non-LTE Corrections Research Articles

Departures from LTE for neutral Li in late-type stars

We perform non-LTE calculations of lithium in late-type stars for a wide range of stellar parameters, including quantum mechanical cross-sections for collisions with neutral hydrogen and the negative hydrogen ion. Non-LTE abundance corrections for the lithium resonance line at 670.7nm and the subordinate line at 610.3nm, are calculated using 1D MARCS model atmospheres spanning a grid Teff=[4000,8000]K, log(g)=[1.0,5.0], and [Fe/H]=[0.0,-3.0], for lithium abundances in the range A(Li)=[-0.3,4.2]. The competing effects of ultraviolet over-ionization and photon losses in the resonance line govern the behaviour of the non-LTE effects with stellar parameters and lithium abundance. The size and sign of the non-LTE abundance corrections vary significantly over the grid for the 670.7nm line, but are typically positive and below 0.15dex for the 610.3nm, line. The new collisional data play a significant role in determining the abundance corrections.

The effects of deviations from LTE in sulphur lines for late-type stars

We analyze the formation of lines of neutral sulfur in the spectra of F-K stars taking into account the effects of deviations from local thermodynamical equilibrium (LTE). Our calculations were carried out for Kurucz model atmospheres with Teff = 5000–6500 K, log g = 2−4 and [Fe/H] = −4−0, using a 65-level model of the SI atom. Deviations from LTE affect lines of different multiplets of the sulfur atom differently. Non-LTE corrections, which are relatively small (to −0.10 dex) for the 6543–6557 A lines, increase to −0.26 dex for the 8694 A line, and reach −1.1 dex for the 9212–9237 A IR triplet. The model of the atom was verified by modeling the sulfur lines of the studied multiplets in the spectra of the Sun, two main sequence stars, and two supergiants. Good consistency with the observed line profiles was obtained. Failure to take into account strong non-LTE-effects may explain the large sulfur excesses detected in stars with very low metal abundances.

Neutral oxygen spectral line formation revisited with new collisional data: large departures from LTE at low metallicity

We present a detailed study of the non-Local Thermodynamic Equilibrium (non-LTE) formation of the high-excitation neutral oxygen 777 nm triplet in MARCS model atmospheres representative of late-type stars with spectral types F to K. We carried out the calculations using the statistical equilibrium code MULTI, including estimates of the impact on elemental abundance analysis. The atomic model employed includes, in particular, recent quantum-mechanical electron collision data. We confirm that the O I triplet lines form under non-LTE conditions in late-type stars, suffering negative abundance corrections with respect to LTE. At low metallicity, large line opacity stems from triplet-quintet intersystem electron collisions, a form of coupling previously not considered or seriously underestimated. The non-LTE effects become generally severe for models (both giants and dwarfs) with higher T_eff. Interestingly, in metal-poor turn-off stars, the negative non-LTE abundance corrections tend to rapidly become more severe towards lower metallicity. When neglecting H collisions, they amount to as much as ~ 0.9 dex and ~ 1.2 dex, respectively at [Fe/H]=-3 and [Fe/H]=-3.5. Even when such collisions are included, the LTE abundance remains a serious overestimate, correspondingly by ~ 0.5 dex and ~ 0.9 dex at such low metallicities. Although the poorly known inelastic hydrogen collisions thus remain an important uncertainty, the large metallicity-dependent non-LTE effects seem to point to a resulting "low" (compared to LTE) [O/Fe] in metal-poor halo stars.

The C/O ratio at low metallicity: constraints on early chemical evolution from observations of Galactic halo stars

<i>Aims. <i/>We present new measurements of the abundances of carbon and oxygen derived from high-excitation C i and O i absorption lines in metal-poor halo stars, with the aim of clarifying the main sources of these two elements in the early stages of the chemical enrichment of the Galaxy.<i>Methods. <i/>We target 15 new stars compared to our previous study, with an emphasis on additional C/O determinations in the crucial metallicity range -3 [Fe/H] -2. The stellar effective temperatures were estimated from the profile of the H<i>β<i/> line. Departures from local thermodynamic equilibrium were accounted for in the line formation for both carbon and oxygen. The non-LTE effects are very strong at the lowest metallicities but, contrary to what has sometimes been assumed in the past due to a simplified assessment, of different degrees for the two elements. In addition, for the 28 stars with [Fe/H] < -1 previously analysed, stellar parameters were re-derived and non-LTE corrections applied in the same fashion as for the rest of our sample, giving consistent abundances for 43 halo stars in total.<i>Results. <i/>The new observations and non-LTE calculations strengthen previous suggestions of an upturn in C/O towards lower metallicity (particularly for [O/H] -2). The C/O values derived for these very metal-poor stars are, however, sensitive to excitation via the still poorly quantified inelastic H collisions. While these do not significantly affect the non-LTE results for C i, they greatly modify the O i outcome. Adopting the H collisional cross-sections estimated from the classical Drawin formula leads to [C/O] <i>≈<i/> 0 at [O/H] <i>≈<i/> -3. To remove the upturn in C/O, near-LTE formation for O i lines would be required, which could only happen if the H collisional efficiency with the Drawin recipe is underestimated by factors of up to several tens of times, a possibility which we consider unlikely.<i>Conclusions. <i/>The high C/O values derived at the lowest metallicities may be revealing the fingerprints of Population III stars or may signal rotationally-aided nucleosynthesis in more normal Population II stars.

Non-LTE line formation for Pr ii and Pr iii in A and Ap stars

<i>Aims. <i/>Non-local thermodynamical equilibrium (non-LTE) line formation for singly-ionized and doubly-ionized praseodymium is considered for a range of effective temperatures between 7250 K and 9500 K. We evaluate the influence of departures from LTE on Pr abundance determinations and determine a distribution of the Pr abundance in the atmosphere of the roAp star HD 24 712 from a non-LTE analysis of the Pr ii and Pr iii lines.<i>Methods. <i/>A comprehensive model atom for Pr ii/iii is presented based on the measured and the predicted energy levels, in total, 6708 levels of Pr ii and Pr iii and the ground state of Pr iv. Calculations of the Pr ii energy levels and oscillator strengths for the transitions in Pr ii and Pr iii are described.<i>Results. <i/>The dependence of non-LTE effects on the atmospheric parameters is discussed. At 8000 K, departures from LTE lead to the overionization of Pr ii and, therefore, to systematically depleted total absorption in the line and positive abundance corrections. At the lower temperatures, different lines of Pr ii may be either weakened or amplified depending on the line strength. The non-LTE effects strengthen the Pr iii lines and lead to negative abundance corrections. Non-LTE corrections grow with effective temperature for the Pr ii lines, and, in contrast, they decline for the Pr iii lines. The Pr ii/iii model atom is applied to determine the Pr abundance in the atmosphere of the roAp star HD 24 712 from the lines of two ionization stages. In the chemically uniform atmosphere with [Pr/H] = 3, the departures from LTE may explain only a small part (approximately 0.3 dex) of the difference between the LTE abundances derived from the Pr ii and Pr iii lines (2 dex). We find that the lines of both ionization stages are fitted for the vertical distribution of praseodymium, where the Pr enriched layer with [Pr/H] <i>≥<i/> 4 exists in the outer atmosphere at < -4. The departures from LTE for Pr ii/iii are strong in the stratified atmosphere and have the opposite sign for the Pr ii and Pr iii lines. The praseodymium stratification analysis of roAp stars has to be performed based on non-LTE line formation. Using the revised partition function of Pr ii and experimental transition probabilities, we determine the solar non-LTE abundance to be = -11.15<i>±<i/>0.08.

Abundances of lithium, sodium and potassium in Vega★

Vega's photospheric abundances of Li, Na and K were determined by using considerably weak lines measured on the very high signal-to-noise ratio spectrum, while the non-local thermodynamic equilibrium (non-LTE) correction and the gravity-darkening correction were adequately taken into account. It was confirmed that these alkali elements are mildly underabundant ([Li/H]≃−0.6, [Na/H]≃−0.3 and [K/H]≃−0.2) compared to the Solar system values, as generally seen also in other metals. Since the tendency of Li being more deficient than Na and K is qualitatively similar to what is seen in typical interstellar cloud, the process of interstellar gas accretion may be related with the abundance anomaly of Vega, as suspected in the case of λ Boo stars.

Sulphur and zinc abundances in Galactic halo stars revisited

High resolution UVES spectra of 40 main-sequence stars with -3.3 < [Fe/H] < -1.0 are used to derive S, Fe and Zn abundances from lines in the 400 - 950 nm region. For one star we also present novel observations of the SI triplet at 1.046 micron carried out with the ESO VLT CRIRES spectrograph. Comparison of sulphur abundances from the weak and strong SI lines provides important constraints on non-LTE effects. The high sulphur abundances reported by others for some metal-poor stars are not confirmed; instead, when taking non-LTE effects into account, the Galactic halo stars distribute around a plateau at [S/Fe] = +0.2 dex with a scatter of 0.07 dex only. This indicates that sulphur in Galactic halo stars has been made by alpha-capture processes in massive SNe. The observed scatter in S/Fe is, however, much smaller than predicted from current stochastic models of the chemical evolution of the early Galaxy, suggesting that either the models or the calculated yields of massive SNe should be revised. [Zn/Fe] is close to zero for metallicities in the range -2.0 < [Fe/H] < -1.0 but increases to a level of [Zn/Fe] = +0.15 dex in the range -2.7 < [Fe/H] < -2.0. At still lower metallicities [Zn/Fe] rises steeply to a value around [Zn/Fe] = +0.5 dex at [Fe/H] = -3.2. We also examine the behaviour of S/Zn and find that departures from the solar ratio are significantly reduced at all metallicities if non-LTE corrections to the abundances of these two elements are adopted. This effect, if confirmed, would reduce the usefulness of the S/Zn ratio as a diagnostic of past star-formation activity, but would bring closer together the values measured in damped Lyman-alpha systems and in Galactic stars.

The Solar Heavy‐Element Abundances. I. Constraints from Stellar Interiors

The latest solar atmosphere models including non-LTE corrections and three-dimensional hydrodynamic convection simulations predict a significant reduction in the solar metal abundance. This leads to a serious conflict between helioseismic data and the predictions of solar interiors models. We demonstrate that the helioseismic constraints on the surface convection zone depth and helium abundance combined with stellar interiors models can be used to constrain chemical composition. A detailed examination of the errors in the theoretical models disfavors strongly (disagreeing at the 15 σ level with the seismic data) the proposed new low abundance, while the models constructed with the older and higher solar abundances are consistent (within 2 σ). We then use the sensitivity of the seismic properties to abundance changes to invert the problem and infer a seismic solar heavy-element abundance mix with two components: meteoritic abundances and the light metals CNONe. Seismic degeneracies between the best solutions for the elements arise for changes in the relative CNONe abundances and their effects are quantified. We obtain Fe/H = 7.50 ± 0.045 ± 0.003(CNNe) and O/H = 8.86 ± 0.041 ± 0.025(CNNe) on the logarithmic scale, where H = 12 for the relative CNNe mixtures in the Grevese & Sauval mixture; the second error term reflects the uncertainty in the overall abundance scale from errors in the C, N, and Ne abundances relative to oxygen. These are consistent within the errors with the previous standard solar mixture but in strong conflict with the low oxygen abundance inferred from the three-dimensional hydro models. Changes in the Ne abundance can mimic changes in oxygen for the purposes of scalar constraints. However, models constructed with low oxygen and high neon are inconsistent with the solar sound speed profile. Implications for the solar abundance scale are discussed.

The non-LTE line formation of neutral carbon in late-type stars

Aims. We investigate the non-Local Thermodynamic Equilibrium (non-LTE) line formation of neutral carbon in late-type stars in order to remove some of the potential systematic errors in stellar abundance analyses employing C i features. Methods. The statistical equilibrium code MULTI was used on a grid of plane-parallel 1D MARCS atmospheric models. Results. Within the parameter space explored, the high-excitation C i lines studied are stronger in non-LTE due to the combined effect of line source function drop and increased line opacity due to overpopulation of the lower level for the transitions considered; the relative importance of the two effects depends on the particular combination of Teff ,l ogg ,[ Fe/H] and [C/Fe] and on the analysed C i line. As a consequence, the non-LTE abundance corrections are negative and can be substantially so, for example ∼−0.4 dex in halo turn-off stars at [Fe/H] ∼− 3. The magnitude of the non-LTE corrections is rather insensitive to whether inelastic H collisions are included or not. Conclusions. Our results have implications on studies of nucleosynthetic processes and on Galactic chemical evolution models. When applying our calculated corrections to recent observational data, the upturn in [C/O] at low metallicity might still be present (thus apparently still necessitating contributions from massive Pop. III stars for the carbon production), but at a lower level and possibly with a rather shallow trend of ∼−0. 2d ex/dex below [O/H] ∼− 1.

Hyades Oxygen Abundances from the λ6300 [Oi] Line: The Giant-Dwarf Oxygen Discrepancy Revisited

We present the results of our abundance analysis of Fe, Ni, and O in high signal-to-noise ratio, high-resolution Very Large Telescope UVES and McDonald 2dcoude spectra of nine dwarfs and three giants in the Hyades open cluster. The difference in Fe abundances derived from Fe II and Fe I lines ([Fe /H] - [Fe /H]) and Ni I abundances derived from moderately high-excitation (χ ≈ 4.20 eV) lines is found to increase with decreasing Teff for the dwarfs. Both of these findings are in concordance with previous results of overexcitation/overionization in cool young dwarfs. Oxygen abundances are derived from the [O I] λ6300 line, with careful attention given to the Ni I blend. The dwarf O abundances are in star-to-star agreement within uncertainties, but the abundances of the three coolest dwarfs (4573 K ≤ Teff ≤ 4834 K) evince an increase with decreasing Teff. Possible causes for the apparent trend are considered, including the effects of overdissociation of O-containing molecules. O abundances are derived from the near-UV OH λ3167 line in high-quality Keck HIRES spectra, and no such effects are found; indeed, the OH-based abundances show an increase with decreasing Teff, leaving the nature and reality of the cool dwarf [O I]-based O trend uncertain. The mean relative O abundance of the six warmest dwarfs (5075 K ≤ Teff ≤ 5978 K) is [O/H] = +0.14 ± 0.02, and we find a mean abundance of [O/H] = +0.08 ± 0.02 for the giants. Thus, our updated analysis of the [O I] λ6300 line does not confirm the Hyades giant-dwarf oxygen discrepancy initially reported by King & Hiltgen, suggesting that the discrepancy was a consequence of analysis-related systematic errors. LTE oxygen abundances from the near-IR, high-excitation O I triplet are also derived for the giants, and the resulting abundances are approximately 0.28 dex higher than those derived from the [O I] line, in agreement with non-LTE predictions. Non-LTE corrections from the literature are applied to the giant triplet abundances; the resulting mean abundance is [O/H] = +0.17 ± 0.02, in decent concordance with the giant and dwarf [O I] abundances. Finally, Hyades giant and dwarf O abundances derived from the [O I] λ6300 line and high-excitation triplet, as well as dwarf O abundances derived from the near-UV OH λ3167 line, are compared, and a mean cluster O abundance of [O/H] = +0.12 ± 0.02 is achieved, which represents the best estimate of the Hyades O abundance.

Non-LTE Line-Formation and Abundances of Sulfur and Zinc in F, G, and K Stars

Abstract Extensive statistical-equilibrium calculations on S I and Zn I were carried out, in order to investigate how the non-LTE effect plays a role in the determination of their abundances in F–K stars. Having checked on the spectra of representative F-type stars (Polaris, Procyon, $\alpha$ Per) and the Sun that our non-LTE corrections yield a reasonable consistency between the abundances derived from different lines, we tried an extensive non-LTE reanalysis of published equivalent-width data of S I and Zn I lines for metal-poor halo/disk stars. According to our calculations, S I 9212/9228/9237 lines suffer significant negative non-LTE corrections ($\lesssim 0.2 \hbox{--} 0.3 \,\mathrm{dex}$), while LTE is practically valid for S I 8683/8694 lines. As far as the very metal-poor regime is concerned, a marked discordance is observed between the $\mathrm{[S/Fe]}$ values from these two abundance indicators, in the sense that the former attains a nearly flat plateau (or even a slight downward bending) while the latter shows an ever-increasing trend with a further lowering of metallicity. The characteristics of $\mathrm{[Zn/Fe]}$ reported from recent LTE studies (i.e., an evident/slight increase of $\mathrm{[Zn/Fe]}$ with a decrease of $\mathrm{[Fe/H]}$ for very metal-poor/disk stars) were almost confirmed, since the non-LTE corrections for the Zn I 4722/4810 and 6362 lines (tending to be positive and gradually increasing toward lower $\mathrm{[Fe/H]}$) are quantitatively of less significance ($\lesssim 0.1 \,\mathrm{dex}$).

Effects of line-blocking on the non-LTE Fe I spectral line formation

The effects of background line opacity (line-blocking) in statistical equilibrium calculations for Fe in late-type stellar atmospheres have been investigated using an extensive and up-to-date model atom with radiative data primarily from the IRON Project. The background metal line opacities have been computed using data from the MARCS stellar model atmospheres. While accounting for this line opacity is important at solar metallicity, the differences between calculations including and excluding line-blocking at low metallicity are insignificant for the non-local thermodynamic equilibrium (non-LTE) abundance corrections for Fe I lines. The line-blocking has no impact on the non-LTE effects of Fe II lines. The dominant uncertainty in Fe non-LTE calculations for metal-poor stars is still the treatment of the inelastic H I collisions, which have here been included using scaling factors to the classical Drawin formalism, and whether or not thermalisation of the high Fe I levels to Fe II ground state should be enforced. Without such thermalisation, the Fe I non-LTE abundance corrections are substantial in metal-poor stars: about 0.3 dex with efficient (i.e. Drawin-like) H I collisions and about 0.5 dex without. Without both thermalisation and H I collisions, even Fe II lines show significant non-LTE effects in such stars.

CI non–LTE spectral line formation in late-type stars

We present non-Local Thermodynamic Equilibrium (non-LTE) calculations for neutral carbon spectral line formation, carried out for a grid of model atmospheres covering the range of late-type stars. The results of our detailed calculations suggest that the carbon non-LTE corrections in these stars are higher than usually adopted, remaining substantial even at low metallicity. For the most metal-poor stars in the sample of Akerman et al. (2004), the non-LTE abundance corrections are of the order of -0.35...-0.45 dex (when neglecting H collisions). Applying our results to those observations, the apparent [C/O] upturn seen in their LTE analysis is no longer present, thus revealing no need to invoke contributions from Pop. III stars to the carbon nucleosynthesis.

Chemical abundances of 10 metal-poor halo stars

We present observations of ten metal-poor halo stars with the metallicity range −2.3 < (Fe/H) < −1.4 and derive their stellar parameters, acquire some elemental abundances relative to iron and discuss the relation between the abundance ratio and the metallicity. It was found that oxygen abundances are nearly constant at a level of 0.6 dex for our metal-poor halo stars when the non-LTE correction is considered. The α-elements (Mg, Si, Ca and Ti) are overabundant relative to Fe and decrease with increasing metallicity. We also obtained a significant underabundant non-LTE (Na/Fe) ratio from Na  D lines which have a large deviation from the LTE assumption. Scandium is marginally overabundant with respect to iron and tends to decrease with increasing metallicity like the α-elements. A nearly solar value of (Cr/Fe) ratio and underabundant (Mn/Fe) ratio are obtained.

The evolution of the C/O ratio in metal-poor halo stars

We report new measurements of carbon and oxygen abundances in 34 F and G dwarf and subgiant stars belonging to the halo population and spanning a range of metallicity from [Fe/H] to -3.2 . The survey is based on observations of four permitted lines of near 9100 Å and the triplet, all recorded at high signal-to-noise ratios with the UVES echelle spectrograph on the ESO VLT. The line equivalent widths were analysed with the 1D, LTE, MARCS model atmosphere code to deduce C and O abundances; corrections due to non-LTE and 3D effects are discussed. When combined with similar published data for disk stars, our results confirm the metallicity dependence of the C/O ratio known from previous stellar and interstellar studies: C/O drops by a factor of ~3–4 as O/H decreases from solar to ~1/10 solar. Analysed within the context of standard models for the chemical evolution of the solar vicinity, this drop results from the metallicity dependence of the C yields from massive stars with mass loss, augmented by the delayed release of C from stars of low and intermediate mass. The former is, however, always the dominant factor. Our survey has also uncovered tentative evidence to suggest that, as the oxygen abundance decreases below [O/H] , [C/O] may not remain constant at [C/O] , as previously thought, but increase again, possibly approaching near-solar values at the lowest metallicities ([O/H] ). With the current dataset this is no more than a 3σ effect and it may be due to metallicity-dependent non-LTE corrections to the [C/O] ratio which have not been taken into account. However, its potential importance as a window on the nucleosynthesis by Population III stars is a strong incentive for future work, both observational and theoretical, to verify its reality.

Oxygen Abundances in Metal‐poor Stars

We present oxygen abundances derived from both the permitted and forbidden oxygen lines for 55 subgiants and giants with [Fe/H] values between -2.7 and solar with the goal of understanding the discrepancy in the derived abundances. A first attempt, using Teff values from photometric calibrations and surface gravities from luminosities obtained agreement between the indicators for turn-off stars, but the disagreement was large for evolved stars. We find that the difference in the oxygen abundances derived from the permitted and forbidden lines is most strongly affected by Teff, and we derive a new Teff scale based on forcing the two sets of lines to give the same oxygen abundances. These new parameters, however, do not agree with other observables, such as theoretical isochrones or Balmer-line profile based Teff determinations. Our analysis finds that one-dimensional, LTE analyses (with published non-LTE corrections for the permitted lines) cannot fully resolve the disagreement in the two indicators without adopting a temperature scale that is incompatible with other temperature indicators. We also find no evidence of circumstellar emission in the forbidden lines, removing such emission as a possible cause for the discrepancy.

Observational constraints on potassium synthesis during the formation of stars of the Galactic disk

The non-LTE potassium abundances in the atmospheres of 33 Galactic-disk stars are derived and the parameters of the atmospheres of 23 of the stars are determined. Neglecting departures from LTE results in a systematic overestimation of the potassium abundances and an increase in their dispersion, even for differential analyses relative to the Sun. The non-LTE corrections are significant ((−0.2)–(−0.6) dex) and depend on the surface gravities and effective temperatures of the stars. The mean potassium abundance for a sample of ten stars with [Fe/H]∼0.0 is in agreement with the solar and meteoritic abundances (log ɛ ⊙(K)=5.12). As the stellar metallicity increases from [Fe/H]=(−1.0) to (0.2) dex, the [K/Fe] ratio decreases systematically from 0.3 dex to −0.1 dex. The derived dependence [K/Fe]-[Fe/H] is in agreement with the results of published model calculations of the chemical evolution of the Galaxy. This indicates the dominance of explosive oxygen burning in massive type II supernovae during the synthesis of potassium in the Galactic disk.

Kinetic equilibrium of iron in the atmospheres of cool stars

Non-LTE line formation calculations of are performed for a small number of reference stars to investigate and quantify the efficiency of neutral hydrogen collisions. Using the atomic model that was described in previous publications, the final discrimination with respect to hydrogen collisions is based on the condition that the surface gravities as determined by the / ionization equilibria are in agreement with their astrometric counterparts obtained from Hipparcos parallaxes. High signal-to-noise, high-resolution échelle spectra are analysed to determine individual profile fits and differential abundances of iron lines. Depending on the choice of the hydrogen collision scaling factor SH, we find deviations from LTE in ranging from 0.00 (SH = ∞) to 0.46 dex (SH = 0 for HD 140283) in the logarithmic abundances while follows LTE. With the exception of Procyon, for which a mild temperature correction is needed to fulfil the ionization balance, excellent consistency is obtained for the metal-poor reference stars if Balmer profile temperatures are combined with SH = 3. This value is much higher than what is found for simple atoms like Li or Ca, both from laboratory measurements and inference of stellar analyses. The correct choice of collisional damping parameters (“van-der-Waals” constants) is found to be generally more important for these little evolved metal-poor stars than considering departures from LTE. For the Sun the calibrated value for SH leads to average non-LTE corrections of 0.02 dex and a mean abundance from lines of ε(Fe) = 7.49 ± 0.08. We confront the deduced stellar parameters with comparable spectroscopic analyses by other authors which also rely on the iron ionization equilibrium as a gravity indicator. On the basis of the Hipparcos astrometry our results are shown to be an order of magnitude more precise than published data sets, both in terms of offset and star-to-star scatter.

Non-LTE Analysis of the Sodium Abundance of Metal-Poor Stars in the Galactic Disk and Halo

We performed an extensive non-LTE analysis of the neutral sodium lines of Na {\sc i} 5683/5688, 5890/5896, 6154/6161, and 8183/8195 for disk/halo stars of F--K type covering a wide metallicity range ($-4 \la$ [Fe/H] $\la 0.4$), based on our own data as well as those collected from the literature. For comparatively metal-rich disk stars ($-1 \la$ [Fe/H] $\la 0$) where the weaker 6154/6161 lines are best abundance indicators, we confirmed [Na/Fe] $\sim$ 0 with an ``upturn'' (i.e., a shallow/broad dip around $-0.5 \la$ [Fe/H] $\la 0$) as already reported by previous studies. Regarding the metal-deficient halo stars, where the much stronger 5890/5896 or 8183/8195 lines suffering considerable (negative) non-LTE corrections amounting to 0.5 dex have to be used, our analysis suggests mildly ``subsolar'' [Na/Fe] values down to $\sim -0.4$ (with a somewhat large scatter of $\sim \pm 0.2$ dex) on the average at the typical halo metallicity of [Fe/H] $\sim -2$, while they appear to rise again toward a very metal-poor regime recovering a near-solar ratio of [Na/Fe] $\sim$ 0 ([Fe/H] $\sim -3$ to -4). These results are discussed in comparison with the previous observational studies along with the theoretical predictions from the available chemical evolution models.

Oxygen line formation in late-F through early-K disk/halo stars

In order to investigate the formation of O i 7771–5 and [O i] 6300/6363 lines, extensive non-LTE calculations for neutral atomic oxygen were carried out for wide ranges of model atmosphere parameters, which are applicable to early-K through late-F halo/disk stars of various evolutionary stages. The formation of the triplet O i lines was found to be well described by the classical two-level-atom scattering model, and the non-LTE correction is practically determined by the parameters of the line-transition itself without any significant relevance to the details of the oxygen atomic model. This simplifies the problem in the sense that the non-LTE abundance correction is essentially determined only by the line-strength (), if the atmospheric parameters of Teff, , and ξ are given, without any explicit dependence of the metallicity; thus allowing a useful analytical formula with tabulated numerical coefficients. On the other hand, our calculations lead to the robust conclusion that LTE is totally valid for the forbidden [O i] lines. An extensive reanalysis of published equivalent-width data of O i 7771–5 and [O i] 6300/6363 taken from various literature resulted in the conclusion that, while a reasonable consistency of O i and [O i] abundances was observed for disk stars (), the existence of a systematic abundance discrepancy was confirmed between O i and [O i] lines in conspicuously metal-poor halo stars () without being removed by our non-LTE corrections, i.e., the former being larger by ~0.3 dex at . An inspection of the parameter-dependence of this discordance indicates that the extent of the discrepancy tends to be comparatively lessened for higher stars, suggesting the preference of dwarf (or subgiant) stars for studying the oxygen abundances of metal-poor stars.