The Populations of Carina. II. Chemical Enrichment^*

Carina is an interesting dSph galaxy, with a very complex star formation history as seen in its CMD (Smecker-Hane et al. 1994, 1996; Mighell 1997; Hurley-Keller et al. 1998; Hernandez et al. 2000; Dolphin 2002; Monelli et al. 2003; Bono et al. 2010; Stetson et al. 2011; de Boer et al. 2014; Monelli et al. 2014; Weisz et al. 2014; Kordopatis et al. 2016; Santana et al. 2016). Standard broadband BVRI photometry reveals several distinct sequences, clearly identifying a punctuated star formation history, with individual star-forming events of different epochs and durations. And yet, this dSph has one of the narrowest red giant branches in the Local Group. The degeneracy in age and metallicity/chemical composition on its red giant branch (RGB) seems to have conspired perfectly in these BVRI colors. It is clear that Carina is dominated by an intermediate-aged population, with minor contributions at both old and younger times. In Paper I we reported our investigation of the Carina CMD of Stetson et al. (2011) using synthetic CMDs based on the isochrones of Dotter et al. (2008), in terms of the three basic population parameters [Fe/H], age, and [α/Fe], for the cases when (i) [α/Fe] is held constant and (ii) [α/Fe] is permitted to vary. We found four epochs of star formation, well described in terms of [Fe/H] = −1.85, −1.5, −1.2, and ∼−1.15 and ages of ∼13, 7, ∼3.5, and ∼1.5 Gyr, respectively (for [α/Fe] = 0.1 (constant [α/Fe]) and [α/Fe] = 0.2, 0.1, 0.0, −0.2 (variable [α/Fe])), with small spreads in [Fe/H] and age of order 0.1 dex and 1–3 Gyr.⁴ (In Paper I we referred to these four groups chronologically, as the "first," "second," "third," and "fourth" populations, respectively. We shall adopt this nomenclature later in the present work.) These parameters reproduce five basic observed features in Carina's CMD (two distinct subgiant branches of old and intermediate-age populations, two younger, main-sequence components, and the small color dispersion observed on its RGB).

These complexities notwithstanding, dwarf galaxies such as Carina are simpler systems than spiral galaxies, having lower masses and having undergone fewer accretion episodes, fewer star formation events, and less chemical evolution (see, e.g., Mateo 1998; Tolstoy et al. 2009). Weisz et al. (2014) have shown significant scatter in the star formation history of the Local Group dSph galaxies, even among those with similar masses, indicating the importance of additional factors such as their local environment, the effects of stellar/supernova (SN) feedback, and variations in the metallicity yields and timescales for SN and asymptotic giant branch (AGB) events.

One aspect of current interest in dwarf galaxy research is the importance of inhomogeneous mixing of the interstellar medium (ISM). A poorly mixed ISM aids in the removal of low angular momentum gas in numerical simulations of dwarf galaxies, avoiding the formation of bulges (Governato et al. 2010). Inhomogeneous mixing has also been invoked to explain the large range in metallicities found in the ultrafaint galaxies, presumed to be due to a single core-collapse SN event (Simon et al. 2011; Tominaga et al. 2014, and Frebel & Norris 2015). We note that the metallicity dispersions observed in the ultrafaint systems are nevertheless in excellent agreement with the inhomogeneous and binomial model for the chemical evolution of galaxies presented by Leaman (2012).

The mixing efficiency and timescale for SN Ia events are less clear. The usual assumption is that SN Ia (and AGB) contributions lag those of SNe II by ∼1 Gyr (e.g., Argast et al. 2002; Revaz & Jablonka 2012), due to the lower mass of their progenitor stars. The location of a knee in the [α/Fe] versus [Fe/H] abundances for stars in dwarf galaxies compared with similar-metallicity stars in the Milky Way is one piece of evidence for the late contributions of iron from SN Ia—though that trend has also been attributed to metallicity-dependent SN Ia yields (Kobayashi et al. 1998 and Kobayashi & Nomoto 2009), or a truncated upper IMF (Tolstoy et al. 2003; McWilliam et al. 2013). It could be that several mechanisms are in play.

Direct evidence for inhomogeneous mixing of SN Ia material in a dwarf galaxy was presented for stars in Carina from ESO/FLAMES-UVES and Magellan/MIKE spectra by Venn et al. (2012). Two (of nine) stars showed an enhancement of the iron-group elements (Cr, Mn, Fe) by factors of 3–7 relative to the other elements, which suggested that those stars formed in a pocket of iron-enriched material; one of these (Car-612) is among the most metal-rich stars in Carina, suggesting late-time inhomogeneous mixing. Additional stars observed with ESO VLT FLAMES-GIRAFFE by Lemasle et al. (2012) also showed a wide dispersion in [X/Fe] values, but only three wavelength settings were used (covering ∼1000 Å), providing fewer elements to clearly identify the signatures of inhomogeneous mixing versus smooth/punctuated chemical evolution. Previous analyses of a few stars in Carina did not clearly identify these features as a result of too few stars (Shetrone et al. 2003) and elements (Koch et al. 2008) being analyzed.

We have undertaken a kinematic and chemical analysis of the 63 red giants in Carina in an effort to better understand the formation and evolution of this system. In Section 2 we present our observational material for 32 Carina red giants, based on high-resolution, moderate-S/N spectra obtained with the ESO/FLAMES-UVES combination during ESO Proposal 180.B-0806(B) (PI: G. Gilmore),⁵ which we use in Section 3 to determine chemical abundances for 19 elements for these stars, using model atmosphere techniques. In Section 4 we augment this data set with spectroscopic material of comparable quality for other Carina red giants in the literature. To produce a set of homogeneously determined abundances, we analyze the literature EW values using the same techniques as adopted for the primary sample. The total sample comprises 63 independent Carina red giants. Their [Fe/H] metallicity distribution function (MDF) is presented in Section 5, while Section 6 gives an overview of relative elemental abundances in the [X/Fe] versus [Fe/H] planes. In Section 7 we discuss the abundances of the α-elements and what they have to tell us about Carina's chemical evolution, while Section 8 examines the role played by SNe Ia in its chemical enrichment. In Sections 9 and Section 10 we present rough age estimates and compare them and our observed MDF and [α/Fe] distribution with those obtained using the synthetic CMD predictions in Paper I. Section 11 presents the result of our search for the ubiquitous anticorrelation between sodium and oxygen abundances that exists within individual Galactic globular clusters, while in Section 12 we present the discovery of an extremely lithium-rich Carina red giant. We summarize our results in Section 13.

Our selection of objects is based on unpublished CCD V, I observations that we have made of the Carina galaxy. The only criterion we adopted in the selection was that a star should lie close to the well-defined RGB of the system.⁶ In Figure 1 we show the positions of these stars in the ($V,\,B-I$) CMD, together with that of the larger sample surveyed, for the sample described by Stetson et al. (2011) and made available by P. B. Stetson (2014, private communication). The large red star symbols represent objects for which we have obtained the high-resolution spectra discussed above. The large green circles stand for stars having high-resolution spectroscopic data in the literature, to which we shall return in Section 4 and determine chemical abundances, using the techniques we adopt in the analysis of our program stars.

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High-resolution, moderate-S/N spectra were obtained of 39 Carina red giants, during 2007 November–2008 March, with the FLAMES system at the 8.2 m Kueyen (VLT/UT2) telescope at Cerro Paranal, in UVES-Fiber mode. Of the eight UVES fibers, approximately five were allocated to Carina candidate members and approximately three to nearby sky positions to enable background measurement. We obtained nine individual exposures in Service Mode, eight of duration 60 minutes, leading to an effective total integration time of 8.8 hr. The spectra were obtained using the 580 nm setting and cover the wavelength ranges 4800–5750 Å and 5840–6800 Å. The resolving power was R = 47,000.

The spectra of the individual exposures of the program stars were reduced by using the FLAMES-UVES pipeline (Freudling et al. 2013).⁷ Following this, the individual spectra were cross-correlated to determine relative wavelength shifts between them in order to compensate for Earth's motion during the data-taking interval. After sky-subtracting and shifting the individual spectra to the rest frame, the spectra were co-added to produce the summed spectrum of each star. Our subsequent abundance analysis of these data indicated that the S/N of the spectra of seven objects was too low to permit reliable abundance results, and these will not be considered further here.

Details of the remaining 32 program stars are presented in Table 1, where columns (1) and (2) contain their identification and coordinates. Alternative nomenclatures of these stars, together with the names of others that will be the subject of reanalysis of equivalent data available in the literature, using techniques described below in Section 3, are presented in Table 14 of the Appendix.

Photometry has been obtained from several sources: P. B. Stetson provided us with homogenized BVI, M. J. Irwin furnished JHK from ESO VISTA survey photometry, and M. Gullieuszik supplied BVIJHK_s. Here all BVI magnitudes are corrected to the Johnson–Kron–Cousins system, following Stetson (2005), while JHK_s are corrected to be on the Two Micron All Sky Survey (2MASS) system. A comparison of the photometric data set per star between the three sources shows excellent agreement. We estimate from intercomparison of the photometry that the B, V, I, J, H, and K values have errors of 0.006, 0.006, 0.011, 0.009, 0.009, and 0.016, respectively. We have therefore averaged the magnitudes, and we present the results in Table 1, which we use in our determination of the atmospheric parameters in Section 3.1.

Radial velocities were measured for each of the individual spectra for each star described above. To do this, we used the Fourier cross-correlation techniques described by Norris et al. (2010, Section 2.4) and Gilmore et al. (2013, Section 2.2.1), to which we refer the reader for details. We note here, for completeness, that there were two minor differences in the present work. First, we cross-correlated our spectra against the Arcturus high-resolution spectrum of Hinkle et al. (2000)⁸ (rebinned to have the same pixel size as our data). Second, for each spectrum we cross-correlated over the three wavelength regions 5160–5190 Å, 5400–5498 Å, and 6502–6598 Å to produce three velocity estimates, which we averaged to determine the velocity for that spectrum. Then, for each star we averaged the velocities available for the approximately eight exposures of each star and (having applied appropriate heliocentric corrections) averaged these values, weighted by the inverse square of their errors, to produce the final radial velocity for each object. Our velocities and their internal errors are presented in the final two columns of Table 1. The data are of high precision, with the mean of the errors for the 32 stars being 0.16 km s⁻¹. Velocities for these spectra have also been determined by Fabrizio et al. (2012): comparison between our velocities and theirs shows that the mean velocity difference is 0.03 km s⁻¹ with a dispersion of 0.76 km s⁻¹. The mean radial velocity of our sample of 32 stars (all of which are radial velocity members) is 224.8 ± 1.0 km s⁻¹, with dispersion 5.65 ± 0.71 km s⁻¹. We note that the dispersion agrees well with those of Walker et al. (2009b), within the limits, but is somewhat lower than those of 10.4 ± 1 km s⁻¹, 7.6 ± 0.5 km s⁻¹, and 8.5 ± 0.8 km s⁻¹, reported by Kordopatis et al. (2016) for their metal-poor, intermediate-metallicity, and metal-richer RGB stars. For completeness, we also note that we find no dependence of velocity dispersion on metallicity in our relatively small sample of stars.

Before attempting to determine EWs from the co-added pipelined spectra described in Section 2.2, we undertook three further steps. First, given the somewhat low S/N of a significant number of spectra and the line crowding on some of the relatively high abundance stars in our sample, we resolved to measure EWs only redward of 5300 Å. Inspection of the degree of line blending in the high-resolution spectrum of Arcturus (Hinkle et al. 2000) supports this decision. We also note the previous decision of Norris et al. (1995) in their abundance analysis of the red giants in the globular cluster ω Centauri (of spectra having R ∼ 38,000), who stated, "Initially we sought to measure ... all lines in the wavelength range 5050–6810 Å, but in view of the difficulty of continuum placement in the coolest stars, decided to reduce this to 5285–6810 Å." Second, given the high resolution (R = 47,000) of the present spectra, we double-binned the data to facilitate reliable continuum placement (yielding a pixel size of ∼0.028 Å).⁹ We measured S/N per double-binned pixel in several intervals of width 2.0–5.5 Å in the range 5310–5723 Å, in which the continuum is clearly seen in the Arcturus spectrum of Hinkle et al. (2000). The S/N values (averaged over the several wavelength intervals) for the 32 Carina giants for which we analyze EWs lie in the range of 8–22, with a median value of 12, and are presented for the individual stars in the first rows of Tables 2–4. Third, and finally, we removed the interorder undulations in the pipelined data and renormalized the spectra by determining the position of the "continuum" using five-pixel Gaussian smoothing and fitting a low-order Legendre polynomial, followed by k-sigma clipping using a scale length of 10 Å, following Venn et al. (2012). Examples of the resulting spectra in the wavelength range 5160–5200 Å, including for interest that of the α-challenged star Car-612 discussed in Section 1 (and designated here CC07452), are presented in Figure 2. (We note that these spectra lie outside the region of our abundance analysis; they are presented here for heuristic purposes only.)

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EWs were measured independently for all stars by both J.E.N. and D.Y. for the set of unblended lines formed by the merging of the line lists of Venn et al. (2012) and Yong et al. (2013). Three independent equivalent measures were obtained: J.E.N. used the EW measurement techniques described by Norris et al. (2001), while D.Y. utilized IRAF software as described by Yong et al. (2008), as well as the automated package DAOSPEC (see Stetson & Pancino 2008).¹⁰ As a further check, K.A.V. used IRAF and DAOSPEC for a small subset of the spectra, which confirms the results of J.E.N. and D.Y.

Before accepting an EW measurement, both J.E.N. and D.Y. inspected the Gaussian fits to each spectrum line to ensure an acceptable representation. For each line in a given star, the measurements of J.E.N. and D.Y. produced three independent estimates that were combined as follows: (i) we required that at least two estimates were available; (ii) when three measurements were recorded, we rejected one of them if it clearly disagreed with the average of the other two; and (iii) of the cases where two estimates were averaged, we rejected some 30 lines for which large differences of order greater than 3σ existed between them. We rejected a line from the abundance analysis if an EW was measured for it in only one star, or the majority of stars in the sample had an EW greater than 200 mÅ. Finally, in four cases we rejected a line that was the only representative of an atomic species and yielded an abundance that was clearly in error. Figure 3 presents a comparison of the EWs of the present work with those of Shetrone et al. (2003), Koch et al. (2008), Venn et al. (2012), Lemasle et al. (2012), and Fabrizio et al. (2012, 2015). In these comparisons, there is good agreement between the present work and the results of Shetrone et al. (2003), Venn et al. (2012), and Lemasle et al. (2012).

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We find a systematic difference, however, between our data and those of Koch et al. (2008) between their LG04a_01826 and our CC07452, in the sense that their EWs become systematically smaller than ours with increasing line strength. (Note, however, that Figure 3 shows good agreement between our work and that of Venn et al. [2012] for this object.) We have five other stars (CC06122, CC08469, CC10194, CC11217, CC12039) in common with the work of Koch et al. (2008) and find similar differences in all of these objects as well. In Section 4, when we reanalyze EW data from the literature, we will not include the work of Koch et al. (2008) in view of these systematic EW differences.

We obtain relatively poor agreement between our results and those of Fabrizio et al. (2012, 2015) for CC10686, as may be seen in the bottom panel of Figure 3. To investigate this further, in the top left panel of Figure 4 we present a comparison between the EWs of Fe i lines in the 31 stars in common between the samples of Fabrizio et al. (2012) and the present work,¹¹ and in the bottom left panel we compare the collective Fe i data of Shetrone et al. (2003), Venn et al. (2012), and Lemasle et al. (2012) on the one hand and the present work on the other. In the top right panel of the figure we present a similar comparison for the non-Fe lines, using the EWs of Fabrizio et al. (2015). From these panels we conclude that the line strengths of Fabrizio et al. (2012, 2015) are on average smaller than those of both the present investigation and those of the other workers. As seen in Figure 4, the EWs of Fabrizio et al. (2012) and Fabrizio et al. (2015) are smaller by 18 and 15 mÅ for Fe i and non-Fe lines, respectively, than those of the present work. Offsets of this order in comparison with the work of Venn et al. (2012) and Lemasle et al. (2012) were also reported by Fabrizio et al. (2015). We shall return to the significance of these differences in Section 3.4.

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As part of our quality control, we estimated the smallest EW, W(min), that we could reliably measure in each star. To achieve this, for each spectrum we examined the number of lines we measured as a function of decreasing EW, and on the conservative assumption that at lowest line strength our estimates might not be reliable, we adopted the fifth-smallest EW we measured as a conservative estimate of W(min). These values lie in the range of 14–34 mÅ, with median 24 mÅ, and are presented in the second row of Tables 2–4. If we use the Cayrel (1988) formula, with the correction from Battaglia et al. (2008), to calculate the minimum EW, we find a range from 4 mÅ (S/N = 22) to 11 mÅ (S/N = 8) for our high-resolution data. These values are a factor of three smaller than our conservative estimates above and therefore are consistent with a 3σ certainty for these estimates.

In Section 11 we shall investigate the existence or otherwise of anticorrelation between the abundances of Na and O, which is ubiquitous within individual Galactic globular clusters, and which the work of Shetrone et al. (2003) suggests may not exist in Carina. As part of that exercise we closely estimated the upper limits of the EWs of the lines of these elements (together with Al, which also anticorrelates with O in the globular clusters) by visual inspection of them and nearby lines of other elements. These limits are also presented, for future consideration, in Tables 2–4, specifically for O i λ6300.3, Na i λ5688.2, and Al i λ6696.0.

To form our final EW data set, we accepted lines with wavelengths in the range of 5300–6780 Å and EWs less than 200 mÅ. Our adopted EWs for 211 unblended lines are presented in Tables 2–4. Line identifications, together with their lower excitation potentials, χ, and log gf values, are presented in columns (1)–(4), respectively. The EWs populate the remainder of the tables. These data are suitable for model atmosphere abundance analysis (see Section 3).

In what follows we shall exclude lines weaker than the relevant W(min) values described above, except for the O i λ6300.3, Na i λ5688.2, and Al i λ6696.0 transitions, discussed in the previous paragraph. We consider these weaker lines, but we note that their detections are at the 1σ–2σ level, rather than the 3σ level we have adopted for the other lines.

3.1.1. Effective Temperature (${T}_{\mathrm{eff}}$)

In most abundance analyses of cool giants, effective temperatures are based on either spectroscopic or photometric techniques. The former, denoted "excitation" temperatures, are based on the requirement that model atmosphere analysis of Fe i lines should yield abundances independent of lower excitation potential, while the latter, denoted "photometric" temperatures, rely on calibrations of the stellar continuum energy distribution as a function of effective temperature. Insofar as our spectra have relatively low S/N, on the one hand, while we have access to accurate BVIJHK photometry, on the other, we have chosen to adopt photometric temperatures, which we expect to have considerably higher accuracy in the present case.

We have determined ${T}_{\mathrm{eff}}$ by using the infrared flux method (IRFM), following Casagrande et al. (2006), which solves for ${T}_{\mathrm{eff}}$ in the basic equation

$$\begin{eqnarray}&&\displaystyle \frac{{{ \mathcal F }}_{\mathrm{Bol}}({\rm{Earth}})}{{{ \mathcal F }}_{{\lambda }_{{\rm{IR}}}}({\rm{Earth}})}=\displaystyle \frac{\sigma {T}_{\mathrm{eff}}^{4}}{{{ \mathcal F }}_{{\lambda }_{{\rm{IR}}}}({\rm{model}})},\end{eqnarray} \tag{ 1 }$$

where ${{ \mathcal F }}_{\mathrm{Bol}}({\rm{Earth}})$ and ${{ \mathcal F }}_{{\lambda }_{{\rm{IR}}}}({\rm{Earth}})$ refer to bolometric and monochromatic infrared fluxes at the Earth, while ${{ \mathcal F }}_{{\lambda }_{{\rm{IR}}}}({\rm{model}})$ refers to a corresponding model atmosphere synthetic spectrum.

The observational input data were the BVIJHK values presented in Table 1 and a distance modulus and reddening for Carina of ${(m-M)}_{V}$ = 20.05 ± 0.11 and E(B − V) = 0.06 ± 0.02 (Venn et al. 2012, Section 3.4), while the adopted model synthetic spectra were those of Castelli & Kurucz (2003). As found by Casagrande et al. (2006), these temperatures tend to be slightly ($\leqslant 100$ K) hotter than those determined with the Ramírez and Meléndez (2005) BVIJHK color–temperature calibrations. They tracked this effect primarily to the zero-point calibration of the 2MASS photometric system. The resulting ${T}_{\mathrm{eff}}$, which are the averages of the three independent estimates obtained by applying the IRFM to the observed J, H, and K magnitudes, are presented in column (2) of Table 5, while column (3) contains their uncertainties, based on the spread in the JHK estimates. The average uncertainty in the ${T}_{\mathrm{eff}}$ for the 32 stars in the table is 76 ± 2 K, which we shall use in Section 3.3.

Table 5.  Model Atmosphere Parameters for 32 Carina Red Giants

Object	${T}_{\mathrm{eff}}$	σ${T}_{\mathrm{eff}}$	$\mathrm{log}\,g$	[M/H]	ξt
	(K)	(K)	(cgs)	(dex)	(km s−1)
(1)	(2)	(3)	(4)	(5)	(6)
CC06122	4284	60	0.68	−1.5	2.30
CC06486	4524	62	1.07	−2.0	1.95
CC06975	4563	84	1.18	−1.8	2.30
CC07452	4437	65	0.87	−1.3	2.30
CC07889	4675	55	1.31	−2.3	2.30
CC08447	4418	72	0.93	−1.5	2.15
CC08469	4337	68	0.81	−1.5	2.25
CC08615	4651	84	1.28	−1.7	2.40
CC08695	4337	89	0.84	−1.3	2.10
CC08788	4695	82	1.34	−1.5	2.45
CC09000	4230	116	0.67	−1.8	2.40
CC09179	4561	87	1.15	−1.8	1.85
CC09225	4438	93	0.95	−1.6	2.15
CC09226	4619	76	1.19	−1.5	1.90
CC09430	4509	74	1.10	−2.1	1.95
CC09507	4652	63	1.20	−1.7	2.15
CC09633	4487	80	0.93	−2.2	2.40
CC09869	4459	74	1.01	−1.3	2.10
CC09929	4515	73	1.19	−1.5	2.10
CC10038	4486	73	1.08	−1.2	1.95
CC10194	4352	98	0.80	−1.7	2.05
CC10318	4359	69	0.89	−1.5	2.10
CC10414	4442	66	1.01	−1.4	2.30
CC10686	4312	73	0.76	−1.6	2.05
CC10690	4486	78	1.04	−1.9	2.25
CC10802	4587	72	1.30	−1.3	2.00
CC10944	4425	69	0.85	−1.9	2.40
CC11217	4279	78	0.69	−1.4	2.30
CC11388	4454	81	0.93	−1.5	2.45
CC11560	4514	68	1.06	−1.5	2.20
CC12038	4551	73	1.19	−1.6	1.95
CC12039	4412	65	0.84	−1.6	2.35

A machine-readable version of the table is available.

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3.1.2. Surface Gravity (${log}\,g$)

In many analyses surface gravities are determined by requiring that abundances obtained by using Fe i and Fe ii lines are the same. There are two potential problems with this method. The first is that the results of non-LTE (NLTE) calculations show that while the LTE assumption is acceptable for the analysis of Fe ii lines, it leads to erroneous results for Fe i (e.g., Lind et al. 2012). An additional consideration is that at lowest abundances the number of Fe ii lines decreases dramatically. A second method of gravity determination is to use theoretical isochrones in which the observed ${T}_{\mathrm{eff}}$ is interpolated in the theoretical ($\mathrm{log}\,g$, ${T}_{\mathrm{eff}}$) relationship, or (with color as proxy for ${T}_{\mathrm{eff}}$) in a ($\mathrm{log}\,g$, color) relationship. This method is, however, critically dependent on the accuracy of the model ${T}_{\mathrm{eff}}$ values and the (color, ${T}_{\mathrm{eff}}$) dependence.

A third approach is to use the fundamental definitions of gravity and ${T}_{\mathrm{eff}}$ to express gravity as a function of mass, ${T}_{\mathrm{eff}}$, and luminosity. The basic challenge of this method is that one needs a reliable distance in order to determine luminosity, which is not generally possible for field stars. For star clusters, however, this is not an insuperable problem, insofar as their distances can be obtained with reasonable accuracy. We choose to follow this approach.

The surface gravity, $\mathrm{log}\,g$, of a star of mass M, effective temperature ${T}_{\mathrm{eff}}$, and bolometric magnitude M_Bol, may be written as

$$\begin{eqnarray*}\mathrm{log}\,g & = & \mathrm{log}\,{g}_{\odot }+0.4\times \mathrm{log}(M/{M}_{\odot })+\,4.\times \,\mathrm{log}({T}_{\mathrm{eff}}/{{T}_{\mathrm{eff}}}_{\odot })\\ & & +0.4\times ({M}_{\mathrm{Bol}}-{M}_{\mathrm{Bol}\odot }).\end{eqnarray*}$$

To apply this relationship, we adopt for the Sun $\mathrm{log}\,g$_⊙ = 4.44, T_eff⊙ = 5777 K, and M_Bol⊙ = 4.75, and for the Carina giants we adopt M = 0.8 M_⊙, the distance modulus and reddening of Section 3.1.1, and A(V)/E(B − V) = 3.24 (following Schlegel et al. 1998; Venn et al. 2012). We use the V magnitudes in Table 1, together with V bandpass bolometric corrections (BCs) from Alonso et al. (1999), to determine ${M}_{\mathrm{Bol}}$. The resulting gravities are presented in column (4) of Table 5.

The error budget for $\mathrm{log}\,g$ may be expressed as

$$\begin{eqnarray*}&&{\sigma }_{\mathrm{log}g}^{2}={(0.4)}^{2}\times ({\sigma }_{M}/{(2.302\times M)}^{2}+{(4)}^{2}\\ &&\quad \times ({\sigma }_{{T}_{\mathrm{eff}}}/{(2.302\times {T}_{\mathrm{eff}})}^{2}+{(0.4)}^{2}\times ({\sigma }_{V}^{2}+{\sigma }_{{(m-M)}_{V}}^{2}+{\sigma }_{\mathrm{BC}}^{2}).\end{eqnarray*}$$

We estimate the following representative errors: σ_M/M =0.26 assuming that the bulk of the stars in our sample have ages in the range of 5–12 Gyr and [α/Fe] in the range of −0.2 to 0.4 dex, together with the isochrones of Dotter et al. (2008),¹² and noting that this estimate is relatively insensitive to metal abundance; ${\sigma }_{{T}_{\mathrm{eff}}}$/${T}_{\mathrm{eff}}$ = 0.019 (Section 3.1.1); σ_V = 0.020 (Section 2.3); ${\sigma }_{{(m-M)}_{V}}$ = 0.110 (Section 3.1.1); and σ(BC) = 0.048 (following Alonso et al. 1999), with ${\sigma }_{{T}_{\mathrm{eff}}}$ = 80 K and ${\sigma }_{[\mathrm{Fe}/{\rm{H}}]}$ = 0.15 (Section 3.3). With these values σ_logg = 0.07 dex, and we note in passing that errors in ${T}_{\mathrm{eff}}$ are the dominant contributor to the total error budget.

3.1.3. Metal Abundance ([M/H])

Chemical abundances were determined by using the model atmosphere techniques described in Norris et al. (2010, Section 3), Yong et al. (2013, Section 2), and Gilmore et al. (2013, Section 3.1), to which we refer the reader. Here, we provide only some of the details of our procedures. As before, we adopted the ATLAS9 models of Castelli & Kurucz (2003)¹³ (plane-parallel, 1D, LTE), with α-enhancement [α/Fe] = +0.4 and microturbulent velocity ξ_t = 2 km s⁻¹. The analysis of the EWs presented in Section 2.5 used the LTE stellar-line-analysis program MOOG (Sneden 1973), as modified by Sobeck et al. (2011), to include an improved treatment of continuum scattering. We took into account hyperfine splitting (HFS) for lines of Sc, V, Mn, Co, Cu, and Ba, using data from Kurucz & Bell (1995), and for La, we adopted HFS data from Ivans et al. (2006). For Ba, we assumed the McWilliam (1998) r-process isotopic composition, while for Cu, we assumed solar isotope ratios. Once the atmospheric parameters ${T}_{\mathrm{eff}}$, $\mathrm{log}\,g$, and chemical abundance [M/H] are given, one needs to determine the microturbulent velocity, ξ_t. We achieved this by requiring that the abundance determined from the Fe i lines should be independent of their EWs. During this procedure, we excluded Fe i lines that fell more than either 3σ or 0.5 dex from the mean value. Values of ξ_t are presented in column (6) of Table 5. Other authors have noted that ξ_t is a function of $\mathrm{log}\,g$: we find ξ_t = 2.392–0.313 × $\mathrm{log}\,g$, with an rms scatter of 0.003 km s⁻¹, in excellent agreement with the relationship of Worley et al. (2013), who reported ξ_t = 2.386–0.313 × $\mathrm{log}\,g$. In our error analysis below, we shall adopt an error ${\sigma }_{{\xi }_{t}}$ = 0.2 km s⁻¹.

Detailed results of the abundance analysis are presented in Table 6. In the 32 blocks of this table (one per star) columns (1)–(4) contain the atomic species, the mean absolute abundance log (X) (=log(N_X/N_H) + 12.0), its standard error of the mean, s.e.${}_{\mathrm{log}\epsilon }$, and the number of lines analyzed, respectively. Column (5) presents [Fe/H] or [X/Fe], obtained by using the data in column (2) and the solar abundances of Asplund et al. (2009). In the calculation of [X/Fe], we adopted the value of [Fe/H] determined using the neutral species. Given the much larger number of Fe i lines, this leads to considerably higher precision in our relative abundances. Had we adopted [Fe ii/H], the precision of our [X/Fe] values would be considerably poorer given the small number (2–12) of available Fe ii lines. The question that then remains is, how accurate are the [X/Fe] results? In particular, what is the role of NLTE, which affects Fe i more than Fe ii? According to Lind et al. (2012, see their Figure 2), in our parameter range, the NLTE corrections are ≤+0.1 dex for Fe i and 0.0 for Fe ii. We shall discuss the role of these small effects in Section 6.

Table 6.  Chemical Abundances for 32 Carina Red Giants

Species	log $\epsilon$	s.e.${}_{\mathrm{log}\epsilon }$	N	[X/Fe]	σSys[X/Fe]	σTot[X/Fe]
(1)	(2)	(3)	(4)	(5)	(6)	(7)
CC06122
Fe i	6.07	0.02	74	−1.43a	0.14	0.14
O i	7.58	0.17	1	0.32	0.13	0.21
Na i	4.61	0.17	1	−0.20	0.08	0.19
Mg i	6.48	0.18	2	0.31	0.03	0.18
Al i	<5.38	0.17	1	<0.36	0.10	0.20
Si i	6.29	0.17	1	0.21	0.14	0.22
Ca i	5.09	0.04	19	0.09	0.02	0.04
Sc ii	1.89	0.14	5	0.17	0.11	0.18
Ti i	3.67	0.04	8	0.15	0.09	0.10
Ti ii	3.86	0.08	2	0.34	0.10	0.13
V i	2.43	0.11	10	−0.07	0.11	0.16
Cr i	4.20	0.06	4	−0.01	0.08	0.10
Mn i	3.68	0.04	5	−0.32	0.06	0.07
Fe ii	6.16	0.04	8	0.09	0.17	0.17
Co i	3.53	0.17	1	−0.03	0.08	0.19
Ni i	4.71	0.07	10	−0.08	0.05	0.09
Cu i	2.13	0.17	1	−0.63	0.08	0.19
Ba ii	1.19	0.08	3	0.44	0.11	0.14
La ii	0.16	0.08	3	0.49	0.10	0.13
Nd ii	⋯	⋯	⋯	⋯	⋯	⋯
Eu ii	⋯	⋯	⋯	⋯	⋯	⋯

Note.

^a[Fe/H].

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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The random internal error (s.e.${}_{\mathrm{log}\epsilon }$) of the abundances in column (3) of Table 6 is the standard error of the mean of the abundances from lines analyzed for each element. The abundances are also subject to systematic errors resulting from the uncertainties in our derived model parameters—${T}_{\mathrm{eff}}$, $\mathrm{log}\,g$, [M/H], and ξ_t. The uncertainties we adopt for these quantities are σ_Teff = 80 K (Section 3.1.1), ${\sigma }_{\mathrm{log}g}$ = 0.07 dex (Section 3.1.2), ${\sigma }_{[{\rm{M}}/{\rm{H}}]}$ = 0.15 dex (see below in this section), and ${\sigma }_{{\xi }_{t}}$ = 0.2 km s⁻¹ (Section 3.2). For each of our program stars we varied ${T}_{\mathrm{eff}}$, $\mathrm{log}\,g$, [M/H], and ξ_t, one at a time, by these uncertainties to determine the corresponding abundance differences. Since we shall be interested mainly in relative abundances, [X/Fe], we have determined the corresponding uncertainties in those quantities, while for iron we estimated the uncertainty in [Fe i/H]. To determine the total systematic error, we co-added the four error contributions as follows: first, given that the error in $\mathrm{log}\,g$ is determined primarily by uncertainty in ${T}_{\mathrm{eff}}$, we added the errors in ${T}_{\mathrm{eff}}$ and $\mathrm{log}\,g$ linearly; second, we then quadratically added this error to those associated with [M/H] and ξ_t. For heuristic purposes, Table 7 presents the average systematic abundance errors for the 32 program stars, where columns (1)–(6) contain the species, errors in ${T}_{\mathrm{eff}}$, $\mathrm{log}\,g$, [M/H], and ξ_t, and the total systematic error, respectively.

Table 7.  Average Abundance Uncertainties in [Fe/H] and [X/Fe]

Species	σTeff	${\sigma }_{\mathrm{log}g}$	${\sigma }_{[{\rm{M}}/{\rm{H}}]}$	${\sigma }_{{\xi }_{t}}$	${\sigma }_{[{\rm{X}}/\mathrm{Fe}]}$
	(80 K)	(0.07 dex)	(0.15 dex)	(0.2 km s−1)
(1)	(2)	(3)	(4)	(5)	(6)
Fe i a	0.109	−0.001	−0.015	−0.082	0.136
O i	−0.099	0.029	0.097	0.078	0.128
Na i	−0.043	−0.004	0.000	0.070	0.084
Mg i	−0.035	−0.008	0.002	0.018	0.047
Al i	−0.048	−0.002	0.004	0.077	0.092
Si i	−0.099	0.007	0.030	0.078	0.123
Ca i	−0.015	−0.005	−0.010	0.016	0.027
Sc ii	−0.115	0.028	0.074	0.042	0.111
Ti i	0.034	−0.004	−0.011	0.073	0.079
Ti ii	−0.116	0.026	0.069	0.007	0.104
V i	0.051	−0.004	−0.011	0.071	0.086
Cr i	0.050	−0.002	−0.021	−0.019	0.054
Mn i	0.025	−0.002	−0.006	0.052	0.057
Fe ii	−0.163	0.032	0.079	0.053	0.153
Co i	0.000	0.002	0.015	0.083	0.084
Ni i	−0.001	0.005	0.016	0.044	0.046
Cu i	0.004	0.004	0.016	0.086	0.087
Ba ii	−0.080	0.027	0.074	−0.064	0.100
La ii	−0.084	0.028	0.079	0.075	0.111
Nd ii	−0.082	0.028	0.073	0.051	0.092
Eu ii	−0.110	0.025	0.077	0.073	0.126

Note.

^aErrors pertain to uncertainties in [Fe/H].

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To determine total error estimates, we adopted the following procedure (see Norris et al. 2010). The random errors in column (3) of Table 6 are based on the dispersion in what is often a small number of lines, and hence are themselves uncertain. We replace this estimated random error, s.e.${}_{\mathrm{log}\epsilon }$, from N lines, by max(${{\rm{s.e.}}}_{\mathrm{log}\epsilon }$, ${{\rm{s.e.}}}_{\mathrm{log}\epsilon (\mathrm{Fe}{\rm{I}})}$ $\times$ $\sqrt{{N}_{\mathrm{Fe}{\rm{I}}}/N}$). The second term is what one might expect from a set of N lines having the dispersion we obtained from our more numerous (${N}_{\mathrm{Fe}{\rm{I}}}$) Fe i lines. We then quadratically combine this updated random error and that associated with uncertainty in the atmospheric parameters from column (6) of Table 6 to obtain the total error, σ[X/Fe], which we present in column (7) of Table 6. The mean of the total error σ[Fe/H] for the 32 stars in Table 6 is 0.14 dex, which agrees well with the uncertainty ${\sigma }_{[{\rm{M}}/{\rm{H}}]}=0.15$ dex we have adopted previously in this section.

We summarize our essential abundance results—[Fe/H] and relative abundances [X/Fe]—for the 32 red giants, in Table 8, where the column structure of the table will be self-evident. For each star there are three rows: the first presents abundances, the second the corresponding total abundance errors, and the third the number of lines involved.

In Figure 5 we compare our [Fe/H] values with those presented by Shetrone et al. (2003), Koch et al. (2006), Venn et al. (2012), Lemasle et al. (2012), and Fabrizio et al. (2012). The agreement in the figure is quite satisfactory, except that our values differ systematically from those of Fabrizio et al. (2012), for which there is considerable dispersion. At least part of the difference will result from the fact (see Section 2.5, Figure 4) that the EWs of Fabrizio et al. (2012) are on average smaller than those of the present work.

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We are now in a position to compare our atmospheric parameters with those of Shetrone et al. (2003), Koch et al. (2008), Venn et al. (2012), Lemasle et al. (2012), and Fabrizio et al. (2012). In what follows we present the mean differences in ${T}_{\mathrm{eff}}$, $\mathrm{log}\,g$, and [Fe/H] (in the sense present work — other work), together with N, the number of stars involved. For Shetrone et al. (2003) the differences are $\langle {\rm{\Delta }}{T}_{\mathrm{eff}}\rangle =42\pm 37\,{\rm{K}}$, $\langle {\rm{\Delta }}\mathrm{log}\,g\rangle =0.35\pm 0.07\,\mathrm{dex}$, $\langle {\rm{\Delta }}[\mathrm{Fe}/{\rm{H}}]\rangle =-0.01\pm 0.08,$ and N = 3; for Koch et al. (2008) they are $\langle {\rm{\Delta }}{T}_{\mathrm{eff}}\rangle \,=-95\pm 59\,{\rm{K}}$, $\langle {\rm{\Delta }}\mathrm{log}\,g\rangle =-0.49\pm 0.14\,\mathrm{dex}$, $\langle {\rm{\Delta }}[\mathrm{Fe}/{\rm{H}}]\rangle \,=0.01\pm 0.05$, and N = 6; for Venn et al. (2012) the corresponding values are 113 ± 26 K, 0.08 ± 0.01 dex, −0.07 ± 0.08, and 6; for Lemasle et al. (2012) they are 104 ± 11 K, 0.12 ± 0.03 dex, 0.08 ± 0.04, and 9; and for Fabrizio et al. (2012) they are 7 ± 8 K, 0.10 ± 0.01 dex, 0.33 ± 0.04, and 31. The most significant difference in this comparison is the abundance difference $\langle [\mathrm{Fe}/{\rm{H}}]\rangle =0.33\,\pm 0.04$ between Fabrizio et al. (2012) and the present work, given the good agreement between their ${T}_{\mathrm{eff}}$ and $\mathrm{log}\,g$ values with ours. We note for completeness that Fabrizio et al. (2015) reported that their [Fe/H] values are 0.37 dex smaller than those of Venn et al. (2012).

In Figure 6, we compare our [O/Fe], [Na/Fe], [Mg/Fe], and [Ca/Fe] relative abundances (one set in each of the vertical panels) with those of other works for which data are available—Koch et al. (2008) in the leftmost panel, Shetrone et al. (2003) and Venn et al. (2012) together in the next panel, then Lemasle et al. (2012), and finally Fabrizio et al. (2015) in the rightmost panel. Clearly, the agreement is less than ideal. That said, with typical S/N vales of 10–30 and the small number of lines available for the elements in the figure O (1), Na (1), Mg (1–2), and Ca (∼10–15), the results are not unexpected. Examination of the data for Ca, with ∼10–15 lines, where the scatter is smaller, is supportive of this view.

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In Figure 6 one also sees that there is larger scatter in the comparison with the abundances of Fabrizio et al. (2015), with a tendency to more supersolar values in the latter. This is a somewhat puzzling result, given that we would have expected the Fabrizio et al. (2012, 2015) values of both [Fe/H] and [X/H] (for element X) to be smaller that ours by similar amounts, and to some extent to cancel out in the relative abundance, [X/Fe]. We also comment that if one considers abundances relative to hydrogen, [X/H], rather than relative abundances [X/Fe], the disagreement seen in Figure 6 is significantly reduced. That is, if we define Δ[X/Fe] = [X/Fe]_{This work}–[X/Fe]_Fabrizio and Δ[X/H] = [X/H]_{This work}–[X/H]_Fabrizio for O, Na, Mg, and Ca, we find average values $\langle {\rm{\Delta }}[{\rm{O}}/\mathrm{Fe}]\rangle =0.23\,\pm 0.04$, $\langle {\rm{\Delta }}[\mathrm{Na}/\mathrm{Fe}]\rangle =0.49\pm 0.07$, $\langle {\rm{\Delta }}[\mathrm{Mg}/\mathrm{Fe}]\rangle =0.19\pm 0.05$, and $\langle {\rm{\Delta }}[\mathrm{Ca}/\mathrm{Fe}]\rangle =0.22\pm 0.03$, while in comparison we have $\langle {\rm{\Delta }}[{\rm{O}}/{\rm{H}}]\rangle =-0.09\pm 0.05$, $\langle {\rm{\Delta }}[\mathrm{Na}/{\rm{H}}]\rangle =0.15\pm 0.06$, $\langle {\rm{\Delta }}[\mathrm{Mg}/{\rm{H}}]\rangle =-0.13\pm 0.03$, and $\langle {\rm{\Delta }}[\mathrm{Ca}/{\rm{H}}]\rangle =-0.10\,\pm 0.04$. For all four elements, $\langle {\rm{\Delta }}[{\rm{X}}/{\rm{H}}]\rangle$ is closer to 0 than is $\langle {\rm{\Delta }}[{\rm{X}}/\mathrm{Fe}]\rangle$.

Further work at higher S/N is clearly needed if one is to fully understand the chemical enrichment of Carina.

Abundances of the literature stars were determined by using the procedures outlined in Section 3, for lines in common between our line list and those of the literature sample. There was only one significant difference in the analysis of the literature sample. This was driven by concern about the accuracy of the determination of microturbulence (ξ_t) resulting from the relatively small number of Fe i lines (∼15–30) available for some stars. In Section 3.2, we determined ξ_t by requiring that there should be no dependence of abundance on line strength. It became clear in our analysis of the literature data that having only a small number of Fe i lines could lead to significant uncertainty in ξ_t. As noted above in Section 3.2, an alternative estimate for ξ_t, used by some workers, is to adopt a generic value of ξ_t as a function of $\mathrm{log}\,g$ (e.g., Worley et al. 2013). Insofar as the latter method is independent of the number of Fe i lines and ξ_t is an artifact of 1D (as opposed to 3D) model atmospheres (Asplund et al. 2000), we investigated this as follows. In addition to determining ξ_t as described in Section 3.2, we repeated the analysis of the stars in Tables 1 and 9, with ξ_t defined by ξ_t = 2.39 − 0.31 × $\mathrm{log}\,g$, following Worley et al. (2013). Ideally, the abundances derived by the two methods should give the same results. To investigate how this might depend on the number of Fe i lines available, in Figure 7 we plot Δ[Fe/H], the difference between abundances obtained with the two different prescriptions for ξ_t, as a function of the number of Fe i lines. It is clear that the scatter increases significantly when the number of Fe i lines is smaller than ∼20. To overcome this problem, in what follows we accepted the abundances determined by using the formulaic value of ξ_t for the six most discrepant points in Figure 7 (Car-1087, MKV0556, MKV0577, MKV0733, MKV0743, MKV0812 in Table 9); otherwise, we adopted values obtained using ξ_t as described in Section 3.2.

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Our abundances for the literature samples are presented in Table 10 for the works of Venn et al. (2012) and Shetrone et al. (2003) and in Table 11 for that of Lemasle et al. (2012). The formatting in these tables is the same as in Table 8.

Oxygen and sodium abundances have been determined from only one line each in this analysis (Na i λ5688.2, [O i] λ6300.3; see Table 2). We have selected to restrict our analysis to these lines, which have EW measurements throughout our sample, are known to yield abundances in close accord with other features when these are available, and are in good agreement between various analyses (see, e.g., Venn et al. 2012, Sections 4.4.2 and 4.4.3). Our abundances do not appear to deviate wildly from Galactic halo values, although some stars do show abundances lower than those of the halo by 0.2–0.3 dex, particularly for sodium. As discussed by Venn et al. (2012), the production of sodium follows that of the α-elements until AGB stars contribute, and the latter contributions can be metallicity dependent. Thus, reasonable differences in the mean metallicity of the AGB stars in the Galactic halo versus those in Carina could account for the small differences in some stars.

The mean values, using weights equal to the inverse square of the errors, are $\langle [{\rm{O}}\,{\rm{I}}/\mathrm{Fe}]\rangle =0.46\pm 0.04$ and $\langle [\mathrm{Na}\,{\rm{I}}/\mathrm{Fe}]\rangle =-0.28\pm 0.04$, which may be compared with the Galactic halo values plotted in Figure 9 of 0.60 and 0.00, respectively. As pointed out to us by a referee, if one has low α relative abundances for Mg–Ti in Carina, as seen in our Figures 9–11, one might also expect a significant reduction in oxygen as well. We refer the reader to the work of Ramírez et al. (2012), which confirms the reduction of [O/Fe] in dwarfs of the Galactic halo having [Fe/H] <−0.8 and low relative abundances of the α-elements, Mg–Ti. One might claim that the lower values of [O/Fe] in some of the stars in Figure 9 might offer support for this requirement. That said, we are of the view that further work of considerably higher S/N than available here is needed to resolve this issue.

The most significant result from our data, however, is that there is no strong anticorrelation between the abundances of these two elements, in clear contrast to what is seen in all of the Galactic globular clusters. We shall return to this matter in Section 11.

The α-elements are built through He capture during various stages in the evolution of massive stars and dispersed through SN II events. Thus, the [α/Fe] ratio is a key tracer of the relative contributions of SN II to SN Ia products in a star-forming region. As discussed in Venn et al. (2012), Ti is not a true α-element. It behaves, however, like one since the dominant isotope ⁴⁸Ti forms through explosive Si burning and the α-rich freeze-out during a core-collapse SN event (Woosley & Weaver 1995). In our analysis, we examine 2 lines of Mg i, 3 of Si i, 22 of Ca i, 11 of Ti i, and 5 of Ti ii. Our Ti i and Ti ii abundances are in good agreement when both are measured in the same star, and therefore we average the abundances of the two species. The Mg ii lines near 5200 Å are too strong for the present analysis.

The mean values, using weights equal to the inverse square of the errors, are $\langle [\mathrm{Mg}/\mathrm{Fe}]\rangle =0.12\pm 0.02$, $\langle [\mathrm{Si}/\mathrm{Fe}]\rangle =0.28\,\pm 0.04,\langle [\mathrm{Ca}/\mathrm{Fe}]\rangle =0.04\pm 0.01$, and $\langle [\mathrm{Ti}/\mathrm{Fe}]\rangle =0.18\pm 0.01$. With the exception of Si, which is the least accurately measured, all of these fall below halo values (0.30 dex), which is a well-known signature of dSph systems, well documented for Carina by Shetrone et al. (2003) and Venn et al. (2012). We shall discuss this group of elements at some length in Section 7. An interesting effect that we shall emphasize there is that the quality of the data varies strongly between the four elements. Note the clearer tightness of the [Ca/Fe] versus [Fe/H] relationship in Figure 10, in some contrast to the looser ones for the other α-elements—driven, as we shall discuss in Section 7, by the considerably larger number of lines available for Ca in the wavelength range observed in the present investigation.

Massive stars (M > 8 M_⊙) provide the first contributions to the chemical elements, due to their short lifetimes, producing metals both during their evolution and during core-collapse SNe. It is currently thought that the iron-peak and odd-Z elements are synthesized in these core-collapse SNe through a variety of processes (explosive burning ranging from He to Si, α-rich freeze-out, a range in yields depending on neutron densities, explosion energies, mass of the progenitor, metallicity and initial composition, and the mass cut for the fraction expelled; see, e.g., Woosley & Weaver 1995; Nomoto et al. 2013; Pignatari et al. 2016). Abundances of these elements tend to show a strong odd–even effect in the predicted yields, where the odd-Z nuclei have lower abundances than those with even Z. Only at later times will lower-mass stars contribute to these elements through SN Ia events, possibly dominating the total iron-group inventory. The diversity of SNe Ia has been modeled by Kobayashi et al. (2015), ranging from single- and double-degenerate channels to rare types from hybrid white dwarfs, as well as their impact in metal-poor systems with stochastic star formation, such as Carina.

In general, our odd-Z elements (Sc, V, Mn) are measured from a small number of spectral lines (1–10) and include hyperfine structure corrections (see Section 3.2). The ranges seen in these abundance ratios are quite large, with Δ[Sc/Fe] and Δ[V/Fe] $\sim \,\pm 0.5$. The mean values for Sc and V, using weights equal to the inverse square of the errors, are $\langle [\mathrm{Sc}/\mathrm{Fe}]\rangle =0.00\pm 0.02$ and $\langle [{\rm{V}}/\mathrm{Fe}]\rangle =-0.05\pm 0.03$, while for Mn the value is $\langle [\mathrm{Mn}/\mathrm{Fe}]\rangle =-0.37\pm 0.01$. In comparison, the corresponding Galactic halo values are 0.10, 0.10, and −0.40. Only $\langle [\mathrm{Mn}\,{\rm{i}}/\mathrm{Fe}]\rangle$ tends to be above the Galactic halo data. Kobayashi et al. (2015) have predicted that in inhomogeneously mixed systems, an enhanced [Mn/Fe] value could indicate contributions from SN Iax models (a low-metallicity, hybrid white dwarf, in a close binary system).

Our iron-peak elements Cr and Ni are measured from a small number of lines (4–11) in most of the stars in our sample, and both are in excellent agreement with the Galactic halo trends. The mean values, using weights equal to the inverse square of the errors, are $\langle [\mathrm{Cr}/\mathrm{Fe}]\rangle =-0.07\pm 0.02$ and $\langle [\mathrm{Ni}/\mathrm{Fe}]\rangle =-0.10\pm 0.01$, which compare well with Galactic halo values of 0.00 and 0.00, respectively. We note that larger dispersions and errors are reported for these elements from the Lemasle et al. data set. Also, a small number of Co and Cu abundances are available for $\leqslant 10$ stars from one spectral line each (Co i λ5647.2 and Cu i λ5700.2). Both are limited to the more metal-rich stars in our sample. The [Co/Fe] ratios are in good agreement with the Galactic trend, while the [Cu/Fe] ratios may be slightly below the Galactic halo values. The nucleosynthesis of Cu is more complicated than most of the iron-group and odd-Z elements; for example, Cu can also have a significant contribution from the weak s-process in massive stars (e.g., Pignatari et al. 2016).

[Fe ii/Fe] provides a necessary and fundamental requirement of any chemical abundance analysis in which it can be determined. That is, a sound analysis should yield [Fe ii/Fe] = 0. Inspection of the middle column of Figure 10 shows that this expectation is not met, with the bulk of [Fe ii/Fe] values lying in the range of 0.0 to +0.5 dex. If one considers the results for the 31 stars plotted in the top panel (for which we presented new observational material and determined abundances in Sections 2 and 3), the mean value, determined using weights equal to the inverse square of the errors, is $\langle [\mathrm{Fe}\,{\rm{ii}}/\mathrm{Fe}]\rangle =0.25\pm 0.02$.

Inspection of Table 7 suggests that this is about two times larger than the uncertainties in the analysis, which are dominated for both elements by the uncertainties in ${T}_{\mathrm{eff}}$. In the table, one sees that an average error of Δ${T}_{\mathrm{eff}}$ = −80 K will lead to an error of Δ[Fe ii/Fe] = +0.15.

A second consideration is the overionization of Fe i by the radiation field in the atmosphere of a metal-poor red giant, which is neglected under the assumption of LTE. For the typical stellar parameters of our sample (${T}_{\mathrm{eff}}$ = 4500 K, $\mathrm{log}\,g$ = 1.0, [Fe/H] = −2.0 to −1.0), this effect is estimated to be ≤+0.1 dex (Lind et al. 2012). On the other hand, Mashonkina et al. (2016) find that for Fe i lines with EWs in the range 100–200 mÅ, the effect can be as large as +0.2 dex in the same stellar parameter regime.

Given the magnitude and sign of the NLTE corrections, the LTE Fe i and Fe ii abundances are not anomalous.

We have determined element abundances for four heavy-neutron-capture elements. These are formed in massive stars and core-collapse SNe through rapid neutron-capture reactions, and those other than Eu also form via slow neutron captures during the thermal pulsing AGB stages in intermediate-mass stars. The specific details of these nucleosynthetic processes are a dynamic field of current research. For the core-collapse SNe, new models and calculations of their yields include details of the SN explosion energies, explosion symmetries, early rotation rates, and metallicity distributions (see, e.g., Kratz et al. 2014; Nishimura et al. 2015; Tsujimoto & Nishimura 2015; Pignatari et al. 2016), as well as exploration of contributions from compact binary mergers as a (or as the most) significant site for the r-process (e.g., see Fryer et al. 2012; Korobkin et al. 2012; Perego et al. 2014; Côté et al. 2017). Similarly, predictive yields from AGB stars by mass, age, metallicity distributions, and details of convective-reactive mixing are also an active field of research (see, e.g., Lugaro et al. 2014; Cristallo et al. 2015; Pignatari et al. 2016).

Our abundances for Ba, La, Nd, and Eu are from only a few lines; for example, Eu ii λ6645.1 and Nd ii λ5319.8 are from only the one line each. Barium and lanthanum are from three and four spectral lines each, respectively, but the Ba ii lines tend to be strong, whereas the La ii lines tend to be weak (or absent). There is a tendency in the relative abundances of these four elements to be similar to or higher than those for stars in the Galactic halo at metallicities [Fe/H] $\geqslant \,-\,2.0$, where the highest abundances tend to occur for [La/Fe] and [Ba/Fe]—in all samples (Shetrone et al. 2003; Lemasle et al. 2012; Venn et al. 2012; this paper). We do not interpret this as due to uncertainties in our abundances but rather to a real astrophysical effect; for example, the bulk of our sample has a full range of [Ba/Fe] ∼ 0.0 to +0.5, with 〈[Ba/Fe]〉 = 0.17 ± 0.02 (weighted by the inverse square of the errors, and where we somewhat arbitrarily exclude the two objects with [Ba/Fe] < −0.50). In comparison, the Galactic halo value is [Ba/Fe] = −0.10. The 1σ offset due to ΔT_eff $=\,+\,80$ K (see Table 7) leads to an error of Δ[Ba/Fe] = −0.08, which lessens but does not eliminate the offset from the bulk of the Galactic stars. These offsets are similar for La, Nd, and Eu. This abundance signature is typically seen in dwarf galaxies (see Tolstoy et al. 2009) and interpreted in terms of higher yields of Ba (second-peak s-process element, and thus also La and Nd) from metal-poor AGB stars. What is more surprising are the low [Ba/Fe] values (and even two stars with low [Nd/Fe]) at high metallicities. Venn et al. (2012) interpreted this signature in terms of inhomogeneous mixing in the Carina ISM with pockets of iron-rich SN Ia gas. We shall return to this topic in Section 8.

The α-elements comprise O, Ne, Mg, Si, S, Ar, Ca, Ti (e.g., VandenBerg et al. 2006), while in practice in the present work the available elements are O, Mg, Si, Ca, and Ti—with O and Si determined in only a minority of the sample. This leads to a number of complicating factors concerning the comparison between observation and theory, of which we mention two. The first is that given the results of stellar evolution and nucleosynthesis calculations for massive stars (e.g., Woosley & Weaver 1995), the possibility exists that in the metal-poor regime the α-elements might have a nonsolar relative distribution. This leads to the difficulty that stellar evolution isochrone grids that assume scaled-solar α-ratios will be inaccurate at some unknown level. How does one best compare observation with theory? VandenBerg et al. (2015) have argued that since Mg has a greater relative abundance than the other α-elements, it should therefore be a better probe than the other elements (in particular, the more readily and accurately observed Ca) given that it has a greater effect on a star's evolution. The second point is that, in our opinion, only the abundance of Ca is well determined in currently available RGB samples of Carina. This situation is driven by the small numbers of lines available for analysis (on average 1.8, 0.8, 14.6, and 2.5 lines for Mg i, Si i, Ca i, and Ti ii, respectively) and the relatively low S/N (7–23) per 0.03 Å pixel for the majority of stars having full wavelength coverage in the present analysis. Against this background, we seek to address two questions. First, is there evidence for differences in the relative abundances of the α-elements, one from another—in particular, does [Mg/Ca] differ from the solar value of zero? Second, do the α-abundances change as a function of [Fe/H], in both size and dispersion?

As a first approach, we present in Figure 16 two comparisons of light α- and heavy α-elements versus [Fe/H], together with their difference as a function of [Fe/H], based on the data presented in Figures 9–14. The top panels of each column contain light α-elements, while the middle panels present heavy ones. The bottom panels show the difference between the light and heavy species. One sees that, below [Fe/H] =−1.2, on average the difference between the two species is not large, of order 0.1 dex, with a hint of a dependence on [Fe/H]. For the complete Carina sample in the bottom right panel, $\langle [\mathrm{Mg}/\mathrm{Ca}]\rangle =0.12\pm 0.03$. It will be interesting to see whether data of higher quality support these results.

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A fundamental result of abundance studies of the dSph galaxies is that the α-elements exhibit a very different behavior with respect to [Fe/H], when compared with that found in Galactic halo stars. That is, while the latter exhibit relatively constant and enhanced values of [α/Fe] $\sim \,0.3-0.5$ for [Fe/H] < −1.0, which decrease to ∼0.0 as [Fe/H] decreases to 0.0, for dSph systems the decrease of the α-elements to solar values begins at much lower values of [Fe/H] $\sim \,-1.5$ to −2.0 (see, e.g., Tolstoy et al. 2009). This behavior is understood in terms of different rates of star formation between the two types of systems, in which the dwarf galaxies have lower star formation rates and SNe Ia play a larger role at lower [Fe/H] in reducing [α/Fe] than occurred in the Galactic halo (see, e.g., Gilmore & Wyse 1991). In Carina, the present data suggest that on average the abundance of the α-elements, in particular that of the most accurately measured element, Ca, is lower than Galactic halo values by ∼0.2 dex at all values of [Fe/H], below $\sim -1.0$. We shall return to this in Section 7.3.

A second fundamental relationship involving [α/Fe] is its distribution function, and of considerable importance is the comparison of the Carina distribution with that of the Galactic halo. In Figure 17 we present [α/Fe] values for Mg, Si, Ca, and Ti determined for the Galactic halo, Carina, and the globular cluster ω Cen. (We include ω Cen insofar as it may be of interest given that it is a Galactic globular cluster of baryonic mass 4.0 $\times \,{10}^{6}$ M_⊙ [D'Souza & Rix 2013], similar to that of Carina, and which has chemically enriched itself not only in the light elements but also in iron.) See the figure caption for sample details. We caution that while individual studies might be internally consistent, there are likely to be small zero-point offsets between the various works. The format of Figure 17 is similar to that of Figure 16, and the top four panels in each column present results for Mg, Si, Ca, and Ti, taken from sources listed in the figure caption, while in the bottom panel the value of [α/Fe] is determined by averaging [Mg i/Fe], [Ca i/Fe], and [Ti ii/Fe] when all three quantities are available. In the interest of obtaining the most reliable result for Carina, we have required that a value only be accepted when a star has no fewer than two lines available for each element, and we have weighted the individual abundances by the inverse square of their errors. (We made exceptions for three stars, Car-1087, Car-5070, and Car-7002, which have only one line of Mg and/or Ti but the highest S/N [∼30] in the sample.) The data for the 30 Carina giants that meet these criteria are presented in Table 12 and were used to determine the [α/Fe] distribution function presented in the bottom panel of Figure 18, where the thick red line is based on the means of Mg, Ca, and Ti determined by using weights inversely proportional to the inverse square errors in abundance, while the thin black line presents results when equal weights are assumed. In the top panel the distribution function is presented for the Galactic halo (over the range −3.0 < [Fe/H] < −1.0).

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We make the following points concerning Figures 17 and 18: (i) As noted above, for Carina, our spectroscopic [α/Fe] distribution is determined in large part by that of Ca, given the higher precision of the [Ca/Fe] values. That being said, the lower accuracy of Mg and Ti causes the two distributions in Figure 18 to be offset by only Δ[α/Fe] ∼ 0.05 dex. (ii) The weighted [α/Fe] distribution for Carina is smaller by ∼0.25 dex than that of the Galactic halo. As noted above, the Galactic halo data come from a number of studies and could be affected by zero-point offsets. Inspection of the four halo data sets (Fulbright 2000; Preston & Sneden 2000; Barklem et al. 2005; Yong et al. 2013) plotted in the left panel of Figure 17, however, suggests that this is not the case insofar as each of them has $\langle [\alpha /\mathrm{Fe}]\rangle$ ∼ 0.3. (iii) In Carina, the observed spread in [α/Fe] is small, with dispersion 0.13 ±  0.02 dex. (iv) While the number of stars is not large at lowest abundance, for [Fe/H] < −2.0 one finds $\langle [\alpha /\mathrm{Fe}]\rangle =0.04\pm 0.08$, which is small compared with the higher values of [α/Fe] that one associates with the Galactic halo (i.e., [α/Fe] $\sim \,0.3-0.4$). (v) While more data are required, there appear to be stars with low values of [α/Fe] $\sim \,-0.2$ over the entire range −2.0 < [Fe/H] < −1.0 (where some 80% of the sample lies).

The final two points are of considerable importance. If point (iv) obtains, the absence of Galactic-halo-like [α/Fe] values ([α/Fe] $\sim \,0.3\mbox{--}0.4$) on the RGB would suggest that all of the Carina stars currently observed to date at high resolution formed from material enriched by ejecta from either SNe Ia (e.g., Tolstoy et al. 2009, and references therein) or SNe II in a population having a mass function skewed toward lowest masses (e.g., Kobayashi et al. 2006; Kobayashi & Nakasato 2011), both of which lead to lower [α/Fe] values in subsequent generations. We shall return to point (v) in the next subsection.

The improved data presented in this section may also be used to readdress the question of the dependence of [α/Fe] on atomic species discussed in Section 7.1. Figure 19 presents the dependence of [Mg/Ca] on [Fe/H] for the Galactic halo and Carina, for the samples discussed in the present section and defined in Figure 17, for stars for which both Mg and Ca abundances are available. As noted above, this Carina sample contains only 30 stars, with somewhat conservative selection criteria, and as such might be expected to be of higher quality than the results discussed in Section 7.1. The result in the right panel of Figure 19 leads essentially to the same conclusion as reported in Section 7.1: the difference between the [Mg/Fe] and [Ca/Fe] distributions of Carina is essentially the same, with a mean value of $\langle [\mathrm{Mg}/\mathrm{Ca}]\rangle =0.13\pm 0.03$. For the halo sample in Figure 19 the mean value is $\langle [\mathrm{Mg}/\mathrm{Ca}]\rangle \,=\,-0.025\pm 0.008$.

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We complete this section with a comment on the asymmetry of the [α/Fe] distribution function seen in Figure 18 and the distribution of stars in the ([Ca/Fe], [Fe/H])–plane, where we use [Ca/Fe] as proxy for [α/Fe], recalling that Ca has the most accurately determined abundances among the α-elements. The main point is that the asymmetry of the [α/Fe] distribution function to smaller values of [α/Fe] in Figure 18 is clear. To investigate this further, in Figure 20, in the top panel, we reproduce the [Ca/Fe] results from Figure 10 (second panel from the bottom), and in the bottom panel we present only the higher-quality data in the sample that have errors σ[Ca/Fe] < 0.15. As noted in the previous section (point (v)) and seen more clearly in the bottom panel, there are stars with low values of [Ca/Fe] (i.e., below ∼0.0 dex) at all values of [Fe/H], most significantly in the range −2.0 < [Fe/H] < −1.0, where the density of points is highest. While more and better data are needed, the existence of low [Ca/Fe] values at all [Fe/H] drives the asymmetry of the [α/Fe] distribution function at all values of [Fe/H] and is very likely indicative of inhomogeneous mixing of the ejecta of SNe within each of Carina's generations, between the relatively α-element-poor ejecta from SNe Ia and the ambient medium during the several formation epochs of Carina's populations.

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In Section 5 of Paper I, we discussed the shortcoming of our first population in that while we described it as monomodal with mean metallicity [Fe/H] = −1.85 and with very little spread (Δ[Fe/H] ∼ 0.1), there are in the literature high-resolution spectroscopic abundance analyses of some five Carina red giants with abundances in the range −2.9 < [Fe/H] $\leqslant$ −2.5. The present work essentially confirms this result: while in our Table 15 there is only one star with [Fe/H] < −2.5, there are eight with [Fe/H] < −2.0. Of these, three are also present in the literature sample with −2.9 < [Fe/H] $\leqslant$ −2.5.

In Paper I we determined a mean age and metallicity for each of the four populations, with which we associated spreads in age and metallicity. As discussed there, however, given available information, these spreads were not well constrained. There are a number of possible explanations for the absence of stars with [Fe/H] < −2.0 in our model. One is that our first population is multimodal, and that in Paper I we essentially identified only a major subcomponent of the oldest population, while there exists a more metal-poor, presumably older and minor subcomponent as well.²¹ While this is outside the scope of the present work and we shall not consider it further, it is tempting to conjecture that this minor component contains the first stars to form in Carina. Other, more detailed possibilities include simple inhomogeneous mixing of the early star-forming gas (e.g., Revaz & Jablonka 2012) and/or active accretion of lower-mass systems in the earliest stages of Carina's formation, such as described by the models of Wise et al. (2012).