The Gaia-ESO Survey: Oxygen Abundance in the Galactic Thin and Thick Disks^*

To estimate [O/Fe] ratio abundances, we adopted a spectral synthesis technique. For each of the 2133 stars, we used the stellar atmosphere ATLAS12 code (Kurucz 2005) and the spectral synthesis program SPECTRUM v2.76f (Gray & Corbally 1994) to compute its model atmosphere and synthetic spectrum, respectively. As described in FR20, we adopted ATLAS12, since it allows us to generate on-the-fly models with full consistency between the chemical composition used to build the atmosphere structure and the one actually used in synthesizing the emergent spectrum. In particular, for each ith star, we used its GES iDR5 atmospheric parameter values (T_eff, log g, [Fe/H], and ξ) and individual element abundances with the only exception of [C/Fe] values, which are from FR20 (for those elements with no estimate of [X/Fe] we assumed [X/Fe] = 0) to compute 13 atmosphere models differing only in [O/Fe], i.e., with [O/Fe]${}_{j}=-0.6+(j-1)\times 0.1$ dex (with j = 1, ..., 13).

Then, starting from each i, j (i and j specify the star and the adopted [O/Fe] ratio, respectively) atmosphere model, we used SPECTRUM v2.76f to obtain the corresponding normalized spectrum (S${}_{{\rm{N}}}^{i,j}$) in LTE approximation. The line list of atomic and molecular transitions we used in computing the synthetic spectra is the INTRIGOSS (high-resolution synthetic spectral library; Franchini et al. 2018)²³ line list, updated by the new log gf values of Table 1 in FR20 and extended, by using the same technique described in Franchini et al. (2018), to also cover the wavelength range 6280–6325 Å. For the reference solar abundances, we adopted those obtained by Grevesse et al. (2007).

In conclusion, for each star, we computed a set of 13 normalized synthetic spectra with [O/Fe] consistent with the abovementioned atmosphere models. Since the synthetic spectra were computed at a very high resolving power (∼240,000), they were broadened by using the GES iDR5 $v\sin i$ stellar values and degraded at the resolution of red UVES spectra ($R\sim$ 52,500).

In order to remove the instrumental signature in the [O i] = 6300 Å line region of the observed (stacked) UVES-U580 spectra, for each star i, we used the j normalized synthetic ${{\rm{S}}}_{{\rm{N}}}^{i,j}$ spectra to obtain a set of 13 normalized observed spectra (O${}_{{\rm{N}}}^{i,j}$) from the corresponding observed UVES-U580 spectrum. The normalization was performed by applying the technique described in Franchini et al. (2018, 2020) but only in the region surrounding the stellar [O i] 6300 Å line. Actually, we extracted the 6280–6325 Å wavelength region from the observed spectrum; searched for quasi-continuum flux reference points in ${{\rm{S}}}_{{\rm{N}}}^{i,j}$ (i.e., wavelength points with flux levels in excess of 0.97), taking care to exclude regions affected by telluric features in the observed spectrum; and used the same points in the corresponding observed UVES spectrum to derive the continuum shape via a linear fitting of the ratio between observed and synthetic spectra. Eventually, the observed spectrum is divided by the computed linear fit to obtain the normalized spectrum ${{\rm{O}}}_{{\rm{N}}}^{i,j}$.

For each i star and j pair of spectra, i.e., for different [O/Fe] values, we computed the standard deviation (${\sigma }_{j}^{i}$) between ${{\rm{O}}}_{{\rm{N}}}^{i,j}$ and ${{\rm{S}}}_{{\rm{N}}}^{i,j}$ in a wavelength region centered at 6300.3038 Å and with a width proportional to the stellar rotational velocity ($v\sin i$), taking into account its uncertainty (${\epsilon }_{v\sin i}$; i.e., ${\lambda }_{0}\pm {\rm{\Delta }}{\lambda }_{\mathrm{rot}}$, where λ₀ = 6300.3038 Å,  ${\rm{\Delta }}{\lambda }_{\mathrm{rot}}=(v\,\sin i+{\epsilon }_{v\sin i}){\lambda }_{0}/c$, and c is the speed of light). The above process was implemented after we checked for the presence of

• 1.  
  a badly removed night-sky [O i] = 6300.30 Å emission line in the normalized spectra, and all spectra showing points with normalized flux values greater than 1.05 in the spectral range defined for computing ${\sigma }_{j}^{i}$ were rejected; and
• 2.  
  contaminating telluric lines by rejecting all spectra with regions 1.5 times below the minimum predicted by all ${{\rm{S}}}_{{\rm{N}}}^{i,j}$ spectra in the spectral range defined for computing ${\sigma }_{j}^{i}$.

Then, using a parabolic fitting, we determined the "best" [O/Fe] value corresponding to the position of the minimum (if any) of ${\sigma }_{j}^{i}$ versus [O/Fe] (see FR20 for details, top panels of their Figure 2). In such a way, we were able to obtain [O/Fe] estimates for 869 stars (no clear minimum in ${\sigma }_{j}^{i}$ was detected for the other stars, thus preventing a sound determination of [O/Fe]). We assumed as the uncertainty in the obtained [O/Fe] the half-step of our [O/Fe] grid of models and synthetic spectra, i.e., ${\sigma }_{[{\rm{O}}/\mathrm{Fe}]}\pm 0.05$ dex.

To evaluate the variation of the oxygen abundance determinations when the uncertainties in the adopted model atmosphere parameters are taken into account, we rederived [O/Fe] for some representative stars by varying their input ${T}_{\mathrm{eff}}$, log g, and [Fe/H] values by plus or minus their typical uncertainties, which, for our sample, are 60 K, 0.1 dex, and 0.1 dex, respectively. We choose two pairs of relatively cool and hot stars, one with [O/Fe] ≃ 0 and one with [O/Fe] > 0.3 dex. In any case, the new [O/Fe] determinations differ from the nominal ones by less than 0.05 dex and indicate that the most critical parameter is log g. Furthermore, to avoid any systematic error due to the use of a possible incorrect Ni abundance in evaluating the blend contribution of the Ni lines, we decided to reapply our fitting procedure to only half of the [O i] profile (i.e., the blue wing of the line profile, since the blend effect is much stronger in the red part of the [O i] line profile, as shown in the top panel of Figure 1) and to compare the obtained [O/Fe] with that derived from the whole profile. Eventually, we rejected all stars/spectra with a standard deviation of the two obtained [O/Fe] values greater than $3{\sigma }_{[{\rm{O}}/\mathrm{Fe}]}$, thus obtaining a final sample of 516 dwarf stars with trustworthy [O/Fe] abundance ratios (the adopted values are those from the fit of the whole profile). Moreover, to assess the absence of any other systematic offset in the derived [O/Fe] values, we also applied the above-described procedure to the solar spectrum, obtaining [O/Fe]_⊙ = −0.02.

The comparison of our results for oxygen abundance determination with those available in the literature can, unfortunately, only be done for very few of our stars. In fact, we found only 3, 4, and 10 stars in common with Bensby et al. (2014), Brewer & Fischer (2016), and Buder et al. (2019), respectively. In any case, our results are in reasonable agreement with those obtained in these three works, taking into account that different oxygen lines and NLTE corrections were used (we recall that our results do not require any NLTE correction, since we used the [O i] 6300 line). Actually, we found mean differences in [O/H] of 0.06 ± 0.08, −0.24 ± 0.10, and 0.09 ± 0.12 for the stars in common with Bensby et al. (2014), Brewer & Fischer (2016), and Buder et al. (2019), respectively, where the highest difference is very likely due to the absence of any NLTE correction in Brewer & Fischer (2016).

Out of the 516 stars, 308 also have an age determination (for the other 208 stars, FR20 found too-uncertain ages, i.e., with FWHM_age > 8 Gyr).

Figure 2 shows the histograms of the atmospheric parameters and FR20 ages for the stars in the final sample. The final sample consists of stars spanning T_eff from 4877 to 6561 K, log g from 3.51 to 4.79 dex, and [Fe/H] from −0.84 to 0.46 dex.

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To discriminate between thin and thick disk stars in the UVES-U580 sample, we used, as in FR20, three different selection methodologies: (i) the chemical one based on positions in the [Mg/Fe]–[Fe/H] plane, (ii) the kinematical one based on stellar Galactic velocities, and (iii) the orbital one based on the R_med and $| {Z}_{\max }|$ orbital parameters (see FR20 for details). As already discussed in FR20 (and references therein), there are no conclusive criteria yet for unambiguously separating samples of thin and thick disk stars with null contamination. In fact, depending on the adopted criterion, the number of classified (i.e., as thin or thick disk stars) and unclassified stars in our sample actually varies. In fact, even if thin and thick disk stars should differ in both chemistry and kinematics, the sensitivity of each above-listed classification method varies for different kinds of stars. In particular,

• 1.  
  the adopted chemical classification, taking into account the uncertainties on [Mg/Fe] and [Fe/H] determinations, is less effective for metal-rich stars due to the merging of the two sequences of high- and low-α objects at [Fe/H] > 0;
• 2.  
  the kinematical classification, also affected by uncertainties in the computed Galactic velocities, has difficulty classifying objects that fall in the overlap regions of the Gaussian velocity distributions of the different Galactic components; and
• 3.  
  the classification based on the orbital parameters R_med and $| {Z}_{\max }|$, whose computed values depend not only on the accuracy of the input stellar positions, distances, and velocities but also on the reliability of the adopted Galactic potential, may fail for stars falling close to the somewhat arbitrary separation borders in the orbital parameter plane between the different Galactic components adopted in FR20.

On the other hand, FR20 showed that, independent of the classification method adopted, in all thin and thick disk star subsamples, the behaviors of [C/H], [C/Mg], and [C/Fe] versus [Fe/H], [Mg/H], and age and the Galactic regions they populate (given by the stellar orbit R_med and $| {Z}_{\max }|$) are very similar. Therefore, in this paper, we decided to merge the results of the three abovementioned selection methodologies in the following way:

$$\begin{eqnarray*}&&\begin{array}{l}\mathrm{Thin} \mbox{-} \mathrm{disk}\ \mathrm{star}\ \mathrm{if}\,({\mathrm{Thin}}^{{\rm{C}}}=\mathrm{true}\,\mathrm{and}/\mathrm{or}\,{\mathrm{Thin}}^{{\rm{K}}}\,=\,\mathrm{true}\,\mathrm{and}/\mathrm{or}\,{\mathrm{Thin}}^{{\rm{O}}}=\mathrm{true})\,\mathrm{and}\\ \,({\mathrm{Thick}}^{{\rm{C}}}=\mathrm{false}\,\mathrm{and}\,{\mathrm{Thick}}^{{\rm{K}}}\,=\,\mathrm{false}\,\mathrm{and}\,{\mathrm{Thick}}^{{\rm{O}}}=\mathrm{false})\\ \mathrm{Thick} \mbox{-} \mathrm{disk}\ \mathrm{star}\ \mathrm{if}\,({\mathrm{Thick}}^{{\rm{C}}}=\mathrm{true}\,\mathrm{and}/\mathrm{or}\,{\mathrm{Thick}}^{{\rm{K}}}\,=\,\mathrm{true}\,\mathrm{and}/\mathrm{or}\,{\mathrm{Thick}}^{{\rm{O}}}=\mathrm{true})\,\mathrm{and}\\ \,({\mathrm{Thin}}^{{\rm{C}}}=\mathrm{false}\,\mathrm{and}\,{\mathrm{Thin}}^{{\rm{K}}}\,=\,\mathrm{false}\,\mathrm{and}\,{\mathrm{Thin}}^{{\rm{O}}}=\mathrm{false}),\end{array}\end{eqnarray*}$$

where the superscripts "C," "K," and "O" refer to the results of the chemical, kinematical, and orbital methodology, respectively. In such a way, after discarding the few stars with discordant classification, we obtained two samples of 376 and 20 stars classified by at least one methodology as thin or thick disk stars, respectively, even if they were unclassified by the other methodologies. In such a way, we tried to also deal with the uncertainties on the different parameters used for the different classification approaches. We recognize that the thick disk sample is small; therefore, it is desirable to collect more data for this population to confirm the robustness of the results presented in the following sections.

As mentioned earlier, several studies of the Galactic chemical history make use of Mg instead of the more popular and accessible Fe as a reference element. The choice is based on the potential single origin (SNe II) of Mg (e.g., Bensby et al. 2004; Griffith et al. 2019; Weinberg et al. 2019), although some stellar yield models have provided theoretical evidence that Mg might also be partially released into the interstellar medium by SNe Ia (Magrini et al. 2017; Naiman et al. 2018). In this context, Bensby et al. (2004) recommended being very cautious about promoting one specific reference element, and they instead suggested considering more than one. Following their suggestion, in what follows, we analyze disk stellar populations on the basis of the abundance ratios [O/Fe] and [O/Mg] in terms of [Fe/H] and [Mg/H], respectively. The trends depicted in Figure 4 are computed using a running average (using bins with 100 points partially overlapped by shifting them by 10 points and bins with 10 points partially overlapped by shifting them by two points for the thin and thick disk stars, respectively), while the horizontal and vertical bars correspond to the standard deviations of the bin averages.

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For the [O/Fe]–[Fe/H] tendencies illustrated in the left panel of Figure 4, we distinguish the following properties.

• 1.  
  We found systematic differences between thin and thick disk stars, as already hinted at by the distributions in Figure 3; thick disk stars show a higher [O/Fe] than objects in the thin disk in the common [Fe/H] interval. Thick disk stars show an almost flat distribution in the limited [Fe/H] range they cover, while thin disk stars show a clear monotonic decrease of [O/Fe] for increasing metallicity. As expected, these [O/Fe] versus [Fe/H] trends resemble the behavior of other α-elements versus [Fe/H]. Actually, oxygen being an α-element, for the most metal-poor stars in our sample, an [O/Fe] plateau reflects a steady rate of oxygen and iron enrichment of the interstellar medium by CCSNe. The gradual decrease of [O/Fe] with increasing [Fe/H] reflects the iron enrichment from SNe Ia, which have a delayed distribution in time relative to CCSNe (e.g., Carigi et al. 2005; Maoz et al. 2012). Analogous systematic differences between thick and thin disk abundance distributions have been obtained in several works in the literature (e.g., Bensby et al. 2004, 2014; Reddy et al. 2006; Ramírez et al. 2013; Nissen et al. 2014; Bertran de Lis et al. 2015; Delgado Mena et al. 2019), all confirming that oxygen behaves like Mg and the other α-elements but at high metallicity.
• 2.  
  We can notice that at [Fe/H] ≈ −0.40, there is a difference of Δ[O/Fe] ∼ +0.2 dex between the thin and thick disk star trends. Interestingly, Reddy et al. (2006) found, on the basis of a kinematical selection, that their thick and thin disk samples are also well separated. In their bin centered at [Fe/H] = −0.50, the mean abundance ratios [O/Fe] are 0.36 ± 0.19 and 0.24 ± 0.07 dex for the thick and thin disks, respectively. These values are in agreement with our results within the uncertainties.In this context, the more recent work of Nissen et al. (2014) found that their thin disk stars fall well below the thick disk counterparts in the [O/Fe] versus [Fe/H] diagram by as much as [Fe/H] ∼ −0.3, and they suggested that the two populations merge at higher metallicities. This later feature cannot be corroborated with our data, since we lack thick disk stars with metallicities higher than −0.2 dex.
• 3.  
  At supersolar metallicity ([Fe/H] > 0), we observe that the [O/Fe] of thin disk stars continues to decrease, as also found by several authors (e.g., Castro et al. 1997; Chen et al. 2003; Bensby et al. 2004, 2014; Ecuvillon et al. 2006; Amarsi et al. 2019) in concordance with the prediction of Galactic chemical evolution models (e.g., Chiappini et al. 2003). In contrast, other works have found a flattening of the trend, i.e., a constant value of [O/Fe] ∼ 0 (e.g., Nissen & Edvardsson 1992; Nissen et al. 2002; Ramírez et al. 2013; Bertran de Lis et al. 2015). Our results suggest that the oxygen is produced only by CCSNe with no evidence of any SN Ia or asymptotic giant branch (AGB) star contribution that would produce a flattening of [O/Fe] at [Fe/H] ≃ 0, as observed in other α-elements (Bensby et al. 2004, 2014). We notice that the thin disk star [O/Fe] trend continues down to an underabundance of [O/Fe] ≈ −0.15 at [Fe/H] ≈ 0.30 in agreement with the results from Bensby et al. (2004), who, adopting a kinematic selection for their thin disk sample, showed a decreasing trend leading to [O/Fe] ≈ −0.2 at [Fe/H] ≈ 0.4 dex.
• 4.  
  The linear relation between [O/Fe] and [Fe/H] for the thin disk stars,

  $$\begin{eqnarray*}&&[{\rm{O}}/\mathrm{Fe}]=(-0.33\pm 0.01)\times [\mathrm{Fe}/{\rm{H}}]-(0.027\pm 0.002),\end{eqnarray*}$$

  is in good agreement with the linear regression obtained by Gustafsson et al. (1999) using the abundances of F and G dwarfs by Edvardsson et al. (1993), who found

  $$\begin{eqnarray*}&&[{\rm{O}}/\mathrm{Fe}]=(-0.36\pm 0.02)\times [\mathrm{Fe}/{\rm{H}}]-(0.044\pm 0.010),\end{eqnarray*}$$

  and plausibly reflects that iron enrichment by SNe Ia takes place in larger timescales when compared with the rapid production of oxygen by SNe II (as first suggested by Matteucci & Greggio 1986).
• 5.  
  The thin disk sequence at [Fe/H] = 0 is slightly below zero. At [Fe/H] = 0, we found a value of [O/Fe] = −0.027 ± 0.002, which is, in absolute value, slightly larger than the value we derived for the Sun (see Section 3.2). Similar results were found by Meléndez et al. (2009; an average $\langle [{\rm{O}}/\mathrm{Fe}]\rangle =-0.033\pm 0.011$ for 11 stars) and Ramírez et al. (2009; $\langle [{\rm{O}}/\mathrm{Fe}]\rangle =-0.015\,\pm 0.006$ for 22 stars), who used samples of solar twins. Similar studies based on F-, G-, and K-type stars in the solar neighborhood have also been conducted with compatible results, e.g., Gustafsson et al. (1999; $\langle [{\rm{O}}/\mathrm{Fe}]\rangle =-0.044\pm 0.010$ for 57 stars), Ramírez et al. (2013; $\langle [{\rm{O}}/\mathrm{Fe}]\rangle =-0.02\pm 0.04$ for 47 stars), and Nissen et al. (2014; $\langle [{\rm{O}}/\mathrm{Fe}]\rangle =-0.016\pm 0.04$ for 11 stars). A possible explanation for the observed offset can be found in Nieva & Przybilla (2012), who suggested that the Sun was born at a distance around 5–6 kpc from the Galactic center, where higher metallicity values were reached earlier in the cosmic history of the Galaxy, and it has migrated outward during its lifetime of 4.5 Gyr at the current position. An alternative explanation for this peculiarity is related to the formation of planetary systems like the solar one and, in particular, terrestrial planets (Meléndez et al. 2009).

As far as the [O/Mg]–[Mg/H] trend is concerned (right panel of Figure 4), we can make the following considerations.

• 1.  
  The decrease of [O/Mg] with [Mg/H] > 0.0 for the thin disk stars gives evidence of a different behavior of oxygen and magnesium at high metallicities, i.e., they do not evolve in lockstep, and indicates that, while oxygen is only enriched by CCSNe, magnesium might also be released, to some extent, by SNe Ia and/or AGB stars (Magrini et al. 2017; Ventura et al. 2018).
• 2.  
  Both the thick and thin disk stars at [Mg/H] ≲ −0.1 show trends almost flat with [Mg/H] at [O/Mg] ≃ 0. These flat [O/Mg] trends are in agreement with the results by Bensby et al. (2004; see their Figure 12), even if their thick disk values at [Mg/H] ≲ 0.1 are almost leveled out at a level slightly higher than their thin disk data. The increase in [O/Mg] for the thick disk stars with [Mg/H] ≳ −0.1 may be due to the poor statistic, a selection effect, or the presence of an [O/Mg] gradient with the star distance from the Galactic plane, as also suggested by the results presented below. In fact, since the two bins with higher [Mg/H] contain mainly stars at low $| {Z}_{\max }|$, their high [O/Mg] values may be simply due to the negative vertical gradient of this abundance ratio with $| {Z}_{\max }|$ shown in the third panel in the right column of Figure 6. Therefore, at present, it is premature to draw any conclusions.

The [C/O] ratio in the Galactic disks has also been under debate and is highly relevant in a number of astrophysical scenarios, for example, to understand planet formation processes and the possible existence of terrestrial planets (e.g., Delgado Mena et al. 2010; Nissen 2013; Nissen et al. 2014; Brewer et al. 2017; Amarsi et al. 2019). In the context of this paper, it is particularly useful when discussing the origin and evolution of carbon in the Galaxy. Since oxygen is exclusively produced in massive stars on a relatively short timescale (∼10⁷ yr), the change in [C/O] as a function of [O/H] depends on the yields and timescales of carbon synthesized in different types of stars (Chiappini et al. 2003; Akerman et al. 2004; Carigi et al. 2005; Cescutti et al. 2009; Romano et al. 2020).

Figure 5 shows how [C/O] changes as a function of [Fe/H], [Mg/H], and [O/H] for the thin and thick disk stars. In particular, from Figure 5, we can observe the following.

• 1.  
  There is a slight increment of [C/O] with [Fe/H], [Mg/H], or [O/H] for thin disk stars for $[\mathrm{Fe}/{\rm{H}}]\gtrsim -0.1$. Such an increase can be explained by taking into account a C production contribution from low-mass and/or massive stars at high metallicities due to their enhanced mass loss.
• 2.  
  Thick disk stars show a decrease of [C/O] with [Fe/H], [Mg/H], and [O/H]. A qualitatively similar behavior can be observed in the [C/O] versus [O/H] correlation of Stonkutė et al. (2020, see their Figure 11), even if they interpreted it as due to the presence of a shift (∼−0.3 dex) of their thick disk star sequence with respect to that for the thin disk. On the other hand, Bensby & Feltzing (2006) found a flat behavior for the thick disk stars until [O/H] ≃ 0 and then an increase. In any case, we should point out that the thick disk star bin behavior could be an artifact in our case. Therefore, it would be desirable to expand the thick disk sample, aiming at verifying such a [C/O] decrease and elucidating the effects of the steep vertical gradient of [O/Fe] (see Figure 6) on the observed tendency.

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In this section, we present the trends of oxygen abundance ratios with the mean galactocentric distance, ${R}_{\mathrm{med}}=0.5\,\times ({R}_{\min }+{R}_{\max })$, and the maximum absolute distance from the Galactic plane, $| {Z}_{\max }|$, for the 333 thin disk and 18 thick disk stars for which stellar orbits were calculated in FR20.

Both observed radial and vertical stellar abundance distributions are particularly interesting tools to study the chemical enrichment history of the Galactic disks and their formation processes. Actually, the radial and vertical thin and thick disk star trends collect a lot of very important information to disentangle the embedded aspects of inflow, star formation, outflow, and radial and vertical mixing that gave rise to the present state of the Milky Way disk (for example, a radial gradient of the disk that is produced in an inside-out formation scenario can be partially reduced/canceled by a radial mixing process). The radial metallicity gradients of the Milky Way disk have been measured using a number of different stellar (e.g., Cepheids, open clusters) and interstellar medium tracers (H ii regions, etc.) that represent the composition of the interstellar gas at the time they were formed (e.g., Cheng et al. 2012; Mikolaitis et al. 2014, and references therein) or the present time, respectively, thus probing the metallicity gradient at different epochs. In addition, the vertical gradients of the global metallicity and different elements have also been derived by using different input databases (see, for example, Boeche et al. 2014; Schlesinger et al. 2014; Magrini et al. 2017, and references therein). One of the causes of the different gradient values, both radial and vertical, reported in the literature might be attributed to different input data. In fact, gradients may be affected by the chemical evolution of the Galaxy (i.e., by the time the analyzed objects were formed), local inhomogeneities, moving groups, and stellar streams. Moreover, the measured gradients may be biased by systematics and/or inhomogeneities in the spatial and age distributions of the input data samples; i.e., derived vertical gradients may be more affected by stars located in the outer or inner galactic radius, R, and/or younger or older stars if the Z bins do not contain evenly distributed objects in R and age. Therefore, the interpretation of the derived gradients as result of the star formation history of the galactic disk(s) is very challenging. In the following, we will take advantage of the fact that the stars in our thin and thick disk stellar samples display, to some extent, different dependencies on R_med and $| {Z}_{\max }|$ and span different age ranges (see Figures 6 and 7), but it is worthwhile to remark that our interpretation of the results may still be affected by systematics, particularly for the thick disk stellar sample.

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In Figure 6, we show the radial and vertical gradients of [O/H], [O/Fe], [O/Mg], and [C/O] for the thin and thick disk star samples, again using running average bins as in Figures 4 and 5.

As far as the trends as a function of R_med are concerned, we recall that FR20 did not have deviations from axisymmetry in their Galactic potential like those introduced by the bar and the spiral arms and did not take into account radial stellar migration. However, R_med values can provide an indication of the stellar birthplaces (Edvardsson et al. 1993; Rocha-Pinto et al. 2004), which could be used, at least, in a differential form.

As can be seen, the thin and thick disk stars fall in different $| {Z}_{\max }|$ ranges: most of the thin disk bins have $| {Z}_{\max }| \lt 0.8\,\mathrm{kpc}$, while all of the thick disk bins have $| {Z}_{\max }| \gt 0.8\,\mathrm{kpc}$. Moreover, as discussed in the next section, most of the thin disk star bins have ages <10 Gyr, while all of the thick disk objects have ages >10 Gyr (see Figure 8). Therefore, the trends with R_med of our thin and thick disk stars may give hints of the radial gradients of relatively young stars at low $| {Z}_{\max }|$ and old stars at higher $| {Z}_{\max }|$, respectively.

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By inspection of Figure 6, we can observe the following.

• 1.  
  The [O/H] and [C/O] show negative gradients as a function of R_med for the thin disk sample. The abundance ratios [O/H] and [C/O] decrease significantly with the mean galactocentric distance, while the thick disk sample exhibits flat trends or perhaps very mild positive gradients, as indicated by the fits of Table 3. The positive radial gradient of [C/O] for the thick disk stars might not be real, since it could actually be a result of the fact that our data bins correspond to groups of stars with different average $| {Z}_{\max }|$ values and are actually reflecting the presence of the steep [C/O] vertical gradient shown in the bottom right panel of Figure 6. A dichotomy between thin and thick disk stars was found by several authors (e.g., Allende Prieto et al. 2006; Katz et al. 2011; Cheng et al. 2012; Boeche et al. 2013; Anders et al. 2014; Mikolaitis et al. 2014; Recio-Blanco et al. 2014; Hayden et al. 2015, 2018; Kordopatis et al. 2015) and could indicate that either the thick disk formed from a well-mixed interstellar material or, if gradients were present, they disappeared because of a migration effect more efficient in the thick disk than in the thin one (Minchev et al. 2013). Esteban et al. (2005), using recombination lines from echelle spectrophotometry of eight H ii regions with galactocentric distances in the range 6–10 kpc, derived a value of −0.044 ± 0.010 dex kpc⁻¹ for the [O/H] radial gradient. Rudolph et al. (2006), also based on the analysis of H ii regions, derived values of −0.060 and −0.041 dex kpc⁻¹ by using optical and infrared data, respectively. More recently, Wang (2019) used spectra of 101 H ii regions in the Galactic anticenter area from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) and derived the oxygen abundance gradient with a slope of −0.036 ± 0.004 dex kpc⁻¹. Wenger et al. (2019), using the National Radio Astronomy Observatory Karl G. Jansky Very Large Array to observe ∼8–10 GHz hydrogen radio recombination line and radio continuum emission toward 82 Galactic H ii regions, found an oxygen abundance gradient across the Milky Way disk with a slope of −0.052 ± 0.004 dex kpc⁻¹. All of these values are in good agreement, within the uncertainties, with our slope value (the small errors given in Table 3 are due to the fact that we fitted the abundances of the average bins and not the individual stars). Of course, we compare our gradients with those from H ii regions, which actually reflect the present situation, while in our trends, we mix stars of somewhat different ages with only a rough separation between young/thin and old/thick disk populations. As a further comparison, Cescutti et al. (2007) found a gradient of −0.035 dex kpc⁻¹ for O for a galactocentric distance of 4–14 kpc, in good agreement with our results. A negative radial gradient of [C/O] was observed by Esteban et al. (2005) from H ii region recombination lines. They found a steeper gradient, $\tfrac{d[{\rm{C}}/{\rm{O}}]}{d| {Z}_{\max }| }\,=-0.058\,\pm 0.018$, than us. On the theoretical side, Carigi et al. (2005) showed that, by varying carbon, nitrogen, and oxygen yields, Galactic chemical evolution models predict slopes between −0.005 and −0.068 dex kpc⁻¹.We notice that most of the [O/H] and all of the [C/O] values of the thin disk bins are negative, suggesting that solar neighborhood stars have less oxygen and C/O than the Sun. To explain these results, Nieva & Przybilla (2012) stated that the Sun may be an immigrant to its current Galactic neighborhood; i.e., the birthplace of the Sun could be at an inner galactocentric distance (R = ∼ 5–6 kpc) where higher metallicity values were reached earlier in cosmic history. If this is true, they claimed that "a telltaling signature is left only in the C/O ratio" (but they did not discuss [O/H]). Our results suggest that a solar [O/H] value should be characteristic of ${R}_{\mathrm{med}}=\sim 7\,\mathrm{kpc}$, while solar [C/O] would imply ${R}_{\mathrm{med}}\lesssim 6\,\mathrm{kpc}$, but we recall again that, due to the simplified Galactic potential used by FR20 to compute stellar orbits, R_med gives only a rough indication of the actual stellar birthplaces.
• 2.  
  The [O/Fe] and [O/Mg] versus R_med show flat (or slightly positive for the thin disk star bins) trends (see Table 3). Mikolaitis et al. (2014) found a slightly positive slope of [α/M] in their clean thin disk sample (0.014 ± 0.004 dex kpc⁻¹) and a flat trend in their clean thick disk sample (−0.005 ± 0.006 dex kpc⁻¹). Unfortunately, their results cannot be directly compared with our [O/Fe] trends, since their α-elements do not include oxygen. The [O/Mg] versus R_med shows even flatter trends and a much smaller systematic difference between the values for thick and thin disk stars than the [O/Fe]. These results might indicate that SNe Ia not only produce an enrichment of Fe in the thin disk but also a small increase of Mg, while oxygen seems to be enriched only by CCSNe.

For the abundance trends as a function of $| {Z}_{\max }|$, we identify the following features.

• 1.  
  The [O/H] bins show a negative vertical gradient with slope increasing from lower (thin disk star bins) to higher (thick disk star bins) $| {Z}_{\max }|$ (see Table 4, where the thin disk fits refer to bins with $| {Z}_{\max }| \lt 0.8$ kpc). Similar behaviors for $\tfrac{d[\mathrm{Fe}/{\rm{H}}]}{d| {Z}_{\max }| }$ and $\tfrac{d[\mathrm{Si}/{\rm{H}}]}{d| {Z}_{\max }| }$ were found by Boeche et al. (2014). In an analysis of α-elements, Mikolaitis et al. (2014) found $\tfrac{d\alpha }{d| Z| }=+0.036\pm 0.006$ dex kpc⁻¹ for their thin disk clean sample. However, we want to remark that these authors did not include oxygen in their α mixture.
• 2.  
  The [O/Fe] and [O/Mg] thin disk star bins show positive trends with $| {Z}_{\max }|$ (see Table 4) that could be explained by the increasing contribution of iron and magnesium by SNe Ia (we recall that our stars at low $| {Z}_{\max }|$ are also the youngest ones, as shown in Figure 14 of FR20). The thick disk star bins have negative trends like [O/H] but with lower slopes. The fact that [O/Mg] shows a smaller difference between the average values of thick and thin disk star bins than [O/Fe] (as already seen in the radial gradient panels) is a consequence of the greater yields of iron than magnesium in SNe Ia.
• 3.  
  The [C/O] shows an almost flat trend for the thin disk star bins, suggesting that both carbon and oxygen were produced by massive stars. The positive trend of the thick disk star bins reflects the steep negative trend of [O/H] with $| {Z}_{\max }|$ shown in the top right panel of Figure 6.²⁴

Table 3.  Radial Gradients

	$\tfrac{d[{\rm{O}}/{\rm{H}}]}{{{dR}}_{\mathrm{med}}}$	χr	$\tfrac{d[{\rm{O}}/\mathrm{Fe}]}{{{dR}}_{\mathrm{med}}}$	χr	$\tfrac{d[{\rm{O}}/\mathrm{Mg}]}{{{dR}}_{\mathrm{med}}}$	χr	$\tfrac{d[{\rm{C}}/{\rm{O}}]}{{{dR}}_{\mathrm{med}}}$	χr
	(dex kpc−1)		(dex kpc−1)		(dex kpc−1)		(dex kpc−1)
Thin	−0.041 ± 0.001	0.145	0.014 ± 0.004	0.269	0.009 ± 0.002	0.193	−0.020 ± 0.001	0.146
Thick	0.006 ± 0.002	0.062	0.003 ± 0.001	0.074	0.000 ± 0.001	0.032	0.020 ± 0.004	0.147

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Table 4.  Vertical Gradients

	$\tfrac{d[{\rm{O}}/{\rm{H}}]}{d| {Z}_{\max }| }$	χr	$\tfrac{d[{\rm{O}}/\mathrm{Fe}]}{d| {Z}_{\max }| }$	χr	$\tfrac{d[{\rm{O}}/\mathrm{Mg}]}{d| {Z}_{\max }| }$	χr	$\tfrac{d[{\rm{C}}/{\rm{O}}]}{d| {Z}_{\max }| }$	χr
	(dex kpc−1)		(dex kpc−1)		(dex kpc−1)		(dex kpc−1)
Thin	−0.04 ± 0.01	0.229	0.09 ± 0.01	0.350	0.020 ± 0.004	0.234	0.007 ± 0.001	0.053
Thick	−0.41 ± 0.03	0.203	−0.20 ± 0.02	0.310	−0.24 ± 0.02	0.278	0.35 ± 0.02	0.141

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Nominal ages for 233 and 15 stars belonging to our thin and thick disk star samples, respectively, were given by FR20. The thick disk stars are, in general, older than members of the thin disk. Figure 7 shows the normalized, generalized age histograms of both populations, built by summing the individual age probability distributions, for the thin (red) and thick (blue) disk stars. The extended wings and, therefore, the overlap of the two distributions are likely due to the large uncertainties affecting individual stellar ages. Most of the thin disk stars span a range from 2 to 8 Gyr, while the thick disk stars are mostly older than 8 Gyr. This is in agreement with the common understanding of Galactic chemical evolution based on serial and two-infall models (e.g., Chiappini et al. 1997; Calura & Menci 2009; Romano et al. 2010; Grisoni et al. 2017) and chemical abundance studies matched with asteroseismologic age determinations, which suggest a delay of ∼4 Gyr between the first and second accretion episodes that were the origin of the Milky Way disks (Haywood et al. 2015; Snaith et al. 2015; Spitoni et al. 2019).

Figure 8 shows the trends of [O/H], [O/Fe], [O/Mg], and [C/O] versus age. As for previous figures, we plot in red and blue the thin and thick disk stellar samples, with the bins constructed using a running average.

In Figure 8, we identify the following properties of the abundance ratios versus age.

• 1.  
  A difference in the age intervals spanned by thin (in general younger) and thick (older) disk star bins is clearly evident with only a small overlap between 10 and 11 Gyr. Recalling the intrinsic uncertainties in FR20 age estimates, it is possible that such an overlap could actually be less pronounced.
• 2.  
  Both thin and thick disk stars show almost flat trends of [O/H] versus age. A similar behavior was observed by Delgado Mena et al. (2019), who, by using the oxygen abundances from Bertran de Lis et al. (2015), derived two similar flat trends of [O/H] with age for thin and thick disk stars for the HARPS-GTO sample. The small negative slope (−0.004 ± 0.001) for our thin disk star bins and the slightly larger positive one (0.028 ± 0.004) for our thick disk star bins with age are likely to be remnants of the radial and vertical gradients (plus selection effects) shown in Figure 6 (red points in the top left panel and blue points in the top right panel, respectively). The higher average value for the thin disk stars indicates that the thin disk formation started only after many CCSNe had already produced O enrichment of the interstellar medium.
• 3.  
  Both thin and thick disk stars show increasing trends of [O/Fe] and [O/Mg] with age with an almost zero slope for the youngest objects. Since our stars do not show a strong spatial gradient in [O/Fe] and [O/Mg] (see the middle panels of Figure 6), we think that they really indicate abundance ratio trends with age. There is a jump from higher to lower [O/Fe] values in the common age region, while the [O/Mg] sequences merge smoothly. The steeper trends at the oldest ages confirm that oxygen is indeed mainly produced in the early phases of Galaxy formation by massive stars. Such correlations were also in other [α/Fe] ratios (see, for example, Nissen & Gustafsson 2018; Delgado Mena et al. 2019, and references therein). In fact, steep age trends at old ages and flat trends at young ages should be expected for [O/Fe] if the CCSNe are the predominant (or even the only) suppliers of oxygen in the interstellar medium, while a less clear behavior can be foreseen in the case of other α-elements, which are also partially released by SNe Ia (e.g., Carigi et al. 2005; Nomoto et al. 2013). We also found steeper slopes for [O/Fe] than for [O/Mg], which is consistent with the fact that SNe Ia release much more iron than magnesium in the interstellar medium. The slopes of [O/Fe] and [O/Mg] versus age for our thin disk star bins are 0.019 and 0.01 dex Gyr^–1, respectively, and in qualitative agreement with the results by Delgado Mena et al. (2019), who found 0.026 and 0.02 dex Gyr^–1 using a HARPS-GTO sample. The smooth merger of the thin and thick trends of [O/Mg] seems to indicate that [O/Mg] should be preferred to [O/Fe] as a proxy of age, and its shape suggests that the correlation is nonlinear in the whole age interval from 3 to 12 Gyr.
• 4.  
  The [C/O] trends show a steep decrease for the oldest objects (age ≳ 10 Gyr) and an almost flat trend for younger objects. As in the case of [O/H], this behavior with age can actually be the result of hidden spatial [C/O] gradients (see the bottom panels of Figure 6). This interpretation agrees with the results by Nissen (2015), who, using HARPS spectra of 21 solar twins in the solar neighborhood, showed that the C/O ratio evolves very little with time, although the [C/Fe] and [O/Fe] ratios evolve significantly. He showed a good agreement between the data (see his Figure 11) and the predictions of the Galactic chemical evolution model by Gaidos (2015), in which the dominant contribution of C and O comes from massive stars. It is also argued that C/O has only a moderate rise during the first ∼5 Gyr due to an increasing contribution of carbon from stars of lower mass. This is also in agreement with what was found by FR20.