Alpha Element Populations Among Local Halo Stars

Previous studies have shown that the halo of the Milky Way galaxy is made up of two distinct stellar populations, one from dissipative collapse and the other accreted. Elemental abundances with small relative uncertainties along with kinematics are determined for 20 local halo stars in the metallicity range −2.2 ≤ [Fe/H] ≤−1.2. Stars with metallicities [Fe/H] > −1.75 show clear separation into high-α and low-α groups. New results extend the work of Nissen & Schuster to the elements Co and K and to lower metallicities. The five program stars with [Fe/H] < −1.75 appear to follow the low-α sequence and may be distinguishable by lower [Ba/Fe] abundances. The results for potassium help to clarify its behavior for −2.2 ≤ [Fe/H] ≤ −1.2 with [K/Fe] ∼ 0.25 and approximately constant with [Fe/H]. Evidence is discussed regarding the cause of the low [α/Fe] abundances, i.e., whether a lower star-formation rate resulted in slower chemical evolution or if the initial mass function was deficient in high-mass stars. The low-α stars show larger dispersions in U and W velocities, as expected for an accreted population, but unlike Nissen & Schuster we find that the high-α and low-α stars do not have significantly different net orbital rotation (V).


Introduction
The mechanisms by which the the Milky Way was formed have long been studied and debated.The model put forth by Eggen et al. (1962) consisted of a monolithic collapse of a large and slowly rotating protogalactic gas cloud.Searle & Zinn (1978) proposed that a number of smaller protogalactic gas clouds and dwarf galaxies accreted to form the outer halo.
Later evidence from both globular clusters (Zinn 1993) and field stars (Norris 1994;Chiba & Beers 2000;Carollo et al. 2007Carollo et al. , 2010;;Beers et al. 2012) indicated that the halo consists of two distinct populations, supporting formation models that combine the ideas of Eggen et al. and Searle & Zinn.An inner halo population is more flattened, has a slight prograde rotation, and has higher metallicities on average, suggesting an early dissipative collapse.An outer halo population is more spherical, has a slight retrograde rotation, and extends to lower metallicities, suggesting later accretion of protogalactic fragments.
The work of Nissen & Schuster (2010, 2011; hereafter NS10 and NS11) was a milestone in our understanding of the halo populations and clearly demonstrates two distinct sequences in [Mg/Fe] and [α/Fe] (combining Mg with the other alpha elements Si, Ca, and Ti) among nearby halo stars.As [Fe/H] increases from −1.6 to −0.4, the high-α stars define a narrow sequence with [Mg/Fe] gradually decreasing from about +0.4 to about +0.3, while the low-α stars form a separate sequence (up to [Fe/H ; −0.8) with [Mg/Fe] roughly 0.2 lower.They found that other abundances are also correlated with [α/Fe], including higher [Na/Fe], [Ni/Fe], [Cu/Fe], [Zn/Fe], and [Y/Ba] in the high-α stars.Nissen et al. (2014) showed similar correlations for [C/Fe] and [O/Fe].NS10 also discussed the kinematics of their stars.They connected the high-α stars to a dissipative component of the Galaxy because they generally have prograde orbital velocities, as well as a similar abundance pattern as thick disk stars in their sample.A majority of the low-α stars have retrograde orbital velocities and a larger dispersion in U and W velocities. Using computed orbits, Schuster et al. (2012) found that the high-α stars are 2-3 Gyr older and are limited to the inner halo, while the low-α stars extend to larger Galactic radii and distances from the plane.This work demonstrated the existence of two separate halo populations with different abundance patterns, and hence different chemical evolution, which along with their kinematics and ages, provide vital information about their origin.
Many more studies have confirmed and extended the evidence for a dual halo.Additional element ratios have been shown to correlate with [α/Fe], including [C/Fe] and [O/Fe] (e.g., Nissen et al. 2014;Amarsi et al. 2019), [Al/Fe] (e.g., Hawkins et al. 2015;Hayes et al. 2018;Das et al. 2020;Horta et al. 2021;Buder et al. 2022), [Sc/Fe], and various neutron-capture element ratios (e.g., Fishlock et al. 2017).The GALAH (Buder et al. 2022) and APOGEE (Hayes et al. 2018;Jönsson et al. 2020) surveys have measured abundances for various elements in a large number of low-α and high-α stars, although with lower precision than Nissen & Schuster.Stars with lower [α/Fe] ratios have orbits with larger maximum distances out of the plane and larger apogalacticon distances (Ishigaki et al. 2010;Schuster et al. 2012).APOGEE results for giant stars over a much larger volume confirmed the bimodal [α/Fe] abundances, with high-α stars concentrated in an inner halo with significant orbital rotation and lower eccentricity orbits, and low-α stars in an outer halo having little or no rotation and higher eccentricity orbits (Hawkins et al. 2015;Fernández-Alvar et al. 2017;Hayes et al. 2018;Mackereth et al. 2019).The color-magnitude diagram for high-velocity stars from the Gaia data release 2 revealed two parallel main sequences (Gaia Collaboration et al. 2018), with stars in the bluer sequence having little or no systematic rotation and larger orbital energies (Haywood et al. 2018;Helmi et al. 2018;Koppelman et al. 2018).However, as noted by Gaia Collaboration et al. (2018) and Helmi (2020), the peak metallicities of the two sequences, [Fe/H] ∼ −1.3 and −0.5, are significantly higher than the dual halo peaks of −2.2 and −1.6 identified by Carollo et al. (2007), and −2.1 and −1.5 identified by Fernández-Alvar et al. (2017), for example.
The relative ages of the halo components are especially important to our understanding of their origin.Most studies have found that for [Fe/H]  −1.4 low-α, outer halo stars are about 2 Gyr younger than inner halo stars and thick disk star ages probably fall in between on average but with a broader distribution (Marquez & Schuster 1994;Schuster et al. 2012;Hawkins et al. 2014;Ge et al. 2016).However, Hawkins et al. (2014) found that the two components have similar ages for more metal-poor stars.Gallart et al. (2019) found that the blue and red main sequences seen in the Gaia DR2 data are coeval, and that the thick disk stars are mostly younger and span a wide range of ages.By comparison, halo globular clusters fall into two age groups, i.e., an old group with a small dispersion and a younger group spanning 5-6 Gyr (Zinn 1993;Marín-Franch et al. 2009).
The α/Fe abundance ratio is a key indicator of chemical evolution, particularly the star formation rate (SFR).The α elements are primarily produced in type II supernovae (SNII) from short-lived massive stars, but iron is also produced in type Ia supernovae (SNIa), whose progenitors have longer lifetimes, 10 8 -10 9 yr.As a result, [α/Fe] is high initially, but sharply declines with increasing [Fe/H] when SNIa begin to contribute, creating a "knee" in the [α/Fe]-[Fe/H] relation.A higher SFR causes faster chemical enrichment, so the knee occurs at a higher [Fe/H].Thus, the high-α halo stars are usually interpreted as originating in regions with a high SFR resulting in a knee at [Fe/H]  −0.5, whereas the low-α stars experienced a lower SFR and only reached [Fe/H]  −1.6 when SNIa began to contribute.The timescale for chemical enrichment could also help account for differences in sodium and neutron-capture elements due to their production in longerlived asymptotic giant branch (AGB) stars (e.g., Nissen & Schuster 2010;Fishlock et al. 2017).If the high-α and low-α stars are coeval as Gallart et al. (2019) suggest, low [α/Fe] values would require some other cause than a slower chemical evolution.The metallicity dependence of SNII yields is expected to produce a slight negative slope in [α/Fe] before the knee (e.g., Ramírez et al. 2007), which can be seen in the NS10 data for high-α stars.
An alternative explanation for low α/Fe is a different initial mass function (IMF).The production of α elements, O and Mg in particular, is concentrated in the highest-mass stars, so an IMF with fewer high-mass stars (or an environment in which SNII ejecta are not fully retained) would produce a lower [α/ Fe] ( Kobayashi et al. 2014;Fernández-Alvar et al. 2018).Because SNII yields are mass-dependent, the value of [α/Fe] before the knee is an indicator of the IMF.The figures in McWilliam (1997)  The evidence for a dual halo generally points to a scenario with a dissipative collapse creating an early disk, followed by the accretion of one or more smaller fragments (Zolotov et al. 2009;Purcell et al. 2010;Zolotov et al. 2010).These merger events would cause some stars within the disk to be heated, giving them halo kinematics.These stars would have higher [α/Fe] due to the higher SFR or an IMF with more massive stars in the disk.The original stars from the fragment would have lower [α/Fe] due to the lower SFR or an IMF with fewer high-mass stars in the fragment before the merger and would have kinematics reflecting the fragment itself.Abundance similarities between the low-α stars and stars in ω Centauri and dwarf spheroidal galaxies lend further support to this scenario (Tolstoy et al. 2009;Nissen & Schuster 2011;Monty et al. 2020).There is evidence that most of the low-α stars in the solar neighborhood may be the result of a single accretion event (Helmi et al. 2018;Mackereth et al. 2019;Monty et al. 2020).While the dual populations of the halo in the solar neighborhood will be the focus of this work, it is increasingly clear that there is a complicated array of streams and other substructures within the halo that provide evidence for specific merger events (Koppelman et al. 2019;Myeong et al. 2019;Helmi 2020;Naidu et al. 2020;Limberg et al. 2021).
Several issues remain, particularly regarding the low-α sequence.NS10 note that the distinction between high-α and low-α becomes less clear for −1.6 < [Fe/H] < −1.4 as the two sequences start to merge.Ishigaki et al. (2012Ishigaki et al. ( , 2013) )  It is especially important to determine the location of the low-α knee, which has been determined to be at [Fe/H] as low as −2.5 and as high as −1.0 (Reggiani et al. 2017;Fernández-Alvar et al. 2018;Mackereth et al. 2019;Matsuno et al. 2019;Monty et al. 2020;Aguado et al. 2021), and to consider abundance ratios that may also help distinguish between the effects of SFR and IMF.
The abundance scatter among the low-α stars is of particular interest to determine the uniformity of their chemical history.If there were significant variations within a merging fragment or if there were multiple merger events, then we might expect multiple low-α sequences.The scatter is larger for the low-α stars than for the high-α stars (NS11, Amarsi et al. 2019), and multiple sequences have apparently been identified (Matsuno et al. 2019;Monty et al. 2020).It would be very useful to explore this possibility further.
The highest possible precision will be needed to address these questions.As a step in that direction, we follow a similar approach to NS10, extended to stars with [Fe/H] down to −2.2.Section 2 presents the observational data and derived kinematics and Section 3 describes the determination of the stellar parameters and abundances.In Section 4, the abundance and kinematic trends are discussed.Section 5 contains a summary.

Observations
We observed stars taken from the high proper-motion survey of Carney et al. (1994), plus their extension to additional stars in the New Luyten Two Tenths catalog (Luyten 1979(Luyten , 1980)).A sample of 20 stars was selected to have metallicities of −1.25 [Fe/H] −2.25 and space velocities greater than 220 km s −1 with respect to the local standard of rest (LSR) in an effort to select halo stars and exclude thick disk stars (Schönrich & Binney 2009).
To calculate UVW velocities, radial velocities were provided by D. Latham (private correspondence), as described by Carney et al. (1994).The average uncertainty of the radial velocities is 0.2 km s −1 .Positions, proper motions, and parallaxes were adopted from Gaia data release 3 (Gaia Collaboration et al. 2016, 2023).UVW velocities were calculated following formalism of Johnson & Soderblom (1987) and solar peculiar velocities with respect to the LSR were taken from Coşkunoǧlu et al. (2011).The average uncertainty of the UVW velocities is less than 1 km s −1 .The adopted radial velocities and UVW velocities are shown in Table 1.
Spectra were obtained with the 2.7 m telescope at the McDonald Observatory at The University of Texas at Austin using a cross-dispersed echelle spectrograph at the coudé focus (Tull et al. 1995) with a Tektronix 2048x2048 CCD.The spectra cover roughly 4000-10000 Å at a spectral resolution ;60,000, and have a peak signal-to-noise (S/N) ranging from 85 to 300 per pixel with a median of 170.The data were reduced using IRAF in the typical way including bias subtraction and flat-fielding, and the spectra were extracted and wavelength calibrated using the echelle package.
Equivalent widths were measured with IRAF using Gaussian fits.With few exceptions, lines weaker than 5 mÅ were ignored due to their larger relative uncertainties.Lines with reduced equivalent widths 4.8 (equivalent width W λ > 95 mÅ at 6000 Å) were not used because strong lines lose their Gaussian shape as they saturate, so a Gaussian fit becomes an increasingly poor approximation to measure the equivalent width.Excluding stronger lines also reduces the importance of uncertainties in damping constants.Stray light in the spectrograph creates a "picket fence" structure in the images (Tull et al. 1995).We did not measure equivalent widths where the continuum was noticeably affected, typically in the range 4750-5000 Å.
While the majority of program stars had multiple spectra, most were able to be co-added in order to increase the S/N.However, BD-17 484, G8-16, G176-53, and G165-39 had two spectra that could not easily be co-added because small shifts in the instrument caused a given wavelength to fall on different pixels.Therefore, equivalent widths were measured independently on each spectrum and then averaged.A comparison of the two independent sets of equivalent widths showed excellent agreement, with a mean difference of 0.1 mÅ and a standard deviation of 2.4 mÅ.The typical uncertainties in equivalent widths are expected to be even smaller for the other stars because the co-added spectra generally had higher S/N.This is supported by a direct comparison of equivalent widths to NS11, which shows a mean difference of 0.4 mÅ with a standard deviation of 1.5 mÅ.
To improve the internal precision of the abundances, we adjusted the gf-values using four reference stars having especially high S/N spectra and spanning the range of stellar parameters: HD 84937, HD 108177, HD 111980, and HD 132475.These stars were analyzed using the initial gf-values.For each star, the mean abundance for a given ion was adopted.Because of their larger uncertainties, weaker lines were assigned half weight (8-10 mÅ) or zero weight (< 8 mÅ).Assuming that each line should yield the mean abundance implied a small adjustment to the gf-value, D gf log .Additionally, gf-values adopted by NS10 were considered as reference values.They also adjusted gf-values relative to two metal-poor stars, and across all species there was a mean difference of 0.02 between our gf-values and theirs.We thus had up to five reference values of D gf log for a given line.For lines that had four or five reference values or if no laboratory gf-value was available, the average D gf log was adopted to adjust the original gf-value.When only one to three reference values were available, the average D gf log was not automatically accepted to avoid introducing additional random errors.For lines with two or three values, the uncertainty of the mean, σ μ = s N , was calculated and the mean was adopted if σ μ 0.04 or if the mean was 1.65 σ μ (90% confidence).If only one reference value was available, then it was adopted only if  D gf log 2 times the standard deviation of abundances for that ion (95% confidence).
The default damping constants calculated by WIDTH9 (Castelli 2005;Kurucz 2022) were adopted for natural and Stark damping.When available, van der Waals damping constants were adopted from a series of papers by Barklem and collaborators (Barklem & O'Mara 2000;Barklem et al. 2000;Barklem & Aspelund-Johansson 2005), unpublished values from Barklem (see Barklem 2016) in the VALD database (Piskunov et al. 1995;Ryabchikova et al. 2015), or values calculated using the computer code of Barklem et al. (1998;see Barklem 2022).If no value was available from these sources, then we adopted the damping constant calculated using the Unsöld approximation (Unsöld 1955;e.g., Gray 2005) enhanced by a factor of two.
Table 2 presents the adopted line data, including wavelength, ion, excitation potential, gf-value and its source, and van der Waals damping constant and its source.Although Table 2 lists the original sources of the gf-values, the adopted values are those determined from the process described above.

Stellar Parameters
We employed ATLAS9 model atmospheres (Kurucz 1970;Castelli & Kurucz 2003;Castelli 2022), with enhanced alpha-element abundances ([α/Fe] = +0.6)and a microturbulent velocity of 2 km s −1 .New models consistent with the Castelli & Kurucz (2003) grid were computed as needed using opacities interpolated between metallicity grid points.A final model matching each star's effective temperature, surface gravity, and iron abundance was used for the abundance analysis.The equivalent widths were analyzed using Kurucz's WIDTH9 (Castelli 2005(Castelli , 2022;;Kurucz 2022) program to calculate the abundance from each line.
To determine the effective temperature of each star, we required that [Fe/H] derived from different Fe I lines was independent of excitation potential.We determined the microturbulence (ξ turb ) by requiring that [Fe/H] was independent of reduced equivalent width, log(W λ /λ).Finally, surface gravity was determined by requiring that Fe I and Fe II lines give the same abundance.The adopted stellar parameters are listed in Table 1.
The internal uncertainties in the stellar parameters can be estimated from the statistical uncertainties of these constraints.The typical uncertainty of the fit of Fe abundance versus excitation potential corresponds to about 25 K in T eff , and the uncertainty of the fit of Fe abundance versus log(W λ /λ) corresponds to about 0.05 km s −1 in ξ turb .Given the large number of Fe lines, the formal uncertainty of the difference between Fe I and Fe II abundances is small, corresponding to less than 0.05 dex in log g.
We also assess the uncertainty in the stellar parameters by comparing to the results of NS10.For the 12 stars in common, the mean difference (and standard deviation) of our values minus theirs is: −75 (27) K in T eff , −0.30 (0.06) dex in log g, −0.17 (0.02) dex in [Fe/H], and −0.27 (0.13) km s −1 in ξ turb .Although there are systematic differences, the scatter in pleasingly small in each case, especially for [Fe/H], and is consistent with the internal uncertainties estimated above.
The difference in log g is largely attributable to our use of the Fe ionization equilibrium, whereas NS10 use parallax, mass, and bolometric correction to calculate log g.We have assumed local thermodynamic equilibrium (LTE) in our analysis, but it is known that departures from LTE (non-LTE or NLTE) lead to the overionization of Fe compared to LTE.As a result, LTE analysis yields a lower abundance from Fe I lines than from Fe II lines and forcing them to agree requires a lower surface gravity (e.g., NS11, Lind et al. 2012;Bensby et al. 2014;Amarsi et al. 2016).Nevertheless, our use of the ionization equilibrium avoids other uncertainties and should improve our internal consistency.Fortunately, Table 3 indicates that adjusting log g by 0.3 would have a relatively small effect on the abundance ratios [X/Fe] and, since all of the stars would be similarly adjusted, the star-to-star effect should be minimal.
Table 3 presents the uncertainty in abundance ratios based on a typical star (G180-24) due to the uncertainty in stellar parameters.Each parameter was changed while holding the others fixed, as if they are independent, and the Fe abundance used for each ratio is based on the same ionization state (neutral or ionized) as the other element, except that Fe II was used for C I and O I. The resulting abundance changes are small.

Non-LTE Effects
Abundances were derived under the assumption of LTE in both the model atmospheres and the line formation.The detailed effect of departures from LTE depends on the stellar parameters, and also on the elemental species and the specific spectral line.Asplund (2005) and Bergemann & Nordlander (2014) provide useful reviews.It is hoped that the NLTE effects of similar elements will cancel out to some extent for abundances with respect to Fe, [X/Fe], but some variations, perhaps quite significant, will surely remain and the LTE abundances should be viewed with caution.Our primary focus is comparing stars with different [α/Fe] but similar in other respects, which should further reduce the impact of NLTE effects.For some elements, we applied NLTE corrections based on published tables, as discussed below.
Carbon and oxygen abundances were determined from highexcitation C I lines (9061-9111 Å) and O I lines (7771-7775 and 8446 Å), which are known to have significant NLTE effects (Asplund 2005;Fabbian et al. 2009;Amarsi et al. 2019).NLTE effects lead to stronger lines, and thus LTE abundances are too high.We estimated NLTE corrections for each line by interpolating in the tables of Amarsi et al. (2019) The NLTE corrections for K I can be quite large and can be especially important for understanding the chemical evolution of potassium (Takeda et al. 2002;Andrievsky et al. 2010;Reggiani et al. 2019).Based on the work of Reggiani et al. (2019), we calculated corrections which ranged from −0.18 to −0.42 and generally increase in magnitude with increasing Fe abundance.
Ba II has an available grid of line-by-line NLTE calculations from Korotin et al. (2015).Interpolating in their grid directly gave NLTE abundances, yielding differences from our LTE abundances ranging from −0.12 to +0.12 and averaging 0.00.
For Ti and Cr NLTE effects are much smaller for ionized lines than for neutral lines (Bergemann & Cescutti 2010;Bergemann 2011;Reggiani et al. 2017;Mallinson et al. 2022), similar to Fe (Bergemann et al. 2012;Lind et al. 2012;Amarsi et al. 2016).Therefore, we restrict our results to lines of Ti II and Cr II, which are expected to give more reliable [Ti/Fe] and [Cr/Fe].

Abundance Results and Comparisons
The abundances relative to Fe are presented in Tables 4 and 5, which include the NLTE corrections for C, O, Na, K, and Ba described above.In Table 4, [α/Fe] represents the mean of [X/Fe] for the four α elements Mg, Si, Ca, and Ti.The typical uncertainties of [X/Fe] based on multiple lines of the same element range from 0.01 (for Ca and Ti) to 0.04 (for C, Co, and Y) and 0.05 (for Zr).Machine-readable versions of Tables 4 and 5 list the uncertainties and number of lines used for each star.
A comparison of abundances to NS10 and NS11 is shown in Table 6, using our LTE abundances for Na and Ba for consistency because Nissen & Schuster (2010) assumed LTE.This table gives the mean difference (our value minus theirs) and the standard deviation for the 7-12 stars in common for each element.We also compared our C and O abundances to Amarsi et al. (2019), using their 1D NLTE results.The mean difference (and standard deviation) is 0.04 (σ = 0.06) for [C/Fe] in nine stars and 0.02 (σ = 0.07) for [O/Fe] in 12 stars.
The majority of elements show excellent agreement and remarkably small scatter, especially given that these comparisons include uncertainties from both studies.
The most glaring exception is Ba, where there is a large systematic difference.The scatter is consistent with the internal uncertainties of either study alone, so the offset is very consistent.Our adopted gf-values for the Ba II 5853.7 and 6141.7 Å lines are 0.07 lower, which explains part of the difference.A comparison to other published results is significantly better.We found four studies with [Ba/Fe] reported for at least four stars in common with ours.Comparing LTE abundances for consistency, the differences (our value -theirs) are 0.00 ± 0.05 for six stars in Fulbright (2000), −0.02 ± 0.05 for five stars in Zhang & Zhao (2005), 0.02 ± 0.03 for nine stars in Ishigaki et al. (2013), and 0.13 ± 0.17 for four stars in Bensby et al. (2014).

Alpha Elements
We first consider whether our sample shows distinct high-α and low-α groups.Figure 1 shows [Mg/Fe] versus [Fe/H] for our data along with that of NS10.NS10 used the solid-black line in Figure 1 to separate their high-α and low-α groups using [Mg/Fe].The two dotted lines are our linear fits to the stars in their two groups.Our stars with [Fe/H] > −1.75 are also well separated, in agreement with the NS10 groups, and we designate them high-α and low-α.We note that the dividing line utilized by Hayes et al. (2018) and Fernández-Alvar et al.
gives the same classification for our stars.We are particularly interested in the five stars with [Fe/H] < −1.75.To follow them more carefully in the comparisons below, we designate the three most metal-poor stars as a low-Fe group and the other two as intermediate-Fe.Table 4 shows the group assignment for each star.   in Section 3, we have systematic differences from NS10 of −0.17 in [Fe/H] and 0.02 in [α/Fe] for the stars in common.Both the high-α and low-α sequences show the clear trend of decreasing [α/Fe] as [Fe/H] increases.We expect the high-α stars to include contributions only from SNII, before SNIa start at the knee ([Fe/H]  −0.5), so the slope is presumably due to the metallicity dependence of the SNII yields or possibly a variation in the IMF.There is no evidence for a knee in the low-α sequence in our metallicity range.The steeper slope is due either to the increasing contribution of SNIa if the knee is at [Fe/H]  −2.0 or to a different IMF if the knee is at [Fe/H]  −1.2.We return to this question in Section 4.7.

Sodium and Potassium
Our results for Na, shown in Figure 5, agree well with the more metal-poor stars of NS10.[Na/Fe] is correlated with    Large scatter is clear among the metal-poor stars in Figure 6 and also in the data of Hayes et al. (2018).It is difficult to assess how much of the scatter is real.We note that the scatter of our stars is significantly smaller, 0.06 compared to 0.16 for Reggiani et al. (2019), so much of the scatter is probably due to observational uncertainties.However, the scatter is noticeably larger among our low-α stars (see Figure 7), so may be real.
The behavior of [K/Fe] for our different α groups is shown in Figure 7.While [K/Fe] is roughly constant as a function of [Fe/H], it appears to be weakly correlated with [α/Fe], consistent with the results of Hayes et al. (2018) and Buder et al. (2022) for more metal-rich stars and with its behavior like an alpha element noted above.This seems to indicate that K production is tied to α-element production, as also suggested, e.g., by Zhang et al. (2006b) and Zhao et al. (2016).
K is produced by explosive oxygen burning in massive stars, but theoretical models of K production are not generally consistent with its observed behavior, as has been noted in many of the papers cited above.SNII models significantly underproduce K, and thus predict [K/Fe] < 0 for metal-poor stars.(e.g., Kobayashi et al. 2006;Heger & Woosley 2010;Prantzos et al. 2018).Zhao et al. (2016) and Reggiani et al. (2019) compare various chemical evolution models and the observational results to illustrate the problem.Samland (1998) achieved reasonable agreement with the data by empirically increasing the yields from Woosley & Weaver (1995) by a factor of 1.7.The yields for rotating stars by Prantzos et al. (2018) show marked improvement, but still fall short.The improved data in our metallicity range will help to constrain improved models.
SNII models also predict that the K production will increase with metallicity because it depends on the supply of neutrons, which in turn depends on the C and O abundances (Kobayashi et al. 2006, NS11).The metallicity dependence is reduced compared to Na, for example, because K is produced in explosive O burning rather than by hydrostatic burning (Samland 1998).Given the large scatter, it is difficult to discern a trend in the observational data, but there is no obvious conflict with the models.

Iron-peak Elements
The results for the iron-peak elements Sc, Cr, Mn, Co, Ni, and Zn are shown in Figure 8. [Cr/Fe] shows no significant trend with [α/Fe], nor does [Mn/Fe] apart from G112-43/44 (discussed below), indicating that the production of these two elements is very similar to Fe.This is somewhat unexpected for Mn if SNIa have contributed to the low-α stars because larger Mn production relative to Fe is predicted in SNIa (Nomoto et al. 2013).
[  2022) for Co. Co was not studied in these earlier papers.Thus, these four elements behave like alpha elements, indicating they are produced preferentially in high-mass stars relative to Fe.If low-α stars are enriched by SNIa, then it is most notable that Ni is apparently not produced in large amounts in SNIa, which disagrees with theoretical predictions (Kobayashi et al. 2006).We note that Kobayashi et al. (2006) found that Sc and Co are significantly underproduced in theoretical models, which will be exacerbated if positive NLTE corrections are applied (Bergemann et al. 2010;Mashonkina & Romanovskaya 2022).The production of Fe-peak elements is discussed further in Section 4.7.
The binary pair G112-43 and G112-44 have significantly enhanced [Zn/Fe], a small enhancement in [Mn/Fe], and very slight enhancements in [Cr/Fe] and [Ni/Fe], as also found by NS10 and NS11.Nissen et al. (2021) studied these stars and discuss the abundance anomalies, also identified in three other lowα stars, and suggest they might be explained by helium shell detonation of SNIa.Our results for [Co/Fe], an element not included by Nissen et al. (2021), show normal abundances in G112-43/44, which matches the prediction from the helium shell detonation model of Lach et al. (2020), and thus lends further support to that explanation.We note that Nissen et al. (2021) found a possible correlation between abundance differences between the two stars and the elemental condensation temperature, which may indicate planet-star interactions.Nissen et al. (2021) also found that the kinematics of this pair show that they belong to the Helmi streams (Helmi et al. 1999;Koppelman et al. 2019).

Neutron-capture Elements
The results for Y, Zr, and Ba are shown in Figure 9. Ignoring the high-Ba outlier, all three elements show a significant correlation with α with similar slope.Figure 10  One of the main questions that we wanted to investigate was whether the high-α and low-α groups remain distinct at lower metallicities, in [α/Fe] or perhaps some other abundance ratio.Our sample includes five stars at lower metallicities, two with [Fe/H] ;−1.8 (intermediate-Fe) and three with [Fe/H] < −2 (low-Fe).
As noted in Section 4.1, two of the low-Fe stars are clearly low-Mg (Figure 1) and all five stars appear to follow the low-α sequence in Figure 2. Given metallicity peaks at −2.1 for lowα and −1.5 for high-α (Fernández-Alvar et al. 2017), we would expect more low-α stars at lower [Fe/H].For other abundances, we have used different symbols for these stars in the figures to see if, given their [α/Fe], they seem to follow the trend of the low-α or high-α stars.Although some abundance ratios for one or more of these stars sometimes falls high or low, in general they are not clearly aligned with either the lowα or high-α group.The larger scatter among the low-α stars makes it even more difficult to make the comparison.
The clearest case is for [Ba/Fe] (see Figure 9(c)), where all five stars have [Ba/Fe] lower than (most of) the high-α stars

SFR or IMF?
Although most authors have interpreted the low [α/Fe] abundances as the result of slower chemical evolution due to a lower SFR, such that SNIa and AGB stars contribute, an IMF deficient in high-mass stars has also been suggested (e.g., Kobayashi et al. 2014;Fernández-Alvar et al. 2018).An IMF deficient in high-mass stars naturally accounts for lower [α/Fe], particularly for Mg and O, but the IMF would have to be metallicity dependent to account for the increasing difference between high-α and low-α stars as [Fe/H] increases, as pointed out by NS11.
Whether the two components differ in age becomes a key question.If the ages are close enough that longer-lived nucleosynthesis sources such as SNIa and AGB stars do not contribute, then differences in IMF would seem to be required.Unfortunately, a difference of only 10 8 -10 9 yr is enough to be important and is extremely difficult to rule out.If there is a significant age difference, then the SFR naturally explains low [α/Fe] and an explanation based on IMF would require some mechanism to prevent enrichment by SNIa and AGB stars.Conflicting results regarding an age difference are summarized in the introduction.Most determinations do find a significant age difference, typically around 2 Gyr, which supports an SFR explanation.
The metallicity of the [α/Fe] knee should provide a simple test.If the cause of low [α/Fe] is the SFR, then the low-α stars will have metallicities above the knee, whereas if it is the IMF, then they will have metallicities below the knee.Since we find low-α stars down to at least [Fe/H] = −1.6, a knee for the lowα population or a subpopulation significantly above that value would seem to require a modified IMF.Although straightforward in principle, it can be difficult to determine the knee because it requires fairly precise abundances for a large enough sample of stars over a significant range of metallicity spanning the knee.In some cases, different selection criteria may identify different subpopulations, which may have different knees.The larger scatter for abundances of low-α stars (e.g., NS11, Amarsi et al. 2019) makes identifying a knee more difficult and may be a result of the mixing of subpopulations.
Using APOGEE data for a sample of low-α giants, Fernández-Alvar et al.The symbols are the same as in Figure 3. Aguado et al. 2021).Interestingly, some results have indicated multiple knees (Matsuno et al. 2019;Monty et al. 2020).The present data combined with that of NS10 do not show a clear change of slope in [α/Fe] over the range −2.0 < [Fe/H] < −0.8 (see Figure 2).However, a sharper decline starting at [Fe/H] ; −1.0, as found by Fernández-Alvar et al. (2018), cannot be ruled out and the slope at the metal-poor end is not well defined.Overall, a knee at or below [Fe/H] = −1.6 is favored, which supports a lower SFR.
Another and very powerful way to distinguish a lower SFR from a different IMF is the detailed abundance pattern.Perhaps the tightest constraint comes from the neutron-capture elements.These elements are produced in multiple sites, including massive stars by the r-process and s-process, and in AGB stars by the s-process.The low-α stars have lower [Ba/Fe], [Y/Fe], and [Zr/Fe], and the stars with [Fe/H] < −1.75 extend that trend for [Ba/Fe].The reason for this is not clear.Weak s-process production in massive stars is difficult to model, but Ba production is apparently higher in lower-mass SNII (Cescutti et al. 2006), so a modified IMF would not explain a lower [Ba/Fe].However, lower α element abundances would likely lower Ba production through a reduced supply of neutrons.A lower SFR would allow enrichment by AGB stars of s-process elements such as Ba, which should raise rather than lower [Ba/Fe] in the low-α stars, so a somewhat larger increase in Fe from SNIa would be necessary to reduce [Ba/Fe].The lower s-process production in metal-poor AGB stars (Busso et al. 1999;Cescutti et al. 2006) may help, and would also explain the slow increase in [Ba/Fe] with [Fe/H] in the low-α NS11 stars.Kobayashi et al. (2020a) suggest that the predicted AGB Ba yields are too large.
Comparing neutron-capture elements, NS11 found that the low-α stars have lower [Y/Ba] and the present work also extends that result to [Zr/Ba].Adding several measurements of additional neutron-capture elements for some of the NS11 stars, Fishlock et al. (2017) find a general pattern that light s-process elements (ls: Y and Zr) are underabundant compared to heavy s-process elements (hs: Ba, La, Ce, and Nd) in low-α stars, along with slightly higher [Eu/Fe], lower [ls/Eu], and slightly lower [hs/Eu].Similar patterns have been found in stars associated with accretion fragments (Aguado et al. 2021;Matsuno et al. 2021Matsuno et al. , 2022aMatsuno et al. , 2022b;;Carrillo et al. 2022).Lower [ls/hs] is naturally explained by the contribution of low-mass (<3M e ) metal-poor AGB stars, whose production strongly favors the hs over ls elements (Busso et al. 1999;Fishlock et al. 2014).Their contribution to the low-α stars would be consistent with a slower chemical enrichment.It would be challenging to reproduce the observed ls and hs abundances from massive stars alone, although the yields are not well determined.
The higher Eu abundances in low-α stars are more difficult to explain because Eu is predominantly produced by the r-process.If formed in massive stars, then its enrichment is reflected by the abundances in the high-α stars.Later enrichment of the low-α stars by SNIa would lower [Eu/Fe] by the addition of Fe, and AGB stars would raise [ls/Eu] and [hs/Eu] by the addition of s-process elements, which are both opposite the observed differences from the high-α stars.To explain the observed differences based on massive star enrichment alone, the sources contributing to the lowα stars must have produced slightly enhanced [Eu/Fe] but lower [Y/Eu] and [Zr/Eu] by a process that is dependent on mass or on the α-element abundances.Perhaps only the relatively rare SNII events that produce large r-process yields (Cowan et al. 2021) were about the same in both populations.An important alternative is a longer-lived site for the r-process.Neutron star mergers have been identified as such a site (Skúladóttir & Salvadori 2020;Cowan et al. 2021), which might naturally explain the observed low-α star abundances via a lower SFR.
The Fe-peak elements do not provide clear evidence.The similar [Mn/Fe] in low-α and high-α stars is at odds with SNIa enrichment, which should increase [Mn/Fe] (Nomoto et al. 2013;Kobayashi et al. 2014), and so has been seen as support for a modified IMF.Lower Mn yields in metal-poor SNIa as found empirically by Cescutti et al. (2008) could fit the observations, but a strong metallicity dependence in Mn yields is not found in theoretical models (Nomoto et al. 2013;Kobayashi et al. 2020b).Compared to LTE results, NLTE Mn abundances from Amarsi et al. (2020) and Eitner et al. (2020) show a much more gradual or perhaps even no increase of [Mn/Fe] for −3 < [Fe/H] < 0, indicating the need for reduced Mn yields from SNIa.Eitner et al. (2020) reproduce no increase in [Mn/Fe] by assuming that about 75% of the SNIa are from white dwarfs below the Chandrasekhar mass (sub-Ch-mass).Whatever the cause of reduced Mn yields, the similarity of [Mn/Fe] in low-α and high-α stars does not provide a strong argument against SNIa enrichment.Nomoto et al. (2013) note that lower-mass SNII produce more Mn, so a modified IMF would help align SNII and SNIa yields.However, the lowermass SNII also produce significantly more Ni (Kobayashi et al. 2006), which is inconsistent with the lower [Ni/Fe] abundances in low-α stars.Enrichment by SNIa also predicts higher [Ni/Fe] in the low-α stars, but the overproduction of Ni by SNIa is a known problem for modeling [Ni/Fe] in the disk, so again the discrepancy does not constitute strong evidence against the contribution of SNIa.Kobayashi et al. (2020b) find lower Ni yields from SNIa and also note that sub-Ch-mass models also produce less Ni, and so can better match the observed [Ni/Fe].The production of Co and Zn is higher in massive star hypernovae, so an IMF with fewer massive stars could explain why these elements are less abundant in the lowα stars.However, both Co and Zn are significantly underproduced by SNII (Nomoto et al. 2013;Kobayashi et al. 2014), so the low-α IMF must still include a significant number of hypernovae or else [Co/Fe] and [Zn/Fe] would be too low.
As a whole, the abundance patterns are most easily accounted for by a lower SFR.While a high-mass deficient IMF can explain lower [α/Fe], it would not naturally account for other correlated abundances, especially among the neutronrich species.Combined with the determinations of an age difference and the location of the [α/Fe] knee, the evidence supports the SFR rather than the IMF to explain low-α stars.In any case, these two alternatives are not mutually exclusive.

Kinematics
A Toomre diagram for our stars is shown in Figure 11.The vast majority of stars are very similar in V, within 65 km s −1 of V = −220 km s −1 , plus two more retrograde high-α stars and two more prograde low-α stars (G112-43 and G112-44, whose points are virtually identical).Table 7 gives the number of stars for each sample, followed by the mean value with its standard error and the dispersion with its standard error for each velocity component, and for U and W combined.(To calculate the statistics shown in Table 7 and discussed below, we have combined the binary pair G112-43 and G112-44.)As expected from the Toomre diagram, the high-α stars have a more retrograde average V, −278 versus −218 km s −1 .We note that the difference, 60 ± 42 km s −1 (combining the uncertainties of the mean in quadrature), is not statistically significant because of the small number of stars.We also note our sample has complicated kinematic biases.It is noteworthy, however, that the more retrograde motion of the high-α stars is contrary to the conclusion of NS10 and other results showing a more prograde high-α population.We see that the high-α population is kinematically diverse.
Table 7 also includes results for the stars from NS10, which have much smaller uncertainties due to their larger sample.An important result is that they find that the high-α stars are prograde on average and the low-α stars are mostly retrograde, which is opposite the result that we find.Their data give a mean difference in V of 49 ± 16 km s −1 .However, their Toomre diagram indicates that the prograde mean for the high-α stars comes primarily from stars with total space velocities close to V tot = 180 km s −1 , which is their adopted dividing line between halo and thick disk stars.For example, if they had adopted 220 km s −1 instead, then 17 of the 40 high-α stars (plus one low-α star) would have been classified as thick disk.(Applying the more elaborate procedure of Bensby et al. (2014) to estimate population memberships gives a similar result.)Table 7 shows the results for their sample restricted to V tot > 220 km s −1 , in which case the mean V velocities are very similar for the high-α and low-α stars.
Even when reclassifying some of the NS10 halo stars as thick disk, the low-α and high-α velocity distributions are still somewhat different.The low-α stars span a wider range in ( ) + U W 2 21 2 , as is clear from their Toomre diagram and from the larger mean and dispersion in Table 7.We note that distinguishing between the high-α halo and the thick disk might not be meaningful if they had a common origin in one or more merger events.They appear to follow a common pattern of chemical abundances, indicating a very similar chemical history, so the distinction (if any) is probably unimportant in that context.
Our high-α stars have smaller U and W velocity dispersions, σ U = 95 km s −1 and σ W = 64 km s −1 versus 219 and 91 km s −1 for the low-α stars.The data from NS10 also show smaller velocity dispersions in U and W for the high-α stars.In addition, Schuster et al. (2012) have computed orbital parameters for their stars, confirming that the high-α stars are confined to smaller Galactic radii and vertical distances from the plane.
These results are consistent with other spatial and kinematic descriptions of these two populations and their proposed origins.The larger dispersions of the low-α stars are expected for an accreted population due to the more random nature of accretion events.The high-α stars, heated from an early disk by mergers, would have a smaller scale height perpendicular to the disk and would be confined to smaller orbits, and thus have a smaller dispersions in U and W in the solar neighborhood.The Astronomical Journal, 167:6 (17pp), 2024 January

Conclusion
We have measured the chemical abundances and kinematics of 20 local halo stars to gain insight into the dual halo populations of high-α and low-α stars.Abundances have been measured for the α elements Mg, Si, Ca, and Ti, plus C, O, Na, K, Sc, Cr, Mn, Co, Ni, Zn, Y, Zr, and Ba.Most element abundances are measured with uncertainties of 0.02-0.03.Most of the stars were identified as high-α or low-α to investigate differences in different elemental abundances.The five most metal-poor stars, [Fe/H] < −1.75, were followed separately to see if their abundance patterns trended with the high-α or lowα stars.
Most element ratios [X/Fe] are correlated with [α/Fe], indicating that these elements have production histories similar to the α elements.Notable exceptions are [Cr/Fe] and [Mn/Fe], which are approximately constant.Our results generally confirm earlier results by NS10, NS11, Amarsi et al. (2019), andFishlock et al. (2017) among others, but extend to more metal-poor stars.Unlike earlier work, we do not find a clear separation of high-α and low-α stars in [Y/Ba], probably due to the lower metallicity range of our stars where the two [α/Fe] sequences substantially overlap.The abundance scatter is typically larger among the low-α stars, as also found in previous studies (e.g., NS11; Fernandez-Alvar et al. 2018;Amarsi et al. 2019).
Co and K are added to the list of elements compared in high-α and low-α stars by NS10 and NS11.Although the low-α stars show larger scatter, [K/Fe] is also correlated with [α/Fe], confirming that K production is tied to the formation of α elements.The new data for [K/Fe], which include NLTE corrections and have relatively small uncertainties, help to clarify its behavior for −2.2 < [Fe/H < −1.2, a range that has been less well studied and sometimes with conflicting results.Our results indicate that [K/Fe] ;0.25 and, in contrast to [Na/Fe], is approximately constant with [Fe/H].As noted by other authors, the high [K/Fe] is inconsistent with SNII models.The lack of metallicity dependence is now better established and provides a useful constraint that improved models must satisfy.
Special attention was given to five stars with [Fe/H] < −1.75, more metal-poor than the sample of NS10, to investigate whether or not the high-α and low-α populations remain distinct at lower metallicities where the two sequences are converging.Two of the most metal-poor stars are noticeably low-Mg and all five appear to follow the low-α sequence with decreasing [Fe/H].Other abundance ratios do not clearly identify the more metal-poor stars with either the high-α or low-α groups, with the exception of [Ba/Fe].The metal-poor stars all have lower [Ba/Fe], similar to the low-α stars.
We confirm the NS11 result of high [Ba/Fe] in one low-α star, G53-41, and lower [Ba/Fe] in the high-α star G180-24.It would be particularly interesting to measure Ba and other s-process elements in these and additional similar stars.We also confirm significantly enhanced [Zn/Fe] in the binary pair G112-43 and G112-44 (Nissen et al. 2021), and find they have normal [Co/Fe].
There is ample evidence that the low-α stars were accreted in merger events early in the Galaxy's history, and that the merging fragments experienced a different chemical evolution than the Milky Way.Most authors have explained the low-α abundances as the result of a lower SFR in the fragments because the time delay in reaching a given [Fe/H] allowed enrichment by low-mass AGB stars in addition to SNIa, but an IMF deficient in high-mass stars has also been proposed.We discuss the evidence for these two alternatives.
The increasing separation of the high-α and low-α sequences with [Fe/H], and the measured age differences between high-α and low-α stars generally favor a different SFR for the two populations.The location of a [α/Fe] knee caused by the introduction of SNIa should mark the beginning of abundance changes due to a lower SFR, so could distinguish between SFR and IMF effects.Determinations of the knee in various low-α samples have not agreed, with some too metal-rich ([Fe/H]  −1.3) to explain the low-α stars, but most are comfortably metal-poor ([Fe/H]  −1.6).In addition to different sample selections, some of the differences may reflect real differences between subpopulations.The present work extending the NS10 sample to lower [Fe/H] strengthens somewhat the trend consistent with no knee down to [Fe/H] ∼ −2 for local halo stars.
The abundance patterns support a lower SFR for the low-α stars.The ratios of light and heavy s-process elements in the low-α stars, including present new results for Zr and for Ba and Y in lower-metallicity stars, are consistent with the production of these elements in low-mass metal-poor AGB stars.Differences in abundances of the r-process element Eu are difficult to understand by either the SFR or IMF if only SNII are responsible.Neutron star mergers have been identified as an r-process site and their longer timescale for evolution would be consistent with a time delay.Based on the predicted yields, the [Mn/Fe] abundances are not easily explained if SNIa contributed to the low-α stars, but lower yields are indicated by the behavior of [Mn/Fe] over all metallicities.Ni is also overproduced in SNIa models.Observed [Co/Fe] and [Zn/Fe] require production by hypernovae for both high-α and low-α stars.
We find that there is not a strong difference in the average V velocities of our high-α and low-α stars, with the high-α slightly more retrograde, in contrast to NS10, who found the low-α stars were more retrograde.The net rotation depends strongly on the cutoff in total space velocity used to define a halo sample.The two populations show nearly the same net rotation if one adopts V tot > 220 km s −1 instead of 180 km s −1 for the NS10 sample.Like NS10, we find the low-α stars have larger dispersions in U and W velocities, and a larger mean ( ) + U W 2 21 2 , as expected for an accreted population.
The final NLTE corrections, which are added to the LTE abundances, ranged from −0.05 to −0.11 for [C/H] and from −0.05 to −0.20 for [O/H].Lind et al. (2022) provided detailed results for Na I, which yield net NLTE corrections for our stars ranging from −0.04 to −0.23.
Following NS10 and Fernández-Alvar et al. (2018), Figure 1 focuses on separating stars based on [Mg/Fe].The two sequences are well separated, plus Mg has a simpler chemical history, forming almost exclusively in SNII, whereas the α Figure 2(b) includes adjustments to the present data of +0.17 in [Fe/H] and −0.02 in [α/Fe] to align with the NS10 data.The agreement is excellent, with a scatter of less than 0.03 for the high-α and low-α groups compared to their respective lines fit to the NS10 data.Turning to the intermediate-Fe and low-Fe stars, we wish to know which sequence, if either, they follow.In Figure 1, two of the low-Fe stars have markedly lower [Mg/Fe], although [α/Fe] is higher in Figure 2. The same two stars have below average [O/Fe], which could be a signature of less contribution from the highest-mass stars, where the Mg and O production is concentrated.In Figure 2(b), all five intermediate-Fe and low-Fe stars appear to follow the low-α sequence.They show a mean offset of 0.00 from the low-α line and −0.04 from the high-α line, and their scatter around the low-α line is 0.02, the same as that of our low-α stars.Nevertheless, the separation of the two sequences narrows considerably, reaching 0.07 at [Fe/H] = −1.65 (near the two intermediate-Fe stars) and only 0.03 at [Fe/H] = −2.It would be useful to have high-precision abundances of additional stars in this metallicity range.

Figure 1 .
Figure 1.[Mg/Fe] vs. [Fe/H].Triangles represent high-α (black upward) and low-α (blue downward) stars from Nissen & Schuster (2010).The solid-black line is their division between the two groups, extended to lower metallicity.The dashed lines are our linear fits to the stars in their two groups.Red circles represent the present data.The error bars represent typical uncertainties of the present data.

Figure 2 .
Figure 2. [α/Fe] vs. [Fe/H].Triangles represent high-α (black upward) and low-α (blue downward) stars from Nissen & Schuster (2010).The solid-black line is their division between the two groups, extended to lower metallicity.The dashed lines are our linear fits to the stars in their two groups.Red circles represent the present data (a) as determined and (b) adjusted by +0.17 in [Fe/H] and −0.02 in [α/Fe], the offsets from the Nissen & Schuster (2010) data determined from stars in common.The error bars represent typical uncertainties of the present data.
[α/Fe], clearly indicating that Na is primarily produced in massive stars, as discussed by NS11.Potassium has been less well studied, in large part because only two K I lines are usually accessible, 7664.9 and 7699.0Å, which fall near strong telluric lines.Strong NLTE effects further complicate obtaining accurate abundances.The evidence to date is that K behaves much like an alpha element.For disk stars, [K/Fe] increases with decreasing [Fe/H] until [Fe/H] ∼ −1(Chen et al. 2000;Shimansky et al. 2003;Zhang et al. 2006b;Hawkins et al. 2016;Zhao et al. 2016; Takeda 2020).For more metal-poor stars [K/Fe] levels off to a roughly constant value, although the abundances typically show a large scatter and there are conflicting claims that [K/Fe] may increase or decrease with decreasing [Fe/H],(Takeda et al. 2002;Cayrel et al. 2004;Zhang & Zhao 2005;Takeda et al. 2009;Andrievsky et al. 2010;Carretta et al. 2013;Roederer et al. 2014;Zhao et al. 2016;Hayes et al. 2018;Buder et al. 2022).Somewhat surprisingly, the metallicity range covered by the present sample, −2.2 < [Fe/H] < −1.2, is the least well studied.
Figure 6 shows [K/Fe] versus [Fe/H] for the full range of metallicity including data from Zhao et al. (2016) and Reggiani et al. (2019), along with the present results.Although the Reggiani et al. (2019) data alone indicate [K/Fe] may decrease with increasing [Fe/H] for [Fe/H] < −1, adding the present data and that of Zhao et al. (2016) indicates that [K/Fe] is approximately constant.The details depend somewhat on the NLTE corrections, which are metallicity dependent.Reggiani et al. (2019) reanalyzed

Figure 3 .
Figure 3. [C/Fe] and [O/Fe] vs. [α/Fe].Upward blue triangles correspond to high-α (Hα) stars, downward red triangles to low-α (Lα) stars, open circles to the intermediate-Fe (IFe) stars, and filled circles to the low-Fe (LFe) stars.The error bars represent typical uncertainties of the present data.
Sc/Fe], [Co/Fe], [Ni/Fe], and [Zn/Fe] show slight increases with increasing [α/Fe], in agreement with NS10 and NS11 for Ni and Zn, with Nissen et al. (2000) and Fishlock et al. (2017) for Sc, and with Buder et al. ( shows [Y/Ba] and [Zr/Ba].Again ignoring the high-Ba outlier, we see a noticeable difference in [Zr/Ba] between low-α and high-α stars, but not a significant difference in [Y/Ba].NS11 did find a difference in [Y/Ba], although their data show almost complete merging of low-α and high-α stars for [Fe/H] < −1.2, very similar to our result.Fishlock et al. (2017) measured Zr and other neutron-capture elements to supplement Y and Ba in a subset of the NS11 stars.Their four stars with −1.45 < [Fe/H] < −1.2 similarly show a small difference in [Y/Ba] and a larger difference for [Zr/Ba].Matsuno et al. (2021) find a somewhat larger difference in [Y/Ba] between low-α and high-α halo giants with −1.55 < [Fe/H] < −0.6.One low-α star, G53-41, has an enhanced [Ba/Fe], as also found by NS11 and Ishigaki et al. (2013).G53-41 also has high [Na/Fe] and [N/Fe] and low [C/Fe] and [O/Fe], indicating it may have been formed as a second generation star in a globular cluster (Ramírez et al. 2012; Nissen et al. 2014; Amarsi et al. 2019; Nissen et al. 2021; Spite et al. 2022).G180-24 appears unusual as a high-α star with relatively low [Ba/Fe], although it is not peculiar in any other element.The NS11 data show this and several other high-α stars with unusually low [Ba/Fe] (including G125-13, which we reclassify as low-α).The five stars in our intermediate-Fe and low-Fe groups all have lower [Ba/Fe], similar to the low-α stars (aside from G53-41).4.6.Stars With [Fe/H] < −1.75
(2018) find that the knee occurs near [Fe/H] = −1.0.Unfortunately, the number of low-α stars quickly declines for [Fe/H]  −0.8 (e.g., NS10 have only one), making the determination more difficult.Mackereth et al. (2019) also used APOGEE abundances and find a knee at [Fe/H] = −1.3 for high eccentricity halo stars.Other studies find a knee in the range −2.5  [Fe/H]  −1.6 for stars kinematically associated with accretion events (Reggiani et al. 2017; Vincenzo et al. 2019;

Figure 11 .
Figure 11.Toomre diagram for the present sample.The symbols are the same as in Figure 3.The vertical dashed line represents V = −220 km s −1 .The dotted line represents a total space velocity of 220 km s −1 .
and Reggiani et al. (2017)find that the sequences become indistinguishable at lower [Fe/H], whereas Fernández-Alvar et al. (2018) find a clear separation even down to [Fe/H] = -2.2.It would be useful to test further whether the sequences remain separate in [α/Fe], due to either enrichment by longer-lived stars or a different IMF, but even if not, whether they remain distinct in some other abundances.

Table 3
Abundance Uncertainties due to Model Atmosphere Parameters elements Si, Ca, and Ti also have significant production in SNIa.Alternatively, Figure2(a) shows [α/Fe] versus [Fe/H], where [α/Fe] is the average of [Mg/Fe], [Si/Fe], [Ca/Fe], and [Ti/Fe].The separation of the high-α and low-α groups is even more clear, despite the smaller separation of the two sequences because the star-to-star scatter is significantly smaller.As noted

Table 4
Abundances of Alpha and Odd-Z Light Elements Table4is published in its entirety in the electronic edition of the Astrophysical Journal.A portion is shown here for guidance regarding its form and content.