11institutetext: Universidade de São Paulo, Instituto de Astronomia, Geofísica
e Ciências Atmosféricas, IAG, Departamento de Astronomia,
Rua do Matão 1226, Cidade Universitária, 05508-090, SP, Brazil
11email<EMAIL_ADDRESS><EMAIL_ADDRESS>
# The [Y/Mg] chemical clock in the Galactic Disk ††thanks: Based on data
obtained from the ESO Science Archive Facility with DOI
https://doi.org/10.18727/archive/33

The influence of metallicity and Galactic population in the solar
neighbourhood

J. Shejeelammal  Jorge Meléndez  Anne Rathsam  Giulia Martos

(Received XXX; accepted YYY)

###### Abstract

Context. Stellar ages are an important parameter to study the chemical
evolution of the Galaxy. To further the age estimates, various complementary
methods to the conventional isochrone-fitting method have been implemented in
the last decade. In recent years, several studies have established the
existence of a relationship between chemical clocks and stellar ages. The
[Y/Mg] clock is a promising technique, but there are still several open
questions, such as its validity for metal-poor stars and differences between
the thin and thick disk populations.

Aims. Our aim is to study the behaviour of the [Y/Mg] chemical clock with
stellar ages for a sample of solar-type disk stars and to provide the
empirical dating relation(s) for the stellar age determination from their
precise chemical abundances. We also intend to study the effect of metallicity
and population on this chemical clock.

Methods. We have derived the precise stellar atmospheric parameters as well as
the elemental abundances of Mg and Y through line-by-line differential
spectroscopic analysis for a sample of 48 metal-poor solar-type stars based on
high-quality, high-resolution ESO/HARPS spectra. From the high-precision Gaia
astrometric data, stellar masses and ages were estimated through isochrone-
fitting using Yonsei-Yale isochrones. A joint analysis of our sample, together
with a sample of 185 solar-twins and analogues from our previous works, is
performed to calibrate the [Y/Mg] chemical clock in the Galactic disk for
$-$0.71 $\leq$ [Fe/H] $<$ +0.34. Open clusters and stars with asteroseismic
ages have been used to validate our relations.

Results. Two different populations could be clearly seen in the [Mg/Fe] -
[Fe/H] plane - the thick and thin disks. Thick disk stars show an Age-
Metallicity Relation (AMR), whereas the thin disk shows a flatter age-
metallicity distribution. We found a strong anti-correlation between the
[Y/Mg] ratio and the stellar ages of our sample, which is metallicity-
dependent. For the first time in the literature, we report similar
correlations for the thin and thick disk stars.

Conclusions. We find that the [Y/Mg] relation(s) found here for solar-type
stars in a wide metallicity range is compatible with the literature using
solar-twins. Our relation provides higher accuracy and precision of 0.45 and
0.99 Gyr, respectively, comparable with the best accuracy achieved for the
solar-twins till date.

###### Key Words.:

stars: abundances – Galaxy: disk – stars: solar-type – solar neighborhood –
techniques: spectroscopic

##  1 Introduction

Besides the precise chemical abundances, the stellar age is an important
parameter to study Galactic archaeology. Combining the accurate age estimates
with the existing high-precision abundance data can pave the way to a better
understanding of the Galactic chemical evolution (Bland-Hawthorn & Gerhard,
2016; Alfredo Collazos, 2023). To overcome the problems in the conventional
isochrone fitting technique, several complementary methods have been
investigated for the precise determination of stellar ages in the last decade
(e.g. Soderblom 2010; Howes et al. 2019). Chemical clocks - abundance ratios
that show a linear relationship with stellar ages - are important among these
(e.g. Nissen 2015; Tucci Maia et al. 2016; Feltzing et al. 2017; Jofré et al.
2020).

da Silva et al. (2012) provided the first evidence of linear relation between
abundance ratios and stellar ages. One of the most studied chemical clocks is
the [Y/Mg] ratio, and it has been identified that it is a potential indicator
of age in the case of solar-twins (da Silva et al., 2012; Nissen, 2015, 2016;
Tucci Maia et al., 2016; Spina et al., 2016, 2018). Later, this relation was
found to be valid for solar analogues (Nissen et al., 2017, 2020), solar-
metallicity giants (Slumstrup et al., 2017), and red clump stars (Casamiquela
et al., 2021) in the solar neighbourhood. Skúladóttir et al. (2019) explored
the chemical clock outside the Galaxy and found that [Y/Mg] can be used as a
chemical clock in dwarf galaxies.

Feltzing et al. (2017) identified for the first time the metallicity
dependence of the [Y/Mg] clock and noted that it is valid only for [Fe/H] $>$
$-$0.5. The metallicity dependence of the [Y/Mg] chemical clock has been later
confirmed by Delgado Mena et al. (2018, 2019); Casali et al. (2020). Casali et
al. (2020) first identified that the [Y/Mg] - Age relation is not universal
and depends on the Galactocentric distance (RGC), which was further
investigated by Viscasillas Vázquez et al. (2022). It shows large dispersion
outside the solar neighbourhood (Casali et al., 2020; Casamiquela et al.,
2021).

The dependence of the chemical clocks on other parameters, such as stellar
mass and temperature, has been explored by Delgado Mena et al. (2019). The
validity of the [Y/Mg] clock for thin and thick disk populations of the Galaxy
has also been investigated in the literature and different correlations for
these two components have been identified (Delgado Mena et al., 2018;
Titarenko et al., 2019; Tautvaišienė et al., 2021). These studies have shown
that the chemical clock is applicable only to thin disk stars.

The chemical dating can be closely related to the chemical evolution of the
Galaxy and its different components (e.g. Haywood et al. 2013, 2016). The aim
of this paper is to study the [Y/Mg] - Age relation in the solar neighbourhood
of the Galactic disk over a wide metallicity range. Our analysis is based on a
combined sample of 233 solar-type stars spanning the metallicity $-$0.7 $\leq$
[Fe/H] $<$ +0.34. We have examined the metallicity dependence of the [Y/Mg]
chemical clock using this sample. There are not many studies in the literature
exploring the trend of [Y/Mg] with stellar ages for the thick disk, and the
findings are not always consistent. This has also been investigated in this
study. This paper is structured as follows: Sect. 2 discusses the stellar
sample and source of high-resolution spectroscopic data. In Sect. 3, we
present the spectroscopic analysis. Results are discussed in Sect. 4. Finally,
concluding remarks are presented in Sect. 5.

##  2 Stellar sample and spectroscopic data

Our analysis is based on a sample that contains three classes of stars of
different similarity to the Sun - solar-twins, solar-analogues and solar-type
(solar-like) stars. Solar-twins are the stars with parameters $\Delta$Teff =
100 K, $\Delta$log g = 0.1 dex, and $\Delta$[Fe/H] = 0.1 dex of the solar
values (Meléndez et al., 2006; Ramírez et al., 2009). Solar-analogues are the
dwarf stars with parameters $\Delta$Teff = 500 K and $\Delta$[Fe/H] = 0.3 dex
of the solar values (Soderblom & King, 1998; Yana Galarza et al., 2016).
Solar-type stars are those similar to the Sun in mass and evolutionary stage,
belonging to the F8V to K2V spectral types with a B-V color in the range of
0.5 to 1.0 (Cayrel de Strobel, 1996; Soderblom & King, 1998).

The stellar sample consists of 48 solar-type Galactic disk stars selected from
an updated catalogue of stellar parameters from Ramírez & Meléndez (2005),
with parameters 5600 K $\leq$ Teff $\leq$ 6400 K, 4.1 $\leq$ log g $\leq$ 4.6,
$-$0.71 $\leq$ [Fe/H] $\leq$ $-$0.3, and 0.85 $\leq$ M $\leq$ 1.05 M⊙. To have
a wider metallicity range in the sample, in addition to these 48 metal-poor
objects, we have included 185 solar-twins and analogues ($-$0.3 $\leq$ [Fe/H]
$<$ +0.34) from our previous studies (Spina et al., 2018; Martos et al., 2023;
Rathsam et al., 2023). Thus, our final sample consists of 233 solar-type
111Hereafter, we refer to the whole sample as solar-type stars because it
contains all the three type stars stars spanning the metallicity range $-$0.71
$\leq$ [Fe/H] $<$ +0.34.

For all the stars, the high-resolution spectra at R$\sim$115,000 acquired
using HARPS spectrograph were taken from the ESO (European Southern
Observatory) archive
(http://archive.eso.org/wdb/wdb/adp/phase3_spectral/form). These spectra cover
the wavelength range 3780 - 6910 Å. Since we need high-quality spectra for a
high-precision analysis, we have selected multiple spectra of the same objects
with individual S/N in the range 30 - 370. In order to minimise the effect of
telluric contamination on the spectral lines, we have used at least five
spectra taken on different nights. Then the spectra were radial velocity
corrected using IRAF (Image Reduction and Analysis Facility; https://iraf-
community.github.io/), and then combined to get the final spectra. The final
S/N of the combined spectra ranges from 360 to $\sim$ 1000\. The combined
spectra were normalized by splitting them into seven segments, using IRAF. The
continuum normalization of each individual segment was done iteratively using
cubic spline polynomial of similar orders for the same segments, by evaluating
the residuals as well as the visual fit to the continuum. Finally, the
normalized segments are combined using IRAF. The spectra taken before and
after the HARPS upgrade (June, 2015) were treated separately due to the
difference in the shape of the continuum, and combined afterwards. In addition
to the spectra of the stellar sample, we have also acquired HARPS solar
spectra at the same resolution obtained from the asteroid Vesta.

##  3 Spectroscopic Analysis

The stellar atmospheric parameters as well as the elemental abundances were
determined through a line-by-line differential analysis (Meléndez et al.,
2012, 2014; Bedell et al., 2014) with respect to the Sun using the Python code
q2 (qoyllur-quipu; https://github.com/astroChasqui/q2; Ramírez et al. 2014),
adopting the line list from Meléndez et al. (2014). The equivalent width (EW)
of each spectral line is measured on a star-by-star basis, including those in
the Sun, performing deblending whenever necessary. For these calculations, q2
uses the ATLAS9 Kurucz grid of model atmospheres (Castelli & Kurucz, 2003) and
the ABFIND driver of the code MOOG (version 2019; Sneden 1973; Sneden et al.
2012) that employs Local Thermodynamic Equilibrium (LTE).

###  3.1 Stellar atmospheric parameters

We have used the EW measurements of 91 Fe I and 18 Fe II lines to determine
the atmospheric parameters. The final atmospheric parameters were determined
in an iterative process from the initial guess of parameters using the
differential excitation, ionization, and reduced EW (= EW/$\rm\lambda$)
balances. The adopted solar atmospheric parameters are Teff = 5777 K, log g =
4.44 dex, $\rm\zeta$ = 1 km s-1, and [Fe/H] = 0 dex (Cox, 2000). The code also
evaluates the uncertainty on each atmospheric parameter following the
procedures in Epstein et al. (2010) and Bensby et al. (2014), which is the
cumulative uncertainty that includes the uncertainty on the measurements as
well as the uncertainty that arises due to the mutual dependence of the
atmospheric parameters. The typical precisions on the estimated atmospheric
parameters of our sample are $\sigma$(Teff) = 10 K, $\sigma$(log g) = 0.03
dex, $\sigma$($\zeta$) = 0.02 km s-1, and $\sigma$([Fe/H]) = 0.007 dex.

Following the determination of the stellar atmospheric parameters and their
uncertainties, q2 automatically uses the appropriate model atmospheres to
calculate the chemical abundances using the MOOG code under LTE.

###  3.2 Chemical abundances: Mg and Y

The abundances of the elements Mg and Y are measured for each star using the
same differential equivalent width method as the above. All the elemental
abundances are scaled relatively to those obtained for the Sun on a line-by-
line basis. We noted that, in all the metal-poor stars, the differential
abundance derived from the Mg I 4730.040 Å line is lower by around $\sim$ 0.05
dex compared to other Mg I lines. So, in order to get the consistent abundance
values from all the Mg lines, we have applied an offset of $-$4 mÅ to the
measured EW of this line in the Sun. The Mg I lines at 6318.717 and 6319.236 Å
are contaminated by nearby telluric absorption features in a few stars, and in
those cases these lines were not considered in their abundance determination.

Yttrium shows hyperfine splitting (HFS), and is taken into consideration while
calculating its abundances. It is employed by q2 through the blends driver in
the MOOG code and the adopted Y hyperfine lines from the Kurucz database.

The mean errors on the estimated abundances of Mg and Y are
$\rm\langle\sigma[Mg/Fe]\rangle$ = 0.01 dex and
$\rm\langle\sigma[Y/Fe]\rangle$ = 0.02 dex, respectively.

###  3.3 Stellar masses and ages

The masses and ages of the stellar sample were determined using the code q2,
employing the spectroscopically determined atmospheric parameters and the
Yonsei-Yale isochrones (Yi et al., 2001; Kim et al., 2002). Since our stars
show non-solar abundances ([$\alpha$/Fe]$\neq$0), the [Fe/H] values do not
represent their actual metallicity. Hence, to account for the effect of
$\alpha$-enhancement on the global metallicity of the stars, we applied a
correction factor +log10(0.64 $\times$ 10[α/Fe] \+ 0.36) (Salaris et al.,
1993), together with an offset of $-$0.04 to recover the age and mass of a
star with solar parameters, to the [Fe/H], as described in Spina et al.
(2018). However, for the stars with [Fe/H] $<$ 0, the effect of
$\alpha$-enhancement is already incorporated in the Yonsei-Yale isochrones to
follow the Galactic trend, using the [$\alpha$/Fe] values given in Meléndez et
al. (2010). We have to subtract this factor to avoid double
$\alpha$-enhancement. For the stars in the metallicity range $-$1 $\leq$
[Fe/H] $\leq$ 0, the value is given by [$\alpha$/Fe] = $-$0.3 $\times$ [Fe/H].
So, the final global metallicity ([M/H]) of the stars in our sample is given
by Eq. 1, where we have used our estimates of [Mg/Fe] as a proxy for
[$\alpha$/Fe].

$\begin{split}\rm[M/H]=\rm[Fe/H]&-0.04+\rm log_{10}(0.64\times
10^{\rm[Mg/Fe]}+0.36)\\\ &-\rm log_{10}(0.64\times
10^{-0.3\times\rm[Fe/H]}+0.36)\\\ \end{split}$ (1)

The q2 code produces a probability distribution for stellar masses and ages
through an isochrone fitting, where the spectroscopic stellar parameters are
compared with those obtained from the grid of isochrones (Ramírez et al.,
2014). The most probable values of these probability distributions are adopted
as stellar masses and ages, and the 1-$\sigma$ range around the most probable
values are taken as their respective uncertainties.

For this calculation, we have used the parallax values adopted from the Gaia
DR3 (Gaia Collaboration et al. 2016, 2022; Babusiaux et al. 2022;
https://gea.esac.esa.int/archive/), and the V magnitudes from the SIMBAD. If
the V magnitudes were not available, then we estimated it using the Gaia G
magnitudes and (BP - RP) colour-indices through the calibration equation given
by Rathsam et al. (2023).

The ages and masses of the solar-twins from Spina et al. (2018) were
recalculated using the same procedure as our sample, for consistency in the
analysis, and are listed in Martos et al. (2023). The typical uncertainties in
the isochrone ages and masses of the stellar sample are $\sim$0.4 Gyr and 0.01
M⊙, respectively.

##  4 Results and discussion

Here, we discuss the results of our analysis of the combined sample of 233
disk stars (48 solar-type stars from this study and 185 solar-twins and
analogues from our previous studies). The estimated stellar atmospheric
parameters, masses, ages, and the abundance ratios of our sample are given in
Table 3, and those of solar twins and analogues are given in Table 4. The
parameters of the combined sample are 5149 K $\leq$ Teff $\leq$ 6210 K, 4.04
$\leq$ log g $\leq$ 4.57, $-$0.71 $\leq$ [Fe/H] $<$ 0.34, and 0.82 $\leq$ M
$\leq$ 1.1 M⊙, and all the stars lie in the solar neighbourhood (RGC $\sim$ 8
kpc).

###  4.1 Bi-modality of the Galactic disk and Age-Metallicity-Relation (AMR)

Figure 1 shows the [Mg/Fe] ratio with respect to the [Fe/H] of the combined
sample. From this figure, we can clearly see two populations of [Mg/Fe] at
low-metallicity, the high-$\alpha$ or thick disk and the low-$\alpha$ or thin
disk. At higher metallicities ([Fe/H] $\geq$ 0), both populations are
indistinguishable. This bimodality of the Galactic disk in the [$\alpha$/Fe] -
[Fe/H] plane has already been identified in several previous studies (e.g.
Reddy et al. 2006; Adibekyan et al. 2011, 2012; Haywood et al. 2013; Nidever
et al. 2014; Bensby et al. 2014; Ness et al. 2019; Weinberg et al. 2019; Xiang
& Rix 2022; Leung et al. 2023; Imig et al. 2023; Patil et al. 2023). It is the
consequence of different chemo-dynamical evolution and star formation history
of the Milky Way disk (e.g. Haywood et al. 2013; Bergemann et al. 2014;
Casagrande et al. 2011). Generally, thick disk is composed of old, metal-poor,
$\alpha$-enhanced stars, whereas thin disk is composed of younger,
$\alpha$-poor stars (Fuhrmann, 1998; Bensby et al., 2005; Lee et al., 2011).
However, there is no obvious method to completely disentangle these two
components of the Galactic disk and to identify purely thin/thick disk stars
in the solar neighbourhood (Bensby et al., 2003; Adibekyan et al., 2012;
Haywood et al., 2013). Furthermore, the separation between the
$\alpha$-sequences and even the existence of boundary between these two
populations (Bovy et al., 2012a) are still topics of debate. A detailed review
on Galactic disk can be found in Rix & Bovy (2013).

Previously, the thin/thick disk stars were distinguished either from a pure
kinematical approach (e.g. Bensby et al. 2003; Reddy et al. 2006) or from an
approach combining kinematics, metallicity, and age (e.g. Haywood 2008).
However, both these methods are found to be prone to
$\textquoteleft$contamination’ or overlap between the two components (Bensby
et al., 2003; Adibekyan et al., 2012; Bovy et al., 2012b). In addition to
this, the radial migration is proposed to have redistributed the stars in the
solar neighbourhood (e.g. Liu & van de Ven 2012; Haywood et al. 2013). This
radial migration and the higher eccentric orbits lead to the contamination of
the kinematically selected thin/thick disk stars in the solar vicinity (e.g.
Schönrich & Binney 2009).

The advent of several large sky multi-object spectroscopic surveys in the last
decade allowed the chemo-kinematic analysis of much larger samples of stars.
As a consequence, a purely chemical approach to dissect the Galactic disk
began to gain significance. Several studies have shown that chemical
dissection of the Galactic disk is more reliable because the chemical
composition of a star is a more stable property that is closely related to the
time and place of birth, whereas the kinematics and spatial positions change
all the time (Navarro et al., 2011; Adibekyan et al., 2011; Liu & van de Ven,
2012; Bovy et al., 2012b; Adibekyan et al., 2012, 2013). It has also been
proposed that various properties (scale height, kinematics etc.) of different
Galactic stellar populations can be parametrized using their chemical
composition (Bovy et al., 2012b).

For a given age, the solar vicinity exhibits a broader metallicity
distribution since stars of different birth radii (and hence different
metallicities) contribute to the local neighbourhood (Liu & van de Ven, 2012).
As a result, despite the fact that the thick disk is comparatively older,
stars with a range of ages and metallicities can contribute to both thin and
thick disks, giving rise to a large overlap in metallicity. Hence, even though
the chemical composition is the more reliable approach, the metallicity
([Fe/H]) alone is not an ideal choice. From the chemo-orbital analysis of a
sample of SDSS/SEGUE (Yanny et al., 2009) data, Liu & van de Ven (2012) have
shown that the $\alpha$-abundance is preferred because it is relatively
independent of birth radii and is a more appropriate proxy for age. The
distribution of [$\alpha$/Fe] - [Fe/H] ratio has been used in several studies
to distinguish between the two disk populations (e.g. Adibekyan et al. 2011;
Haywood et al. 2013). The limit characterizing the thin/thick disk populations
is defined empirically, by examining the chemical separation in [$\alpha$/Fe]
between the high-$\alpha$ (thick disk) and low-$\alpha$ (thin disk) sequences.
Recent studies based on the chemo-kinematical and statistical methods using
large samples from high-resolution spectroscopic surveys like APOGEE (e.g.
Anders et al. 2014; Patil et al. 2023), Gaia - ESO Survey (e.g. Gent et al.
2024), GALAH (e.g. Cantelli & Teixeira 2024) etc. have shown that the
decomposition of the Galactic disk is better understood in terms of the
chemical enrichment ($\alpha$ abundance).

On the ground of the above discussion, we have adopted the chemical separation
given in Adibekyan et al. (2011) to separate the thin and thick disk
sequences. This is shown as a red solid line in the [Mg/Fe] - [Fe/H] plane in
Fig. 1. We identified the stars above this line as thick disk stars and those
below as thin disk stars 222Chemically defined. The behaviour of [Mg/Fe] ratio
with respect to various orbital properties and the Toomre diagram of our
sample are shown in Figs. 12 and 13. As seen in the several previously
mentioned works, our chemically defined thick and thin disk stars are mixed in
the kinematic plane. The thick disk contains the older stars (age $>$ 8 Gyr;
two stars have ages 6.7 and 7.5 Gyr) of the sample, whereas the thin disk
shows an age spread. All the youngest stars of the sample belong to the thin
disk.

We note that a younger star with an age of 4.6 Gyr is a member of the thick
disk (cyan circle; Fig. 1 lower panel). This object, HD 65907, show anomalous
behaviour compared to other stars of the sample. As could be seen from the
figures, it lies well off the other objects of its kind. Fuhrmann et al.
(2012) analysed this anomalous object, and from its chemical abundance they
identified it as an old, population II, thick disk star with an age of 12 or
13 Gyr. However, the age inferred from the evolutionary tracks is
5.6${}^{+2.2}_{-1.8}$ Gyr, which contradicts its chemical properties.
According to Fuhrmann et al. (2012), this discrepancy could be resolved only
with a mass accretion scenario on HD 65907. So, this object is probably a
product of former mass-transfer event, like the solar analogue HIP 10725
(Schirbel et al., 2015).

The Age-Metallicity Distribution (AMD) of the whole sample is shown in Fig. 2.
From earlier studies, it has been identified that the age and metallicity are
not strongly correlated in the solar neighbourhood, and the metallicity shows
a significant scatter for the same age (e.g. Edvardsson et al. 1993; Feltzing
et al. 2001; Haywood 2006; Casagrande et al. 2011; Bensby et al. 2014; Lin et
al. 2020; Sahlholdt et al. 2022; Patil et al. 2023). From Fig. 2, it is clear
that stars of similar age show a large range of metallicities. The thick disk
stars in the sample show an Age-Metallicity-Relation (Fig. 2, upper panel), as
previously noted by Schuster et al. (2006); Bensby et al. (2014); Patil et al.
(2023), and others. Meanwhile, the age and metallicity are uncorrelated for
the thin disk stars, and show an almost flat distribution. However, both the
populations are indistinguishable from each other in the Age - [Fe/H] space.

From the contour plot for the AMD of the stellar sample (bottom panel, Fig.
2), we note the following: (i) up to the age of $\sim$ 12 Gyr and for [Fe/H]
$>$ $-$0.2, we see a flat AMR with a scatter in the metallicity (ii) for the
older (age $>$ 7 Gyr), metal-poorer stars in the sample ([Fe/H] $<$ $-$0.2),
we see a downward trend in the AMD (iii) the majority of the distribution is
centred at [Fe/H] $\sim$ 0 with a peak around ages between 4 - 9 Gyr. This is
on par with the findings in the previous studies of the Galactic disk (e.g.
Edvardsson et al. 1993; Feltzing et al. 2001; Bergemann et al. 2014). The AMR
and the evolution of the Galactic disk are broader topics, and their detailed
discussion is beyond the scope of this paper. There are several studies
dedicated to the AMR in the Galactic disk using quite larger samples, to name
a few, Feltzing et al. (2001); Lin et al. (2020); Sahlholdt et al. (2022);
Patil et al. (2023).

Figure 1: [Mg/Fe] ratio as a function of [Fe/H] for the combined sample. The
red solid line shows the separation between thin and thick disk stars based on
the [Mg/Fe] ratio similar to Adibekyan et al. (2011); [Mg/Fe] = +0.19 for
[Fe/H] $\leq$ $-$0.6, [Mg/Fe] = $-$0.217 $\times$ [Fe/H] + 0.06 for $-$0.6 $<$
[Fe/H] $\leq$ 0, [Mg/Fe] = +0.06 for [Fe/H] $>$ 0\. Stars above this line
belong to the Galactic thick disk. The cyan circle is the anomalous star HD
65907.

Figure 2: Age-Metallicity Distribution of the sample. The red star that is off
the other thick disk objects in the upper panel is the anomalous star HD
65907. The bottom panel is the density plot for the AMD of the sample.

###  4.2 Abundance trend with age

The distributions of [Mg/Fe], [Y/Fe], and [Y/Mg] with respect to stellar ages
of the combined sample are shown in Fig. 3. As could be seen from the [Mg/Fe]
- [Fe/H] distribution (Fig. 1), the thin and thick disk objects show a clear
dichotomy in the [Mg/Fe] - Age plane as well. The [Mg/Fe] and [Y/Fe] ratios
show positive and negative slopes, respectively, with respect to age, as
expected from their origin and chemical evolution models. Mg is an
$\alpha$-element produced by Type II Supernovae (SNe II) on a shorter time
scale ($\leq$ 107 yrs; e.g. Kobayashi et al. 2006). SNe II were the main
contributors of metals to the Interstellar Medium (ISM) during the early
stages of the chemical evolution. So, $\alpha$-elements show a positive trend
with respect to age. Y is an s-process element produced in low- and
intermediate-mass Asymptotic Giant Branch (AGB) stars, which contributed to
the chemical evolution much later compared to SNe II. As a result, Y shows a
negative trend with stellar ages (Nomoto et al. 2013; Matteucci 2014; Karakas
& Lattanzio 2014; Spina et al. 2016 and references therein).

As a consequence of different origins and chemical evolution, the [Y/Mg] ratio
has a steeper dependence on stellar ages. As seen from Fig. 3 (bottom panel),
the [Y/Mg] ratio of our sample shows a strong anti-correlation with age. The
scatter in the [Y/Mg] ratio of our sample is small compared to that found in
other samples of solar-type stars in the literature (e.g. Feltzing et al.
2017; Titarenko et al. 2019; Casali et al. 2020). We note continuity in the
[Y/Mg] - Age correlation between the thin and thick disk stars. We also note
that there is no significant gradient of [Y/Mg] with respect to [Fe/H], as was
seen in Feltzing et al. (2017).

Figure 3: [Mg/Fe], [Y/Fe], and [Y/Mg] ratios as a function of age for the
combined sample, colour-coded by [Fe/H]. The star at $\sim$ 5 Gyr is HD 65907,
probably a result of a former mass-transfer event.

###  4.3 The [Y/Mg] chemical clock

In this section, we analyse the [Y/Mg] - Age correlation in our sample. The
stellar ages derived from the isochrone fitting have been used in this
analysis. We have performed a simple linear regression fitting to derive the
empirical relation connecting the [Y/Mg] ratio and stellar ages, of the form
[Y/Mg] = a $\times$ Age + b. From the linear fitting, we found that the [Y/Mg]
of the sample is correlated to the stellar age through the relation (Fig. 4):

$\begin{split}\rm[Y/Mg]=-0.040(\pm 0.001)\times\rm Age\,(Gyr)+0.186(\pm
0.036)\\\ \end{split}$ (2)

In order to get the best possible relation, we have eliminated a few stars
that lie outside the bulk of the sample in the [Y/Mg] - Age space. The outlier
limit is set at the 2$\sigma$ level of the trend (Eq. 2), which is given by
the linear function [Y/Mg] = $-$0.040 $\times$ Age (Gyr) + 0.356, as shown in
Fig. 4. We have also excluded the anomalous star HD 65907 from this analysis.
We did not make any distinction between the thin and thick disk objects. From
the linear fit shown in Fig. 5 for the sample after excluding the outliers, we
obtained a relation of the form:

$\begin{split}\rm[Y/Mg]=-0.041(\pm 0.001)\times\rm Age\,(Gyr)+0.187(\pm
0.040)\\\ \end{split}$ (3)

However, from the analysis of a sample of 714 solar-type stars, Feltzing et
al. (2017) first identified the metallicity dependence of the [Y/Mg] chemical
clock, which was subsequently found in the samples of Delgado Mena et al.
(2019) and Casali et al. (2020). In order to check the metallicity dependence
of Eq. 3, we have examined the distribution of [Y/Mg] residuals
($\rm\Delta[Y/Mg]$ = [Y/Mg]obs \- [Y/Mg]pred) with respect to metallicity to
see if there exist any trend. As we can see from Fig. 6, the $\rm\Delta[Y/Mg]$
is independent of metallicity up to a value of [Fe/H] $\sim$ $-$0.17 and show
a trend below that. This confirms that the [Y/Mg] chemical clock depends on
the metallicity and the whole sample could not be represented using a single
relation given in Eq. 3. Hence, we divided the sample into two metallicity
bins, $-$0.71 $\leq$ [Fe/H] $<$ $-$0.17 and $-$0.17 $\leq$ [Fe/H] $<$ +0.34,
and performed the fitting separately, as shown in Fig. 7. This simple linear
fitting resulted in the following relations:

$\begin{split}\rm[Y/Mg]=-0.0362(\pm 0.0004)\times\rm Age\,(Gyr)+0.0867(\pm
0.0285);\\\ (\rm for-0.71\leq[Fe/H]<-0.17)\\\ \rm[Y/Mg]=-0.0340(\pm
0.0006)\times\rm Age\,(Gyr)+0.1656(\pm 0.0346);\\\ (\rm
for-0.17\leq[Fe/H]<+0.34)\\\ \end{split}$ (4)

We have performed this fitting for five different metallicity bins of width
0.2 dex as well, and note that the results do not produce significant
deviations from the results obtained using Eq. 4.

We then inverted the relations in Eq. 4 to get the stellar dating relations of
the form:

$\begin{split}\rm Age\,(Gyr)=-27.6243(\pm 0.3053)\times\rm[Y/Mg]+2.3950(\pm
0.8139);\\\ (\rm for-0.71\leq[Fe/H]<-0.17)\\\ \rm Age\,(Gyr)=-29.4118(\pm
0.5191)\times\rm[Y/Mg]+4.8706(\pm 1.1039);\\\ (\rm
for-0.17\leq[Fe/H]<+0.34)\\\ \end{split}$ (5)

Figure 4: Linear fit to the [Y/Mg] - Age distribution of the whole sample
(black solid line) and the outlier cut (black dashed line). The outlier limit
is set at the 2$\sigma$ level of the trend. The triangle at the lower part of
the plot is the anomalous star HD 65907. Figure 5: Best linear fit (blue solid
line) for the [Y/Mg] - Age distribution of the sample. The fitting function is
described in the text. Figure 6: Distribution of [Y/Mg] residuals
($\rm\Delta[Y/Mg]$) with respect to metallicity of the sample. The vertical
dashed line at [Fe/H] = $-$0.17 represents the point below which
$\rm\Delta[Y/Mg]$ shows an offset with metallicity. Figure 7: [Y/Mg] - Age
linear fits for the sample in two metallicity bins $-$0.71 $\leq$ [Fe/H] $<$
$-$0.17 (blue solid line) and $-$0.17 $\leq$ [Fe/H] $<$ +0.34 (green solid
line).

Since we identified the metallicity dependence of the [Y/Mg] ratio in the
sample, we have also performed a multivariate linear regression fitting by
incorporating the [Fe/H] as well. The obtained relation as a function of
stellar age and metallicity is given by:

$\begin{split}\rm[Y/Mg]=&-0.036(\pm 0.001)\times\rm Age\,(Gyr)\\\ &+0.125(\pm
0.010)\times\rm[Fe/H]+0.165(\pm 0.034)\\\ \end{split}$ (6)

The chemical age is given by the relation:

$\begin{split}\rm Age\,(Gyr)=&-27.701(\pm 0.461)\times\rm[Y/Mg]\\\ &+3.454(\pm
0.329)\times\rm[Fe/H]+4.576(\pm 1.013)\\\ \end{split}$ (7)

Figure 8 shows the relation in Eq. 6 for three different metallicity values,
[Fe/H] = $-$0.5, $-$0.1 and +0.3.

The chemical ages of the sample are calculated using both Eq. 5 and Eq. 7 and
compared with the isochrone ages and with each other. The chemical ages do not
show any trend with the isochrone ages (offset $\sim$ 0). The standard
deviation (S.D) of the single variate chemical age (Eq. 5, SV chemical age
hereafter) with respect to the isochrone age is 1.55 Gyr and that of the
multivariate chemical age (Eq. 7, MV chemical age hereafter) is 1.66 Gyr. We
note that the average uncertainty in the isochrone ages of the sample is
$\sim$0.4 Gyr. As could be seen from the comparison between SV and MV chemical
ages shown in Fig. 9, both ages match quite well with an offset of $-$0.005
Gyr. The mean scatter and SD between them are 0.50 and 0.62 Gyr respectively.

Figure 8: Multivariate linear fits for the [Y/Mg] - Age distribution of the
sample for three different metallicities. The fitting function is described in
the text. Figure 9: Correlation between single variate (SV; Eq. 5) and
multivariate (MV; Eq. 7) chemical ages of the stellar sample.

####  4.3.1 Validation using open clusters and stars with asteroseismic ages

In order to validate our relations in Eqs. 5 and 7, we have used the data for
open clusters (OCs) and stars with asteroseismic ages. OCs are one of the
powerful tools to validate the chemical clocks because the member stars of
each cluster show homogeneity in age and chemical composition. As a result,
their ages have been precisely determined through isochrone-fitting from the
observation of several member stars (e.g. Casali et al. 2019; Viscasillas
Vázquez et al. 2022). Casali et al. (2020) have presented a list of OCs
selected from the iDR5 of the Gaia-ESO Survey (GES; Gilmore et al. 2012;
Randich et al. 2013), with cluster membership probability of at least 80%.
From this list, we have selected 13 OCs with RGC $\geq$ 6.5 kpc.

In the case of single stars, asteroseismology provides the reliable ages from
the solar-like oscillations on the stellar surface (Chaplin & Miglio, 2013;
Silva Aguirre et al., 2012; Christensen-Dalsgaard, 2016). Silva Aguirre et al.
(2017) have presented the asteroseismic ages for a sample of 66 main-sequence
stars (Kepler LEGACY sample; KLS hereafter) based on the asteroseismic data
from the Kepler mission. The KLS is claimed to have the best asteroseismic
data available among the solar-like stars. We have selected 10 stars from the
KLS for which the precise abundances are available in the literature. The
validation sample of OCs and KLS stars used to calibrate our chemical clocks
are given in Table 1. The Y and Mg abundances of OCs and KLS stars are adopted
from Casali et al. (2020) and Nissen et al. (2017), respectively.

Figure 10 shows the comparisons of the SV (upper panel) and MV (middle panel)
chemical ages of the validation sample calculated using our relations with
their literature ages. The lower panel of this figure shows the correlation
between the SV and MV chemical ages of this sample. As can be seen from the
figure, the OCs show a larger scatter compared to the KLS stars, but both
agree with the [Y/Mg] clock within 1 or 2-$\sigma$. This may be because these
cluster members are giant/sub-giants, whereas our relations are derived based
on a sample of dwarf stars. In addition to this, even though the OCs lying in
the inner Galactic disk (RGC $<$ 6.5 kpc) are excluded from our comparison,
there could be a possibility that some of them originally belonged to this
region and are currently in the solar-neighborhood as a result of radial
migration (e.g. Viscasillas Vázquez et al. 2022). Since our stellar sample
lies in the solar neighbourhood, this also may have contributed to the scatter
seen in Fig. 10.

Single variate chemical clock (Eq. 5): In the case of KLS stars with
asteroseismic ages, the mean scatter (accuracy) of this chemical clock is 0.91
Gyr, with a standard deviation (S.D; precision) of 0.96 Gyr and a mean
relative error (MRE) 333RE = $\frac{\lvert Literatute\,age-
Chemical\,age\rvert}{Literature\,age}$ of 38%. The average uncertainty in the
seismic ages of the sample is $\sim$0.52 Gyr, and the [Y/Mg] has a mean error
of 0.013 dex, which translates to $\sim$0.32 Gyr. By incorporating these two
errors in to the mean scatter, the actual accuracy of the SV chemical age is
estimated to be $\sim$0.67 Gyr for the KLS stars. In the case of OCs, the mean
scatter and the S.D of the SV chemical clock are 1.10 and 1.24 Gyr,
respectively. The average uncertainty in their isochrone ages is 0.23 Gyr and
that from the [Y/Mg] ratio is 0.73 Gyr ($\equiv$ 0.03 dex). Subtracting these
errors results in an accuracy of 0.79 Gyr in the SV chemical ages of the OCs.

Multivariate chemical clock (Eq. 7): The mean scatter and the S.D are 0.76 Gyr
and 0.99 Gyr, respectively, with a MRE of 33% for the KLS stars. In the case
of OCs, the mean scatter and the S.D for this chemical clock are 1.17 Gyr and
1.45 Gyr, respectively. Incorporating the uncertainties in the literature ages
and the [Y/Mg] ratios, the accuracy of the MV chemical ages is estimated to be
0.45 Gyr and 0.88 Gyr, respectively, for the KLS stars and the OCs.

In summary, the accuracy we have obtained using our chemical clocks based on
the KLS stars with asteroseismic ages and the OCs with isochrone ages
respectively are $\sim$0.67 and 0.79 Gyr (SV chemical age) and $\sim$0.45 and
0.88 Gyr (MV chemical age). These values are similar to the accuracy achieved
for the solar-twin stars in the solar neighbourhood ($\sim$0.8 - 1 Gyr; Nissen
2015, 2016; Tucci Maia et al. 2016; Spina et al. 2018). Since the KLS stars
are dwarfs and lie in the close vicinity of the Sun as our stellar sample, the
validation using them is likely more accurate compared to the OCs.

Figure 10: Comparison of the literature ages of the OCs and KLS stars with
their single variate (SV; upper panel) and multivariate (MV; middle panel)
chemical ages. The bottom panel shows the correlation between the two chemical
ages. The green line represents the one-to-one fit. Table 1: Properties of the
OCs and KLS stars used in this study.

ID | [Fe/H] | [Y/Mg] | Age | ID | [Fe/H] | [Y/Mg] | Age
---|---|---|---|---|---|---|---
| (dex) | (dex) | (Gyr) |  | (dex) | (dex) | (Gyr)
|  OCs∗ |  |  |  |  KLS stars† |  |
Berkeley 31 |  $-$0.270$\pm$0.060 |  $-$0.010$\pm$0.030 |  2.50$\pm$0.30 | KIC 3427720 |  $-$0.024$\pm$0.017 |  $-$0.017$\pm$0.015 |  2.40$\pm$0.30
Berkeley 36 |  $-$0.160$\pm$0.100 |  $-$0.050$\pm$0.060 |  7.00$\pm$0.50 | KIC 6106415 |  $-$0.037$\pm$0.012 |  0.002$\pm$0.011 |  4.80$\pm$0.60
Berkeley 44 |  0.270$\pm$0.060 |  0.140$\pm$0.070 |  1.60$\pm$0.30 | KIC 6225718 |  $-$0.110$\pm$0.014 |  0.051$\pm$0.012 |  2.60$\pm$0.40
M 67 |  $-$0.010$\pm$0.040 |  0.000$\pm$0.010 |  4.30$\pm$0.50 | KIC 7940546 |  $-$0.126$\pm$0.012 |  0.056$\pm$0.010 |  2.40$\pm$0.30
Melotte 71 |  $-$0.090$\pm$0.030 |  0.070$\pm$0.010 |  0.83$\pm$0.18 | KIC 9139151 |  0.096$\pm$0.019 |  0.101$\pm$0.017 |  1.90$\pm$0.70
NGC 2243 |  $-$0.380$\pm$0.040 |  $-$0.040$\pm$0.030 |  4.00$\pm$1.20 | KIC 10162436 |  $-$0.073$\pm$0.021 |  0.071$\pm$0.017 |  2.50$\pm$0.40
NGC 2420 |  $-$0.130$\pm$0.040 |  0.070$\pm$0.030 |  2.20$\pm$0.30 | KIC 10644253 |  0.130$\pm$0.019 |  0.066$\pm$0.017 |  1.30$\pm$0.70
NGC 4815 |  0.110$\pm$0.010 |  0.110$\pm$0.090 |  0.57$\pm$0.07 | KIC 12069424 |  0.093$\pm$0.007 |  $-$0.090$\pm$0.009 |  7.00$\pm$0.50
NGC 6067 |  0.200$\pm$0.080 |  0.080$\pm$0.040 |  0.10$\pm$0.05 | KIC 12069449 |  0.062$\pm$0.007 |  $-$0.085$\pm$0.009 |  7.10$\pm$0.50
NGC 6633 |  $-$0.010$\pm$0.110 |  0.080$\pm$0.020 |  0.52$\pm$0.10 | KIC 12258514 |  0.027$\pm$0.007 |  $-$0.051$\pm$0.016 |  4.50$\pm$0.80
NGC 6802 |  0.100$\pm$0.020 |  0.170$\pm$0.020 |  1.00$\pm$0.10 |  |  |  |
Pismis 18 |  0.220$\pm$0.040 |  0.050$\pm$0.040 |  1.20$\pm$0.04 |  |  |  |
Trumpler 20 |  0.150$\pm$0.070 |  0.120$\pm$0.020 |  1.50$\pm$0.15 |  |  |  |

References: ∗ Casali et al. (2020) and references therein, † Nissen et al.
(2017) and references therein

####  4.3.2 Chemical clock in the thin and thick disks

While the studies using solar-twins, analogues, and solar-type stars with
[Fe/H] $\geq$ $-$0.3 confirmed the tight correlation between the [Y/Mg] ratio
and stellar ages irrespective of the population (thin/thick disk; Nissen 2016;
Tucci Maia et al. 2016; Spina et al. 2016, 2018; Nissen et al. 2017, 2020;
Jofré et al. 2020), a few recent studies have suggested that the [Y/Mg]
chemical clock could only be used for thin disk stars, and may not be valid
for lower metallicities or thick disk stars (e.g. Feltzing et al. 2017;
Delgado Mena et al. 2018, 2019; Titarenko et al. 2019; Tautvaišienė et al.
2021). Feltzing et al. (2017) have suggested that the [Y/Mg] - age
distribution is almost flat and has no predictive power on age for [Fe/H] $<$
$-$0.5. However, Delgado Mena et al. (2018) have shown that it still has a
correlation with age (up to [Fe/H] $\sim$ $-$0.8), but only for thin disk
stars. The trend becomes flat for thick disk stars, and for thin disk stars
with ages $\geq$ 8 Gyr. From an AMBRE sample of solar-type stars, Titarenko et
al. (2019) identified different slopes for thin disk and thick disk stars with
the thick disk stars showing a steeper dependence. Recently, Tautvaišienė et
al. (2021) found that thick disk stars (233 stars including dwarfs and giants)
show no trend of [Y/Mg] with age (slope$\sim$ $-$0.002), contrarily to the
slopes identified for the thick disk stars of Titarenko et al. (2019) and
Bensby et al. (2014). This may be due to the different luminosity classes in
their sample.

We have examined the dependence of the [Y/Mg] chemical clock on stellar age
for the thin and thick disk stars separately and found that both components
show almost the same correlation, with slopes $-$0.039($\pm$0.001) and
$-$0.034($\pm$0.001), respectively. The linear fits (Eq. 8) for the two
populations are shown in Fig. 11.

$\begin{split}\rm[Y/Mg]_{Thin}=-0.039(\pm 0.001)\times\rm Age\,(Gyr)+0.178(\pm
0.038)\\\ \rm[Y/Mg]_{Thick}=-0.034(\pm 0.001)\times\rm Age\,(Gyr)+0.089(\pm
0.015)\\\ \end{split}$ (8)

Our results disagree with previous studies, which found that either the thick
disk stars showed no trend at all or a different trend than the thin disk
stars. In particular, the thick disk stars in Spina et al. (2018) seem to have
a small offset relative to the [Y/Mg] - age relation defined by their thin
disk sample. However, their sample of thick disk stars is relatively small,
making it difficult to perform a separate fit for the [Y/Mg] - age relation of
the thick disk. Although our sample size of thick disk stars has increased
relative to the study of Spina et al. (2018), we have to keep in mind that our
number is still relatively small (36 objects without outliers). We note that
the results may be somewhat biased due to the selection biases of thick and
thin disk stars in different studies.

Figure 11: Best linear fits for thin (blue solid line) and thick disk (red
solid line) stars separately. The fitting functions are described in the text.

####  4.3.3 Comparison with the previous works

The slopes of the [Y/Mg] - Age distribution for solar-twins and solar-type
stars from different studies, along with our estimates, are given in Table 2.
These estimates are based on the linear relation between [Y/Mg] and the
stellar ages. We note that, while the relations obtained for the solar-twins
by different authors are similar irrespective of the sample size, the solar-
type stars give different slopes. However, Nissen et al. (2017); Delgado Mena
et al. (2019); Nissen et al. (2020); Tautvaišienė et al. (2021) show similar
values that match those of solar-twins. The lowest metallicity of these
samples is $-$0.6, and other studies of solar-type stars have comparatively
wider range of metallicities. Hence, the difference in the slopes plausibly
results from the metallicity dependence, as discussed in Feltzing et al.
(2017); Delgado Mena et al. (2018, 2019). However, when we consider the sample
irrespective of the population, our relations are compatible with those found
for the solar-twins by Nissen (2016) and for solar-type stars by Nissen et al.
(2017) and Nissen et al. (2020). While our estimate for the thick disk stars
matches the estimate of Tautvaišienė et al. (2021) from a sample of 76 thick
disk giants, it disagrees with other samples of thick disk stars. In the case
of thin disk stars, our estimate is comparable with the value obtained by
Delgado Mena et al. (2019).

The values listed in Table 2 are based on a simple linear regression fit
between the chemical clock and the stellar ages. In light of the results from
Feltzing et al. (2017); Delgado Mena et al. (2018), and the non-universality
of the chemical clock - age relation in the Galactic disk (Casali et al.,
2020), a few recent studies have attempted to perform multiple variable linear
regression fitting by including the stellar atmospheric parameters,
Galactocentric distances, stellar masses, etc. in addition to the stellar ages
(Delgado Mena et al., 2019; Casali et al., 2020; Viscasillas Vázquez et al.,
2022).

The accuracy and precision of the [Y/Mg] chemical clock when considered as
function of age, [Fe/H], and RGC are 1.6 Gyr and 2.8 Gyr, respectively
(Viscasillas Vázquez et al., 2022). Delgado Mena et al. (2019) could determine
the ages with a precision of 1.85 Gyr and MRE$\sim$57% using their 1D [Y/Mg]
chemical clock. When using 2D relations, including Teff/[Fe/H]/mass as well,
they got precisions and MRE (1.57 Gyr, 48%), (1.73 Gyr, 40%), and (1.71 Gyr,
37%), respectively, whereas their 3D relations (Teff and [Fe/H] along with
age) resulted in a precision of 1.47 Gyr with an MRE of 51%. The accuracy
achieved by Titarenko et al. (2019) using their 1D dating relation is 2 Gyr.
Meanwhile, the accuracy and precision of the chemical ages calculated using
our relation (Eq. 5) are $\sim$0.45 Gyr and 0.99 Gyr respectively, with a MRE
of 33%. Since our sample lies in the solar neighbourhood, we have only
discussed the results valid in this region.

Table 2: Slopes of [Y/Mg] - Age distribution of stars in the solar
neighbourhood

Slope |  N† |  Pop∗ | Ref | Slope |  N† |  Pop∗ | [Fe/H] | Ref
---|---|---|---|---|---|---|---|---
(dex Gyr-1) |  |  |  |  (dex Gyr-1) |  |  |  |
solar-twins |  |  |  | solar-type |  |  |  |
$-$0.0404$\pm$0.0019 | 18 | Thin disk | Nissen (2015) |  $-$0.0362$\pm$0.0004 | 57 |  |  $-$0.71 - $-$0.17 | This work
$-$0.0371$\pm$0.0013 | 21 |  | Nissen (2016) |  $-$0.0340$\pm$0.0006 | 166 |  |  $-$0.17 - +0.34 | This work
$-$0.0410$\pm$0.0010 | 65 |  | Tucci Maia et al. (2016) |  $-$0.0390$\pm$0.0010 | 187 | Thin disk |  $-$0.71 - +0.34 | This work
$-$0.0410$\pm$0.0017 | 45 |  | Spina et al. (2016) |  $-$0.0340$\pm$0.0010 | 36 | Thick disk |  $-$0.71 - +0.05 | This work
$-$0.0460$\pm$0.0020 | 76 |  | Spina et al. (2018) |  $-$0.0347$\pm$0.0012 | 31 |  |  $-$0.15 - +0.15 | Nissen et al. (2017)
$-$0.0420$\pm$0.0030 | 66 | Thin disk | Spina et al. (2018) |  $-$0.0199 |  | Thin disk |  $-$0.80 - $-$0.20 | Delgado Mena et al. (2018)
$-$0.0410$\pm$0.0230 |  | Thin disk | Delgado Mena et al. (2019) |  $-$0.0420$\pm$0.0010 | 265 | Thin disk |  $-$0.60 - +0.55 | Delgado Mena et al. (2019)
$-$0.0420$\pm$0.0030 | 80 |  | Jofré et al. (2020) |  $-$0.0290$\pm$0.0020 | 22 | Thin disk |  $-$0.80 - +0.40 | Titarenko et al. (2019)
$-$0.0400$\pm$0.0020 |  |  | Casali et al. (2020) |  $-$0.0820$\pm$0.0020 | 11 | Thick disk |  $-$0.80 - +0.20 | Titarenko et al. (2019)
|  |  |  |  $-$0.0383$\pm$0.0010 | 68 |  |  $-$0.30 - +0.30 | Nissen et al. (2020)
|  |  |  |  $-$0.0270$\pm$0.0030 | 368 | Thin disk |  $-$0.60 - +0.40 |  Tautvaišienė et al. (2021)‡
|  |  |  |  $-$0.0410$\pm$0.0130⋆ | 76 | Thick disk |  $-$0.46$\pm$0.12 | Tautvaišienė et al. (2021)
|  |  |  |  $-$0.0140$\pm$0.0040 | 66 | Thick disk |  $-$1.00 - +0.40 |  Tautvaišienė et al. (2021) (for Bensby et al. (2014) sample)
|  |  |  |  $-$0.0020$\pm$0.0030 | 233 | Thick disk |  $-$1.00 - +0.40 |  Tautvaišienė et al. (2021) and references therein‡

† No. of stars used to derive the relation
∗ Fitting includes both the populations if not mentioned
‡ Sample includes dwarf and giants
⋆ Only giants

##  5 Conclusions

Based on high-resolution and high-quality HARPS spectra, we have estimated the
precise stellar atmospheric parameters and chemical abundances of Mg and Y
through a line-by-line differential analysis for a sample of 48 metal-poor
solar-type stars in the solar neighbourhood. Through the isochrone fitting
method, stellar masses and ages of the sample were also estimated. We have
performed a joint analysis of these 48 objects, together with 185 solar-twins
and analogues from our previous studies. The combined sample consist of 233
solar-type stars in the solar neighbourhood, with metallicity in the range
$-$0.71 $\leq$ [Fe/H] $<$ +0.34. The main results of our homogeneous analysis
are summarised here.

  * •

The sample shows a clear bimodality in the [Mg/Fe] - [Fe/H] plane, the thin
and thick disk populations are clearly distinguishable. Thick disk stars show
higher [$\alpha$/Fe] values compared to thin disk stars. While the thick disk
stars are older than 8 Gyr, the thin disk shows an age spread. Nonetheless,
there is no age discontinuity between the two populations.

  * •

Our chemically defined thick disk and thin disk stars show overlap in the
kinematic space, a behaviour already noted in several previous studies.

  * •

The thick disk stars show an Age-Metallicity-Relation, however, the age and
metallicity exhibit an essentially flat distribution and are uncorrelated for
the thin disk stars. On the other hand, both populations are blended in the
Age - [Fe/H] distribution.

  * •

There exists a correlation between [Mg/Fe] and stellar ages for both
populations. However, in the case of [Y/Fe], only the thin disk stars show a
correlation. We note a clear dichotomy between these two populations in the
[Mg/Fe] - Age distribution, whereas there is no separation between them in the
[Y/Fe] - Age space.

  * •

The [Y/Mg] ratio shows strong anti-correlation with stellar age. Our analysis
confirms the metallicity dependence of the [Y/Mg] chemical clock. We note the
least scatter in the [Y/Mg] - Age distribution compared to previous studies of
solar-type stars. There is no discontinuity between the thin and thick disks
in the [Y/Mg] - Age correlation. Our estimates of the slope is compatible with
those found for the solar-twins and other samples of solar-type stars in the
higher metallicity bin ([Fe/H] $>$ $-$0.30) as our sample.

  * •

For the first time in the literature, we report similar slopes of [Y/Mg] - Age
correlation for thin ($-$0.039) and thick disk ($-$0.034) stars.

  * •

Using the dating relations (Eqs. 5 and 7), we could achieve high accuracies
(0.67 and 0.45 Gyr, respectively) and precisions (0.96 and 0.99 Gyr,
respectively). These accuracies are compatible with the best accuracy achieved
for solar-twins till date ($\sim$0.8 - 1.0 Gyr) in the solar neighbourhood.
The MRE in the chemical ages using these relations are 38% and 33%,
respectively. The chemical clock based on the MV relation (Eq. 7) has somewhat
better performance than the SV relations in two metallicity regimes (Eq. 5).

The relations connecting the abundance ratios and stellar ages are related to
the chemo-dynamical evolution of the Galaxy, and can be used to study
different components of it (Haywood et al., 2013, 2016). From our analysis, we
found that the [Y/Mg] chemical clock can be used as an age proxy for the
solar-type stars. The empirical relations showcased in this work should be
used only for the stars in the solar neighbourhood, with the parameter range
as our sample. The high-precision outcomes of our work are expected to provide
contributions to the understanding of different populations of the Galaxy and
its chemical evolution.

###### Acknowledgements.

JS and JM acknowledge the support from FAPESP (2022/10325-3 and 2018/04055-8).
This work made use of the SIMBAD astronomical database, operated at CDS,
Strasbourg, France, and the NASA ADS, USA. This work has made use of data from
the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. Based on data collected at
the European Southern Observatory under ESO programs 60.A-9036(A),
60.A-9700(G), 60.A-9709(G), 072.C-0488(E), 073.C-0733(A), 077.C-0295(A),
077.C-0295(B), 078.C-0209(A), 080.C-0712(A), 082.C-0212(A), 082.C-0212(B),
084.C-0229(A), 085.C-0019(A), 085.C-0063(A), 086.C-0284(A), 087.C-0831(A),
088.C-0323(A), 089.C-0732(A), 091.C-0034(A), 091.C-0936(A), 092.C-0579(A),
092.C-0721(A), 093.C-0409(A), 094.C-0797(A), 096.C-0053(A), 096.C-0210(A),
098.C-0366(A), 106.21TJ.001, 183.C-0972(A), 184.C-0815(A), 184.C-0815(C),
184.C-0815(F), 190.C-0027(A), 192.C-0852(A), 196.C-0042, 196.C-0042(D),
196.C-0042(E), 0100.C-0097(A), 1102.C-0923(A), and 1102.C-0923(C).

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##  Appendix A Stellar atmospheric parameters, mass, age, and the elemental
abundance ratios

Table 3: Stellar atmospheric parameters, mass, age, and the elemental
abundance ratios of the sample analysed in this study.

HD | HIP |  Teff | log g | [Fe/H] | $\zeta$ | Age | Mass | [Mg/Fe] | [Y/Fe] | [Y/Mg]
---|---|---|---|---|---|---|---|---|---|---
|  | (K) | (dex) | (dex) |  (km s-1) | (Gyr) |  (M⊙) | (dex) | (dex) | (dex)
208 | 569 |  5929$\pm$7 |  4.45$\pm$0.02 |  $-$0.324$\pm$0.006 |  1.25$\pm$0.02 |  7.50${}_{-0.24}^{+0.28}$ |  0.95${}_{-0.01}^{+0.01}$ |  0.06$\pm$0.01 |  $-$0.08$\pm$0.01 |  $-$0.13$\pm$0.01
4308 | 3497 |  5688$\pm$6 |  4.40$\pm$0.02 |  $-$0.319$\pm$0.004 |  1.00$\pm$0.01 |  10.40${}_{-0.24}^{+0.29}$ |  0.91${}_{-0.02}^{+0.01}$ |  0.22$\pm$0.01 |  $-$0.12$\pm$0.01 |  $-$0.34$\pm$0.01
4597 | 3704 |  6027$\pm$12 |  4.36$\pm$0.03 |  $-$0.432$\pm$0.009 |  1.42$\pm$0.03 |  7.60${}_{-0.25}^{+0.31}$ |  0.96${}_{-0.01}^{+0.01}$ |  0.09$\pm$0.01 |  $-$0.13$\pm$0.01 |  $-$0.22$\pm$0.01
7134 | 5578 |  5992$\pm$9 |  4.52$\pm$0.02 |  $-$0.315$\pm$0.005 |  1.24$\pm$0.02 |  6.60${}_{-0.25}^{+0.77}$ |  0.99${}_{-0.02}^{+0.01}$ |  0.10$\pm$0.01 |  $-$0.03$\pm$0.01 |  $-$0.13$\pm$0.02
17548 | 13128 |  6004$\pm$14 |  4.36$\pm$0.04 |  $-$0.586$\pm$0.010 |  1.50$\pm$0.04 |  9.50${}_{-0.32}^{+0.30}$ |  0.89${}_{-0.01}^{+0.02}$ |  0.12$\pm$0.01 |  $-$0.16$\pm$0.01 |  $-$0.28$\pm$0.02
17865 | 13267 |  5882$\pm$11 |  4.25$\pm$0.03 |  $-$0.631$\pm$0.008 |  1.39$\pm$0.03 |  10.90${}_{-0.28}^{+0.29}$ |  0.90${}_{-0.01}^{+0.01}$ |  0.25$\pm$0.01 |  $-$0.11$\pm$0.01 |  $-$0.35$\pm$0.01
20407 | 15131 |  5877$\pm$8 |  4.47$\pm$0.02 |  $-$0.458$\pm$0.006 |  1.27$\pm$0.02 |  8.60${}_{-0.27}^{+0.73}$ |  0.88${}_{-0.01}^{+0.02}$ |  0.08$\pm$0.01 |  $-$0.11$\pm$0.01 |  $-$0.19$\pm$0.01
21938 | 16365 |  5812$\pm$8 |  4.40$\pm$0.02 |  $-$0.484$\pm$0.007 |  1.24$\pm$0.02 |  11.00${}_{-0.29}^{+0.27}$ |  0.90${}_{-0.02}^{+0.01}$ |  0.25$\pm$0.01 |  $-$0.11$\pm$0.01 |  $-$0.36$\pm$0.01
26887 | 19809 |  6045$\pm$11 |  4.42$\pm$0.03 |  $-$0.395$\pm$0.008 |  1.40$\pm$0.02 |  7.00${}_{-0.27}^{+0.24}$ |  0.97${}_{-0.02}^{+0.01}$ |  0.07$\pm$0.01 |  $-$0.10$\pm$0.01 |  $-$0.17$\pm$0.01
28701 | 20677 |  5742$\pm$6 |  4.41$\pm$0.02 |  $-$0.320$\pm$0.004 |  1.07$\pm$0.01 |  10.40${}_{-0.25}^{+0.25}$ |  0.93${}_{-0.02}^{+0.01}$ |  0.25$\pm$0.01 |  0.23$\pm$0.01 |  $-$0.02$\pm$0.01
40865 | 28403 |  5727$\pm$5 |  4.47$\pm$0.02 |  $-$0.390$\pm$0.004 |  1.05$\pm$0.01 |  10.20${}_{-0.39}^{+0.23}$ |  0.87${}_{-0.01}^{+0.01}$ |  0.10$\pm$0.00 |  $-$0.14$\pm$0.01 |  $-$0.24$\pm$0.01
41248 | 28460 |  5746$\pm$8 |  4.50$\pm$0.02 |  $-$0.361$\pm$0.006 |  1.02$\pm$0.01 |  7.30${}_{-0.40}^{+0.57}$ |  0.88${}_{-0.01}^{+0.02}$ |  0.06$\pm$0.00 |  $-$0.03$\pm$0.01 |  $-$0.08$\pm$0.01
41323 | 28604 |  5774$\pm$12 |  4.51$\pm$0.02 |  $-$0.309$\pm$0.009 |  1.01$\pm$0.02 |  5.20${}_{-0.88}^{+0.64}$ |  0.92${}_{-0.02}^{+0.01}$ |  0.04$\pm$0.01 |  $-$0.01$\pm$0.01 |  $-$0.05$\pm$0.01
48938 | 32322 |  6029$\pm$12 |  4.38$\pm$0.03 |  $-$0.425$\pm$0.009 |  1.44$\pm$0.03 |  7.90${}_{-0.28}^{+0.29}$ |  0.96${}_{-0.01}^{+0.01}$ |  0.09$\pm$0.01 |  $-$0.13$\pm$0.01 |  $-$0.22$\pm$0.01
56274 | 35139 |  5777$\pm$11 |  4.56$\pm$0.02 |  $-$0.539$\pm$0.009 |  1.14$\pm$0.02 |  8.40${}_{-0.88}^{+0.52}$ |  0.84${}_{-0.02}^{+0.01}$ |  0.07$\pm$0.01 |  $-$0.10$\pm$0.01 |  $-$0.17$\pm$0.01
61902 | 37240 |  6148$\pm$19 |  4.14$\pm$0.05 |  $-$0.710$\pm$0.013 |  1.82$\pm$0.07 |  8.10${}_{-0.28}^{+0.39}$ |  0.95${}_{-0.01}^{+0.02}$ |  0.11$\pm$0.02 |  $-$0.14$\pm$0.01 |  $-$0.25$\pm$0.02
61986 | 37419 |  5742$\pm$6 |  4.45$\pm$0.02 |  $-$0.359$\pm$0.004 |  1.07$\pm$0.01 |  10.30${}_{-0.81}^{+0.24}$ |  0.88${}_{-0.01}^{+0.02}$ |  0.09$\pm$0.01 |  $-$0.15$\pm$0.00 |  $-$0.25$\pm$0.00
65907 | 38908 |  5992$\pm$9 |  4.52$\pm$0.02 |  $-$0.315$\pm$0.005 |  1.24$\pm$0.02 |  4.60${}_{-0.69}^{+0.53}$ |  1.02${}_{-0.02}^{+0.01}$ |  0.23$\pm$0.01 |  $-$0.09$\pm$0.01 |  $-$0.32$\pm$0.01
78558 | 44860 |  5757$\pm$8 |  4.36$\pm$0.02 |  $-$0.435$\pm$0.007 |  1.14$\pm$0.01 |  11.70${}_{-0.25}^{+0.28}$ |  0.90${}_{-0.01}^{+0.02}$ |  0.28$\pm$0.01 |  $-$0.04$\pm$0.01 |  $-$0.32$\pm$0.01
87838 | 49615 |  6094$\pm$12 |  4.35$\pm$0.03 |  $-$0.456$\pm$0.008 |  1.53$\pm$0.03 |  6.90${}_{-0.28}^{+0.51}$ |  0.98${}_{-0.02}^{+0.01}$ |  0.10$\pm$0.01 |  $-$0.13$\pm$0.01 |  $-$0.23$\pm$0.02
94444 | 53244 |  6013$\pm$16 |  4.26$\pm$0.04 |  $-$0.647$\pm$0.011 |  1.52$\pm$0.04 |  10.10${}_{-0.29}^{+0.31}$ |  0.89${}_{-0.01}^{+0.01}$ |  0.09$\pm$0.01 |  $-$0.15$\pm$0.01 |  $-$0.24$\pm$0.01
97507 | 54779 |  5774$\pm$8 |  4.37$\pm$0.02 |  $-$0.392$\pm$0.006 |  1.15$\pm$0.01 |  11.30${}_{-0.27}^{+0.26}$ |  0.91${}_{-0.01}^{+0.02}$ |  0.24$\pm$0.01 |  $-$0.09$\pm$0.01 |  $-$0.32$\pm$0.01
97998 | 55013 |  5702$\pm$8 |  4.51$\pm$0.02 |  $-$0.446$\pm$0.006 |  1.01$\pm$0.02 |  8.90${}_{-0.47}^{+0.63}$ |  0.84${}_{-0.01}^{+0.02}$ |  0.07$\pm$0.01 |  $-$0.07$\pm$0.01 |  $-$0.14$\pm$0.01
102365 | 57443 |  5647$\pm$4 |  4.40$\pm$0.01 |  $-$0.318$\pm$0.003 |  0.98$\pm$0.01 |  10.50${}_{-0.41}^{+0.22}$ |  0.88${}_{-0.01}^{+0.01}$ |  0.15$\pm$0.01 |  $-$0.14$\pm$0.01 |  $-$0.29$\pm$0.01
105837 | 59380 |  5920$\pm$9 |  4.49$\pm$0.03 |  $-$0.532$\pm$0.006 |  1.33$\pm$0.02 |  9.40${}_{-0.30}^{+0.27}$ |  0.87${}_{-0.01}^{+0.01}$ |  0.09$\pm$0.01 |  $-$0.14$\pm$0.01 |  $-$0.23$\pm$0.01
109310 | 61323 |  5912$\pm$10 |  4.46$\pm$0.03 |  $-$0.530$\pm$0.007 |  1.30$\pm$0.02 |  10.10${}_{-0.49}^{+0.28}$ |  0.87${}_{-0.01}^{+0.01}$ |  0.09$\pm$0.01 |  $-$0.15$\pm$0.01 |  $-$0.24$\pm$0.01
109684 | 61539 |  6012$\pm$12 |  4.32$\pm$0.03 |  $-$0.370$\pm$0.009 |  1.46$\pm$0.02 |  7.50${}_{-0.27}^{+0.77}$ |  0.99${}_{-0.02}^{+0.01}$ |  0.08$\pm$0.01 |  $-$0.14$\pm$0.01 |  $-$0.22$\pm$0.02
117105 | 65737 |  5904$\pm$8 |  4.33$\pm$0.02 |  $-$0.300$\pm$0.006 |  1.25$\pm$0.02 |  8.80${}_{-0.35}^{+0.24}$ |  0.96${}_{-0.01}^{+0.01}$ |  0.10$\pm$0.01 |  $-$0.14$\pm$0.01 |  $-$0.24$\pm$0.01
119173 | 66815 |  5888$\pm$13 |  4.42$\pm$0.03 |  $-$0.670$\pm$0.009 |  1.34$\pm$0.03 |  12.00${}_{-0.30}^{+0.36}$ |  0.82${}_{-0.01}^{+0.02}$ |  0.12$\pm$0.01 |  $-$0.18$\pm$0.01 |  $-$0.31$\pm$0.01
123651 | 69202 |  5922$\pm$8 |  4.46$\pm$0.03 |  $-$0.509$\pm$0.006 |  1.30$\pm$0.02 |  8.80${}_{-0.26}^{+0.69}$ |  0.88${}_{-0.01}^{+0.02}$ |  0.10$\pm$0.01 |  $-$0.12$\pm$0.01 |  $-$0.22$\pm$0.01
136352 | 75181 |  5708$\pm$5 |  4.44$\pm$0.02 |  $-$0.340$\pm$0.004 |  1.04$\pm$0.01 |  10.90${}_{-0.52}^{+0.27}$ |  0.90${}_{-0.01}^{+0.02}$ |  0.22$\pm$0.01 |  $-$0.09$\pm$0.01 |  $-$0.31$\pm$0.01
141624 | 77818 |  5914$\pm$7 |  4.40$\pm$0.02 |  $-$0.401$\pm$0.006 |  1.28$\pm$0.02 |  8.70${}_{-0.25}^{+0.28}$ |  0.93${}_{-0.02}^{+0.01}$ |  0.11$\pm$0.01 |  $-$0.16$\pm$0.01 |  $-$0.27$\pm$0.01
143114 | 78330 |  5804$\pm$10 |  4.38$\pm$0.03 |  $-$0.426$\pm$0.008 |  1.16$\pm$0.02 |  10.60${}_{-0.27}^{+0.86}$ |  0.91${}_{-0.02}^{+0.01}$ |  0.22$\pm$0.01 |  $-$0.09$\pm$0.01 |  $-$0.32$\pm$0.01
148211 | 80587 |  5917$\pm$12 |  4.21$\pm$0.03 |  $-$0.660$\pm$0.008 |  1.51$\pm$0.03 |  10.80${}_{-0.28}^{+0.28}$ |  0.89${}_{-0.01}^{+0.02}$ |  0.21$\pm$0.01 |  $-$0.11$\pm$0.01 |  $-$0.32$\pm$0.01
150433 | 81681 |  5683$\pm$6 |  4.41$\pm$0.02 |  $-$0.371$\pm$0.004 |  1.03$\pm$0.01 |  11.30${}_{-0.27}^{+0.23}$ |  0.89${}_{-0.01}^{+0.01}$ |  0.26$\pm$0.01 |  $-$0.11$\pm$0.00 |  $-$0.36$\pm$0.01
162396 | 87523 |  6077$\pm$14 |  4.18$\pm$0.03 |  $-$0.399$\pm$0.010 |  1.60$\pm$0.03 |  6.60${}_{-0.28}^{+0.29}$ |  1.05${}_{-0.01}^{+0.01}$ |  0.09$\pm$0.01 |  $-$0.01$\pm$0.01 |  $-$0.10$\pm$0.02
172568 | 91805 |  5727$\pm$7 |  4.49$\pm$0.02 |  $-$0.394$\pm$0.005 |  1.05$\pm$0.01 |  9.10${}_{-0.29}^{+0.53}$ |  0.87${}_{-0.01}^{+0.01}$ |  0.09$\pm$0.00 |  $-$0.14$\pm$0.01 |  $-$0.23$\pm$0.01
177758 | 93827 |  5874$\pm$10 |  4.31$\pm$0.03 |  $-$0.630$\pm$0.007 |  1.41$\pm$0.02 |  12.10${}_{-0.27}^{+0.27}$ |  0.87${}_{-0.01}^{+0.01}$ |  0.25$\pm$0.01 |  $-$0.11$\pm$0.01 |  $-$0.36$\pm$0.01
181720 | 95262 |  5792$\pm$12 |  4.17$\pm$0.03 |  $-$0.558$\pm$0.009 |  1.39$\pm$0.02 |  10.40${}_{-0.26}^{+0.29}$ |  0.94${}_{-0.01}^{+0.01}$ |  0.25$\pm$0.01 |  $-$0.13$\pm$0.01 |  $-$0.38$\pm$0.01
188815 | 98355 |  6210$\pm$18 |  4.27$\pm$0.05 |  $-$0.599$\pm$0.012 |  1.81$\pm$0.06 |  7.10${}_{-0.30}^{+0.29}$ |  0.97${}_{-0.01}^{+0.01}$ |  0.07$\pm$0.01 |  $-$0.10$\pm$0.02 |  $-$0.16$\pm$0.02
197536 | 102339 |  6082$\pm$13 |  4.27$\pm$0.03 |  $-$0.466$\pm$0.009 |  1.61$\pm$0.03 |  7.50${}_{-0.25}^{+0.24}$ |  0.99${}_{-0.01}^{+0.01}$ |  0.09$\pm$0.01 |  $-$0.11$\pm$0.01 |  $-$0.2$\pm$0.02
203608 | 105858 |  6139$\pm$15 |  4.40$\pm$0.04 |  $-$0.685$\pm$0.010 |  1.64$\pm$0.05 |  7.80${}_{-0.39}^{+0.46}$ |  0.91${}_{-0.02}^{+0.01}$ |  0.09$\pm$0.01 |  $-$0.13$\pm$0.01 |  $-$0.22$\pm$0.02
207190 | 107599 |  6178$\pm$15 |  4.22$\pm$0.03 |  $-$0.470$\pm$0.010 |  1.72$\pm$0.04 |  6.40${}_{-0.25}^{+0.28}$ |  1.04${}_{-0.01}^{+0.01}$ |  0.07$\pm$0.01 |  $-$0.08$\pm$0.02 |  $-$0.15$\pm$0.02
210752 | 109646 |  5936$\pm$11 |  4.41$\pm$0.03 |  $-$0.627$\pm$0.008 |  1.39$\pm$0.03 |  11.20${}_{-1.16}^{+0.27}$ |  0.85${}_{-0.02}^{+0.01}$ |  0.09$\pm$0.01 |  $-$0.15$\pm$0.01 |  $-$0.24$\pm$0.01
214385 | 111746 |  5695$\pm$5 |  4.45$\pm$0.02 |  $-$0.347$\pm$0.003 |  1.01$\pm$0.05 |  9.70${}_{-0.62}^{+0.27}$ |  0.87${}_{-0.01}^{+0.01}$ |  0.09$\pm$0.01 |  $-$0.14$\pm$0.01 |  $-$0.23$\pm$0.01
215257 | 112229 |  6027$\pm$16 |  4.29$\pm$0.04 |  $-$0.690$\pm$0.011 |  1.63$\pm$0.05 |  10.20${}_{-0.31}^{+0.32}$ |  0.88${}_{-0.01}^{+0.01}$ |  0.11$\pm$0.02 |  $-$0.16$\pm$0.01 |  $-$0.27$\pm$0.02
218504 | 114276 |  5953$\pm$13 |  4.25$\pm$0.03 |  $-$0.602$\pm$0.009 |  1.49$\pm$0.03 |  10.30${}_{-0.29}^{+0.29}$ |  0.91${}_{-0.01}^{+0.01}$ |  0.16$\pm$0.01 |  $-$0.13$\pm$0.01 |  $-$0.29$\pm$0.01
224393 | 118123 |  5776$\pm$11 |  4.50$\pm$0.02 |  $-$0.395$\pm$0.008 |  1.06$\pm$0.02 |  6.00${}_{-0.69}^{+0.60}$ |  0.89${}_{-0.02}^{+0.01}$ |  0.06$\pm$0.01 |  $-$0.03$\pm$0.01 |  $-$0.08$\pm$0.01

Table 4: Stellar atmospheric parameters, mass, age, and the elemental
abundance ratios of the solar-twins and analogues.

HD | HIP |  Teff | log g | [Fe/H] | $\zeta$ | Age | Mass | [Mg/Fe] | [Y/Fe] | [Y/Mg]
---|---|---|---|---|---|---|---|---|---|---
|  | (K) | (dex) | (dex) |  (km s-1) | (Gyr) |  (M⊙) | (dex) | (dex) | (dex)
361 | 669 |  5902$\pm$7 |  4.52$\pm$0.01 |  $-$0.122$\pm$0.005 |  1.10$\pm$0.01 |  1.60${}_{-0.30}^{+0.42}$ |  1.02${}_{-0.01}^{+0.02}$ |  $-$0.02$\pm$0.02 |  0.06$\pm$0.01 |  0.08$\pm$0.03
1233 | 1292 |  5549$\pm$18 |  4.55$\pm$0.03 |  0.151$\pm$0.015 |  1.10$\pm$0.04 |  0.40${}_{-0.20}^{+1.00}$ |  0.99${}_{-0.02}^{+0.02}$ |  $-$0.07$\pm$0.01 |  0.10$\pm$0.04 |  0.16$\pm$0.04
1461 | 1499 |  5751$\pm$4 |  4.33$\pm$0.01 |  0.182$\pm$0.003 |  1.01$\pm$0.01 |  4.70${}_{-0.35}^{+0.36}$ |  1.07${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  $-$0.03$\pm$0.01 |  $-$0.03$\pm$0.02
2071 | 1954 |  5720$\pm$2 |  4.46$\pm$0.01 |  $-$0.090$\pm$0.003 |  0.96$\pm$0.01 |  4.80${}_{-0.25}^{+0.39}$ |  0.97${}_{-0.01}^{+0.01}$ |  0.01$\pm$0.01 |  0.03$\pm$0.01 |  0.02$\pm$0.01
3821 | 3203 |  5868$\pm$9 |  4.54$\pm$0.02 |  $-$0.050$\pm$0.007 |  1.16$\pm$0.02 |  0.53${}_{-0.34}^{+0.34}$ |  1.04${}_{-0.02}^{+0.01}$ |  $-$0.04$\pm$0.01 |  0.10$\pm$0.01 |  0.14$\pm$0.02
3964 | 3311 |  5734$\pm$3 |  4.47$\pm$0.01 |  0.064$\pm$0.003 |  0.96$\pm$0.01 |  3.40${}_{-0.44}^{+0.25}$ |  1.01${}_{-0.01}^{+0.01}$ |  $-$0.01$\pm$0.01 |  0.04$\pm$0.01 |  0.05$\pm$0.01
6204 | 4909 |  5861$\pm$7 |  4.50$\pm$0.02 |  0.048$\pm$0.006 |  1.11$\pm$0.01 |  0.90${}_{-0.31}^{+0.31}$ |  1.06${}_{-0.01}^{+0.01}$ |  $-$0.05$\pm$0.01 |  0.09$\pm$0.01 |  0.14$\pm$0.01
6718 | 5301 |  5723$\pm$3 |  4.40$\pm$0.01 |  $-$0.074$\pm$0.003 |  0.98$\pm$0.01 |  6.90${}_{-0.26}^{+0.25}$ |  0.96${}_{-0.01}^{+0.01}$ |  0.02$\pm$0.00 |  $-$0.02$\pm$0.01 |  $-$0.04$\pm$0.01
7661 | 5938 |  5450$\pm$14 |  4.52$\pm$0.02 |  0.032$\pm$0.010 |  1.08$\pm$0.03 |  3.70${}_{-2.22}^{+0.71}$ |  0.92${}_{-0.01}^{+0.03}$ |  $-$0.05$\pm$0.02 |  0.11$\pm$0.03 |  0.16$\pm$0.04
BD$-$12 243 | 6276 |  5384$\pm$18 |  4.54$\pm$0.03 |  $-$0.014$\pm$0.012 |  1.14$\pm$0.03 |  3.60${}_{-2.23}^{+1.58}$ |  0.89${}_{-0.01}^{+0.02}$ |  $-$0.09$\pm$0.03 |  0.08$\pm$0.03 |  0.18$\pm$0.04
8291 | 6407 |  5775$\pm$7 |  4.51$\pm$0.01 |  $-$0.058$\pm$0.006 |  0.98$\pm$0.01 |  2.00${}_{-0.57}^{+0.78}$ |  1.00${}_{-0.01}^{+0.01}$ |  $-$0.01$\pm$0.01 |  0.06$\pm$0.01 |  0.08$\pm$0.01
8406 | 6455 |  5731$\pm$4 |  4.48$\pm$0.01 |  $-$0.105$\pm$0.003 |  0.96$\pm$0.01 |  4.20${}_{-0.49}^{+0.33}$ |  0.96${}_{-0.01}^{+0.01}$ |  $-$0.01$\pm$0.01 |  0.05$\pm$0.01 |  0.06$\pm$0.02
8828 | 6762 |  5398$\pm$6 |  4.39$\pm$0.02 |  $-$0.142$\pm$0.005 |  0.72$\pm$0.02 |  10.40${}_{-0.30}^{+0.85}$ |  0.85${}_{-0.01}^{+0.01}$ |  0.04$\pm$0.01 |  $-$0.07$\pm$0.02 |  $-$0.12$\pm$0.02
8859 | 6744 |  5518$\pm$4 |  4.39$\pm$0.01 |  $-$0.069$\pm$0.004 |  0.82$\pm$0.01 |  7.20${}_{-0.28}^{+0.26}$ |  0.91${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.01 |  $-$0.04$\pm$0.01 |  $-$0.07$\pm$0.01
9986 | 7585 |  5822$\pm$3 |  4.45$\pm$0.01 |  0.083$\pm$0.003 |  1.01$\pm$0.01 |  3.70${}_{-0.32}^{+0.28}$ |  1.04${}_{-0.01}^{+0.01}$ |  $-$0.01$\pm$0.00 |  0.06$\pm$0.00 |  0.07$\pm$0.01
10008 | 7576 |  5316$\pm$9 |  4.49$\pm$0.02 |  $-$0.055$\pm$0.008 |  0.93$\pm$0.03 |  6.00${}_{-1.42}^{+0.64}$ |  0.86${}_{-0.01}^{+0.01}$ |  $-$0.05$\pm$0.02 |  0.13$\pm$0.03 |  0.18$\pm$0.04
11195 | 8507 |  5717$\pm$3 |  4.46$\pm$0.01 |  $-$0.099$\pm$0.003 |  0.96$\pm$0.01 |  5.50${}_{-0.55}^{+0.39}$ |  0.96${}_{-0.01}^{+0.01}$ |  0.02$\pm$0.01 |  0.04$\pm$0.00 |  0.03$\pm$0.01
12264 | 9349 |  5818$\pm$6 |  4.52$\pm$0.01 |  $-$0.006$\pm$0.005 |  1.09$\pm$0.01 |  1.80${}_{-0.94}^{+0.24}$ |  1.04${}_{-0.01}^{+0.02}$ |  $-$0.03$\pm$0.01 |  0.06$\pm$0.01 |  0.10$\pm$0.01
13060 | 9400 |  5231$\pm$11 |  4.36$\pm$0.03 |  0.090$\pm$0.01 |  0.68$\pm$0.04 |  7.70${}_{-1.22}^{+0.98}$ |  0.88${}_{-0.01}^{+0.01}$ |  0.01$\pm$0.02 |  0.11$\pm$0.03 |  0.10$\pm$0.04
13357A | 10175 |  5719$\pm$3 |  4.49$\pm$0.01 |  $-$0.028$\pm$0.002 |  0.97$\pm$0.01 |  4.10${}_{-0.48}^{+0.63}$ |  0.99${}_{-0.02}^{+0.01}$ |  $-$0.01$\pm$0.00 |  0.07$\pm$0.00 |  0.07$\pm$0.01
13612B | 10303 |  5712$\pm$3 |  4.40$\pm$0.01 |  0.104$\pm$0.003 |  0.94$\pm$0.01 |  5.10${}_{-0.26}^{+0.28}$ |  1.01${}_{-0.01}^{+0.01}$ |  0.02$\pm$0.00 |  0.02$\pm$0.00 |  0.00$\pm$0.01
14374 | 10818 |  5413$\pm$6 |  4.45$\pm$0.02 |  $-$0.018$\pm$0.006 |  0.81$\pm$0.02 |  5.90${}_{-0.78}^{+0.51}$ |  0.90${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  0.07$\pm$0.03 |  0.07$\pm$0.03
16008 | 11915 |  5769$\pm$4 |  4.48$\pm$0.01 |  $-$0.067$\pm$0.004 |  0.99$\pm$0.01 |  4.10${}_{-0.35}^{+0.36}$ |  0.99${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  0.04$\pm$0.01 |  0.04$\pm$0.01

Table 5: continued

HD | HIP |  Teff | log g | [Fe/H] | $\zeta$ | Age | Mass | [Mg/Fe] | [Y/Fe] | [Y/Mg]
---|---|---|---|---|---|---|---|---|---|---
|  | (K) | (dex) | (dex) |  (km s-1) | (Gyr) |  (M⊙) | (dex) | (dex) | (dex)
16297 | 12119 |  5396$\pm$6 |  4.43$\pm$0.02 |  0.008$\pm$0.006 |  0.81$\pm$0.02 |  6.80${}_{-0.46}^{+0.92}$ |  0.89${}_{-0.01}^{+0.02}$ |  $-$0.02$\pm$0.01 |  0.07$\pm$0.02 |  0.09$\pm$0.03
17925 | 13402 |  5149$\pm$18 |  4.44$\pm$0.06 |  0.088$\pm$0.015 |  0.97$\pm$0.06 |  6.10${}_{-1.89}^{+2.07}$ |  0.84${}_{-0.01}^{+0.01}$ |  $-$0.09$\pm$0.02 |  0.13$\pm$0.06 |  0.22$\pm$0.06
19467 | 14501 |  5738$\pm$4 |  4.31$\pm$0.01 |  $-$0.153$\pm$0.003 |  1.07$\pm$0.01 |  9.80${}_{-0.25}^{+0.19}$ |  0.98${}_{-0.01}^{+0.01}$ |  0.17$\pm$0.01 |  $-$0.08$\pm$0.01 |  $-$0.25$\pm$0.01
19518 | 14614 |  5803$\pm$4 |  4.45$\pm$0.01 |  $-$0.109$\pm$0.004 |  1.03$\pm$0.01 |  5.60${}_{-0.47}^{+0.38}$ |  0.99${}_{-0.01}^{+0.01}$ |  0.01$\pm$0.01 |  0.02$\pm$0.01 |  0.01$\pm$0.01
19668 | 14684 |  5501$\pm$18 |  4.57$\pm$0.03 |  0.010$\pm$0.013 |  1.15$\pm$0.04 |  1.00${}_{-0.40}^{+1.15}$ |  0.93${}_{-0.01}^{+0.01}$ |  $-$0.08$\pm$0.02 |  0.09$\pm$0.05 |  0.18$\pm$0.06
20003 | 14530 |  5483$\pm$5 |  4.40$\pm$0.02 |  0.075$\pm$0.006 |  0.76$\pm$0.02 |  7.60${}_{-0.72}^{+0.26}$ |  0.93${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  0.04$\pm$0.02 |  0.03$\pm$0.02
20782 | 15527 |  5779$\pm$4 |  4.34$\pm$0.01 |  $-$0.064$\pm$0.003 |  1.07$\pm$0.01 |  8.10${}_{-0.25}^{+0.23}$ |  0.99${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.01 |  $-$0.12$\pm$0.00 |  $-$0.15$\pm$0.01
21693 | 16085 |  5447$\pm$6 |  4.41$\pm$0.02 |  0.044$\pm$0.006 |  0.73$\pm$0.02 |  7.40${}_{-0.30}^{+0.71}$ |  0.91${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.01 |  0.02$\pm$0.02 |  $-$0.01$\pm$0.02
21175 | 15799 |  5223$\pm$12 |  4.35$\pm$0.03 |  0.127$\pm$0.010 |  0.69$\pm$0.04 |  10.30${}_{-1.22}^{+1.02}$ |  0.86${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.02 |  0.03$\pm$0.03 |  0.03$\pm$0.03
25874 | 18844 |  5734$\pm$3 |  4.37$\pm$0.01 |  0.014$\pm$0.003 |  1.01$\pm$0.01 |  7.50${}_{-0.27}^{+0.23}$ |  1.00${}_{-0.01}^{+0.01}$ |  0.07$\pm$0.01 |  $-$0.08$\pm$0.01 |  $-$0.15$\pm$0.01
26913 | 19855 |  5692$\pm$14 |  4.56$\pm$0.03 |  0.015$\pm$0.010 |  1.20$\pm$0.03 |  0.40${}_{-0.21}^{+0.88}$ |  0.99${}_{-0.01}^{+0.01}$ |  $-$0.07$\pm$0.02 |  0.10$\pm$0.04 |  0.18$\pm$0.04
28185 | 20723 |  5655$\pm$6 |  4.32$\pm$0.02 |  0.232$\pm$0.007 |  0.96$\pm$0.02 |  4.40${}_{-0.38}^{+0.29}$ |  1.04${}_{-0.01}^{+0.02}$ |  0.02$\pm$0.01 |  $-$0.05$\pm$0.01 |  $-$0.07$\pm$0.01
30306 | 21731 |  5547$\pm$9 |  4.27$\pm$0.02 |  0.223$\pm$0.008 |  0.89$\pm$0.02 |  7.50${}_{-0.42}^{+0.39}$ |  1.00${}_{-0.01}^{+0.02}$ |  0.03$\pm$0.01 |  $-$0.06$\pm$0.03 |  $-$0.08$\pm$0.03
30495 | 22263 |  5870$\pm$7 |  4.54$\pm$0.01 |  0.037$\pm$0.006 |  1.10$\pm$0.01 |  0.63${}_{-0.34}^{+0.34}$ |  1.05${}_{-0.01}^{+0.01}$ |  $-$0.04$\pm$0.01 |  0.11$\pm$0.01 |  0.15$\pm$0.01
31527 | 22905 |  5907$\pm$5 |  4.38$\pm$0.02 |  $-$0.185$\pm$0.004 |  1.15$\pm$0.01 |  5.90${}_{-0.24}^{+0.28}$ |  1.00${}_{-0.01}^{+0.01}$ |  0.05$\pm$0.00 |  $-$0.07$\pm$0.01 |  $-$0.12$\pm$0.01
32724 | 23627 |  5826$\pm$8 |  4.16$\pm$0.02 |  $-$0.184$\pm$0.005 |  1.22$\pm$0.01 |  8.50${}_{-0.25}^{+0.24}$ |  1.02${}_{-0.01}^{+0.01}$ |  0.12$\pm$0.01 |  $-$0.12$\pm$0.01 |  $-$0.24$\pm$0.01
34449 | 22504 |  5854$\pm$3 |  4.47$\pm$0.01 |  $-$0.098$\pm$0.003 |  1.07$\pm$0.01 |  2.70${}_{-0.27}^{+0.29}$ |  1.01${}_{-0.01}^{+0.01}$ |  $-$0.01$\pm$0.01 |  0.02$\pm$0.01 |  0.03$\pm$0.02
36152 | 25670 |  5760$\pm$3 |  4.42$\pm$0.01 |  0.054$\pm$0.003 |  0.98$\pm$0.01 |  5.10${}_{-0.54}^{+0.27}$ |  1.01${}_{-0.01}^{+0.01}$ |  0.01$\pm$0.01 |  0.02$\pm$0.01 |  0.01$\pm$0.01
39881 | 28066 |  5742$\pm$4 |  4.30$\pm$0.01 |  $-$0.147$\pm$0.003 |  1.07$\pm$0.01 |  9.00${}_{-0.20}^{+0.26}$ |  0.99${}_{-0.01}^{+0.01}$ |  0.19$\pm$0.01 |  $-$0.08$\pm$0.01 |  $-$0.27$\pm$0.01
40397 | 28267 |  5522$\pm$5 |  4.38$\pm$0.01 |  $-$0.116$\pm$0.004 |  0.84$\pm$0.01 |  11.30${}_{-0.25}^{+0.24}$ |  0.89${}_{-0.01}^{+0.01}$ |  0.13$\pm$0.01 |  $-$0.08$\pm$0.01 |  $-$0.21$\pm$0.01
41087 | 28518 |  5588$\pm$13 |  4.53$\pm$0.02 |  $-$0.105$\pm$0.009 |  1.07$\pm$0.02 |  2.90${}_{-1.03}^{+1.09}$ |  0.93${}_{-0.01}^{+0.02}$ |  $-$0.07$\pm$0.01 |  0.08$\pm$0.02 |  0.15$\pm$0.02
41593 | 28954 |  5306$\pm$14 |  4.49$\pm$0.03 |  0.034$\pm$0.011 |  0.93$\pm$0.04 |  4.50${}_{-2.23}^{+0.92}$ |  0.88${}_{-0.01}^{+0.02}$ |  $-$0.05$\pm$0.02 |  0.20$\pm$0.05 |  0.25$\pm$0.06
42618 | 29432 |  5762$\pm$3 |  4.45$\pm$0.01 |  $-$0.112$\pm$0.003 |  1.01$\pm$0.01 |  6.00${}_{-0.72}^{+0.28}$ |  0.97${}_{-0.02}^{+0.01}$ |  0.00$\pm$0.00 |  $-$0.02$\pm$0.00 |  $-$0.02$\pm$0.01
42807 | 29525 |  5741$\pm$9 |  4.52$\pm$0.02 |  $-$0.012$\pm$0.007 |  1.09$\pm$0.02 |  0.80${}_{-0.30}^{+0.90}$ |  0.90${}_{-0.01}^{+0.01}$ |  $-$0.06$\pm$0.01 |  0.09$\pm$0.01 |  0.14$\pm$0.01
43162 | 29568 |  5658$\pm$13 |  4.55$\pm$0.03 |  0.025$\pm$0.009 |  1.15$\pm$0.02 |  0.90${}_{-0.27}^{+0.25}$ |  0.98${}_{-0.01}^{+0.02}$ |  $-$0.08$\pm$0.02 |  0.10$\pm$0.03 |  0.18$\pm$0.04
43834 | 29271 |  5593$\pm$5 |  4.38$\pm$0.02 |  0.123$\pm$0.005 |  0.86$\pm$0.01 |  5.50${}_{-0.38}^{+0.38}$ |  0.99${}_{-0.01}^{+0.02}$ |  0.02$\pm$0.01 |  0.01$\pm$0.01 |  $-$0.01$\pm$0.02
45021 | 30037 |  5666$\pm$3 |  4.42$\pm$0.01 |  0.007$\pm$0.003 |  0.91$\pm$0.01 |  6.40${}_{-0.42}^{+0.26}$ |  0.96${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  $-$0.02$\pm$0.01 |  $-$0.02$\pm$0.01
44665A | 30158 |  5678$\pm$4 |  4.37$\pm$0.01 |  $-$0.004$\pm$0.003 |  0.95$\pm$0.01 |  7.30${}_{-0.25}^{+0.29}$ |  0.96${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.01 |  $-$0.04$\pm$0.01 |  $-$0.08$\pm$0.01
45289 | 30476 |  5709$\pm$4 |  4.28$\pm$0.01 |  $-$0.033$\pm$0.003 |  1.05$\pm$0.01 |  9.40${}_{-0.26}^{+0.19}$ |  0.99${}_{-0.01}^{+0.02}$ |  0.11$\pm$0.01 |  $-$0.10$\pm$0.01 |  $-$0.21$\pm$0.01
45346 | 30502 |  5731$\pm$4 |  4.40$\pm$0.01 |  $-$0.057$\pm$0.004 |  0.98$\pm$0.01 |  7.30${}_{-0.59}^{+0.25}$ |  0.97${}_{-0.01}^{+0.01}$ |  0.02$\pm$0.01 |  $-$0.03$\pm$0.01 |  $-$0.05$\pm$0.01
47186 | 31540 |  5674$\pm$6 |  4.33$\pm$0.02 |  0.253$\pm$0.007 |  0.97$\pm$0.02 |  4.30${}_{-0.28}^{+0.37}$ |  1.06${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  $-$0.03$\pm$0.01 |  $-$0.04$\pm$0.02
50806 | 33094 |  5629$\pm$7 |  4.11$\pm$0.02 |  0.023$\pm$0.005 |  1.10$\pm$0.01 |  8.70${}_{-0.09}^{+0.09}$ |  1.06${}_{-0.01}^{+0.01}$ |  0.16$\pm$0.01 |  $-$0.07$\pm$0.01 |  $-$0.24$\pm$0.01
51608 | 33229 |  5370$\pm$6 |  4.38$\pm$0.02 |  $-$0.023$\pm$0.006 |  0.70$\pm$0.02 |  10.40${}_{-0.25}^{+0.95}$ |  0.86${}_{-0.01}^{+0.01}$ |  0.05$\pm$0.01 |  $-$0.05$\pm$0.03 |  $-$0.10$\pm$0.04
53705 | 34065 |  5826$\pm$8 |  4.29$\pm$0.02 |  $-$0.230$\pm$0.006 |  1.17$\pm$0.02 |  9.20${}_{-0.26}^{+0.25}$ |  0.99${}_{-0.01}^{+0.02}$ |  0.13$\pm$0.01 |  $-$0.14$\pm$0.01 |  $-$0.27$\pm$0.02
54351 | 34511 |  5812$\pm$4 |  4.45$\pm$0.01 |  $-$0.091$\pm$0.003 |  1.04$\pm$0.01 |  5.20${}_{-0.46}^{+0.40}$ |  1.00${}_{-0.01}^{+0.01}$ |  0.01$\pm$0.01 |  0.03$\pm$0.01 |  0.02$\pm$0.01
59468 | 36210 |  5617$\pm$4 |  4.39$\pm$0.01 |  0.045$\pm$0.004 |  0.91$\pm$0.01 |  7.60${}_{-0.27}^{+0.22}$ |  0.96${}_{-0.01}^{+0.02}$ |  0.03$\pm$0.01 |  $-$0.06$\pm$0.01 |  $-$0.09$\pm$0.01
59711 | 36512 |  5744$\pm$2 |  4.45$\pm$0.01 |  $-$0.126$\pm$0.002 |  0.99$\pm$0.01 |  6.30${}_{-0.24}^{+0.29}$ |  0.96${}_{-0.01}^{+0.01}$ |  0.02$\pm$0.01 |  $-$0.01$\pm$0.00 |  $-$0.03$\pm$0.01
59967 | 36515 |  5855$\pm$12 |  4.56$\pm$0.02 |  $-$0.029$\pm$0.009 |  1.23$\pm$0.02 |  0.50${}_{-0.25}^{+0.28}$ |  1.03${}_{-0.01}^{+0.01}$ |  $-$0.07$\pm$0.01 |  0.09$\pm$0.01 |  0.16$\pm$0.02
61005 | 36948 |  5581$\pm$20 |  4.51$\pm$0.04 |  0.069$\pm$0.015 |  1.43$\pm$0.04 |  3.60${}_{-1.84}^{+2.16}$ |  0.96${}_{-0.02}^{+0.01}$ |  $-$0.07$\pm$0.02 |  0.03$\pm$0.06 |  0.10$\pm$0.06
63487 | 38072 |  5860$\pm$9 |  4.51$\pm$0.02 |  0.085$\pm$0.007 |  1.15$\pm$0.02 |  2.10${}_{-0.76}^{+0.36}$ |  1.06${}_{-0.02}^{+0.01}$ |  $-$0.02$\pm$0.01 |  0.03$\pm$0.01 |  0.06$\pm$0.01
63765 | 38041 |  5445$\pm$4 |  4.48$\pm$0.02 |  $-$0.137$\pm$0.004 |  0.81$\pm$0.01 |  5.60${}_{-0.46}^{+0.55}$ |  0.88${}_{-0.01}^{+0.02}$ |  $-$0.01$\pm$0.02 |  0.06$\pm$0.01 |  0.07$\pm$0.03
65216 | 38558 |  5634$\pm$4 |  4.47$\pm$0.01 |  $-$0.155$\pm$0.004 |  0.91$\pm$0.01 |  5.20${}_{-0.69}^{+0.31}$ |  0.92${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  0.04$\pm$0.01 |  0.03$\pm$0.02
66221 | 39298 |  5625$\pm$6 |  4.32$\pm$0.02 |  0.202$\pm$0.007 |  0.93$\pm$0.02 |  6.00${}_{-0.30}^{+0.30}$ |  1.03${}_{-0.01}^{+0.01}$ |  0.04$\pm$0.01 |  $-$0.02$\pm$0.02 |  $-$0.06$\pm$0.02
66653 | 39330 |  5869$\pm$4 |  4.43$\pm$0.01 |  0.145$\pm$0.004 |  1.07$\pm$0.01 |  1.40${}_{-0.32}^{+0.22}$ |  1.10${}_{-0.01}^{+0.02}$ |  $-$0.03$\pm$0.00 |  0.01$\pm$0.01 |  0.04$\pm$0.01
67458 | 39710 |  5904$\pm$7 |  4.43$\pm$0.02 |  $-$0.172$\pm$0.006 |  1.13$\pm$0.02 |  3.30${}_{-0.37}^{+0.39}$ |  1.02${}_{-0.02}^{+0.01}$ |  0.03$\pm$0.01 |  $-$0.02$\pm$0.01 |  $-$0.05$\pm$0.01
68168 | 40133 |  5745$\pm$3 |  4.37$\pm$0.01 |  0.116$\pm$0.002 |  0.99$\pm$0.01 |  5.30${}_{-0.24}^{+0.27}$ |  1.04${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.00 |  $-$0.01$\pm$0.00 |  $-$0.05$\pm$0.01
69830 | 40693 |  5399$\pm$5 |  4.41$\pm$0.02 |  $-$0.029$\pm$0.006 |  0.71$\pm$0.02 |  8.30${}_{-0.29}^{+0.73}$ |  0.88${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.01 |  0.02$\pm$0.03 |  $-$0.01$\pm$0.03
70642 | 40952 |  5692$\pm$4 |  4.37$\pm$0.01 |  0.194$\pm$0.004 |  0.94$\pm$0.01 |  3.30${}_{-0.26}^{+0.27}$ |  1.05${}_{-0.01}^{+0.01}$ |  0.01$\pm$0.01 |  $-$0.01$\pm$0.01 |  $-$0.03$\pm$0.02
71334 | 41317 |  5706$\pm$3 |  4.39$\pm$0.01 |  $-$0.081$\pm$0.003 |  0.99$\pm$0.01 |  7.70${}_{-0.24}^{+0.32}$ |  0.96${}_{-0.01}^{+0.01}$ |  0.06$\pm$0.00 |  $-$0.08$\pm$0.01 |  $-$0.14$\pm$0.01
71835 | 41529 |  5464$\pm$4 |  4.44$\pm$0.01 |  0.005$\pm$0.004 |  0.78$\pm$0.01 |  7.30${}_{-0.35}^{+0.26}$ |  0.90${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  0.03$\pm$0.02 |  0.03$\pm$0.02
72769 | 42011 |  5635$\pm$8 |  4.27$\pm$0.02 |  0.339$\pm$0.008 |  0.98$\pm$0.02 |  5.40${}_{-0.26}^{+0.28}$ |  1.07${}_{-0.01}^{+0.01}$ |  0.01$\pm$0.02 |  $-$0.02$\pm$0.01 |  $-$0.03$\pm$0.02
73350 | 42333 |  5846$\pm$8 |  4.50$\pm$0.02 |  0.132$\pm$0.006 |  1.11$\pm$0.01 |  0.90${}_{-0.24}^{+0.29}$ |  1.07${}_{-0.01}^{+0.01}$ |  $-$0.05$\pm$0.01 |  0.09$\pm$0.01 |  0.14$\pm$0.01
74014 | 42634 |  5570$\pm$9 |  4.29$\pm$0.02 |  0.262$\pm$0.008 |  0.91$\pm$0.02 |  6.30${}_{-0.44}^{+0.40}$ |  1.02${}_{-0.01}^{+0.02}$ |  0.02$\pm$0.02 |  $-$0.04$\pm$0.02 |  $-$0.06$\pm$0.03
75302 | 43297 |  5705$\pm$4 |  4.51$\pm$0.01 |  0.082$\pm$0.003 |  1.00$\pm$0.01 |  2.60${}_{-0.71}^{+0.26}$ |  1.01${}_{-0.01}^{+0.01}$ |  $-$0.02$\pm$0.01 |  0.09$\pm$0.01 |  0.11$\pm$0.01
76151 | 43726 |  5785$\pm$3 |  4.44$\pm$0.01 |  0.109$\pm$0.004 |  1.01$\pm$0.01 |  1.40${}_{-0.55}^{+0.44}$ |  1.06${}_{-0.01}^{+0.02}$ |  $-$0.02$\pm$0.00 |  $-$0.01$\pm$0.01 |  0.01$\pm$0.01
78429 | 44713 |  5759$\pm$3 |  4.28$\pm$0.01 |  0.063$\pm$0.004 |  1.09$\pm$0.01 |  7.60${}_{-0.22}^{+0.27}$ |  1.03${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.01 |  $-$0.10$\pm$0.01 |  $-$0.13$\pm$0.01
78534 | 44935 |  5771$\pm$4 |  4.37$\pm$0.01 |  0.038$\pm$0.004 |  1.04$\pm$0.01 |  6.60${}_{-0.28}^{+0.26}$ |  1.01${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.00 |  $-$0.05$\pm$0.01 |  $-$0.08$\pm$0.01
78538 | 44890 |  5804$\pm$9 |  4.53$\pm$0.02 |  $-$0.006$\pm$0.006 |  1.07$\pm$0.01 |  0.40${}_{-0.20}^{+0.94}$ |  1.02${}_{-0.01}^{+0.02}$ |  $-$0.06$\pm$0.01 |  0.10$\pm$0.02 |  0.16$\pm$0.02
78612 | 44896 |  5846$\pm$9 |  4.18$\pm$0.02 |  $-$0.260$\pm$0.007 |  1.25$\pm$0.02 |  9.00${}_{-0.27}^{+0.24}$ |  1.00${}_{-0.01}^{+0.01}$ |  0.11$\pm$0.01 |  $-$0.12$\pm$0.01 |  $-$0.23$\pm$0.02
78660 | 44997 |  5728$\pm$3 |  4.41$\pm$0.01 |  $-$0.012$\pm$0.003 |  0.96$\pm$0.01 |  5.10${}_{-0.42}^{+0.40}$ |  0.97${}_{-0.01}^{+0.01}$ |  $-$0.01$\pm$0.00 |  0.01$\pm$0.01 |  0.02$\pm$0.01
83529 | 47225 |  5916$\pm$7 |  4.28$\pm$0.02 |  $-$0.244$\pm$0.005 |  1.23$\pm$0.01 |  6.90${}_{-0.22}^{+0.27}$ |  1.00${}_{-0.01}^{+0.01}$ |  0.07$\pm$0.01 |  $-$0.13$\pm$0.01 |  $-$0.20$\pm$0.02
88072 | 49756 |  5789$\pm$3 |  4.44$\pm$0.01 |  0.023$\pm$0.003 |  1.03$\pm$0.01 |  5.20${}_{-0.37}^{+0.25}$ |  1.01${}_{-0.01}^{+0.01}$ |  0.01$\pm$0.01 |  0.01$\pm$0.00 |  0.00$\pm$0.01
89454 | 50534 |  5732$\pm$4 |  4.50$\pm$0.01 |  0.139$\pm$0.004 |  0.98$\pm$0.01 |  1.40${}_{-0.40}^{+0.66}$ |  1.03${}_{-0.01}^{+0.01}$ |  $-$0.06$\pm$0.02 |  0.08$\pm$0.01 |  0.14$\pm$0.03
92719 | 52369 |  5812$\pm$3 |  4.47$\pm$0.01 |  $-$0.114$\pm$0.003 |  1.03$\pm$0.01 |  4.40${}_{-0.32}^{+0.29}$ |  0.98${}_{-0.01}^{+0.02}$ |  0.00$\pm$0.01 |  0.03$\pm$0.01 |  0.03$\pm$0.02
94151 | 53087 |  5618$\pm$3 |  4.43$\pm$0.01 |  0.072$\pm$0.003 |  0.89$\pm$0.01 |  5.50${}_{-0.62}^{+0.40}$ |  0.97${}_{-0.01}^{+0.01}$ |  0.01$\pm$0.01 |  0.03$\pm$0.01 |  0.01$\pm$0.01
95521 | 53837 |  5774$\pm$4 |  4.48$\pm$0.01 |  $-$0.155$\pm$0.004 |  1.02$\pm$0.01 |  5.00${}_{-0.38}^{+0.29}$ |  0.96${}_{-0.01}^{+0.02}$ |  0.00$\pm$0.01 |  0.03$\pm$0.01 |  0.03$\pm$0.02
96064 | 54155 |  5507$\pm$17 |  4.56$\pm$0.03 |  0.067$\pm$0.011 |  1.16$\pm$0.03 |  0.70${}_{-0.26}^{+0.35}$ |  0.94${}_{-0.01}^{+0.01}$ |  $-$0.07$\pm$0.02 |  0.12$\pm$0.04 |  0.19$\pm$0.04
96116 | 54102 |  5845$\pm$6 |  4.51$\pm$0.01 |  0.011$\pm$0.005 |  1.06$\pm$0.01 |  1.40${}_{-0.58}^{+0.43}$ |  1.05${}_{-0.01}^{+0.01}$ |  $-$0.04$\pm$0.01 |  0.08$\pm$0.01 |  0.12$\pm$0.01
96423 | 54287 |  5714$\pm$4 |  4.34$\pm$0.01 |  0.107$\pm$0.004 |  0.99$\pm$0.01 |  5.90${}_{-0.29}^{+0.34}$ |  1.02${}_{-0.01}^{+0.01}$ |  0.04$\pm$0.01 |  $-$0.03$\pm$0.01 |  $-$0.07$\pm$0.01
96700 | 54400 |  5878$\pm$6 |  4.33$\pm$0.02 |  $-$0.189$\pm$0.004 |  1.16$\pm$0.01 |  6.80${}_{-0.24}^{+0.64}$ |  1.00${}_{-0.01}^{+0.01}$ |  0.07$\pm$0.01 |  $-$0.13$\pm$0.01 |  $-$0.20$\pm$0.02
97037 | 54582 |  5883$\pm$5 |  4.28$\pm$0.01 |  $-$0.096$\pm$0.004 |  1.20$\pm$0.01 |  7.70${}_{-0.26}^{+0.26}$ |  1.03${}_{-0.01}^{+0.02}$ |  0.05$\pm$0.01 |  $-$0.12$\pm$0.01 |  $-$0.17$\pm$0.01
97343 | 54704 |  5400$\pm$6 |  4.35$\pm$0.02 |  $-$0.032$\pm$0.006 |  0.69$\pm$0.02 |  11.20${}_{-0.32}^{+0.28}$ |  0.88${}_{-0.01}^{+0.02}$ |  0.10$\pm$0.01 |  $-$0.05$\pm$0.02 |  $-$0.16$\pm$0.02
100777 | 56572 |  5552$\pm$9 |  4.32$\pm$0.02 |  0.298$\pm$0.01 |  0.88$\pm$0.03 |  5.40${}_{-0.48}^{+0.44}$ |  1.03${}_{-0.02}^{+0.01}$ |  0.02$\pm$0.02 |  0.01$\pm$0.02 |  $-$0.01$\pm$0.02
102195 | 57370 |  5314$\pm$11 |  4.48$\pm$0.03 |  0.073$\pm$0.009 |  0.92$\pm$0.03 |  3.90${}_{-1.12}^{+1.20}$ |  0.89${}_{-0.01}^{+0.01}$ |  $-$0.07$\pm$0.02 |  0.11$\pm$0.03 |  0.18$\pm$0.04
104263 | 58558 |  5484$\pm$5 |  4.32$\pm$0.02 |  0.051$\pm$0.005 |  0.82$\pm$0.01 |  11.10${}_{-0.27}^{+0.24}$ |  0.90${}_{-0.01}^{+0.02}$ |  0.10$\pm$0.02 |  $-$0.06$\pm$0.01 |  $-$0.17$\pm$0.03
106116 | 59532 |  5681$\pm$4 |  4.34$\pm$0.01 |  0.157$\pm$0.004 |  0.98$\pm$0.01 |  4.70${}_{-0.37}^{+0.46}$ |  1.04${}_{-0.01}^{+0.01}$ |  0.02$\pm$0.01 |  $-$0.05$\pm$0.01 |  $-$0.07$\pm$0.02
108309 | 60729 |  5789$\pm$5 |  4.18$\pm$0.01 |  0.131$\pm$0.005 |  1.13$\pm$0.01 |  7.10${}_{-0.27}^{+0.21}$ |  1.09${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.01 |  $-$0.10$\pm$0.01 |  $-$0.14$\pm$0.01
110537 | 62039 |  5742$\pm$3 |  4.34$\pm$0.01 |  0.104$\pm$0.003 |  1.02$\pm$0.01 |  6.10${}_{-0.22}^{+0.27}$ |  1.04${}_{-0.01}^{+0.01}$ |  0.04$\pm$0.01 |  $-$0.06$\pm$0.01 |  $-$0.10$\pm$0.01
114174 | 64150 |  5747$\pm$2 |  4.37$\pm$0.01 |  0.049$\pm$0.003 |  1.02$\pm$0.01 |  6.70${}_{-0.38}^{+0.34}$ |  1.01${}_{-0.01}^{+0.01}$ |  0.05$\pm$0.01 |  0.27$\pm$0.01 |  0.22$\pm$0.01
112540 | 64109 |  5526$\pm$6 |  4.46$\pm$0.02 |  $-$0.164$\pm$0.007 |  0.84$\pm$0.02 |  5.50${}_{-0.46}^{+0.76}$ |  0.89${}_{-0.01}^{+0.01}$ |  0.02$\pm$0.01 |  0.06$\pm$0.02 |  0.04$\pm$0.03
114729 | 64459 |  5847$\pm$9 |  4.11$\pm$0.02 |  $-$0.307$\pm$0.007 |  1.34$\pm$0.02 |  8.20${}_{-0.24}^{+0.26}$ |  1.04${}_{-0.02}^{+0.01}$ |  0.14$\pm$0.01 |  $-$0.13$\pm$0.02 |  $-$0.27$\pm$0.02
115031 | 64673 |  5912$\pm$5 |  4.29$\pm$0.01 |  $-$0.017$\pm$0.004 |  1.20$\pm$0.01 |  6.30${}_{-0.25}^{+0.23}$ |  1.07${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.00 |  $-$0.09$\pm$0.01 |  $-$0.12$\pm$0.01

Table 6: continued

HD | HIP |  Teff | log g | [Fe/H] | $\zeta$ | Age | Mass | [Mg/Fe] | [Y/Fe] | [Y/Mg]
---|---|---|---|---|---|---|---|---|---|---
|  | (K) | (dex) | (dex) |  (km s-1) | (Gyr) |  (M⊙) | (dex) | (dex) | (dex)
115169 | 64713 |  5788$\pm$4 |  4.44$\pm$0.01 |  $-$0.043$\pm$0.003 |  1.00$\pm$0.01 |  5.40${}_{-0.41}^{+0.40}$ |  0.99${}_{-0.01}^{+0.02}$ |  0.01$\pm$0.00 |  0.01$\pm$0.01 |  0.00$\pm$0.01
115617 | 64924 |  5568$\pm$4 |  4.39$\pm$0.01 |  0.006$\pm$0.004 |  0.84$\pm$0.01 |  7.70${}_{-0.26}^{+0.28}$ |  0.93${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.01 |  $-$0.06$\pm$0.02 |  $-$0.08$\pm$0.02
117126 | 65708 |  5746$\pm$5 |  4.22$\pm$0.01 |  $-$0.063$\pm$0.005 |  1.12$\pm$0.01 |  9.10${}_{-0.24}^{+0.25}$ |  1.01${}_{-0.01}^{+0.02}$ |  0.11$\pm$0.01 |  $-$0.08$\pm$0.01 |  $-$0.19$\pm$0.01
117207 | 65808 |  5659$\pm$7 |  4.30$\pm$0.02 |  0.242$\pm$0.007 |  0.97$\pm$0.02 |  5.40${}_{-0.26}^{+0.29}$ |  1.05${}_{-0.01}^{+0.02}$ |  $-$0.01$\pm$0.02 |  $-$0.04$\pm$0.03 |  $-$0.03$\pm$0.03
122194 | 68468 |  5845$\pm$5 |  4.33$\pm$0.01 |  0.071$\pm$0.004 |  1.10$\pm$0.01 |  5.80${}_{-0.25}^{+0.29}$ |  1.06${}_{-0.01}^{+0.01}$ |  0.05$\pm$0.01 |  $-$0.05$\pm$0.01 |  $-$0.10$\pm$0.01
124292 | 69414 |  5458$\pm$4 |  4.39$\pm$0.01 |  $-$0.113$\pm$0.004 |  0.79$\pm$0.01 |  9.90${}_{-0.46}^{+0.24}$ |  0.87${}_{-0.01}^{+0.01}$ |  0.06$\pm$0.01 |  $-$0.08$\pm$0.02 |  $-$0.13$\pm$0.02
124523 | 69645 |  5751$\pm$3 |  4.44$\pm$0.01 |  $-$0.026$\pm$0.004 |  1.00$\pm$0.01 |  5.70${}_{-0.41}^{+0.31}$ |  0.99${}_{-0.01}^{+0.01}$ |  0.02$\pm$0.01 |  0.00$\pm$0.01 |  $-$0.02$\pm$0.01
126525 | 70695 |  5668$\pm$3 |  4.42$\pm$0.01 |  $-$0.075$\pm$0.003 |  0.94$\pm$0.01 |  6.50${}_{-0.30}^{+0.46}$ |  0.96${}_{-0.01}^{+0.01}$ |  0.05$\pm$0.01 |  $-$0.06$\pm$0.01 |  $-$0.11$\pm$0.01
129814 | 72043 |  5845$\pm$4 |  4.34$\pm$0.01 |  $-$0.026$\pm$0.003 |  1.12$\pm$0.01 |  6.80${}_{-0.22}^{+0.26}$ |  1.03${}_{-0.01}^{+0.02}$ |  0.06$\pm$0.01 |  $-$0.10$\pm$0.01 |  $-$0.16$\pm$0.01
130322 | 72339 |  5368$\pm$7 |  4.42$\pm$0.02 |  0.036$\pm$0.007 |  0.74$\pm$0.02 |  7.30${}_{-0.68}^{+0.70}$ |  0.89${}_{-0.01}^{+0.02}$ |  0.00$\pm$0.01 |  0.07$\pm$0.03 |  0.07$\pm$0.03
131923 | 73241 |  5661$\pm$5 |  4.22$\pm$0.01 |  0.092$\pm$0.005 |  1.00$\pm$0.01 |  8.70${}_{-0.50}^{+0.28}$ |  1.03${}_{-0.02}^{+0.01}$ |  0.12$\pm$0.01 |  $-$0.09$\pm$0.01 |  $-$0.2$\pm$0.01
133600 | 73815 |  5790$\pm$3 |  4.33$\pm$0.01 |  0.023$\pm$0.003 |  1.07$\pm$0.01 |  7.30${}_{-0.29}^{+0.33}$ |  1.01${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.01 |  $-$0.10$\pm$0.01 |  $-$0.13$\pm$0.01
134330 | 74271 |  5623$\pm$5 |  4.46$\pm$0.02 |  0.102$\pm$0.005 |  0.98$\pm$0.01 |  4.00${}_{-0.31}^{+0.30}$ |  0.98${}_{-0.01}^{+0.01}$ |  $-$0.02$\pm$0.01 |  0.05$\pm$0.02 |  0.07$\pm$0.03
134606 | 74653 |  5625$\pm$9 |  4.29$\pm$0.02 |  0.311$\pm$0.008 |  0.97$\pm$0.02 |  5.50${}_{-0.28}^{+0.29}$ |  1.06${}_{-0.01}^{+0.01}$ |  0.02$\pm$0.02 |  $-$0.03$\pm$0.02 |  $-$0.06$\pm$0.03
134664 | 74389 |  5845$\pm$3 |  4.44$\pm$0.01 |  0.083$\pm$0.003 |  1.05$\pm$0.01 |  3.50${}_{-0.42}^{+0.45}$ |  1.05${}_{-0.01}^{+0.01}$ |  $-$0.01$\pm$0.01 |  0.04$\pm$0.01 |  0.04$\pm$0.01
135101 | 74432 |  5679$\pm$5 |  4.17$\pm$0.01 |  0.048$\pm$0.005 |  1.09$\pm$0.01 |  8.50${}_{-0.25}^{+0.24}$ |  1.06${}_{-0.01}^{+0.01}$ |  0.14$\pm$0.01 |  $-$0.09$\pm$0.01 |  $-$0.23$\pm$0.01
136894 | 75363 |  5451$\pm$5 |  4.39$\pm$0.02 |  $-$0.062$\pm$0.006 |  0.79$\pm$0.02 |  8.30${}_{-0.43}^{+0.44}$ |  0.89${}_{-0.01}^{+0.01}$ |  0.02$\pm$0.01 |  $-$0.06$\pm$0.03 |  $-$0.08$\pm$0.03
138549 | 76200 |  5586$\pm$3 |  4.45$\pm$0.01 |  0.032$\pm$0.005 |  0.89$\pm$0.01 |  4.70${}_{-0.49}^{+0.25}$ |  0.96${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  0.02$\pm$0.01 |  0.02$\pm$0.01
138573 | 76114 |  5740$\pm$3 |  4.41$\pm$0.01 |  $-$0.024$\pm$0.003 |  0.97$\pm$0.01 |  6.50${}_{-0.42}^{+0.29}$ |  0.98${}_{-0.01}^{+0.01}$ |  0.01$\pm$0.00 |  $-$0.03$\pm$0.01 |  $-$0.04$\pm$0.01
140538 | 77052 |  5687$\pm$3 |  4.45$\pm$0.01 |  0.051$\pm$0.003 |  0.96$\pm$0.01 |  3.90${}_{-0.34}^{+0.35}$ |  0.99${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  0.08$\pm$0.01 |  0.08$\pm$0.01
140901 | 77358 |  5619$\pm$4 |  4.43$\pm$0.02 |  0.107$\pm$0.004 |  0.95$\pm$0.01 |  4.40${}_{-0.56}^{+0.24}$ |  0.98${}_{-0.01}^{+0.01}$ |  $-$0.01$\pm$0.01 |  0.03$\pm$0.02 |  0.04$\pm$0.02
142331 | 77883 |  5699$\pm$3 |  4.38$\pm$0.01 |  0.017$\pm$0.003 |  0.99$\pm$0.01 |  7.60${}_{-0.29}^{+0.23}$ |  0.97${}_{-0.01}^{+0.01}$ |  0.02$\pm$0.01 |  $-$0.08$\pm$0.01 |  $-$0.10$\pm$0.01
145809 | 79524 |  5758$\pm$9 |  4.04$\pm$0.02 |  $-$0.296$\pm$0.008 |  1.25$\pm$0.01 |  8.50${}_{-0.23}^{+0.28}$ |  1.03${}_{-0.01}^{+0.01}$ |  0.12$\pm$0.01 |  $-$0.14$\pm$0.01 |  $-$0.26$\pm$0.02
145825 | 79578 |  5810$\pm$3 |  4.47$\pm$0.01 |  0.048$\pm$0.003 |  1.02$\pm$0.01 |  3.20${}_{-0.33}^{+0.31}$ |  1.03${}_{-0.01}^{+0.01}$ |  $-$0.01$\pm$0.01 |  0.03$\pm$0.01 |  0.04$\pm$0.01
145927 | 79715 |  5816$\pm$4 |  4.38$\pm$0.01 |  $-$0.037$\pm$0.004 |  1.09$\pm$0.01 |  6.70${}_{-0.32}^{+0.35}$ |  1.02${}_{-0.01}^{+0.01}$ |  0.08$\pm$0.01 |  $-$0.07$\pm$0.01 |  $-$0.15$\pm$0.01
146233 | 79672 |  5808$\pm$3 |  4.44$\pm$0.01 |  0.041$\pm$0.003 |  1.02$\pm$0.01 |  4.30${}_{-0.27}^{+0.28}$ |  1.00${}_{-0.01}^{+0.01}$ |  $-$0.05$\pm$0.00 |  0.04$\pm$0.01 |  0.09$\pm$0.01
147512 | 80218 |  5535$\pm$4 |  4.41$\pm$0.01 |  $-$0.061$\pm$0.004 |  0.81$\pm$0.01 |  8.30${}_{-0.24}^{+0.38}$ |  0.91${}_{-0.01}^{+0.02}$ |  0.05$\pm$0.01 |  $-$0.05$\pm$0.01 |  $-$0.09$\pm$0.02
149661 | 81300 |  5248$\pm$10 |  4.45$\pm$0.03 |  0.012$\pm$0.011 |  0.89$\pm$0.04 |  1.80${}_{-0.77}^{+3.19}$ |  0.91${}_{-0.02}^{+0.01}$ |  $-$0.03$\pm$0.02 |  0.06$\pm$0.02 |  0.09$\pm$0.03
150248 | 81746 |  5715$\pm$3 |  4.37$\pm$0.01 |  $-$0.091$\pm$0.003 |  0.99$\pm$0.01 |  8.10${}_{-0.39}^{+0.24}$ |  0.96${}_{-0.01}^{+0.01}$ |  0.06$\pm$0.00 |  $-$0.10$\pm$0.01 |  $-$0.16$\pm$0.01
151504 | 82265 |  5443$\pm$6 |  4.34$\pm$0.02 |  0.098$\pm$0.006 |  0.72$\pm$0.02 |  9.10${}_{-0.23}^{+0.83}$ |  0.93${}_{-0.01}^{+0.01}$ |  0.06$\pm$0.02 |  $-$0.01$\pm$0.02 |  $-$0.07$\pm$0.03
152391 | 82588 |  5483$\pm$10 |  4.53$\pm$0.02 |  $-$0.003$\pm$0.008 |  0.97$\pm$0.02 |  0.90${}_{-0.24}^{+1.05}$ |  0.94${}_{-0.01}^{+0.01}$ |  $-$0.04$\pm$0.02 |  0.11$\pm$0.03 |  0.15$\pm$0.04
153631 | 83276 |  5886$\pm$6 |  4.24$\pm$0.02 |  $-$0.093$\pm$0.005 |  1.23$\pm$0.01 |  6.60${}_{-0.34}^{+0.33}$ |  1.03${}_{-0.02}^{+0.01}$ |  0.02$\pm$0.01 |  $-$0.14$\pm$0.01 |  $-$0.16$\pm$0.01
157172 | 85017 |  5435$\pm$7 |  4.34$\pm$0.02 |  0.140$\pm$0.006 |  0.73$\pm$0.02 |  7.40${}_{-0.56}^{+0.52}$ |  0.94${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.01 |  0.01$\pm$0.02 |  $-$0.02$\pm$0.03
157347 | 85042 |  5685$\pm$3 |  4.35$\pm$0.01 |  0.030$\pm$0.003 |  0.97$\pm$0.01 |  7.20${}_{-0.26}^{+0.23}$ |  0.97${}_{-0.01}^{+0.02}$ |  0.03$\pm$0.00 |  $-$0.04$\pm$0.01 |  $-$0.07$\pm$0.01
161612 | 87116 |  5620$\pm$5 |  4.42$\pm$0.02 |  0.200$\pm$0.007 |  0.85$\pm$0.02 |  2.60${}_{-0.90}^{+0.29}$ |  1.03${}_{-0.01}^{+0.02}$ |  0.03$\pm$0.01 |  $-$0.03$\pm$0.01 |  $-$0.05$\pm$0.01
162236 | 87369 |  5365$\pm$6 |  4.43$\pm$0.02 |  $-$0.076$\pm$0.005 |  0.79$\pm$0.02 |  6.00${}_{-0.83}^{+1.01}$ |  0.87${}_{-0.01}^{+0.02}$ |  $-$0.01$\pm$0.01 |  0.03$\pm$0.02 |  0.04$\pm$0.03
163441 | 87769 |  5828$\pm$3 |  4.40$\pm$0.01 |  0.072$\pm$0.004 |  1.03$\pm$0.01 |  5.00${}_{-0.38}^{+0.30}$ |  1.04${}_{-0.01}^{+0.01}$ |  0.01$\pm$0.01 |  0.01$\pm$0.01 |  0.00$\pm$0.01
167060 | 89650 |  5851$\pm$3 |  4.42$\pm$0.01 |  $-$0.015$\pm$0.003 |  1.10$\pm$0.01 |  5.60${}_{-0.24}^{+0.27}$ |  1.03${}_{-0.01}^{+0.01}$ |  0.04$\pm$0.01 |  $-$0.05$\pm$0.01 |  $-$0.08$\pm$0.01
168746 | 90004 |  5592$\pm$5 |  4.36$\pm$0.01 |  $-$0.09$\pm$0.005 |  0.90$\pm$0.01 |  10.30${}_{-0.26}^{+0.24}$ |  0.94${}_{-0.01}^{+0.01}$ |  0.18$\pm$0.01 |  $-$0.04$\pm$0.01 |  $-$0.22$\pm$0.02
171665 | 91287 |  5667$\pm$3 |  4.44$\pm$0.01 |  $-$0.037$\pm$0.003 |  0.94$\pm$0.01 |  4.80${}_{-0.25}^{+0.35}$ |  0.96${}_{-0.01}^{+0.02}$ |  0.00$\pm$0.01 |  0.02$\pm$0.01 |  0.02$\pm$0.02
172513 | 91700 |  5525$\pm$4 |  4.46$\pm$0.01 |  $-$0.023$\pm$0.004 |  0.86$\pm$0.01 |  5.70${}_{-0.30}^{+0.46}$ |  0.92${}_{-0.01}^{+0.01}$ |  $-$0.01$\pm$0.01 |  0.08$\pm$0.02 |  0.09$\pm$0.03
183658 | 95962 |  5805$\pm$3 |  4.38$\pm$0.01 |  0.029$\pm$0.003 |  1.04$\pm$0.01 |  5.90${}_{-0.28}^{+0.28}$ |  1.01${}_{-0.01}^{+0.02}$ |  0.02$\pm$0.00 |  $-$0.03$\pm$0.00 |  $-$0.04$\pm$0.01
183579 | 96160 |  5798$\pm$4 |  4.48$\pm$0.01 |  $-$0.036$\pm$0.003 |  1.02$\pm$0.01 |  3.10${}_{-0.37}^{+0.41}$ |  1.01${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  0.05$\pm$0.01 |  0.05$\pm$0.01
185615 | 96854 |  5578$\pm$7 |  4.28$\pm$0.02 |  0.11$\pm$0.007 |  0.93$\pm$0.02 |  8.90${}_{-0.75}^{+0.25}$ |  0.97${}_{-0.01}^{+0.02}$ |  0.11$\pm$0.02 |  $-$0.07$\pm$0.01 |  $-$0.17$\pm$0.02
186302 | 97507 |  5694$\pm$6 |  4.48$\pm$0.02 |  0.007$\pm$0.007 |  0.92$\pm$0.02 |  4.70${}_{-0.46}^{+0.46}$ |  0.98${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  0.04$\pm$0.01 |  0.04$\pm$0.02
186803 | 97358 |  5684$\pm$9 |  4.54$\pm$0.02 |  $-$0.009$\pm$0.007 |  0.96$\pm$0.02 |  1.10${}_{-0.55}^{+0.64}$ |  0.99${}_{-0.01}^{+0.01}$ |  $-$0.05$\pm$0.01 |  0.11$\pm$0.03 |  0.16$\pm$0.03
188748 | 98621 |  5629$\pm$4 |  4.42$\pm$0.01 |  $-$0.114$\pm$0.004 |  0.92$\pm$0.01 |  7.80${}_{-0.27}^{+0.30}$ |  0.92${}_{-0.01}^{+0.01}$ |  0.04$\pm$0.01 |  $-$0.05$\pm$0.02 |  $-$0.09$\pm$0.02
190647 | 99115 |  5615$\pm$11 |  4.09$\pm$0.02 |  0.242$\pm$0.009 |  1.07$\pm$0.02 |  8.50${}_{-0.25}^{+0.26}$ |  1.08${}_{-0.01}^{+0.01}$ |  0.06$\pm$0.02 |  $-$0.05$\pm$0.02 |  $-$0.11$\pm$0.03
196390 | 101905 |  5906$\pm$5 |  4.50$\pm$0.01 |  0.088$\pm$0.004 |  1.08$\pm$0.01 |  1.40${}_{-0.29}^{+0.28}$ |  1.08${}_{-0.01}^{+0.02}$ |  $-$0.03$\pm$0.01 |  0.08$\pm$0.01 |  0.11$\pm$0.01
197027 | 102152 |  5718$\pm$4 |  4.33$\pm$0.01 |  $-$0.016$\pm$0.003 |  0.99$\pm$0.01 |  8.40${}_{-0.43}^{+0.23}$ |  0.98${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.01 |  $-$0.10$\pm$0.01 |  $-$0.14$\pm$0.01
197076 | 102040 |  5853$\pm$4 |  4.48$\pm$0.01 |  $-$0.080$\pm$0.003 |  1.05$\pm$0.01 |  2.60${}_{-0.27}^{+0.32}$ |  1.02${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.00 |  0.05$\pm$0.01 |  0.05$\pm$0.01
197210 | 102203 |  5583$\pm$3 |  4.47$\pm$0.01 |  $-$0.009$\pm$0.004 |  0.85$\pm$0.01 |  4.70${}_{-0.35}^{+0.31}$ |  0.94${}_{-0.01}^{+0.01}$ |  $-$0.01$\pm$0.01 |  0.06$\pm$0.01 |  0.07$\pm$0.02
197823 | 102580 |  5400$\pm$7 |  4.40$\pm$0.02 |  0.164$\pm$0.007 |  0.79$\pm$0.02 |  4.40${}_{-0.47}^{+0.53}$ |  0.94${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  0.07$\pm$0.03 |  0.07$\pm$0.03
198075 | 102664 |  5829$\pm$6 |  4.45$\pm$0.02 |  $-$0.283$\pm$0.005 |  1.10$\pm$0.01 |  4.20${}_{-0.42}^{+0.36}$ |  0.96${}_{-0.01}^{+0.01}$ |  0.04$\pm$0.01 |  $-$0.05$\pm$0.01 |  $-$0.10$\pm$0.02
200633 | 104045 |  5826$\pm$3 |  4.41$\pm$0.01 |  0.051$\pm$0.003 |  1.04$\pm$0.01 |  5.00${}_{-0.28}^{+0.24}$ |  1.03${}_{-0.01}^{+0.02}$ |  $-$0.01$\pm$0.00 |  0.02$\pm$0.01 |  0.03$\pm$0.01
201219 | 104318 |  5669$\pm$11 |  4.54$\pm$0.02 |  0.132$\pm$0.008 |  1.02$\pm$0.02 |  0.50${}_{-0.36}^{+0.36}$ |  1.03${}_{-0.01}^{+0.00}$ |  $-$0.03$\pm$0.01 |  0.04$\pm$0.02 |  0.07$\pm$0.02
202628 | 105184 |  5843$\pm$6 |  4.51$\pm$0.01 |  0.003$\pm$0.004 |  1.05$\pm$0.01 |  1.20${}_{-0.45}^{+0.54}$ |  1.05${}_{-0.01}^{+0.01}$ |  $-$0.01$\pm$0.01 |  0.10$\pm$0.01 |  0.11$\pm$0.01
203384 | 105483 |  5560$\pm$10 |  4.31$\pm$0.02 |  0.276$\pm$0.010 |  0.94$\pm$0.03 |  5.40${}_{-0.72}^{+0.34}$ |  1.02${}_{-0.01}^{+0.02}$ |  0.02$\pm$0.01 |  $-$0.04$\pm$0.02 |  $-$0.07$\pm$0.02
203432 | 105606 |  5646$\pm$6 |  4.37$\pm$0.02 |  0.328$\pm$0.007 |  1.01$\pm$0.02 |  3.40${}_{-0.39}^{+0.31}$ |  1.06${}_{-0.01}^{+0.02}$ |  $-$0.01$\pm$0.02 |  $-$0.05$\pm$0.02 |  $-$0.03$\pm$0.03
204313 | 106006 |  5760$\pm$5 |  4.32$\pm$0.01 |  0.181$\pm$0.005 |  1.03$\pm$0.01 |  4.50${}_{-0.26}^{+0.24}$ |  1.07${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  $-$0.05$\pm$0.01 |  $-$0.05$\pm$0.02
205536 | 107022 |  5438$\pm$5 |  4.39$\pm$0.02 |  $-$0.021$\pm$0.006 |  0.73$\pm$0.02 |  9.00${}_{-0.59}^{+0.31}$ |  0.89${}_{-0.01}^{+0.01}$ |  0.05$\pm$0.01 |  $-$0.04$\pm$0.01 |  $-$0.10$\pm$0.01
205891 | 106931 |  5574$\pm$4 |  4.40$\pm$0.01 |  $-$0.138$\pm$0.004 |  0.86$\pm$0.01 |  8.60${}_{-0.24}^{+0.82}$ |  0.90${}_{-0.01}^{+0.02}$ |  0.05$\pm$0.01 |  $-$0.06$\pm$0.02 |  $-$0.11$\pm$0.03
207700 | 108158 |  5675$\pm$4 |  4.29$\pm$0.01 |  0.055$\pm$0.003 |  1.01$\pm$0.01 |  8.10${}_{-0.24}^{+0.33}$ |  1.02${}_{-0.01}^{+0.01}$ |  0.14$\pm$0.01 |  $-$0.08$\pm$0.01 |  $-$0.22$\pm$0.01
207832 | 107985 |  5730$\pm$4 |  4.44$\pm$0.01 |  0.154$\pm$0.004 |  1.01$\pm$0.01 |  1.20${}_{-0.41}^{+0.25}$ |  1.07${}_{-0.02}^{+0.01}$ |  $-$0.02$\pm$0.00 |  0.01$\pm$0.01 |  0.03$\pm$0.01
207970 | 108065 |  5562$\pm$6 |  4.32$\pm$0.02 |  0.086$\pm$0.005 |  0.89$\pm$0.01 |  10.90${}_{-0.29}^{+0.25}$ |  0.92${}_{-0.01}^{+0.01}$ |  0.08$\pm$0.01 |  $-$0.06$\pm$0.02 |  $-$0.14$\pm$0.02
208704 | 108468 |  5841$\pm$4 |  4.35$\pm$0.01 |  $-$0.096$\pm$0.004 |  1.13$\pm$0.01 |  7.20${}_{-0.25}^{+0.26}$ |  1.01${}_{-0.01}^{+0.01}$ |  0.04$\pm$0.01 |  $-$0.12$\pm$0.01 |  $-$0.16$\pm$0.01
210277 | 109378 |  5513$\pm$10 |  4.26$\pm$0.03 |  0.205$\pm$0.011 |  0.91$\pm$0.03 |  8.60${}_{-0.25}^{+0.88}$ |  0.98${}_{-0.01}^{+0.02}$ |  0.08$\pm$0.02 |  $-$0.02$\pm$0.02 |  $-$0.10$\pm$0.03
210918 | 109821 |  5747$\pm$4 |  4.31$\pm$0.01 |  $-$0.108$\pm$0.004 |  1.06$\pm$0.01 |  8.90${}_{-0.25}^{+0.23}$ |  0.98${}_{-0.01}^{+0.01}$ |  0.08$\pm$0.01 |  $-$0.09$\pm$0.01 |  $-$0.17$\pm$0.01
211415 | 110109 |  5871$\pm$5 |  4.38$\pm$0.02 |  $-$0.230$\pm$0.004 |  1.15$\pm$0.01 |  6.50${}_{-0.31}^{+0.50}$ |  0.98${}_{-0.01}^{+0.01}$ |  0.06$\pm$0.01 |  $-$0.11$\pm$0.01 |  $-$0.17$\pm$0.01
212708 | 110843 |  5671$\pm$8 |  4.27$\pm$0.02 |  0.293$\pm$0.008 |  1.00$\pm$0.02 |  5.20${}_{-0.29}^{+0.30}$ |  1.07${}_{-0.01}^{+0.01}$ |  0.01$\pm$0.02 |  $-$0.05$\pm$0.01 |  $-$0.06$\pm$0.02
213628 | 111349 |  5549$\pm$5 |  4.41$\pm$0.02 |  0.026$\pm$0.005 |  0.81$\pm$0.01 |  6.70${}_{-0.35}^{+0.29}$ |  0.94${}_{-0.01}^{+0.02}$ |  0.01$\pm$0.01 |  0.03$\pm$0.01 |  0.01$\pm$0.02
218544 | 114328 |  5775$\pm$4 |  4.36$\pm$0.01 |  $-$0.017$\pm$0.004 |  1.04$\pm$0.01 |  6.80${}_{-0.30}^{+0.40}$ |  0.99${}_{-0.01}^{+0.01}$ |  0.03$\pm$0.01 |  $-$0.06$\pm$0.01 |  $-$0.09$\pm$0.01
219057 | 114615 |  5819$\pm$5 |  4.51$\pm$0.01 |  $-$0.063$\pm$0.004 |  1.03$\pm$0.01 |  2.90${}_{-0.50}^{+0.33}$ |  1.03${}_{-0.01}^{+0.01}$ |  0.00$\pm$0.01 |  0.05$\pm$0.01 |  0.05$\pm$0.01
220507 | 115577 |  5694$\pm$4 |  4.26$\pm$0.01 |  0.013$\pm$0.003 |  1.04$\pm$0.01 |  8.70${}_{-0.24}^{+0.24}$ |  1.02${}_{-0.01}^{+0.01}$ |  0.15$\pm$0.01 |  $-$0.09$\pm$0.01 |  $-$0.24$\pm$0.01
222422 | 116819 |  5467$\pm$5 |  4.45$\pm$0.02 |  $-$0.104$\pm$0.006 |  0.77$\pm$0.02 |  5.30${}_{-0.84}^{+0.43}$ |  0.89${}_{-0.01}^{+0.02}$ |  0.01$\pm$0.01 |  0.11$\pm$0.02 |  0.10$\pm$0.03
222582 | 116906 |  5790$\pm$3 |  4.37$\pm$0.01 |  $-$0.005$\pm$0.003 |  1.08$\pm$0.01 |  6.80${}_{-0.24}^{+0.25}$ |  1.01${}_{-0.01}^{+0.01}$ |  0.06$\pm$0.01 |  $-$0.07$\pm$0.01 |  $-$0.13$\pm$0.01
222595 | 116937 |  5649$\pm$3 |  4.47$\pm$0.01 |  0.039$\pm$0.003 |  0.92$\pm$0.01 |  3.30${}_{-0.27}^{+0.52}$ |  0.98${}_{-0.01}^{+0.02}$ |  $-$0.01$\pm$0.01 |  0.03$\pm$0.01 |  0.04$\pm$0.01
223238 | 117367 |  5867$\pm$3 |  4.35$\pm$0.01 |  0.024$\pm$0.003 |  1.12$\pm$0.01 |  5.90${}_{-0.23}^{+0.26}$ |  1.04${}_{-0.01}^{+0.02}$ |  0.03$\pm$0.01 |  $-$0.05$\pm$0.01 |  $-$0.09$\pm$0.01
224383 | 118115 |  5798$\pm$4 |  4.28$\pm$0.01 |  $-$0.036$\pm$0.003 |  1.10$\pm$0.01 |  8.20${}_{-0.26}^{+0.23}$ |  1.01${}_{-0.01}^{+0.01}$ |  0.05$\pm$0.00 |  $-$0.11$\pm$0.00 |  $-$0.16$\pm$0.01
290327 | 25191 |  5524$\pm$5 |  4.42$\pm$0.02 |  $-$0.103$\pm$0.006 |  0.78$\pm$0.02 |  9.40${}_{-0.52}^{+0.58}$ |  0.89${}_{-0.01}^{+0.02}$ |  0.04$\pm$0.01 |  $-$0.03$\pm$0.01 |  $-$0.07$\pm$0.02

##  Appendix B Kinematics of the stellar sample

Various orbital characteristics and Galactic space velocities of the sample
are calculated using the galpy (http://github.com/jobovy/galpy) Python package
(Bovy 2015). The components of spatial velocities (U, V, and W) are calculated
with respect to the Local Standard of Rest (LSR) and the adopted solar motion
about the LSR is (U, V, W)⊙ = (11.1, 12.2, 7.3) km/s (Schönrich et al. 2010).
The detailed procedure can be found in Shejeelammal & Goswami (2024). The
behaviour of the [Mg/Fe] ratio observed in the sample as functions of maximum
height above the Galactic plane (Zmax), eccentricity, Galacto-centric distance
(RGC) and apocentric distance (Rapo) are shown in Fig. 12. The Toomre diagram
for the sample is shown in Fig. 13. As can be seen, it is difficult to
separate the thin and thick disk from purely kinematic criteria.

Figure 12: Observed [Mg/Fe] of the entire sample with respect to various
orbital parameters. The cyan circle is the anomalous star HD 65907. Figure 13:
Toomre diagram for the entire sample. The dotted inner and outer circles have
radii 100 km/s and 200 km/s, respectively.