z-$axis along the
symmetric axis of the system and denote the zenith and azimuth angles by
$\theta$ and $\phi$. Then, the specific luminosity for an observer on the line
of sight (LOS) of $(\Theta,\Phi)$ can be obtained by integrating the specific
intensity over the visible photosphere as

$L_{\nu}\left(\Theta,\Phi\right)=4\pi r_{\rm ph}^{2}\int_{\mu\geq
0}I_{\nu}\left(\mu,\theta,\phi\right)\mu d\Omega\left(\theta,\phi\right),$
(20)

which is viable for an unresolved emitting source Rybicki (1970); Collins
(1973); Kandel (1973); Rybicki and Hummer (1983), where
$\mu=\hat{n}\left(\theta,\phi\right)\cdot\hat{k}\left(\Theta,\Phi\right)$ with
$\hat{n}$ and $\hat{k}$ being the unit vectors of the normal of the
differential solid angle and the direction of the LOS, respectively. For an
ideal black-body surface, the angular distribution of emergent intensities is
uniform and, thus, the value of $I_{\nu}$ can in principle be derived from Eq.
(19) to
$I_{\nu}\left(\mu,\theta,\phi\right)=F_{\nu}\left(\theta,\phi\right)/\pi$.
However, as a more realistic consideration, the hot, expanding ejecta should
contain an abundance of free electrons, especially, in the fastest head of
dynamical ejecta. In other words, the atmosphere above the photosphere can
deviate from the thermal equilibrium and become scattering dominated. In this
case, the limb darkening effect needs to be taken into account, which is
widely discussed in the radiation transfer of stellar atmosphere Hopf (1930);
Chandrasekhar (1960); Mihalas (1978). Here we simply consider pure isotropic
scattering, which leads the emergent intensities to be different for different
directions as Bronstein (1929); Hopf (1930); Chandrasekhar (1960)

$I_{\nu}\left(\mu,\theta,\phi\right)=\frac{5}{4}\mathcal{H}\left(\mu\right)F_{\nu}\left(\theta,\phi\right).$
(21)

where222An exact expression of $\mathcal{H}\left(\mu\right)$ had been given by
Mihalas (1978) as
$\mathcal{H}\left(\mu\right)=\frac{1}{\left(1+\mu\right)^{1/2}}\mathrm{exp}\left[\frac{1}{\pi}\int_{0}^{\pi/2}\frac{\theta\tan^{-1}\left(\mu\tan\theta\right)}{1-\theta\cot\theta}\right].$
(22)

$\mathcal{H}\left(\mu\right)=\frac{I_{\nu}\left(\tau=0,\mu\right)}{I_{\nu}\left(\tau=0,\mu=1\right)}=\frac{3}{5}\left[(\mu+q\left(\tau=0\right)\right]$
(23)

for $\mathcal{H}\left(\mu=1\right)=1$ and $q\left(\tau\right)$ is the Hopf
function. This function implies that the intensity emerging from the limb is
about $40\%$ of that from the center of the emission source, when the
Eddington approximation is taken $q\left(\tau=0\right)=2/3$, which is in fair
agreement with the observations of the Sun.

Figure 3: Mult-band light curves of the magnetar-driven SBO (i.e., the first
bump at around $10^{3-4}$ s) and mergernova (i.e., the second bump at around
$10^{5-6}$ s) emission from an anisotropic merger ejecta for parameters listed
in Table 1, including 0.1 keV (Green), 6 keV (Purple), 2 eV (Yellow), 0.5 eV
(Red) and the bolometric ones (black). For a comparison, the GRB X-ray
($0.1\,\mathrm{KeV}$) afterglow is also presented by the cyan dotted-dashed
lines for three viewing angles of $0^{\circ}$, $4^{\circ}$ and $8^{\circ}$,
which are yielded from the afterglowpy Ryan et al. (2020) for a top-hat jet
model with a half-opening angle of $3^{\circ}$, where the typical parameter
values as inferred from the GRB 170817A observations are taken as
$E_{\mathrm{iso}}=10^{51}\,\mathrm{erg}$, $n=10^{-3}\,\mathrm{cm}^{-3}$,
$p=2.3$, $\epsilon_{e}=0.1$, and $\epsilon_{\mathrm{B}}=10^{-4}$. Due to the
limb darkening effect, the SBO emission can slightly vary with the
observational directions, as labeled by the solid ($\Theta=0^{\circ}$), dotted
($30^{\circ}$), dashed ($60^{\circ}$), and dashed–dotted ($90^{\circ}$) lines.
Figure 4: The intensity distribution on the emission surface for different
times (rows) and different viewing angles (columns), for the Model A parameter
values.

##  3 Results

For the parameter values listed in Table 1, we calculate the light curves of
the SBO and mergernova emission, as presented in Fig. 3. First of all, the SBO
emission is mainly in the UV and soft X-ray bands, while the mergernova
emission is in optical, just as found in Li and Yu (2016). In comparison with
the GRB afterglow emission, the SBO emission is most likely to be detected in
soft X-rays, especially, when the GRB jet is deviate from the LOS.

The anisotropic structure of the merger ejecta can broaden the bolometric
light curve of the SBO emission. This is because the SBO occurs at different
times for different directions and thus it takes a relatively long period to
observe the total SBO emission. In more detail, the harder emission can emerge
earlier than the softer emission, since the former corresponds to a smaller
SBO radius due to a thin merger ejecta in the polar direction while the later
comes from the thick equatorial ejecta. Such a shift of the highlight on the
emission surface is clearly shown in Fig. 4. In more detail, the comparison
between the different panels shows that the profile of the light curves, in
particular, of the increasing phase is highly dependent on the structure
parameters of the ejecta, which thus enables us to probe the ejecta structure
by observing this SBO emission.

In addition, the SBO light curves show a slight dependence of the viewing
angle. This a result of the limb darkening effect, which leads to the on-axis
observation on an emitting element can receive more intensity than the off-
axis observation. Therefore, when the highlight point moves on the emission
surface, observers on different directions would detect different light
curves, as also shown in Fig. 4. Here, it is worth mentioning that this
viewing angle-dependence of the SBO emission would be likely to cause a
significant difference in the polarization of the emission between different
observational directions, although its influence on the light curve profile is
unremarkable.

##  4 Conclusions and Discussion

In this paper, we investigate the influence of the anisotropic structure of
merger ejecta on the SBO emission driven by a magnetar wind. In view of the
possible suppression of the magnetic field of the magnetar at late time, the
early SBO emission (in particular, in the soft X-ray band) can provide an
important observational signature for the existence of a remnant magnetar.

It is found that, due to the different density distribution in different
directions, the occurring time of the SBO can vary with the angle relative to
the symmetric axis of the system. This leads to the broadening of the
bolometric light curve of the SBO emission, which makes it more possible to be
detected. Furthermore, in future, as some detailed observations can be
achieved (e.g., by the Einstein Probe Yuan (2022)), we can even use the SBO
light curve to probe the structure of the merger ejecta, where of course a
more realistic structure description must be involved for elaborate modelings.
In addition, we also find the observational SBO emission can be slightly
dependent on the viewing angle. This is because the anisotropic structure of
the merger ejecta leads to a highlight point moving from the polar to the
equatorial direction on the emission surface. This could simultaneously lead
to a significant variation in the polarization of the emission for different
observational directions, which is worth to be investigated carefully in
future.

Recently, some fast X-ray transients have been detected and suspected to be
powered by a spinning-down magnetar Xue et al. (2019); Lin et al. (2022),
which could be directly contributed by the dissipating magnetic wind if it is
not trapped by thick material Zhang (2013). Alternatively, as presented in
this paper, even if the magentar wind is surrounded by a merger ejecta, the
SBO driven by the magnetar wind could still generate an X-ray transient. In
contrast to the highly-beamed GRB emission, this SBO emission can in principle
be detected at arbitrary directions, which therefore provides a valuable
signal for test the existence of the remnant magnetar. Additionally, in view
of the similarity of the mergernovae and superluminous supernovae, such a SBO
signal can also be expected to appear in these supernova emission, probably
with a relatively longer timescale Liu et al. (2021); Zhang et al. (2022).

## Acknowledgments

This work is supported by the National Key R&D Program of China
(2021YFA0718500), the National SKA Program of China (2020SKA0120300), and the
National Natural Science Foundation of China (grant No. 11833003).

[custom]

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# Korean-Specific Dataset for Table Question Answering

###### Abstract

Existing question answering systems mainly focus on dealing with text data.
However, much of the data produced daily is stored in the form of tables that
can be found in documents and relational databases, or on the web. To solve
the task of question answering over tables, there exist many datasets for
table question answering written in English, but few Korean datasets. In this
paper, we demonstrate how we construct Korean-specific datasets for table
question answering: Korean tabular dataset is a collection of 1.4M tables with
corresponding descriptions for unsupervised pre-training language models.
Korean table question answering corpus consists of 70k pairs of questions and
answers created by crowd-sourced workers. Subsequently, we then build a pre-
trained language model based on Transformer and fine-tune the model for table
question answering with these datasets. We then report the evaluation results
of our model. We make our datasets publicly available via our GitHub
repository and hope that those datasets will help further studies for question
answering over tables, and for the transformation of table formats.

Keywords: Table question-answering, KO-TaBERT, KorWikiTableQuestions

languageresourceLanguage Resources

Korean-Specific Dataset for Table Question Answering

Changwook Jun, Jooyoung Choi, Myoseop Sim, Hyun Kim, Hansol Jang, Kyungkoo Min
---
LG AI Research
ISC, 30, Magokjungang 10-ro, Gangseo-gu, Seoul, 07796, Korea
{cwjun, jooyoung.choi, myoseop.sim, hyun101.kim, hansol.jang,
<EMAIL_ADDRESS>

Abstract content

## 1\. Introduction

The task of question answering is to correctly answer to given questions,
which requires a high level of language understanding and machine reading
comprehension abilities. As pre-trained language models on Transformer
[Vaswani et al., 2017] have brought significant improvements in performance in
many natural language processing tasks, there have been many studies in
machine reading comprehension (MRC) and question answering (QA) tasks [Devlin
et al., 2018, Lan et al., 2019, Yang et al., 2019, Yamada et al., 2020, Liu et
al., 2019, Clark et al., 2020]. There are Stanford Question Answering Dataset
(SQuAD) benchmarks [Rajpurkar et al., 2016, Rajpurkar et al., 2018], well-
known machine reading comprehension benchmarks in the NLP area, that involve
reasoning correct answer spans in the evidence document to a given question.
Since SQuAD datasets are composed of pairs of natural language questions and
answers, and the corresponding documents are unstructured textual data, the
task is mainly to focus on predicting answers from plain texts.

Much of the world’s information produced daily is stored in structured formats
such as tables in databases and documents, or tables on the web. Question
answering over these structured tables has been generally considered a
semantic parsing task in which a natural language question is translated to a
logical form that can be executed to generate the correct answer [Pasupat and
Liang, 2015, Zhong et al., 2017, Dasigi et al., 2019, Wang et al., 2019, Rubin
and Berant, 2020]. There have been many efforts to build semantic parsers with
supervised training datasets such as WikiSQL [Zhong et al., 2017] consisted of
pairs of questions and structured query language (SQL) and Spider dataset [Yu
et al., 2018] that aims for a task of converting text to SQL. However, it is
expensive to create such data, and there are challenges in generating logical
forms. In recent years, a few studies attempt the task of question answering
over tables without generating logical forms [Herzig et al., 2020, Yin et al.,
2020, Chen et al., 2020, Zayats et al., 2021, Zayats et al., 2021]. They
introduce approaches of pre-trained language models based on BERT [Devlin et
al., 2018] to learn representations of natural language sentences and
structured tables jointly by extending embeddings, and these models achieve
strong performance on the semantic parsing datasets.

In this paper, for the Korean-specific table question answering task, we
present KO-TaBERT, a new approach to train BERT-based models that learn
jointly textual and structured tabular data by converting table structures. To
address this, we first create two datasets written in the Korean language: the
tabular dataset contains conversion formats of around 1.4M tables extracted
from Korean Wikipedia documents for pre-training language models, and the
table question answering dataset for fine-tuning the models. The table
question answering dataset consists of 70k pairs of questions and answers, and
the questions are generated by crowdsourced workers considering question
difficulty. Additionally, we introduce how structured tables are converted
into sentence formats. The conversion formats play a crucial role for models
to learn table structural information effectively without changing embeddings.
Second, we follow BERT architecture [Devlin et al., 2018] to pre-train a
language model with the converted strings from millions of tables, and fine-
tune models on the table question answering dataset. All resources we create
in this study are released via our GitHub repository111https://github.com/LG-
NLP/KorWikiTableQuestions.

We evaluate our model on the downstream task of table question answering. For
performance evaluation, we create the test dataset that includes around 10k
question-answer pairs related to tables in Korean Question Answering Dataset
(KorQuAD 2.0)222https://korquad.github.io/, and 20% splits of the crowdsourced
dataset. KO-TaBERT achieves EM 82.8% and F1 86.5% overall. Comparisons of the
model performance according to question difficulty and different table
conversion formats are also reported in this study.

We summarize our main contributions as follows:

  * •

We construct two Korean-specific datasets: Korean Wikipedia Tabular dataset
(KorWikiTabular) consisting of 1.4M tables that are converted into sentence
strings containing tabular structural information, and Korean Wikipedia Table
Questions dataset (KorWikiTQ) including 70k pairs of questions and answers
generated according to question difficulty by paid crowdsourced workers.

  * •

We introduce approaches to converting tabular data into sentence strings,
which allows models to represent table structural properties and information.

  * •

We present KO-TaBERT, a pre-trained language model that learns syntactic and
lexical information and as well structural information from tables.

  * •

We build table question answering models based on the pre-trained language
model using our datasets. Our model is evaluated on the table-related subset
of the KorQuAD 2.0 corpus, and they can be treated as baselines for future
research.

## 2\. Related Works

There have been many studies to reason the correct answer to a given question
over tables. A semantic parsing task is applied for question answering over
tables, which translates natural language questions to logical forms such as
SQL. Several works [Hwang et al., 2019, Lyu et al., 2020, Lin et al., 2020,
Cao et al., 2021] introduce approaches that leverage BERT [Devlin et al.,
2018], a pre-trained language model (PLM), in the text-to-SQL task, since PLMs
with a deep contextualized word representation have led noticeable
improvements in many NLP challenges. Word contextualization has contributed to
improving accuracy for the generation of logical forms, but there still
remains difficulties to generate logical forms obeying decoding constraints.
There is also a limitation that the text-to-SQL approaches require table data
to be stored in a database. Many recent studies have shown that supervised
question answering models successfully reason over tables without generating
SQL. TAPAS [Herzig et al., 2020] is a new approach to pre-training a language
model that extends BERT by inserting additional embeddings to better
understand tabular structure. Similarly, TURL [Deng et al., 2020] implements
structure-aware Transformer encoder to learn deep contextualised
representations for relational table understanding. Masked Entity Recovery as
a novel pre-training objective is proposed to capture complex semantics
knowledge about entities in relational tables. TABERT [Yin et al., 2020] and
TABFACT [Chen et al., 2019] also use BERT architecture to jointly understand
contextualised representations for textual and tabular data. Unlike other
approaches, TABERT encodes a subset of table content that is most relevant to
a question in order to deal with large tables. In this study, we propose a
BERT-based approach to learn deep contextualised representations of table
structural information via conversion of table formats for the task of table
question answering.

## 3\. Korean Table Question Answering Dataset

In this study, we pre-train a language model with structured data extracted
from Korean Wikipedia for the task of question answering over table, since
pre-training models have shown significant improvements in many natural
language understanding tasks. For pre-training input data, we generate
KorWikiTabular containing pairs of structured tabular data and related texts
to the tables. We also create KorWikiTQ, a corpus of question-answer pairs
with tables in which the answers are contained for the table question
answering task.

### 3.1. Tabular Dataset for Pre-training

We collect about 1.4M tables (T) from the Korean Wikipedia dump in order to
pre-train a Transformer-based language model for tabular contextualised
embeddings. Since we hypothesis that descriptions (D) in the article of
wikipedia that contains a table benefit building improved representations of
the table for question answering, pairs of tables and their description texts
are extracted from Wikipedia. As pre-training inputs for tabular
contextualization, we extract Infobox which is formatted as a table on the top
right-hand corner of Wikipedia documents to summarise the information of an
article on Wikipedia, and WikiTable as shown in Figure 1. As description texts
for a table, an article title, the first paragraph in the article, table
captions if exist, heading and sub-heading titles for the article are
considered as the pre-training dataset. That is, D = {d1,d2, …, dn}.

Figure 1: Example of Infobox and WikiTable in a Wikipedia document

For pre-training a language model, we generate input sequences by converting
the extracted infoboxes and wikitables into sentence string texts. Figure 2
explains how a table format is converted into sentence strings when the table
is a relational table that contains columns (Tc) or fields describing rows
(Tr) of data. Each table is formed in two-dimensional tabular data consisting
of columns and rows, denoted as T = {t(c1,r1),t(c2,r1),t(cn,r1) …,
t(c1,rm),t(c2,rm),t(cn,rm)} when n and m are sizes of column and row
respectively. Table column headers are identified with rows and cells, and
then the columns are concatenated with corresponding cells with predefined
special characters, which allows the model to learn structural relations
between cells of columns and table headers.

Figure 2: Converting WikiTable format into string sequences for pre-training
input. The converted table strings are added with descriptions for the
Wikipedia article.

For Infobox, the table headers mainly located in the first column are also
recognised using the $<$th$>$ tags, then they are converted into the string
sequences associated with relevant cells like wikitables.

### 3.2. Crowdsourcing for Table Question Answering Corpus

Figure 3: Examples of a natural language question set related to a table for
football match-results in UEFA Euro 2004 according to question levels

Unfortunately, there do not exist datasets written in Korean aiming for the
table question-answering task publicly available. Even though KorQuAD 2.0 [Lim
et al., 2019] contains some questions that their answers are related to
tables, they are insufficient to train models for the task.

For conducting the downstream task of question answering over tables, we
create a large dataset consisting of 70k pairs of questions and answers by
hiring paid, crowdsourced workers. We select about 20k tables that contain
rows greater than 5 and less than 15 for this crowdsourcing task. Larger
tables including columns greater than 10 are ignored, since the length of the
converted sentence strings from a table may exceed the maximum sequence length
of 512 tokens. This is because column headers are repeatedly inserted into the
strings as the number of table headers increases.

We define the five-question variations by extending to the previous work [Park
et al., 2020], considering question difficulties that our model can predict
answers as follows:

  * •

Level1: Question [column$-$others] where [column$-$base] has [value]

  * •

Level2: Question [column$-$others] where [column$-$base] has [condition]

  * •

Level3: Question [column$-$base] where [column$-$others] has [value]

  * •

Level4: Variation of the questions in other levels

  * •

Level5: Question min or max in [column$-$base] where [column$-$others] has
[value of numbers, dates, ranks, etc.]

Figure 3 describes question types generated regarding the question
difficulties. Our crowd-sourced workers generate the five types of natural
language questions for a given table. As shown in Figure 3, an example
question of Level1 is KR: UEFA 유로 2004 A조에서 포르투갈팀의 승점은 몇 점인가? (EN: how many
points did Portugal obtain in UEFA Euro 2004 Group A?): querying values of
other columns such as Points (Pts) when the value of the base column Team is
Portugal. In this case, we intend an answer value to be located on the right
of the base column. For Level3, on the contrary, an answer is located in the
left column from the base column as shown in the example, KR: UEFA 유로 2004
A조에서 승점이 6점인 팀은 어디인가? (EN: which team obtained 6 points in UEFA Euro 2004
Group A?). We include these various types of questions for improvement of
model performance since our model tends to produce a lower performance on the
type of Level3 question than Level1. A variety of sentence expressions such as
honorific, informal, colloquial, and written formats are used in the Korean
language. To enhance the robustness of our model to various types of natural
language questions, we incorporate sentence variations of the questions in the
other levels by changing adverbs or prepositions, replacing them with
synonyms, inverting word orders, or converting sentences into honorific
expressions, formal and informal languages. Numeric data such as numbers,
ranks, money, or dates are stored in tables. For these tables, we generate
questions related to operations (minimum, maximum, count, or average) for
columns, for example, KR: 승점이 가장 낮은팀은 어디? (EN: Which team has the lowest
points in UEFA Euro 2004 Group A?).

The Korean table question-answering dataset consists of table contexts (C) in
the form of two-dimensional lists, natural language questions (Q), and answers
(A), along with URLs (U) and titles (T) of Wikipedia documents where tables
are contained. This dataset is provided in the JSON format.

## 4\. Modeling of Table Question Answering

In this study, we pre-train a language model with the converted tabular
dataset described in Section 3.1 for a better understanding of structural
information and as well syntactic and lexical information considering the
downstream task of table question-answering. We also fine-tune the model using
the table question answering corpus. We evaluate our model, and the fine-
tuning results in the task of question-answering over tables are described in
detail.

### 4.1. Pre-training Language Model

We use the Transformer [Vaswani et al., 2017] approach for pre-training a
language model. In specific, we follow the original architecture of BERT
[Devlin et al., 2018] which is a transformer-based pre-trained language model,
which learns context in text using masked language modeling (MLM) and the next
sentence prediction (NSP) objectives for self-supervised pre-training.
BERTBase model is adopted in our experiments, and we use the same percentage
of 15% for masking table cells or text segments for the MLM training, but the
NSP objective is not used. We build a new vocabulary of 119,547 Korean word-
pieces. We generate input sequences with the special tokens [CLS] and [SEP],
and description texts including relevant sentences such as the article title
and heading titles are inserted between them. Tabular data converted to string
sequences is followed by the [SEP] token. During a pre-training procedure, our
model learns contextual representations jointly from unstructured natural
language sentences and structured tabular data. Details of hyperparameters
that we used for pre-training KO-TaBERT are summarised in Appendix A.

### 4.2. Fine-tuning Model

For fine-tuning of the table question-answering task, we prepare datasets from
different sources: the table question-answering dataset created by crowd-
sourced workers described in 3.2, and about 2k pairs of questions and answers
related to tables selected from KorQuAD 2.0 corpus. We split the selected
KorQuAD 2.0 corpus and the crowdsourced dataset with a 20% ratio respectively
as the test dataset for evaluation. The rest of the data is used for fine-
tuning training. We train a question-answering model on the dataset. Similar
to SQuAD which is a major extractive question-answering benchmark [Rajpurkar
et al., 2016, Rajpurkar et al., 2018], the fine-tuning model aims to predict
the correct span of an answer defined as a start and end boundaries for a
given question. We describe the experimental details for the downstream task
in Appendix B.

### 4.3. Evaluation and Results

We evaluate our model on the test dataset consisting of the subsets from the
KorQuAD 2.0 and the crowdsourced table question-answering datasets, which are
not used during the training of the model. As for evaluation metrics, Exact
Match (EM) scores if each character of a predicted answer is exactly the same
as the ground truth and F1-score (F1) that calculates token overlaps between a
predicted answer and the ground-truth as F1 are used in our experiments.

Dataset source |  | EM |  | F1
---|---|---|---|---
KorQuAD 2.0 |  | 64.5 |  | 74.5
Crowd-sourced |  | 83.9 |  | 87.2
Overall |  | 82.8 |  | 86.5
Table 1:  Performance with EM and F1 scores according to the data sources of
the test dataset for the task of table question answering.

The performance of the table question-answering model is summarised in Table
1. Our model achieves EM 82.8% and F1 86.5% overall. We compare the
performance of different data sources in the test dataset. We observe that our
model performs better in the crowdsourced dataset than in the KorQuAD 2.0
corpus. With detailed error analysis, we find that there are a few parsing
errors and table format conversion errors.

Question difficulty |  | EM |  | F1
---|---|---|---|---
Level1 |  | 89.6 |  | 93.1
Level2 |  | 89.1 |  | 92.3
Level3 |  | 86.1 |  | 89.4
Level4 |  | 81.7 |  | 85.5
Level5 |  | 67.8 |  | 70.6
Overall |  | 83.9 |  | 87.2
Table 2:  Comparison of model performance according to each level of questions
in the crowdsourced dataset.

The test dataset consists of questions with their difficulties generated by
crowdsourced workers as described in Section 3.2. The performance according to
the levels of questions is described in Table 2. The results show that the
performance decreases as the difficulty of questions increases. In particular,
the table question-answering model performs poorly on the Level5 questions
that require comprehensive machine understanding capabilities such as ordering
and counting table cell values, and operations such as minimum, maximum or
average in a table column.

Figure 4: Example of the new conversion approach for complicated structured
tables that consisting of merged and multi column headers into sentence
strings.

We conduct additional experiments with the new approach of table format
conversion by mapping the cell values in the first column (called row header)
into the first column header. As illustrated in Figure 4, column 1 accompanied
by the value of cell 1 is added to table cell values in the same row. This
aims to apply important information in a table to the converted sentence
strings by considering table structural characteristics. We also take account
of tables informed of complicated structures. For converting those tables into
sentence strings, we classify tables into single, multi, and merged column
headings using $<$th$>$ tags. Then, column headers are concatenated if table
columns have multi headers as shown in the example of Figure 4. In this
conversion approach, the length of converted sentence strings increases since
the headers are repeatedly inserted. Thus, we limit the word length of a
converted sentence string from 250 to 300 tokens for pre-training input.

Dataset source |  | Format |  | EM |  | F1
---|---|---|---|---|---|---
KorQuAD 2.0 |  | v1 |  | 64.5 |  | 74.5
KorQuAD 2.0 |  | v2 |  | 69.1 |  | 78.4
Crowd-sourced |  | v1 |  | 83.9 |  | 87.2
Crowd-sourced |  | v2 |  | 87.2 |  | 91.2
Table 3:  Comparison of model performance with different table parsing
approaches. Format v1 is the table conversion described in Figure 2.

We compare the performance of models pre-trained with different table
conversion formats in Table 3. Using the new format of table conversion
considering structural complexity improves the performance of models on the
table question answering task. The results indicate that the new table
conversion format can effectively apply table structural features.

## 5\. Conclusions

In this paper, we introduce two new Korean-specific datasets, KorWikiTabular
and KorWikiTQ for the task of table question-answering in the Korean language,
and present KO-TaBERT, a pre-trained language model for the task. In
particular, we demonstrate how tabular data is converted into linearlised
texts containing structural information and properties. We construct a tabular
dataset by extracting tables and converting them into sentence strings with
tabular structural information for pre-training a language model. We also
create a table question answering corpus with paid crowdsourced workers. The
corpus consists of 70k pairs of questions and answers related to tables on
Wikipedia articles, and those questions are generated specifically considering
levels of question difficulty. We conduct experiments on the table question
answering task. Our model achieves the best performance when converted table
sentence strings include richly structural features. In future work, we aim to
extend the model for complex question answering over texts and tables with the
generation of multimodal questions to jointly handle question answering from
textual and tabular sources. We hope that our datasets will help further
studies for question answering over tables, and for the transformation of
table formats.

## 6\. References

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## Appendices

### A. Pre-training Details

Table 4 summarises hyperparameters that we use for pre-training KO-TaBERT. We
use the maximum sequence length of 512, and the Adam optimization with the
learning rate of 1e-4 is set for the model. Our model is trained on 64 TPU v3
for 1M steps with the batch size of 1024, and it takes about 5 days.

Hyper-parameters | KO-TaBERT
---|---
Number of layers | 12
Hidden size | 768
FFN inner hidden size | 3072
Attention heads | 12
Attention head size | 64
Dropout | 0.1
Warmup steps | 10k
Learning rates | 1e-4
Batch size | 1024
Weight decay | 0.01
Max steps | 1M
Learning rate decay | Linear
Adam $\varepsilon$ | 1e-6
Adam $\beta_{1}$ | 0.9
Adam $\beta_{2}$ | 0.999
Number of TPU | 64
Training time | 5 days
Table 4:  Hyperparameters for pre-training KO-TaBERT.

### B. Fine-tuning Experiment

We describe the fine-tuning results of our model KO-TaBERT transferred to the
task of question answering over tables in Section 4.3. For the experiments, we
use the maximum sequence length of 512 and the Adam optimization with the
learning rate of 5e-5. Our model is fine-tuned on 8 TPU v3 with a batch size
of 32 and 3 epochs. Other hyperparameters are the same as the ones used for
pre-training.