# Connections between Planetary Populations and the Chemical Characteristics
of their Host Stars

Sol Yun Department of Astronomy, Space Science, and Geology, Chungnam National
University, Daejeon 34134, South Korea<EMAIL_ADDRESS>Young Sun Lee
Department of Astronomy and Space Science, Chungnam National University,
Daejeon 34134, South Korea<EMAIL_ADDRESS>Department of Physics and
Astronomy, University of Notre Dame, Notre Dame, IN 46556, USA  Young Kwang
Kim Department of Astronomy and Space Science, Chungnam National University,
Daejeon 34134, South Korea  Timothy C. Beers Department of Physics and
Astronomy, University of Notre Dame, Notre Dame, IN 46556, USA  Joint
Institute for Nuclear Astrophysics – Center for the Evolution of the Elements
(JINA-CEE), USA  Berfin Togay  Department of Astronomy, Space Science, and
Geology, Chungnam National University, Daejeon 34134, South Korea  Dongwook
Lim Department of Astronomy, Yonsei University, Yonsei-ro, Seodaemun-gu Seoul,
03722, South Korea

###### Abstract

Chemical anomalies in planet-hosting stars (PHSs) are studied in order to
assess how the planetary nature and multiplicity affect the atmospheric
chemical abundances of their host stars. We employ APOGEE DR17 to select thin-
disk stars of the Milky Way, and cross-match them with the Kepler Input
Catalog to identify confirmed PHSs, which results in 227 PHSs with available
chemical-abundance ratios for six refractory elements. We also examine an
ensemble of stars without planet signals, which are equivalent to the selected
PHSs in terms of evolutionary stage and stellar parameters, to correct for
Galactic chemical-evolution effects, and derive the abundance gradient of
refractory elements over the condensation temperature for the PHSs. Using the
Galactic chemical-evolution corrected abundances, we found that PHSs do not
show a significant difference in abundance slope from the stars without
planets. Furthermore, we examine the depletion trends of refractory elements
of PHSs depending on total number of planets and their types, and find that
the PHSs with giant planets are more depleted in refractory elements than
those with rocky planets. Among the PHSs with rocky planets, the refractory-
depletion trends are potentially correlated with the terrestrial planets’
radii and multiplicity. In the cases of PHSs with giant planets, sub-Jovian
PHSs demonstrated more depleted refractory trends than stars hosting Jovian-
mass planets, raising questions on different planetary-formation processes for
Neptune-like and Jupiter-like planets.

Star-planet interactions (2177), Planetary system formation (1257), Chemical
abundances (224), Stellar abundances (1577), Stellar kinematics (1608), Galaxy
chemical evolution (580)

††facilities: Irénée du Pont telescope (APOGEE-2), Sloan 2.5m telescope
(APOGEE), Gaia, NASA Exoplanet Archive.††software: numpy (Harris et al.,
2020), matplotlib (Hunter, 2007), pandas (McKinney et al., 2010), scipy
(Virtanen et al., 2020), scikit-learn (Pedregosa et al., 2011), astropy
(Astropy Collaboration et al., 2013).

##  1 Introduction

A star and its planets are thought to have formed from the same molecular
cloud. The composition of a star could influence the protoplanetary disk where
planets form, and the accreting material from the protoplanetary disk onto the
host star may be chemically imprinted in the atmosphere of the star. These
interactions may result in an intricate relationship between the chemical
composition of a star and the formation and evolution of its planets. Various
approaches have been conducted to find such connections between the chemical
composition of a planet-hosting star (PHS) and its planet formation and
architecture. Notably, the amount of heavy elements in a stellar atmosphere,
often characterized by metallicity ([Fe/H]), has received attention due to its
expected implications for the occurrence and properties of planetary
companions (e.g., Gonzalez, 1997; Heiter & Luck, 2003; Santos, N. C. et al.,
2004; Fischer & Valenti, 2005; Udry & Santos, 2007; Adibekyan et al., 2012b).

Meléndez et al. (2009) first reported, based on an analysis of 11 Solar twin
stars, that the Sun’s refractory elements (Mg, Al, Si, etc.), which have
condensation temperatures ($T_{\rm C}$) over 1200 K, are relatively depleted
compared to those of the volatile elements (C, N, O, etc.). They suggested
that refractory depletion is correlated with the presence of terrestrial
planets; the material to form the rocky planet readily incorporates elements
with high $T_{\rm C}$ in the solid phase, while the low $T_{\rm C}$ volatile
elements likely remain in the gas phase. This was further supported by
Chambers (2010), who claimed that the deficit of the refractory elements in
the solar photosphere could account for roughly four Earth masses of
terrestrial material. These studies have triggered numerous efforts to
identify differences in the chemical abundances between PHSs and non-PHSs
(NPHSs) using chemical-abundance trends as a function of condensation
temperature (e.g., Ramírez et al., 2009; González Hernández et al., 2011,
2013; Adibekyan et al., 2014; Nissen, 2015; Bedell et al., 2018; Liu et al.,
2020; Nibauer et al., 2021; Tautvaišienė et al., 2022).

When investigating the chemical-abundance trends of a star, one also needs to
carefully take into account how Galactic chemical evolution (GCE) affects the
chemical-abundance pattern. Bedell et al. (2018) identified the relative
depletion of refractory elements from an analysis of 26 elements for 79 Solar
twins. At the same time, they recognized that some of the depletion trend may
be caused by GCE. They further demonstrated that the depletion trend is real,
after carefully correcting for the GCE effects in their Sun-like stars. Such
study indicates that the GCE correction is a vital step when comparing stars
with different ages but similar metallicity and temperatures (e.g., Gibson et
al., 2003; Spina et al., 2016, 2018; Pignatari et al., 2023). Other studies
(Adibekyan et al., 2014; Nissen, 2015; Spina et al., 2016) also show that a
careful selection of the comparison stars with similar stellar parameters is
crucial, due to the presence of correlations between stellar parameters and
chemical-abundance patterns before application of the GCE correction. As the
GCE correction is non trivial, in order to minimize systematic uncertainties
resulting from GCE (and adopted stellar models) several studies focused their
attention on wide binaries whose evolutionary states are nearly identical, so
that these effects are not significant for the analysis (e.g., Liu et al.,
2014; Tucci Maia et al., 2014; Ramírez et al., 2015; Saffe et al., 2015; Teske
et al., 2016; Oh et al., 2018; Liu et al., 2021; Biazzo et al., 2022).

In spite of great progress, the chemical anomalies observed in the Sun
relative to Solar twins has not been consistently confirmed as a unique
feature in other studies (e.g., Gonzalez et al., 2010; Meléndez et al., 2012;
González Hernández et al., 2013; Nissen, 2015; Liu et al., 2020; Nissen et
al., 2020; Nibauer et al., 2021). Additionally, studies that examined the
relationship between stellar-chemical anomalies and planet formation were not
successful in detecting a definitive signal of such a relationship, and
triggered more controversy (Adibekyan et al., 2014; Liu et al., 2020;
Tautvaišienė et al., 2022; Behmard et al., 2023). Nibauer et al. (2021), for
instance, found two groups of stars: chemically depleted and non-depleted
ones, by introducing a likelihood-based approach to determine elemental
abundances in Solar analog stars identified in Apache Point Observatory
Galactic Evolution Experiment Data Release 16 (APOGEE DR16; Jönsson et al.,
2020). They agreed on the refractory depletion of the Sun with Bedell et al.
(2018), arguing that the Sun is one of the stars in their refractory-depleted
group.

Similarly, Liu et al. (2020) analyzed 16 PHSs and 68 comparative NPHSs,
following the methods of Bedell et al. (2018), and found various
abundance-$T_{\rm C}$ trends among PHSs without a clear signature of the
depletion of the refractory elements for the PHSs. They suggested that a range
of possible planet-induced effects are responsible. Behmard et al. (2023)
carried out a study on the chemical dissimilarity of 12 elements between 130
known/candidate Kepler Objects of Interest (KOIs) of PHSs and so-called
doppelgängers stars, selected based on the proximity of four parameters:
effective temperature ($T_{\rm eff}$), surface gravity ($\log~{}g$), [Fe/H],
and [Mg/H] in high-resolution near-infrared spectra from APOGEE DR17
(Abdurro’uf et al. 2022). They reported that the median intrinsic dispersion
between the KOI and doppelgänger samples were consistently under 0.05 dex, and
argued that there are no noticeable signatures for different chemical-
abundance patterns associated with PHSs.

Based on the studies to date, a consensus on the connection between the
chemical properties of a PHS and its planet-formation history has yet to be
achieved, nor have any clear differences in the chemical properties between
PHSs and NPHSs been identified. This leads us to investigate how the planet
population (number of planets and their types; often referred to as the
“architecture" of a planetary system) affects the chemical-abundance patterns
of its host star, which has not been thoroughly explored previously. To
achieve this goal, we employ a large sample of stars from APOGEE DR17 with
well-determined stellar parameters and chemical abundances.

This paper is arranged as follows. In Section 2, we identify dwarfs and sub-
giants that are likely members of the Galactic thin disk, based on their
chemical and kinematic properties. We confirm the stars that are PHSs and
NPHSs by cross-matching the APOGEE sample with the Kepler Input Catalog (KIC)
and Kepler catalogs, respectively. We also identify likely twin stars within
these sub-samples. We apply GCE corrections to both sub-samples in Section 3.
Section 4 presents the abundance trends as a function of $T_{\rm C}$ for the
PHSs. In Section 5, we present the results of our detailed analysis on the
overall trends of the abundance slopes between the terrestrial planets and the
Jovian planets. In addition, we consider the dependency of chemical-abundance
depletion on the nature of the host’s planet population. We discuss the
implications of our findings regarding planet architecture, along with those
of other studies, in Section 6. A summary and conclusions are provided in
Section 7.

##  2 Data

###  2.1 Identification of Thin-disk Stars

To identify a star with planets, we first selected likely thin-disk stars of
the Milky Way (MW) of various chemical abundances, using the large
spectroscopic survey data from APOGEE DR17 (Abdurro’uf et al. 2022). APOGEE
DR17 provides high-resolution ($R\sim$ 22,500) spectra in the $H$-band across
the MW. The stellar parameters and abundance ratios for numerous chemical
elements in these spectra are delivered by the APOGEE Stellar Parameters and
Abundances Pipeline (ASPCAP; García Pérez et al. 2016).

We computed the space-velocity components and orbital parameters of the APOGEE
stars using astrometric data from Gaia Data Release 3 (Gaia DR3; Gaia
Collaboration et al. 2023) and a Stäckel-type potential, as employed in
several previous studies (e.g., Chiba & Beers, 2000; Kim et al., 2019, 2021,
2023; Lee et al., 2019, 2023; Kang et al., 2023). For these calculations, we
adopted a local standard of rest velocity ($V_{\mathrm{LSR}}=236$ km s-1;
Kawata et al. 2019), a Solar location of $R_{\odot}=8.2$ kpc and
$Z_{\odot}=20.8$ pc from Bland-Hawthorn & Gerhard (2016) and Bennett & Bovy
(2019), respectively, and a Solar peculiar motion
($U,V,W)_{\odot}=(-11.10,12.24,7.25)$ km s-1 (Schönrich et al., 2010). Among
the orbital parameters, we derived the maximum distance ($Z_{\mathrm{max}}$)
from the Galactic plane, which is often used as one of the conditions to
select disk stars. We applied the –0.017 mas systematic offset reported in
Gaia DR3 (Lindegren et al., 2021) when calculating the distances.

To select the disk-star population, we imposed the following criteria: 3100
$\leq$ $T_{\rm eff}$ $\leq$ 6500 K, $\log~{}g$ $\geq$ 3.5, [Fe/H] $>$ –1.2,
$7\leq R\leq 11$ kpc, $d$ $<$ 4 kpc, $Z_{\rm max}$ $<$ 3 kpc, signal-to-noise
ratio (S/N) $>$ 50, $V_{\rm\phi}$ $>$ 50 km s-1, $V_{\rm Z}$ $<$ 100 km s-1,
and relative parallax error less than 20%. $R$ is the distance from the
Galactic center projected onto the Galactic plane, $d$ is the heliocentric
distance, $V_{\rm\phi}$ is the rotational velocity, and $V_{\rm Z}$ is the
vertical velocity component. Then, the identification of likely thin-disk
members was conducted following the methodology of Han et al. (2020), who used
both chemical abundances ([Fe/H] and [$\alpha$/Fe]) and kinematics to derive
the membership probability of each star. Note that, in this study, we attempt
to analyze PHSs in the Galactic thin disk, because the thin-disk stars
generally do not exhibit chemical peculiarities, unlike the thick-disk and
halo stars. Additionally, we excluded in our program stars the likely accreted
stars, whose origins and natures are not similar to the canonical disk stars.
Following the chemical criteria of Belokurov & Kravtsov (2022), we identified
30,265 stars with [Fe/H] $<$ –0.4 and [Al/Fe] $<$ –0.075 as accreted objects.
These various selection criteria left us with 101,393 dwarf stars likely to
belong to the MW’s thin disk.

###  2.2 Chemical Elements

We now characterize PHSs through examination of their chemical-abundance
trends. Among the abundance ratios of 18 elements made available in APOGEE
DR17, we employed those with elemental abundances having uncertainties that
are sufficiently small to achieve the sensitivity required to detect abundance
trends as a function of $T_{\rm C}$ (Lodders, 2003) in a star; less than 0.03
dex, as demonstrated in previous studies (Adibekyan et al., 2012a; Bedell et
al., 2014; Liu et al., 2020; Nibauer et al., 2021). We chose six refractory
elements (Mg, Al, Si, Ca, Mn, and Ni) with the following conditions in mind.
First, their $T_{\rm C}$ is over 1000 K, the lowest temperature of the
refractory elements (Meléndez et al., 2009; Ramírez et al., 2009; Liu et al.,
2020). Secondly, their absolute abundance errors are less than 0.02 dex, with
no flags raised in $X$_$FE$_$FLAG$ for each element. Thirdly, they are key
elements for studying and testing planet-formation scenarios (McDonough & Sun,
1995; Wang et al., 2022). These conditions allowed us to select 47,988 stars
from our thin-disk candidate stars with well-determined abundances of Mg, Al,
Si, Ca, Mn, and Ni. We did not include the abundances for the volatile
elements, because their relatively larger abundance errors in APOGEE DR17
makes their abundance-$T_{\rm C}$ trends uncertain.

###  2.3 Planet-Hosting Stars and their Twins

####  2.3.1 Selection of Planet-Hosting Stars

We identify PHSs by cross-matching our selected thin-disk stars from APOGEE
DR17 with the KIC Data Release 10 (Brown et al. 2011) and the cumulative
catalog of KOI in NASA Exoplanet
Archive888https://exoplanetarchive.ipac.caltech.edu/. Within the catalog
provided on the NASA Exoplanet Archive website, we used the PHS data with
“koi_disposition = Confirmed” to avoid any confusion between the other stellar
and planetary signals from various sources. Furthermore, we compiled the
planetary parameters, such as the planetary radius, of the selected PHS
samples from the confirmed planet catalog (published on October 18, 2023) with
“default_flag = 1”, resulting in a sample of 283 stars hosting 423 planets.

Similarly, we selected 2,356 comparison stars by cross-matching with the
Kepler data without planetary signatures, which we take to be NPHSs, after
excluding 142 stars with candidate flags. Once again, we cross-matched our
data with the TESS Object of Interest (Guerrero et al. 2021) candidate list to
make sure of the absence of any possible planetary signals in our comparison
sample. This sample is used for selecting the twin stars of the PHSs, as
described below.

####  2.3.2 Selection of Twins for Planet-Hosting Stars

To search for chemical distinctions among PHSs, we require a sample of stars
without planets to compare with, and used to correct for GCE effects. It is
also necessary for them to be in similar evolutionary stages and metallicities
to the PHSs. However, it is extremely difficult and time-consuming to identify
the NPHSs that are exact counterparts of the PHSs. Following the work of
Nibauer et al. (2021) and Behmard et al. (2023), we employ $twins$ of the PHSs
(TPHSs), which are similar spectral types and luminosity classes to their
counterpart PHSs.

The definition of a stellar twin is diverse in the literature. In order to
demonstrate the depletion of the Sun’s refractory elements with respect to
volatile elements, Meléndez et al. (2009) considered as Solar twins the stars
with $T_{\rm eff}$, $\log~{}g$, and [Fe/H] are less than 75 K, 0.1 dex, and
0.07 dex, respectively from those of the Sun, $T_{\rm eff}$ = 5777 K,
$\log~{}g$ = 4.44, [Fe/H] = 0.0. Similarly, Ramírez et al. (2009) and Bedell
et al. (2018) adopted the criteria of $\Delta$100 K in $T_{\rm eff}$,
$\Delta$0.1 dex in $\log~{}g$, and $\Delta$0.1 dex in [Fe/H] to select Solar
twins, while Berke et al. (2023) used the condition of $\Delta$100 K in
$T_{\rm eff}$, $\Delta$0.2 dex in $\log~{}g$, and $\Delta$0.1 dex in [Fe/H].
In contrast, Liu et al. (2020) considered only effective temperature and
metallicity to increase the number of Solar analogs, while Behmard et al.
(2023) introduced [Mg/H] as an additional criterion to evaluate the
similarities among their stars.

Having reviewed the selection criteria used in previous studies, among the
NPHSs identified in Section 2.3.1, we sorted out the TPHSs by adopting the
"twin regions" of $\Delta$100 K in $T_{\rm eff}$, $\Delta$0.1 dex in
$\log~{}g$, and $\Delta$0.1 dex in [Fe/H] from the parameters of each PHS to
closely match their evolutionary states. Each PHS in our sample has, on
average, 43 TPHSs within their twin regions. We further confirmed that the
selected TPHSs have close proximity to the target PHS by enforcing the total
distance of the parameters to the minimum in a $\chi^{2}$ fashion, as employed
by Behmard et al. (2023):

$\begin{split}D^{2}&=\left(\frac{T_{\text{eff}P}-T_{\text{eff}T}}{\sqrt{\sigma_{T_{\text{eff}P}}^{2}+\sigma_{T_{\text{eff}T}}^{2}}}\right)^{2}+\left(\frac{\log
g_{P}-\log g_{T}}{\sqrt{\sigma_{\log gP}^{2}+\sigma_{\log
gT}^{2}}}\right)^{2}\\\
&+\left(\frac{[\mathrm{Fe}/\mathrm{H}]_{P}-[\mathrm{Fe}/\mathrm{H}]_{T}}{\sqrt{\sigma_{[\mathrm{Fe}/\mathrm{H}]P}^{2}+\sigma_{[\mathrm{Fe}/\mathrm{H}]T}^{2}}}\right)^{2},\end{split}$
(1)

where $P$ indicates a PHS, and $T$ is the twin of a PHS. We only used the
first 20 TPHSs with the smallest $D^{2}$ value for further analysis.

Of 283 PHSs, 40 stars have less than 20 TPHSs, with 12 TPHSs on average within
their twin regions. When relaxing the selection criteria of TPHS to include up
to 20 TPHSs for those PHSs, their stellar parameters significantly vary,
ranging from $\Delta$0.6 dex in [Fe/H] and $\Delta$1.0 dex in $\log~{}g$,
which is far from our definition of the twins. We thus excluded these 40 stars
from our analysis, leaving 243 PHSs hosting 397 planets in total.

##  3 Corrections for Galactic Chemical Evolution

Previous studies recognized that corrections for GCE are a crucial step for
accurately evaluating the abundance trend of PHSs in the abundance-$T_{\rm C}$
plane (Adibekyan et al., 2014; Spina et al., 2016; Bedell et al., 2018). GCE
refers to how chemical elements formed and were distributed in the MW (Gibson
et al., 2003; Spina et al., 2016; Pignatari et al., 2023). The formation rate
and the amount of elements created vary depending on the star-formation rate
and initial mass function. For instance, our target elements, Mg, Si, and Ca,
which are often called “alpha elements”, are mostly created during massive-
star evolution and distributed into the interstellar medium (ISM) by Type II
supernovae (SNe), while Mn and Ni (iron-peak elements) are formed during the
explosion of Type Ia SNe, an event involving relatively low-mass stars. Since
the timescales for these progenitors differ, depending on how the ISM has been
chemically enriched, a star formed out of the ISM exhibits a distinctive
chemical-abundance pattern that can vary from star-to-star according to its
age. To elucidate the chemical trend that represents the stellar-birth
environment, we need to remove the stochastic variation of chemical abundances
caused by chemical evolution. This is known as the “GCE correction.”

Stellar age is a crucial parameter for the GCE correction. In this regard,
some studies (Bedell et al., 2018; Liu et al., 2020) excluded alpha-enhanced,
old thick-disk stars from estimating GCE effects. However, we do not exclude
stars older than 10 Gyr, because our samples are selected as likely thin-disk
stars based on their chemical and kinematic properties. Moreover, we did not
find old stars whose abundances of the six refractory elements significantly
deviated from the main abundance trend of relatively younger stars, which was
the primary reason for excluding the old stars in other studies. Nonetheless,
to ensure the accuracy of our stellar ages, we eliminated the stars whose age
errors are larger than 3 Gyr in the catalog provided by Mackereth et al.
(2019). The stellar ages reported in this catalog are determined by the
astroNN 999https://github.com/henrysky/astroNN package, and it includes
asteroseismic ages from APOKASC-2 (Pinsonneault et al., 2018) and low-
metallicity asteroseismic ages (Montalbán et al., 2021). This additional age
constraint leaves us with 227 PHSs and 2344 TPHSs with well-determined ages.
We note that TPHSs are repetitively used for each PHS.

Most of previous studies corrected for GCE by subtracting the abundance trend
of each element with respect to the stellar age (Nissen, 2015, 2016; Bedell et
al., 2018; Spina et al., 2018; Liu et al., 2020; Nissen et al., 2020).
Similarly, we attempted to correct for it by following the methodology of
Spina et al. (2016) and Nissen et al. (2020). We derived a best linear fit to
each element as a function of stellar age using the 20 TPHS samples for each
PHS. We did not include PHSs when deriving the linear fit, because of the
possibility of stellar-abundance variations associated with the existence of
planets. The measured slope ($m$) and intercept ($b$) of each element were
applied to correct for GCE effects in the following manner:

$[\text{X}/\text{Fe}]_{\text{correct}}=[\text{X}/\text{Fe}]_{\text{raw}}-(m\times\text{age}+b),$
(2)

where X represents each element.

Note that, unlike the previous studies, we did not attempt to homogeneously
apply the same GCE correcting parameter ($m$, $b$) to all samples. Rather, we
calculated the GCE correction parameter for individual PHSs separately, using
the TPHSs selected for each PHS, and then applied the slope and intercept to
correct the GCE for each PHS. We believe that our GCE correction more clearly
reflects the evolution effects of PHS by using TPHSs, which have similar
atmospheric parameters with PHS within various age ranges.

For the Sun, the values of the GCE correction parameters did not change
significantly by varying the choice of the selected TPHS number from 10 to 30.
We also found that the Sun’s abundance trend against $T_{\rm C}$ was nearly
identical regardless of the selected number of TPHSs. For the PHS sample,
however, we found that the abundances of Al and Mn after GCE correction change
significantly when we decrease the TPHS number from 20 to 10, but not when it
was increased from 20 to 30 TPHSs for each PHS. This is the main reason for
choosing 20 TPHS. We corrected the GCE effect for each TPHS in the same way as
well, using the selected TPHSs of each PHS.

Figure 1: The Sun’s GCE-corrected abundance trend as a function of $T_{\rm
C}$. Each dot represents the six elements (Mn, Si, Mg, Ni, Ca, and Al in order
of $T_{\rm C}$) placed at corresponding $T_{\rm C}$, with error bars
indicating the 1$\sigma$ of abundance value measured by 1000 random
resamplings of the TPHSs, while correcting for GCE effects. The black-dotted
line is the best-fit line, with the blue-shaded region displaying the
1$\sigma$ of the slopes. The derived slope, intercept, and their 1$\sigma$
values are indicated in the legend. Figure 2: Distributions of the
abundance-$T_{\rm C}$ slopes for our PHSs (orange) and TPHSs (blue). The left
panel represents the results before the GCE correction, while the right panel
is after the GCE correction. The smoothed distribution is a kernel density
estimation (KDE). The median slope and 1$\sigma$ value for each group are
denoted in each panel. The red and black dashed vertical lines are the Solar
slope and zero point, respectively. The distribution is normalized to the
total number of stars in each group.

##  4 Derivation of the Abundance-$T_{\rm C}$ Slope

We employed the method of the abundance gradient over $T_{\rm C}$, which is
the most widely used one to identify the chemical depletion or enhancement in
a star. We have learned from previous studies that the accuracy of the
chemical abundances of the PHSs plays a pivotal role in drawing a robust
abundance slope over $T_{\rm C}$. At the same time, it is imperative that the
comparison sample (TPHSs in our case) accurately reflects the evolutionary
stage of their counterparts as closely as possible. To robustly detect the
variation of the abundance ratios, we made use of high-$T_{\rm C}$ refractory
elements with the most reliable abundance determinations, as reported in
Jönsson et al. (2020). These are Mg, Al, Si, Ca, Mn, and Ni. We did not
include volatile elements with $T_{\rm C}$ under 900 K, because they fall
outside the steepest portion of the depletion trend (Meléndez et al., 2009;
Chambers, 2010; Bedell et al., 2018).

Figure 1 shows an example of the derived abundance trend as a function of
$T_{\rm C}$. The figure shows the abundance slope of refractory elements of
the Sun after the GCE correction. Each dot represents the six elements (Mn,
Si, Mg, Ni, Ca, and Al in order of $T_{\rm C}$) placed at their corresponding
$T_{\rm C}$; error bars were calculated from 1000 random resamplings of the
Sun’s twins while correcting for GCE. The dotted line is the abundance
gradient derived from linear fit to the 6 elemental abundances. The blue-
shaded region shows the 1$\sigma$ variation of the slope values, and the
figure clearly indicates that the Sun is deficient with the refractory
elements after the GCE correction.

Other studies also reported the depletion of refractory elements in the Sun.
For instance, Bedell et al. (2018) analyzed 79 Solar twins to find evidence of
the depletion of 26 elements in the Sun after the GCE correction. Similarly,
Liu et al. (2020) demonstrated that the Sun’s refractory elements are
relatively depleted compared to its analog stars. Nibauer et al. (2021)
successfully reproduced the results of Bedell et al. (2018) using only five
refractory elements from APOGEE DR16 (Jönsson et al., 2020), supporting the
depletion argument.

Using six refractory elements from APOGEE DR17, we reach the same conclusion.
Note that our approach is somewhat different from the previous studies, in
that our abundance slope is not derived from the star-to-star abundance
differences between the PHSs and NPHSs, as done in most of the other studies
(Meléndez et al., 2009; Bedell et al., 2018; Liu et al., 2020; Nibauer et al.,
2021; Tautvaišienė et al., 2022). Instead, the derived slope value represents
the trends of the Sun’s abundance values after correction of the chemical
evolution of the MW.

##  5 Results

###  5.1 Distribution of Abundance-$T_{\rm C}$ Slopes

The primary reasons for the depletion of the Sun’s refractory elements are
still under discussion. Meléndez et al. (2009) argued that this depletion
arose due to the presence of rocky planets such as Earth. However, other
studies (González Hernández et al., 2013; Liu et al., 2020; Mishenina et al.,
2021) failed to find evidence to support this hypothesis, even with much
higher-quality abundance analyses for limited samples. Extending the idea to
other planetary systems, some studies reported a weak correlation between
planetary mass and stellar chemical abundance (Mishenina et al., 2021;
Tautvaišienė et al., 2022), while others using large survey data concluded
that there is no clear sign of the correlation resulting from the existence of
planets (Nibauer et al., 2021; Behmard et al., 2023).

Based on our much larger sample of PHSs and TPHSs, we have investigated these
issues by comparing the abundance-$T_{\rm C}$ slopes of PHSs with those of the
TPHSs (stars without planetary detections), as shown in Figure 2. The
abundance-$T_{\rm C}$ slopes of TPHSs are measured in the same manner as for
the PHSs, using 20 TPHSs for each TPHS. In the figure, the orange lines
represent the distribution of the PHSs and the blue lines are for the TPHSs.
The left panel is before the GCE correction, while the right panel is after
the GCE correction.

Comparison of the two panels in Figure 2 reveals that the GCE-corrected
samples exhibit a consistently greater fraction of negative slopes, indicating
that the GCE correction is an important step to apply when examining any
abundance depletion or enhancement. Inspection of the right panel suggests
that the PHSs do not exhibit a significant difference in the distribution of
slopes from the TPHSs, although we observe a small enhancement of relative
numbers of stars around the slope of –2.0$\times 10^{-4}$ dex K-1 for the
PHSs, which was not observed before the GCE correction. We conclude that the
existence of planetary systems does not strongly influence the chemical
properties of their host stars, as pointed out by previous studies. To
quantitatively evaluate the significance of the difference in the
distributions, we carried out a Kolmogorov–Smirnov (KS) two-sample test under
the null hypothesis that the two groups of stars share the same parent
chemical properties. From the distribution with the GCE correction (right
panel), we obtained a $p$-value of 0.1, implying that we cannot rule out the
null hypothesis completely. We have thus focused on the existence of any
chemical discrepancies among the PHSs with different planet populations and
architectures.

Figure 3: Distributions of the abundance-$T_{\rm C}$ slopes for two sub-groups
of stars, after application for GCE effects, divided by the mean radius
($R_{\rm M}$) of the planetary system for each PHS. The blue histogram
represents for PHSs with $R_{\rm M}$ $<$ 3 $R_{\oplus}$, while the orange one
applies to PHSs with $R_{\rm M}$ $\geq$ 3 $R_{\oplus}$. See Section 5.2 for
details of the choice of 3 $R_{\oplus}$ as the dividing line. The smoothed
distribution is a KDE. The median slope value for each sub-group is denoted in
the legend. The red-dashed vertical line is the Solar slope. The distributions
are normalized by the total number of stars in each sub-group.

###  5.2 Terrestrial Versus Jovian Planets

Before exploring how the different types of planets affect the chemical
characteristics of their host stars, we need to distinguish the terrestrial
planets from the Jovian planets by considering their observables such as mass
and radius. Most recent studies, such as Mishenina et al. (2021) and
Tautvaišienė et al. (2022), attempted to correlate the planetary system
properties with the chemical composition of their host stars by the use of the
planetary mass. Out of the 338 planets in our sample, only 80 have known mass
information, while the radius information is available for 323 planets,
determined by transit observations. Since more planets provide more robust
statistics, we decided to use the planetary-radius information to distinguish
the terrestrial from the Jovian planets, and examine any connection to the
abundance patterns of their host stars. We used a total of 216 PHSs with known
planets and their radii.

No super-Earth located at larger than 3 $R_{\oplus}$ has been found to date,
and according to the planetary orbital period-radius diagram, the Neptune
desert spans from 2 to 10 $R_{\oplus}$ with an orbital period of less than 10
days. Referring to these two observational constraints, we decided to set the
distinguishing criterion at 3 $R_{\oplus}$ between rocky and gas giant
planets. If the mean radius ($R_{\rm M}$) of all known planets in a planetary
system is less than 3 $R_{\oplus}$, we assume that the system is dominated by
terrestrial planets, and by gas giants for $R_{\rm M}$ $\geq$ 3 $R_{\oplus}$.
It should be noted that our dividing condition for the types of planets is not
an absolute standard, and is subject to change as more diverse planetary
systems are discovered in different environments. Our sample comprises 155
single planetary systems and 61 multiple planetary systems.

To gain a deeper understanding of how the formation of different types of
planets (e.g., rocky versus gaseous) influences the chemistry of their host
stars, once again we derived the abundance slope of the refractory elements
over $T_{\rm C}$ for the sub-groups of PHSs with terrestrial or Jovian
planetary systems. Figure 3 presents these distributions. The blue histogram
represents the terrestrial planets with $R_{\rm M}$ $<$ 3 $R_{\oplus}$, while
the orange histogram is for the Jovian planets with $R_{\rm M}$ $\geq$ 3
$R_{\oplus}$. The red-dashed vertical line is the Solar slope.

Figure 4: Elemental-abundance slopes as a function of the total radius of a
planetary system; $R_{\rm tot}$ is the sum of the radii of all planets that
belong to a star. Our full PHS sample (top panel) is divided into terrestrial
(middle panel) and giant planets (bottom panel) by the mean radius of 3
$R_{\oplus}$ of each planetary system. The color code indicates the total
number of planets in each PHS. The magenta symbols represent the median values
of slopes grouped by 3 $R_{\oplus}$. Each bin is overlapped with the
neighboring bin by 1.5 $R_{\oplus}$, and the error bar is the standard
deviation in each bin. Note that the right-most bin includes all points larger
than the bin value. The square in the top and bottom panels denote the Sun’s
slope. The typical error bar of each slope is indicated in the lower-right
corner in each panel. Figure 5: Left panel: distribution of the abundance
slopes for the selected terrestrial planets. The planetary systems are further
divided into two sub-groups: one with one or two planets (blue lines) and the
other with more than two planets (orange lines). The distributions are
normalized by the total number of PHSs in each category. Curved lines
represent the KDE of each sub-group. The median slope for each sub-group is
listed in the legend. The PHSs with larger numbers of planets are shifted
toward more negative slopes. Right panel: same as in the left panel, but for
the sub-Jovian (blue lines) and Jovian (orange lines) sub-groups. We
considered the systems with $R_{\rm M}$ $<$ $5~{}R_{\oplus}$ as sub-Jovian,
while the one with $R_{\rm M}$ $\geq 5~{}R_{\oplus}$ as Jovian.

One interesting aspect of Figure 3 is that the peak and overall shape of the
larger mean-radius sub-group is shifted to more negative slope values compared
with those of the smaller mean-radius sub-group. The median value of the
smaller-radius sub-group is also twice as high as the larger-radius sub-group.
This implies that the sub-group dominated by giant planets exhibits slightly
more chemical depletion than that dominated by terrestrial planets.
Intriguingly, the peak of the Jovian sub-group distribution is closer to the
Solar slope than that of the terrestrial sub-group. Note that, according to
our definition, our Solar System falls into the category of the Jovian-
dominated sub-group.

To further examine possible connections of the planet number and type with the
chemical characteristics of their host stars, we consider the slope
distributions as a function of the total radius ($R_{\rm tot}$) of the planets
for each PHS, as shown in Figure 4. $R_{\rm tot}$ is the sum of the radii of
all planets that belong to a star. The top panel is the full PHS sample, while
the middle and bottom panels are for the systems dominated by terrestrial and
giant planets, respectively, following the same division as in Figure 3. The
color code represents the number of planets in each system. The magenta
symbols are the median value of the slopes in a bin of 3 $R_{\oplus}$
overlapped 50% with the neighboring bin, and the error bar of each PHS is the
standard deviation in each bin. The typical error bar of each slope is denoted
at the bottom right corner of each panel. As the Sun belongs to the Jovian-
dominant sub-group in our definition, the Solar slope appears in the bottom
panel.

Inspection of Figure 4 reveals the following features. First, we see that most
of the PHSs are dominated by a single-planet system. The top plot exhibits a
tendency for having more negative slopes for $R_{\rm tot}>5$ $R_{\oplus}$,
with more planets, indicating a greater depletion of the refractory elements.
These trends can be read off from the middle and bottom panels. The middle
panel implies that, the more rocky planets a PHS has, the more depletion of
the refractory elements has taken place. In other words, the depletion trend
becomes stronger as the total radius and the number of planets increase. The
bottom plot also shows a small, but relatively consistent negative slope, and
this tendency becomes even stronger for $R_{\rm tot}>15$ $R_{\oplus}$ and for
more planets. However, the sample size of the giant sub-group is much smaller
than that of the terrestrial sub-group, which may suffer from small number
statistics. We discuss in depth the significance and implications of these
findings in section 6.3.

Figure 6: Abundance-$T_{\rm C}$ slopes of the PHS sample, corrected for GCE
effects, as functions of the stellar parameters: age (upper left), effective
temperature (upper right), surface gravity (lower left), and metallicity
(lower right). The error bar on each star is calculated from 1000 random
resamplings of the TPHSs for each PHS, when correcting for GCE. The red line
in each panel is the linear fit to the distribution, while the black line
comes from the PHSs without the GCE correction. The derived slope and its
error are denoted at the top of each panel.

###  5.3 Number of Planets and their Type

Figures 3 and 4 indicate that the number and type of planets may be related to
the general chemical properties of their host stars. We investigate this
possibility more closely in Figure 5. We divided the terrestrial group into
two sub-groups by the number of planets ($N_{\rm P}$) and the gas-giant group
according to their type. The left panel of Figure 5 represents the terrestrial
group. The blue histogram is for $N_{\rm P}$ $\leq$ 2, while the orange
histogram is for $N_{\rm P}$ $>$ 2\. The smoothed curves are the KDE of each
histogram. We notice that there is a tendency for the host stars having more
rocky planets to be more deficient in their refractory elements, as they
exhibit more negative slopes. The median value of the slopes of the systems
with $N_{\rm P}$ $\leq$ 2 is five times smaller than the systems with $N_{\rm
P}$ $>$ 2\. Overall, the fraction of PHSs with the negative slopes is 56.8$\%$
for $N_{\rm P}$ $\leq$ 2, but 85.7$\%$ for $N_{\rm P}$ $>$ 2\. These fractions
indicate a greater depletion of the refractory elements for a star with more
rocky planets.

The right panel of Figure 5 shows the slope distribution of the PHSs with the
sub-Jovian (blue lines) and Jovian planets (orange lines). The division line
for these two sub-groups is the mean radius of 5 $R_{\oplus}$: sub-Jovian for
$R_{\rm M}$ $<$ 5 $R_{\oplus}$, Jovian for $R_{\rm M}$ $\geq$ 5 $R_{\oplus}$.
The plot clearly illustrates that the peaks between the two sub-groups and the
overall fraction of the PHSs with negative slopes differ significantly. The
sub-Jovian sub-group has more negative slopes, demonstrating a stronger
depletion of the refractory elements than for the Jovian sub-group. This
suggests that the PHSs with smaller gas giants are expected to be more
depleted in the refractory elements than the ones with the larger gas giants.
We obtained consistent results even if we decreased the mean planet radius to
$R_{\rm M}$ = 2 $R_{\oplus}$ to divide the sub-groups, which is frequently
used as a threshold for dividing the terrestrial planets. Our conclusion from
Figures 4 and 5 is that the number and type of the planets can influence the
chemical properties of their host stars. However, we also note that the sample
size of the sub-groups is not sufficiently large provide a strong conclusion
(See section 6.3).

##  6 Discussion

###  6.1 Correlation between Stellar Parameters and Abundance-$T_{\rm C}$
Slopes

It remains possible that the different behaviors seen in the abundance-$T_{\rm
C}$ slopes between the terrestrial and giant planets may be caused by
different spectral and luminosity classes of their host stars, as well as
their age and metallicity. Previous studies were also concerned whether or not
the magnitude and the sign of the abundance gradient with $T_{\rm C}$ depend
on stellar parameters. For instance, Ramírez et al. (2009) reported that the
abundance gradients with $T_{\rm C}$ measured by the refractory elements with
$T_{\rm C}$ $>$ 900 K exhibited correlations with surface gravity and
metallicity, but not with effective temperature. In addition, Adibekyan et al.
(2014) demonstrated that the abundance trend, regardless of the presence of
the planet, had a strongly negative correlation with surface gravity and a
positive correlation with stellar age. On the other hand, González Hernández
et al. (2013), using 25 elements, starting from carbon with $T_{\rm C}$ = 40
K, could not find any correlation of their abundance slopes with the stellar
temperature and metallicity. Similarly, Liu et al. (2020) claimed that there
is no significant correlation between the abundance slopes of PHSs and stellar
age, metallicity, or temperature with a 3$\sigma$ confidence, while the NPHSs
have a large scatter with the three parameters.

The present lack of consensus requires us to carefully examine possible
correlations between the stellar parameters and the abundance slope in our
program stars. Figure 6 shows the derived slopes of the PHSs as functions of
age (upper left), effective temperature (upper right), surface gravity (lower
left), and metallicity (lower right). The red line in each panel is the linear
fit to the PHSs distribution after the GCE correction, while the black line is
the fit to these stars without the GCE correction. The error bar for each PHS
is calculated from 1000 random resamplings of TPHSs, as in Figure 1. These
plots clearly exhibit no significant trends of the abundance slopes against
the various stellar parameters, after applying the GCE correction. This figure
demonstrates that the disparate patterns found in the abundance slopes for the
stars dominated by rocky and gas giant planets do not arise from different
evolution stages, chemistry, or age of the host stars.

However, the abundance-$T_{\rm C}$ slopes of our uncorrected PHSs do exhibit
negative correlations with respect to surface gravity and metallicity, and a
positive correlation with effective temperature, similar to other studies that
did not correct for GCE (e.g., Ramírez et al., 2009; Adibekyan et al., 2014).
This once more highlights the importance of the correction of the GCE when it
comes to deriving the abundance slopes. The main reason for the lack of the
correlation between the abundance-$T_{\rm C}$ slope and stellar parameters may
stem from the fact that, unlike previous papers applying the same GCE
correction to all the samples, we selected the TPHSs sharing the same
evolutionary states with each PHS to correct for the effects of GCE. It
appears that our approach has removed any clear correlations with stellar
parameters.

###  6.2 Correlation of Chemical Depletion with the Presence of Planets

We have found that the Sun exhibits a negative abundance-$T_{\rm C}$ slope of
refractory elements after correcting for GCE, using twin stars in similar
evolutionary states. This implies that some of the refractory elements are
depleted, as reported in other previous studies (e.g., Meléndez et al., 2009;
Bedell et al., 2018).

Our PHSs indicate a slightly lower abundance of refractory elements compared
to their counterparts of TPHSs, although most of the abundance-$T_{\rm C}$
slope values of PHSs agree well with the previous results of Meléndez et al.
(2009); Bedell et al. (2018); Nibauer et al. (2021), on the order of
4$\times~{}10^{-4}$ dex K-1. However, we recall that a K-S two-sample test
cannot reject the null hypothesis that the PHS and TPHSs abundance slopes are
drawn from the same population, as shown in Figure 2. This argument is in line
with other studies claiming very weak or no correlation between the presence
of the planets and chemical anomalies of their host stars.

As illustrated in Figures 3, 4, and 5, all terrestrial PHSs do not show
refractory-element depletion; rather, some of them exhibit an enhancement of
refractory elements. Some studies (e.g., Liu et al., 2020) attempted to
explain the enhancement of the heavy elements as due to the engulfment of
planets. That is, planetary bodies could be engulfed by their host star during
its red giant phase, contributing to the higher abundance trends (Pinsonneault
et al., 2001; Saffe et al., 2017; O’Connor et al., 2023; Xie et al., 2023).
However, our sample of PHSs selected from APOGEE DR17 primarily consist of
dwarf stars and sub-giants whose evolutionary stage is too early to engulf
their planets. The case of the positive slopes (or the abundance enhancements)
requires more investigation.

We find that our PHSs have two unique chemical features associated with their
planet populations: (1) The more rocky planets a star has, the greater the
depletion of refractory elements in its host, and (2) the greater the total
number of planets a star has, the more depletion of refractory elements in its
host (see Figure 4). Only a few studies have attempted to explore these
aspects, probably due to the limited sample size of the high-resolution
spectroscopic data (Ramírez et al., 2009; González Hernández et al., 2013;
Nissen, 2015; Bedell et al., 2018; Mishenina et al., 2021) and the different
sample-selection criteria with limited planet information (Liu et al., 2020;
Tautvaišienė et al., 2022). For instance, by analyzing 24 elements from 740
bright slow-rotating stars, including 25 PHSs, Tautvaišienė et al. (2022)
claimed that the metallicity of the dwarf stars hosting low-mass planets is
usually high, while those with high-mass planets exhibit a greater diversity.
Still, to clarify the chemical effects of the planet on the host star,
additional studies with larger numbers of samples are needed.

###  6.3 The Impact of Planets on Chemical Anomalies of their Host Stars

As described above, the depletion level of the refractory elements for our
PHSs is correlated with their planet population. This provides us with an
opportunity to relate their behavior to the suggested planet-formation
scenarios. Following the rocky-planet argument of Meléndez et al. (2009), 60 %
of our samples with negative abundance slope should be depleted with
refractory elements, implying the presence of rocky planets. However, because
all of our PHSs do not possess rocky planets, but some of them also include
giant planets, the terrestrial planets alone cannot explain the
abundance-$T_{\rm C}$ slope distribution; we need the giant planets to explain
the abundance-slope distributions as well. Booth & Owen (2020) showed that the
pressure gap generated by forming giant planets can prevent refractory
material from accreting onto their host stars. This scenario may explain the
negative slope of the PHSs with large total-radius planets. It follows that
our findings are likely to be explained by the rocky-planet theory of Meléndez
et al. (2009) and the giant-planet hypothesis by Booth & Owen (2020).

Figure 5 shows a very interesting aspect of this problem, that the sub-Jovian
population exhibits more negative abundance slopes than that of the Jovian
population. According to the work by Hühn & Bitsch (2023), the opening gap of
a protoplanetary disk from planetary formation hinders the accretion of heavy
elements to the host star, leaving room for an example of a wide-binary model
that explains the difference in the element-abundance ratios of each star,
depending on the formation position of its giant gas planets. This model may
explain the reason for the lower median abundance slope of the giant planets
compared with that of the terrestrial planets seen in Figures 3 and 5. Thus,
this may raise various questions about the planetary-formation process of
Neptune-like and Jupiter-like planets.

Our present findings cannot be solely explained by current planet-formation
theories. The difference in the abundances of the refractory elements between
PHSs and TPHSs and the wide range of the abundance slopes may require us to
take into account a variety of planet-induced effects as well. Liu et al.
(2020) pointed to planet-induced effects, such as the sequestration of rocky
material (depleted with refractory elements) and the engulfment of planets
(enhanced with refractory elements) (Pinsonneault et al., 2001; Saffe et al.,
2017; Booth & Owen, 2020) for the diverse abundance trends in the PHSs. These
are related to the timescale, accretion efficiency of matter, and occurrence
rate of the planet formation or protoplanetary-disk chemical evolution
(Johansen et al., 2009; Hühn & Bitsch, 2023). These effects could potentially
affect the chemical composition of the PHSs seen in this study.

One of the planet-induced effects to consider to explain the diverse
abundance-$T_{\rm C}$ slopes among our PHSs is the planet-occurrence rate.
Even though it is actively debated at present (Hsu et al., 2019), it has been
reported to be as high as 1.0 (Zink et al., 2020). Microlensing studies (e.g.,
Cassan et al., 2012) also report a high probability for a given star to have a
planet. These observational results suggest that most stars host planets that
have not yet been discovered. Detecting the presence of planets by transit
studies makes it difficult to discover long-period planets due to their weak
signals and observational limitations. Consequently, we cannot rule out that
our selected PHSs may contain more undetected planets. In turn, a high planet-
occurrence rate greatly complicates the identification of abundance
differences among PHSs with different types of stars. Although it is unclear
how much the existence of undiscovered planets influences our analysis, it is
certain that, depending on the type and number of undetected planets among our
PHSs, our results are subject to change.

##  7 Summary and Conclusions

We have analyzed a sample of PHSs selected from APOGEE DR17 to search for
chemical differences compared to the TPHSs without planets. We found very weak
evidence that the PHSs are more depleted with refractory elements than the
TPHSs. However, we demonstrated that the amount of material contributed to
planetary formation can result in the depletion of refractory elements in
their host stars. Overall, the PHSs with giant planets are more depleted with
heavy elements than the ones with rocky planets. Among the PHSs with rocky
planets, the more rocky planets a star has, the more depletion of the
refractory elements a host star exhibits. Interestingly, the sub-Jovian
hosting stars exhibit more chemical depletion than the Jovian hosting stars.
This may raise various questions about the planetary-formation process of
Neptune-like and Jupiter-like planets.

Our study indicates that the wide range of observed abundance-$T_{\rm C}$
slopes for PHSs cannot be explained solely by present planet-formation
scenarios; we also need to understand how planet-induced effects affect the
characterization of the PHSs. Our understanding of the relationship between
the elemental-abundance patterns of host stars and the formation of planets is
still far from complete, and many complexities remain to be unraveled.
Observations with the James Webb Space Telescope (Gardner et al., 2006) should
help clarify the relationship(s) between planet formation and the chemistry of
host stars, with its capability to stack enormous direct infrared images of
planetary systems, and test protoplanetary disk-formation theories around host
stars in various stages of evolution.

Y.S.L. acknowledges support from the National Research Foundation (NRF) of
Korea grant funded by the Ministry of Science and ICT (NRF-2021R1A2C1008679).
Y.S.L. also gratefully acknowledges partial support for his visit to the
University of Notre Dame from OISE-1927130: The International Research Network
for Nuclear Astrophysics (IReNA), awarded by the US National Science
Foundation. T.C.B. acknowledges partial support for this work from grant PHY
14-30152; Physics Frontier Center/JINA Center for the Evolution of the
Elements (JINA-CEE), and OISE-1927130: The International Research Network for
Nuclear Astrophysics (IReNA), awarded by the US National Science Foundation.
D.L. acknowledges support from the National Research Foundation of Korea to
the Center for Galaxy Evolution Research (2022R1A6A1A03053472). Y.K.K.
acknowledges support from Basic Science Research Program through the NRF of
Korea funded by the Ministry of Education (NRF-2021R1A6A3A01086446).

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.
Sloan Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions.

SDSS-IV acknowledges support and resources from the Center for High Performance Computing at the University of Utah. The SDSS website is www.sdss4.org. SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, Center for Astrophysics | Harvard & Smithsonian, the Chilean Participation Group, the French Participation Group, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU) / University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional / MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

This research has made use of the NASA Exoplanet Archive, which is operated by
the California Institute of Technology, under contract with the National
Aeronautics and Space Administration under the Exoplanet Exploration Program.

This work presents results from the European Space Agency (ESA) space mission
Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis
Consortium (DPAC). Funding for the DPAC is provided by national institutions,
in particular the institutions participating in the Gaia MultiLateral
Agreement (MLA). The Gaia mission website is https://www.cosmos.esa.int/gaia.
The Gaia archive website is https://archives.esac.esa.int/gaia.

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Table 12: List of xP3 datasets [Muennighoff et al., 2023c]. Dataset |  #Langs |  Dataset Language |  $\bar{L}_{prompt}$ |  $\bar{L}_{compl.}$ |  License |  Task
---|---|---|---|---|---|---
adversarial_qa dbert [Bartolo et al., 2020; maxbartolo, 2023a] |  1 |  eng |  655 |  263 |  CC BY-SA 3.0 |  Question Answering
adversarial_qa dbidaf [Bartolo et al., 2020; maxbartolo, 2023b] |  1 |  eng |  669 |  256 |  CC BY-SA 4.0 |  Question Answering
adversarial_qa droberta [Bartolo et al., 2020; maxbartolo, 2023c] |  1 |  eng |  742 |  243 |  CC BY-SA 4.0 |  Question Answering
ag_news [Gulli, 2005; jxmorris12 et al., 2023] |  1 |  eng |  292 |  40 |  BSD-3-Clause |  Text Classification
ai2_arc ARC-Challenge [Clark et al., 2018] |  1 |  eng |  351 |  33 |  GPL-3 |  Question Answering
ai2_arc ARC-Easy [Clark et al., 2018] |  1 |  eng |  307 |  26 |  GPL-3 |  Question Answering
amazon_polarity [Zhang et al., 2015] |  1 |  eng |  454 |  83 |  BSD-3-Clause |  Sentiment Analysis
app_reviews [Grano et al., 2017] |  1 |  eng |  159 |  28 |  Unknown |  Sentiment Analysis
clue c3 [Xu et al., 2020] |  1 |  zho |  338 |  7 |  Apache 2.0 |  Question Answering
clue cmrc2018 [Cui et al., 2019] |  1 |  zho |  426 |  178 |  CC BY-SA 4.0 |  Question Answering
clue csl [Li et al., 2022] |  1 |  zho |  315 |  64 |  Apache 2.0 |  Question Answering
clue drcd [Shao et al., 2019] |  1 |  zho |  436 |  128 |  CC BY-SA 3.0 |  Question Answering
clue tnews [Xu et al., 2020] |  1 |  zho |  235 |  7 |  Apache 2.0 |  Question Answering
cnn_dailymail_3.0.0 [Nallapati et al., 2016] |  1 |  eng |  1699 |  646 |  Unknown |  Summarization
common_gen [Lin et al., 2020] |  1 |  eng |  96 |  49 |  MIT |  Generation
cos_e_v1.11 [Rajani et al., 2019] |  1 |  eng |  208 |  19 |  BSD-3-Clause |  Generation
cosmos_qa [Huang et al., 2019] |  1 |  eng |  547 |  51 |  Unknown |  Question Answering
dbpedia_14 [Lehmann et al., 2014] |  1 |  eng |  378 |  64 |  Apache 2.0 |  Topic Classification
dream [Gu et al., 2022] |  1 |  eng |  511 |  152 |  Apache 2.0 |  Question Answering
duorc ParaphraseRC [Saha et al., 2018] |  1 |  eng |  1438 |  663 |  MIT |  Question Answering
duorc SelfRC [Saha et al., 2018] |  1 |  eng |  1411 |  645 |  MIT |  Question Answering
GEM/BiSECT [Kim et al., 2021] |  3 |  eng, spa, fra |  346 |  251 |  Unknown |  Text Simplification
GEM/xlsum [Hasan et al., 2021] |  2 |  eng, ben |  1156 |  636 |  CC BY-NC-SA 4.0 |  Summarization
gigaword [Rush et al., 2015; Graff et al., 2003] |  1 |  eng |  181 |  80 |  Unknown |  Summarization
glue mrpc [Warstadt et al., 2018; Wang et al., 2018; Dolan & Brockett, 2005] |  1 |  eng |  270 |  38 |  MIT |  Text Classification
glue qqp [Warstadt et al., 2018; Wang et al., 2018; Iyer et al., 2012] |  1 |  eng |  199 |  4 |  Unknown |  Text Classification
imdb [Maas et al., 2011] |  1 |  eng |  1089 |  106 |  Unknown |  Sentiment Analysis
tydiqa-goldp [Clark et al., 2020] |  6 |  arb, ben, eng, ind, swh, tel |  526 |  115 |  Apache 2.0 |  Question Answering
tydiqa-primary [Clark et al., 2020] |  6 |  arb, ben, eng, ind, swa, tel |  1110 |  332 |  Apache 2.0 |  Question Answering
kilt_tasks hotpotqa [Petroni et al., 2021] |  1 |  eng |  137 |  15 |  MIT |  Question Answering
multi_news [Fabbri et al., 2019] |  1 |  eng |  3466 |  1442 |  Custom license |  Summarization
openbookqa main [Mihaylov et al., 2018] |  1 |  eng |  163 |  16 |  Apache 2.0 |  Question Answering
xlwic xlwic [Raganato et al., 2020] |  1 |  eng |  225 |  3 |  CC BY-NC 4.0 |  Text Classification
paws labeled_final [Zhang et al., 2019] |  1 |  eng |  285 |  12 |  Custom license |  Paraphrase Identification
paws-x [Yang et al., 2019] |  4 |  eng, spa, fra, zho |  255 |  11 |  Custom license |  Paraphrase Identification
piqa [Bisk et al., 2020] |  1 |  eng |  256 |  72 |  AFL 3.0 |  Question Answering
qasc [Khot et al., 2020] |  1 |  eng |  314 |  38 |  Apache 2.0 |  Question Answering
quail [Rogers et al., 2020] |  1 |  eng |  1752 |  18 |  CC BY-NC-SA 4.0 |  Question Answering
quarel [Tafjord et al., 2019a] |  1 |  eng |  289 |  10 |  CC BY 4.0 |  Question Answering
quartz [Tafjord et al., 2019b] |  1 |  eng |  307 |  9 |  CC BY 4.0 |  Question Answering
quoref [Dasigi et al., 2019] |  1 |  eng |  1556 |  388 |  CC BY 4.0 |  Question Answering
race high [Lai et al., 2017] |  1 |  eng |  1723 |  229 |  Custom license |  Question Answering
race middle [Lai et al., 2017] |  1 |  eng |  1141 |  144 |  Custom license |  Question Answering
ropes [Lin et al., 2019] |  1 |  eng |  886 |  97 |  CC BY 4.0 |  Question Answering
rotten_tomatoes [Pang & Lee, 2005] |  1 |  eng |  152 |  18 |  Unknown |  Sentiment Analysis
samsum [Gliwa et al., 2019] |  1 |  eng |  473 |  170 |  CC BY-NC-ND 4.0 |  Summarization
sciq [Welbl et al., 2017] |  1 |  eng |  346 |  139 |  CC BY-NC 3.0 |  Question Answering
social_i_qa [Sap et al., 2019] |  1 |  eng |  182 |  15 |  CC BY 4.0 |  Question Answering
squad_v2 [Rajpurkar et al., 2016] |  1 |  eng |  689 |  82 |  CC BY-SA 4.0 |  Question Answering
super_glue boolq [Clark et al., 2019; Wang et al., 2019] |  1 |  eng |  653 |  76 |  CC BY-SA 3.0 |  Question Answering
super_glue multirc [Khashabi et al., 2018] |  1 |  eng |  1509 |  120 |  Custom license |  Question Answering
super_glue record [Zhang et al., 2018a] |  1 |  eng |  1175 |  70 |  Apache 2.0 |  Question Answering
super_glue wic [Pilehvar & Camacho-Collados, 2019] |  1 |  eng |  170 |  3 |  CC BY-NC 4.0 |  Text Classification
trec [Li & Roth, 2002; Hovy et al., 2001] |  1 |  eng |  144 |  9 |  Unknown |  Text Classification
trivia_qa unfiltered [Joshi et al., 2017] |  1 |  eng |  148 |  92 |  Unknown |  Question Answering
web_questions [Berant et al., 2013] |  1 |  eng |  70 |  17 |  Unknown |  Question Answering
wiki_bio [Lebret et al., 2016] |  1 |  eng |  586 |  328 |  CC BY-SA 3.0 |  Generation
wiki_hop original [Tu et al., 2019] |  1 |  eng |  6363 |  748 |  CC BY-SA 3.0 |  Question Answering
wiki_qa [Yang et al., 2015] |  1 |  eng |  224 |  26 |  Custom license |  Question Answering
wiqa [Tandon et al., 2019] |  1 |  eng |  408 |  44 |  Apache-2.0 |  Question Answering
xquad [Artetxe et al., 2019] |  2 |  zho, vie |  652 |  173 |  CC BY-SA 4.0 |  Question Answering
xsum [Narayan et al., 2018] |  1 |  eng |  1412 |  250 |  MIT |  Summarization
yelp_review_full [Zhang et al., 2015] |  1 |  eng |  620 |  91 |  Custom license |  Sentiment Analysis
|  |  |  |  |  |

##  Appendix J Data Cards

Following Pushkarna et al. [2022] and the HuggingFace data card
template191919https://huggingface.co/docs/datasets/v2.15.0/en/dataset_card, we
present the data card for the Dataset.

The Dataset is a multilingual instruction fine-tuning dataset curated by an
open-science community. The dataset contains a total of 204,114 annotated
prompt-completion pairs. • Curated by: 2,007 contributors from 110 countries •
Language(s): 65 languages • License: Apache 2.0 • Repository:
https://huggingface.co/datasets/CohereForAI/aya_dataset Authorship

Publishing Organization:
Cohere For AI Industry Type:
Not-for-profit - Tech Contact Details:
https://aya.for.ai/

Example of Data Points The dataset contains multilingual prompts and
completions in the following format: {prompt: "What day is followed by
Saturday?", completion : "Saturday is followed by Sunday.", language:
"English" }  Motivations & Intentions Curation Rationale: The curation effort
employed an open-science approach to create a diverse instruction-style
dataset through annotators across the globe that ensures comprehensive
representation across all languages. The success of the curation effort, led
by volunteers across diverse backgrounds, was significantly influenced by
their hope to meaningfully bring NLP advancements to their languages.
Provenance

Methods Used
crowd-sourced through volunteer annotations, followed by a quality assessment
phase in which samples from the dataset were checked. Methodology Details
Source: Original annotations and edits of open-source NLP datasets Platform:
Annotation Platform Dates of Collection: Jun 2023 - Dec 2023

Dataset Version and Maintenance

Maintenance Status
Actively Maintained Version Details
Current version: 1.0 Last Update: 12/2023 First Release: 02/2024 Maintenance
Plan
Updates will be periodically made available based on volunteer contributions

The Collection incorporates instruction-style templates from fluent speakers
and applies them to a curated list of 44 datasets. It also includes
translations of 19 instruction-style datasets into 101 languages. This
collection provides 513,579,625 instances of prompts and completions covering
a wide range of tasks.. • Curated by: 2007 contributors from 110 countries •
Language(s): 114 languages • License: Apache 2.0 • Repository:
https://huggingface.co/datasets/CohereForAI/aya_collection Authorship

Publishing Organization:
Cohere For AI Industry Type:
Not-for-profit - Tech Contact Details:
https://aya.for.ai

Example of Data Points The dataset contains multilingual prompts and
completions in the following format: {‘prompt’: "Generate an article for the
given headline: {{headline}}", ‘completion’: "{{news_article}}", ‘lang’:
"English" }  Motivations & Intentions Curation Rationale: Automatic
augmentation of existing datasets serves to enhance the available linguistic
resources for multiple languages. List of languages were established from mT5
and aligned with annotators’ language list and NLLB translation model. The
datasets were translated directly from English for all languages. Provenance

Methods Used
combination of crowd-sourced templating and automatic translation. Methodology
Details
Source: Existing NLP datasets Platform: Annotation Platform Dates of
Collection: Jun 2023 - Dec 2023

Dataset Version and Maintenance

Maintenance Status
Actively Maintained Version Details
Current version: 1.0 Last updated: 12/2023 Release date: 02/2024 Maintenance
Plan
No updates planned.

The Evaluation Suite contains a total of 25,750 open-ended conversation-style
prompts covering 101 languages of three subsets: aya-human-annotated: 250
original human-written prompts in 7 languages each. dolly-machine-translated:
200 human-selected prompts from Conover et al. [2023], automatically
translated with the NLLB model [NLLB-Team et al., 2022] from English into 101
languages. dolly-human-edited: 200 dolly-machine-translated prompts post-
edited by fluent speakers for 6 languages. • Curated by: contributors,
professional annotators, and synthetic generation • Language(s): 101 languages
• License: Apache 2.0 • Repository:
https://huggingface.co/datasets/CohereForAI/aya_evaluation_suite Authorship

Publishing Organization:
Cohere For AI Industry Type:
Not-for-profit - Tech Contact Details:
https://aya.for.ai

Example of Data Points The dataset contains multilingual prompts in the
following format: {‘prompt’: "Which is a species of fish? Bleak or Weary",
‘lang’: "English" }  Motivations & Intentions Curation Rationale: This
evaluation suite is tailored for testing the generation quality of
multilingual models, with the aim to balance language coverage and human-
sourced quality. It covers prompts originally written in each language, as
well as English-centric translated and manually curated or edited prompts for
a linguistically broad but rich testbed. The list of languages was established
from mT5 and aligned with annotators’ language list and the NLLB translation
model. Provenance

Methods Used
combination of original annotations by volunteers, automatic translation, and
post-editing of translations by professional annotators. Methodology Details
Source: Original annotations and translations and post-edits of Dolly
Platform: Annotation Platform Dates of Collection: Jun 2023 - Dec 2023

Dataset Version and Maintenance

Maintenance Status
Actively Maintained Version Details
Current version: 1.0 Last updated: 02/2024 Release date: 02/2024 Maintenance
Plan
No updates planned.

See pages - of figures/aya_tables_2_v3.pdf