APOGEE DR14/DR15 Abundances in the Inner Milky Way

We use data from the SDSS Data Release 14 (DR14; Abolfathi et al. 2018), which includes spectra, stellar parameters, and stellar abundances from the APOGEE-1 and APOGEE-2 surveys (Majewski et al. 2017). These data are identical to those appearing in SDSS DR15 (K. Masters et al. 2018, in preparation). APOGEE-1 was a component of the SDSS-III (Eisenstein et al. 2011), and APOGEE-2 is part of the SDSS-IV (Blanton et al. 2017). Both APOGEE-1 and APOGEE-2 North projects utilize the 2.5 m Sloan Telescope at Apache Point Observatory (Gunn et al. 2006), coupled to a 300-fiber, high-resolution (R ∼ 22,000), H-band spectrograph (Wilson et al. 2012). A second spectrograph is currently taking observations as part of APOGEE-2 South on the 2.5 m du Pont Telescope at Las Campanas Observatory; inner MW data from this southern survey component will be available in future data releases.

The primary APOGEE sample comprises spectra of red giant stars in the magnitude range 7 ≲ H ≲ 13.8, reduced with a custom pipeline. For details of the target selection in APOGEE-1 and -2, see Zasowski et al. (2013) and Zasowski et al. (2017), respectively. Nidever et al. (2015) describe the reduction and RV measurement pipelines, and García Pérez et al. (2016) describe the APOGEE Stellar Parameter and Abundances Pipeline (ASPCAP).

Throughout this paper, we use the DR14/DR15 calibrated abundances. Details of the data calibration and available data products can be found in Mészáros et al. (2013), Holtzman et al. (2015), and Holtzman et al. (2018). The APOGEE abundances are calibrated to remove systematic uncertainties as much as possible; using comparisons to optical-based abundances for the same stars, Jönsson et al. (2018) show that while some systematics are likely to remain for certain elements (e.g., N, K, V), this procedure is generally effective. The individual, random abundance uncertainties are estimated by deriving an empirical fit for the abundance scatter within stellar clusters. This fit is a function of T_eff, [M/H], and signal-to-noise ratio (S/N); it does not explicitly include systematics, but the comparison in Jönsson et al. (2018) gives us reason to believe that these are generally small. For the majority of elements in the majority of stars, the quoted uncertainties are <0.1 dex.

Starting with the full DR14/DR15 catalog, we first removed stars flagged as not part of the primary red giant sample (i.e., ancillary targets and pre-selected Galactic Center supergiants). We also removed stars without reliable effective temperatures, surface gravities, and metallicities derived by ASPCAP, since without well-determined parameters any derived elemental abundances are highly uncertain. For these culls, we required that the ASPCAPFLAG bits 19, 20, and 23 and STARFLAG bit 9 not be set (the METALS_BAD, ALPHAFE_BAD, STAR_BAD, and PERSIST_HIGH flags,¹⁹ respectively). We also removed stars outside the ranges 3600 K ≤ T_eff ≤ 4500 K and −0.75 ≤ log g ≤ 3.5 to ensure a sample of similarly evolved, inner MW giant stars with the most reliable parameters. Abundances with uncertainties larger than 0.15 dex are eliminated from the analyses described below.

Heliocentric distances for the stars in DR14/DR15 have been calculated by multiple groups, including Wang et al. (2016), Schultheis et al. (2017), and Queiroz et al. (2018, using an updated version of the code from Santiago et al. 2016).²⁰ A detailed comparison of these distance sets is beyond the scope of this paper, but in general the agreement is good. We adopt the distances of Queiroz et al. (2018), which incorporate the recent extinction law of Schlafly et al. (2016) and newer Galactic structural priors from Robin et al. (2012) and Bland-Hawthorn & Gerhard (2016). From this catalog, we used the median posterior distance and the posterior distance standard deviation for the distance and distance uncertainty, respectively; we confirmed that the additional probability density function (pdf) percentiles reported are consistent with Gaussian pdf's, so we treat the uncertainties as Gaussian throughout this paper (e.g., in Figure 1 and Section 3.3). We note that the qualitative conclusions in this paper are independent of which distance set is used. The variance in sample size when using different sets for the distance limits below is ∼20%, but we find no systematic trend (in terms of stellar parameters) in the stars that meet our requirements using one particular distance set.

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Using a solar distance of R₀ = 8.3 kpc (e.g., Chatzopoulos et al. 2015), we apply a Galactocentric distance limit on the stellar sample of R_GC ≤ 4.0 kpc, a range that includes the so-called long or thin bar (e.g., Wegg et al. 2015), and a fractional R_GC uncertainty limit of ≤40%. The resulting sample comprises 4058 stars, with the stellar parameter and heliocentric distance distributions shown in Figure 1. The dotted line in the bottom right panel shows the distance distribution as a summation of N Gaussians, one for each star in the sample, where each Gaussian is centered at the star's calculated distance and broadened by the distance uncertainty (the median fractional uncertainty in the sample is 12.2%, with a standard deviation of 4%). This distribution is broader than the simple histogram, unsurprisingly, but the similar shape suggests that the true distance distribution is not significantly different than what is assumed in the following analyses by using the quoted values.

This selected spatial region includes stars in the bar, the inner halo, the α-enhanced and α-solar components of the disk, and any other structural components in the center of the MW. We do not attempt to disentangle these components kinematically or chemically; our goal here is to describe the abundance patterns of the sum total of the populations residing in the inner regions of the Galaxy.

The APOGEE DR14/DR15 release includes elemental abundances for 23 elements: C, N, O, Na, Mg, Al, Si, P, S, K, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Ge, Rb, Yb,²¹ and Nd. However, as discussed in Jönsson et al. (2018), several of these abundances show unexpectedly large scatter, due primarily to the impact of weak lines and/or line blending. Here we restrict our discussion to 11 elements: O, Mg, Si, Ca, Cr, Mn, Co, Ni, Na, Al, and K, a selection motivated by the removal of species dominated by scatter unreflected in the uncertainties and of those whose surface abundances undergo substantial evolution during a stellar lifetime (e.g., C and N). This set of elements largely corresponds to the abundances assessed by Jönsson et al. (2018) to have small systematic and random differences when compared to abundances from optical spectroscopy. However, we also include some with large scatter or other unusual behavior (e.g., K and Co), because these abundance uncertainties seem to be mostly systematic in nature (Jönsson et al. 2018) and can be used in a differential comparison between the inner MW sample and a disk sample of similar stars (below) that should display the same systematics.

Throughout the discussion below, we refer to several literature studies, as well as two primary APOGEE references: the mean trends observed in literature data sets compared with APOGEE DR13 abundances in Baade's Window analyzed in Schultheis et al. (2017), and the detailed assessment of APOGEE DR13–DR15 abundance accuracy, precision, and consistency with literature values provided by Jönsson et al. (2018). We also refer to a useful stellar comparison sample: stars at approximately the solar circle (solar radius; SR) selected with quality criteria identical to those described in Section 2.2, but with 6 kpc < R_GC < 10 kpc and $| {Z}_{\mathrm{GC}}| \,\lt 1.25\,\mathrm{kpc}$. The SR stars are then subsampled to have a very similar joint T_eff–[Fe/H] distribution to that of the inner Galaxy sample; this facilitates direct comparison of the abundance patterns without the impact of the disparate metallicity distributions and differently sampled RGBs in the two Galactic regions (Appendix A).

Figure 2 contains the [X/Fe]–[Fe/H] distributions for our chosen elements in the inner MW stars. Figure 3 shows the comparable distributions for the SR sample, as well as the median and ±1σ trends of the inner MW stars from Figure 2 for comparison. We discuss each of these abundance distributions in Sections 3.1.1–3.1.3 and provide some summary statistics of the distributions in Table 1. For a detailed comparison of overall ASPCAP abundances to various literature sources, see Jönsson et al. (2018). Here we focus on the observed patterns as released in DR14/DR15 and on literature values from the inner Galaxy, with some comparisons to chemical enrichment yield patterns from Andrews et al. (2017) that use nucleosynthetic yields compiled from Woosley & Weaver (1995), Iwamoto et al. (1999), Chieffi & Limongi (2004), Limongi & Chieffi (2006), and Karakas (2010).

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Figure 2 also contains one-zone chemical evolution sequences for the [O/Fe] and [Mg/Fe] abundances (black dotted lines). These sequences have been shifted vertically by an arbitrary amount because we want to emphasize that these are not fits to the data, but rather that the similarity in shape demonstrates that the α-abundances, at least, appear dominated by a simple evolutionary track (in contrast to the SR distributions in Figure 3). These tracks, computed with the flexCE code²² of Andrews et al. (2017), have the same parameters as the fiducial model in that paper, with the exception of the outflow mass-loading factor (here, η = 2.0). A comprehensive fitting and comparison to a wider range of chemical evolution models are deferred to future work; here we provide empirical descriptions of the data and its internal relationships, which will serve as observational constraints to these chemical evolution models.

3.1.1. Alpha Elements: O, Mg, Si, Ca

Oxygen: The inner MW [O/Fe] abundances follow the typical mean α-element behavior: enhanced abundances, with [O/Fe] ∼ +0.25 for [Fe/H] < −0.1, that decrease to roughly solar abundance at higher metallicities. In the range −1.0 < [Fe/H] < +0.5, the APOGEE sample has a rather tight sequence and is less scattered than in, e.g., Fulbright et al. (2006). In both the inner Galaxy and SR samples, the oxygen abundances at a given metallicity increase with decreasing stellar temperature, a trend that is noticeable at nearly all metallicities above [Fe/H] ∼ −0.9. At the most metal-poor end ([Fe/H] < −1.0), the temperature trend seems to reverse, as the O abundances become higher with increasing temperature.

APOGEE finds lower [O/Fe] values at lower metallicity than the bulge sample of, e.g., Johnson et al. (2014) and other stellar samples from the literature (Jönsson et al. 2018). [O/Fe] abundances derived from observed spectra can be shifted by the inclusion of non-LTE (NLTE) and 3D model corrections (e.g., Dobrovolskas et al. 2015), though less work has been done to calculate the need for corrections at high metallicity. In literature comparisons to chemical enrichment models, [O/Fe] discrepancies at low metallicity are often attributed to different models' mass cutoffs, due to the dependence of O yields on core-collapse SN (CCSN) progenitor mass, or to variations in the models' assumed metallicity dependence of the CCSNe's O and Fe yields (e.g., Andrews et al. 2017). In APOGEE DR14/DR15, the [O/Fe] abundances at all metallicities are at roughly the same level of enhancement as [Mg/Fe] and [Si/Fe].

The nearly flat trend in [O/Fe] at increasingly higher metallicity (above [Fe/H] = 0) is also noteworthy; in the context of the Weinberg et al. (2017) analytic chemical evolution models, this extension could indicate temporal variations in the ejected and recycled gas fractions (see, e.g., their Figure 13). A thorough exploration of these trends in the context of different evolutionary model parameters will be explored in future work.

We also note a group of seemingly [O/Fe]-enhanced stars at high metallicities, with [O/Fe] ≳ +0.18 and [Fe/H] > +0.2 (denoted by green points in Figure 2). These stars tend to have lower temperatures and higher α-element abundances than the average values of the rest of the sample, but they are not distinctly separated except in [O/Fe] and [Ca/Fe], and they show no difference in the non-α-elements.

After extensive investigation, we hypothesize that these seemingly enhanced abundances are most likely due to nonoptimal synthetic spectral fits. The ASPCAP pipeline computes a global fit for several stellar parameters, including T_eff, $\mathrm{log}g$, metallicity, and [α/M]; these parameters are then used in the derivation of individual elemental abundances. The abundance results presented here have been derived with parameters computed using the Kurucz grid of model atmospheres (the default one employed in DR14/DR15 for all of our stars; Holtzman et al. 2018). In examining all of the results for these "high-O" stars, we observed that their global [α/M] values are also strongly enhanced, whereas the [α/M] values from the MARCS model grid for these stars are much more consistent with those of the rest of the sample (at a given metallicity). The [α/M] ratio is expected to be correlated with [O/Fe] owing to the large number of OH features in cool, metal-rich stars, so this offset suggests that the O abundances for these particular stars would be better extracted using the MARCS grid. Unfortunately, individual elemental abundances using the MARCS grid results are not available in DR14/DR15. We exclude these stars from the analyses in the rest of the paper, but we note them in the summary plots of Figure 2, in this discussion, and as a list in Appendix B as a caveat to other users.

Magnesium: As Schultheis et al. (2017) show for stars in Baade's Window, the APOGEE Mg abundances in the bulge region are in generally good agreement with those from Gaia-ESO and other optical studies (e.g., Gonzalez et al. 2011; Hill et al. 2011). Jönsson et al. (2018) argue that Mg is the most precise α-element in DR14/DR15, with practically zero offset and very small scatter compared to optically derived values (for the same stars).

Similar to [O/Fe], we see a slight decrease in [Mg/Fe] toward lower metallicity ([Fe/H] ≲ −0.8) for both the inner MW and SR stars. The slope of this trend is small enough that we describe this portion as "flat" in Table 1, but we note that this inflection point is also seen in several simulated yields (e.g., Andrews et al. 2017), possibly due to the (slight) metallicity dependence of CCSN Mg yields. Unlike O, however, no temperature trend is visible for the Mg abundances across the entire metallicity range shown. A small number of the "high-O" stars are slightly enhanced in Mg, but the majority are completely consistent with the rest of the sample.

See Section 3.3 for an analysis of the [Mg/Fe]–[Fe/H] downturn due to contributions of SNe Ia.

Silicon: Si is the α-element with the smallest dispersion in our sample, especially at the metal-rich end. This low dispersion is also confirmed by other inner Galaxy studies in the infrared (e.g., Rich & Origlia 2005; Ryde et al. 2010; Schultheis et al. 2017) and in the optical (e.g., Fulbright et al. 2007; Gonzalez et al. 2011). However, we note a temperature trend (especially where [Fe/H] ≲ −0.4) in the sense that cooler stars show lower Si abundances than warmer ones at the same metallicity. Unlike O and Mg, which plateau to their "metal-poor" value by [Fe/H] ∼ −0.25, [Si/Fe] continues to increase until [Fe/H] ∼ −0.5; because of the T_eff trend, [Si/Fe] of the warmer stars appears to increase more steeply at lower metallicities, but the increase is present in all temperature ranges. Interestingly, the temperature trend appears to be much less obvious in the SR sample, but the metallicity range [Fe/H] < −0.5 (where the trend is most apparent in the inner Galaxy stars) is very poorly sampled near the SR.

Calcium: [Ca/Fe] exhibits slightly different behavior compared with the other α-elements. Stars with [Fe/H] < −0.5 are less enhanced in Ca (compared to solar) than in O, Mg, and Si, a phenomenon seen also in the SR sample. Past the onset of SNe Ia, which produce more Ca than other α-elements, [Ca/Fe] declines to slightly supersolar values (more enhanced than at the SR), but [Ca/O], [Ca/Mg], and [Ca/Si] slowly rise at increasing metallicity (Figure 4), in particular at metallicities higher than the [Mg/Fe] "knee" discussed in Section 3.3. We also note a slight increase in [Ca/Fe] as [Fe/H] becomes increasingly supersolar, which could indicate a metallicity dependence in the Ca yields of CCSNe (not found in subsolar-metallicity progenitors; Andrews et al. 2017) or of SNe Ia.

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One striking feature is the nearly horizontal sequence of cool stars (T_eff < 3800 K) with a nearly constant [Ca/Fe] abundance of roughly +0.25 at high [Fe/H]. These stars overlap at the metal-richest end with the "high-O" stars and are most likely also related to the difficulty of analyzing certain cool stars (see the [O/Fe] discussion above). This sequence also creates a seeming temperature trend in the metallicity range [Fe/H] > −0.5, though the distribution becomes clearly bimodal at [Fe/H] > −0.2 owing to this likely artifact. As for Mg, the metal-poor stars show no relation between T_eff and [Ca/Fe].

As highlighted in Table 1, all of the α-elements share the same qualitative behavior across metallicity: constant abundance at [Fe/H] < −0.8, decreasing abundance from [Fe/H] > −0.8 to [Fe/H] < 0, and constant (near-solar) abundance for supersolar [Fe/H].

3.1.2. Iron-peak Elements: Cr, Mn, Co, Ni

3.1.3. Odd-Z Elements: Na, Al, K

Figure 5 shows the two-sample Anderson–Darling statistic (Scholz & Stephens 1987) for the abundance distributions [X/Fe] of the inner MW and SR samples, measured at different [Fe/H]. This statistic measures the likelihood that given samples of data are drawn from the same parent distribution. Because of the difficulties of matching the inner MW's coolest, most metal-poor stars at the SR (Appendix A), we restrict these compared samples to T_eff ≥ 3800 K and [Fe/H] ≥ −1.0 and remove bins without at least 30 stars in both samples. We also do not show Na and Co, the elements with the largest dispersions. The exact values of the statistic on the y-axis are less informative than the relative trends across metallicity and between elements. The horizontal gray bar at the bottom of Figure 5 indicates the critical value above which the hypothesis that these samples are drawn from the same distribution can be rejected at the 1% significance level.

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As expected, the α-elements are the most dissimilar in the metallicity range −0.5 ≲ [Fe/H] ≲ −0.1, where the SR stars have a bimodal distribution in [α/Fe] and the inner MW stars have a single sequence. In this same range, Al, K, and Ni also exhibit differences, smaller than those in O, Mg, Si, and Ca. Both the α-elements and these three are more similar between the two samples at lower and higher metallicities, though [Ca/Fe] and [Ni/Fe] show increased differences at the highest metallicities. In the case of [Ca/Fe], this may be due to the increased dispersion in the inner MW stars compared to the SR and to the smattering of cooler stars (near the 3800 K cutoff) with seemingly enhanced [Ca/Fe]. The differences in [Ni/Fe] at high [Fe/H] are most likely due to the steeper upturn in [Ni/Fe] in the inner Galaxy stars, again potentially driven by the greater fraction of cooler stars. In contrast, the distributions of the Fe-peak elements Cr and Mn are measured to be much more similar between the inner MW and SR samples at all metallicities.

In Figure 6, this statistic is computed separately for the SR's "high-α" and "low-α" sequences (shown in dark and light gray, respectively, in the left panel's inset), in comparison with the inner MW. We define "high-α" here as [α/M] > +0.12 and "low-α" as [α/M] < +0.1, to emphasize the differences. The trend lines are noisier owing to the smaller sample sizes, and the restricted metallicity ranges mean that measurements cannot be made in all [Fe/H] bins. Nevertheless, it is clear that the SR's "high-α" stellar abundances are more similar to the inner MW, even for non-α-elements. Similarly, the "low-α" SR stars have elemental abundances that are, in general, more discrepant from the inner MW's stars at the same metallicity. (Cr again appears to be the exception.) A more thorough investigation of the relationship between chemistry and kinematical properties in both samples will shed light on the relationship between the inner bar/bulge structure and the inner Galactic disk.

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The shape of a stellar population in the canonical [α/Fe]–[Fe/H] plane contains information about the efficiency and duration of star formation. In particular, when the SNe Ia  begin to explode and contribute their higher yields of Fe (relative to the α-elements), the [α/Fe] ratios of new stars drop, even as [Fe/H] continues to increase. The downturn imprinted in the sequence by this [α/Fe] decrease is often referenced colloquially as the "knee." The [Fe/H] value at which this occurs marks the point at which SN Ia events become a significant source of Fe, which in turn depends on the early star formation rate of the population (e.g., Matteucci 2003, 2012).

Johnson et al. (2014) compared the knee position of the Galactic bulge to that of the local thick disk and found that the bulge knee position lies at a higher [Fe/H] value compared with the thick disk, which is in agreement with measurements by Bensby et al. (2017) based on bulge dwarf stars. However, Bensby et al. (2017) also point out that there are inconsistencies in the direction of the knee position's metallicity shift between Mg and Ca (positive shifts with R_GC) and between Si and Ti (negative shifts). In Nidever et al. (2014) and Hayden et al. (2015), the near constancy of the knee's position across a large range of R_GC (3–15 kpc) is interpreted as qualitative evidence for spatial and chemical homogeneity of the star-forming disk at early times. In Rojas-Arriagada et al. (2017), the position of the α-enhanced disk's [Mg/Fe]–[Fe/H] downturn was measured quantitatively over a range of R_GC using Gaia-ESO stars and was also found to be consistent with a constant [Fe/H] position (though with a potentially significant shift to lower [Fe/H] at radii beyond R_GC ≈ 8 kpc). In that study, all stars with R_GC < 4 kpc were considered in a single bin. Here we use our sample of R_GC < 4 kpc stars to measure the position of the [Mg/Fe]–[Fe/H] downturn²³ in multiple radial bins (with ΔR_GC = 0.75 kpc).

There exist multiple metrics by which one could define the location of this turnover. Rojas-Arriagada et al. (2017) use the intersection of two straight lines, one fit to the high-[Mg/Fe] sequence and one to the low one, but for the APOGEE data set's distribution, we found this method to be rather sensitive to outliers and to the choice of where to separate high- and low-[Fe/H] stars. We explored a wide range of alternative "[Mg/Fe] downturn" indicators, two of which are demonstrated in Figures 7–8.

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Figure 7 contains the [Mg/Fe]–[Fe/H] distributions of the stars in different R_GC bins, as labeled, overplotted with the same fiducial cubic polynomial in each bin (black–yellow dashed line). The two [Mg/Fe] downturn metrics demonstrated here are calculated using N = 500 independent realizations in which the R_GC, [Fe/H], and [Mg/Fe] values of each star are drawn from normal distributions centered on the star's nominal values with standard deviations equivalent to the star's R_GC, [Fe/H], and [Mg/Fe] uncertainties. Thus, the exact set of stars in each R_GC bin and their [Mg/Fe]–[Fe/H] distribution are allowed to vary between realizations. The median of the 500 measurements is taken as the final value of each metric, with an uncertainty of 3× the median absolute deviation (MAD) of the 500 measurements.

The black vertical line in each panel of Figure 7 indicates the local maximum of a cubic polynomial, as determined from the first derivative, fitted to just the stars in that R_GC bin. We restricted the fitting range to −1.0 ≤ [Fe/H] ≤ +0.1, to avoid variations in the fits driven by the different numbers of stars with [Fe/H] < −1.0 in the bins. These values are plotted against R_GC in Figure 8 with colored circles connected with a dashed black line. The accompanying vertical black dashed lines in Figure 7, shown as uncertainty bars in Figure 8, are the 3× MAD values from the N = 500 realizations.

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The gray vertical lines in Figure 7 labeled "Turnover" correspond to the [Fe/H] value at which the local derivative, $d[\mathrm{Mg}/\mathrm{Fe}]/d[\mathrm{Fe}/{\rm{H}}]$, equals −0.25. This derivative value, though semi-arbitrary, was chosen to reproduce where a set of human observers visually identified the downtown in the full sample's [Mg/Fe]–[Fe/H] distribution, but, unlike visual identification, it can be computed quantitatively for any subset of stars. These [Fe/H] values are plotted in Figure 8 as colored squares connected by a gray dotted line; as with the local maximum metric, the uncertainty bars on the turnover metric are the 3× MAD values resulting from the multiple data realizations.

Both of these metrics produce [Mg/Fe] downturn positions that are largely constant with R_GC, with a potential decrease to lower metallicities at larger radii. We do not consider this decrease strongly significant, since the "turnover" values are mutually consistent within the uncertainties of the inner and outermost bins, and the most metal-poor "maximum [Mg/Fe]" points have noticeably larger uncertainties (due to the relative dearth of metal-poor stars in those bins to firmly anchor the polynomial). We note that the decrease observed is within the uncertainties of the downturn position measured by Rojas-Arriagada et al. (2017) in their single bulge bin, shown as the blue box in Figure 8. We have also confirmed that the placement and size of the bins themselves have no impact on the conclusions drawn.

Other downturn indicators that we evaluated include the cubic fit's inflection point (i.e., ${d}^{2}[\mathrm{Mg}/\mathrm{Fe}]/d{\left[\mathrm{Fe}/{\rm{H}}\right]}^{2}=0$), the metallicity at which the cumulative distribution function of metallicities of the high-[Mg/Fe] stars reaches some selected value, and alternative values of $d[\mathrm{Mg}/\mathrm{Fe}]/d[\mathrm{Fe}/{\rm{H}}]$. All of these produce downturn positions that are reasonable approximations to what previous efforts have historically termed the "knee," and which either are flat with R_GC or exhibit a small decrease as in Figure 8. There is no widely accepted definition of this morphological feature against which to test these different metrics, so we emphasize here the mean behavior and defer a detailed assessment of the metrics in the context of physical interpretation to future work.

The approximate constancy of the downturn positions is indicative of either similar star formation environments across a large fraction of the young Galaxy, perhaps due to a well-mixed interstellar medium (ISM) in the early star-forming disk and bulge region (e.g., Bournaud et al. 2009), or significant radial mixing since that era (e.g., Minchev et al. 2013) that has smoothed out any initial trends due to gradients in the star formation rate. The former is the conclusion reached by Nidever et al. (2014) and Hayden et al. (2015) for the high-α sequence at larger R_GC beyond the bulge, but the potential importance of radial mixing in the densely packed inner MW cannot be discounted (e.g., Loebman et al. 2016). Indeed, if confirmed, the slight shift of the downturn position to lower metallicities at larger R_GC would support the latter scenario operating at some level, since a well-mixed ISM with no radial migration would not easily produce a coherent gradient. Such a downturn could also result from a gradient in star formation rate, even in a chemically well-mixed ISM. Recently, Mackereth et al. (2018) showed that the properties of the high-α sequence are relatively consistent throughout the EAGLE simulations, even as the presence of a bimodal sequence (as seen at larger R_GC in the MW, including in our SR sample) is rare in the simulations.

The large sample size, in terms of number of elements and number of stars, gives us increased statistical power for constraining the correlation between pairs of elements in different populations of stars. These are useful measures for identifying similarities and differences driven by nucleosynthetic yields from various pathways (including the metallicity dependence of CCSN and SN Ia yields), and they also provide a simple way to parameterize the high-dimensional chemical space for data-model comparison. In this section, we explore the linear correlation between pairs of elements for the entire sample and for high- and low-[α/Fe] stars separately. In the latter case, we focus on pairs of elements whose correlation exhibits interesting similarities or significant differences between the two groups.

Figure 9 is a visualization of the Spearman linear correlation coefficient (ρ_S; e.g., Kokoska & Zwillinger 2000) for all pairs of elements. Each horizontal line represents one element, and points are placed along it at the ρ_S correlation value between that element and the one labeled above the point. The color of each point is the same as that element's horizontal line. For example, the bottom line represents [O/Fe], and the points along that line indicate the linear correlation coefficient between [O/Fe] and [X/Fe] for each of the other elements. This line for [O/Fe] is orange, so the points indicating [O/Fe]'s correlation with the other elements are also orange. Points for correlations with a p-value of ≥0.05 are shown as open circles.

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The α-elements are well correlated with each other, as expected; Ni, K, and Cr are also correlated with the α-elements, though more weakly. One dramatic feature is the anticorrelation of [Mn/Fe] with most other elements, especially the α-elements, but including the other iron-peak elements Cr and Ni. This trend would be even stronger if the T_eff dependency seen in [Mn/Fe] (Section 3.1.2) were taken into account. On the other hand, Mn shows a positive correlation with Co; the abundances of both elements increase with increasing [Fe/H] at low (<−0.5) and high (>0.0) metallicities, likely due to metallicity-dependent CCSN yields.

These correlations can also be calculated separately for high- and low-α-enhancement stars (as in Section 3.2, [α/M] < +0.1 and [α/M] > +0.12), which is roughly equivalent to a metallicity separation at [Fe/H] ∼ −0.1. Three main patterns emerge: (1) nearly identical ρ_S and behavior in the [X₁/Fe]–[X₂/Fe] plane between the high- and low-α groups, (2) very similar ρ_S values but offset trends in the [X₁/Fe]–[X₂/Fe] plane, and (3) very different ρ_S values. Exemplars of the latter two patterns are shown in Figure 10, where stars have been restricted to those with T_eff ≥ 3800 K to reduce the systematic scatter described in Section 3.1.

• 1.  
  Frequently, pairs of elements with identical behavior in the [X₁/Fe]–[X₂/Fe] plane between the high- and low-α groups are those with high scatter.
• 2.  
  All pairs of α-elements share behavior similar to [O/Fe]–[Si/Fe], shown in Figure 10(a). The horizontal and vertical "offsets" here are expected from the bimodal distribution (by construction) of the α-elements and their correlations; the very similar quantitative relationship between these elements is also expected owing to their similar formation sites at all metallicities.
• 3.  
  In contrast, Figure 10(b) shows that the relationship between [Si/Fe] and [Mn/Fe] differs significantly between the high-α and low-α groups—[Si/Fe] and [Mn/Fe] are not measurably correlated in the metal-rich, low-α population but are anticorrelated in the metal-poor population. The lack of metal-rich correlation is driven by the flat trend in [Si/Fe] at the same supersolar metallicities where [Mn/Fe] continues to rise. At lower metallicities, the anticorrelation reflects the fact that the CCSN Mn yields have a metallicity dependence while the Si ones do not.

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A graphical summary of the differences in all ρ_S(X₁, X₂) between the high- and low-α stars is shown in Figure 11. The values shown in both grids are identical, but the colors are scaled to emphasize small differences on the left and large differences on the right (as in Figure 9, pairs with p-values greater than 0.05 are blanked out). For example, in the right panel, [Mn/Fe] stands out as having different correlations in high- and low-α stars with elements whose correlation with [Fe/H] changes in different metallicity regimes (e.g., Ni) or whose trend is flat in the two bins considered here (e.g., Ca and Si). In the left panel, [O/Fe], which is dominated by weakly metallicity-dependent CCSN contributions, has a similar correlation at all α-abundance with elements whose yields' metallicity dependence does not change significantly across the [Fe/H] range probed here. The inclusion of Cr in this set, which has non-negligible production in SNe Ia, may indicate that SN Ia [Cr/Fe] yields are metallicity independent, as the CCSN yields appear to be.

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