# Transition probabilities of near-infrared Ce III lines from stellar spectra:
applications to kilonovae

Nanae Domoto Astronomical Institute, Tohoku University, Aoba, Sendai 980-8578,
Japan  Jae-Joon Lee Korea Astronomy and Space Science Institute, 776 Daedeok-
daero, Yuseong-gu, Daejeon, 34055, Republic of Korea  Masaomi Tanaka
Astronomical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan
Division for the Establishment of Frontier Sciences, Organization for Advanced
Studies, Tohoku University, Sendai 980-8577, Japan  Ho-Gyu Lee Korea Astronomy
and Space Science Institute, 776 Daedeok-daero, Yuseong-gu, Daejeon, 34055,
Republic of Korea  Space Policy Research Center, Science and Technology Policy
Institute, 370 Sicheong-daero, Sejong, 30147, Republic of Korea  Wako Aoki
National Astronomical Observatory, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
Astronomical Science Program, The Graduate University for Advanced Studies,
SOKENDAI, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Miho N. Ishigaki
National Astronomical Observatory, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
Shinya Wanajo Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-
Institut), Am Mühlenberg 1, D-14476 Potsdam-Golm, Germany  Interdisciplinary
Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN, Wako, Saitama
351-0198, Japan  Daiji Kato National Institute for Fusion Science, 322-6
Oroshi-cho, Toki 509-5292, Japan  Interdisciplinary Graduate School of
Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
Kenta Hotokezaka Research Center for the Early Universe, Graduate School of
Science, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan  Kavli IPMU (WPI),
UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan

###### Abstract

Kilonova spectra provide us with information of $r$-process nucleosynthesis in
neutron star mergers. However, it is still challenging to identify individual
elements in the spectra mainly due to lack of experimentally accurate atomic
data for heavy elements in the near-infrared wavelengths. Recently, Domoto et
al. (2022) proposed the absorption features around 14500 Å in the observed
spectra of GW170817/AT2017gfo as Ce III lines. But they used theoretical
transition probabilities ($gf$-values) whose accuracy is uncertain. In this
paper, we derive the astrophysical $gf$-values of the three Ce III lines,
aiming at verification of this identification. We model high resolution
$H$-band spectra of four F-type supergiants showing the clear Ce III
absorption features by assuming stellar parameters derived from optical
spectra in literatures. We also test the validity of the derived astrophysical
$gf$-values by estimating Ce III abundances in Ap stars. We find that the
derived astrophysical $gf$-values of the Ce III lines are systematically lower
by about 0.25 dex than those used in previous work of kilonovae, while they
are still compatible within the uncertainty range. By performing radiative
transfer simulations of kilonovae with the derived $gf$-values, we find that
the identification of Ce III as a source of the absorption features in the
observed kilonova spectra still stands, even considering the uncertainties in
the astrophysical $gf$-values. This supports identification of Ce in the
spectra of GW170817/AT2017gfo.

line: identification — stars: neutron — stars: general — atomic data

##  1 Introduction

Binary neutron star (NS) mergers have been considered as promising sites of
$r$-process nucleosynthesis (e.g., Eichler et al., 1989; Freiburghaus et al.,
1999; Goriely et al., 2011; Korobkin et al., 2012; Wanajo et al., 2014). In
2017, associated with the detection of gravitational waves (GWs) from a NS
merger (GW170817, Abbott et al., 2017a), the electromagnetic counterpart
AT2017gfo was observed (Abbott et al., 2017b). The observed properties of
AT2017gfo in ultraviolet, optical, and near-infrared (NIR) wavelengths are
consistent with the theoretical expectation of a kilonova (Li & Paczyński,
1998; Metzger et al., 2010), thermal emission from NS merger ejecta powered by
radioactive decays of $r$-process nuclei (e.g., Arcavi et al., 2017; Evans et
al., 2017; Pian et al., 2017; Smartt et al., 2017; Utsumi et al., 2017;
Valenti et al., 2017). This electromagnetic counterpart has provided us with
evidence that NS mergers are sites of $r$-process nucleosynthesis (e.g., Kasen
et al., 2017; Perego et al., 2017; Shibata et al., 2017; Tanaka et al., 2017;
Kawaguchi et al., 2018; Rosswog et al., 2018).

To extract the detailed information of elements synthesized in NS merger
ejecta, it is important to identify the individual elements. However, element
identification in the kilonova spectra remains challenging. This is mainly due
to lack of atomic data for heavy elements. While detailed spectral studies
require spectroscopically accurate atomic data, such data for heavy elements
have been highly incomplete, especially for the NIR wavelengths. So far, the
absorption features around 8000 Å in the photospheric spectra of AT2017gfo
have been identified as Sr II (Watson et al., 2019; Domoto et al., 2021;
Gillanders et al., 2022), although the same features may be caused by He I
(Perego et al., 2017; Tarumi et al., 2023).

Recently, Domoto et al. (2022) systematically studied kilonova spectra over
the entire wavelength range. They identified important elements that produce
strong transitions in kilonvoae, such as Ca, Sr, Y, Zr, Ba, La, and Ce. Then,
they constructed a hybrid line list combined with experimentally accurate data
for important elements and complete theoretical data for weak transitions of
the other elements (Tanaka et al., 2020). By performing radiative transfer
simulations, they found that the broad line features at $\sim$13000 Å and
14500 Å in the spectra of AT2017gfo can be explained by La III and Ce III,
respectively. However, this identification can be still a subject of
discussion as they adopted the transition probabilities (i.e., $gf$-values) of
the La III and Ce III lines from theoretical calculations (Tanaka et al.,
2020) due to lack of experimental measurements.

The lack of experimental atomic data is problematic in any spectra for
astrophysical objects, such as stars. Compared with the optical region, line
identification in stellar spectra in the NIR region is incomplete and still in
progress (e.g., Matsunaga et al., 2020). Also, as few experiments have been
performed on heavy elements such as lanthanides, $gf$-values from theoretical
calculations are commonly used even for the optical wavelengths. In many
cases, no or few data are provided for the NIR wavelengths (e.g., Biémont et
al., 1999; Quinet & Palmeri, 2020).

In general, the accuracy of atomic calculations is difficult to assess without
experimental measurements. It has been shown that the theoretical $gf$-values
for given ions differ from the experimental values several times for strong
transitions, and even more for weak transitions (see, e.g., Appendix of Domoto
et al., 2022). The $gf$-values directly affect the absorption depths in the
spectra, which influences derived parameters, e.g., abundances. In the case of
kilonova model of Domoto et al. (2022), the absorption features at the NIR
wavelengths can disappear if the $gf$-values of the NIR lines are $\sim 10$
times smaller than the values they adopted. Therefore, it is important to
measure the $gf$-values to firmly identify elements in kilonova spectra.

For the use in astrophysics, one can estimate the $gf$-values of atomic lines
by using stellar spectra. This is often called as “astrophysical $gf$-values”.
Such work has been performed for many metal lines in the NIR wavelengths using
the spectra of well-observed stars, e.g., the Sun (e.g., Meléndez & Barbuy,
1999). In fact, it has been shown that the astrophysical $gf$-values can be
useful to extract elemental information from stars without laboratory
experiments (Hasselquist et al., 2016; Cunha et al., 2017).

In this paper, we derive the astrophysical $gf$-values of three Ce III lines
at the $H$-band (around 1.6 µm) using high resolution stellar spectra. This
aims to verify the identification of Ce in the spectra of AT2017gfo. Note that
we cannot test the absorption by La III in the same way, because the La III
lines at rest lie in the wavelength region of strong atmospheric absorption.
In Section 2, we describe the targeted Ce III lines in more detail. We present
the stellar spectra showing the Ce III line features in Section 3, and derive
the $gf$-values of the Ce III lines by modeling these spectra in Section 4. In
Section 5, we apply the derived $gf$-values of the Ce III lines to kilonova
spectra by performing radiative transfer simulations. Finally, we give a
summary in Section 6. We also show the validity of our results by estimating
the Ce abundances with Ce III lines in Ap stars in Appendix A. Throughout of
the paper, line wavelengths are written as those in vacuum unless otherwise
mentioned.

Table 1: The targeted Ce III lines at $H$-band.

$\lambda_{\rm vac}$a |  $\lambda_{\rm air}$b |  $E_{\rm lower}$c |  $E_{\rm upper}$d | Theoretical log $gf^{e}$ | Astrophysical log $gf^{f}$
---|---|---|---|---|---
(Å) | (Å) | (${\rm cm^{-1}}$) | (${\rm cm^{-1}}$) | (1) | (2) | (3) | (4) | (5) | (6) | (7) | This work
15851.880 | 15847.550 | 1528.32 | 7836.72 |  $-$0.613 |  $-$0.838 |  $-$1.030 |  $-$1.190 |  $-$0.439 |  $-$0.673 |  $-$2.105 |  $-$0.861
15961.157 | 15956.797 | 0.00 | 6265.21 |  $-$0.721 |  $-$0.926 |  $-$1.120 |  $-$1.290 |  $-$2.926 |  $-$1.098 |  $-$0.345 |  $-$0.966
16133.170 | 16128.763 | 3127.10 | 9325.51 |  $-$0.509 |  $-$0.722 |  $-$0.920 |  $-$1.070 |  $-$0.429 |  $-$1.950 |  $-$0.920 |  $-$0.702

Note. — a Vacuum transition wavelength.

b Air transition wavelength.

c Lower energy level.

d Upper energy level.

e $gf$-values from theoretical calculations (1: Tanaka et al., 2020, see also
Domoto et al., 2022; 2: Wyart & Palmeri, 1998; 3: taken from Hubrig et al.,
2012 and Chojnowski et al., 2019. These values were computed in the same way
as in Biémont et al., 2002 and provided to Hubrig et al., 2012 and Chojnowski
et al., 2019 as private communication; 4: Carvajal Gallego et al., 2021). For
(1) and (4), theoretical $gf$-values are shown as they are, without
calibration by considering the differences in the theoretical energy levels
relative to the experimental energy levels.

f Astrophysical $gf$-values in the APOGEE line list (5: Shetrone et al., 2015,
Table 7 of; 6: taken from here through the SDSS Science Archival Server (SAS),
see Holtzman et al., 2018; 7: taken from here through the SDSS SAS, see Smith
et al., 2021), and those derived in this work (Section 4).

##  2 Ce III lines at $H$-band

We focus on the three Ce III lines at the $H$-band (Table 1). It has been
shown that these are the strongest lines of Ce III in the NIR region, which
can produce broad absorption features in kilonova spectra (Domoto et al.,
2022). In fact, these lines have been detected in the spectra of Ap/Bp stars
that exhibit enhanced Ce abundances (Hubrig et al., 2012; Chojnowski et al.,
2019; Tanaka et al., 2023).

Although the transition wavelengths of these lines have been measured by
experiments (Johansson & Litzén, 1972), their transition probabilities are
experimentally unknown. Thus, Domoto et al. (2022) adopted the theoretical
results of Tanaka et al. (2020). Other theoretical calculations are also
available, i.e., used for studies of optical stellar spectra (Wyart & Palmeri,
1998; Biémont et al., 2002) and for application to kilonovae (Carvajal Gallego
et al., 2021). However, it is usually difficult to assess the accuracy of
these calculations, and the $gf$-values vary over the range of $\sim 0.5$ dex
as shown in Table 1.

Recently, the APOGEE survey has observed many Galactic stars at the $H$-band
with the spectral resolution of $R\sim 22500$ (Majewski et al., 2017). To
analyze the APOGEE spectra, the line lists for the $H$-band have been provided
(Shetrone et al., 2015; Holtzman et al., 2018; Smith et al., 2021). They
collected the atomic data from theoretical and experimental studies, and
adjusted the $gf$-values by fitting those to the spectra of the Sun and
Arcturus. It is shown that such astrophysical $gf$-values can improve the
agreement between the observed spectra and the model spectra. In fact, the
APOGEE line lists include the three Ce III lines that we focus on (Table 1).
However, their astrophysical $gf$-values are quite uncertain, because there is
no clear Ce III absorption in the spectra of the Sun and Arcturus. As a
result, the $gf$-values vary by an order of magnitude across the different
versions of the APOGEE line lists. This fact demonstrates that, if lines are
not clearly detected in the spectra which is the case of Ce III lines for the
Sun and Arcturus, it is difficult to derive the astrophysical $gf$-values even
though the spectra are well characterized. To derive $gf$-values of the Ce III
lines, we select stars clearly showing these Ce III line features (Section 3),
although the uncertainties in stellar parameters can be larger than those of
well-known stars such as the Sun and Arcturus (Section 4.3).

We mention that near the three lines, there is another Ce III line at 15964.93
Å. According to the theoretical $gf$-values of this line ($-$1.272 by Tanaka
et al., 2020, $-$1.660 by Biemont et al., see Chojnowski et al., 2019, or
$-$1.690 by Carvajal Gallego et al., 2021), this line is weaker than the three
Ce III lines. In fact, it is found that the absorption at this wavelength is
usually dominated by the strong Si I $\lambda$15964.41 Å line (see Figure 1).
Thus, we will not focus on this line in this work.

Figure 1:  The IGRINS spectra around the Ce III lines of the selected stars.
Black and gray lines show the spectra for the objects used as the final sample
and for the excluded objects, respectively (see the text). The positions of
the three Ce III lines that we focus on are indicated by thick orange lines
(Table 1), while that of another Ce III line is also indicated by thin orange
line (see Section 2). Al I and Si I lines that may contaminate the Ce III
lines are labeled in blue. Other lines are also shown in gray.

##  3 Stellar spectra with Ce III lines

###  3.1 Sample selection

Compared with the NIR wavelengths, the line list in the optical region is more
comprehensive and accurate. Ce abundances in many stars are indeed reported
from optical observations, e.g., in Hypatia Catalog for Solar neighborhoods
(Hinkel et al., 2014), the catalogue of luminous stars (Luck, 2014), and the
catalogue of chemically peculiar (CP) stars (Ghazaryan et al., 2018). While
not all the stars in these catalogues have Ce abundances, measurements are
available for a good fraction of stars. Thus, we will derive the astrophysical
$gf$-values of the Ce III lines using the stars that (1) show the Ce III line
features in the NIR $H$-band and (2) have known Ce abundances from optical
spectra.

We obtain NIR $H$-band high resolution spectra from the spectral archive of
the Immersion GRating INfrared Spectrometer (IGRINS, Park et al., 2014; Mace
et al., 2016, 2018). IGRINS provides spectra spanning the full $H$ and $K$
bands with the spectral resolution of $R\sim 45000$. The Raw & Reduced IGRINS
Spectral Archive (RRISA)111https://igrinscontact.github.io/ contains the
IGRINS archive for the period of July 2014–December 2021 on the 2.7 m Harlan
J. Smith Telescope at McDonald Observatory, the Discovery Channel Telescope at
Lowell Observatory, and the Gemini south telescope. RRISA includes IGRINS data
from more than 850 nights on-sky, resulting in 2800 unique target observations
from over 3000 hours of the total science time. RRISA also includes the IGRINS
observations of $>1200$ distinct A0V standard stars.

RRISA provides reduced one-dimensional (1D) spectra processed using the IGRINS
pipeline (Lee et al., 2017). The pipeline applies flat-fielding and flagging
of bad pixels, and the 1D spectra are extracted using the optimal extraction
of Horne (1986). The wavelength solutions are derived using OH lines from sky
spectra. In the $H$-band, the accuracy of wavelength solution is better than
0.01 Å ($\sim$ 0.2 km s-1). RRISA further refines the wavelength of the
pipeline product by improving the pixel alignment between the A0V star
spectrum and the target spectrum using strong telluric sky lines between
16452–16458 Å and 21740–21752 Å in the $H$\- and $K$-band, respectively.
Telluric absorption is corrected using the spectra of A0V stars observed
closely in time and airmass with intrinsic features of A0V stars removed using
a model spectrum of the Vega (Castelli & Kurucz, 1994).

We crossmatch the RRISA archive with the two stellar catalogues of measured
abundances: Luck (2014) and Ghazaryan et al. (2018). Not all entries in these
catalogues have Ce abundances reported, and they are not used as we need
abundance information to derive the $gf$-values (see below). Luck (2014)
reports abundances for 451 luminous stars including Ce measurement for 448
stars. RRISA contains spectra for 27 of them. Ghazaryan et al. (2018) reports
abundances of 429 CP stars with 121 stars of Ce measurement. RRISA contains
spectra of 8 stars.

Figure 2:  EW of the Ce III $\lambda$15961.157 Å line in the model spectra
(colormap) and in the observed spectra (diamonds). Note that the region
without color (upper left) is the parameter space where no ATLAS model exists.

For the matched data, we apply Doppler correction using strong C I, Si I, and
Fe I lines. Then, we visually check the absorption lines at the wavelengths of
the Ce III lines. We impose the detection of all three lines to ensure the
origin of these lines. As a result, six stars showing clear Ce III line
features are selected: HD 29647, HD 56126, $\varphi$ Cas, $\nu$ Aql, HD
190323, and d Dra. The spectra of six stars around the regions of the Ce III
lines are shown in Figure 1.

While the six stars are selected above, we decide not to use two out of them:
HD 29647 and HD 56126 (gray lines in Figure 1). This is because their
atmospheric parameters are found to be rather uncertain, although they are
listed in the catalogues. For HD 29647, a HgMn star (Straizys et al., 1985),
Adelman et al. (2001) have reported the atmospheric parameters, but they
mentioned that the parameters are not very accurate. For HD 56126, a post-AGB
star (e.g., Hony et al., 2003), atmospheric parameters seem to change
depending on the epoch when spectra are taken (De Smedt et al., 2016; Puķītis
et al., 2022). Puķītis et al. (2022) also pointed out the chemical depletion
of neutron-capture elements in other post-AGB star, likely due to dust
condensation. Also, the IGRINS spectrum of HD 56126 shows double-peak like
features, whose origins are unknown.

Finally, we use four stars as our samples (black lines in Figure 1). The S/N
ratios of the spectra around the targeted Ce III lines are $>100$ for $\nu$
Aql and $>200$ for the others. Since the Ce III $\lambda$15851.88 Å and
$\lambda$16133.170 Å lines are located around the broad hydrogen features, the
spectra are normalized by fitting the broad features as a pseudo-continuum.
After the normalization, we measure the equivalent widths (EWs) of the Ce III
lines by Gaussian fitting (see the top panels of Figure 3 as examples). The
measured EWs of the Ce III lines in each star are shown in Table 3, which are
used to derive those astrophysical $gf$-values in Section 4.

Table 2: Adopted stellar parameters for the sample stars.

Star | Spectral type | Model | $T_{\rm eff}$ | log $g$ | [Fe/H] | $\xi$ | $v\sin i$ | [Al/H] | [Si/H] | [Ce/H] |  $\sigma_{\rm[Ce/H]}$a
---|---|---|---|---|---|---|---|---|---|---|---
|  |  | (K) | (cm s-2) |  | (km s-1) | (km s-1) |  |  |  |
$\varphi$ Cas | F0Ia | ATLAS | 7347 | 0.76 |  $-$0.07 | 5.21 | 23.0∗ | 0.00b | 0.49 | 0.16 | 0.30
$\nu$ Aql | F2Ib | ATLAS | 7152 | 1.65 | 0.10 | 3.74 | 12.0∗∗ | 0.22 | 0.32 | 0.27 | 0.22
HD 190323 | F8Ia | MARCS | 6169 | 1.11 | 0.12 | 4.31 | 15.0‡ | 0.42 | 0.27 | 0.25 | 0.15
d Dra | F8Ib-2 | MARCS | 6157 | 1.78 |  $-$0.10 | 3.93 | 10.0† | 0.16 | 0.06 | 0.27 | 0.24

Note. — All the parameters are adopted from Luck (2014), but $v\sin i$ from
Abt & Morrell (1995) (∗), Uesugi & Fukuda (1970) (∗∗), Lyubimkov et al. (2012)
(†), and estimated in this work using the Ce III line because of no available
measurement (‡).

a Standard deviations of the Ce abundances measured in Luck (2014) (see
Section 4.3).

b The solar abundance (Asplund et al., 2009) is assumed because it is not
measured in Luck (2014).

###  3.2 Properties of sample stars

The four stars in our final sample are all F-type supergiants (see Table 2).
Our primary catalogue of Luck (2014) consists primarily of (super)giants with
$T_{\rm eff}\sim$ 4000–8000 K, and the Ce III lines are only seen in warmer
supergiants of $T_{\rm eff}>6000$ K. To check the presence of the Ce III lines
in wider parameter range of $T_{\rm eff}$ and surface gravity log $g$, we also
crossmatch the RRISA with Hinkel et al. (2014). RRISA contains spectra of 132
sources out of 2685 stars from Hinkel et al. (2014), primarily of nearby dwarf
stars. But none of the spectra show clear signature of the Ce III lines. We
further check RRSIA with $T_{\rm eff}$ and log $g$ from the PASTEL catalogue
(Soubiran et al., 2016). RRISA contains spectra of 168 stars with $T_{\rm
eff}\sim 5500$–8000 K, mostly dwarfs with some (super)giants. Note that this
catalogue does not provide abundance measurements and is not subject to our
analysis of deriving the $gf$-values. We find five stars showing the Ce III
line features, which are the same four stars as our sample selected from Luck
(2014) and an additional F-type supergiant.

We briefly discuss the reason why the Ce III lines tend to appear in warm
supergiants. To see the behavior of the Ce III absorption in spectra, we
generate model spectra for the wavelength regions around the Ce III lines,
varying $T_{\rm eff}$ and log $g$. We use Turbospectrum (Plez, 2012)
implemented through iSpec (Blanco-Cuaresma et al., 2014; Blanco-Cuaresma,
2019) to perform spectral synthesis, assuming local thermodynamic equilibrium
(LTE). The parameter ranges are $T_{\rm eff}$ = 5000–10000 K and log $g$ =
0.5–4.5 dex with intervals of 500 K and 0.5 dex, respectively. For simplicity,
we fix the microturbulent velocity $\xi$ = 2 km s-1, the solar abundance ratio
(Asplund et al., 2009), and the projected rotational velocity $v\sin i$ = 10
km s-1as typical values (e.g., Matsunaga et al., 2020), and assume the
macroturbulent velocity $v_{\rm mac}=0$ km s-1(see also Section 4.1). We use
ATLAS, 1D plane-parallel atmosphere model (Castelli & Kurucz, 2003). For the
atomic data, we use the APOGEE line list (Holtzman et al., 2018; Smith et al.,
2021, see Section 4.1) as a baseline, with the line list of the Ce III lines
from Domoto et al. (2022). These choices do not affect the dependence on
$T_{\rm eff}$ and log $g$ discussed here.

Since the dependence of the absorption on the atmospheric parameters is
expected to be the same among the Ce III lines, we focus only on the Ce III
$\lambda$15961.157 Å line. Note that this Ce III line may be contaminated by
Al I $\lambda$15961.03 Å line at lower $T_{\rm eff}$ and higher log $g$,
although the Ce III line is dominant (Section 4.1). We measure the EWs of the
Ce III line in the model spectra by Gaussian fitting as done in the observed
spectra. The measured EWs for different $T_{\rm eff}$ and log $g$ are shown in
Figure 2. It is seen that the EW of the Ce III line peaks at $T_{\rm eff}\sim$
6000–7000 K and log $g<$ 2\. The peak $T_{\rm eff}$ can be understood as the
region where the doubly ionized Ce is the most abundant under LTE. Also, the
line becomes strong toward low gravity, due to low-density and geometrically
thick atmosphere (Gray, 2005). A similar trend is observed for other lines of
metal ions (Matsunaga et al., 2020).

We also show the observed EWs of the Ce III $\lambda$15961.157 Å line for the
four sample stars as shown with diamonds in Figure 2. Although the Ce
abundances are not exactly same as the solar abundances for these stars, it is
seen that the observed trend is consistent with the trend in our model grid.
Also, models are consistent with the fact that only warm (F-type) supergiants
show the Ce III lines but not normal dwarfs.

Of course, the behavior of the Ce III lines are also dependent on the Ce
abundance. If the Ce abundance is higher, the parameter range of $T_{\rm eff}$
and log $g$ showing the Ce III lines becomes wider. For example, as shown in
Figure 1, HD 29647 shows Ce III absorption in the NIR wavelengths even under
high temperature and strong surface gravity ($T_{\rm eff}\sim 12500$ K and log
$g\sim 4$, Adelman et al., 2001), because the Ce abundance is $\sim 3$ dex
higher than the solar value (see also Appendix A). We note that CP stars are
main sequences; supergiants used in our analysis do not show such anomaly in
abundances of lanthanides.

Figure 3:  The Ce III lines of HD 190323 (black). In the top panels, the
observed spectra are compared with the fitted Gaussian profile (green). In the
bottom panels, the observed spectra are compared with the model spectra using
the derived $gf$-values (red). Note that the observed spectrum at $\sim 15963$
Å of HD 190323 (the middle panels) may be affected by unknown lines.

##  4 Astrophysical $gf$-values of the Ce III lines

###  4.1 Methods

In this section, we derive the astrophysical $gf$-values of the Ce III lines.
For each sample star, we perform spectral synthesis calculations with the
fixed Ce abundances based on the measurements with the optical spectra, and
then adjust $gf$-values. We use Turbospectrum (Plez, 2012) through iSpec
(Blanco-Cuaresma et al., 2014; Blanco-Cuaresma, 2019) to synthesize spectra as
in Section 3.2.

We adopt atmospheric parameters ($T_{\rm eff}$, log $g$, metallicity, and
$\xi$) derived from the analysis of optical spectra. Luck (2014) provided the
stellar parameters of sample stars using MARCS models (Gustafsson et al.,
2008). For the stars with $T_{\rm eff}$ higher than $\sim 6300$ K, they also
used ATLAS models (Castelli & Kurucz, 2003). In our sample, when a star has
two parameter sets determined using both models, we use the atmospheric
parameters that better reproduce the $H$-band IGRINS spectra. Then, for
spectral synthesis, we consistently use MARCS or ATLAS models used in the
estimates of the adopted atmospheric parameters. The adopted atmospheric
parameters and models of sample stars are summarized in Table 2.

We use the elemental abundances derived using the adopted atmospheric
parameters in Luck (2014). Luck (2014) used observational data from multiple
archives and provided abundances for each of the available data for a given
star. When multiple abundance sets are provided for our sample stars, we
simply take the averages. While all the elements are included in our
calculations, only Ce, Al, and Si are important for our analysis: Ce
abundances directly affect the absorption depths of the Ce III lines, while Al
and Si may also affect the Ce III absorption due to the contamination by Al I
$\lambda$15961.03 Å and Si I $\lambda$16133.42 Å lines, respectively. For the
elements without measurements, we assume the solar abundances (Asplund et al.,
2009). For example, the Al abundance for $\varphi$ Cas is assumed as the solar
abundance. But this assumption does not affect the results because most Al is
expected to be ionized in a high $T_{\rm eff}$ ($\sim 7300$ K) and low log $g$
($\sim 0.8$ dex) atmosphere (see also Section 4.3 and Table 4). For all the
samples, the contamination from the Al I and Si I lines for the Ce III
absorption features are estimated to be $<10$% and $<30$%, respectively, by
measuring the EWs of the lines in the model spectra without the Ce III lines.
The adopted abundances of important elements are also summarized in Table 2.

It should be cautioned that, although the Ce abundances are fixed in our
analysis, they are also subject to the uncertainties (see also Section 4.3).
The standard deviations of the Ce abundances measured in Luck (2014) are also
shown in Table 2. We confirmed that the absorption of Ce II lines at the
$H$-band (Cunha et al., 2017) is reasonably reproduced for HD 190323 and d
Dra, which confirms the validity of the abundances. There is no or little Ce
II absorption for $\varphi$ Cas and $\nu$ Aql with $T_{\rm eff}>7000$ K.
Nevertheless, we emphasize that the Ce abundances in these two stars are
rather robust, because they were derived using optical lines with experimental
$gf$-values (Luck, 2014).

Spectral synthesis also needs to consider effects of line broadening. It is
usually difficult to separate the effects of $v\sin i$ and $v_{\rm mac}$ on
the line profiles in F-type supergiants (e.g., Lyubimkov et al., 2012). Here,
we ignore $v_{\rm mac}$ and consider only $v\sin i$. These parameters for
$\varphi$ Cas, $\nu$ Aql, and d Dra are taken from literatures (see Table 2).
We find that these choices reasonably reproduce the line profiles in the
IGRINS spectra. On the other hand, no measurement of $v\sin i$ for HD 190323
was found. Thus, we estimate $v\sin i$ using the Ce III lines in the IGRINS
spectra (see Table 2). Although this is not very accurate measurement, this
assumption does not affect our results.

The line list for other elements is also an important factor in the estimate
of $gf$-values. This is because some Ce III lines are contaminated by Al I or
Si I lines. Thus, the $gf$-values of these lines may affect the estimates of
the $gf$-values of the Ce III lines. By comparing the $H$-band model spectra
using the VALD (Piskunov et al., 1995; Kupka et al., 1999; Ryabchikova et al.,
2015) and the APOGEE line lists (Holtzman et al., 2018; Smith et al., 2021),
we find that the APOGEE line list reproduces the observed features of the
IGRINS spectra better. Thus, we adopt the APOGEE line list for our analysis.
Note that, as iSpec implements the APOGEE line list of DR13/14 (Holtzman et
al., 2018), we updated the line list using the newest DR16 line list (Smith et
al., 2021) except for hyperfine structure lines.

For the model spectra, we measure the EWs of the Ce III lines by Gaussian
fitting as done in the observed spectra. These EWs are compared with those of
the observed spectra (Section 3.1). Comparison is repeated by changing the
$gf$-values of the Ce III lines. Finally, we adopt the $gf$-values that give
the EWs in agreement with the EWs of the observed spectra. Examples of the
final model spectra are shown in the bottom panels of Figure 3.

Figure 4:  Astrophysical $gf$-values of the Ce III lines derived in four stellar spectra (blue dots), and their average (red dots). Each panel shows the results of each transition as shown in the legend. Black diamonds show the theoretical $gf$-values (T20: Tanaka et al., 2020; WR98: Wyart & Palmeri, 1998; B02: Biemont et al., see Table 1; CG21: Carvajal Gallego et al., 2021). Error bars indicate the estimated systematic uncertainties (see Section 4.3 and Table 4).  Table 3: Observed EWs and derived $gf$-values for the three Ce III lines in four sample stars. Star | EW (mÅ) | log $gf$ | EW (mÅ) | log $gf$ | EW (mÅ) | log $gf$
---|---|---|---|---|---|---
| 15851.880 Å | 15961.157 Å | 16133.170 Å
$\varphi$ Cas | 184 |  $-$0.82 | 201 |  $-$0.80 | 166 |  $-$0.72
$\nu$ Aql | 102 |  $-$0.93 | 120 |  $-$0.96 | 96 |  $-$0.83
HD 190323 | 183 |  $-$0.78 | 182 |  $-$0.90 | 180 |  $-$0.65
d Dra | 81 |  $-$0.92 | 71 |  $-$1.20 | 113 |  $-$0.61
Table 4: Systematic uncertainties in the astrophysical $gf$-values of the Ce III lines for the fixed Ce abundances in each star. Star | $\lambda_{\rm vac}$ | $\Delta T_{\rm eff}$ |  $\Delta$log $g$ |  $\Delta$[Fe/H] | $\Delta\xi$ |  $\Delta$[Al/H] |  $\Delta$[Si/H] | $\Delta_{\rm sys}$
---|---|---|---|---|---|---|---|---
| (Å) | (+200 K) | (+0.3 dex) | (+0.3 dex) | (+0.5 km s-1) | (+0.5 dex) | (+0.3 dex) |
$\varphi$ Cas | 15851.880 | 0.146 | 0.067 | 0.035 |  $-$0.018 | - | - | 0.165
| 15961.157 | 0.105 | 0.085 | 0.029 |  $-$0.030 |  $-$0.002 | - | 0.141
| 16133.170 | 0.139 | 0.070 | 0.034 |  $-$0.010 | - |  $-$0.022 | 0.161
$\nu$ Aql | 15851.880 | 0.048 | 0.153 | 0.028 |  $-$0.017 | - | - | 0.164
| 15961.157 | 0.054 | 0.151 | 0.025 |  $-$0.019 |  $-$0.015 | - | 0.164
| 16133.170 | 0.067 | 0.151 | 0.046 |  $-$0.014 | - |  $-$0.088 | 0.193
HD 190323 | 15851.880 | 0.000 | 0.176 | 0.066 |  $-$0.030 | - | - | 0.190
| 15961.157 | 0.003 | 0.179 | 0.057 |  $-$0.021 |  $-$0.031 | - | 0.192
| 16133.170 | 0.018 | 0.175 | 0.100 |  $-$0.026 | - |  $-$0.099 | 0.227
d Dra | 15851.880 |  $-$0.015 | 0.196 | 0.055 |  $-$0.011 | - | - | 0.204
| 15961.157 |  $-$0.002 | 0.194 | 0.056 |  $-$0.005 |  $-$0.121 | - | 0.235
| 16133.170 | 0.014 | 0.194 | 0.081 |  $-$0.014 | - |  $-$0.149 | 0.258

###  4.2 Results

The estimated $gf$-values of the three Ce III lines using the spectra of four
stars are shown by blue dots in Figure 4, and listed in Table 3. As our final
astrophysical $gf$-values of each Ce III line, we take the averages of those
derived for each star. They are plotted as red dots in each panel of Figure 4,
and listed in Table 1. The validity of our final $gf$-values is also discussed
in Appendix A.

The $gf$-values of the Ce III lines from available theoretical calculations
are also shown by black diamonds in Figure 4 (see Table 1). All of our
$gf$-values are consistently smaller than those of Tanaka et al. (2020), which
were used for the kilonova model of Domoto et al. (2022). This suggests that
the strength of absorption could have been overestimated in the kilonova model
of Domoto et al. (2022) (see Section 5). On the other hand, it is seen that
the estimated final $gf$-values are the closest to those of Wyart & Palmeri
(1998), while higher than those of Biémont et al. (2002) and Carvajal Gallego
et al. (2021). Overall, our $gf$-values of the Ce III lines, which are
independently estimated from theoretical calculations, broadly agree with the
available theoretical calculations within the margin of the estimated
uncertainties discussed in Section 4.3.

###  4.3 Uncertainties in $gf$-values

Uncertainties in the astrophysical $gf$-values can be evaluated by considering
the uncertainties in the stellar parameters of each star. The systematic
uncertainty of stellar parameters can generally be caused by difference in the
analysis methods. Even with common atmospheric parameters and line lists,
there remain variety in the abundances determined by different codes and
methods (Hinkel et al., 2016) as well as different spectral data used in the
analysis (Luck, 2014). All of these factors can affect the depth of absorption
lines, which leads to uncertainties in the astrophysical $gf$-values derived
for the fixed Ce abundances.

We estimate the systematic uncertainties in our astrophysical $gf$-values by
varying stellar parameters of each star. To take uncertainties of stellar
parameters into account, we vary $T_{\rm eff}$ by $\pm$200 K, log $g$ by
$\pm$0.3 dex, [Fe/H] by $\pm$0.3 dex, and $\xi$ by $\pm$0.5 km s-1. Also, we
vary [Al/H] and [Si/H] by $\pm$0.5 and $\pm$0.3 dex, respectively, which
affect the level of the contamination. These ranges are typical systematic
uncertainties caused by different codes and methods used to determine stellar
parameters (Hinkel et al., 2016). While Hinkel et al. (2016) used dwarfs to
show these uncertainty ranges, the uncertainties for supergiants are similar
to those in dwarfs (Luck, 2014).

Table 4 summarizes the estimated systematic uncertainties in the astrophysical
$gf$-values of the Ce III lines. Only the results for the positive shifts are
shown, but the results for the negative shifts are smaller than the
uncertainties given in Table 4 (see also Table 3 of Cunha et al., 2017). We
find that the largest uncertainties are caused by $T_{\rm eff}$ or log $g$.
The systematic uncertainties in total in each $gf$-value for each star
($\Delta_{\rm sys}$) are estimated by taking root sum squares (Cunha et al.,
2017). Note that the values of $\Delta_{\rm sys}$ estimated here are the upper
limits of the uncertainties: all the stellar parameters are not independent,
and the uncertainties caused by each parameter may be cancelled among
parameters (Cunha et al., 2017). In most cases, the total systematic
uncertainties are smaller than 0.2 dex, and up to $\sim 0.26$ dex. These
systematic uncertainties are shown as the error bars for the blue dots in
Figure 4.

Finally, we assign the systematic uncertainties of the average astrophysical
$gf$-values by taking root mean squares of the $\Delta_{\rm sys}$ in four
stars. The systematic uncertainties in the $gf$-values for $\lambda$15851.880
Å, $\lambda$15961.157 Å, and $\lambda$16133.170 Å lines are 0.182, 0.186, and
0.213, respectively (shown as the error bars for the red dots in Figure 4). It
is worth noting that our astrophysical $gf$-values are broadly agree with
available theoretical calculations, considering the systematic uncertainties.

Here we did not show the uncertainties in continuum levels of the observed
spectra in $\Delta_{\rm sys}$. They may affect the observed EWs and in turn
astrophysical $gf$-values. However, the uncertainties in continuum leveles and
their contributions to $\Delta_{\rm sys}$ are estimated to be $\lesssim$ 1%,
which are smaller than the uncertainties from most stellar parameters (see
also Table 3 of Cunha et al., 2017).

Note that, although we fix the Ce abundances of each star to derive
astrophysical $gf$-values, the Ce abundances are still uncertain within the
range of $\lesssim 0.3$ dex (standard deviations, Section 4.1). The Ce
abundances scale the resultant $gf$-values: for example, if the Ce abundance
is altered by the standard deviation (Table 2) to the positive direction, the
derived $gf$-values are also affected by the same degree to the negative
direction. Furthermore, it should be noted that the Ce abundances in Luck
(2014) as well as the astrophysical $gf$-values here were derived under the
assumption of LTE. Non-LTE treatment may affect the abundances of heavy
elements (e.g., Mashonkina et al., 2005), especially in supergiants. This may
result in systematic changes in the derived $gf$-values. Nevertheless, the
fact that the derived $gf$-values are consistent among samples suggests that
the Ce abundance of each star adopted in this work is reasonable. Independent
measurements of stellar parameters may be able to reduce the uncertainties in
the astrophysical $gf$-values, but this is beyond the scope of this work. The
uncertainties present here are found not to significantly affect the final
results on kilonova spectra, as discussed in Section 5.

Figure 5:  Comparison between the synthetic spectra (blue) and the observed
spectra of AT2017gfo taken with the VLT (gray, Pian et al., 2017; Smartt et
al., 2017) at $t=1.5$, 2.5, and 3.5 days after the merger (dark to light
colors). The spectrum taken with the HST at $t=4.5$ days after the merger
(Tanvir et al., 2017) is also shown in black line. The green curves are the
synthetic spectra of Domoto et al. (2022, see their Figure 8). Spectra are
vertically shifted for visualization. Gray shade shows the regions of strong
atmospheric absorption.  Figure 6:  Enlarged view of the synthetic spectra for
the NIR region at $t=2.5$ days. Blue curves show the synthetic spectra using
the derived $gf$-values, and green curves show those of Domoto et al. (2022).
Orange and red curves show the synthetic spectra when using the lower and
upper $gf$-values, which are considering the sum of the uncertainties
negatively and positively, respectively (see the text). The curves in light
colors show the original results, while those in dark colors show smoothed
spectra for visualization.

##  5 Applications to kilonova spectra

We apply the derived $gf$-values of the Ce III lines to calculate kilonova
spectra. To calculate synthetic spectra of kilonovae, we use a wavelength-
dependent radiative transfer simulation code (Tanaka & Hotokezaka, 2013;
Tanaka et al., 2014, 2017, 2018; Kawaguchi et al., 2018, 2020). The photon
transfer is calculated by the Monte Carlo method. The setup of simulation is
identical to that in Domoto et al. (2022), but we adopt the final
astrophysical $gf$-values of the three Ce III lines derived in Section 4. For
more details of the simulation, we refer the readers to Domoto et al. (2022).

Figure 5 shows the comparison between our new synthetic spectra (blue) and the
observed spectra of AT2017gfo taken with the Very Large Telescope (VLT) (gray)
at $t=1.5$, 2.5, and 3.5 days after the merger (Pian et al., 2017; Smartt et
al., 2017). The observed spectra at $t=4.5$ days after the merger taken with
the Hubble Space Telescope (HST), which are not affected by telluric
absorption, is also shown by a black line (Tanvir et al., 2017). We find that
the absorption features around 14500 Å are caused by the Ce III lines in the
new spectra. These features are blueshifted according to the velocity of the
line-forming region at the NIR wavelengths, e.g., $v\sim 0.1\ c$ at $t=2.5$
days. In fact, the features caused by the Ce III lines in the new synthetic
spectra are almost the same as those in Domoto et al. (2022, green), which
used the $gf$-values of Tanaka et al. (2020) (see Figure 6 for the enlarged
view at $t=2.5$ days). This is consistent with the observed features in the
spectra of AT2017gfo.

To see the effects of the uncertainties in the $gf$-values to the spectra, we
also perform the same simulations by varying the $gf$-values of the Ce III
lines. Orange and red curves in Figure 6 show the results when using the lower
and upper $gf$-values, respectively. Here, for the lower (upper) values, we
take the averages of the estimated $gf$-values for each star negatively
(positively) shifed by $\sigma_{\rm[Ce/H]}$, and then further shift the
averages by $\Delta_{\rm sys}$ negatively (positively). We find that the
changes in fluxes around 14500 Å are $\sim 10$%. The absorption features by Ce
III are still seen even using the lower $gf$-values (orange curves), although
the depth of absorption is weakened.

When using the final astrophysical $gf$-values, the Sobolev optical depths of
the Ce III lines for the line forming region ($\rho\sim 10^{-14}$ g cm-3 and
$T\sim 5000$ K, see Domoto et al., 2022) are $\sim 4$. The lower $gf$-values
of the Ce III lines are smaller than the nominal values by a factor of $\sim
2.7$. Thus, even by adopting the lower $gf$-values, the Sobolev optical depths
of the Ce III lines are still larger 1. This confirms the identification of Ce
in the spectra of AT2017gfo.

The changes in $gf$-values of the strong lines affect not only absorption but
also emission in the spectra. A stronger absorption tends to cause a stronger
emission in P-Cygni type line profile. As shown in Figure 6, the increase of
the $gf$-values results in the increase of the flux at emission component
around the rest wavelengths, and vice versa. Note that, for particularly large
$gf$-values (red and green lines), the optical depths of the Ce III lines are
large enough that the depth of the absorption is saturated, while the effect
in the emission component is still apparent.

##  6 Summary

We have derived the astrophysical $gf$-values of the three Ce III lines at the
$H$-band using the IGRINS spectra of four F-type supergiants. The derived
$gf$-values are systematically lower by about 0.25 dex than those used in
Domoto et al. (2022), but they are broadly agree with available theoretical
calculations within the estimated uncertainties. Using the derived
astrophysical $gf$-values of the Ce III lines, we have performed radiative
transfer simulations of kilonovae. We have found that the Ce III lines with
the new $gf$-values produce the absorption features around 14500 Å in kilonova
spectra, even considering the uncertainties. This supports the identification
of Ce in the observed spectra of AT2017gfo (Domoto et al., 2022).

We have also shown that the F-type supergiants with near solar metallicity
show strong absorption of Ce III. To our knowledge, this is the first report
of the detection of the Ce III lines at the $H$-band in stars with near solar
abundances. As the line blending is not severe in the NIR spectra compared
with the optical spectra, those lines may also be useful for stellar
spectroscopic studies.

We thank R. E. Luck for providing his detailed abundance data, and K.
Kawaguchi for valuable discussions. This work used the Immersion Grating
Infrared Spectrometer (IGRINS) that was developed under a collaboration
between the University of Texas at Austin and the Korea Astronomy and Space
Science Institute (KASI) with the financial support of the Mt. Cuba
Astronomical Foundation, of the US National Science Foundation under grants
AST-1229522 and AST-1702267, of the McDonald Observatory of the University of
Texas at Austin, of the Korean GMT Project of KASI, and Gemini Observatory.
Part of the observations in this work were also carried out within the
framework of Subaru-Gemini time exchange program which is operated by the
National Astronomical Observatory in Japan. We are honored and grateful for
the opportunity of observing the Universe from Maunakea, which has the
cultural, historical and natural significance in Hawaii. Part of numerical
simulations presented in this paper were carried out on Cray XC50 at Center
for Computational Astrophysics, National Astronomical Observatory of Japan.
This work was supported by JST FOREST Program (Grant Number JPMJFR212Y,
JPMJFR2136), NIFS Collaborative Research Program (NIFS22KIIF005), the Grant-
in-Aid for JSPS Fellows (22KJ0317), and the Grant-in-Aid for Scientific
Research from JSPS (19H00694, 20H00158, 21H04997, 23H00127, 23H04891,
23H04894, 23H05432). N.D. acknowledges support from Graduate Program on
Physics for the Universe (GP-PU) at Tohoku University.

##  Appendix A Abundance estimates in Ap stars as a test of astrophysical
$gf$-values

We assess the validity of our astrophysical $gf$-values by adopting them to
spectra of Ap stars. Ap stars are a kind of CP stars that exhibit extremely
high metal abundances. Thanks to the high abundances, Ap stars show clear Ce
III absorption lines that we focus on. However, it is also known that they
show inconsistent abundances between singly and doubly ionized rare-earth
elements (REE), called REE anomaly (Ryabchikova et al., 2004; Ryabchikova &
Romanovskaya, 2017). Even if Ce abundances have been measured from Ce II
lines, it does not necessarily represent the Ce abundances. Therefore, these
stars cannot be used to derive $gf$-values in Section 4.

Here, we estimate the Ce abundances from Ce III lines (hereafter Ce III
abundances) in Ap stars using the derived astrophysical $gf$-values. We use
three Ap stars, HD 101065 (Przybylski’s Star), HD 201601 ($\gamma$ Equ), and
HD 24712. These stars have quite different log $g$ from the supergiants used
to derive the $gf$-values. Thus, the abundance estimates serve as independent
assessment of the derived $gf$-values.

The spectrum of HD 101065 was taken with Gemini south/IGRINS on UT 2022
December 18 in two ABBA sequences with each exposure time of 33 sec. An A0V
star (HIP 55019) was also observed for the telluric standard. Those IGRINS
spectra are reduced through the pipeline (Lee et al., 2017), as described in
Section 3.1. The 1D spectra are normalized by continuum fitting.

The spectra of HD 201601 and HD 24712 were taken with the Gemini Near-Infrared
Spectrograph (GNIRS, Elias et al., 2006a, b) at Gemini north telescope on UT
2022 July 17 and August 18, respectively. We use 110.5 l/mm grating and long
camera with a 0.1” slit, which gives the spectral resolution of $R\sim$17800\.
Central wavelength is set to be 1.6 µm to cover the three Ce III lines. HD
201601 and HD 24712 were observed in one and two ABBA sequence(s) with each
exposure time of 60 sec, respectively. For the telluric standards, A0V stars
(HD 208108 and HD 15130) were also observed. The GNIRS spectra are reduced
using the Gemini IRAF package, and followed standard procedure, which includes
flat-fielding, sky subtraction, wavelength calibration based on Ar-Xe lamp
spectra, and extraction of 1D spectra. The 1D spectra are normalized by
continuum fitting. Telluric absorption in the normalized target spectra is
corrected by dividing by the normalized spectra of the A0V stars.

The spectra of three Ap stars around the region of the Ce III lines are show
in Figure 7. For those spectra, we measure EWs of the three Ce III lines by
Gaussian fitting. Then, we perform spectral synthesis as in Section 4 but by
changing the Ce abundance and by using the derived $gf$-values of the Ce III
lines. We use the stellar parameters of the Ap stars derived in literatures
using optical spectra as summarized in Table 5. Although there are the
atmospheric parameters derived using more sophisticated models that consider
stratification of elements for all the samples (Shulyak et al., 2009, 2010,
2013), we adopt those derived using 1D atmospheric models (ATLAS) that we use
for spectral synthesis. We measure EWs of the Ce III lines in model spectra by
Gaussian fitting and compare with the EWs in the observed spectra. Comparison
is repeated by varying Ce abundances until the model EWs match with the EWs in
the observed spectra.

We show the results of the Ce III abundances estimated using the three Ce III
lines in Table 6. It is seen that the line-by-line variation of the abundances
is small in each star. This fact demonstrates that the derived $gf$-values of
the Ce III lines are reasonable.

Table 6 also shows the Ce II and III abundances reported in literatures, which
confirms clear REE anomaly. It is worth noting that, although Hubrig et al.
(2012) showed that the derived Ce III abundances in HD 201601 deviate about 2
dex depending on the lines, the abundances derived by using the three Ce III
lines here are consistent with each other. Also, this is the first measurement
of the Ce III abundance for HD 24712.

Figure 7:  The observed spectra around the Ce III lines of the Ap stars.
Absorption lines are labeled as in Figure 1.  Table 5: Adopted stellar
parameters for the Ap stars.

Star | Model | $T_{\rm eff}$ | log $g$ | [Fe/H] | $\xi$ | $v\sin i$ | [Al/H] | [Si/H] | Reference
---|---|---|---|---|---|---|---|---|---
|  | (K) | (cm s-2) |  | (km s-1) | (km s-1) |  |  |
HD 101065 | ATLAS | 6600 | 4.20 |  $-$0.72 | 1.00 | 3.5 |  $-$1.11 | 0.11 | Cowley et al. (2000)
HD 201601 | ATLAS | 7700 | 4.20 | 0.19 | 2.00 | 7.0a | 0.66 | 0.11 | Ryabchikova et al. (1997a)
HD 24712 | ATLAS | 7250 | 4.20 |  $-$0.21 | 1.00 | 6.6a | 0.06 |  $-$0.18 | Ryabchikova et al. (1997b)

Note. — All $v\sin i$ are smaller than spectral resolution ($R\sim 45000$ or
17800) and does not affect results.

a Adopted from Sikora et al. (2019).

Table 6: Ce abundances derived using Ce III or II lines in the Ap stars.

[Ce/H] |  | HD 101065 | HD 201601 | HD 24712
---|---|---|---|---
Ce III | 15851.880 Å | 4.11 | 4.09 | 3.86
| 15961.157 Å | 4.06 | 4.04 | 3.72
| 16133.170 Å | 4.16 | 4.26 | 3.83
| Mean $\pm$ standard error | 4.11$\pm$0.03 | 4.13$\pm$0.07 | 3.78$\pm$0.03
| Literatures | 4.76a | 3.46–5.36c |
Ce II |  | 2.93a | 1.26d | 1.42e
|  | 3.07b |  |

Note. — a Shulyak et al. (2010). b Cowley et al. (2000). c Hubrig et al.
(2012). d Ryabchikova et al. (1997a). e Ryabchikova et al. (1997b).

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