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. Reference Sheinis2015), hereafter GALAH, is a high-resolution (R $\sim$ 28 000) spectroscopic sample of stars in the Milky Way Galaxy containing atmospheric parameters and abundance information for nearly 600 000 stars as of the current data release (Buder et al. Reference Buder2021).

GALAH is an extensive stellar spectroscopic survey like SEGUE (Yanny et al. Reference Yanny2009), RAVE (Kordopatis et al. Reference Kordopatis2013), and APOGEE (Anders et al. Reference Anders2014). These surveys serve as a window to study the formation and evolutionary history of the Galaxy and astrophysical processes using traces of gas that have been transported and incorporated into the formation of generations of stars throughout the Galactic history. Primarily, GALAH targets relatively bright stars in the magnitude range of $9 \lt V \lt 14$ , which are typically closer than $2\,\mathrm{kpc}$ . In GALAH DR3, up to 30 elemental abundances are provided for each star, along with their uncertainties and quality flags. Additional physical properties such as surface gravity, effective temperature, and age are also reported. The ages were determined using the Bayesian stellar parameter estimation code (BSTEP; Sharma et al. Reference Sharma2018).

Figure 1. Different representations of the age-iron-sodium abundance relations for solar-type stars of Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020) and GALAH DR3 (see Equations 5 and 6). Panel (a) shows age vs. [Na/Fe] measurements by Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020) 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 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 spread show the 16th to 84th percentiles. Panel (c) 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 with $\odot$ .

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. Reference Sheinis2015). The abundances were derived using the 1D MARCS model atmospheres (Gustafsson et al. Reference Gustafsson, Edvardsson, Eriksson, Jørgensen, Nordlund and Plez2008), and a modified version of the Spectroscopy Made Easy (SME) spectrum synthesis code (Valenti & Piskunov Reference Valenti and Piskunov1996; Piskunov & Valenti Reference Piskunov and Valenti2017). Of these elements, 11 were computed using TE (Amarsi et al. Reference Amarsi2020) and the remaining 19 elements were determined using local thermodynamic equilibrium (LTE). Na is among the 11 elements for which NLTE effects were included in the analysis of GALAH spectra. 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 ( $v_{\text{rad}}$ ). The elemental abundances of element ‘A’ to element ‘B’ are expressed as logarithmic ratios of number densities N, that is,

(1) \begin{equation} \left[\text{A}/\text{B}\right] \equiv \mathrm{log}_{10}(N_{\text{A}}/N_{\text{B}}){_\star} - \mathrm{log}_{10}(N_{\text{A}}/N_{\text{B}}){_\odot} \end{equation}

where abundances are normalised to the solar values and are defined in the usual way as [X/Fe] $=$ [X/H] minus; [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. Reference Sharma2018) with an elaborate step-by-step distribution given in section 3 of Sharma et al. (Reference Sharma2018).

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 thea into a smaller sample of solar-type stars, which are defined as cool main-sequence dwarfs located below the red edge of the classical instability strip (including spectral types from late F, G, and up to K dwarfs, Soderblom & King Reference Soderblom, King and Hall1998; García & Ballot Reference García and Ballot2019) for the GALAH data, this can be applied through the following masks:

(2) \begin{align} \texttt{flag_sp} == 0, \texttt{flag_fe_h} == 0, \texttt{flag_Na_fe} == 0, \end{align}

(3) \begin{align} \texttt{e_age_bstep}/\texttt{age_bstep} \lt 0.2 \text{ or }\texttt{e_age_bstep} \lt 2, \end{align}

(4) \begin{align} \texttt{snr_c2_iraf} \gt 50, \end{align}

(5) \begin{align} 5\,600 \lt T_{\text{eff}} \lt 5\,950, \log g \gt 4.15 , \end{align}

(6) \begin{align} -0.3 \lt \mathrm{[Fe/H]} \lt 0.3. \end{align}

We employ basic quality cuts to select only unflagged measurements (Equation 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 $2\,\mathrm{Gyr}$ (Equation 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 (Equation 4). We further limit our sample to solar-type stars via Equations (5) and (6) following the definition of Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020).

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

(7) \begin{equation} \texttt{flag_X_fe} == 0\end{equation}

where X replaces the respective element, for example, Na, for acceptable sodium measurements.

3.1. The upturn of [Na/Fe] at [Fe/H] $\, \gt \,0$

In Fig. 1b we show the [Na/Fe] versus [Fe/H] relation with bin median ages in a step size of 2 Gyr. The important takeaway is that within all age bins explored in Fig. 1b, stars are visibly more enriched in [Na/Fe] at high metallicity for ages between 4–6 Gyr. 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. Reference Katz, Gómez, Haywood, Snaith and Di Matteo2021). Several surveys have provided large statistical samples of stars with detailed chemical abundances, such as RAVE (Kunder et al. Reference Kunder2017), Gaia-ESO (Randich et al. Reference Randich and Gilmore2013), APOGEE (Alam et al. Reference Alam2015), LAMOST (Zhao et al. Reference Zhao, Zhao, Chu, Jing and Deng2012), and GALAH (Buder et al. Reference Buder2018), combined with very precise Gaia astrometry (Lindegren et al. Reference Lindegren2018), 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. Reference Lee2011; Delgado Mena et al. Reference Delgado Mena, Adibekyan, Santos, Tsantaki, González Hernández, Sousa and Bertrán de Lis2021; Bensby et al. Reference Bensby, Feltzing and Oey2014; Recio-Blanco et al. Reference Recio-Blanco2014; Hayden et al. Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017) have devised preliminary techniques to separate the contamination of the two-disc sequences. However, kinematics and chemo-dynamics have proven to be rather inaccurate in distinguishing both sequences, especially at intermediate ages (Hayden et al. Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017) in the metallicity range of $-0.3$ to $+0.5$ dex, where both sequences overlap (e.g. Bensby et al. Reference Bensby, Feltzing and Oey2014).

The Milky Way’s stellar disc is a complex structure, and its formation and evolution are still widely debated (e.g. Katz et al. Reference Katz, Gómez, Haywood, Snaith and Di Matteo2021). Several surveys have provided large statistical samples of stars with detailed chemical abundances, such as RAVE (Kunder et al. Reference Kunder2017), Gaia-ESO (Randich et al. Reference Randich and Gilmore2013), APOGEE (Alam et al. Reference Alam2015), LAMOST (Zhao et al. Reference Zhao, Zhao, Chu, Jing and Deng2012), and GALAH (Buder et al. Reference Buder2018), combined with very precise Gaia astrometry (Lindegren et al. Reference Lindegren2018), 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. Reference Lee2011; Delgado Mena et al. Reference Delgado Mena, Adibekyan, Santos, Tsantaki, González Hernández, Sousa and Bertrán de Lis2021; Bensby et al. Reference Bensby, Feltzing and Oey2014; Recio-Blanco et al. Reference Recio-Blanco2014; Hayden et al. Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017) have devised preliminary techniques to separate the contamination of the two-disc sequences. However, kinematics and chemo-dynamics have proven to be rather inaccurate in distinguishing both sequences, especially at intermediate ages (Hayden et al. Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017) in the metallicity range of $-0.3$ to $+0.5$ dex, where both sequences overlap (e.g. Bensby et al. Reference Bensby, Feltzing and Oey2014).

We continue our analysis by reproducing the selection of young and old sequences in the age-abundance plane similar to Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020). However, contrary to Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020), 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. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020) are superimposed over the GALAH DR3 solar-type stars data (see Fig. 1).

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. Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020, 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 Equation (8). 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.

Fig. 1a, in particular, shows an initial selection (hereafter standard cut) based on a separation ‘by eye’ of the Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020) stars as an orange line. We classify stars as young or old whether they are below or above the line as:

(8) \begin{equation}\left.\begin{aligned}\text{old stars} & \,:\, \text{[Na/Fe]}_{\text{old}} \,\,\,\,\,\, \gt 0.55 - 0.5/5.5 \,\times\tau \\\text{young stars} & \,:\, \text{[Na/Fe]}_{\text{young}} \lt 0.55 - 0.5/5.5\,\times\tau\end{aligned}\right\},\end{equation}

where $\tau$ represents the stellar age. We discuss the sensitivity of our results to variations of our standard cut in Section 3.3 in which we test the robustness of our selection criteria for the GALAH data sample. For the smaller data set of Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020), 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. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020) overlaid on GALAH DR3 solar-type thick (orange) and thin disc (sky blue) stars, respectively. Further to this, we show the distribution of our stellar sample population with contours in the [Fe/H]–age plane in Fig. 3. The GALAH DR3 solar-type population in our work follows a similar trend in separation in the [Fe/H] vs. age space as depicted in Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020). Since our dataset comprises nearly 2 orders of magnitude more stars than the Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020) sample, it includes stars at about $6.3$ Gyr, the age that roughly corresponds to the transition between young and old sequence and is sparsely populated in the Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020) work (see Section 4.5 for further discussion). We note that the ages of younger stars tend to be larger than those of Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020), but the trends agree in a relative sense, which thus does not change the implications of this study. Recent works, for example, Xiang & Rix (Reference Xiang and Rix2022) and Anders et al. (Reference Anders2023) have confirmed the existence of two sequences in the [Fe/H]–age diagram.

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 (Fig. 4. 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, some alpha elements (i.e. C, O, and Ca) show overall decreasing trends as we consider younger stellar ages; see also Table 1. 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. The distribution of stars in the [Fe/H]-age plane for both older and younger sequences of solar-type stars in GALAH DR3 is shown using contours. The contour levels are $0.1, 0.2, 0.3, 0.4,$ and $0.5,$ with each level representing the probability of selecting a star belonging to a specific classification. The contour levels are increasing inwards. The larger dots represent stars from the old and young sequence as per Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020), and they are colour-coded according to the classification defined in Fig. 2.

3.3. Quantifying age-abundance trends and testing the newly suggested selection via the age-[Na/Fe] plane

Here we test how robust our age-abundance trends are regarding the particular selection function (cut guided by eye) chosen in the [Na/Fe]-age plane. The results of the age-abundance trends for each element are displayed in Fig. 4. The outcomes of the linear fits performed on our population of stars are presented in Table 1.

To test the robustness of our [Na/Fe] versus age trend against the details of the choice of the standard cut in Equation (8), we consider further cuts (as shown in Fig. 6) defined by the equations below:

(9) \begin{align}\text{upper cut} & \,:\, \text{[Na/Fe]} = 0.55\,({-}0.05) - 0.5/5.5 \,\times\tau, \end{align}

(10) \begin{align}\text{lower cut} & \,:\, \text{[Na/Fe]} = 0.55\,({+}0.05) - 0.5/5.5\,\times\tau, \end{align}

(11) \begin{align}\text{steep cut} & \,:\, \text{[Na/Fe]} = 0.75 - 0.68/5.5\,\times\tau\text, \end{align}

(12) \begin{align}\text{shallow cut} & \,:\, \text{[Na/Fe]} = 0.35 - 0.32/5.5\,\times\tau,\end{align}

where is the age of stars in Gyr. The effect of these various cuts is shown in Fig. 7.

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

Table 1. We report the gradient for the entire 5–8 Gyr age range, as well as the trend for stars younger/older than $6.3$ Gyr motivated by Fig. 4. Note that in this case, the linear fits were performed on the individual stars and not on the binned abundances, since the ages within a bin are not uniformly distributed and therefore using a representative age value (as done in Fig. 4) would introduce unnecessary uncertainties. A graphical representation is given in Fig. 5.

Figure 4. Age-median abundance trends of the old-solar type stars with ages 5–8 Gyr as reported in GALAH DR3. Each panel shows its corresponding element on the top-left corner, and scatter dots represent the median abundance in a $0.5$ Gyr width bin. Uncertainties are taken from the abundance distribution in a given age bin, with the lower (upper) uncertainty equalling the 16th (84th) percentile. For visualisation purposes, all median abundances have been shifted so the value at the first bin ( ${\sim}7.75$ Gyr) has solar abundance. An empty marker is used at $6.25$ Gyr to highlight the position at which we find a break in the linear trend for elements such as C, Na, and Sc (see Section 4.5). The linear fit for stars above/below this limit are shown as solid orange lines and motivate the results shown in Table 1, where we report the results for linear fits to the individual stars above/below $6.3$ Gyr and also the entire 5–8 Gyr age range.

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

Sodium is an odd-Z element synthesised in exploding massive stars and dying low-mass stars. In massive stars, Na is synthesised during the hydrostatic carbon burning phase (Cameron Reference Cameron1959; Salpeter Reference Salpeter1952; Woosley & Weaver Reference Woosley and Weaver1995). Also, during the neon-sodium (Ne-Na) and magnesium-aluminium (Mg-Al) cycles in dying low-mass stars, Na is produced (Denisenkov & Denisenkova Reference Denisenkov and Denisenkova1990) and mixed to the surface (e.g. El Eid & Champagne Reference El Eid and Champagne1995; Mowlavi Reference Mowlavi1999; Karakas Reference Karakas2010; Cinquegrana & Karakas Reference Cinquegrana and Karakas2022).

Figure 5. 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 Equation (8). 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 $6.3$ and 5 Gyr ago, for example, during the birth of stars representing the younger end of the old sequence as given in Table 1

Figure 6. Similar to Fig. 1a for the entire age range considered (8–5 Gyr), but now including different cuts to separate old from young solar-type stars (see Equations 9–12).

Figure 7. Gradients for the old sequence stars from this work, similar to Fig. 5, but this time, the gradient value is taken over the larger age range that is shown in Fig. 6 for the various selection cuts that are displayed. Colours correspond to those used in Fig. 6. We note that modifying the slope or moving the y-intercept up or down does not significantly change our findings, for example, the gradient values remain mostly clustered.

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. Reference Bedell2018). For instance, the trend of [Na/Fe] first increases with [Fe/H] because of the contributions from massive stars that produce Na and Fe (Bensby et al. Reference Bensby2017, see Fig. 21); 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. Reference Ruiter, Belczynski, Sim, Hillebrandt, Fryer, Fink and Kromer2011, 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 Reference McWilliam2016). This trend is important for our consideration because the bulge shares the same abundance trend with the thin and thick discs (Bensby et al. Reference Bensby2017). The study of Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020) reported a rise in [Na/Fe] of $0.15$ dex for the same stellar population at the same age range (5–8 Gyr). Similarly, we find that a linear fit to the old sequence at intermediate ages of 5–8 Gyr gives a gradient value of $0.0260 \pm 0.0009\,\mathrm{dex/Gyr}$ , that is, $0.077$ dex for the stated age range for [Na/Fe]. Also, a steeper rise for [Na/Fe] occurs between the ages of 5–6.3 Gyr with an abundance gradient of $0.0673 \pm 0.0031\,\mathrm{dex/Gyr}$ (see red data points in Fig. 5) compared with that of $0.0066 \pm 0.0021\,\mathrm{dex/Gyr}$ (see Table 1).

We indeed see an explicit ‘knee’ behaviour (McWilliam Reference McWilliam2016) 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 ${\sim} 6.3$ Gyr knee. We can see a decline for some elements relative to iron as we observe younger (generally more metal-rich) stars owing to the (generally long) delay times attributed to SNe Ia (Matteucci & Brocato Reference Matteucci and Brocato1990; Ruiter, Belczynski, & Fryer Reference Ruiter, Belczynski and Fryer2009; Maoz, Mannucci, & Brandt Reference Maoz, Mannucci and Brandt2012). 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 synthesised in SNe Ia arising from massive white dwarf stars close to the Chandrasekhar mass limit, Seitenzahl et al. Reference Seitenzahl, Cescutti, Röpke, Ruiter and Pakmor2013b). However, Na also shows an upward trend with decreasing age, though 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 massive stars. The knee effect we see in Na here would be consistent with Na being synthesised by core-collapse supernova progenitors with a metallicity-dependent yield – the ‘metallicity effect’ – which we describe in the following three paragraphs.

Many of the light odd-Z elements only have one stable isotope (e.g. $^{23}\text{Na}$ (11p,12n), $^{27}\text{Al}$ (13p,14n), $^{31}\text{P}$ (15p,16n), $^{45}\text{Sc}$ (21p,24n), etc.). These odd-Z stable isotopes are neutron-rich with nuclei having 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.

Another potential source of Na-enhancement to reasonably consider is Novae. Novae are (recurring) thermonuclear eruptions on accreting white dwarfs and could also be considered as a plausible source of Na given their range of delay times (see Fig. 12, Kemp et al. Reference Kemp, Karakas, Casey, Izzard, Ruiter, Agrawal, Broekgaarden and Temmink2021). 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).

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

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 Reference Woosley and Weaver1994; Kobayashi et al. Reference Kobayashi, Umeda, Nomoto, Tominaga and Ohkubo2006; Nomoto et al. Reference Nomoto, Kobayashi and Tominaga2013; Limongi & Chieffi Reference Limongi and Chieffi2018, see Section 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, Gehren, & Zhao Reference Shi, Gehren and Zhao2004; Kobayashi et al. Reference Kobayashi, Karakas and Umeda2011; Cinquegrana & Karakas Reference Cinquegrana and Karakas2022).

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 the 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 ages of $\sim$ 8–6.3 Gyr age range, after which there is a gradual decrease (so-called knee; first reported by McWilliam Reference McWilliam1997) 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, we find that, light elements (C and O), as well as the neutron capture element Ba show a decreasing trend towards younger stellar ages.

Of the elements that showed enrichment in their abundances, of copper is most prominent, followed by sodium (see Table 1). On average, for these elements, more enrichment occurred at around 6.3 Gyr and this manifests as an increase by a factor of ${\sim}10$ in their respective gradients. Although copper (atomic number $=29$ ) and zinc (atomic number $= 30$ ) lie close on the periodic table, they have different age-abundance gradient values. Cu and Zn abundance trends are somewhat flat in the 8 and $6.3$ Gyr age group. However, Zn quickly rises and remains flat in the 6 and 5 Gyr age range. 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 belonging to the thin disc was carried out by Spina et al. (Reference Spina, Meléndez, Karakas, Ramírez, Monroe, Asplund and Yong2016) to trace the chemical evolution by examining the [X/Fe] versus age for 24 elements from carbon (C) to europium (Eu). Spina et al. (Reference Spina, Meléndez, Karakas, Ramírez, Monroe, Asplund and Yong2016) used the high-resolution and high signal-to-noise UVES optical spectrograph of the VLT to obtain spectra of nine solar twins to make 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 (Ca, Ti, Mg, Si, etc.) are characterised by a [X/Fe] decrease with age, while the iron-peak elements (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. In addition to previous work by Spina et al. (Reference Spina, Meléndez, Karakas, Ramírez, Monroe, Asplund and Yong2016) on Solar twin stars, Buder et al. (Reference Buder2021) compared the Solar twin stars in GALAH DR3 to that of Spina et al. (Reference Spina, Meléndez, Karakas, Ramírez, Monroe, Asplund and Yong2016) and found a significant agreement for these elements: O, Na, Si, Ca, Sc, Ti, Mn, Zn, Y, and Ba. However, elements such as Mg and Cr had a slight offset due to few lines being used in the calibration red (see Fig. 15 of Buder et al. Reference Buder2021). The presence of few lines in our data for Cr is the reason for the offset when compared with other elements that agree with that of Nissen et al. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020) data.

4.5. The significance of an enrichment change at 6.3 Gyr

We appreciate that, at first glance, we have made a seemingly arbitrary cut when fitting the age-abundance trends above and below 6.3 Gyr. However, this decision is also corroborated by previous reports of a knee-age effect by Edvardsson et al. (Reference Edvardsson, Andersen, Gustafsson, Lambert, Nissen and Tomkin1993) and McWilliam (Reference McWilliam1997). Since then, other studies have reported this knee-age effect, mostly seen in $\alpha-$ element plots (Bensby et al. Reference Bensby, Feltzing and Oey2014; Spina et al. Reference Spina, Meléndez, Karakas, Ramírez, Monroe, Asplund and Yong2016). 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 (Reference McWilliam1997), 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. (Reference Nissen, Christensen-Dalsgaard, Mosumgaard, Silva Aguirre, Spitoni and Verma2020), suggests that the knee can be interpreted as evidence of gas accretion onto the Galactic disc, with a quenching of star formation in between.

Our 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 (see Section 4.2), 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. Reference Thielemann2002). Furthermore, we also consider the decreasing trend of alpha and light elements as the point where core-collapse supernovae has reached their peak, consequently leading to a decrease in their [X/Fe] as most of these elements are produced through explosions of massive stars (Arnett Reference Arnett1995; Iwamoto et al. Reference Iwamoto, Brachwitz, Nomoto, Kishimoto, Umeda, Hix and Thielemann1999; Kobayashi et al. Reference Kobayashi, Karakas and Umeda2011). We conclude by noting again that the knee-age effect from this work is an indication of the variation in star formation rate due to the differences between older and younger stellar populations. This also suggests that there is a change in how gas is accreted onto the younger stellar sequence, which is influenced by the presence of the older sequence.

4.6. How does our new selection criterion improve the selection of the thick and 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. (Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017) in the [Fe/H] vs. [Mg/Fe] plane and we show where these stars are in the Age-[Na/Fe] plane in Fig. 8.

Figure 8. Visualisation of the selection difference of old and young disc stars with the method by Hayden et al. (Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017). Panel a) shows the plane of [Fe/H] vs. [Mg/Fe] that was used by Hayden et al. (Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017) to select thin and thick disc stars. Panel b) shows that the same stars are less clearly separated in the [Na/Fe]–age plane we propose in our study. Thick disc stars are orange, while a bluish colour represents the thin disc stars.

To compare how similar our new selection method is to the selection criteria of Hayden et al. (Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017), we construct a confusion matrix (see Fig. 9). We see that 59% of the stars are attributed to opposite populations. Most notably, Hayden et al. (Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017) would allocate 55% (i.e. 3 415 stars) of the old sequence as defined in our work as thin disc stars when using [Mg/Fe] criteria. Also, 4% of young sequence stars (248 stars) as described in this work would be categorised as thick disc stars when using the [Mg/Fe] selection method. In all, only 41% are allocated to the same populations (i.e. 21% thin and 20% thick disc stars).

Figure 9. Confusion matrix of the selection of thin and thick disc by Hayden et al. (Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017) 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).

Figure 10. Galactocentric pericenter radius distribution of the stars in our sample taken from the value-added catalogues presented in Buder et al. (Reference Buder2021) and based on Gaia Collaboration et al. (2021). The Old and Young sequences have been separated by using the age-[Na/Fe] selection presented in this work in panel (a), and the selection presented by Hayden et al. (Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017) in panel (b). A significant number of the old sequence stars in our work have smaller Galactocentric pericentre radii in comparison to the young sequence stars, which contrasts the Hayden et al. (Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017) [Mg/Fe] based selection where both sequences of stars between 3–5 kpc display significant overlap.

To further check as to whether our selection method results in less contaminated old and young sequences than the method of Hayden et al. (Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017), we also compare the orbital peri-galactocentric distances of the stars from both works. We indeed see a difference in the two populations: we find the older sequence stars are found to have smaller peri-galactocentric distances, for example, distances closer to the Galactic centre, on average, compared to the younger sequence. We can clearly see a distinction between the old and young sequences, especially between 3–5 kpc from the histogram plot in Fig. 10 (panel a), where both sequences are distinctly differentiated in our Na-based selection compared to the Mg-based selection where they experience more overlap (Fig. 10, panel b). We find a stronger correlation (supporting the notion that old sequence stars are more readily found closer to the inner Galaxy) than Hayden et al. (Reference Hayden, Recio-Blanco, de Laverny, Mikolaitis and Worley2017). 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 Reference Matteucci and Francois1989; Recio-Blanco et al. Reference Recio-Blanco2014).