Publications of the Astronomical Society of Australia Owusu et al.

113 2024 10.1017/pasa.xxxx.xx

Research Paper

E. K. Owusu, Email<EMAIL_ADDRESS>
Owusu et al. 2024, PASA, submitted.

(Received 30 04 2024; revised xx xx xxxx; accepted xx xx xxxx)

# At the same age, metallicity, and alpha-enhancement, sodium is a more
effective tracer of the young and old sequences of the Milky Way disc

Evans K. Owusu1,3 Sven Buder2,3 Ashley J. Ruiter1,3,4 Ivo R. Seitenzahl1 and
Nicolas Rodriguez-Segovia1 1School of Science, University of New South Wales
Canberra, Australia Defence Force Academy, ACT 2600, Australia
2Research School of Astronomy and Astrophysics, Australian National
University, ACT 2611, Australia
3ARC Centre of Excellence for All-Sky Astrophysics in 3 Dimensions (ASTRO-3D)
4 OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery,
Hawthorn, VIC 3122, Australia

###### Abstract

Trends in the enrichment of elements with stellar ages are a powerful avenue
to identify unexplained origins of the elements. We investigate the stellar
abundance trends of low to intermediate-mass stars using the GALAH DR3 high-
resolution spectroscopic dataset of 6234 solar-type stars. Our study explores
the elemental abundance [X/Fe] of sodium (Na) with age. We find a pronounced
enrichment in [Na/Fe] at super solar metallicity (i.e., [Fe/H] $>~{}0$) in the
old sequence of Milky Way disc stars, a trend demanding a deeper understanding
of the underlying source(s) responsible for the nucleosynthesis. This
progressive [Na/Fe] enrichment at the young end of the old sequence has
essential implications for Galactic archaeology. In this work, we propose a
novel selection technique for separating the Milky Way’s thick and thin disc
stellar populations (i.e., old and young sequences) based on the observed
[Na/Fe] rise of $\sim$0.1 dex for stars around $5-8\,\mathrm{Gyr}$ old. We
also compare our selection method to the conventional [Mg/Fe] vs [Fe/H]
selection approach, and we find that our new Na-based selection method better
disentangles the overlap between young- and old-sequence disc stars at these
intermediate ages. This is especially true at super solar [Fe/H], where
[Mg/Fe] vs [Fe/H] or [alpha/Fe] vs [Fe/H] separation approaches exhibit a lot
of overlap. This new selection method should help us better understand the
Milky Way disc’s formation history.

###### keywords:

Galaxy: abundances – Galaxy: evolution - Stars: abundances - Nucleosynthesis

##  1 Introduction

Understanding the origin of the elements is a long-standing, unresolved
fundamental problem of astrophysics. Numerous works over the last several
decades have focused on understanding the production sites (Burbidge et al.,
1957; Timmes et al., 1995; José & Iliadis, 2011; Kobayashi et al., 2020, to
name a few). Extensive modern spectroscopic surveys like the Galactic
Archaeology with HERMES survey (GALAH, De Silva et al., 2015; Buder et al.,
2018, 2021), provide a chance to advance our knowledge of the synthesis and
enrichment of elements in the Milky Way and its satellite galaxies through the
measurement of chemical abundances for about $30$ elements in hundreds of
thousands of stars. These surveys give us the capability to observe a large
number of stars that cover a wide range of Galactic environments, i.e., the
Milky Way’s stellar halo, bulge and discs, and in some cases, even stars that
were born outside of our Milky Way (e.g. Buder et al., 2022). Their uniform
data acquisition also enables uniform data reduction and analysis, thus
reducing systematic uncertainties. Such stellar abundance data sets are ideal
for evaluating theoretical stellar nucleosynthesis models.

Of the many elements covered by the GALAH survey, we focus in this paper
mostly on sodium (Na), an odd-Z element with only one stable isotope, 23Na,
which has 11 protons and 12 neutrons in its nucleus. In the low-metallicity
regime ($-3.0\leq$ [Fe/H] $\leq-1$), Na is diagnostic of a star’s birthplace
in terms of whether it was born inside or outside of the Milky Way (Nissen &
Schuster, 2010; Smiljanic et al., 2016; Das et al., 2020; Buder et al., 2022;
Lombardo et al., 2022). However, the diagnostic potential of Na has not been
tested extensively in the metal-rich regime (i.e., above solar metallicity),
although the data show promising possibilities. It was noted already over 40
years ago that the abundance of Na relative to Fe tended to decrease toward
low metallicities (Peterson, 1981). We notice that in the pioneering papers by
Bensby et al. (2014), Nissen et al. (2020) and Griffith et al. (2022), the Na
abundance increases much above the solar ratio for stars with super-solar
metallicity (Bensby et al., 2017). This is interesting because this metal-rich
regime is populated by stars of the young, dynamically cold and thus thin
stellar disc and the old, dynamically hotter and thick stellar disc. After the
first identification of two disc populations in our Milky Way’s stellar disc
by Yoshii (1982) and Gilmore & Reid (1983), considerable effort has been put
into studying the overlap of these populations (e.g. Bensby et al., 2014;
Buder et al., 2019; Nissen et al., 2020). Until now, no simple, simultaneously
observationally- and computationally economical way to separate the stars of
these two-disc populations without contamination has thus far been identified.

Nissen et al. (2020) extended earlier high-precision investigations of
elemental abundances in solar twin stars (e.g. da Silva et al., 2012; Nissen,
2015; Spina et al., 2018; Bedell et al., 2018) to a more extensive metallicity
range to examine how [Fe/H] influences trends in elemental ratios with stellar
age. To determine the ages of 72 nearby solar-type stars with metallicities in
the range of $-0.3\leq\text{[Fe/H]}\leq 0.3$, Nissen et al. (2020) analysed
High Accuracy Radial velocity Planet Searcher (HARPS) spectra with signal-to-
noise ratios S/N $\geq$ 600 at $\lambda\sim~{}6000~{}\text{\AA}$. The Århus
STellar Evolution Code (ASTEC; Christensen-Dalsgaard 2008) stellar models were
used to determine heavy element abundances, stellar ages from effective
temperatures, and luminosities obtained via Gaia DR2 parallax. From their
study, the age and metallicity distribution is as follows: Two different
populations were distinguished, namely: an older sequence of stars with a high
rise in [Fe/H] to $+0.3$ dex at the age of $7$ Gyr and a younger sequence with
an increase in [Fe/H] from $-0.3$ dex to $+0.2$ dex during the previous $6$
Gyr (see their figures 3 and 4). Additionally, as a function of stellar age,
the trends of some abundance ratios, including [O/Fe], [Na/Fe], [Ca/Fe], and
[Ni/Fe], are divided into two corresponding sequences. On the other hand, the
[Y/Mg]-age relation exhibits no offset between the two age sequences and has
no appreciable dependence on [Fe/H]. More striking, the age-metallicity
distribution being split into two sequences indicates two instances of gas
accretion onto the galactic disc with a quenching of star formation in
between. Hereafter, we will follow the notation of Nissen et al. (2020) and
refer to the old high-alpha, thick disc as the ”old sequence” and the young
low-alpha, thin disc as the ”young sequence”.

In a study exploring the solar neighbourhood model, Kobayashi et al. (2011)
found that there was an overproduction of [Na/Fe] ([Na/Fe] $\sim$ 0.3 dex).
However, this issue was resolved in a subsequent study by Kobayashi et al.
(2020), which used updated reaction rates and considered non-local
thermodynamic equilibrium (NLTE) factors that cause variation towards higher
metallicities. The decrease in [Na/Fe] occurs due to Type Ia supernovae, which
produce more Fe than Na. Nevertheless, high metallicities were observed to
show adequate Na abundances (Andrievsky et al., 2011; Zhao et al., 2012).

Among $\alpha$-elements, Ca is under-abundant relative to the other
$\alpha$-elements in elliptical galaxies (Kobayashi et al., 2011). However, a
recent study by Cinquegrana & Karakas (2022) predicts an upturn for Na yields
at higher metallicities (see Fig. $4$, bottom right-hand panel). The increase
in Na is attributed to the competition between the production of 23Na via the
Ne–Na chain and the two main destruction channels: 23Na(p, $\alpha$)20Ne and
23Na(p, $\gamma$)24Mg. These reactions depend heavily on the temperature in
the stellar envelope and the extent of the burning. Although the intermediate-
mass models endure Hot Bottom Burning (HBB), none reach temperatures capable
of activating the Ne–Na chain until M $\geq$ 7 M⊙. As a result, the 23Na
surface abundance also increases during the second dredge-up (SDU), which
occurs consistently with the increased sodium for the range of metallicities
studied.

In this paper, we show that the observed upturn (enrichment) of Na abundance
in the metal-rich regimes, that is $\text{[Fe/H]}_{\odot}>0$, appears to be a
unique characteristic of the older stellar disc, which allows for a separation
method yielding a less-contaminated sampling of the thin and thick disc. If
such a selection is reasonable, one could more efficiently study the stellar
populations of the discs when they otherwise overlap in many characteristics
like age, metallicity, alpha-enhancement and dynamics. To this end, we use the
third data release of the GALAH Survey (Buder et al., 2021), which provides us
with stellar chemical abundances and isochrone interpolated ages through the
overlap with the Gaia satellite (Gaia Collaboration et al., 2021).

The following issues are explored in this study:

  * •

We report the [Na/Fe] overproduction in GALAH DR3 at $\text{[Fe/H]}_{\odot}>0$
and highlight possible reasons for it. We additionally carry out a brief
discussion of several other elements in the context of nucleosynthesis and
Galactic enrichment.

  * •

We analyse how much our proposed new selection criteria improve the old and
young sequence selection.

In Section 2, we detail our data, selection criteria, and methodology for
obtaining abundances in GALAH DR3. We also describe the age determination
using the BSTEP method and explore various Galactic components. In Section 3,
we highlight the results from our work and Section 4 delves into a discussion
of the findings and their implications. Finally, in Section 5, we offer some
perspectives for future research.

Figure 1: Different representations of the age-iron-sodium abundance relations
for solar-type stars of Nissen et al. (2020) and GALAH DR3 (selected via Eq.
5). Panel (a) shows age vs. [Na/Fe] measurements by Nissen et al. (2020) with
old (red) and young (blue) sequences. The density distribution of GALAH DR3
solar-type stars is shown in greyscale in the background. Panel (b) shows the
2-dimensional distribution of [Na/Fe] vs [Fe/H] of the GALAH DR3 solar-type
stars coloured by median age, with the Sun indicated via $\odot$. Panel (c)
shows the same plane but with the distribution of [Na/Fe] in 2 Gyr age bins
for 0.1 dex [Fe/H] bins. The lines represent the median, whereas the contours
show the 16th to 84th percentiles.

##  2 Data

###  2.1 The GALAH Survey

The third data release (DR3) of the GALactic Archaeology with High Efficiency
and Resolution Multi-Element Spectrograph (HERMES; at the Anglo-Australian
Telescope)(Sheinis et al., 2015), hereafter GALAH, is a high-resolution (R
$\sim$28000) spectroscopic sample of stars in the Milky Way Galaxy that offers
atmospheric parameters and abundances for 30 elements for almost 600 000 stars
(Buder et al., 2021). GALAH is, therefore, another extensive stellar
spectroscopic survey like SEGUE (Yanny et al., 2009), RAVE (Kordopatis et al.,
2013), and APOGEE (Anders et al., 2014). These surveys serve as a window to
study the formation and evolutionary history of our Galaxy and astrophysical
processes that have occurred using traces of gas that have been transported
and incorporated into the formation of new generations of stars throughout
history. Primarily, GALAH targets relatively bright stars in the magnitude
range of $9<V<14$, which are therefore mostly nearby, typically closer than
$2\,\mathrm{kpc}$. In GALAH DR3, up to 30 elemental abundances are provided,
along with their uncertainties, quality flags, surface gravity, effective
temperatures, and ages. The ages were determined using the Bayesian stellar
parameter estimation code (BSTEP; Sharma et al. 2018).

###  2.2 Abundances and how they are determined in GALAH DR3

GALAH DR3 provides analyses of stellar spectra from the HERMES spectrograph,
which covers four wavelength bands in the optical and near-infrared (4 713 – 4
903, 5 648 – 5 873, 6 478 – 6 737, and 7 585 – 7 887 Å) (Sheinis et al.,
2015). The abundances of up to 30 elements were derived using the 1D MARCS
model atmospheres (Gustafsson et al., 2008), and a modified version of the
Spectroscopy Made Easy (SME) spectrum synthesis code (Valenti & Piskunov 1996;
Piskunov & Valenti 2017). Of these elements, 11 were computed using non-local
thermodynamic equilibrium (NLTE; Amarsi et al. 2020) and the remaining 19
elements were determined using local thermodynamic equilibrium (LTE). The
abundance analysis is preceded by a step that derives the global stellar
parameters from the spectra, namely effective temperature ($T_{\text{eff}}$),
surface gravity ($\log g$), iron abundance [Fe/H], micro-turbulence velocity
($v_{\text{mic}}$), broadening velocity ($v_{\text{broad}}$) and radial
velocity ($v_{\text{rad}}$). For ease, the elemental abundances as logarithmic
ratios of number densities $N$, that is,

$\left[\text{A}/\text{B}\right]\equiv{\rm
log}_{10}(N_{\text{A}}/N_{\text{B}}){{}_{\star}}-{\rm
log}_{10}(N_{\text{A}}/N_{\text{B}}){{}_{\odot}}$ (1)

for two elements A and B, are normalised to iron and the solar values
($\odot$), and abundances are reported as [X/Fe] $=$ [X/H] $-$ [Fe/H].

The ages of stars in GALAH DR3 were computed using a Bayesian Scheme known as
the Bayesian Stellar Parameters estimator (BSTEP Sharma et al., 2018) with an
elaborate step-by-step distribution given in section $3$ of Sharma et al.
(2018).

###  2.3 Sample Selection

To assess the nature of the abundance enrichment and its correlation with
stellar age, we apply an overall quality cut and then divide the overall data
set into a smaller sample of solar-type stars, which are cool main-sequence
dwarfs located below the red edge of the classical instability strip (spectral
types from late F, G and K dwarfs, Soderblom & King, 1998; García & Ballot,
2019).

For this study, we apply the following quality cuts:

$\displaystyle\texttt{flag\\_sp}==0,\texttt{flag\\_fe\\_h}==0,\texttt{flag\\_Na\\_fe}==0,$
(2) $\displaystyle\texttt{e\\_age\\_bstep}/\texttt{age\\_bstep}<0.2\text{ or
}\texttt{e\\_age\\_bstep}<2,$ (3) $\displaystyle\texttt{snr\\_c2\\_iraf}>50,$
(4) $\displaystyle 5600<T_{\text{eff}}<5950,\log g>4.15\text{, and
}-0.3<\mathrm{[Fe/H]}<0.3$ (5)

We employ basic quality cuts to select only unflagged measurements (Eq. 2).
Because our study relies on reasonably determined ages, we further limit our
sample to stars with either less than $20\%$ age uncertainty or age
uncertainties below $2\,\mathrm{Gyr}$ (Eq. 3). To ensure a reasonable quality
of measurements, we set a lower spectrum quality cut of signal-to-noise in the
green CCD of 50 per pixel (Eq. 4). We further limit our sample to solar-type
stars via Eq. 5, following the definition of Nissen et al. (2020).

Whenever we use elemental abundances [X/Fe], we further apply a quality cut of

$\texttt{flag\\_X\\_fe}==0.$ (6)

X replaces the respective element, e.g. Na, for good sodium measurements.

##  3 Analysis

The motivation for this project is the Nissen et al. (2020) age-metallicity
separation (see their figs. 3 and 4) of old and young solar-type stars, which
were historically equated as thick and thin disc sequences, respectively. The
upturn in [Na/Fe] with age for the old solar-type stars in their measurements
especially caught our eye. We reproduce this plot in Fig. 1a and also identify
an upturn of Na in the [Na/Fe] vs [Fe/H] (Fig. 1b) and [Fe/H] versus [Na/Fe]
relationship with age bin in step size of 2 Gyr (see Fig. 1c) for
$\mathrm{[Fe/H]}_{\odot}>0$ in the GALAH data. In Fig. 1b), the standard
deviation of the ages for stars around solar metallicity is $\pm 2$ Gyr.

Our analysis, therefore, first focuses on the dissection of the upturn of
[Na/Fe] at iron abundances above $\mathrm{[Fe/H]}>0$ in Sec. 3.1. We then show
that increasing [Na/Fe] vs age can improve the selection of co-natal young and
old sequence stars in Sec. 3.2. In Sec. 3.3, we then assess the trends of
young and old sequences in the other age-abundance planes available with GALAH
DR3 data before confirming the robustness of our selection function in Sec.
3.4.

Figure 2: Age-abundance distributions of young and old solar-type stars for
the elements measured by GALAH DR3 (small dots in the background) and Nissen
et al. (2020, larger dots in foreground). Reddish colours represent stars of
the old sequence and blueish colours represent stars of the young sequence,
respectively, as selected via Eq. 5. The elements are indicated in each panel.
The black lines indicate a linear fit to the old sequence of GALAH DR3 between
$5$ and $8\,\mathrm{Gyr}$. Typical uncertainties in this age range are shown
as error bars in the bottom right.

###  3.1 The upturn of [Na/Fe] at [Fe/H]$~{}>~{}0$

We show the [Na/Fe] versus [Fe/H] relation with bin median ages in a step size
of $2$ Gyr (see Fig. 1c). The important observation takeaway is that for all
the age bins explored in this work, ages between $2-6~{}\text{Gyr}$ for
[Na/Fe] are more enriched; the abundance rises from solar value to 0.12 dex
followed by 6 - 8 Gyr, which are stars mostly confined to the thick disc. The
resulting differences in [Na/Fe] enhancement for different ages motivated us
to test its potential to separate stars of the young and old sequence of the
Milky Way disc.

###  3.2 Selecting young and old stars in the [Na/Fe]-Age plane

The Milky Way’s stellar disc is a complex structure, and its formation and
evolution are still widely debated (e.g. Katz et al., 2021). Several surveys
have provided large statistical samples of stars with detailed chemical
abundances, such as RAVE (Kunder et al., 2017), Gaia-ESO (Randich et al.,
2013), APOGEE (Alam et al., 2015), LAMOST (Zhao et al., 2012) and GALAH (Buder
et al., 2018), combined with very precise Gaia astrometry (Lindegren et al.,
2018), making it possible to examine the formation of the Galactic disc with
an unprecedented level of detail. The sample includes mainly thin and thick
disc stars of all ages selected based on various criteria, such as the
relative abundance of alpha-elements and stellar ages within the old sequence
of the Milky Way disc. Due to the overlap of the thin and thick disc stars,
several studies (see for instance Lee et al., 2011; Delgado Mena et al., 2021;
Bensby et al., 2014; Recio-Blanco et al., 2014; Hayden et al., 2017) have come
up with preliminary techniques to separate the contamination of the two-disc
sequences. However, kinematics and chemo-dynamics have proven not to be
accurate in distinguishing both sequences, especially at intermediate ages
(Hayden et al., 2017) in the metallicity range of $-0.3$ to $+0.5$ dex, where
both sequences overlap (e.g. Bensby et al., 2014).

We continue our analysis by reproducing the selection of young and old
sequences in the age-abundance plane similar to Nissen et al. (2020). However,
contrary to Nissen et al. (2020), who use a selection in the age vs. [Fe/H]
space, we select stars via age and [Na/Fe]. Thick and thin solar-type stars
from the study of Nissen et al. (2020) (old thick disc stars in red and young
thin disc stars in royal blue) are superimposed over the GALAH DR3 solar-type
stars data (shown in grey, see Fig. 1).

Fig 1a, in particular, shows an initial selection (hereafter standard cut)
based on a separation ‘by eye’ of the Nissen et al. (2020)-stars as an orange
line. We classify stars as young or old, whether they are below or above the
line as:

$\left.\begin{aligned} \text{old
stars}&:\text{[Na/Fe]}_{\text{old}}\,\,\,\,\,\,>0.55-0.5/5.5~{}\times\tau\\\
\text{young
stars}&:\text{[Na/Fe]}_{\text{young}}<0.55-0.5/5.5~{}\times\tau\end{aligned}\right\\},$
(7)

Where $\tau$ represents the stellar age, we discuss the sensitivity of our
results to variations of our standard cut in Sec. 3.4 to test the robustness
of our selection criteria for the GALAH data sample. For Nissen et al. (2020),
this cut is robust mainly due to the difference of [Na/Fe] rise of
$\sim~{}0.30$ dex around $5\,\mathrm{Gyr}$.

Our selection now allows us to assess the age-abundance distribution for all
other elements in Fig. 2, which shows the solar-type thick (red colour) and
thin (royal blue colour) disc stars from Nissen et al. (2020) overlaid on
GALAH DR3 solar-type thick (orange) and thin disc (sky blue) stars
respectively.

While we have established the clear upturn of [Na/Fe] for the old sequence,
the trends for other elements are more diverse. While other odd-Z elements
like aluminium (Al) and scandium (Sc) also demonstrate a rise in their
abundance with decreasing stellar age, their rise is less pronounced than that
of sodium. When we consider potassium (K), another odd-Z element, it shows a
unique trend (i.e., it remains flat), though we note K is less well-
constrained in the [X/Fe] axis. Furthermore, alpha elements (i.e., C, O, Si,
Ca and Mg) show decreasing trends. On the other hand, elements near the iron
peak (i.e., Cr, Mn, Ni, Cu, Co and Zn) demonstrate increasing upward trends.
More so, the neutron capture element yttrium (Y) remains flat, while barium
(Ba) shows a decreasing trend. Section 4.2 discusses possible underlying
reasons for these trends.

Figure 3: Age-abundance distributions and fits these distributions of the old solar-type stars between 5 and 8 Gyr as measured by GALAH DR3. Each panel shows median abundances within $0.5\,\mathrm{Gyr}$ bins as dots for the element in the top left. Error bars represent each bin’s spread between the 16th and 84th percentile. To allow a better comparison of trends across all considered elements, the abundances have been artificially shifted for Fig. 2 so that all bins of the oldest stars (${\sim}$7.85 Gyr) have Solar abundance. In addition to a linear fit to the full age range (from 5 to 8 Gyr), we performed linear fits to the stars above and below 6.3 Gyr, with gradients of $\Delta\mathrm{[X/Fe]}/\mathrm{Gyr}$. While this figure shows the binned data, the fits were performed on the sets of individual stars. We show the result of the fits in Tab. 1. Figure 4:  Gradient estimates of abundances, $\Delta\mathrm{[X/Fe]}/\Delta\mathrm{Age}$ of different elements X for old solar-type stars as selected with the Standard Cut from Eq. 7. Positive values indicate an increase of element X over iron with time, whereas negative values show a relative decrease in the abundance of element X relative to iron with time. Error bars indicate the fitting uncertainties. We note that most of the enrichment for intermediate mass and iron peak elements occurs between $5$ and $6.5$ Gyr, e.g. during the birth of stars representing the younger end of the old sequence. Table 1: Gradient estimates for the age-abundance trends for elements of the old solar-type stars of GALAH DR3 between 5 and $8\,\mathrm{Gyr}$. We report both median slopes between 5 and $8\,\mathrm{Gyr}$ as well as those for intervals of $5-6.5\,\mathrm{Gyr}$ and $6.5-8\,\mathrm{Gyr}$. Atomic Number | Element | Gradient $5.0-8.0\,\,\mathrm{Gyr}$ | Gradient $6.5-8.0\,\,\mathrm{Gyr}$ | Gradient $5.0-6.5\,\mathrm{Gyr}$
---|---|---|---|---
|  | $\mathrm{dex\,Gyr^{-1}}$ | $\mathrm{dex\,Gyr^{-1}}$ | $\mathrm{dex\,Gyr^{-1}}$
6 | C | $-0.0145\pm 0.0024$ | $-0.0125\pm 0.0053$ | $-0.0199\pm 0.0078$
8 | O | $-0.0339\pm 0.0025$ | $-0.0210\pm 0.0056$ | $-0.0652\pm 0.0084$
11 | Na | $\,\,\,\,0.0260\pm 0.0009$ | $\,\,\,\,0.0066\pm 0.0021$ | $\,\,\,\,0.0673\pm 0.0031$
12 | Mg | $-0.0022\pm 0.0012$ | $-0.0090\pm 0.0027$ | $\,\,\,\,0.0119\pm 0.0041$
13 | Al | $\,\,\,\,0.0066\pm 0.0012$ | $-0.0113\pm 0.0027$ | $\,\,\,\,0.0263\pm 0.0041$
14 | Si | $-0.0011\pm 0.0011$ | $-0.0068\pm 0.0024$ | $\,\,\,\,0.0053\pm 0.0035$
19 | K | $-0.0051\pm 0.0016$ | $-0.0058\pm 0.0035$ | $\,\,\,\,0.0021\pm 0.0053$
20 | Ca | $-0.0043\pm 0.0014$ | $-0.0017\pm 0.0031$ | $-0.0059\pm 0.0046$
21 | Sc | $\,\,\,\,0.0062\pm 0.0009$ | $-0.0052\pm 0.0021$ | $\,\,\,\,0.0256\pm 0.0031$
22 | Ti | $-0.0095\pm 0.0011$ | $-0.0103\pm 0.0024$ | $-0.0144\pm 0.0035$
22 | Ti2 | $-0.0011\pm 0.0012$ | $-0.0054\pm 0.0029$ | $\,\,\,\,0.0065\pm 0.0037$
24 | V | $\,\,\,\,0.0063\pm 0.0027$ | $-0.0019\pm 0.0062$ | $\,\,\,\,0.0292\pm 0.0094$
25 | Cr | $\,\,\,\,0.0164\pm 0.0013$ | $\,\,\,\,0.0092\pm 0.0029$ | $\,\,\,\,0.0388\pm 0.0043$
27 | Mn | $\,\,\,\,0.0236\pm 0.0012$ | $\,\,\,\,0.0137\pm 0.0027$ | $\,\,\,\,0.0516\pm 0.0041$
28 | Co | $-0.0230\pm 0.0031$ | $\,\,\,\,0.0544\pm 0.0077$ | $-0.0698\pm 0.0099$
29 | Ni | $\,\,\,\,0.0199\pm 0.0013$ | $\,\,\,\,0.0064\pm 0.0029$ | $\,\,\,\,0.0433\pm 0.0043$
30 | Cu | $\,\,\,\,0.0285\pm 0.0010$ | $\,\,\,\,0.0080\pm 0.0023$ | $\,\,\,\,0.0723\pm 0.0034$
39 | Zn | $\,\,\,\,0.0092\pm 0.0015$ | $-0.0076\pm 0.0034$ | $\,\,\,\,0.0257\pm 0.0051$
56 | Y | $\,\,\,\,0.0027\pm 0.0022$ | $\,\,\,\,0.0160\pm 0.0048$ | $-0.0262\pm 0.0071$
57 | Ba | $-0.0226\pm 0.0016$ | $-0.0016\pm 0.0035$ | $-0.0652\pm 0.0052$

###  3.3 Quantifying Age-Abundance Trends

Next, we test how robust our age-abundance trends are regarding the particular
selection function (cut) chosen in the [Na/Fe]-age plane.

###  3.4 How robust is the newly suggested selection via the age-[Na/Fe]
plane?

To test the robustness of our [Na/Fe] versus age trend against the details of
the choice of the standard cut in Eq. 7, we consider further cuts (as shown in
Fig. 5) defined by the equations below:

upper cut $\displaystyle:\text{[Na/Fe]}=0.55\,(-0.05)-0.5/5.5~{}\times\tau,$
(8) lower cut
$\displaystyle:\text{[Na/Fe]}=0.55\,(+0.05)-0.5/5.5~{}\times\tau,$ (9) steep
cut $\displaystyle:\text{[Na/Fe]}=0.75-0.68/5.5~{}\times\tau\text{ ~{}and}$
(10) shallow cut $\displaystyle:\text{[Na/Fe]}=0.35-0.32/5.5~{}\times\tau.$
(11)

Figure 5: Similar to Fig. 1a for the entire age range considered (5-8 Gyr),
but now including different cuts to separate old from young solar-type stars
(see Eqs. 8-11).

The effect of these various cuts is shown in Fig. 6, where $\mathrm{\tau}$ is
the age of stars in Gyr.

From Fig. 1, we observed a [Na/Fe] enhancement of ($\sim 0.12$) dex from
approximately solar value through to high metallicity (see Figs. $\sim$1a and
1b). Also, in Fig. 1c, we see an upturn of [Na/Fe] beyond solar metallicity.

Figure 6: Gradients for the same elements as in Fig. 4, but this time, the
gradient value is taken over the larger age range that is shown in Fig. 5 for
the various selection cuts that are displayed. Colours correspond to those
used in Fig. 5.

It has been noted that cobalt (Co) has large uncertainty values because only a
few lines are present in GALAH DR3. However, for all other elements, the
trends obtained from different separation cuts agree with the scatter, meaning
that the slopes characterise abundance relative to iron with decreasing
stellar age all cluster around the same value for the various elements. This
suggests that the slope estimates for different cuts of each component are in
close agreement, indicating a robust selection technique for our old sequence.

##  4 Discussion

We have established a strong correlation [Na/Fe]-age enhancement for the old
sequence of the Milky Way. We now discuss both the implications on the
nucleosynthetic channels at play and what we could learn from this about the
thin and thick disc. As the main feature of our analysis, we first discuss the
age-abundance relation of Na (Sec. 4.1) in detail before turning to all other
elements in Sec. 4.2. This will inform our discussion of the nucleosynthetic
implications for the old sequence in Sec. 4.3. Having focused on the old
sequence, we will then put our results into the context of the young disc in
Sec. 4.4. Given the overlap of young and old discs around $6.3\,\mathrm{Gyr}$,
we further discuss the nature of the change in age-abundance trends for our
old sequence selection in Sec. 4.5, before discussing how much the selection
of the two sequences improves when including [Na/Fe] in Sec. 4.6.

###  4.1 The age-abundance trend of Na for the old sequence

Sodium is an odd-Z element synthesised in i.e. exploding massive stars and
dying low-mass stars. In massive stars, Na is synthesised during the
hydrostatic carbon burning phase Cameron (1959); Salpeter (1952); Woosley &
Weaver (1995). Also, during the neon-sodium (Ne-Na) and magnesium-aluminium
(Mg-Al) cycles in dying low-mass stars, Na is produced Denisenkov &
Denisenkova (1990) and mixed to the surface when approaching the red giant
branch phase (e.g. El Eid & Champagne 1995; Mowlavi 1999; Karakas 2010;
Cinquegrana & Karakas 2022).

Owing to the diverse sources from which Na is synthesised, its abundance
pattern as a function of metallicity is considered a complex one (Bedell et
al., 2018). This assertion is further highlighted by Bensby et al. (2017),
where, in a study conducted in the solar neighbourhood for the bulge, the
trend of [Na/Fe] first increases with [Fe/H] because of the contributions from
massive stars that produce Na and Fe; however when the nucleosynthetic
products of SNe Ia begin to have a significant impact on a stellar population
${\sim}0.4-1$ Gyr after star formation (Ruiter et al., 2011, see fig. 2),
[Na/Fe] starts to drop with [Fe/H]. As a result, the trend of [Na/Fe] over
time (i.e., metallicity and age) has been described as a “zigzag” one
(McWilliam, 2016). This trend is important for our consideration because the
bulge shares the same abundance trend with the thin and thick disc (Bensby et
al., 2017).

The study of Nissen et al. (2020) reported a rise in [Na/Fe]-age of $0.15$ dex
for the same stellar population at the same age range (i.e., 5 - 8 Gyr).
Similarly, a linear fit to the old sequence at intermediate ages of $5-8$ Gyr
gives a gradient value of ($0.0260\pm 0.0009\,\mathrm{dex/Gyr}$ , i.e, $0.077$
dex for the stated age rang) for [Na/Fe]. Which is much lower than the value
reported by Nissen et al. (2020). Also, a steeper rise for [Na/Fe] occurs
between the ages of ($5-6.5$) Gyr with abundance gradient of $0.0673\pm
0.0031\,\mathrm{dex/Gyr}$ (see red data points in Fig 4) compared with that of
($0.0066\pm 0.0021\,\mathrm{dex/Gyr}$ ; see Tab. 1).

We indeed see an explicit knee behaviour McWilliam (2016) for several elements
in our study, with a plateau behaviour for stars aged 8-6.3 Gyr followed by a
change in slope – going up or down – from ages 6.3 to 5 Gyr. One may assume
then that iron enrichment from SNe Ia becomes more critical around the time of
the knee. We can see a drop for some elements that start to decline relative
to iron as we look at younger (generally more metal-rich) stars owing to the
(generally long) delay times attributed to SNe Ia (Matteucci & Brocato, 1990;
Ruiter et al., 2009; Maoz et al., 2012). An upward trend in [X/Fe] with
decreasing age would be expected for some elements, particularly around the
iron peak (i.e. Mn, which is mainly synthesized in SNe Ia arising from massive
white dwarf stars Seitenzahl et al., 2013). However, Na also shows an upward
trend with decreasing age, but Na is not canonically associated with SNe Ia
but more often with short-lived, massive stars. This means something is
driving Na-enrichment other than simply the products of short-lived, massive
stars. The knee effect we see in Na here would be consistent with Na being
synthesised by SNII progenitors with a metallicity-dependent yield, i.e., the
‘metallicity effect’.

Novae, which are (recurring) thermonuclear eruptions on accreting white
dwarfs, could also be considered as a plausible source of Na given their range
of delay times (see fig 12, Kemp et al., 2021). However, preliminary work
indicates that novae are not a leading contributor to sodium enrichment in the
Galaxy above solar metallicity (A. Kemp, Private Comm. 2024).

Gas enrichment from massive stars that give rise to core-collapse supernovae
likely contributes to the overall enrichment of sodium as we consider stellar
populations at higher metallicity (i.e., younger ages). At higher metallicity,
a star will typically have a lower electron fraction (i.e., Ye, i.e., more
neutrons available), where ($Y_{e}=N_{p}/(N_{p}+N_{n})$). Low Ye favours the
production of odd-Z elements, such as Na, Al, or Sc. The reason why odd-Z
elements can be produced in more significant (relative to their neighbouring
even-Z elements) abundance as the metallicity of the progenitor increases is
as follows: Many of the light odd-Z elements only have one stable isotope
(e.g., ${}^{23}\text{Na}$ (11,12), ${}^{27}\text{Al}$ (13,14),
${}^{31}\text{P}$ (15,16), ${}^{45}\text{Sc}$ (21,24), etc.). These odd-Z
stable isotopes are neutron-rich – the nuclei have more neutrons than protons.
At low progenitor metallicity, a pre-supernova star will have $Y_{e}$ very
close to 0.5 in the relevant layers where explosive nucleosynthesis occurs
since core helium burning produces mostly self-conjugate nuclei like
${}^{12}\text{C}$,${}^{16}\text{O}$, and ${}^{20}\text{Ne}$. However, with
increasing metallicity, more C, N, and O nuclei are already present during
hydrogen burning. The CNO cycle turns most of the nuclei present as CNO to
${}^{14}\text{N}$.

Importantly, a main reaction during core helium burning then is
${}^{14}\text{N}(\alpha,\gamma)^{18}\text{F}(\beta^{+}\nu_{e})^{18}\text{O}(\alpha,\gamma)^{22}\text{Ne}$.
In effect, by number, most CNO nuclei initially present are turned into
${}^{22}\text{Ne}$, which, owing to the beta-decay of ${}^{18}\text{F}$, is
neutron-rich, with two extra neutrons. Since the relative number of protons to
neutrons is largely conserved for many environments where explosive
nucleosynthesis occurs, the extra neutrons available allow the more efficient
nucleosynthesis of the neutron-rich odd-Z isotopes.

In contrast, alpha elements (i.e., the even-Z elements such as Mg, S, or Ca)
have more stable isotopes that extend from self-conjugate stable nuclei on the
alpha-chain [e.g., ${}^{24}\text{Mg}$ (12,12), ${}^{32}\text{S}$ (16,16),
${}^{40}\text{Ca}$ (20,20)] to several neutron-rich stable isotopes (e.g.
${}^{25}\text{Mg}$, ${}^{26}\text{Mg}$, $\ldots,^{48}\text{Ca}$). This means
we can make stable even-Z element isotopes at high and low (no) neutron
excess. Still, we can synthesise odd-Z elements more efficiently in
environments with extra neutrons (which means higher metallicity). Higher
progenitor metallicity here also means that the neutron-rich isotopes like
${}^{25}\text{Mg}$ of these even-Z elements are produced in greater abundance;
however, this comes at the expense of the also stable ${}^{24}\text{Mg}$ and
so the total production of the element Mg is hence overall less affected.

###  4.2 Age-abundance trends other than Na for the old sequence

####  4.2.1 Light elements

In the older sequence of the younger stellar population (i.e., from 6.3 Gyr),
[(C, O)/Fe] has a decreasing trend with age (see Fig. 3). The carbon gradient
remains relatively consistent across the different age ranges where the fits
were conducted (i.e., $5-8,6.5-8,\text{and}5–6.5$ Gyr). However, the abundance
of oxygen relative to iron shows a significant change, decreasing by more than
threefold between the fits for $5-8\text{and}5-6.5$ Gyr (see Tab. 1). This
indicates that most of the decrease in oxygen abundance occurred between 6.5
and 5 Gyr, although, despite the decline, the ratio remains below the solar
value.

##### Carbon (C)

is primarily synthesised and expelled back into space by exploding massive
stars and dying low-mass stars as well as during earlier stages of stellar
evolution like core helium burning (CHeB). The trend in [C/Fe] is mainly due
to the reduced impact of SNII due to the short life-cycle of $\lesssim 10^{7}$
years for high-mass stars. In terms of enrichment, dying low-mass stars play a
more dominant role, hence the decrease in solar value. [C/Fe] remains flat
compared to other light elements (i.e., O).

##### Oxygen (O)

enjoys the distinction as the most abundant nucleus synthesised in stars
because it is the natural end product of helium burning. The majority of O is
synthesised in exploding massive stars, partly in dying low-mass stars, and
released by exploding white dwarfs (WD) (Timmes et al., 1995; Röpke et al.,
2012). The contributions of SNe Ia and exploding WDs to the synthesis of O are
relatively small compared to SNII.

Oxygen is one of the elements where the gradient of [O/Fe] vs age sharply
changes around 6.5 Gyr (see Fig. 3). This is reflected in the fact that the
gradient for the young end (from 5.0 to 6.5 Gyr) of the old sequence is much
steeper than the gradient for the whole time window (from 5 -8 Gyr, see Fig.
4). This trend indicates a decline in oxygen over iron production within the
old sequence in this time frame, perhaps due to SNe Ia producing iron peak
elements in the younger generation of old disc stars. The decrease is
consistent with the prevalent notion (e.g. Timmes et al., 1995) that [O/Fe]
decreases with decreasing age as SNe Ia progressively becomes more dominant
and becomes an essential source of iron. Also, we can see an apparent “knee”
effect, which is interpreted as the accretion of gas onto the thin disc with a
quenching of star formation (SFR) in between (McWilliam 1997; Nissen et al.
2020).

####  4.2.2 Alpha elements

Alpha-elements are thought to originate and expelled back into the
interstellar medium, mostly from core-collapse supernovae. Several alpha-
elements also have considerable contributions from low-mass stars. As a
result, they are valuable indicators of the chemical development of the galaxy
(Bensby et al., 2017). From Fig. 4, we see that the alpha (e.g., Mg, Si, Ca,
and Ti) elemental abundances are flat in the 5-8 Gyr range. There is a slight
“knee” for Mg and Si around 6.3 Gyr, where the gradient slightly turns upwards
(see Fig. 4), and Ca remains essentially unchanged.

##### Magnesium (Mg)

is synthesised primarily during explosive carbon-burning in exploding massive
stars (Arnett, 1995; Woosley & Weaver, 1995) and dying low-mass stars
(Thielemann et al., 2002). On average, SNII ejects about ten times as much Mg
as Type Ia supernovae, and SNII also occur about five times more frequently.
From Fig. 3, Mg has an initial flat plateau with a transition to an increasing
trend at around 6.3 Gyr. We note that this is different from the conventional
“knee” seen in the solar neighbourhood that describes a decrease of alpha/Fe
with age as low mass stars (mostly via Fe-group producing thermonuclear
supernovae) begin to modify the abundance trends (e.g. Bensby et al., 2017).
Notably, if anything, we see a slight increase in [Mg/Fe] in the old sequence
around 6.3 Gyr towards younger stars. The conventional wisdom is that SNe Ia
produces sub-solar [Mg/Fe] (e.g. Timmes et al., 1995; Seitenzahl et al., 2013;
Lach et al., 2020), making this upward trend difficult to explain with an
increasing contribution from thermonuclear supernovae.

##### Silicon (Si)

exists primarily due to oxygen-burning (Woosley, 1986). Simply put, two 16O
nuclei collide, causing the reaction 16O$\,\,+\,^{16}$O
$\longrightarrow\,^{28}$Si$\,\,+\,^{4}$He. In addition, some Si is synthesised
in exploding WDs and dying low-mass stars (Matteucci & Greggio, 1986; Timmes
et al., 1995). We see that Si is relatively flat like Ti and other alpha
process elements (e.g., Mg, Ca) with a slight increase in abundance at 6.3 Gyr
(see Tab. 1; Fig. 4). Also, the trend in the older sequence of the younger
stellar population (i.e., from 6.3 Gyr) for [Si/Fe] slightly increases with
age. The discontinuity occurring at ${\sim}6.3$ Gyr could be indicative of a
different star formation rate, or gas accretion/enrichment phase, between the
old and young sequence discs (McWilliam 1997; Nissen et al. 2020).

##### Calcium (Ca)

is primarily synthesised owing to oxygen-and silicon-burning processes (both
explosive and non-explosive) in massive stars (Timmes et al., 1995). The age
vs. abundance trend for Ca across all ages remains the same.

##### Titanium (Ti)

is primarily synthesised through the alpha-rich freezout in core-collapse
supernovae and explosive helium burning processes(i.e. Tur et al., 2010;
Kromer et al., 2010; Crocker et al., 2017). In GALAH DR3, Ti2 is the ionised
Ti line (all other alpha-elements are measured from their neutral lines).
Table 1 lists the gradients for the age-abundance trend for titanium. The age-
abundance trend for Ti remains flat in the old sequence.

####  4.2.3 Odd-Z elements

Odd-Z elements (Na, Al, K and Sc) provide crucial information about
nucleosynthetic processes and chemical evolution in the early Galaxy. When
non-LTE effects are considered, abundance trends for odd-Z elements display
different trends when compared to the case when NLTE effects are not taken
into account (Cayrel et al., 2004; Bandyopadhyay et al., 2020). The age-
abundance trend of the younger populations (from 6.3 Gyr) of the old sequence
for the odd-Z elements increases more than other elements, with Na having the
most pronounced rise.

##### Aluminium (Al)

is mainly synthesised during carbon-neon (C-Ne) burning in massive stars and
the magnesium-aluminium (Mg-Al) cycle in massive AGB stars (i.e., 9 -12 M⊙;
Siess 2006; Karakas 2010). The gradient of Al for the younger population
(5–6.5) Gyr of the older sequence is approximately four times steeper than the
trend for the old sequence (5 - 8) Gyr.

More so, even though Al is an odd-Z element, we found a behavioural trend
similar to most $\alpha-$elements, i.e., a plateau between 6.5-8 Gyr before an
increase that gives rise to a visible “knee” effect at ${\sim}6.3$ Gyr. An Al-
enhancement at younger stellar ages has been noted in previous studies for
stars in the bulge by Bensby et al. (2014, 2017).

##### Potassium (K)

is primarily synthesised during the burning of oxygen in massive stellar
explosions (Woosley & Weaver, 1995; Timmes et al., 1995; Cayrel et al., 2004).
K exhibits a flat plateau trend compared to other odd-Z elements (Na, Al, and
Sc). Still, again, we caution that uncertainty values are relatively high for
potassium, particularly at young stellar ages (see Tab. 1).

The different production sites for K compared with Na and Al could contribute
to the observed trend difference.

##### Scandium (Sc)

The two main nucleosynthesis processes in Type II supernovae that produce
scandium are oxygen-burning and the alpha-rich freeze-out reassembly of alpha
particles close to the collapsed core, which is the same zone where titanium
is synthesised (Nakamura et al., 1999; Kobayashi et al., 2011). Factors such
as stellar rotation (Prantzos et al., 2018) and two-dimensional (2D) jet-
induced supernovae Kobayashi et al. (2020) can lead to increased production of
Sc. On the other hand, at all metallicities, Sc is under-produced when
theoretical models are compared to observations (Kobayashi et al., 2006). The
gradient shows a clear increase as we go to younger stellar ages (e.g. see
Tab.1).

####  4.2.4 Elements near the iron peak

Elements near the iron peak (V, Cr, Mn, Ni, Cu and Zn) follow the expected
predictions from nucleosynthesis in that their abundance increases over time
due to the increasingly important role of SNe Ia, which produce large amounts
of these elements (in addition to iron) compared to other sources. From Fig.
3, an “elbow” effect, having the opposite trend as a knee effect, is apparent,
which could indicate the onset of different star formation rates between the
old and young sequences. Such an effect is seen around 6.3 Gyr for the
following elements: Cr, Mn, Ni, Cu and Zn. Co shows an opposite, “knee-like”
trend (though we note the cobalt data has comparatively large errors, so we
are currently unable to quantify the validity of this apparent trend). While
Cr, Mn and Ni (and also V) show a somewhat steady increase in abundance toward
younger ages, Cu and Zn exhibit the most prominent elbow effect, where the
behaviour from near-flat to strongly increasing abundance is quite clear.

##### Vanadium (V)

: V is produced both in massive stellar explosions (Weaver & Woosley, 1978)
and thermonuclear SNe (Seitenzahl & Pakmor, 2023). V’s most abundant stable
isotope is 51V, with one dominant source plausibly being helium-shell
detonations in sub-Chandrasekhar mass white dwarf SNe Ia (Timmes et al., 1995,
see also Panther et al. (2021) for future prospects on detection of V lines in
double-detonation SNe Ia). Taken over the entire age range considered for the
old disc (5 - 8 Gyr), the V abundance steadily increases; however, upon closer
inspection, we can see that the gradient over the younger part of the range (5
- 6.5 Gyr) is quite a bit steeper (see Tab. 1). Also, the younger population
of the old sequence has a gradient variation of a factor of 2, although with a
relatively more significant uncertainty. The factor of 2 variation is
consistent with the findings of Timmes et al. (1995) for the evolution of
[V/Fe] as a function of [Fe/H].

##### Chromium (Cr)

is predominantly synthesised during incomplete silicon burning in SNe Ia from
near-Chandrasekhar mass white dwarfs (Seitenzahl & Townsley, 2017) and
explosive oxygen and silicon burning more generally (see Côté et al. (2020);
Bergemann & Cescutti (2010)).The more neutron-rich isotopes of Cr (such as
54Cr) are produced in high-density Chandrasekhar mass SNe Ia, where electron
captures drive the material to be more neutron-rich. This was argued by Bravo
et al. (2022) as further support for the idea that the majority of SNe Ia must
come from sub-Chandrasekhar (lower density) white dwarfs. Our work shows a
rise in the abundance of Cr relative to iron, similar to the behaviour of
other Fe-peak elements. More so, more Cr is produced between $5-6.5$ Gyr as we
see a rise in the gradient by a factor of ${\sim}1.5$ compared to the $6.5-8$
(older) age range.

##### Manganese (Mn)

Type Ia supernovae are an essential nucleosynthesis site for the mono-isotopic
manganese (Mn) element. Mn has evolved to a critical element for inferences on
the nature of SNe Ia from Galactic Chemical Evolution studies, both in the
Milky Way (Seitenzahl et al., 2013; Lach et al., 2020; Eitner et al., 2020,
2023) as well as in Dwarf Galaxies (North et al., 2012; McWilliam et al.,
2003, 2018; de los Reyes et al., 2020). The creation of Mn in near-
Chandrasekhar mass SNe Ia depends crucially on the entropy during freeze-out
from nuclear statistical equilibrium (for reviews see Seitenzahl & Townsley,
2017; Seitenzahl & Pakmor, 2023). For sub-Chandrasekhar mass models, Mn
production occurs chiefly in incomplete silicon burning, where the outcome
depends on the metallicity of the explosion (Lach et al., 2020). In this
study, we observe a consistent enrichment and a noticeable increase between 5
– 6.5 Gyr (see Fig. 4).

##### Nickel (Ni)

is mostly synthesised by SN Ia explosions with roughly ${\sim}1/3$ of the
contribution coming from core-collapse supernovae (Woosley & Weaver, 1995;
Timmes et al., 1995) in both explosive silicon burning and through alpha-rich
freeze-out. The increase in Ni observed for younger stellar populations has
also been observed in Feltzing et al. (2009) and Nissen et al. (2020).

##### Copper (Cu)

We see a relatively high copper (Cu) enrichment in the young population of the
old sequence from Fig. 4 between $6.3$ and $5$ Gyr. The overproduction of Cu
was first reported by Sneden et al. (1991). Also, according to a study by
Bisterzo et al. (2004), the synthesis of Cu in massive stars is attributed to
a weak neutron capture process during hydrostatic He-burning and C-burning
phases in massive stars. In addition, Weaver & Woosley (1978) andIwamoto et
al. (1999) predict a high abundance of copper at solar metallicity, citing the
overproduction of the element due to the metallicity effect from the
progenitors of core-collapse SNe (see 4.1). Canonically, it has been predicted
that Cu is mostly synthesised through exploding massive stars (Woosley &
Weaver, 1995). As a result, as we approach higher metallicities, the
expectation is that the abundance of Cu should decrease. However, our result
shows a significant increase (see Tab. 1). Although Type Ia supernovae are
generally not considered to make a substantial contribution to the production
of Cu, Lach et al. (2020) found from their theoretical approach that the
helium shell detonation model of SNe Ia produces high Cu relative to Fe. Taken
together, these findings consequently challenge the existing paradigm for
nucleosynthesis of copper.

##### Zinc (Zn)

is synthesised primarily in massive and dying low-mass stars (Nomoto et al.,
1997; Mishenina et al., 2002; Nomoto et al., 2013).

Kobayashi et al. (2006) underscores the usefulness of Zn for the study of
damped Lyman $\alpha$ systems. We do see a change in the abundance gradient as
a function of age around 6.3 Gyr, which is also seen for some other elements
around the iron peak (see 4.2.4). Though Zn lies near the Fe-peak, we note
from Fig. 3 that it initially exhibits a somewhat flat, slightly decreasing
trend, after which we see a rise in its abundance (the elbow effect) around
6.3 Gyr, which is similar to the trend we observe in the $\alpha$ element Mg
(and possibly Si).

####  4.2.5 Others

Both Y and Ba are neutron-capture elements. The gradient of Ba in the younger
stellar population of the old sequence shows a decrease in its elemental
abundance per Gyr by a factor of 3 compared with the gradient of the entire
range of the old sequence.

##### Yttrium (Y)

is a neutron capture element mainly synthesised in AGB stars (Bensby et al.,
2017; Kobayashi et al., 2020). At higher temperatures, Y suffers from NLTE
effects, i.e., the lines are weakened due to increasing [Fe/H] or increasing
effective temperature $T_{\mathrm{eff}}$ of the stellar model atmosphere
(Delgado Mena et al., 2021; Bensby et al., 2014, 2017; Storm & Bergemann,
2023). We note that the abundance of Y is well below solar over the old
sequence (see Fig. 2) and remains rather flat (though overall rising) over the
entire old sequence age range.

##### Barium (Ba)

is another neutron capture element. We find the difference in the gradient
between 5-8 Gyr and 5-6.5 Gyr varies by a factor of two. We note the older age
range of the old sequence exhibits a rather flat trend (perhaps a slight
decrease) up to about 6.3 Gyr (Fig. 3). One could say this particular trend is
unique among all elements studied in this work, though alpha element Ca and
possibly Ti arguably show a similar trend.

####  4.2.6 Key findings for age-abundance trends

We found the following overall trends among the element groups:

  * •

Strong, positive enhancement trends for most odd-Z elements (Na, Al, Sc) and
most elements near the iron peak (V, Cr, Mn, Ni, Cu, Zn)

  * •

We found a relatively flat abundance trend for alpha-process elements (Mg, Si,
Ca, and also Ti)

  * •

We found a decreasing trend for O, as well as C (but less so) on the light
side and Ba on the heavy side of the periodic table

  * •

For K, Co and La, our results were inconclusive. We attempted to explain
possible reasons for the behaviour exhibited by Y, though we note that Y is
one of the elements we analysed that has relatively high uncertainty.

###  4.3 Implications for nucleosynthesis

The increasing trend of [(Na, Al, Sc)/Fe] differs from what we expect based on
their canonically assumed primary nucleosynthetic origins. One potential
factor leading to an increasing abundance of Na with decreasing stellar age
could be the effect of increasing metallicity on Galactic enrichment from
core-collapse supernova explosions (Woosley & Weaver, 1994; Kobayashi et al.,
2006; Nomoto et al., 2013; Limongi & Chieffi, 2018, see 4.1). Another could be
asymptotic giant branch (AGB) stars; AGB stars have been proposed as a
possible reason for the rising abundance trend at super-solar metallicity (Shi
et al. 2004; Kobayashi et al. 2011; Cinquegrana & Karakas 2022).

For most Fe-group elements, the observed rising trend is consistent with
predictions for the existing nucleosynthetic paradigm due to the increasingly
dominant role of exploding white dwarfs with time (i.e. as we look at younger
stars in our Galaxy, we increasingly see the footprint of SN Ia
nucleosynthesis). Furthermore, $\alpha-$elements (i.e., Mg, Si, Ca, and
additionally Ti) generally remain flat for the old sequence between $\sim
6.3-8$ Gyr, after which there is a gradual decrease (so-called knee; first
reported by McWilliam (1997)) in their elemental abundances due to the
diminishing contribution of core-collapse SNe and increasing birthrate of SNe
Ia. The trend in magnesium (Mg) follows the same age-abundance trend seen in
all iron-peak elements in the younger old disc sequence (with a positive
gradient), contrary to what we may expect (i.e. that Mg should follow a
similar behaviour as other $\alpha$ elements relative to iron and flatten out
or become more negative with decreasing age). Also, light elements carbon (C),
oxygen (O), and neutron capture elements (Ba and Y) show a decreasing trend
towards younger stars.

Of the elements that showed enrichment in their abundances, copper (Cu) upward
trend has the highest age-abundance trend, followed by sodium (Na; see Tab.
1). On average, for these elements, more enrichment occurred at 6.3 Gyr by a
factor of 3 in their respective gradients. Although copper (Cu $=29$) and zinc
(Zn $=30$) lie close on the periodic table, they have different age-abundance
gradient values. Cu and Zn abundance trends are somewhat flat between $8$ and
$6.3$ Gyr. However, Zn quickly rises and remains flat between $6$ and $5$ Gyr.
On the other hand, Cu has a gradual but sustained increase in its abundance
from ${\sim}6$ Gyr.

###  4.4 Putting the old sequence trends into the perspective of the young
sequence

While our study focuses on the old sequence of the Milky Way, a similar survey
for solar-twin stars was carried for stars of the thin disc out by Spina et
al. (2016) to trace the chemical evolution of the Galactic thin disc by
examining the [X/Fe] versus age for $24$ elements from carbon (C) to europium
(Eu). Spina et al. (2016) used the high-resolution data and high signal-to-
noise UVES optical spectrograph of the VLT spectra of nine solar twins to
obtain precise estimates of stellar ages and chemical abundances. The study
revealed that each class of elements showed a distinct evolution with time,
depending on the different characteristics, rates, and timescales of the
nucleosynthesis sites from which they are produced. Findings from the study
showed that $\alpha$-elements (i.e., Ca, Ti, Mg, Si, e.t.c.) are characterised
by a [X/Fe] decrease with time, while the iron-peak elements (i.e., V, Cr, Mn,
Ni, Co, etc.) show an early [X/Fe] increase that peaks at around $6$ Gyr
followed by a decrease towards the youngest stars.

###  4.5 The significance of an enrichment change at 6.3 Gyr

We appreciate that we have made a seemingly arbitrary cut fitting the age-
abundance trends above and below 6.3 Gyr. However, this decision is inspired
by previous reports of a knee-age effect by Edvardsson et al. (1993) and
McWilliam (1997). After this, several other studies have reported this knee-
age effect, mostly seen in $\alpha-$element plots (Bensby et al., 2014; Spina
et al., 2016). The occurrence of the “knee” indicates the onset of the
dominant role of (ideally) one nucleosynthesis source relative to another.
Various authors have provided different explanations for the presence of the
“knee” phenomenon. One view, proposed by McWilliam (1997), suggests that the
knee effect indicates varying star formation rates between distinct stellar
populations such as the bulge, halo, and Galactic discs. Another view,
expressed by Nissen et al. (2020), suggests that the knee can be interpreted
as evidence of gas accretion onto the Galactic disc, with a quenching of star
formation in between.

This work shows the occurrence of the knee-age effect (or elbow-age effect) in
most elements considered around 6.3 Gyr. For odd-Z and Fe-peak elements, we
see an upward trend in the [X/Fe] beyond the knee – which we have coined an
elbow – and for light and alpha-elements, we notice a decreasing trend
afterwards (classic knee). For elements near the iron peak, we interpret this
trend as the point at which SNe Ia start to make a significant impact on
chemical enrichment of the stellar population under study, considering that
most of these elements are readily synthesised during SN Ia explosions
(Thielemann et al., 2002). Furthermore, we also consider the decreasing trend
of alpha and light elements as the point where Type II SNe has reached its
peak, consequently leading to a decrease in their [X/Fe] as most of these
elements are produced through explosions of massive stars (Arnett, 1995;
Iwamoto et al., 1999; Kobayashi et al., 2011). We conclude by noting that the
knee-age effect from this work could be interpreted as a different star
formation rate (SFR) taking place between the old and young sequences or
possibly different gas accretion onto the younger sequence by the old
sequence.

###  4.6 How does our new selection criterion improve the selection of the
thick and thin disc stars?

Figure 7: Visualisation of the selection difference of old and young disc
stars with the method by Hayden et al. (2017). Panel a) shows the plane of
[Fe/H] vs. [Mg/Fe] that was used by Hayden et al. (2017) to select thin and
thick disc stars. Panel b) shows that the same stars are less clearly
separated in the age-[Na/Fe] we propose in our study. Thick disc stars are
orange, while a bluish colour represents the thin disc stars.

One of our motivations was to try and identify a less contaminated selection
method of thin and thick disc stars in the high-metallicity regime, where
stars significantly overlap in their dynamics and alpha enhancement. To this
end, we have reproduced the linear selection in [Fe/H] vs. [Mg/Fe] used by
Hayden et al. (2017) in the [Fe/H] vs [Mg/Fe] plane and we show where these
stars are in the Age-[Na/Fe] plane in Fig. 7. To emphasise the point that our
selection method is less contaminated, we construct a confusion matrix: the
selection criteria of Hayden et al. (2017) is compared against the selection
criteria of this work and is presented in Fig. 8. We see that 55% of the stars
are attributed to opposite populations. Most notably, Hayden et al. (2017)
would allocate 50% (i.e., 3093 stars) of the young sequence as defined in our
work as thick disc stars when using [Mg/Fe]. Also, 5% (293 stars) old sequence
stars, as described in this work, would be categorised as thin disc stars when
using the [Mg/Fe] selection method. In all, only 45% are allocated to the same
populations (i.e., 26% thick and 19% thin disc stars). This significant
difference in the allocation of stars to the two populations can have critical
implications for the study of abundance trends in the Milky Way – most notably
the high-metallicity regime, which is more dominant in the inner Galaxy
(Matteucci & Francois, 1989; Recio-Blanco et al., 2014).

Figure 8: Confusion matrix of the selection of thin and thick disc by Hayden
et al. (2017) via low and high [Mg/Fe] (x-axis) and our newly suggested
selection method of young and old sequence disc stars via the age-[Na/Fe]
plane (y-axis).

##  5 Conclusions

In this study, we have presented an analysis of solar-type stars from GALAH
DR3 and quantified the abundances of elements at intermediate ages (5-8 Gyr)
for solar-type stars (as defined by Nissen et al. 2020). We also presented
abundance trends as a function of stellar age for light elements, alpha
elements, odd-Z elements, iron peak elements, and neutron capture elements. We
offered possible explanations for these elemental abundance trends where
feasible. There are two main outcomes of this work:

  * •

Our selection function (Eq. 7) allows us to identify age-abundance trends for
the youngest thick disc (young end of the old sequence) stars that are
challenging current nucleosynthetic ideas. This is most striking for Na, which
shows an increase of $0.0260\pm 0.0009\,\mathrm{dex/Gyr}$ for old sequence
stars between 5-8 Gyr (see Fig. 4). We also present trends for some elemental
abundances (relative to iron) as a function of age (see Tab. 1) that can be
used for improving Galactic chemical evolution models.

  * •

We have shown that at the same age and metallicity, sodium (Na) is a better
tracer than [Mg/Fe] vs [Fe/H] to disentangle the old and young sequence disc
stars. Our new approach using Na allows us to better separate stars with
similar [Fe/H] vs [Mg/Fe] into the old and young sequences, respectively (Fig.
7). Our new selection method using Na improves the false positives by 50% and
true negatives by 5%, compared to the [Mg/Fe] vs [Fe/H] approach (see Fig. 8).

In conclusion, we have shown that the different behaviour of Na at
intermediate ages is a powerful discriminant to chemically separate the old
and young sequence for solar-type stars in the Galactic disc.

## Acknowledgements

We acknowledge the traditional owners of the land on which the AAT stands, the
Gamilaraay people. We pay our respects to elders past and present and are
proud to continue their tradition of surveying the night sky in the Southern
Hemisphere. The authors acknowledge fruitful discussions with colleagues,
including Alex Kemp, Benoît Côté, Simon Murphy, Giulia Cinquegrana, Philipp
Eitner, and Nicholas Storm. This work was supported by the Australian Research
Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO
3D) through project number CE170100013. Part of this research was funded
through AJR’s Australian Research Council Future Fellowship FT170100243 and
SB’s Australian Research Council DECRA Fellowship DE240100150.

## Facilities

AAT with 2df-HERMES at Siding Spring Observatory: The GALAH Survey is based on
data acquired through the Australian Astronomical Observatory, under programs:
A/2013B/13 (The GALAH pilot survey); A/2014A/25, A/2015A/19, A2017A/18 (The
GALAH survey phase 1), A2018 A/18 (Open clusters with HERMES), A2019A/1
(Hierarchical star formation in Ori OB1), A2019A/15 (The GALAH survey phase
2), A/2015B/19, A/2016A/22, A/2016B/10, A/2017B/16, A/2018B/15 (The HERMES-
TESS program), and A/2015A/3, A/2015B/1, A/2015B/19, A/2016A/22, A/2016B/12,
A/2017A/14, (The HERMES K2-follow-up program). This paper includes data that
has been provided by AAO Data Central (datacentral.aao.gov.au). Gaia:  This
work has made use of data from the European Space Agency (ESA) mission Gaia
(http://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
http://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, particularly the institutions
participating in the Gaia Multilateral Agreement. Other facilities: This
publication makes use of data products from the Two Micron All Sky Survey
(Skrutskie et al., 2006) and the CDS VizieR catalogue access tool (Ochsenbein
et al., 2000).

## Software

The research for this publication was coded in python (version 3.7.4) and
included its packages astropy (v. 3.2.2; Astropy Collaboration et al., 2013,
2018), corner (v. 2.0.1; Foreman-Mackey, 2016), galpy (version 1.6.0; Bovy,
2015), IPython (v. 7.8.0; Pérez & Granger, 2007), matplotlib (v. 3.1.3;
Hunter, 2007), NumPy (v. 1.17.2; Walt et al., 2011), scipy (version 1.3.1;
Virtanen et al., 2020), We further made use of topcat (version 4.7; Taylor,
2005);

## Data Availability

The data used for this study is published by Buder et al. (2021) and can be
accessed publicly via https://docs.datacentral.org.au/galah/dr3/overview/

## References

  * Alam et al. (2015) Alam S., et al., 2015, ApJS, 219, 12
  * Amarsi et al. (2020) Amarsi A. M., et al., 2020, A&A, 642, A62
  * Anders et al. (2014) Anders F., et al., 2014, A&A, 564, A115
  * Andrievsky et al. (2011) Andrievsky S. M., Spite F., Korotin S. A., François P., Spite M., Bonifacio P., Cayrel R., Hill V., 2011, A&A, 530, A105
  * Arnett (1995) Arnett D., 1995, ARA&A, 33, 115
  * Astropy Collaboration et al. (2013) Astropy Collaboration et al., 2013, A&A, 558, A33
  * Astropy Collaboration et al. (2018) Astropy Collaboration et al., 2018, AJ, 156, 123
  * Bandyopadhyay et al. (2020) Bandyopadhyay A., Thirupathi S., Beers T. C., Susmitha A., 2020, MNRAS, 494, 36
  * Bedell et al. (2018) Bedell M., et al., 2018, ApJ, 865, 68
  * Bensby et al. (2014) Bensby T., Feltzing S., Oey M. S., 2014, A&A, 562, A71
  * Bensby et al. (2017) Bensby T., et al., 2017, A&A, 605, A89
  * Bergemann & Cescutti (2010) Bergemann M., Cescutti G., 2010, A&A, 522, A9
  * Bisterzo et al. (2004) Bisterzo S., Gallino R., Pignatari M., Pompeia L., Cunha K., Smith V., 2004, Mem. Soc. Astron. Italiana, 75, 741
  * Bovy (2015) Bovy J., 2015, ApJS, 216, 29
  * Bravo et al. (2022) Bravo E., Piersanti L., Blondin S., Domínguez I., Straniero O., Cristallo S., 2022, MNRAS, 517, L31
  * Buder et al. (2018) Buder S., et al., 2018, MNRAS, 478, 4513
  * Buder et al. (2019) Buder S., et al., 2019, A&A, 624, A19
  * Buder et al. (2021) Buder S., et al., 2021, MNRAS, 506, 150
  * Buder et al. (2022) Buder S., et al., 2022, MNRAS, 510, 2407
  * Burbidge et al. (1957) Burbidge E. M., Burbidge G. R., Fowler W. A., Hoyle F., 1957, Reviews of Modern Physics, 29, 547
  * Cameron (1959) Cameron A. G. W., 1959, ApJ, 130, 429
  * Cayrel et al. (2004) Cayrel R., et al., 2004, A&A, 416, 1117
  * Christensen-Dalsgaard (2008) Christensen-Dalsgaard J., 2008, Ap&SS, 316, 13
  * Cinquegrana & Karakas (2022) Cinquegrana G. C., Karakas A. I., 2022, MNRAS, 510, 1557
  * Côté et al. (2020) Côté B., Jones S., Herwig F., Pignatari M., 2020, ApJ, 892, 57
  * Crocker et al. (2017) Crocker R. M., et al., 2017, Nature Astronomy, 1, 0135
  * Das et al. (2020) Das P., Hawkins K., Jofré P., 2020, MNRAS, 493, 5195
  * De Silva et al. (2015) De Silva G. M., et al., 2015, MNRAS, 449, 2604
  * Delgado Mena et al. (2021) Delgado Mena E., Adibekyan V., Santos N. C., Tsantaki M., González Hernández J. I., Sousa S. G., Bertrán de Lis S., 2021, A&A, 655, A99
  * Denisenkov & Denisenkova (1990) Denisenkov P. A., Denisenkova S. N., 1990, Soviet Astronomy Letters, 16, 275
  * Edvardsson et al. (1993) Edvardsson B., Andersen J., Gustafsson B., Lambert D. L., Nissen P. E., Tomkin J., 1993, A&A, 275, 101
  * Eitner et al. (2020) Eitner P., Bergemann M., Hansen C. J., Cescutti G., Seitenzahl I. R., Larsen S., Plez B., 2020, A&A, 635, A38
  * Eitner et al. (2023) Eitner P., Bergemann M., Ruiter A. J., Avril O., Seitenzahl I. R., Gent M. R., Côté B., 2023, A&A, 677, A151
  * El Eid & Champagne (1995) El Eid M. F., Champagne A. E., 1995, ApJ, 451, 298
  * Feltzing et al. (2009) Feltzing S., Primas F., Johnson R. A., 2009, A&A, 493, 913
  * Foreman-Mackey (2016) Foreman-Mackey D., 2016, The Journal of Open Source Software, 1, 24
  * Gaia Collaboration et al. (2021) Gaia Collaboration et al., 2021, A&A, 650, C3
  * García & Ballot (2019) García R. A., Ballot J., 2019, Living Reviews in Solar Physics, 16, 4
  * Gilmore & Reid (1983) Gilmore G., Reid N., 1983, MNRAS, 202, 1025
  * Griffith et al. (2022) Griffith E. J., Weinberg D. H., Buder S., Johnson J. A., Johnson J. W., Vincenzo F., 2022, ApJ, 931, 23
  * Gustafsson et al. (2008) Gustafsson B., Edvardsson B., Eriksson K., Jørgensen U. G., Nordlund Å., Plez B., 2008, A&A, 486, 951
  * Hayden et al. (2017) Hayden M. R., Recio-Blanco A., de Laverny P., Mikolaitis S., Worley C. C., 2017, A&A, 608, L1
  * Hunter (2007) Hunter J. D., 2007, Comput Sci Eng, 9, 90
  * Iwamoto et al. (1999) Iwamoto K., Brachwitz F., Nomoto K., Kishimoto N., Umeda H., Hix W. R., Thielemann F.-K., 1999, ApJS, 125, 439
  * José & Iliadis (2011) José J., Iliadis C., 2011, Reports on Progress in Physics, 74, 096901
  * Karakas (2010) Karakas A. I., 2010, MNRAS, 403, 1413
  * Katz et al. (2021) Katz D., Gómez A., Haywood M., Snaith O., Di Matteo P., 2021, A&A, 655, A111
  * Kemp et al. (2021) Kemp A. J., Karakas A. I., Casey A. R., Izzard R. G., Ruiter A. J., Agrawal P., Broekgaarden F. S., Temmink K. D., 2021, MNRAS, 504, 6117
  * Kobayashi et al. (2006) Kobayashi C., Umeda H., Nomoto K., Tominaga N., Ohkubo T., 2006, ApJ, 653, 1145
  * Kobayashi et al. (2011) Kobayashi C., Karakas A. I., Umeda H., 2011, MNRAS, 414, 3231
  * Kobayashi et al. (2020) Kobayashi C., Karakas A. I., Lugaro M., 2020, ApJ, 900, 179
  * Kordopatis et al. (2013) Kordopatis G., et al., 2013, AJ, 146, 134
  * Kromer et al. (2010) Kromer M., Sim S. A., Fink M., Röpke F. K., Seitenzahl I. R., Hillebrandt W., 2010, ApJ, 719, 1067
  * Kunder et al. (2017) Kunder A., et al., 2017, AJ, 153, 75
  * Lach et al. (2020) Lach F., Röpke F. K., Seitenzahl I. R., Coté B., Gronow S., Ruiter A. J., 2020, A&A, 644, A118
  * Lee et al. (2011) Lee Y. S., et al., 2011, ApJ, 738, 187
  * Limongi & Chieffi (2018) Limongi M., Chieffi A., 2018, ApJS, 237, 13
  * Lindegren et al. (2018) Lindegren L., et al., 2018, A&A, 616, A2
  * Lombardo et al. (2022) Lombardo L., et al., 2022, A&A, 665, A10
  * Maoz et al. (2012) Maoz D., Mannucci F., Brandt T. D., 2012, MNRAS, 426, 3282
  * Matteucci & Brocato (1990) Matteucci F., Brocato E., 1990, ApJ, 365, 539
  * Matteucci & Francois (1989) Matteucci F., Francois P., 1989, MNRAS, 239, 885
  * Matteucci & Greggio (1986) Matteucci F., Greggio L., 1986, A&A, 154, 279
  * McWilliam (1997) McWilliam A., 1997, ARA&A, 35, 503
  * McWilliam (2016) McWilliam A., 2016, PASA, 33, e040
  * McWilliam et al. (2003) McWilliam A., Rich R. M., Smecker-Hane T. A., 2003, ApJ, 593, L145
  * McWilliam et al. (2018) McWilliam A., Piro A. L., Badenes C., Bravo E., 2018, ApJ, 857, 97
  * Mishenina et al. (2002) Mishenina T. V., Kovtyukh V. V., Soubiran C., Travaglio C., Busso M., 2002, A&A, 396, 189
  * Mowlavi (1999) Mowlavi N., 1999, A&A, 350, 73
  * Nakamura et al. (1999) Nakamura T., Umeda H., Nomoto K., Thielemann F.-K., Burrows A., 1999, ApJ, 517, 193
  * Nissen (2015) Nissen P. E., 2015, A&A, 579, A52
  * Nissen & Schuster (2010) Nissen P. E., Schuster W. J., 2010, A&A, 511, L10
  * Nissen et al. (2020) Nissen P. E., Christensen-Dalsgaard J., Mosumgaard J. R., Silva Aguirre V., Spitoni E., Verma K., 2020, A&A, 640, A81
  * Nomoto et al. (1997) Nomoto K., Iwamoto K., Nakasato N., Thielemann F. K., Brachwitz F., Tsujimoto T., Kubo Y., Kishimoto N., 1997, Nucl. Phys. A, 621, 467
  * Nomoto et al. (2013) Nomoto K., Kobayashi C., Tominaga N., 2013, ARA&A, 51, 457
  * North et al. (2012) North P., et al., 2012, A&A, 541, A45
  * Ochsenbein et al. (2000) Ochsenbein F., Bauer P., Marcout J., 2000, A&AS, 143, 23
  * Panther et al. (2021) Panther F. H., Seitenzahl I. R., Ruiter A. J., Siegert T., Sim S., Crocker R. M., 2021, MNRAS, 508, 1590
  * Pérez & Granger (2007) Pérez F., Granger B. E., 2007, Comput Sci Eng, 9, 21
  * Peterson (1981) Peterson R. C., 1981, ApJ, 244, 989
  * Piskunov & Valenti (2017) Piskunov N., Valenti J. A., 2017, A&A, 597, A16
  * Prantzos et al. (2018) Prantzos N., Abia C., Limongi M., Chieffi A., Cristallo S., 2018, MNRAS, 476, 3432
  * Randich et al. (2013) Randich S., Gilmore G., Gaia-ESO Consortium 2013, The Messenger, 154, 47
  * Recio-Blanco et al. (2014) Recio-Blanco A., et al., 2014, A&A, 567, A5
  * Röpke et al. (2012) Röpke F. K., et al., 2012, ApJ, 750, L19
  * Ruiter et al. (2009) Ruiter A. J., Belczynski K., Fryer C., 2009, ApJ, 699, 2026
  * Ruiter et al. (2011) Ruiter A. J., Belczynski K., Sim S. A., Hillebrandt W., Fryer C. L., Fink M., Kromer M., 2011, MNRAS, 417, 408
  * Salpeter (1952) Salpeter E. E., 1952, ApJ, 115, 326
  * Seitenzahl & Pakmor (2023) Seitenzahl I. R., Pakmor R., 2023, Handbook of Nuclear Physics, pp 3809–3842
  * Seitenzahl & Townsley (2017) Seitenzahl I. R., Townsley D. M., 2017, in Alsabti A. W., Murdin P., eds, , Handbook of Supernovae. Springer, Cham, p. 1955, doi:10.1007/978-3-319-21846-5˙87
  * Seitenzahl et al. (2013) Seitenzahl I. R., Cescutti G., Röpke F. K., Ruiter A. J., Pakmor R., 2013, A&A, 559, L5
  * Sharma et al. (2018) Sharma S., et al., 2018, MNRAS, 473, 2004
  * Sheinis et al. (2015) Sheinis A., et al., 2015, Journal of Astronomical Telescopes, Instruments, and Systems, 1, 035002
  * Shi et al. (2004) Shi J. R., Gehren T., Zhao G., 2004, A&A, 423, 683
  * Siess (2006) Siess L., 2006, A&A, 448, 717
  * Skrutskie et al. (2006) Skrutskie M. F., et al., 2006, AJ, 131, 1163
  * Smiljanic et al. (2016) Smiljanic R., et al., 2016, A&A, 589, A115
  * Sneden et al. (1991) Sneden C., Gratton R. G., Crocker D. A., 1991, A&A, 246, 354
  * Soderblom & King (1998) Soderblom D. R., King J. R., 1998, in Hall J. C., ed., Solar Analogs: Characteristics and Optimum Candidates.. p. 41
  * Spina et al. (2016) Spina L., Meléndez J., Karakas A. I., Ramírez I., Monroe T. R., Asplund M., Yong D., 2016, A&A, 593, A125
  * Spina et al. (2018) Spina L., et al., 2018, MNRAS, 474, 2580
  * Storm & Bergemann (2023) Storm N., Bergemann M., 2023, MNRAS, 525, 3718
  * Taylor (2005) Taylor M. B., 2005, in Shopbell P., Britton M., Ebert R., eds, Astronomical Society of the Pacific Conference Series Vol. 347, Astronomical Data Analysis Software and Systems XIV. p. 29
  * Thielemann et al. (2002) Thielemann F. K., et al., 2002, Ap&SS, 281, 25
  * Timmes et al. (1995) Timmes F. X., Woosley S. E., Weaver T. A., 1995, ApJS, 98, 617
  * Tur et al. (2010) Tur C., Heger A., Austin S. M., 2010, arXiv e-prints, p. arXiv:1012.4732
  * Valenti & Piskunov (1996) Valenti J. A., Piskunov N., 1996, A&AS, 118, 595
  * Virtanen et al. (2020) Virtanen P., et al., 2020, Nature Methods, 17, 261
  * Walt et al. (2011) Walt S. v. d., Colbert S. C., Varoquaux G., 2011, Comput Sci Eng, 13, 22
  * Weaver & Woosley (1978) Weaver T. A., Woosley S. E., 1978, Evolution and explosion of massive stars, Presented at the 13th Texas Symp. on Relativistic Astrophys., Munich, 14-19 Dec. 1979
  * Woosley (1986) Woosley S. E., 1986, in Audouze J., Chiosi C., Woosley S. E., eds, Saas-Fee Advanced Course 16: Nucleosynthesis and Chemical Evolution. p. 1
  * Woosley & Weaver (1994) Woosley S. E., Weaver T. A., 1994, ApJ, 423, 371
  * Woosley & Weaver (1995) Woosley S. E., Weaver T. A., 1995, ApJS, 101, 181
  * Yanny et al. (2009) Yanny B., et al., 2009, AJ, 137, 4377
  * Yoshii (1982) Yoshii Y., 1982, PASJ, 34, 365
  * Zhao et al. (2012) Zhao G., Zhao Y.-H., Chu Y.-Q., Jing Y.-P., Deng L.-C., 2012, Research in Astronomy and Astrophysics, 12, 723
  * da Silva et al. (2012) da Silva R., Porto de Mello G. F., Milone A. C., da Silva L., Ribeiro L. S., Rocha-Pinto H. J., 2012, A&A, 542, A84
  * de los Reyes et al. (2020) de los Reyes M. A. C., Kirby E. N., Seitenzahl I. R., Shen K. J., 2020, ApJ, 891, 85