STELLAR NUCLEOSYNTHESIS IN THE HYADES OPEN CLUSTER^*

Figure 1 shows the composition profiles after the end of core H burning, before the first dredge-up of our 2.5 M_☉ stellar model. Figure 2 shows the composition profiles after the first dredge-up but before core He burning ignites. The first dredge-up lasts a very short time (∼1.5 × 10⁷ yr) relative to the duration of core H (5.12 × 10⁸ yr) or core He burning (∼2.8 × 10⁸ yr). However, many isotopic surface abundances change dramatically during the dredge-up process.

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Comparing the energy generation rate of the proton–proton (p–p) chains with that of the CNO bi-cycle we find that a star with a mass larger than ∼1.3M_☉ or having a central temperature greater than ∼1.7 × 10⁷ K has its energy generation dominated by the CNO bi-cycle (Arnett 1996). To understand the features of the composition profiles in Figure 1, we look at the properties of the p–p chains, CNO bi-cycle (Clayton 1968), and the NeNa and MgAl cycles (Rolfs & Rodney 1988). Examining the profiles from the surface inward, the temperature in the star increases, and we note the first observable consequence of the p–p chains, i.e., the destruction of ⁷Li through ⁷Li(p,α)⁴He reaction (T ≳ 3.8 × 10⁶ K). Somewhat further inward, we encounter the location where most of the ¹⁰B has been destroyed through the ¹⁰B(p,α)⁷Li reaction (T ≳ 6.0 × 10⁶ K). During the early evolution of H burning, the ⁷Li and ¹⁰B profiles trail each other as their steep destruction profiles move further outward. Furthermore, due to their steep profiles and their proximity in the stellar atmosphere, the mass–thickness ratio of the ⁷Li and ¹⁰B profiles before the first dredge-up can be estimated by the ⁷Li and ¹⁰B abundance ratios in the dwarf and giant stars. Further inward, we find another product of the p–p chains, ³He, that was predominantly produced through ²D(p,γ)³He (T ≳ 7.7 × 10⁶ K). However, at higher temperatures (T ≳ 13.5 × 10⁶ K), ³He is predominantly self-destructed through ³He(³He,2p)⁴He reactions.

With respect to the CNO bi-cycle, the first effective reaction sequence at low temperature (T ≳ 10.2 × 10⁶ K) is the CN cycle, ¹²C(p,γ)¹³N(e⁺ν)¹³C(p,γ)¹⁴N(p,γ)¹⁵O(e⁺ν)¹⁵N(p,α)¹²C. The CN cycle starts by depleting ¹²C and producing ¹³C, which is then converted predominantly into ¹⁴N; the initial abundance of ¹⁵N is also depleted. The steady-state abundances of the secondary nuclei ¹³C and ¹⁵N are a function of temperature, such that there is a peak of ¹³C and a valley of ¹⁵N abundances and an equilibrium ratio of ¹⁵N/¹⁴N (horizontal sections of ¹⁴N and ¹⁵N curves).

Further inward where the temperatures are higher (T ≳ 13.2 × 10⁶ K), the ON cycle becomes effective, resulting in the production of ¹⁷O and the depletion of ¹⁶O and ¹⁸O through ¹⁶O(p,γ)¹⁷F(e⁺ν)¹⁷O and ¹⁸O(p,α)¹⁵N reactions, respectively. Approaching the previously convective core, the abundances of ¹²C, ¹³C, ¹⁷O, and ¹⁸O increase, as does that of ²³Na, indicating the action of the NeNa cycle. At these high temperatures (T ≳ 15 × 10⁶ K), the ²²Ne(p,γ)²³Na reaction depletes ²²Ne and produces ²³Na; the consequence of this reaction is that any surface abundance enhancement in ²³Na should be accompanied by the concomitant reduction in ²²Ne by approximately the same amount by number.

As noticed by El Eid (1994), inside the H convective core the CNO bi-cycle reaches an equilibrium state, and all O isotopes and ¹⁹F are depleted. On the contrary, ¹⁴N and ⁴He are strongly produced together, accompanied by the enhancements in ¹²C and ¹³C. In Figure 3, we show the ratio of the surface abundance before and after the first dredge-up. Enhancements of surface abundances, ranked from the largest to the smallest, are ¹⁷O, ³He, ¹³C, ¹⁴N, ²³Na, and ⁴He. Reductions of surface abundances, ranked from the largest to the smallest, are ⁷Li, ¹⁰B, ¹⁵N, ¹²C, ¹⁸O, ²²Ne, ¹⁶O, and ¹⁹F. The ranking shows the relative degree of sensitivity required for dwarf and giant observations to detect the dredge-up process.

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High-resolution, high signal-to-noise ratio (S/N) spectra of our Hyades sample were obtained with the Harlan J. Smith 2.7 m telescope and the"2dcoude" cross-dispersed echelle spectrometer at the McDonald Observatory in 2004 October. The instrument configuration and spectra have been described previously in Schuler et al. (2006b). The nominal spectral resolution of our data is R = λ/Δλ ≈ 60, 000 (∼2.1 pixels), with a typical S/N ratio of 150–200 for the dwarfs and 400–600 for the giants. Reductions of the spectra followed standard routines for bias subtraction, flat-fielding, scattered light removal, order extraction, and wavelength calibration using the IRAF⁵ package.

Additional spectra of the Hyades giants were obtained with the Harlan J. Smith 2.7 m telescope and the 2dcoude cross-dispersed echelle spectrometer on 2008 March 18. The instrument configuration included the cs23 setting, E2 echelle grating, TK3 detector with 24 μm pixels, and a 1 × 1 pixel binning, resulting in a nominal resolving power of R = 60, 000. This configuration matches exactly that from our 2004 October observations except for the echelle grating position, which was set in the more recent observations to maximize throughput in the 8727 Å [C i] region. Two 240 s integrations were taken of each γ, δ, and Tau, resulting in S/N ratios of 365, 495, and 590, respectively, in the λ8727 region.

The stars used for the current analysis are a subset of our larger Hyades sample for which we have high-S/N, high-resolution spectra. Stellar parameters have been derived in a consistent manner for our entire Hyades dwarf sample using published photometry for T_eff, the Y² isochrones (Yi et al. 2003) for log g, and the empirical relation of Allende Prieto et al. (2004) for microturbulent velocity (ξ). For the giants, the stellar parameters have been collated from the literature. The derivation and adoption of the stellar parameters are described in Schuler et al. (2006a, 2006b), where a discussion of the related uncertainties can also be found. The stellar parameters of the current sample are given in Table 1. The adopted uncertainties in the stellar parameters are provided in the footnotes of Table 1; these uncertainties are the uncertainties in the absolute stellar parameters and are most appropriate for estimating the uncertainties in the derived dwarf and giant abundances. We note that the relative parameter uncertainties between the dwarfs themselves or between the giants themselves are likely smaller.

Table 1. Hyades Parameters and LTE Abundances

	HIP 14976	HIP 19793	HIP 21099	γ Tau	δ Tau	Tau
Parameters
Teff (K)a	5487	5722	5487	4965	4938	4911
log g (cgs)b	4.54	4.49	4.54	2.63	2.69	2.57
ξ (km s−1)	1.24	1.34	1.24	1.32	1.40	1.47
Abundances
log N(Li)	1.51	2.36	1.20	1.06	0.93	0.72
log N(C)
CH	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	8.16	⋅⋅⋅	⋅⋅⋅
C2	8.57	8.48	8.56	8.18	8.15	8.13
[C i]	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	8.16	8.21	8.19
log N(N)	7.62	⋅⋅⋅	7.53	8.01	7.95	7.90
log N(O)	8.74	8.82	8.84	8.74	8.80	8.76
[Na/H]	0.06	0.13	0.07	0.63	0.58	0.61
[Mg/H]	0.09	0.09	0.12	0.57	0.50	0.57
[Al/H]	0.09	0.12	0.11	0.34	0.30	0.35

Notes. ^aThe 1σ_s.d. errors in T_eff are 55 and 75 K for the dwarfs and giants, respectively. ^bThe 1σ_s.d. errors in log g are 0.10 and 0.15 dex for the dwarfs and giants, respectively.

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The chemical abundances presented herein have been derived by means of a local thermodynamic equilibrium (LTE) analysis using an updated version of MOOG, the LTE line analysis and spectrum synthesis software package (Sneden 1973; C. Sneden 2004, private communication). Model atmospheres used in the analyses were interpolated from Kurucz ATLAS9 grids generated with the convective overshoot approximation and are the same as those used in our previous Hyades studies (Schuler et al. 2006a, b). The method and atomic parameters used to derive the CNO abundances are described below.

3.3.1. Carbon

Multiple features have been used to derive the C abundances of the Hyades stars in our sample. The primary features used for this purpose are two lines of the C₂ Swan system located at 5086.3 and 5135.6 Å, although reliable measurements could only be made of the latter in the spectra of the giants. The C₂ features are blends of multiple components of the C₂ system, and therefore the abundances were derived using the spectrum synthesis method (Figure 4). The linelists for these features have been constructed using atomic data from the Vienna Atomic Line Database (VALD; Piskunov et al. 1995; Ryabchikova et al. 1997; Kupka et al. 1999, 2000) and C₂ molecular data from Lambert & Ries (1981). The transition probabilities (log gf) of the C₂ and other features have been altered slightly from those given by Lambert & Reis in order to fit the λ5086 and λ5135 C₂ features in the Kurucz solar atlas assuming a solar C abundance of A_☉(C) = log N_☉(C) = 8.39 (Asplund et al. 2005a).

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Carbon abundances of the giants have also been derived using spectral synthesis of the forbidden [C i] line at 8727.13 Å. The λ8727 [C i] line arises from an electric quadrapole (D¹₂–S¹₀) transition that is strongly coupled through collisions to the C i ground state, which is populated according to Boltzmann statistics. Its strong collisional coupling to the ground state ensures that the [C i] transition also obeys Boltzmann statistics and that the λ8727 line forms in LTE (Stürenburg & Holweger 1990). Temperature inhomogeneities due to photospheric granulation, the so-called three-dimensional (3D) effects, are also not expected to greatly affect this line; 3D corrections for the Sun and other solar-type stars have been calculated to be ⩽0.05 dex (Asplund 2005). For solar-metallicity giants, the correction is of similar magnitude but positive (M. Asplund 2008, private communication). Thus, the λ8727 [C i] line is expected to be an accurate abundance indicator for the Hyades giants. We adopt the transition probability (log gf = −8.136) for this line from Allende Prieto et al. (2002), and the linelist of the surrounding features has been constructed using atomic data from VALD and CN molecular data from Gustafsson et al. (1999). As first identified by Lambert & Swings (1967), the λ8727 C i feature is blended with a weak Fe i line at 8727.10 Å. This Fe i line has been determined to contribute negligibly to the [C i] line strength in the solar spectrum (e.g., Lambert & Swings 1967; Gustafsson et al. 1999; Allende Prieto et al. 2002), but Bensby & Feltzing (2006) found that the Fe i line contributes more significantly to the λ8727 feature in the spectra of stars with T_eff < 5700 K and those at high [Fe/H]. The Hyades giants (T_eff ∼ 4940 K, [Fe/H] = +0.13) meet both of these criteria, and thus we have included the Fe i line in our linelist. The synthetic fit to the [C i] line in the spectrum of γ Tau is shown in Figure 5 as an example of our results.

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In addition to the forbidden [C i] and the C₂ Swan lines, we have analyzed 10 CH molecular features in the wavelength interval of 4323–4327 Å in the spectrum of γ Tau. Abundances were derived by fitting a synthetic spectrum to each individual line so that 10 separate abundance estimates were obtained. Similar to the procedure used for C₂, the linelist for the 4325 Å region has been calibrated by fitting the Kurucz solar atlas assuming a solar C abundance of A_☉(C) = 8.39.

The C abundances derived from the various features described above are given in Table 1. The mean abundance of the three dwarfs is A(C) = 8.54 ± 0.03 (uncertainty in the mean: $\sigma _{\mu } = \sigma _{{\rm s.d.}} / \sqrt{N-1}$), corresponding to a relative abundance of [C/H] = +0.15 when adopting the solar abundance of A_☉(C) = 8.39. The fits to the C₂ Swan lines in the dwarf spectra are only mildly sensitive to the adopted T_eff and log g (Table 2), and we estimate the per star uncertainty due to fitting synthetic spectra to the observed blended features is ±0.05 dex. The typical total per star uncertainty in the derived dwarf C abundances, which is obtained by adding in quadrature the individual uncertainties due to the adopted parameters and synthetic fits, is ±0.07 dex. Inasmuch as the standard deviation about the mean is an empirical measure of actual scatter introduced by measurement and parameter uncertainties, the slight difference in the standard deviation about the mean dwarf abundance (σ_s.d. = 0.05) and our estimated total per star uncertainty (±0.07 dex) suggests that, if anything, we slightly overestimate the expected uncertainties in the relative dwarf parameters based upon the adopted parameter uncertainties listed in Table 1.

Table 2. Abundance Sensitivities

Species	ΔTeff (±150 K)	Δlog g (±0.25 dex)	Δξ (±0.30 km s−1)
Dwarfs
C2	±0.03	±0.03	0.00
N	±0.25	∓0.05	0.00
O	±0.01	±0.11	0.00
Na	∓0.09	±0.06	±0.02
Mg	∓0.08	±0.05	±0.07
Al	∓0.06	±0.05	±0.02
Giants
C2	+0.10−0.18	+0.04−0.01	0.00
[C i]	−0.08+0.12	±0.15	0.00
N	±0.37	∓0.03	0.00
O	0.00	±0.12	0.00
Na	∓0.13	±0.05	±0.09
Mg	∓0.10	±0.04	±0.13
Al	∓0.08	±0.03	±0.07

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Our mean dwarf abundance of [C/H] = +0.15 is consistent with previously derived values, which range from [C/H] = +0.02 to [C/H] = +0.18 (Tomkin & Lambert 1978; Friel & Boesgaard 1990; Varenne & Monier 1999; Schuler et al. 2006a). All of the previously derived C abundances for Hyades dwarfs are from analyses of high-excitation C i lines; these lines are known to be sensitive to non-LTE (NLTE) effects in solar-type stars (Asplund 2005) and potentially over-excitation effects in late-G and K dwarfs (Schuler et al. 2004). The C₂ lines, which arise from electronic transitions, are not expected to be influenced by NLTE effects in solar-type stars (Asplund et al. 2005b), and the abundances of the Hyades dwarfs presented here should need no NLTE corrections.

The C abundances of the giants, derived from the three different C spectral features, are in excellent agreement and have a mean value of A(C) = 8.17 ± 0.01 (uncertainty in the mean) or [C/H] = −0.22. The shape of the λ5135 C₂ feature is much less affected by blends in the spectra of the giants (Figure 4), and the uncertainty in the synthetic fit is lower than that for the dwarfs and is in fact negligible relative to the errors due to the adopted T_eff. The typical per star uncertainty in the C₂-based abundances of the giants, dominated by uncertainties in the parameters, is ±0.09 dex. Similar to C₂, total per star uncertainties in the [C i]-based abundances are dominated by uncertainties in T_eff and log g and have a typical value of ±0.11 dex. The expected standard deviation about the mean giant C abundance is thus ∼0.10 dex, significantly larger than the observed value of 0.03 dex; it could be the case that the inferred uncertainty in the observed mean abundance is a systematically low fluctuation from the expected uncertainty in the mean. Also, the difference in the observed and expected standard deviations about the mean could suggest that the uncertainties in the giants' relative parameters, particularly T_eff, are significantly smaller than the uncertainties we have adopted (Table 1).

The concordance in the abundances derived from the various C features for each giant is not unspectacular given the potential issues involved with deriving abundances of evolved stars from the set of spectral lines presented here. The [C i] feature is blended with a Fe i line that may be problematic in the spectra of metal-rich giants, as described above. The molecular features may also suffer from unidentified or inaccurately modeled blends in the spectra of evolved stars, as well as possibly being influenced by 3D effects due to their acute temperature sensitivity. The consistency of the abundances suggests that neither blending features, NLTE effects, nor three-dimensional effects are a concern for these atomic and molecular lines in the Hyades giants. Our derived mean abundance is in excellent agreement with that of Lambert & Ries (1981), who found a mean abundance of [C/H] = −0.20 (σ_μ = 0.01) with typical uncertainties of ±0.15 dex, and with the more recent work of Mishenina et al. (2006). In the latter study, the authors derived the abundances of 177 local field clump giants, including the three Hyades giants included in our study plus the fourth giant in the cluster, θ¹ Tau. These authors find for the Hyades giants a mean abundance of [C/H] = −0.23 (σ_μ = 0.03), with a typical uncertainty of ±0.20 dex.

3.3.2. Nitrogen

3.3.3. Oxygen

Qualitatively, the observed dwarf and giant CNO abundances follow the predicted chemical evolution of our stellar model (Figure 3). Relative to the dwarfs, the giants' C is depleted, N enhanced, and O essentially unchanged. This abundance pattern is indicative of the CN cycle and first dredge-up mixing. The lack of variation in the observed O abundances further indicates that the expanding surface convection zone did not extend deep enough to reach material processed by the ON cycle.

A more quantitative comparison verifies that the observed N and O abundances are in excellent agreement with predictions. The surface abundances of our model—in both mass fraction (X) and logarithmic form—before and after the first dredge-up are given in Table 3. The surface ¹⁴N abundance is predicted to increase by a factor of 2.3 after the first dredge-up. The observed mean N abundance (Table 1) of the giants, A(N) = 7.95, is a factor of 2.3 higher than that of the dwarfs, A(N) = 7.58, in perfect concordance with the prediction. The ¹⁶O mass fraction is predicted to change only slightly, by less than 3%, after the first dredge-up. This small change is not manifested in the logarithmic abundances seen in Table 3 because of a similarly small dip in the H mass fraction. Regardless, this minute difference in O abundance would be lost in observational uncertainty and is considered negligible. Our observed O abundances of the dwarfs and giants, which are statistically indistinguishable, agree with the model.

The consistent observational and computational results do not extend to C. Observationally, the Hyades giants have a C abundance that is a factor of 2.33 (0.37 dex) lower than the dwarfs. The surface ¹²C abundance of the model is depleted by a factor of 1.5 (0.19 dex) after the first dredge-up. The observed C abundance of the giants compared to that of the dwarfs is 0.18 dex, or about a factor of 1.5, lower than the model prediction. As a consequence, the sum of C+N+O is not constant; the abundance of the giants (A(C +  N +  O) = 8.91) is only 79% of that for the dwarfs (A(C +  N +  O) = 9.01). The model predicts that this sum should remain unchanged as a MS dwarf evolves to the RGB giant clump.

The difference in the observed and modeled ¹²C abundances cannot be attributed to the random uncertainties in the mean observed abundances, which are σ_μ = 0.03 and 0.01 for the dwarfs and giants, respectively; the 0.18 dex discrepancy represents a ∼6σ_μ result. As discussed in Section 3.3.1, the observed standard deviation about the mean abundance (σ_s.d. = 0.03) of the giants is significantly smaller than the expected value (0.10 dex) estimated by the total per star measurement and stellar parameter uncertainties. This expected standard deviation, as well as that for the dwarfs (0.07 dex), leads to expected uncertainties in the mean abundances of σ_μ = 0.05 and 0.04 for the dwarfs and giants, respectively. The expected uncertainty in the dwarf-giant abundance difference is then 0.064 dex, and the observed 0.18 dex discrepancy is still significant at a ∼3σ_μ level.

Uncertainties in the mean (actual or expected) are a measure (empirical or theoretical) of the internal random uncertainties introduced into the analysis from the relative measurement and parameter (T_eff, log g, and ξ) uncertainties. The excellent agreement among the dwarf C abundances and among the giant C abundances suggest that these random uncertainties are very small, especially for the giants since the T_eff sensitivities of the C₂ and [C i] abundances are grossly similar but opposite in direction. If, however, there are systematic errors between the dwarf and giant parameter scales, then abundance differences significantly larger than those expected from internal random uncertainties may become manifest. This does not appear to be the case here: any systematic change in the dwarf or giant stellar parameters in an effort to account for the 0.18 dex discrepancy between the observed C abundances and model predictions eliminates existing agreements between different C abundance indicators and creates new discrepancies among the abundances of other elements. For instance, the dwarfs T_eff would have to be decreased by 900 K to account for the C abundance discrepancy; aside from being highly improbable, such a large T_eff error would mean that the derived dwarf N abundances are overestimated by 1.5 dex. A change of +270 K would be needed for the giants T_eff to raise their C₂-based abundance 0.18 dex; this would, however, result in a −0.14 dex decrease in the [C i]-based abundance and create a 0.32 dex discordance in the C abundances of each giant derived from these two features. Furthermore, the change in T_eff would raise the giant N abundances by 0.67 dex. Similarly large (>1 dex) changes in log g are needed to bring the observed C abundances into agreement with the model, and similar disagreements among the various elements, particularly O in this case, result.

Fitting the synthetic spectra to the observed C₂ features introduces additional error into the derived abundances of the dwarfs. This can arise from both the actual matching of the observed line shapes, which are defined by multiple blending lines (Figure 4), and uncertainties in the linelist. The latter is not expected to be a significant contributor to the error in the abundances, because the dwarfs in our sample have parameters similar to those of the Sun. The linelist may be more of an issue for the giants; however, the consistent abundances derived from the CH, C₂, and [C i] lines suggest otherwise. As for fitting the λ5135 feature in the giant spectra, the blending of this line is less severe than for the dwarfs, and the error due to fitting the observed spectrum is negligible compared to the uncertainties due to T_eff and log g.

As a check of the dwarf C₂ results, the C abundance of HIP19793 was derived from the equivalent widths (EWs) of two C i lines. C i lines in the spectra of solar-type dwarfs result from high-excitation transitions, and to one degree or another, all form out of LTE (Asplund 2005). The magnitude of the NLTE corrections for these lines is dependent on T_eff, log g, [Fe/H], and [C/Fe], and for the Sun, the corrections range from −0.03 to −0.25 dex (LTE analyses overestimate the abundances), depending on the specific line in question (Asplund et al. 2005b; Fabbian et al. 2006). Because of uncertainty associated with NLTE calculations, C i lines were not used to determine the C abundances of the dwarfs and giants. However, NLTE corrections similar to those for the Sun are expected for HIP 19793 because of the similarities in their stellar parameters.⁷ The relative [C/H] abundance of HIP 19793 as derived from high-excitation C i lines should be a reliable indicator of its C content. The measured EWs of the two C i lines analyzed and the resulting abundances are provided in Table 4. Atomic data for these transitions were taken from Asplund et al. (2005b). The mean abundance from the C i lines is [C/H] =+0.14 ± 0.02, in excellent agreement with the C₂-based values. Combining the C₂ and C i results gives a Hyades dwarf abundance of [C/H] =+0.15 ± 0.02 (uncertainty in the mean).

The discordance between observed C abundances of clump giants and stellar evolution model predictions may not to be limited to the Hyades. Mishenina et al. (2006) derived the abundances of numerous elements for a collection of giants in the Galactic disk—including the four Hyades giants, as mentioned in Section 3.3.1—and compared those of C, N, and Na to predictions based on STAREVOL stellar evolution models assuming [C/Fe] =0 (Figures 21–23, therein). The giants are divided into three metallicity bins defined by [Fe/H] <−0.15, −0.15< [Fe/H] <+0.12, and [Fe/H] > + 0.12. For the two more metal-rich bins, the observed C abundances fall below the [C/Fe] =0 evolutionary models. The evolutionary curves fit better the data if the model [C/Fe] ratios are shifted by −0.15 and −0.20 dex, respectively, as Mishenina et al. show in their Figures 22 and 23; the shifts are motivated by the empirical [C/Fe] versus [Fe/H] trend for the giants shown in their Figure 10.

While the initial MS C abundances of the field giants cannot be recovered, the MS abundances would be expected to be higher than those of the giants, because the latter have been diluted by first dredge-up mixing of material processed by the CN cycle. Better indicators of the MS C abundances are those of current MS dwarfs at similar metallicities (e.g., Luck & Heiter 2007). C abundances of dwarfs have been the focus of numerous high-resolution spectroscopic studies focusing on Galactic chemical evolution (e.g., Gustafsson et al. 1999). There is debate as to whether or not [C/Fe] ratios increase with decreasing [Fe/H] (e.g., Gustafsson et al. 1999; Takeda & Honda 2005; Reddy et al. 2006) or remain flat (Bensby & Feltzing 2006) at subsolar metallicities; however the behavior near [Fe/H] =0 is consistent: [C/Fe] ≈0. Down to about [Fe/H] =−0.3, the results remain consistent with [C/Fe] ≈+0.10, and at slightly supersolar metallicities, [Fe/H] =+0.2, C abundances range from 0⩾ [C/Fe] ⩾−0.10, depending on the study (e.g., Gustafsson et al. 1999; Bensby & Feltzing 2006). These data, when compared to the results of Mishenina et al. (2006), confirm that C abundances of dwarfs are larger than those for giants at a given metallicity. Consequently, the [C/Fe] =−0.15 and −0.20 stellar evolutionary models that best fit the data of the two more metal-rich bins of Mishenina et al. (2006), and indeed the [C/Fe] =0 model that fits the [Fe/H] ≈−0.15 bin, may not be appropriate for those metallicities and need to be increased by 0.10–0.15 dex. The implication would in that case be that the stellar evolution models do not accurately predict the observed C abundances of clump giants in the Galactic disk.

A critical diagnostic of stellar evolution is the surface ¹²C/¹³C ratio. The first reaction of the CN cycle converts ¹²C into ¹³N which then e⁺ decays to ¹³C, and ¹³C is subsequently converted to ¹⁴N by proton capture. The ¹³C(p,γ)¹⁴N reaction lags behind the first reaction, so a decrease in ¹²C and an accompanying increase in ¹³C occurs. The surface ¹²C/¹³C ratio will be attenuated after the first dredge-up mixing of core material to the outer layers. Our stellar model evolves onto the MS with a surface ¹²C/¹³C ratio of about 90, the solar value, and decreases to 23.4 after the first dredge-up. This prediction matches well the observed ¹²C/¹³C ratios of the Hyades giants. Tomkin et al. (1976) analyzed ¹²CN and ¹³CN lines near 6300 and 8000 Å in high-resolution spectra of the four Hyades giants and found a mean value of 21.0 (σ_s.d. = 1.8), and Gilroy (1989) derived a mean value of 25.8 (σ_s.d. = 1.4) using the same ¹²CN and ¹³CN lines near 8000 Å.

The agreement between the observed and predicted ¹²C/¹³C ratios of the giants complicates the interpretation of the discrepant observed and modeled ¹²C abundances. If the ¹²C abundance of the giants has been overdepleted relative to standard stellar model predictions, the accurately predicted ¹²C/¹³C ratios suggest that the overdepletion must extend to ¹³C, as well. It is not known what mechanism could be responsible for this overdepletion, but in light of the agreement between the observed and predicted N and O abundances, it would appear that it has to lie outside of the CNO bi-cycle. Apropos, it is not clear how the stellar evolution model can correctly reproduce the observed N, O, and ¹²C/¹³C results while concurrently failing to do the same for ¹²C. Nonetheless, there is no compelling evidence to suggest that the highly consistent observed abundances of the dwarfs and giants are erroneous.

We have calculated additional stellar models in an attempt to better match the observed C abundances of the Hyades dwarfs and giants while at the same time conserving the agreement with the N, O, and ¹²C/¹³C results. The model mass, metallicity, and nuclear reaction rates have all been varied to test their effect on the predicted CNO abundance evolution, but none of the changes resolve the discrepancy with the observed abundances. The empirically determined masses of the Hyades giants are well constrained to be 2.2–2.4 M_☉ (Tomkin et al. 1995; de Bruijne et al. 2001; Armstrong et al. 2006), so significant deviations from the adopted mass of our stellar model (2.5 M_☉) are not expected. We thus evolved a 2.2 M_☉ model and found that the ¹²C depletion factor remained unchanged at 1.5, and the ¹⁴N enhancement factor was reduced from 2.3 to 2.1.

The metallicity of the Hyades open cluster has been determined by many groups, and recent determinations fall in a small range of [Fe/H] =+0.08 to +0.16 (Paulson et al. 2003; Taylor & Joner 2005; Schuler et al. 2006a). Our stellar evolution model is characterized by a metallicity of [m/H] =+0.10 (i.e., the solar composition scaled by +0.10 dex). Our observations of Hyades dwarfs, however, indicate that the cluster has a MS composition which includes a slightly more enhanced C abundance ([C/H] =+0.15) and a low N abundance ([N/H] =−0.21). Adopting these C and N abundances while keeping the abundances of the other elements at [m/H] =+0.10, we have evolved a stellar model with a modified metallicity. The ¹²C depletion factor increased marginally from 1.5 to 1.6; a more significant change occurred for the ¹⁴N enhancement factor, increasing from 2.3 to 3.8.

In all of the models discussed above, the reaction rates from the NACRE compilation (Angulo et al. 1999) have been used for the CN cycle reactions (please see Section 2). The ¹⁴N(p, γ)¹⁵O reaction is the slowest of these, and as a result, the preceding ¹²C(p, γ)¹³N(e⁺ν)¹³C and ¹³C(p, γ)¹⁴N reactions increase the local ¹⁴N abundance at the expense of ¹²C. A new measurement of the reaction rate for the important ¹⁴N(p, γ)¹⁵O reaction has been reported by Imbriani et al. (2005), who find a rate that is a factor of ∼2 lower than that of the NACRE compilation. Incorporating the Imbriani et al. reaction rate into our stellar model produces only minor changes in the ¹²C depletion (1.5–1.6) and ¹⁴N enhancement (2.3–2.2) factors. We attempted to further increase the ¹²C depletion factor by adopting a ¹²C(p, γ)¹³N rate that is a factor of 3 higher than the NACRE rate and combining that with the ¹⁴N(p, γ)¹⁵O rate of Imbriani et al. In this model, the ¹²C depletion factor increased to 1.7, while the ¹⁴N enhancement factor remained unchanged at 2.3. In a more extreme attempt, we used the previously mentioned increased ¹²C(p, γ)¹³N rate plus the ¹⁴N(p, γ)¹⁵O rate of Imbriani et al. decreased by a factor of 5. This model produced a ¹²C depletion factor of 1.9 and a ¹⁴N enhancement factor of 2.5. The combination of the modified rates results in a small improvement in the discrepancy between the observed and predicted level of ¹²C depletion in the Hyades giants, but these rates are well beyond the statistical uncertainties of the experimental cross section measurements used to determine the reaction rates. Furthermore, any changes in the reaction rates affect only the CNO abundances relative to each other and cannot resolve the discrepancy between the observed dwarf and giant A(C + N + O) abundances.

Finally, we tested the effect of the mixing length parameter α (and thus the efficiency of the convective energy transport) on the ¹²C and ¹⁴N surface abundance evolution of the model. In all of the models discussed above, α = 2, and new calculations with ±1 of the adopted value were carried out. The changes in α had essentially no effect on the ¹²C depletion and ¹⁴N enhancement factors.

Once our stellar model reaches the MS, most of the initial ⁷Li present in the star has been destroyed as a result of convective mixing during its pre-MS evolution. At this stage, any surviving ⁷Li is located near the stellar surface at an interior radius of M_r = 2.45–2.50 M_☉ (Figure 1). For the model with simultaneous nuclear burning and mixing, the star arrives on the MS with a ⁷Li surface mass fraction of 1.15 × 10⁻⁸; for the model in which the nuclear burning and mixing are calculated sequentially, the ⁷Li surface mass fraction is 1.18 × 10⁻⁸. After the first dredge-up and before the onset of core He burning, the total amount of ⁷Li is diluted to surface mass fractions of 1.82 × 10⁻¹⁰ in the first model and 1.92 × 10⁻¹⁰ in the second model. This dilution results from mixing over the mass radii of M_r = 0.34–2.50 M_☉. Therefore, the surface abundance of ⁷Li in both models is diluted by a factor of ∼63 as a result of the first dredge-up. During core He burning, a small amount of ⁷Li is destroyed in the inner regions of the star, but the surface abundance is not affected by this.

Using our dwarfs to infer the initial Hyades Li abundance and thus test the stellar model predictions for Li evolution in our giants is complicated by the pre-MS and MS Li depletion manifest in cool Hyades dwarfs (Thorburn et al. 1993). Before circumventing this obstacle, we note that our LTE Li abundances of HIP 19793 and 21099, A(Li)=2.36 and 1.20, are in outstanding agreement with those derived by Balachandran (1995), 2.32 and 1.29, from reanalysis of the (Thorburn et al. 1993) λ6707 Li i line strengths using T_eff values identical to our own within the uncertainties. The Li abundances of HIP 14976 and HIP 21099 differ by a factor of 2, a significant result given the ±0.05 dex per star uncertainty. This result confirms previous findings of modest but significant star-to-star Li scatter at fixed color in cool Hyades dwarfs—scatter that implicates the action of rotationally induced main-sequence mixing (Thorburn et al. 1993).

We estimate the initial Hyades Li abundance from the maximum abundances exhibited by stars on the warm side of the F-star Li dip and at the G star Li peak in Figure 3 of Balachandran (1995). Employing the NLTE corrections (for solar metallicity) from Carlsson et al. (1994), typically −0.10 to −0.20 dex, suggests an initial Hyades Li abundance of A(Li)∼3.15. The NLTE corrections for the giants are ∼+0.19 dex. The NLTE Li abundance difference between γ Tau and the initial cluster value, ∼1.9 dex, is in excellent agreement with the 1.8 dex difference predicted by our model.

However, the Hyades giants evince a spread in Li abundance that is not explained by standard stellar models. The ∼0.35 dex difference in A(Li) between γ Tau and  Tau is significant given the ±0.07 dex per star uncertainty. In Figure 6, we overplot the spectra of these two giants, showing the marked disparity in the strength of their Li features relative to other lines in the spectra. There are several possible explanations of the Li abundance spread in the Hyades giants: differences in their evolutionary states, small mass loss (⩽0.02M_☉; see Figure 1) in  Tau prior to the RGB, additional mixing during the post-MS not predicted by standard stellar models (Böhm-Vitense 2004; Charbonneau & Michaud 1990) that depletes Li in  Tau, or uniform additional mixing for the Hyades giants accompanied by subsequent RGB Li production in γ Tau (Pasquini et al. 2001, 2004).

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de Bruijne et al. (2001) constructed a high-precision Hertzsprung–Russell diagram of the Hyades open cluster using Hipparcos-based secular parallaxes, and the authors showed, using a solar-metallicity 631 Myr isochrone of Girardi et al. (2000), that the giants are of the same evolutionary state and fall squarely on the RGB clump. Furthermore, the surface gravities of the giants, both Hipparcos-based physical gravities (de Bruijne et al. 2001) and spectroscopic gravities (Smith 1999), differ by less than 0.10 dex. The mass-loss hypothesis was originally proposed by Boesgaard et al. (1977), and the small amount required to explain the lower Li abundance in  Tau is very tightly constrained by the steep Li profile of the stellar model shown in Figure 1.

If differential additional post-MS mixing is to explain the giant Li abundance differences, the remarkable uniformity of the CNO, Na, Mg, Al abundances suggests that this mixing must be shallow. Additional valuable constraints can be provided by Be and B, which are depleted by proton capture at slightly higher temperatures than Li. Unfortunately, Boesgaard et al. (1977) were only able to derive upper limits to Be in Hyades giants, and there is no indication in the work of Duncan et al. (1998) that potential differences in B abundances in the Hyades giants were examined. New data and updated analyses of Be and B in the Hyades giants that could stringently constrain any star-to-star differences and the depth of an assumed extra-mixing mechanism to explain such differences would have great worth.

Additional theoretical work beyond the scope of that carried out here is needed to securely identify the constraints that the uniformity of CNO and Na, Mg, Al (please see below, Section 4.4) abundances provide on a putative Li production mechanism in γ Tau, as well as any accompanying nucleosynthetic signatures that may betray such production. If, for example, a hot bottom burning (hbb) process (believed to be responsible for Li production in some more highly evolved AGB stars; Sackmann & Boothroyd 1992) is at work, then the uniformity of the ¹³C/¹²C ratios and ¹⁴N abundances in all the giants can only be understood if the ¹³C and ¹⁴N also produced in a hbb process is negligible or can be transmuted. In principle, the latter can be accomplished via α capture, resulting in both a neutron source (from ¹³C) and ¹⁹F production (from ¹⁴N). Thus, n-capture elements and ¹⁹F abundances (perhaps as well as the ²⁶Al isotopic abundance) may be key diagnostics of such production. We have compared spectral regions containing several features of the light and intermediate mass s-process elements Sr, Zr, Y, and Ba. The line strengths in γ Tau and  Tau are indistinguishable. Observations of HF features in the near-IR to examine F differences in the Hyades giants would be worthwhile future work.

A final test of the standard stellar evolution model can be made with Na, Mg, and Al. The surface abundances of the predominant Na, Mg, and Al isotopes (²³Na, ²⁴Mg, and ²⁷Al) of intermediate-mass MS stars may be altered if (1) the NeNa and MgAl cycles are active in the core regions, and (2) if the convection zone extends deep enough during the first dredge-up to mix to the surface material processed by these cycles. Our stellar evolution model does show signs of NeNa and to a lesser extent MgAl cycle processing in the core; however, it is only the products of the former that get mixed to the surface during the first dredge-up. The surface abundance of ²³Na is predicted to increase by a factor of 1.38 (0.14 dex) and the surface abundances of ²⁴Mg and ²⁷Al remain unchanged (Table 3).

We have derived Na, Mg, and Al abundances of the Hyades dwarfs and giants using an LTE EW analysis. EWs of a set of presumably unblended Na, Mg, and Al lines were determined by fitting Gaussian profiles to the spectral features using the one-dimensional spectral analysis routine SPECTRE (Fitzpatrick & Sneden 1987). Only lines that are measurable in both our dwarf and giant spectra were utilized, and our final linelist contains three lines for each Na, Mg, and Al. Uncertainties in the EWs have been estimated by comparing the results of numerous measurements of each line; these uncertainties are generally <5 mÅ. The EW measurements, along with the adopted atomic parameters from VALD, are given in Table 5.

Table 5. Na, Mg, and Al: Spectral Line Data and Equivalent Widths

Species	λ (Å)	χ (eV)	log gf	Sun EW (mÅ)	HIP 14976 (mÅ)	HIP 19793 (mÅ)	HIP 21099 (mÅ)	γ Tau (mÅ)	δ Tau (mÅ)	Tau (mÅ)
Na i	5682.63	2.10	−0.70	104.0	131.0	122.8	129.8	169.7	171.3	171.3
	6154.23	2.10	−1.56	38.0	55.0	47.9	56.7	104.4	102.9	108.7
	6160.75	2.10	−1.26	58.6	76.2	69.3	78.2	120.0	120.7	125.1
Mg i	4571.10	0.00	−5.69	108.5	130.3	113.9	131.8	200.7	201.0	215.5
	4730.03	4.35	−2.52	71.2	93.4	83.8	94.8	122.0	122.6	129.0
	5711.09	4.35	−1.83	105.1	123.3	113.6	127.9	157.1	156.8	161.8
Al i	6698.67	3.14	−1.65	21.0	32.5	27.0	32.9	62.0	61.4	65.5
	7835.32	4.02	−0.65	45.0	59.2	56.0	62.8	80.8	78.7	82.8
	7836.13	4.02	−0.49	59.3	78.5	72.8	81.3	90.2	90.7	97.8

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The observed Na, Mg, and Al abundances are given in Table 1. The abundances are given relative to self-consistently derived solar values which negates the effects of gf value errors and mitigates NLTE and line blending effects (at least for the dwarfs). Solar EWs were measured from a high-quality sky spectrum (S/N ≈950) obtained with the Harlan J. Smith 2.7 m telescope and the 2dcoude echelle spectrometer at the McDonald Observatory during our 2004 October observing run. Abundance sensitivities to the adopted parameters are given in Table 2 and result in typical uncertainties in these abundances of about ±0.10 dex for both the dwarfs and giants.

Similar to CNO, the Na, Mg, and Al abundances show a high level of internal consistency for the dwarfs and giants. The uncertainties in the mean abundances are no more than σ_μ = 0.03 for each element. The mean [m/H] dwarf abundances range from +0.09 to +0.11 and relative to Fe are essentially solar. The derived abundances of the giants, on the other hand, are found to be markedly larger than those of the dwarfs; the mean abundances are [Na/H] =+0.61 ± 0.02, [Mg/H] =+0.55 ± 0.03, and [Al/H] =+0.33 ± 0.02 (uncertainties in the means). Such large overabundances relative to the dwarfs are in stark contrast to the model predictions. As stated above, Na is the only one of these elements that is expected to have its surface abundance affected by first dredge-up mixing, and the predicted increase is only 0.14 dex. Applying this increase to the difference in the observed dwarf and giant abundances, a 0.38 dex difference remains.

No existing self-enrichment scenario can explain the large enhancements in Na, Mg, and Al abundances of the Hyades giants. The likely culprit for the highly enhanced abundances is unaccounted for NLTE effects. Unfortunately, targeted NLTE calculations for these elements in supersolar metallicity giants have not been carried out. NLTE corrections for Na abundances at [Fe/H] =0 have in general been shown to be negative (Mashonkina et al. 2000; Takeda et al. 2003; Mishenina et al. 2006), in line with theoretical expectations (Asplund 2005), but positive corrections have also been suggested (Gratton et al. 1999). In light of the derived Na overabundances of the Hyades giants compared to the dwarfs, and the larger consensus in the literature, negative NLTE corrections for Na seem more likely.

From the large grid of corrections provided by Takeda et al. (2003) we can roughly estimate a NLTE Na abundance for the Hyades giants. The corrections are dependent on line strength (or metallicity) and vary from line-to-line for a given star. This effect seems to be present in our data; the strongest Na line (λ5683; Table 5) for the giants consistently results in an abundance that is 0.10–0.15 dex larger than the other two Na lines (Table 6). The NLTE models of Takeda et al. (2003) are divided into 500 K and 0.1 dex in log g grid steps. The T_eff =5000 K model with [m/H] =0 is the most suitable for the Hyades giants, but with surface gravities of log g ≈ 2.6, they fall in between the log g = 3.0 and log g = 2.0 grids. We adopt the corrections of the latter, because the predicted NLTE line strengths better match our observed EWs. Applying the corrections to the individual lines of the Hyades giants (Takeda et al. models t50g20m0) and the Sun (Table 5 therein), a mean NLTE abundance [Na/H]_NLTE = 0.50 ± 0.02 is obtained. While the line-by-line agreement in the relative abundances for each giant is improved, the overall NLTE correction amounts to only 0.11 dex, far smaller than the 0.38 dex needed to bring the observed Na abundances into agreement with the model.

Table 6. Na, Mg, and Al: Line-by-Line Abundances

Species	λ (Å)	Suna	HIP 14976	HIP 19793	HIP 21099	γ Tau	δ Tau	Tau
[Na/H]	5682.63	6.20	0.07	0.16	0.06	0.73	0.68	0.68
	6154.23	6.28	0.07	0.12	0.10	0.61	0.54	0.59
	6160.75	6.26	0.04	0.11	0.06	0.56	0.52	0.55
[Mg/H]	4571.10	7.54	0.06	0.04	0.09	0.55	0.47	0.56
	4730.03	7.87	0.14	0.15	0.16	0.58	0.53	0.61
	5711.09	7.61	0.06	0.08	0.11	0.57	0.50	0.54
[Al/H]	6698.67	6.22	0.11	0.12	0.11	0.35	0.31	0.35
	7835.32	6.41	0.07	0.12	0.11	0.36	0.30	0.33
	7836.13	6.43	0.10	0.13	0.12	0.31	0.28	0.36

Note. ^aA(m) abundances are given for the Sun.

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The situation for Mg and Al is more uncertain due to the dearth of NLTE calculations for giants, even at solar metallicities. Further complicating the matter is that theoretical considerations generally point to positive corrections for LTE abundances due to large photo-ionization cross-sections of the lower excitation levels of Mg and the ground state of Al (Asplund 2005), although actual calculations find negative corrections for at least some stars and particular transitions (Shimanskaya et al. 2000; Liu et al. 2007). Shimanskaya et al. (2000) calculated NLTE abundances for multiple Mg i lines, including two analyzed in this study, and found corrections ranging from −0.05 to +0.02 dex for stars with [m/H] =0 and log g = 2.5. Liu et al. (2007) derived Na, Mg, and Al NLTE abundances of field clump giants, and the corrections for Mg for stars with parameters similar to the Hyades giants are of the same order as those from Shmanskaya et al. The Al corrections for the Hyades-type giants are negative, with typical values of about −0.08 dex. Similar to Na, existing Mg and Al NLTE calculations fall short of the differences in the observed abundances of the Hyades dwarfs and giants.

Our stellar evolution model and observations suggest that newly synthesized Na may have been mixed from the core regions to the surface of the giants, but as Jacobson et al. (2008) point out, no firm conclusions can be made until reliable NLTE corrections are available. If NLTE effects are to account for the discrepancies between the dwarf and giant Na, Mg, and Al abundances, calculations for supersolar metallicity stars will have to produce corrections that are 0.15 to 0.40 dex larger than those from existing solar metallicity calculations. This may not be unreasonable given the sensitivity of the NLTE corrections to line strengths. Finally, we point out that the observed overabundances of Na and Al are common characteristics of open cluster giants. Jacobson et al. (2007) has compiled from the literature Na and Al abundances of numerous open cluster giants (Figure 7 therein); the Hyades abundances fall squarely among these other data. As for Mg, many studies find near solar abundance ratios for open cluster giants (e.g., Hamdani et al. 2000; Pasquini et al. 2004), but large Mg overabundances similar to those seen in the Hyades have been observed in other open clusters (e.g., Yong et al. 2005).