ABUNDANCES IN THE LOCAL REGION. I. G AND K GIANTS

The line list used here is the one Luck (2014) used in a study of class I and II stars of types F, G, and K. It was created by merging the Cepheid line list of Kovtyukh & Andrievsky (1999) with the G/K giant line list of Luck & Heiter (2006). It was supplemented by lines from the unblended solar line lists of Rutten & van der Zalm (1984a, 1984b) and lines selected from numerous solar abundance analyses. The final line list has 2943 entries. Solar gf values were derived from equivalent widths measured by direct integration from the Delbouille et al. (1973) solar intensity atlas.

To determine gf values from the solar line measures, the solar abundances of Scott et al. (2015a, 2015b) and Grevesse et al. (2015) were adopted. van der Waals damping coefficients were taken from Barklem et al. (2000) and Barklem & Aspelund-Johanson (2005) or computed using the van der Waals approximation (Unsöld 1938). Hyperfine data for Mn, Co, and Cu were taken from Kurucz (1992). The solar atmosphere was from the MARCS model code (Gustafsson et al. 2008), which uses plane-parallel geometry with effective temperature 5777 K and log g = 4.44, and was used with a microturbulent velocity of 0.8 km s⁻¹ for gf determinations.

While the line list works well for solar-type dwarfs, it is more tailored to work with stars with temperatures in the FGK range. The inclusion of unblended solar lines is predicated upon the idea that an unblended solar line has a better than average chance of being unblended in a G/K giant. The line measurement process and the filtering process applied during abundance/parameter determination pares the initial list by eliminating obvious blends.

Abundances for all program stars were calculated using spherical MARCS model atmospheres (Gustafsson et al. 2008) for gravities below log g = 3.5 and plane-parallel models above that limit. Models were interpolated to the desired parameters using an interpolation code developed by R. Earle Luck. The code was tested by interpolating grid models and in all cases tested the interpolations matched the grid models in temperature to within 5 K and the remaining variables to within 1%–2%. The line calculations were made using the LINES and MOOG codes (Sneden 1973) as maintained by R. Earle Luck since 1975.

Effective temperatures for the program stars were determined using the photometric calibration of Ramírez & Meléndez (2005). This choice was predicated on the desire to use all photometry extant for these mostly bright stars. The photometry was obtained from the General Catalog of Photometric Data (Mermilliod et al. 1997), 2MASS photometry (Cutri et al. 2003) from SIMBAD, and Tycho photometry from the Tycho-2 catalog (Hog et al. 2000). Line of sight extinctions were determined using the code of Hakkila et al. (1997) and adopting distances computed from the Hipparcos parallaxes (van Leeuwen 2007). The extinctions are principally determined from (l, b, d) versus A_V relations. However, the extinction within 75 pc of Sun (the "Local Bubble") is essentially nil (e.g., Vergely et al. 1998; Leroy 1999; Sfeir et al. 1999; Breitschwerdt et al. 2000; Lallement et al. 2003). To correct for this, the extinctions (and reddenings) of all stars within 75 pc were set to 0. For the remaining stars, the extinction out to 75 pc was subtracted from the total extinction. The parallaxes, and hence the distances, to these giants are well determined. Of the 1087 stars with Hipparcos data, 1080 have parallaxes greater than the expected uncertainty. The median uncertainty in the parallax of these 1080 stars is 4%. It follows that the absolute V magnitudes are good to the ±0.1 mag level.

From 14 open clusters in this study, 57 stars are identified in Table 1 in the column labelled Cluster. For the two northern clusters, Mellote 25 (the Hyades) and Mellote 111 (the Coma Berenices cluster), included stars have measured parallaxes. Parallax data is often unavailable for the stars in the southern clusters. If no parallax data is available for an individual star, the cluster distance given by Kharchenko et al. (2005) was adopted. These stars are easily identified in Table 1 by having a cluster identifier but no parallax data—see for example NGC 6705 MMU 1423.

All available colors were utilized for the temperature determination. The [Fe/H] values used in the Ramírez & Meléndez (2005) calibration were taken from LH07, the PASTEL database (Soubrian et al. 2010), or assumed to be solar. The individual effective temperature values were examined if the standard deviation of the mean exceeded 100 K. Colors involving 2MASS magnitudes were examined more closely for the brightest stars due to possible saturation effects in the photometry. If there was an obvious outlier, it was eliminated from the final average. Examination of the derived temperatures revealed that if there was an outlier, it most often was V − J, where J is the 2MASS J magnitude; thus, it was decided that the better approach would be to eliminate that color in the effective temperature determination. Table 2 shows the $E(B-V)$ for each star, the adopted photometric temperature, its standard deviation, and the number of colors utilized. These temperatures are, on the whole, well determined: the mean standard deviation of the temperature for the stars below 6000 K is 54 K and the median is 41 K. The mean and median number of temperatures utilized is 10. However, there are cases that are not so well defined. The worst case is the K5 III star HR 3803 (N Vel), which has a standard deviation for the 10 colors of nearly 600 K. While the star is not especially variable according to the General Catalog of Variable Stars, it is possible that the photometry does exhibit some anomalous behavior, making temperature determinations difficult. The mean temperature for this star and the other nine stars with standard deviation in excess of 200 K are consistent with their spectral types; thus they remain in the data set, but caution that their parameters and abundances are not on the same level of reliability as the others.

Table 2.  Reddening, Temperature, Mass, and Age for the Program Stars

							Mass in Solar Masses				Age in Gyr
Primary ID	S	$E(B-V)$	Teff	σ	N	log(L/L⊙)	B	D	Y	$\langle \mathrm{Mass}\rangle$	B	D	Y	$\langle \mathrm{Age}\rangle$
* 1 Aqr	S	0.000	4715	15	10	1.72	1.71	1.29	1.91	1.64	2.52	6.35	1.73	3.53
* 1 Aur	S	0.029	4043	30	8	2.75	1.31	1.23	1.94	1.49	3.91	6.25	1.62	3.93
* 1 Peg	S	0.000	4620	67	13	1.82	1.50	1.71	2.11	1.77	3.81	1.92	1.20	2.31
* 1 Psc	S	0.002	7728	89	7	1.50	1.94	1.93	2.00	1.96	⋯	1.05	1.07	1.06
* 1 Ser	S	0.002	4627	69	12	1.79	1.65	1.78	1.95	1.79	2.69	1.75	1.83	2.09
* 2 Aur	E	0.040	4153	50	11	2.92	3.74	1.97	⋯	2.86	0.26	3.34	⋯	1.80
* 2 Boo	S	0.002	4836	84	10	1.83	1.55	1.86	2.25	1.89	2.46	1.70	0.90	1.69
* 2 Dra	S	0.000	4802	45	10	1.70	1.06	1.08	1.89	1.34	6.18	6.25	1.50	4.64
* 2 Lib	S	0.003	4874	40	8	1.58	⋯	1.31	1.89	1.60	⋯	4.81	1.50	3.16
* 2 Psc	S	0.001	4831	119	12	1.80	1.57	1.31	⋯	1.44	2.68	3.25	⋯	2.96

Notes. $E(B-V)$: Computed using the reddening maps of Hakkila et al. (1997), the parallax distance, and a correction for the lack of reddening within 75 pc.T_eff: Adopted effective temperature derived using the calibration of Ramírez & Meléndez (2005).σ: Standard deviation of the mean effective temperature.N: Number of colors used to determine the effective temperature.Log(L/L_⊙): Logarithm of the luminosity in solar units. Derived from the distance, apparent V magnitude, and the bolometric corrections of Bessell et al. (1998).Mass: B = Mass determined from the Bertelli et al. (1994) isochrones.D = Mass determined from the Dotter et al. (2008) isochrones.Y = Mass determined from the Demarque et al. (2004) isochrones. $\langle \mathrm{Mass}\rangle$: Mean value of the mass determinations.Age: B = Age determined from the Bertelli et al. (1994) isochrones.D = Age determined from the Dotter et al. (2008) isochrones.Y = Age determined from the Demarque et al. (2004) isochrones. $\langle \mathrm{Age}\rangle$: Mean value of the age determinations.

Only a portion of this table is shown here to demonstrate its form and content. Machine-readable and Virtual Observatory (VOT) versions of the full table are available.

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Once the photometric temperatures are obtained, the surface acceleration due to gravity (e.g., the gravity) is needed. The gravity can be found using the absolute magnitude (M_V) or luminosity, effective temperature, and the mass. To derive the mass, isochrones were utilized in the same fashion as in Allende Prieto & Lambert (1999) and LH07. Isochrones were taken from Bertelli et al. (1994), Demarque et al. (2004), and Dotter et al. (2008), and used in conjunction with the photometric effective temperature, the absolute magnitude, and their expected uncertainties to obtain the mass, age, and luminosity for each star. Isochrone fitting is also dependent on the metallicity of the star in question. If the star is in LH07 or in the PASTEL database (Soubrian et al. 2010), the metallicity given there was used, otherwise a solar metallicity was assumed. This is warranted because more than 90% of the sample has a metallicity within a factor of two of the Sun. The mass and age value from each isochrone set is given in Table 2. The luminosity given in Table 2 is derived from the distance, apparent V magnitude, and the bolometric corrections of Bessell et al. (1998). These luminosities agree to within 0.02 dex of those derived from the isochrone fit.

The sensitivity of the mass and age on the adopted effective temperature and metallicity is well illustrated by π For (see Table 2), which is present in both the Sandiford and HARPS data sets. The temperatures used in the two cases are different by 4 K and the isochrone input metallicity was −0.5 in one case and −0.6 in the other. The Bertelli et al. isochrone results were 1.40 and 1.49 solar masses, respectively. For the ages, the results were 2.5 and 3.2 Gyr. The difference is due to the assumed metallicity. The fit process has to select an isochrone set based on the metallicity, and in this case different metallicity isochrones were used—the first was a −0.4 dex set, whereas the latter was −0.7. What is apparent is that the masses are better determined than the ages.

Inter-comparison of the mass and age data between the isochrone sets in Table 2 reveals no obvious systematic trends, but in some cases there are significant differences in mass and age estimates between isochrone sets. For example, the mass estimates for 13 Lyn vary from 1.05 to 2.20 solar masses. In other cases, such as δ Eri, the total range is only 0.07 solar masses. The average range in the mass estimate is about 30% of the mean value. The mean mass and age from the Bertelli et al. isochrones are 1.88 solar masses and 2.25 Gyr, 1.65 solar masses and 3.25 Gyr from Dotter et al., and 1.83 solar masses and 2.28 Gyr from Demarque et al. It appears that the Dotter et al. masses are marginally lower, but the uncertainty in the estimates makes it impossible to favor one estimate over another. Therefore, the masses and ages have been averaged to form the adopted mass and age. The mean adopted mass is 1.83 solar masses and the mean adopted age is 2.6 Gyr.

The analysis preferentially assumes the photometric temperature, and starts with the gravity determined from the mass determination. This parameter group is the mass-derived gravity set. In Figure 1 (top panel), the mass-derived gravity is plotted against the effective temperature; the distribution is much as expected. Although all these stars are nominally of luminosity class III, it appears that a few are dwarfs. The stars without parallax data (but having photometry)—denoted in the panel as assumed mass or gravity—sometimes fall as hoped in the bulk of the distribution, however other times they do not. A further culling of the sample will be discussed in Section 4.1.

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The next analysis parameter needed is the microturbulent velocity, which is found by demanding that the iron abundance as determined from Fe i lines show no dependence on equivalent width. Initial examination of Fe i data is often accompanied by an editing of the abundance data through an interactive line-editing process. However, in this case individual examination of each star is too time consuming. For Fe i, we assume there is no dependence of abundance on the excitation potential, and determine the best-fitting microturbulent velocity. The individual Fe i line abundances are then binned, and a Gaussian is fit to the Fe i histogram. Using a fit to the histogram deemphasizes the outliers and thus gives a better representation of the actual mean and dispersion. A symmetric 2σ clip is performed and the process repeated, except that in the second iteration a 2.5σ clip is done so that only real outliers will be eliminated. All stars are treated in this way, and the final clip line list is generated by tallying which lines are eliminated most often. The criterion for line elimination is that if a line is cut in 20% or more of the stars, it is eliminated in all stars by the final clip process. The number of Fe i lines prior to clipping is of order 700; after clipping it is about 500. Fe ii has an insufficient numbers of lines to pursue such a statistical process. Thus, for Fe ii, if there are more than 50 lines then the highest 10 and the lowest 3 are eliminated; at more than 20 lines the cuts are seven high and two low. After the Fe ii cuts are accumulated, the overall cut list is assembled in the same fashion as for Fe i. The number of Fe ii lines is typically 40–60 before trimming and 30–50 afterward. After arriving at the final Fe i and Fe ii data for each star, the microturbulent velocity was tweaked to a final value.

The Fe i data provide excitation information that can be interpreted in terms of the effective temperature. After final line trimming and setting of the microturbulent velocity, the Fe i line data shows a mean ${\rm{\Delta }}{\rm{\Theta }}$ (${\rm{\Theta }}$ = 5040/T and ${\rm{\Delta }}{\rm{\Theta }}$ is the slope of the abundance versus excitation potential relation) of about −0.01, with an uncertainty of about the same value. At 4800 K, this translates into an increased effective temperature of about 50 K to achieve excitation balance. If one limits the effective temperature range to 4000–5500 K—the regime where the excitation analysis has highest sensitivity and accuracy—the mean temperature increase needed falls to about 25 K. These changes are well within the uncertainties of the changes, as well as the accuracy of the photometric effective temperatures; thus, to within the uncertainties, the excitation data is consistent with the photometric effective temperatures. A caveat here is that the editing of the Fe I lines assumes that there are no intrinsic temperature trends within the data. Inspection of the deleted Fe i lines finds no preference for them to be of any particular excitation energy or equivalent width.

In examining the Fe i and Fe ii data, an imbalance in the total iron abundance is found in the general sense that the mass-derived gravity is too high (i.e., the Fe ii derived total iron abundance exceeds the Fe i value; see Figure 1—middle panel). To rectify this a new gravity was determined using an ionization balance, which involves forcing the neutral and ionized species of iron to give the same total abundance using the gravity as the free parameter. This was done by interpolating a small grid of models and then determining the best-fit gravity and microturbulence together. Parameter confirmation was done by interpolating a new model at the proper parameters. The iron data relations were recomputed to confirm the ionization balance, along with the lack of dependence of iron abundance on line strength.

These stars exhibit a range of metallicities and this is taken into account as the analysis proceeds. Below [Fe/H] of −0.3, models with [M/H = −0.5 are used, from [Fe/H] of −0.3 to +0.15 solar metallicity models are employed, and above [Fe/H] = +0.15 models with [M/H] = +0.25 are used. The preferred models are 2 M_⊙, α enhancement proportional to [Fe/H], moderate CN processing (i.e., carbon diluted to [C/Fe] = −0.13, nitrogen enhanced to [N/Fe] = +0.31 with ¹²C/¹³C = 20), and 2 km s⁻¹ Doppler velocity. There is little effect on the abundances due to a change from 2 to 1 M_⊙, or from a change of 2–5 km s⁻¹, so if a preferred model is not available, a change in grid is made.

Table 3 includes parameters, iron abundance details, an average macroturbulent/rotational velocity, and lithium, carbon, and oxygen data. Information for both mass and ionization-balance derived gravities is presented. There are a few stars that lack parallax and/or photometric data. For these stars, identifiable in Table 3 by the lack of a mass-derived analysis, a traditional excitation and ionization-balance analysis was performed. Average abundances for 25 elements with Z > 10 are in Table 4. The averages have been computed in the same manner as for Fe ii, except no master kill list was generated for species other than iron. If the neutral and first ionized species are both available for an element, the final average is merely the average of all retained lines. Note that the Mn, Co, and Cu abundances have been computed allowing for hyperfine structure. Details of the abundances (per species average, σ, and number of lines) are available upon request.

For lithium, carbon, nitrogen, and oxygen, spectrum syntheses for the features of interest have been performed using laboratory oscillator strengths where available. For the lithium feature, all components of ⁷Li (using the data presented by Andersen et al. 1984) in the 670.7 nm hyperfine doublet were used to match the observed profiles. There is no evidence in the observed spectra for the presence of ⁶Li, and therefore it was not considered in the syntheses. Lithium LTE abundance data are presented in Table 3, including the synthesized equivalent width of the Li blend. Also included are non-LTE lithium abundance corrections from the data of Lind et al. (2009).

Carbon abundances have been derived from C i lines at 505.2 nm and 538.0 nm, and the C₂ Swan system lines at 513.5 nm. For the atomic lines, the oscillator strengths of Biémont et al. (1993) or Hibbert et al. (1993) were adopted. These oscillator strengths have been used in determinations of the solar carbon abundance (Asplund et al. 2005). For the Swan C₂ syntheses, f (0, 0) = 0.0303 (Grevesse et al. 1991) was adopted with the relative band f values of Danylewych & Nicholls (1974), along with D₀ = 6.210 eV (Grevesse et al. 1991) and theoretical line wavelengths (as needed) from C. Amiot (1982, private communication). To form the carbon abundance on a per spectrum basis, the individual features are combined as follows: for T_eff < 4800 K: C₂ 513.5 only. At T > 4800 K and less than 5500 K, C i 505.2 and 538.0 have weight 1 and C₂ 513.5 has weight 3. For T > 5500 K, the two C i lines have equal weight and C₂ is not used. The weights are based on relative strength and blending. Typical spreads in abundance for the features are 0.15 dex. For the purpose of abundances with respect to solar values, we adopt log _C = 8.43, which is the Asplund et al. (2009) recommended solar carbon abundance. Table 3 has the average C and O data on a per star basis.

Oxygen abundance indicators in the available spectral range are rather limited: the O i triplet at 615.6 nm and the [O i] lines at 630.0 and 636.3 nm. The O i 615.6 nm lines are problematic in abundance analyses with only the 615.8 nm line being retained in solar oxygen analyses (Asplund et al. 2004). The O i lines were synthesized using the NIST atomic parameters (Kramida et al. 2013) that were also used by Asplund et al. (2009). For the forbidden oxygen lines, only 630.0 nm is usable because 636.3 nm is weak, heavily blended, and complicated by the presence of the Ca i autoionization feature. In the syntheses of 630.0 nm, the line data presented by Allende Prieto et al. (2001) was used, except that the experimental oscillator strength for the blending Ni i line (Johansson et al. 2003) was adopted. The syntheses assumed [Ni/Fe] = 0. In G and K giants, the [O i] 630.0 nm equivalent width typically runs from 3 to 8 nm, and the Ni i intrusion about 0.5 nm. An uncertainty of 20% in the Ni I strength is therefore not a major concern. To form a final oxygen abundance, the data was average in the following manner: for T_eff < 5500 K,only [O i] is used, whereas for T_eff > 5500 K, O i has weight 1 and [O i] has weight 3. At an effective temperature of 6225 K, [O i] is essentially undetectable and the abundance depends only on O i 615.8 nm. For T_eff < 5500 K, the C–O dependence has been explicitly taken into account.

3.4.1. Internal Comparison

This study affords two types of internal comparisons: there are 19 stars with two analyses, and for each star/spectra there is the mass-derived gravity abundance determination and the ionization-balance gravity analysis. The 19 stars with two analyses shall be dealt with first.

Comparing the effective temperature data for the 19 stars, a mean difference of 4 K with a total range of 39 to −20 K is found. There can be a difference because the determinations were made for each data source separately, without reference any previous determination, and thus different colors can be eliminated in each determination. Note that a difference of 40 K in this temperature range is less than 1% in the temperature. The mass-derived gravities show a mean difference of 0 with a total range of −0.08 to +0.05 dex. The abundance data associated with the mass-derived gravity is very consistent: the mean differences for iron (Fe i), carbon, and oxygen are −0.01, −0.01, and −0.02, respectively. The standard deviation about the mean is of order 0.1 for three species. For the ionization-balance gravities, the mean difference in log g is 0.08 dex (σ = 0.12). The mean difference for the iron, carbon, and oxygen abundance between the two analyses is about 0.02 dex for each species, with the standard deviation once again being of order 0.1 dex.

As noted, the total data set shows a systematic difference in the gravities derived from the mass and from the ionization balance. The iron abundance difference (Fe i−Fe ii) in the mass-derived gravity analysis is dependent on the temperature: at 5000 K the difference is of order 0.2 dex increasing to about 0.5 dex at 4000 K—see Figure 1 (middle panel). In comparing the mass-derived and ionization-balance gravities, this difference manifests itself as progressively larger differences between the two as a function of effective temperature (bottom panel of Figure 1). Bruntt et al. (2011) noted this type of variation in Kepler field red giants using astroseismology-determined parameters. The effect is also present in the data of LH07. The dependence of the gravity difference on the effective temperature could indicate a failure in the model atmospheres. However, a brief sanity check using ATLAS9 models (Kurucz 1992) yields the same results to within 0.1 dex in log g and 0.05 dex in total iron abundance. The mass difference implied by the change in gravity is certainly non-physical. A 0.2 dex lower gravity at constant temperature and luminosity yields a 40% lower mass, whereas lowering the gravity by 0.6 dex implies a 75% lower mass. The average mass then would decrease to 0.5–1.0 solar masses depending on the temperature, which is not an especially appealing result.

Smoothed (x I–x II) data is presented for Ti, V, Cr, and Fe in Figure 2 (top panel). The immediate conclusion drawn from this figure is that all of these species suffer from the same problem. Whatever is affecting iron also affects the ionized data of other species, and yields the same problem relative to the neutral species: the total abundance inferred from the first ionized species is too large. The ionization balance performed using Fe i and Fe ii rectifies most of the problems, with the difference between the Ti, V, and Cr neutral and ionized total abundances declining; but, more important, the dependence on effective temperature is ameliorated (see bottom panel of Figure 2).

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A possible reason behind this problem is that the ionized lines, and specifically the Fe ii lines, are affected by progressively stronger blending with decreasing temperature. While possible, this would demand that that all Fe ii lines be similarity affected. A weak check is available on this possibility: metal-poor giants should not show the effects of line blending to the extent that solar or above-solar abundance giants do. This is not true if the features in the Fe ii blend are nearly coincident in wavelength. The situation envisioned here is that lines within 0.015 nm of an Fe ii line progressively make the centroid and FWHM of the Fe ii line less secure, as the overall line strength increases with decreasing temperature. Since metal-poor stars have intrinsically weaker lines, their lines should remain less "blended." In the middle panel of Figure 1, the solid red line is the smoothed differences in Fe i–Fe ii computed from stars with [Fe/H] < −0.3. In the smoothing, outliers have been excluded although they tend to exhibit large overabundances of Fe ii. As can be seen, the metal-poor-stars show differences that indicate that Fe ii is larger than Fe i in the bulk of sample, and in the 4500 K and below region the differences tail off in much the same way as the entire sample. While not conclusive, this indicates that line blending in Fe ii is not the sole culprit of the problem.

Two other possibilities relative to the gravity are significant non-LTE effects in iron, or that lower temperature, lower gravity stellar atmospheric models do not reflect the actual structure of stars. The latter possibility is difficult to assess, but the non-LTE alternative has been examined in other studies.

The first study of non-LTE effects in iron in cooler stars is likely that of Tanaka (1971), and these studies have proceeded through the work of Mashonkina et al. (2011) to the review by Mashonkina (2013), as well as the studies of Ezzedine et al. (2013) and Lapenna et al. (2014). The primary results from the latter two papers are that non-LTE calculations may yield better agreement between Fe i and Fe ii using parameters much like the mass-derived parameters used here, and that the non-LTE effects become stronger with decreasing temperature and metallicity. The non-LTE abundances found are closer to the LTE Fe ii values, but depend strongly on the poorly known strength of inelastic hydrogen collisions.

A counterpoint to the discussion above is found in arguments presented by Morel et al. (2014) and Adamczak & Lambert (2014). Both works argue that a traditional excitation and ionization analysis to determine stellar parameters is a valid approach. They cite the work of Bergemann et al. (2012) and Lind et al. (2012) as showing that iron is not significantly affected by departures from LTE, especially at higher abundances, such as those found in their study and by extension, those determined here. A quandary thus exists at this point as to the importance of non-LTE effects in iron, the resolution of which lies beyond the scope of this work; the priority in this analysis will be to maximize the reliability of these abundances under the current analysis constraints.

At temperatures above 5500 K there is a large spread in in the mass-derived and ionization-balance gravities (see Figure 1, bottom panel). This is because the ionization balance is susceptible to large uncertainties in Fe i and Fe ii equivalent widths. The equivalent width uncertainty arises due to the large (>20 km s⁻¹) line broadening seen in these stars.

3.4.2. External Comparison

Figure 3 shows an HR diagram of the program stars along with mass tracks from Bressan et al. (1993). The tracks are only to serve as an indicator of mass and evolutionary status. The stars shown in this plot form the first cut on the sample: only stars with a Hipparcos parallax or in a cluster are retained. The stars are also identified by broadening velocity (Vm), which can be either a macroturbulent or rotational velocity (see Table 3). The stars with Vm > 40 km s⁻¹ are mostly rotating F giants coming off the Main Sequence. In fact, most of the stars blueward of log T_eff > 3.78 are fast rotators, leading to difficulties in determining accurate line strengths due to velocity smearing of the profiles. As a result, stars with effective temperatures in excess of 6025 K are eliminated from further discussion.

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A number of potential dwarfs are seen in Figure 1 (top panel). These are the stars below the diagonal line starting at log T_eff = 3.78 and log L/L_Sun = +1.4 in Figure 3, and going toward lower temperatures and luminosities, and are eliminated from further discussion. In addition, 12 more stars are removed due to the inability to reach a spectroscopic ionization equilibrium inside the model grids. After the culling, 1006 G and K giants remain. In Table 3 last column, the retained stars are denoted by a "1" and the excluded stars a "2."

The next question to be addressed is which analysis—mass or ionization balance—is more reliable and hence, the basis for further discussion. Figure 4 presents a histogram of the ionization-balance [Fe/H] data, along with a Gaussian fit to the data, the Gaussian centroid values for the mass-derived Fe i and Fe ii data, and the simple mean value for the ionization-balance [Fe/H] values. The Gaussian fits to the distributions all have similar standard deviations of about 0.17 dex. The slight asymmetry in the [Fe/H] distribution is real, as there are more metal-poor than metal-rich stars in the local region. Note that three very metal-poor stars are cut off from the plot, but are included in the fit. The metal-poor asymmetry leads to the difference of 0.1 dex between the simple average and the centroid of the ionization-balance data.

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The metallicity of the local region as evidenced by F, G, and K dwarfs is close to solar (Luck & Heiter 2005, 2006). While the G and K giants of this study are not necessarily coeval with the dwarfs of the local region, one could expect the abundances for larger, non-biased samples for each to be commensurate. While the centroid values for the mass-derived gravity Fe i data and the ionization-balance [Fe/H] values are not vastly different—0.09 and 0.05 dex, respectively—and fall close to our expectation of solar abundance, the mass-derived Fe ii centroid value of +0.18 dex is uncomfortably high.

Another reason for favoring the ionization-balance gravity is that [x/Fe] ratios where x is a specified element are central to the discussion. Such ratios are used to help minimize parameter sensitivity. To form these ratios, one uses total abundances from species with like sensitivity to parameters; in general, ion to ion and neural to neutral. The advantage of the ionization gravities is that neutral and ionized total abundances are equivalent—at least in theory—in practice they are closer than those yielded by the mass gravity (see Figure 2), but are not perfectly matched. Use of the ionization-balance gravity thus allows the formation of the ratio without explicitly worrying about parameter sensitivity. Accordingly, the abundances for the primary discussion will be those of the ionization-balance analysis, with the mass values at the periphery. The mass gravity parameters and abundances are included in the tables, so an interested user can explore that data if so inclined.

Hinkel et al. (2014) gave an extensive discussion of metallicity trends in the local region. While the stars considered in that work are dwarfs, the trends versus [Fe/H], velocity, and position discussed therein are not significantly different from those found in local giants. The history of nucleosynthesis for both local dwarfs and giants is very similar; thus only a brief discussion will be given here to point out salient features in the giant abundances.

Figure 5 presents the average [x/Fe] data for the G and K giants of this study. In this notation, "x" represents a target element. This distribution is much like that of LH07 (see their Table 10) for most elements. The most striking items in Figure 5 are the behaviors of sulfur and zinc. The zinc lines are badly blended, especially at temperatures below 4800 K, resulting in abundances of poor quality. The difficulty with sulfur is a ferocious temperature dependence in the data—see Figure 6. The span in the abundances is over two orders of magnitude, rising from [S/Fe] about +0.2 at 5240 K to greater than +2 at 4000 K. Once again, the problem is blends in the relevant lines. Hyperfine structure was not considered for Mn, Co, and Cu in the analysis of LH07; whereas the abundances here do account for hyperfine structure. However, the mean abundances in this analysis are not vastly different from those of LH07.

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Another way of looking at Z > 10 abundances is to examine either [x/H] or [x/Fe] as a function of [Fe/H]. The overall expectation is that in a sample of disk G and K giants, both [x/H] and [x/Fe] should track [Fe/H]; that is, the slope of [x/H] versus [Fe/H] should be about 1 and the intercept [x/H] should be close to the mean value in the local region. For [x/Fe], the slope should be about 0, with the intercept having the local region [x/Fe] value. There will obviously be exceptions and the strength of the deviations will depend on how metal-poor the stars are. In this sample, we look at the trends down to [Fe/H] = −0.8 and throw out only the four most metal-poor stars. Table 5 gives the values and uncertainties in the trends versus [Fe/H], along with mean values. The expectations are born out in large part in the data. The exceptions, unsurprisingly, are carbon, oxygen, and the α-elements. Other elements, Mn for example, also show gradients with respect to iron. Carbon and oxygen will be discussed in the following section. Note that the gradients in Table 5 do not allow for different slopes as a function of [Fe/H]. This data set is too heavily dominated by thin disk stars to discern differences due to the thin versus the thick disk.

The behavior of the α-elements is well documented in the literature (see, e.g., McWilliam 1997; Allende Prieto et al. 2004; LH07; Hinkel et al. 2014). Shown in Figure 7 (top panel) is the behavior of [Si/Fe] versus [Fe/H]. As expected, [Si/Fe] increases with decreasing [Fe/H]. While the effect is modest, it is real and persists through Ca. Note that a loess smoothing of the data—the gradients in the figure—yields a result akin to the linear fit. The root cause for the decrease in [α/Fe] as [Fe/H] increases is the growing dominance of SN Ia production of the Fe-peak elements over the production of lighter α-elements in SN II as the galaxy ages.

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[Mn/Fe] versus [Fe/H] is shown in the middle panel of Figure 7. There is a definite slope in the data, with lower [Fe/H] ratios showing lower [Mn/Fe]. This effect was noted by LH07 and first demonstrated by Wallerstein (1962) and Wallerstein et al. (1963). Gratton (1989) also noted the effect in a sample of metal-poor to solar-metallicity stars. The effect is the reverse of the trends seen in the α-elements and presumably indicates an SN Ia origin for Mn. However, the adjoining odd elements V and Co show no believable trend with [Fe/H]—see the bottom panel of Figure 7 for Co.

The dwarf data from the Hypatia Catalog (Hinkel et al. 2014) show a curious phenomenon in the Ni abundances. Two [Ni/Fe] ratios appear in the data at essentially all [Fe/H] ratios. There is a group at a slightly subsolar ratio, [Ni/Fe] ∼ −0.03, and another at [Ni/Fe] ∼ −0.2. Hinkel et al. also delineate the abundances based on distance from the Sun. In Figure 8, [Ni/Fe] is presented as a function of [Fe/H], with the stars delineated by heliocentric distance. There is no discernible dependence in the data as a function of distance. There appears to be a downward trend in [Ni/Fe] with decreasing [Fe/H]. The data smoothing shows a flat dependence at [Fe/H] < 0, with increasing [Ni/Fe] for [Fe/H] > 0. There is also a dip in [Ni/Fe] at [Fe/H] about [Fe/H] = 0. However, the actual spread in the data is small. In the bin −0.2 < [Fe/H] < +0.2, the mean [Ni/Fe] ratio is +0.058 with a standard deviation of 0.053 (N = 736). The total spread at [Fe/H] = 0 in [Ni/Fe] is about 0.15 dex. There is no indication of a bimodal distribution of the [Ni/Fe] ratios in the local region giants. All trends in the [Ni/Fe] data are controlled by the stars in the −0.2 < [Fe/H] < +0.2 range. The same is true of all other elements.

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In the Figure 9 panels, three s/r process elements are shown. These elements shown much more scatter than the α- or Fe-peak elements. The small number of lines used to determine these abundances means that the abundance on a per star basis is more uncertain. Overabundances of these elements appear to be more common than overabundances in the lighter elements, leading to question of whether or not there are Ba or related stars in the sample. There are at least five known Ba stars in the sample: HD 46407, HD 104979, HD 139195, HD 202109, and HD 205011. While the highest point in the [Zr/Fe] and [Nd/Fe] data is HD 46407 (the Ba ii lines are too strong for adequate modeling), the bulk of the high points are not associated with known Ba stars. The suspicion is that small number statistics has corrupted the abundance data in these cases. Once again, however, the discrepant points comprise less than 3% percent of the analyzed stars. They are obvious, but do not compromise the overall data.

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A primary point of interest in the s/r data is the behavior of Ba. It appears that [Ba/Fe] decreases once the [Fe/H] ratio goes above solar. LH07 found the same thing in their data and ascribed the effect to either non-LTE or line-formation problems. Both LH07 and this study used a maximum equivalent width cutoff of 20 nm to help control problems in inadequate line-formation modeling. Calculations show that non-LTE effects in Ba for more luminous stars (Andrievsky et al. 2013, 2014) are modest, contributing an uncertainty/non-LTE correction of about 0.1 dex in the Ba abundances. The primary uncertainty detected was inadequate line modeling (i.e., the Ba ii line cores go optically thick at very shallow continuum optical depths). The line strength cutoff applied here is well below the values found in the Cepheids considered in the non-LTE studies. The conclusion is that non-LTE is not the primary culprit in the Ba data for the giants. Because these are stronger lines, a more probable cause is that the equivalent widths are somewhat underestimated due to the Gaussian approximation missing the growing line wings. This possibility is given credence because a consideration of computed Ba ii profiles at 4950 K, log g = 2.5, and V_t = 1.5 km s⁻¹ indicates that the Gaussian approximation underestimates the Voigt profile equivalent width of a true 20.0 pm line by 1.3 pm. While this difference is small, the line is saturated and the abundance needed to match the lesser equivalent width is 0.11 dex lower than that needed to match the Voigt profile value. Any underestimation in equivalent width will lead to potentially significant underabundances.

As a last point, the abundances here are overall in good agreement with those of LH07 and other works. Since the new data in no way contradicts previous analyses, there is no tension between the results of this study and the contention of Reddy et al. (2012, 2013) that field giants are the product of the breakup of open clusters. In fact, the cluster giants that are contained in this work are indistinguishable from the field giants in terms of their abundances.

The discussion of LH07 concerning lithium, carbon, and oxygen abundances in giants is still relevant today and their major points will be revisited briefly here.

4.4.1. Lithium

Lithium abundances have been determined in a range of local objects including dwarfs by Lambert & Reddy (2004) and Luck & Heiter (2006), as well as giants by Brown et al. (1989) and LH07. The base findings for the giants are that lithium is highly depleted with respect to its assumed initial value, and the depletion is a function of the effective temperature and mass. Recent studies of lithium in giants have focused on comparisons of thick and thin disk stars and the effects of rotation (Ramírez et al. 2012; Liu et al. 2014), with the result that thin disk giants are more lithium depleted than thick disk giants. There appears to be no dependence in giants of lithium on the macroturbulent or rotational velocity (LH07; Liu et al. 2014).

Theoretical predictions by Iben (1967a, 1967b) indicate that lithium should be diluted/depleted during the first giant branch by a factor of 60 at 3 M_⊙, decreasing to a factor of 28 at 1 M_⊙. However, recent work has shown that lithium abundance predictions in giants are subject to large numerical treatment uncertainties in thermohaline mixing (Lattanzio et al. 2015). While acknowledging that the theoretical predictions are uncertain, the currently available projected lithium dilutions/depletions correspond to decreases in abundance of 1.8–1.4 dex, relative to the (assumed constant) main sequence initial value. However, the surface lithium content of dwarfs is extremely variable (Lambert & Reddy 2004; Luck & Heiter 2006), spanning up to two orders of magnitude at any temperature/mass. While this makes the lithium content of any one star (giant or dwarf) impossible to predict under any evolutionary scheme, one can hopefully use overall trends in the data to test generic theoretical predictions.

The work of Lambert & Reddy indicates that the general astration level of lithium in dwarfs is independent of metallicity, but dependent upon mass. In Figure 10, we show their LTE abundance data (lithium versus mass), along with the G/K giant data of this study. The data shown in Figure 10 for the giants is from the LTE analysis. The non-LTE corrections from Lind et al. (2009) increase the lithium abundances by about 0.1 to 0.2 dex for both G/K giants and dwarfs. Figure 10 also shows the level of dilution predicted by standard evolution (a representative factor of 40). As apparent from the figure and pointed out by LH07, given the scatter in the dwarf lithium abundances and the mass-dependent astration, it is entirely possible that the bulk of giant lithium abundances are consistent with standard evolution. Because the dilution occurs/starts when the star becomes convective at the base of the first giant branch, the appropriate abundance to use for the dilution can be significantly below the local interstellar value of about 3.0–3.2 (as determined from the dwarfs themselves; see Lambert & Reddy). A detailed consideration of lithium abundances in giants may need additional dilution processes, but certainly not at the level one would need if the initial abundance were 3.0 dex or above.

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Further confounding the interpretation of the giant abundances is the "Li-dip," which is the observed decline in lithium abundance in open cluster dwarfs at a mass of about 1.3–1.4 M_⊙ (Balachandran 1995). Later work has shown that the dip occurs at different temperatures/masses depending on the metallicity (François et al. 2013). However, the "Li-dip" is not an especially distinct feature in field dwarfs (Lambert & Reddy 2004; Luck & Heiter 2006), and so it is difficult to ascribe all of the variation in dwarf and giant lithium abundances to its presence.

In Figure 10, several stars show very high abundances of lithium: HR 7820, HR 8642, HD 188993, HD 9746, HD 95799, and HD 112127. All of these stars have lithium abundances in excess of 3.0 dex, with the last three stars in the super-Li (or Li-rich) list of Charbonnel & Balachandran (2000). The first three are stars in LH07 and all have lithium abundances consistent with the present values in that work. LH07 identified HR 7820 and HR 8642 as K giant super-Li stars. The evolutionary status assumed for a super-Li star is either that it is on the ascent to the first giant branch, or that it resides near the red-giant clump post first dredge-up. In either case, it will be well separated from the main sequence. This means that stars blueward of the clump, such as HD 188993, while having high Li abundances are not super-Li stars. HD 148317, which was not plotted in Figure 10, fails the culling process because it is too close to the main sequence. It shows a lithium abundance of 3.04 dex. The idea is that stars such as HD 188993 and HD 148317 have not yet undergone a strong mixing event and thus show their original lithium content. The status of these two stars will be considered further in the discussion of carbon and oxygen.

About 1% of normal K giants are super-Li stars (Charbonnel & Balachandran 2000). The question is what abundance level constitutes a super-Li star? Some of the stars listed by Charbonnel & Balachandran have lithium abundances as low as 1.5 dex. The number of stars having an abundance at that level or above in this study is 23, or slightly more than 2% of the sample. Note that these stars do not include any F giants near the main sequence or stars like HD 148317 and HD 188993. Thus it appears that this sample has too many super-Li stars. However, lithium abundances are very variable and it is certainly possible that a lithium abundance of 1.5–1.7 dex—dilution of a factor of 20–50—in a giant merely reflects standard evolution operating on the plateau local interstellar lithium abundance. If the lower abundance to consider as super-Li were taken to be 2.0 dex, this sample then has 15 total candidates.

Super-Li stars are "classified" according to their position in the HR diagram. In Figure 11, we see a group of these stars straddling the red-giant clump—the position of one of the two families of such objects (Charbonnel & Balachandran). The four stars, including HD 188993 blueward of the clump, may be from before the first dredge-up and thus have not diluted their surface lithium. Charbonnel & Balachandran gave a working hypothesis for the clump super-Li stars. The mechanism is an "extra" mixing that occurs at this position in the HR diagram between the convective envelope and the top of the H-burning shell. The mixing results in the production of ⁷Li, which is then convected to the surface. However, a trigger mechanism is still missing for the event. This scenario is complicated by the inconsistency in the theoretical lithium predictions found by Lattanzio et al. (2014). The takeaway from their study is that all theoretical lithium predictions should be viewed with caution.

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4.4.2. C and O

The abundances of carbon, nitrogen, and oxygen in K giants will reflect the effects of both galactic chemical evolution and stellar evolution. The properties of both galactic and stellar CNO evolution are well-known, having been studied numerous times (see, e.g., Lambert & Ries 1981; Gustafsson et al. 1999, LH07; Adamczak & Lambert 2014). The primary galactic evolution expectation is that the [O/Fe] (and [C/Fe]) ratio should rise with decreasing [Fe/H]. Stellar evolution will affect the carbon and nitrogen abundances—carbon will be converted to nitrogen with the sum C+N expected to remain constant. The anticipated carbon decrease is modest, perhaps up to 0.2 dex. Oxygen abundances are unchanged during the first dredge-up.

The relationship between [Fe/H] and [C/Fe], [O/Fe], and C/O is shown in Figure 12. As expected, both [C/Fe] and [O/Fe] increase with decreasing [Fe/H]. The C/O ratios are mostly subsolar, as projected based on the predictions of standard stellar evolution. Carbon is diluted/depleted because of the first dredge-up, while oxygen remains unaffected. Note that C/O is not independent of [Fe/H], but decreases, implying an enhancement of O relative to C in the more metal-poor stars. Our giant data is in accord with the C/O ratios found using the dwarf data of Luck & Heiter (2006). Their data gives solar C/O ratios at solar metallicity, with the C/O ratio declining toward lower [Fe/H] values, albeit with significant scatter. Gustafsson et al. (1999) also found this result in dwarfs. This implies that stellar evolution in this mass and metallicity range yields rather uniform results in the carbon dilution/depletion for the first dredge-up.

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There are of order 50 C/O ratios at or slightly above the solar ratio in the current data. If these stars were actually dwarfs, one might expect their [C/Fe] ratio to be near zero, and they should have higher gravities relative to the mean of the sample. However, neither of these expectations are borne out. Perhaps the real question is why should a G/K giant be limited to a subsolar C/O ratio? The C/O ratio in local dwarfs spans a considerable range: 0.1 < C/O < 0.9 (Luck & Heiter 2006). The range seen in the G/K giants is consistent with those initial ratios coupled to standard stellar evolution, yielding a dilution/depletion of the surface carbon abundance by about 0.2 dex relative to the initial composition (Iben 1967a, 1967b; Schaller et al. 1992; Girardi et al. 2000).

LH07 pointed out an interesting result in their clump [C/Fe] abundances: They found that the blue side (i.e., hotter stars) in the clump showed lower [C/Fe] ratios than did the red-side. The difficulty was that an admixture of [Fe/H] ratios could give rise to a spurious result because [C/Fe] correlates with [Fe/H]. The current sample affords the possibility of exploring this effect further because there are more than 350 stars with [Fe/H] ratios between −0.1 and +0.1 dex that fall in the luminosity range 1.0 < log (L/L_⊙) < 2.5. Figure 13 (top panel) shows the temperature-binned [C/Fe] ratios. Looking at the outermost points, we see that they differ in [C/Fe] by about 0.15 dex, with the blue edge having the lower abundance. Note that neither [O/Fe] or [Fe/H] show any dependence on temperature. There is an effect in the C/O ratio, but this is expected given the decrease in [C/Fe] and the lack of a variation in the [O/Fe] values against effective temperature.

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Accepting the trend in [C/Fe] at face value, what could be the cause? The abundance ratios are plotted against mass in the bottom panel of Figure 13. Here we see that the [C/Fe] ratios of −0.3 to −0.4 are associated with higher mass stars (2.5–3.5 M_⊙), whereas [C/Fe] increases to about −0.2 with decreasing mass. The obvious explanation is depth-dependent mixing as a function of mass: higher mass stars mix deeper, bringing more carbon deficient material to the surface than is the case in the lower mass stars. As mass correlates with age, a dependence exists between age and [C/Fe]—the strongest dilutions/depletions exist in the youngest stars. This is in accord both qualitatively and quantitatively with theoretical expectations (Iben 1967a, 1967b; Schaller et al. 1992; Girardi et al. 2000). More advanced stellar mixing/evolution schemes are available than the ones cited above. However, nitrogen abundance is needed to elaborate, and it is unavailable for most of the stars considered. Thus, the overall discussion will stop here. However, a few specific points do need further elaboration.

Figure 13 shows three stars that have very low [C/Fe] ratios. These stars must be akin to the weak G-band and/or the CN-stars discussed by Adamczak & Lambert (2013) and Luck (1991), respectively. Stars in these classes typically show carbon depletions up to 20 times larger than those found in normal giants; but as of now, there is no mechanism to explain them. The stars in this study that show such depletions are HR 6791, HR 40, and HR 1219. HR 6791 is a well-known example also included in both studies noted previously. The other two have not been mentioned in prior works on carbon-poor giants—HR 1219 and HR 40 are warmer objects, and have lower luminosities, placing them nearer the Main Sequence. The rotational/macroturbulent line broadening seen in both is of order 4 to 6 km s⁻¹, making the lack of C i lines very obvious. Perhaps these stars are precursors to the more evolved post first giant branch weak G-band stars.

In the lithium discussion, two stars were identified with high Li contents: HD 188993 and HD 148317. Both stars are warmer and have higher gravities—about 5700 K and 3.5—and thus are likely G subgiants. Their carbon abundances are consistent with the idea that they have yet to ascend the first giant branch and undergo strong mixing: the [C/Fe] ratio in both is about +0.06. These two stars are likely on their redward pass toward the first giant branch.

As a last point, it is generally assumed that older stars are more metal-poor than younger stars, and that there is significant scatter within the age–metallicity relation. The idea of an age–metallicity relation is further complicated by the strong possibility that the stars will migrate during their lifetimes and end up far from their point of origin in radial distance from the galactic center (Sellwood & Binney 2002; Schönrich & Binney 2009). The difficulty with this scenario relative to the age–metallicity relation is that stars from different parts of the Galaxy should have different initial compositions, due to the galactic metallicity gradient (Luck & Lambert 2011). While this study was not designed to look at this problem, it is worth noting that the giant subset used to explore [C/Fe] in the red-giant clump (some 350 stars), has a total range in [Fe/H] of 0.2 dex centered on the solar value; but it has ages spanning more thatn 5 Gyr—from 0.5 to about 6 Gyr. There is little evidence for strong age–metallicity relation in the giants of the local region about the Sun.