# Spectro-polarimetric study to constrain accretion-ejection properties of
MCG-5-23-16 using IXPE and NuSTAR observations

Santanu Mondal  Indian Institute of Astrophysics, II Block, Koramangala,
Bengaluru 560034, India  [ Rwitika Chatterjee  Space Astronomy Group, ISITE
Campus, U. R. Rao Satellite Center, ISRO, Bengaluru, 560037, India  Vivek K.
Agrawal  Space Astronomy Group, ISITE Campus, U. R. Rao Satellite Center,
ISRO, Bengaluru, 560037, India  Anuj Nandi  Space Astronomy Group, ISITE
Campus, U. R. Rao Satellite Center, ISRO, Bengaluru, 560037, India

###### Abstract

We conducted a study on the X-ray polarization properties of MGC-5-23-16 by
analyzing long-term monitoring data from NuSTAR jointly with IXPE observations
in May and November 2022. The re-analysis of IXPE data gives model-dependent
polarization degree, PD (%) = $1.55\pm 0.99$ and $1.31\pm 0.95$ in the energy
band $2-8$ keV, agrees with previous studies within error bars. The model-
independent analysis of PD poses an upper limit of $\leq 3.8$ ($1\sigma$
level) for the same energy band. The observed upper limit of PD, along with
broadband spectral analysis ($3-79$ keV), allowed us to derive corona geometry
(i.e. length and height) and the accretion disk inclination ($\sim
33^{\circ}$). Additional NuSTAR observations were also analyzed to gain
insights into the accretion flow properties of the source and to estimate the
expected polarization during those epochs with PD $\sim 4.3\%$. The radius and
height of the corona exhibited to vary between $28.2\pm 3.1-39.8\pm 4.6$ rs
and $14.3\pm 1.7-21.4\pm 1.9$ rs, with a mass outflow rate from the corona
measuring $0.14\pm 0.03-0.2\pm 0.03$ Eddington rate ($\dot{M}_{\rm Edd}$). The
estimated PD values were nearly constant up to a certain radial distance and
height of the corona and then decreased for increasing corona geometry. The
spectral analysis further provided an estimate for the mass of the central
black hole $\sim 2\times 10^{7}$ M⊙ and the velocity of the outflowing gas
$\sim 0.16-0.19c$. Our modeling of the disk-corona-outflows and polarization
connection can be extended and validated with data from recently launched
India’s first X-ray Polarimeter Satellite, offering potential applications to
other sources.

###### keywords:

keyword entry 1, keyword entry 2, keyword entry 3

###### keywords:

accretion disk, galaxies:active, galaxies: Seyfert, polarization, X-rays:
individual: MCG-5-23-16

S<EMAIL_ADDRESS><EMAIL_ADDRESS>
##  1 Introduction

A recent launch of the Imaging X-ray Polarimetry Explorer
(WeisskopfEtal2016SPIE.9905E..17W, 50, IXPE;) and X-ray Polarimeter Satellite
(XPoSat)11endnote: 1https://www.isro.gov.in/XPoSat_X-
Ray_Polarimetry_Mission.html Missions have renewed interest in measuring X-ray
polarization from diverse astrophysical systems, in particular from accreting
black hole (BH) systems of all scales. Accreting matter puffs up at the inner
region of the disk, which not only upscatters soft photons through inverse
Comptonization SunyaevTitar80 (42, 19, 9, 16, 33, 23) but also polarizes the
radiation depending on its thermodynamic properties, geometry, and inclination
ConnorsEtal1980ApJ…235..224C (12, 43). Therefore, the measurement of
polarization angle (PA) and degree (PD) depends on both corona (Compton cloud)
properties as well as the photon energy. Additionally, the presence of
outflows from the disk can also produce significant polarization due to
scattering effects BegelmaMcKee1983ApJ…271…89B (6). The dependence of PD and
PA on the optical depth and disk inclination was studied using different
geometry of the corona in detail DovciakEtal2008MNRAS.391…32D (17, 28, 40).
Therefore, if the corona properties of a system is well constrained, the PD
can be estimated or the vice-versa. Hence, the spectro-polarimetric studies
using broadband data may shed more light on the measurement of polarization
and the environment of the corona around BHs.

MCG-5-23-16 is a Seyfert 1.9 galaxy Veronetal1980 (46) located at redshift z =
0.00849 WegnerEtal2003AJ….126.2268W (49). The source is relatively bright in
X-rays with F2-10 = $7-10\times 10^{-11}$ erg cm-2 s-1
MattsonWeaver2004ApJ…601..771M (31) and characterized by moderate neutral
absorption ($N_{H}\sim 10^{22}$ cm-2). It has been extensively studied in the
X-ray band to estimate corona properties and spectral high-energy cut-off
using INTEGRAL and NuSTAR observations BeckmannEtal2008A&A…492…93B (5, 32, 4,
52).

Furthermore, the X-ray spectrum of this source showed the presence of a soft
excess and complex Fe K$\alpha$ emission with a broad and asymmetric narrow
line features in ASCA WeaverEtal1997ApJ…474..675W (48), BeppoSAX, Chandra, and
XMM-Newton DewanganEtal2003ApJ…592…52D (14, 3, 8, 29) observations. It
indicates the presence of two reflectors, one for a narrow core at 6.4 keV and
the other for the broad wing, possibly originating closer to the BH. Later,
the broad line was explored with Suzaku ReevesEtal2007PASJ…59S.301R (39) and
reported that the inner radius of the disk is 20 rs that originated the line,
where rs = $2GM_{BH}/c^{2}$ is the Schwarzschild radius, with an inclination
of 50∘. Additionally, an absorption feature at 7.7 keV was unveiled in these
data, pointing to the possible presence of ionized iron outflowing at $\sim
0.1c$. Recently, SerafinelliEatal2023MNRAS.526.3540S (41) estimated the disk
inclination of 41∘ from the broad iron line study using NuSTAR observations.
MarinucciEtal2022MNRAS.516.5907M (30) estimated the disk inclination
$48^{+12^{\circ}}_{-8}$ from broad Fe K$\alpha$ line profile. Therefore, the
estimation of disk inclination angle is not well settled yet. The mass of the
central supermassive BH (SMBH) is $2\times 10^{7}$ M⊙ derived independently
from both X-ray variability PontiEtal2012A&A…542A..83P (38) and infrared lines
Onorietal2017 (36). The spin parameter is $0.856$ YuEetal2017arXiv170307182W
(47) estimated using broadband X-ray data and reflection model.

Along with spectral and timing studies, X-ray polarization provides an
independent tool to constrain the accretion properties and coronal geometry.
It has been reported that the polarization is extremely sensitive to the
geometry of the radiation emitting region and the photon field
SchnittmanKrolik2010ApJ…712..908S (40, 7, 45). To constrain the source coronal
geometry, MCG-5-23-16 was targeted by two pointings in 2022 with IXPE.

The joint analysis of XMM-Newton, NuSTAR, and IXPE observations in May 2022 by
MarinucciEtal2022MNRAS.516.5907M (30) obtained a 4.7% (at 99% confidence
level) upper limit for the polarization degree (PD) in the 2–8 keV energy band
and ruled out the slab geometry of the corona. Later,
TagliacozzoEtal2023MNRAS.525.4735T (44) analyzed the IXPE data from both May
and November 2022 epochs in coordination with NuSTAR and estimated the PD to
be 3.2 % (at 99% confidence level). The authors further compared their
observed estimations with Monte Carlo simulations of the expected polarization
properties for different geometries of the corona.

Therefore, we see that polarization can be used as a probe to understand the
geometry of the corona and accretion-ejection behavior around the central
SMBH. The PD and PA have been measured for the source MCG-5-23-16 using
radiative transfer-based models only. However, to date, no physically
motivated accretion-ejection based models have been directly employed to fit
and understand the polarization properties with the corona geometry or
accretion flow parameters. In this work, we have re-analyzed the IXPE
observations to confirm the previous studies jointly with NuSTAR data for both
epochs (May and November 2022). Further, other data sets available in the
NuSTAR archive also analyzed to constrain the corona properties and to predict
the polarization behavior. Moreover, we have also estimated the mass outflow
rate for all epochs, that connect the disk-corona-outflow geometry with
polarization from a single framework.

The paper is organized as follows: in §2 we discuss the observation and data
reduction procedure. In §3, we describe the spectro-polarimetric data analysis
results, and finally, we draw our conclusions in §4.

##  2 Observation and Data Reduction

Over the past decade, MCG-5-23-16 was observed by NuSTAR Harrisonetal2013
(20), spanning from 2012 to 2022. Most recently, the source was observed in
May and November 2022 by IXPE WeisskopfEtal2016SPIE.9905E..17W (50), launched
on 2021 December 9, consisting of three Wolter-I telescopes, with 3 units of
polarization-sensitive imaging X-ray detector units (DUs) at the respective
foci. We used all archival data from both observatories for this source and
analyzed them. The observation log is given in Table 1.

IXPE provides Level-2 data, which we cleaned and calibrated using standard
FTOOLS tasks with the latest calibration files (CALDB 20230526) available in
IXPE database. A circular region centered at the source of radius
$60^{\prime\prime}$ (TagliacozzoEtal2023MNRAS.525.4735T, 44, see) is used for
all detectors. A source-free background region of radius $100^{\prime\prime}$
is used to produce background subtracted spectra for I, Q, and U Stokes for
all three DUs. Additionally, we applied a weighting scheme, STOKES=NEFF
DiMarcoEtal2022AJ….163..170D (15) in XSELECT to generate the final Stokes
spectra in the $2-8$ keV energy band.

The NuSTAR data were extracted using the standard NUSTARDAS v1.3.1 22endnote:
2https://heasarc.gsfc.nasa.gov/docs/nustar/analysis/ software. We ran a
nupipeline task to produce cleaned event lists and nuproducts along with CALDB
version 20231121 to generate the spectra. We used a region of
$25^{\prime\prime}$ for the source and $40^{\prime\prime}$ for the background
using ds9 JoyeDS92003ASPC..295..489J (25). The data were grouped with a
minimum of 30 counts in each bin using grppha command. For the analysis of
each epoch of observation, we used the data of both IXPE and NuSTAR in the
energy range of $2-8$ keV and $3-79$ keV. We used XSPEC33endnote:
3https://heasarc.gsfc.nasa.gov/xanadu/xspec/ Arnaud1996 (1) version 12.12.0
for spectral analysis.

Table 1:  Log of observations of MCG-5-23-16. The ∗ denotes data used for joint spectro-polarimetric analysis. Obs. Id. | Exp. | Epoch | Start | End
---|---|---|---|---
| (ks) |  | Date | Date
|  | IXPE |  |
01003399 | 436 | I1 | 2022-05-14 | 2022-05-31
02003299 | 160 | I2 | 2022-11-06 | 2022-11-23
|  | NuSTAR |  |
60701014002∗ | 84 | N1 | 2022-05-21 | 2022-05-23
90801630002∗ | 86 | N2 | 2022-11-11 | 2022-11-12
60001046008 | 221 | N3 | 2015-03-13 | 2015-03-18
60001046006 | 98 | N4 | 2015-02-21 | 2015-02-23
60001046004 | 210 | N5 | 2015-02-15 | 2015-02-20
60001046002 | 160 | N6 | 2013-06-03 | 2013-06-07
10002019001 | 34 | N7 | 2012-07-11 | 2012-07-11

##  3 Data Analysis and Results

###  3.1 Model-independent IXPE Analysis

The processed Level-2 data were used for polarimetric analysis, using
IXPEOBSSIM software v30.0.0 BaldiniEtal2022SoftX..1901194B (2). Source and
background events were extracted using XPSELECT task. We obtained the
polarization parameters in the entire IXPE band of $2-8$ keV using the model-
independent PCUBE algorithm of the XPBIN task KislatEtal2015APh….68…45K (27).
To investigate any possible energy dependence of these parameters, we also
binned the $2-8$ keV data into three equal energy bands of 2 keV each and
extracted the polarization parameters (refer 2023MNRAS.521L..74C (11, 24) for
more details).

Table 2:  Results of model-independent polarimetric analysis Parameter | 2-4 keV | 4-6 keV | 6-8 keV |  $2-8$ keV
---|---|---|---|---
| Epoch I1
Q/I (%) | $0.44\pm 1.22$ | $-0.28\pm 1.87$ | $0.60\pm 3.70$ | $0.27\pm 1.26$
U/I (%) | $2.00\pm 1.22$ | $2.54\pm 1.87$ | $-2.20\pm 3.70$ | $1.33\pm 1.26$
PD (%) | $2.05\pm 1.22$ | $2.55\pm 1.87$ | $2.28\pm 3.70$ | $1.36\pm 1.26$
MDP99 (%) | 3.70 | 5.67 | 11.21 | 3.83
| Epoch I2
Q/I (%) | $-1.55\pm 1.12$ | $-0.57\pm 1.85$ | $6.25\pm 4.00$ | $-0.15\pm 1.16$
U/I (%) | $1.08\pm 1.12$ | $-0.96\pm 1.85$ | $4.96\pm 4.00$ | $1.10\pm 1.16$
PD (%) | $1.89\pm 1.12$ | $1.12\pm 1.85$ | $7.98\pm 4.00$ | $1.11\pm 1.16$
MDP99 (%) | 3.39 | 5.62 | 12.15 | 3.50

Figure 1: XSPEC (solid lines) and PCUBE (dashed lines) contour plots between
polarization degree PD and angle PA for May (I1; left) and November (I2;
right) epochs in 2022. The blue, red, and green contours denote $1\sigma$,
$2\sigma$, and $3\sigma$ confidence levels. See the text for details.

The results of our model-independent polarimetric analysis for the two epochs
are summarized in Table 2. The energy-dependent analysis as well as
measurement over the entire energy band yield only upper limits on the PD
(below the minimum detectable polarization at the 99% level), and hence the PA
is not quoted. The measured PD and PA in $2-8$ keV for the two epochs (I1 and
I2) are shown in Fig. 1 along with the contours. The dashed lines correspond
to PCUBE contours with 1$\sigma$ (blue), 2$\sigma$ (red), 3$\sigma$ (green)
levels. As it can be observed, the polarization measurements are constrained
just at the $1\sigma$ level, although lower than the MDP99 in every energy
bin. This also gives the PD upper limit (99% confidence level) of $<3.8\%$ in
epoch I1 and $<3.5$% in epoch I2. It has been mentioned in
TagliacozzoEtal2023MNRAS.525.4735T (44) that the model-dependent contours
match with PCUBE contours, however, for I2, we obtained a small difference,
the possible reason for that is not clear yet. In the next section, we discuss
the model-dependent polarization study.

###  3.2 Model-dependent IXPE Analysis

We further analyzed all Stokes spectra for both epochs using a preliminary
model, consisting of absorbed CUTOFFPL convolved with a constant polarization
POLCONST which reads in XSPEC as CONST*TBABS*POLCONST*CUTOFFPL. All Stokes
spectra for all three DUs in the energy band $2-8$ keV are fitted
simultaneously. The abundance in TBABS model is set to wilm Wilmsetal2000 (51)
throughout the analysis.

We have started the fitting by leaving all the spectral and polarimetric
parameters to vary freely. We found that the obtained values of PD and PA are
highly sensitive to the values of the spectral parameters. Keeping in mind the
limited energy band and the spectral sensitivity of IXPE, we turned to
simultaneous NuSTAR observations for obtaining robust spectral fits. Moreover,
NuSTAR data showed a Fe K line and a small reflection hump, which have also
been taken into account during fitting of spectral data.

The above phenomenological CUTOFFPL model fits to the NuSTAR data returned two
spectral parameters, cutoff energy (Ecut) and photon index ($\Gamma$).
Subsequently, we re-did the IXPE fits by freezing the values of Ecut and
$\Gamma$ to the best-fit values from NuSTAR. Note that the addition of a
Gaussian line and reflection component neither improves the quality of the fit
nor affects the value of the polarisation parameters, hence we did not include
these two components while fitting the IXPE data. Therefore, it gives a robust
estimation of PA and PD. We obtain an acceptable fit for I1 and a good fit for
I2 using this model. We determine the PA = $37.3^{\circ}\pm 20.1^{\circ}$ and
$73.2^{\circ}\pm 23.1^{\circ}$ for the epochs I1 and I2, and the PD (%) =
$1.55\pm 0.99$ and $1.31\pm 0.95$. The confidence contours from the model-
dependent analysis are shown in Fig. 1. The solid blue, red, and green
contours correspond to 1$\sigma$, 2$\sigma$, and 3$\sigma$ levels
respectively. The model-dependent polarimetric results are summarized in Table
3.

Table 3:  All Stokes spectra for all three DUs of IXPE are fitted using TBABS*POLCONST*CUTOFFPL model. The best-fitted parameters of the model-dependent polarimetric analysis are summarized here. All errors are estimated at the $1\sigma$ level. Parameters | I1 | I2
---|---|---
$N_{H}$ ($10^{22}$cm-2) | $3.08\pm 0.03$ | $1.35\pm 0.02$
PD (%) | $1.55\pm 0.99$ | $1.31\pm 0.95$
PA (∘) | $37.3\pm 20.1$ | $73.2\pm 23.1$
$\Gamma$ | $1.66$ | $1.64$
$E_{\rm cut}$ (keV) | $122.2$ | $124.2$
$\chi^{2}/dof$ | 1989/1335 | 1305/1335

###  3.3 IXPE and NuSTAR Analysis

We performed a broadband spectroscopic analysis combining the $2-8$ keV IXPE
spectra and the $3-79$ keV NuSTAR spectra from May and November 2022.
Additionally, we have analyzed all the NuSTAR archival data for the source
MCG-5-23-16 covering a decade of observations (see Table 1) to understand the
variation of accretion parameters and predict the polarization degree from the
model-fitted parameters. The broadband energy range ($2-79$ keV) covered by
the spectra of MCG-5-23-16 showed a broad Fe K$\alpha$ line and a Compton hump
above 10 keV. A Gaussian component is used at $\sim 6.3$ keV for the Fe
K$\alpha$ line for all observations. Each epoch of observation was first
fitted using a simple power-law model, which returned a moderate fit with
$\chi_{r}^{2}\sim 1.29$ (I1+N1) and 1.17 (I2+N2) for the power-law photon
index $\Gamma\sim 1.8\pm 0.01$, this is because the model does not take into
account the Compton hump above 10 keV. However, it indicates the presence of
another component that is contributing to the excess emission, which can
either be reflection Done2007 (16) or the signature of mass loss from the
corona region. Therefore, we further fit the data using an accretion-disk
based two-component advective flow (ChakrabartiTitarchuk1995, 9, TCAF,) model,
including a jet component (MondalChakrabarti2021, 34, JeTCAF,) to understand
the accretion-ejection and polarization behavior of the source. The JeTCAF
model takes into account the radiation mechanisms at the base of the jet and
the bulk motion effect by the outflowing jet on the emitted spectra in
addition to the Compton scattering of soft disk photons by the hot electron
cloud inside the corona. The JeTCAF model has six parameters, namely (i) the
mass of the BH ($M_{\rm BH}$) if it is unknown, (ii) the Keplerian disk
accretion rate ($\dot{m}_{\rm d}$), (iii) the sub-Keplerian halo accretion
rate ($\dot{m}_{\rm h}$), (iv) the size of the dynamic corona or the location
of the shock ($X_{\rm s}$ in $r_{g}=2GM_{\rm BH}/c^{2}$ unit), (v) the shock
compression ratio ($R$), and (vi) the outflow/jet collimation factor ($f_{\rm
col}$), the ratio of the solid angle subtended by the outflow to the inflow
($\Theta_{o}/\Theta_{\rm in}$). The hydrogen column density for Galactic
absorption set fixed to $7.8\times 10^{20}$cm-2 HI4PICollabor2016A&A…594A.116H
(21, 26) during the fitting. For the host galaxy absorption, we used the
ZTBABS model with wilm abundance. The full model reads in XSPEC for IXPE and
NuSTAR as TBABS*ZTBABS(JeTCAF+GAUSS).

Figure 2: Joint spectral modelling of IXPE and NuSTAR data fitted using JeTCAF
model in the energy band $2-79$ keV. The left and right panels are for the
epochs (I1+N1) and (I2+N2). The Fe K$\alpha$ line $\sim 6.3$ is fitted using
GAUSS model as shown by dashed lines. The black, red, and green points
correspond to IXPE data for all three DUs and the blue points correspond to
NuSTAR data. See the text for details.

In Fig. 2, we show the model-fitted spectra of MCG-5-23-16 for the joint IXPE
and NuSTAR observations. The Fe K$\alpha$ line fitted well with a Gaussian
line width of $\sim 0.3$ keV for all observations and the Compton hump fitted
with JeTCAF model that takes it into account by the scattering of corona
photons by the diverging outflow. The disk mass accretion rate in JeTCAF model
varied minimally, whereas the halo accretion rate was nearly constant $\sim
0.4$ $\dot{M}_{\rm Edd}$ and the size of the corona changed significantly from
$\sim 28$ to $40r_{s}$. As the mass of the BH is a parameter in this model,
one can also estimate the BH mass. The model fit to all the epochs gives
nearly a constant mass of the central SMBH $\sim 2\times 10^{7}$ M⊙,
consistent with previous estimations in the literature. For the joint epochs
data (I1+N1 and I2+N2) fits, the $N_{H}$ for the host galaxy absorption
required in ZTBABS model is $2.0-2.2\times 10^{22}$ cm-2, while earlier NuSTAR
epochs (N3-N7) required $N_{H}\sim 1.2-1.5\times 10^{22}$ cm-2. The high value
of the $f_{\rm col}$ parameter implies that the outflow is not well collimated
and the rate is high. The estimated outflow solid angle is $\sim 0.5\pi$. All
model parameters are summarized in Table 4.

Table 4: Joint IXPE and NuSTAR data fitted model parameters are provided in this table. Here, $M_{\rm BH}$, $\dot{m}_{d}$, $\dot{m}_{h}$, $X_{s}$, $R$, and $f_{\rm col}$ are the mass of the BH, disk and halo mass accretion rates, location of the shock or size of the corona, the shock compression ratio, and the outflow collimation factor respectively in JeTCAF model. NH is the hydrogen column density in ZTBABS model. All data sets required GAUSS model for the Fe K$\alpha$ line $\sim 6.3$ keV of width $\sigma_{g}$ given in the table. Model | JeTCAF | ZTBABS | GAUSS |
---|---|---|---|---
Epoch | $M_{\rm BH}$ | $\dot{m}_{\rm d}$ | $\dot{m}_{\rm h}$ | $X_{\rm s}$ | R | $f_{\rm col}$ | $N_{H}$ | $\sigma_{g}$ | $\chi_{\rm r}^{2}/dof$
| $(10^{7}M_{\odot})$ | $(10^{-2}\dot{M}_{\rm Edd})$ | $(\dot{M}_{\rm Edd})$ | $(r_{\rm s})$ |  |  |  $(10^{22}$ cm${}^{-2})$ | (keV) |
I1+N1 | $2.0\pm 0.3$ | $1.3\pm 0.2$ | $0.41\pm 0.03$ | $38.3\pm 4.4$ | $4.91\pm 0.51$ | $0.53\pm 0.07$ | $2.21\pm 0.25$ | $0.30\pm 0.03$ | 1329/1180
I2+N2 | $2.1\pm 0.2$ | $0.9\pm 0.1$ | $0.40\pm 0.03$ | $39.4\pm 3.4$ | $4.36\pm 0.23$ | $0.49\pm 0.04$ | $2.04\pm 0.39$ | $0.31\pm 0.04$ | 1268/1166
N3 | $2.1\pm 0.2$ | $1.2\pm 0.2$ | $0.40\pm 0.02$ | $28.2\pm 3.1$ | $5.24\pm 0.38$ | $0.45\pm 0.04$ | $1.37\pm 0.11$ | $0.27\pm 0.02$ | 1102/989
N4 | $1.9\pm 0.2$ | $1.3\pm 0.1$ | $0.41\pm 0.03$ | $34.9\pm 3.9$ | $5.19\pm 0.32$ | $0.49\pm 0.05$ | $1.22\pm 0.09$ | $0.31\pm 0.03$ | 864/768
N5 | $2.0\pm 0.1$ | $1.3\pm 0.1$ | $0.41\pm 0.02$ | $29.9\pm 2.1$ | $5.28\pm 0.42$ | $0.47\pm 0.03$ | $1.49\pm 0.15$ | $0.31\pm 0.02$ | 1029/928
N6 | $2.1\pm 0.1$ | $1.1\pm 0.1$ | $0.41\pm 0.04$ | $39.8\pm 4.6$ | $4.98\pm 0.37$ | $0.54\pm 0.03$ | $1.27\pm 0.07$ | $0.35\pm 0.03$ | 983/930
N7 | $2.0\pm 0.1$ | $1.3\pm 0.1$ | $0.42\pm 0.02$ | $37.9\pm 2.8$ | $5.06\pm 0.30$ | $0.53\pm 0.04$ | $1.14\pm 0.15$ | $0.27\pm 0.02$ | 609/570

From the JeTCAF model fitted parameters, we have estimated different physical
quantities to understand the variation of polarization with corona geometry
and spectral flux. The height of the corona is basically the height of the
shock, as the shock is the boundary layer of the corona. The height of the
shock ($h_{\rm shk}$) is estimated using Debnathetal2014 (13), $h_{\rm
shk}=[\gamma(R-1)X_{s}^{2}/R^{2}]^{1/2},$ where, $\gamma$ is the adiabatic
index of the flow, which is considered here as 5/3. The estimated $h_{\rm
shk}$ varies in a range between $\sim 14-21$ $r_{s}$.

The mass outflow rate ($\dot{m}_{\rm out}$) is derived for an isothermal base
of the jet Chakrabarti1999 (10), which is given by,

$\dot{m}_{\rm out}=\dot{m}_{\rm in}f_{\rm
col}f_{0}^{3/2}\frac{R}{4}\exp\left[\frac{3}{2}-f_{0}\right],$ (1)

where, $f_{\rm 0}=\frac{R^{2}}{R-1}$ and $\dot{m}_{\rm in}$ is the total mass
inflow rate. The estimated $\dot{m}_{\rm out}$ varies between $0.14\pm
0.03-0.20\pm 0.03$ $\dot{M}_{\rm Edd}$ for this source, which is significant
as was reported earlier in the literature (BraitoEtal2007ApJ…670..978B, 8,
see,). According to this model, as mentioned earlier, both corona and base of
the jet behave as a Comptonizing medium. The radiation scattered by the corona
or wind may exhibit significant polarization. The unpolarized radiation from
the central source scattered by the corona of radius $X_{s}$ at height $h_{\rm
shk}$ above the midplane of the disk will acquire a net fractional
polarization BegelmaMcKee1983ApJ…271…89B (6),

$\Pi_{\rm sc}=\frac{\sin^{2}i[1-2(h_{\rm shk}/X_{s})^{2}]}{2[1+2(h_{\rm
shk}/X_{s})^{2}]+[1-2(h_{\rm shk}/X_{s})^{2}]\sin^{2}i},$ (2)

where $i$ is the disk inclination angle. As this model assumes Thomson
scattering and negligible Comptonization, thereby, the scattering conserves
photon energy. Moreover, the Thomson scattering has no frequency dependence so
it would preserve the incident spectrum for any energy bands including IXPE
coverage. Therefore, for a given or well-estimated corona properties and disk
inclination, one can estimate PD or vice-versa using Eq. 2. As the disk
inclination is not well constrained in the literature, we have estimated it
from the observed upper limit of the PD in TagliacozzoEtal2023MNRAS.525.4735T
(44) and the broadband spectroscopic data fitted JeTCAF model parameters. Our
estimated $i$ ranges between $31^{\circ}-35^{\circ}$ during I2 and I1 epochs.
These estimations are further applied to predict the expected PD for other
epochs during NuSTAR observation. All estimated parameters are given in Table
5. The spectral flux given in the table is calculated using flux err command
in XSPEC for the energy band $2-79$ keV.

Table 5:  Estimated and observed polarization and corona properties of MCG-5-23-16. The $3-79$ keV band flux is in units of $10^{-10}$ erg cm-2 s-1. Here, a,b denotes the references to MarinucciEtal2022MNRAS.516.5907M (30) and TagliacozzoEtal2023MNRAS.525.4735T (44). In the first two rows, c denotes the estimation of $i$ from the observed upper limit of PD, while the expected PDs in column 5 are calculated for $i=33^{\circ}$. Epoch | $\dot{m}_{\rm out}$ | $h_{\rm shk}$ | $F_{\rm 3-79keV}$ | PD(%) | $i$
---|---|---|---|---|---
| $(\dot{M}_{\rm Edd})$ |  ($r_{s}$) |  | Model |  Obs.a,b | (deg)
I1+N1 | $0.19\pm 0.04$ | $19.9\pm 2.5$ | $2.75\pm 0.02$ | $4.2$ | $\leq 4.7$ | $35^{c}$
I2+N2 | $0.20\pm 0.03$ | $21.4\pm 1.9$ | $2.84\pm 0.02$ | $3.7$ | $\leq 3.3$ | $31^{c}$
N3 | $0.14\pm 0.03$ | $14.3\pm 1.7$ | $2.66\pm 0.03$ | $4.5$ | - | 33
N4 | $0.16\pm 0.02$ | $17.8\pm 2.1$ | $2.53\pm 0.01$ | $4.5$ | - | 33
N5 | $0.15\pm 0.02$ | $15.1\pm 1.2$ | $2.30\pm 0.02$ | $4.6$ | - | 33
N6 | $0.19\pm 0.03$ | $20.6\pm 2.5$ | $3.09\pm 0.02$ | $4.3$ | - | 33
N7 | $0.19\pm 0.02$ | $19.5\pm 1.6$ | $2.87\pm 0.02$ | $4.4$ | - | 33

Figure 3: Dependence of PD with the geometry of the Comptonizing corona. The
left and middle panels show the PD variation with the radial distance and
height of the corona, while the right panel shows the PD variation with the
observed flux in the $3-79$ keV band. The red circles show the predicted PD,
estimated using spectral model fitted accretion parameters, and the blue
squares show the observed upper limit in PD measurement.

The left panel of Fig. 3 shows the variation of PD with the radial distance of
the corona. The red circles are the PD values estimated using the model fitted
$h_{\rm shk}$ and $X_{s}$ parameters for a given $i=33^{\circ}$, which is the
average of disk inclination angles estimated from the upper limit of the
observed PD values reported in TagliacozzoEtal2023MNRAS.525.4735T (44). For a
corona of $<35$ rs, the PD was nearly constant and it decreased when the
corona size increased. A similar profile has been observed (middle panel of
Fig. 3) for the height of the corona, which is quite expected as a bigger
corona indicates a hotter electron cloud and more puffed up in the vertical
direction. Our estimated PD variation with corona geometry is in accord with
the simulation results performed by SchnittmanKrolik2010ApJ…712..908S (40) for
a spherical geometry of the corona. The right panel of Fig. 3 shows the PD
variation with estimated spectral flux, which shows a negative correlation as
well.

##  4 Discussions

In this work, we have performed the spectro-polarimetric analysis of the
Seyfert galaxy MCG-5-23-16 to understand the polarization properties and the
X-ray emitting corona using two epochs of data from IXPE and a decade of
observations from NuSTAR. Our model-independent analysis poses the PD with an
upper limit of $\leq 3.8\%$, while the model-dependent estimates give PD
$1.55\pm 0.99\%$ and $1.31\pm 0.95\%$ for the epochs I1 and I2, while the PA
values are $37.3^{\circ}\pm 20.1^{\circ}$ and $73.2^{\circ}\pm 23.1^{\circ}$,
which are in accord with the previous studies within error bar
MarinucciEtal2022MNRAS.516.5907M (30, 44).

The joint IXPE and NuSTAR broadband spectroscopic data fitting gives also the
estimate of disk mass accretion rate to the central SMBH which is $\leq 0.013$
$\dot{M}_{\rm Edd}$, while the halo accretion rate is $\leq 0.4$ $\dot{M}_{\rm
Edd}$. The location of the shock changed from 28 to 40 $r_{s}$ and the shock
compression ratio varied between $4.4-5.3$. Relatively high values of
jet/outflow collimation factor indicate that the outflow is not well-
collimated. The previous studies reported that the source showed significant
mass outflow, here we estimated the mass outflow rate $\sim 0.14-0.20$
$\dot{M}_{\rm Edd}$ from the spectral model fitted parameters. Since mass
outflow carries thermal energy from the hot corona, its geometry changes
Chakrabarti1999 (10, 35). Therefore, the final best-fit corona geometry which
is used to estimate the expected PD has the effect of mass outflows. Hence,
studying polarization using the disk-corona-outflows model is crucial to get a
consistent picture of a system, which has been done in this work.

The estimation of disk inclination for this source is not well constrained to
date. As the scattering of photons inside the Comptonizing corona or outflow
can induce significant polarization, we use it to further estimate the disk
inclination for a given corona geometry, mainly with its radial distance and
height. Using the polarization information we have estimated the upper limit
of the disk inclination $\sim 35^{\circ}$ for the highest measured
polarization in May 2022 and $\sim 31^{\circ}$ in November 2022. After taking
an average of these two estimates, we further use it to determine the expected
polarization during the epochs N3-N7. The estimated PD decreases with
increasing the corona geometry at different epochs (see Fig. 3). Our study not
only relates the polarization with the accretion flow properties but also can
predict expected polarization which can be further applied and verified using
XPoSat observations of this source - which includes a polarimeter (POLIX:
$8-30$ keV) and spectrometer (XSPECT: $0.8-15$ keV) can shed further light on
the accretion properties of this source and verify the model-predicted
results. POLIX, having an energy band complementary to that of IXPE, can help
constrain the polarimetric properties of this source over a wider energy
range. Preliminary analysis suggests that POLIX observations can constrain the
PD of this source in $\sim 1$ Ms, whereas the spectral properties can be
constrained by XSPECT in $\sim 200$ ks. These conservative estimates show that
simultaneous observation of this source by these two instruments can further
reveal its properties and dynamics around the central object. Additionally,
current model prescription can also be applied to other Seyfert galaxies to
study their X-ray polarization in connection with the accretion-ejection
properties, where polarization could be due to reflection
(GianolliEtal2023MNRAS.523.4468G, 18, NGC 4151;) or outflowing jet
(IngramEtal2023MNRAS.525.5437I, 22, 37, IC 4329A;), which will be addressed in
future.

SM thanks Keith A. Arnaud for helping during the data analysis. RC, VKA, and
AN thank GH, SAG, DD, PDMSA, and the Director, URSC for continuous support to
carry out the research activity. This research used data products provided by
the IXPE Team (MSFC, SSDC, INAF, and INFN) and distributed with additional
software tools by the High-Energy Astrophysics Science Archive Research Center
(HEASARC), at NASA Goddard Space Flight Center (GSFC). This research has made
use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the
ASI Science Data Center (ASDC, Italy) and the California Institute of
Technology (Caltech, USA).

#### Funding Statement

SM acknowledges Ramanujan Fellowship (# RJF/2020/000113) by SERB-DST, Govt. of
India for this research.

#### Competing Interests

None

#### Data Availability Statement

Data used in this work are publicly available in NASA’s HEASARC archive.

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# Generating clickbait spoilers with an ensemble of large language models

Mateusz Woźny1 Mateusz Lango1,2
1 Poznan University of Technology, Faculty of Computing and
Telecommunications, Poznan, Poland
2 Charles University, Faculty of Mathematics and Physics, Prague, Czech
Republic
<EMAIL_ADDRESS><EMAIL_ADDRESS>

###### Abstract

Clickbait posts are a widespread problem in the webspace. The generation of
spoilers, i.e. short texts that neutralize clickbait by providing information
that satisfies the curiosity induced by it, is one of the proposed solutions
to the problem. Current state-of-the-art methods are based on passage
retrieval or question answering approaches and are limited to generating
spoilers only in the form of a phrase or a passage. In this work, we propose
an ensemble of fine-tuned large language models for clickbait spoiler
generation. Our approach is not limited to phrase or passage spoilers, but is
also able to generate multipart spoilers that refer to several non-consecutive
parts of text. Experimental evaluation demonstrates that the proposed ensemble
model outperforms the baselines in terms of BLEU, METEOR and BERTScore
metrics.

##  1 Introduction and related works

Catchy headlines or social media posts designed to entice users to click,
known as clickbait, are widespread on the internet. Although they often
increase website traffic and generate revenue, they usually fall short of
readers’ expectations, wasting their time and causing disappointment Molyneux
and Coddington (2020).

To deal with this problem, Rubin et al. (2015) proposed the clickbait
detection task, which received some research attention Potthast et al. (2016);
Chakraborty et al. (2016). More recently, Hagen et al. (2022a) found that
clickbaits can be neutralized by providing short texts that clarify what the
reader can expect from the linked article, often making the clickbait
uninteresting. They developed corpora of clickbait spoilers and classified
them into three types: phrase spoilers (containing a single word or a short
phrase), passage spoilers (a few sentences at most), and multi-part spoilers
(containing many non-consecutive phrases and/or passages). See the examples in
Tab. 1.

Hagen et al. (2022a) also experimented with 20 approaches for clickbait
spoiler generation, which were based on passage retrieval or extractive
question answering algorithms. However, all of these methods were only
evaluated on phrase and passage spoilers, as they are not suitable for
generating multi-part spoilers and their generation requires a specialised
approach.

In this work, we demonstrate that all three types of spoilers can be
effectively generated by means of conditional language generation with large
language models. We put forward a simple yet effective proposal of an ensemble
of LLMs that selects the final spoiler by exploiting learning-to-rank
techniques. Finally, we verify the performance of the proposed approach and
investigate the possibility of combining it with previously developed methods
that provide phrase and passage spoilers.

type |  clickbait |  spoiler
---|---|---
phrase |  You’re missing this major way to save money |  promotional code
passage |  Scientists unearth big surprise near celebrated pyramids |  remains of a bustling port and barracks for sailors or troops
multi |  This is what REALLY happens when you don’t brush your teeth |  Bad breath, Coronary heart disease, Bleeding gums, (…)
Table 1: Abbreviated examples of spoilers and clickbaits from Webis-
Clickbait-22 corpus Hagen et al. (2022a)

##  2 Ensemble of LLMs for clickbait spoiler generation

The task of clickbait spoiler generation is defined as follows. For a given
clickbait text $c$, the content of the linked article $a$ and the requested
spoiler type $t$, generate a textual spoiler $s$ whose goal is to make the
clickbait $c$ uninteresting for the user by providing the additional
information from the referred article $a$. The possible types of spoilers $t$
are phrase, passage, and multi-part.

In this paper, we propose an ensemble of language models for clickbait spoiler
generation. The proposed approach consists of three steps: converting the text
of a clickbait $c$ into a question $q$, generating candidate spoilers from
various prompted large language models, and finally selecting the final
spoiler by a trained scoring model.

###  2.1 Converting clickbaits to questions

Clickbaits usually take the form of declarative or exclamatory sentences. In
contrast, question answering, which is one of the most related tasks according
to related works, naturally deals with problems structured as interrogative
sentences. Due to their popularity, QA datasets are often used as a part of
LLMs’ (pre)training sets, enabling better knowledge transfer for these tasks.
Therefore, to better exploit knowledge acquired by LLMs during pretraining, we
convert each clickbait into a question before passing it for further
processing.

The conversion is made in a zero-shot fashion using the recent Vicuna language
model Chiang et al. (2023). For each clickbait $c$, we construct the following
prompt: ”Below is a sentence from which write a question.\n Sentence: $c$ \n
Question:”, where \n is the sign of a new line. The resulting question $q$ is
generated by initializing the language model with the prompt and completing
the text with the greedy search algorithm until the sign of a new line is
generated.

###  2.2 Generating spoilers with LLMs

The next step of our approach is to use a set of different pretrained language
models to produce a diversified set of spoiler candidates.

Each component of our ensemble is fine-tuned on the standard language modeling
task using an adapter-based approach LoRA Hu et al. (2021). Such transfer
learning approaches allow parameter-efficient fine-tuning by leaving all the
pretrained weights unchanged and modifying the model operations by adding
shallow, trainable feed-forward networks between the transformer layers. The
results of these feed-forward networks are incorporated into the transformer
architecture by adding their output to the output of successive transformer
layers. Such fine-tuning approaches have proven to be well-suited for
relatively small supervised datasets like ours Houlsby et al. (2019).

In order to create training corpora for the language modeling task, each
training example was converted to a textual form by filling in the hand-
designed prompt template: ”Below is a question paired with a context for which
you should generate an answer. Write an answer with type $t$ that
appropriately completes the question.\n Question: $q$ \n Context: $a$ \n
Answer: $s$\n ”. During training, cross-entropy loss was optimized, i.e.

$-\sum_{i=1}^{n}\log P(w_{i}|w_{1},w_{2},...,w_{i-1})$

where $w_{i}$ is the $i$-th token of the filled template and $n$ is its
length. During testing, standard greedy decoding was used to retrieve the
clickbait spoiler.

###  2.3 Selecting the final spoiler with scoring model

After generating several clickbait spoiler candidates, the final step of the
approach is to select the most appropriate spoiler by running a trainable
model that evaluates them. This problem can be viewed as a learning-to-rank
problem Liu (2009), where our goal is to construct the ranking of spoiler
candidates and later select the best candidate i.e. the spoiler at the top of
the ranking. We experiment with two popular learning-to-rank approaches: 1) a
pointwise approach, which assigns a score to each candidate and later uses it
to sort the list of candidates. 2) a pairwise approach, which compares all
pairs of candidates and decides which spoiler from the pair is more suitable.

####  2.3.1 Pointwise approach

To evaluate each candidate, we develop a regressor that tries to predict the
value of BLEU score for each spoiler. As a regressor fine-tuned DeBERTa model
He et al. (2021) with one linear layer on top of CLS token is used. The input
to the model consists of a question (clickbait) $q$, candidate spoiler $s$,
and article $a$, separated by the sign of a new line and concatenated into one
input text. The output of the model is the predicted BLEU score.

The training data for the regressor was generated by running all the LLMs used
in the ensemble on the training data and evaluating their BLEU score against
the available gold standard. During training, the classical sum of squared
errors was optimized.

####  2.3.2 Pairwise approach

The second method considered for selecting the best spoiler among the
candidates is the pairwise approach. This approach relies on a classifier
that, for a given pair of spoiler candidates, decides which of them is more
suitable. More specifically, the BERT-based classifier receives the same input
as in the pointwise approach, but with two spoiler candidates $s_{1}$ and
$s_{2}$. The output of the binary classification model is 1 if $s_{1}$ is
better than $s_{2}$ in terms of BLEU, and 0 otherwise.

The classifier is trained on the generated data as follows. First, all LLMs
used in the ensemble were run on the training set, generating a collection of
spoiler candidates for each clickbait. Later, all possible pairs from each
collection were considered and converted into binary classification instances
by comparing the BLEU scores of the candidates. The pairs containing spoilers
with BLEU$=0$ or pairs containing identical spoilers were removed from the
training data. During training, the standard cross-entropy loss was optimised.

##  3 Experiments

We have performed computational experiments aimed at verifying the
effectiveness of ensembling LLMs with pointwise and pairwise rankers, and
comparing its effectiveness with the previous SOTA methods based on question
answering. In addition, we also investigate the possibility of combining the
previous QA approaches, which are best suited for passage and phrase spoiler
types, with the proposed approach for multi-part spoilers.

###  3.1 Experimental setup

We experiment with an ensemble of three fine-tuned LLMs, which were
constructed from two pretrained models: LLaMA Touvron et al. (2023) and Vicuna
Chiang et al. (2023). Both of these models are open-source and were fine-tuned
using the prompt described in Sec. 2.2. However, we observed additional
improvements with Vicuna model while using specially tailored prompts for each
spoiler type separately (see appendix), therefore we also report the results
of this fine-tuned model and use it as a part of the ensemble.

The obtained results were compared against the performance of two extractive
QA approaches, which on top of pretrained encoder perform begin/end span
classification111This is the default fine-tuning approach for QA-task of BERT
Devlin et al. (2019), more details therein.. These approaches are based on
RoBERTa Liu et al. (2019) and DeBERTa He et al. (2021) models since among 20
approaches compared on clickbait spoiler generation task by Hagen et al.
(2022a) these two were the most effective ones. Note, that the results
reported for these approaches in this work are significantly lower than
therein, since we report the performance over all three types of spoilers,
including multipart.

The ensemble approach with the pointwise ranker used DeBERTa-based regressor,
which obtained MSE of 0.384 on test set. Similarly, the classifier used in the
pairwise approach achieved balanced accuracy of 90,8% on the test data.

Following earlier works, we evaluated the approaches with three metrics: BLEU
Papineni et al. (2002), METEOR Banerjee and Lavie (2005), and BERT Score Zhang
et al. (2020). All experiments were performed on a single Nvidia A100 GPU.

Some additional experiment details and results can be found in the online
appendix222https://www.cs.put.poznan.pl/mlango/publications/inlg23.pdf.

###  3.2 Comparing the proposed approaches with related works

|  |  | BERT Score
---|---|---|---
Model | BLEU | METEOR | Precision | Recall | F1
RoBERTa | 31,78 | 0,387 | 0,904 | 0,883 | 0,893
DeBERTa | 32,20 | 0,398 | 0,907 | 0,884 | 0,894
LLaMA 13B | 37,70 | 0,474 | 0,895 | 0,901 | 0,897
Vicuna 13B | 38,80 | 0,481 | 0,898 | 0,903 | 0,900
Vicuna 13B with type-based prompts | 40,02 | 0,492 | 0,899 | 0,905 | 0,901
Ensemble with pairwise ranker | 40,76 | 0,500 | 0,901 | 0,907 | 0,904
Ensemble with pointwise ranker | 42,13 | 0,517 | 0,902 | 0,909 | 0,905
Table 2:  The experimental results of previous state-of-the-art QA-based methods compared with our ensembling approaches and LLMs. All the metrics are computed on Webis Clickbait 22 corpora Hagen et al. (2022b).  |  |  | BERT Score
---|---|---|---
Model | BLEU | METEOR | Precision | Recall | F1
DeBERTa | 32,20 | 0,398 | 0,907 | 0,884 | 0,894
DeBERTa trained on questions | 37,82 | 0,451 | 0,913 | 0,895 | 0,903
Baseline ensemble | 42,28 | 0,506 | 0,910 | 0,908 | 0,909
Ensemble with pairwise ranker | 43,57 | 0,520 | 0,912 | 0,911 | 0,911
Ensemble with pointwise ranker | 44,45 | 0,532 | 0,911 | 0,913 | 0,911
Table 3:  The experimental results of the ensemble that combines previously
proposed methods for passage and phrase spoiler types (DeBERTa) with the newly
proposed approaches for clickbait spoiler generation.

The results of QA-based approaches, ensemble models as well as individual
fine-tuned LLMs can be found in Table 2. The best-performing approach
according to BLEU, METEOR, and BERT Score F1 is the proposed ensemble with a
pointwise ranker. This ensemble provides the improvement of approx. 2
percentage points in terms of BLEU and METEOR over the best of its components
i.e. Vicuna model with specific prompts for each spoiler type. The second-best
approach was the ensemble with pairwise ranker which offered limited
improvement over the individual LLMs.

Overall, each of the approaches using LLMs obtained better results than
previous state-of-the-art approaches based on extractive question answering.
The only metric on which the QA-based approaches (RoBERTa and DeBERTa) stand
out is BERTScore Precision. Still, BERTScore Recall is higher for LLM and
ensemble approaches, making them more effective in terms of F1 measure, which
combines both precision and recall.

###  3.3 Combining previous SOTA models with the proposed ones

In the final experiment, we decided to verify whether it is possible to obtain
even better results by combining our approaches with QA-based models
previously designed for clickbait spoilers of phrase and passage types only.

As a QA model, we use the fine-tuned DeBERTa model, since it gave the best
results both in our experiments from the previous section and in the
experiments of Hagen et al. (2022a). As we mentioned in Sec. 2.1, our
approaches generate spoilers for clickbaits converted into interrogative
sentences in order to facilitate better knowledge transfer from the pre-
trained models. We also fine-tuned DeBERTa on such preprocessed data and found
improved performance. Therefore, this model (later denoted DeBERTa-q or
”DeBERTa trained on questions”) was used for ensembling.

The operation of ensembles reported in this section slightly differs from what
was described in Sec 2.3 to better account for QA-based approaches’
suitability for passage and phrase spoiler types. If the generated spoiler is
of mutli-part type, the list of candidate spoilers is generated as previously,
i.e. from three fine-tuned LLMs. However, if the generated spoiler is of
phrase/passage type then only spoiler candidates from DeBERTa-q and Vicuna
with customised prompts are considered. As previously, the selection of the
best spoiler among the candidates is performed by a ranker.

The results of these approaches are reported in Table 3. It can be seen that
DeBERTa-q achieves significantly better results than DeBERTa for all metrics
considered. However, the ensemble with LLMs provides further significant
improvements.

As a form of sanity check for our ensemble approach that uses a ranker to
select the best spoiler, we have also implemented a trivial ensemble (baseline
ensemble) that uses DeBERTa-q for all passage and phrase spoilers and Vicuna
with type-based prompts for multi-part spoilers. Although such a form of
ensembling is also advantageous in that the performance obtained is better
than that of the individual models, using any variant of the proposed ensemble
with a ranker still improves the results. For example, for the METEOR measure,
the improvement is almost 2% for the pairwise approach and 3% for the
pointwise approach.

|  |  |  | BERT Score
---|---|---|---|---
Model | spoiler type | BLEU | METEOR | Recall | F1 | Precision
DeBERTa | phrase | 56,00 | 0,569 | 0,934 | 0,932 | 0,931
passage | 20,10 | 0,304 | 0,858 | 0,869 | 0,883
multi-part | 2,07 | 0,204 | 0,822 | 0,860 | 0,902
DeBERTa trained on questions | phrase | 62,50 | 0,627 | 0,946 | 0,942 | 0,939
passage | 21,60 | 0,319 | 0,861 | 0,872 | 0,885
multi-part | 4,10 | 0,224 | 0,829 | 0,862 | 0,900
Ensemble with pairwise ranker | phrase | 63,30 | 0,617 | 0,945 | 0,943 | 0,942
passage | 30,00 | 0,416 | 0,882 | 0,887 | 0,894
multi-part | 27,30 | 0,525 | 0,894 | 0,886 | 0,879
Ensemble with pointwise ranker | phrase | 65,30 | 0,645 | 0,950 | 0,946 | 0,942
passage | 30,30 | 0,424 | 0,884 | 0,887 | 0,892
multi-part | 28,60 | 0,522 | 0,894 | 0,887 | 0,881
Table 4: The performance of clickbait spoiler generation models for each spoiler type.  Clickbait |  Reference |  DeBERTa |  Vicuna
---|---|---|---
Agency might plant a garden on the moon. |  NASA |  NASA |  lunar sunlight
10 habits of incredibly happy people |  1 they slow down to appreciate life’s little pleasure 2 they exercise 3 they spend money on other people (…) |  they have a growth mindset |  1 they slow down to appreciate life’s little pleasure 2 they exercise 3 they spend money on other people (…)
Table 5: Two examples of spoilers generated by different methods. The spoilers
in italics were selected by pointwise ranker (The ensemble also includes the
LLaMA model, the output of which is not shown due to page limits.).

Table 4 presents a more detailed analysis of the performance of the spoiler
generation methods, i.e. the results are reported separately for each spoiler
type. Although the newly proposed ensemble approaches achieve better
performance for each spoiler type, the most significant improvement is
observed for the most difficult multi-part spoilers, which are the focus of
our paper. For example, the best ensemble model achieves an improvement of
over 25 in terms of BLEU score over the previous DeBERTa model.

Two examples of generated spoilers are presented in Table 5 (more examples in
the appendix). It can be observed that the previous SOTA approach (DeBERTa)
fails to extract the correct spoiler of the multi-part type, but Vicuna model
generates it correctly. In contrast, DeBERTa extracts the correct phrase
spoiler and Vicuna fails to do so. In both cases, the pointwise ranker was
able to indicate the correct spoiler.

##  4 Summary

In this paper, we have shown that using fine-tuned LLMs can be a simple, yet
effective way of dealing with clickbait spoiler generation for all three
spoiler types considered, i.e. including multi-part spoilers. We also
demonstrated that ensembling several such models with a ranker that selects
the most suitable spoiler leads to improved results, especially when using a
pointwise ranker. Finally, we show that combining state-of-the-art approaches
for phrase and passage spoiler types based on question answering with the
newly proposed ones based on LLMs leads to further improvements.

##### Supplementary Materials Availability Statement:

Source code is available on Github repository333https://github.com/mateusz-
wozny/spoiler_generation. All experiments were performed on Webis Clickbait 22
corpora which is available on Zenodo Hagen et al. (2022b).

##### Acknowledgments

M. Woźny is supported by AI Tech project sponsored from POPC programme
POPC.03.02.00-00-0001/20. M. Lango is supported by the European Union (ERC,
NG-NLG, 101039303).

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