non-LTE Abundance Corrections Research Articles

Three-Dimensional Non–Local Thermodynamic Equilibrium Abundance Analyses of Late-Type Stars

The chemical compositions of stars encode the history of the universe and are thus fundamental for advancing our knowledge of astrophysics and cosmology. However, measurements of elemental abundances ratios, and our interpretations of them, strongly depend on the physical assumptions that dictate the generation of synthetic stellar spectra. Three-dimensional radiation-hydrodynamic (3D RHD) box-in-a-star simulations of stellar atmospheres offer a more realistic representation of surface convection occurring in late-type stars than do traditional one-dimensional (1D) hydrostatic models. As evident from a multitude of observational tests, the coupling of 3D RHD models with line formation in nonlocal thermodynamic equilibrium (non-LTE) today provides a solid foundation for abundance analysis for many elements. This review describes the ongoing and transformational work to advance the state of the art and replace 1D LTE spectrum synthesis with its 3D non-LTE counterpart. In summary: ▪ 3D and non-LTE effects are intricately coupled, and consistent modeling thereof is necessary for high-precision abundances; such modeling is currently feasible for individual elements in large surveys. Mean 3D (〈3D〉) models are not adequate as substitutes. ▪ The solar abundance debate is presently dominated by choices and systematic uncertainties that are not specific to 3D non-LTE modeling. ▪ 3D non-LTE abundance corrections have a profound impact on our understanding of FGK-type stars, exoplanets, and the nucleosynthetic origins of the elements.

Non-LTE abundance corrections for late-type stars from 2000 Å to 3 µm

Context. It is well known that cool star atmospheres depart from local thermodynamic equilibrium (LTE). Making an accurate abundance determination requires taking those effects into account, but the necessary non-LTE (hereafter NLTE) calculations are often lacking. Aims. Our goal is to provide detailed estimates of NLTE effects for FGK type stars for all spectral lines from the ultraviolet (UV) to the near infrared (NIR) that are potentially useful as abundance diagnostics. The first paper in this series focusses on the light elements Na, Mg, and Al. Methods. The code PySME was used to compute curves of growth for 2158 MARCS model atmospheres in the parameter range 3800 < Teff < 8000 K, 0.0 < log(g) < 5.5, and −5 < [Fe/H] < +0.5. Two microturbulence values, 1 and 2 kms−1, and nine abundance points spanning −1 < [X/Fe] < 1 for element X, are used to construct individual line curves of growth by calculating the equivalent widths of 35 Na lines, 134 Mg lines, and 34 Al lines. The lines were selected in the wavelength range between 2000 Å and 3 µm. Results. We demonstrate the power of the new grids with LTE and NLTE abundance analysis by means of equivalent width measurements of five benchmark stars; the Sun, Arcturus, HD 84937, HD 140283 and HD 122563. For Na, the NLTE abundances are lower than in LTE and show markedly reduced line-to-line scatter in the metal-poor stars. For Mg, we confirm previous reports of a significant ~0.25 dex LTE ionisation imbalance in metal-poor stars that is only slightly improved in NLTE (~0.18 dex). LTE abundances based on Mg II lines agree better with models of Galactic chemical evolution. For Al, NLTE calculations strongly reduce an ~0.6 dex ionisation imbalance seen in LTE for the metal-poor stars. The abundance corrections presented in this work are in good agreement with previous studies for the subset of lines that overlap, with the exception of strongly saturated lines. Conclusions. A consensus between different abundance diagnostics is the most powerful tool available to stellar spectroscopists to assess the accuracy of the models. Here we report that NLTE abundance analysis in general leads to improved agreement, in particular for metal-poor stars. The residual scatter is believed to be caused mainly by unresolved blends and/or poor atomic data, with the notable exception of Mg, which calls for further investigation.

Non-LTE abundances of zinc in different spectral type stars and the Galactic [Zn/Fe] trend based on quantum-mechanical data on inelastic processes in zinc-hydrogen collisions

ABSTRACT We present a new model atom of Zn i-Zn ii based on the most up-to-date photoionization cross-sections, electron-impact excitation rates, and rate coefficients for the Zn i + H i and Zn ii + H− collisions. The latter were calculated using the multichannel quantum asymptotic treatment based on the Born–Oppenheimer approach. Non-LTE analysis was performed for the first time for lines of Zn i and Zn ii in the ultraviolet (UV) spectra of two very metal-poor reference stars: HD 84937 and HD 140283. We found consistent non-LTE abundance from the resonance Zn i 2138 Å line, the subordinate lines, and the lines of Zn ii. In both stars, non-LTE leads to 0.17 dex higher average abundance from Zn i, while, for Zn ii lines, non-LTE corrections are minor and do not exceed 0.06 dex. Using lines of Zn i in the high-resolution spectra, we determined the non-LTE abundances for a sample of 80 stars in the −2.5 ≤ [Fe/H] ≤ 0.2 metallicity range. The [Zn/Fe] versus [Fe/H] diagram reveals a dip, with [Zn/Fe] ≃ 0.3 in the most metal-poor stars, a close-to-solar value for [Fe/H] ∼−1.2, and increasing [Zn/Fe] up to 0.3 in the thick disc stars. The close-to-solar metallicity stars have subsolar [Zn/H] ≃ −0.1, on average. Non-LTE abundances of zinc were derived for the first time for seven reference F- to B-type stars. We provide a grid of the non-LTE abundance corrections.

Accurate Metallicities for Very Metal-poor Stars from the Ca ii Infrared Triplet

Abstract The Ca ii H and K lines are among the few features available to infer the metallicity of extremely metal-poor stars from medium-resolution spectroscopy. Unfortunately, these lines can overlap with absorption produced in the intervening interstellar medium, introducing systematic errors in the derived metallicities. The strength of the Ca ii infrared triplet lines can also be measured at extremely low metallicities, and it is not affected by interstellar absorption, but it suffers significant departures from local thermodynamic equilibrium (LTE). We investigate the feasibility of adopting the Ca ii infrared triplet as a metallicity indicator in extremely metal-poor stars using state-of-the art non-LTE models including the most recent atomic data. We find that the triplet lines exhibit non-LTE abundance corrections that can exceed 0.5 dex. When interstellar absorption affecting the Ca ii resonance lines is accounted for using high-resolution observations, the agreement between non-LTE abundances for the triplet and those for the resonance lines, with only minor departures from LTE, is excellent. Non-LTE effects strengthen the Ca ii IR triplet lines, facilitating measurements at very low metallicities, compared with LTE estimates, down to [Fe/H] = −6.0. This result has important implications for the discovery of primitive stars in our Galaxy and others, since instruments are most sensitive at red/near-infrared wavelengths, and tens of millions of spectra covering the Ca ii IR triplet will soon become available from the Gaia, DESI, WEAVE, and PFS missions.

Inelastic Processes in Strontium-Hydrogen Collisions and Their Impact on Non-LTE Calculations

Inelastic processes rate coefficients for low-energy Sr + H, Sr+ + H−, Sr+ + H, and Sr2+ + H− collisions are calculated using the multichannel quantum model approach. A total of 31 scattering channels of SrH+ and 17 scattering channels of SrH are considered. The partial cross sections and the partial rate coefficients are hence calculated for 1202 partial processes in total. Using new quantum data for Sr ii + H i collisions, we updated the model atom of Sr ii and performed the non-local thermodynamic equilibrium (non-LTE) calculations. We provide the non-LTE abundance corrections for the Sr ii resonance lines in two grids of model atmospheres, which are applicable to very metal-poor ([Fe/H] ≤−2) dwarfs and giants.

Detection of Al ii in the Ultraviolet Spectra of Metal-poor Stars: An Empirical LTE Test of NLTE Aluminum Abundance Calculations*

Abstract We report the detection of an Al ii line at 2669.155 Å in 11 metal-poor stars, using ultraviolet spectra obtained with the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope. We derive Al abundances from this line using a standard abundance analysis, assuming local thermodynamic equilibrium (LTE). The mean [Al/Fe] ratio is −0.06 ± 0.04 (σ = 0.22) for these 11 stars spanning − 3.9 < [Fe/H] < −1.3, or [Al/Fe] = −0.10 ± 0.04 (σ = 0.18) for 9 stars spanning −3.0 < [Fe/H] < −1.3 if two carbon-enhanced stars are excluded. We use these abundances to perform an empirical test of non-LTE (NLTE) abundance corrections predicted for resonance lines of Al i, including the commonly used optical Al i line at 3961 Å. The Al ii line is formed in LTE, and the abundance derived from this line matches that derived from high-excitation Al i lines predicted to have minimal NLTE corrections. The differences between the abundance derived from the Al ii line and the LTE abundance derived from Al i resonance lines are +0.4 to +0.9 dex, which match the predicted NLTE corrections for the Al i resonance lines. We conclude that the NLTE abundance calculations are approximately correct and should be applied to LTE abundances derived from Al i lines.

Influence of inelastic collisions with hydrogen atoms on the non-local thermodynamic equilibrium line formation for Fe I and Fe II in the 1D model atmospheres of late-type stars

Context. Iron plays a crucial role in studies of late-type stars. In their atmospheres, neutral iron is the minority species, and lines of Fe I are subject to the departures from local thermodynamic equilibrium (LTE). In contrast, one believes that LTE is a realistic approximation for Fe II lines. The main source of the uncertainties in the non-LTE (NLTE) calculations for cool atmospheres is a treatment of inelastic collisions with hydrogen atoms. Aims. Our aim is to investigate the effect of Fe I + H I and Fe II + H I collisions and their different treatments on the Fe I/Fe II ionisation equilibrium and iron abundance determinations for three Galactic halo benchmark stars (HD 84937, HD 122563, and HD 140283) and a sample of 38 very metal-poor giants in the dwarf galaxies with well known distances. Methods. We performed the NLTE calculations for Fe I–Fe II by applying quantum-mechanical rate coefficients for collisions with H I from recent papers. Results. We find that collisions with H I serve as efficient thermalisation processes for Fe II, to an extent that the NLTE abundance corrections for Fe II lines do not exceed 0.02 dex, in absolute value, for [Fe/H] ≳−3, and reach +0.06 dex at [Fe/H] ~−4. For a given star, different treatments of Fe I + H I collisions lead to similar average NLTE abundances from the Fe I lines, although discrepancies in the NLTE abundance corrections exist for individual lines. By using quantum-mechanical collisional data and the Gaia-based surface gravity, we obtain consistent abundances from the two ionisation stages, Fe I and Fe II, for red giant HD 122563. For turn-off star HD 84937, and subgiant HD 140283, we analyse the iron lines in the visible and the ultra-violet (UV, 1968–2990 Å) ranges. For either Fe I or Fe II, abundances from the visible and UV lines are found to be consistent in each star. The NLTE abundances from the two ionisation stages agree within 0.10 dex and 0.13 dex for two different treatments of Fe I + H I collisions. The Fe I/Fe II ionisation equilibrium is achieved for each star of our stellar sample in the dwarf galaxies, with the exception of stars at [Fe/H] ≲−3.7.

Carbon, oxygen, and iron abundances in disk and halo stars

The abundances of carbon, oxygen, and iron in late-type stars are important parameters in exoplanetary and stellar physics, as well as key tracers of stellar populations and Galactic chemical evolution. However, standard spectroscopic abundance analyses can be prone to severe systematic errors, based on the assumption that the stellar atmosphere is one-dimensional (1D) and hydrostatic, and by ignoring departures from local thermodynamic equilibrium (LTE). In order to address this, we carried out three-dimensional (3D) non-LTE radiative transfer calculations for C I and O I, and 3D LTE radiative transfer calculations for Fe II, across the STAGGER-grid of 3D hydrodynamic model atmospheres. The absolute 3D non-LTE versus 1D LTE abundance corrections can be as severe as − 0.3 dex for C I lines in low-metallicity F dwarfs, and − 0.6 dex for O I lines in high-metallicity F dwarfs. The 3D LTE versus 1D LTE abundance corrections for Fe II lines are less severe, typically less than + 0.15 dex. We used the corrections in a re-analysis of carbon, oxygen, and iron in 187 F and G dwarfs in the Galactic disk and halo. Applying the differential 3D non-LTE corrections to 1D LTE abundances visibly reduces the scatter in the abundance plots. The thick disk and high-α halo population rise in carbon and oxygen with decreasing metallicity, and reach a maximum of [C/Fe] ≈ 0.2 and a plateau of [O/Fe] ≈ 0.6 at [Fe/H] ≈ −1.0. The low-α halo population is qualitatively similar, albeit offset towards lower metallicities and with larger scatter. Nevertheless, these populations overlap in the [C/O] versus [O/H] plane, decreasing to a plateau of [C/O] ≈ −0.6 below [O/H] ≈ −1.0. In the thin-disk, stars having confirmed planet detections tend to have higher values of C∕O at given [O/H]; this potential signature of planet formation is only apparent after applying the abundance corrections to the 1D LTE results. Our grids of line-by-line abundance corrections are publicly available and can be readily used to improve the accuracy of spectroscopic analyses of late-type stars.

Non-LTE analysis of K I in late-type stars

Context. Older models of Galactic chemical evolution (GCE) predict [K/Fe] ratios as much as 1 dex lower than those inferred from stellar observations. Abundances of potassium are mainly based on analyses of the 7698 Å resonance line, and the discrepancy between GCE models and observations is in part caused by the assumption of local thermodynamic equilibrium (LTE) in spectroscopic analyses. Aims. We study the statistical equilibrium of K I, focusing on the non-LTE effects on the 7698 Å line. We aim to determine how non-LTE abundances of potassium can improve the analysis of its chemical evolution, and help to constrain the yields of GCE models. Methods. We construct a new model K I atom that employs the most up-to-date atomic data. In particular, we calculate and present inelastic e+K collisional excitation cross-sections from the convergent close-coupling (CCC) and the B-Spline R-matrix (BSR) methods, and H+K collisions from the two-electron model (LCAO). We constructed a fine, extended grid of non-LTE abundance corrections based on 1D MARCS models that span 4000 < Teff∕K < 8000, 0.50 < log g < 5.00, − 5.00 < [Fe/H] < + 0.50, and applied the corrections to potassium abundances extracted from the literature. Results. In concordance with previous studies, we find severe non-LTE effects in the 7698 Å line. The line is stronger in non-LTE and the abundance corrections can reach approximately − 0.7 dex for solar-metallicity stars such as Procyon. We determine potassium abundances in six benchmark stars, and obtain consistent results from different optical lines. We explore the effects of atmospheric inhomogeneity by computing for the first time a full 3D non-LTE stellar spectrum of K I lines for a test star. We find that 3D modeling is necessary to predict a correct shape of the resonance 7698 Å line, but the line strength is similar to that found in 1D non-LTE. Conclusions. Our non-LTE abundance corrections reduce the scatter and change the cosmic trends of literature potassium abundances. In the regime [Fe/H] ≲−1.0 the non-LTE abundances show a good agreement with the GCE model with yields from rotating massive stars. The reduced scatter of the non-LTE corrected abundances of a sample of solar twins shows that line-by-line differential analysis techniques cannot fully compensate for systematic LTE modelling errors; the scatter introduced by such errors introduces a spurious dispersion to K evolution.

Even-to-Odd Barium Isotope Ratio in Selected Galactic Halo Stars

We have updated the Ba II model atom by taking into account the H I impact excitation with the rate coefficients from the quantum-mechanical calculations of Belyaev and Yakovleva (2018). Using high-resolution stellar spectra and the non-local thermodynamic equilibrium (non-LTE) line formation for Ba II, we have determined the fraction of barium isotopes with an odd mass number (fodd}) in four Galactic halo giants with well-known atmospheric parameters. We use a method based on the requirement that the abundances from the Ba II 4554 A resonance and Ba II 5853, 6496 A subordinate lines be equal. An accuracy of 0.04 dex in determining the barium abundance from individual lines has been achieved. In three stars (HD 2796, HD 108317, and HD 122563) fodd >= 0.4. This suggests that >= 80 % of the barium observed in these stars was synthesized in the r-process. In HD 128279 fodd = 0.27 exceeds the fraction of odd barium isotopes in the Solar system, but only slightly. The dominance of the r-process at the formation epoch of our sample stars is confirmed by the presence of a europium overabundance relative barium, with [Eu/Ba] > 0.3. We have calculated the non-LTE abundance corrections for five Ba II lines and investigated their dependence on atmospheric parameters in the ranges of effective temperatures from 4500 to 6500 K, surface gravities log g from 0.5 to 4.5, and metallicities [Fe/H] from 0 to -3.

3D non-LTE line formation of neutral carbon in the Sun

Carbon abundances in late-type stars are important in a variety of astrophysical contexts. However C I lines, one of the main abundance diagnostics, are sensitive to departures from local thermodynamic equilibrium (LTE). We present a model atom for non-LTE analyses of C I lines, that uses a new, physically-motivated recipe for the rates of neutral hydrogen impact excitation. We analyse C I lines in the solar spectrum, employing a three-dimensional (3D) hydrodynamic model solar atmosphere and 3D non-LTE radiative transfer. We find negative non-LTE abundance corrections for C I lines in the solar photosphere, in accordance with previous studies, reaching up to around 0.1 dex in the disk-integrated flux. We also present the first fully consistent 3D non-LTE solar carbon abundance determination: we infer log ɛC = 8.44 ± 0.02, in good agreement with the current standard value. Our models reproduce the observed solar centre-to-limb variations of various C I lines, without any adjustments to the rates of neutral hydrogen impact excitation, suggesting that the proposed recipe may be a solution to the long-standing problem of how to reliably model inelastic collisions with neutral hydrogen in late-type stellar atmospheres.

Inelastic e+Mg collision data and its impact on modelling stellar and supernova spectra

Results of calculations for inelastic e+Mg effective collision strengths for the lowest 25 physical states of Mg I (up to 3s6p 1P), and thus 300 transitions, from the convergent close-coupling (CCC) and the B-spline R-matrix (BSR) methods are presented. At temperatures of interest, ~5000 K, the results of the two calculations differ on average by only 4%, with a scatter of 27%. As the methods are independent, this suggests that the calculations provide datasets for e+Mg collisions accurate to this level. Comparison with the commonly used dataset compiled by Mauas et al. (1988), covering 25 transitions among 12 states, suggests the Mauas et al. data are on average ~57% too low, and with a very large scatter of a factor of ~6.5. In particular the collision strength for the transition corresponding to the Mg I intercombination line at 457 nm is significantly underestimated by Mauas et al., which has consequences for models that employ this dataset. In giant stars the new data leads to a stronger line compared to previous non-LTE calculations, and thus a reduction in the non-LTE abundance correction by ~0.1 dex (~25%). A non-LTE calculation in a supernova ejecta model shows this line becomes significantly stronger, by a factor of around two, alleviating the discrepancy where the 457 nm line in typical models with Mg/O ratios close to solar tended to be too weak compared to observations.

The solar silicon abundance based on 3D non-LTE calculations

We present three-dimensional (3D) non-local thermodynamic equilibrium (non-LTE) radiative transfer calculations for silicon in the solar photosphere, using an extensive model atom that includes recent, realistic neutral hydrogen collisional cross-sections. We find that photon losses in the SiI lines give rise to slightly negative non-LTE abundance corrections of the order -0.01 dex. We infer a 3D non-LTE based solar silicon abundance of 7.51 dex. With silicon commonly chosen to be the anchor between the photospheric and meteoritic abundances, we find that the meteoritic abundance scale remains unchanged compared with the Asplund et al. (2009) and Lodders et al. (2009) results.

Influence of departures from LTE on calcium, titanium, and iron abundance determinations in cool giants of different metallicities

Non-local thermodynamic equilibrium (non-LTE) line formation for Ca I-Ca II, Ti I-Ti II, and Fe I-Fe II is considered in model atmospheres of giant stars with an effective temperature of 4000 K $\le$ Teff $\le$ 5000 K and a metal abundance of -4 $\le$ [Fe/H] $\le$ 0. The departures from LTE are analyzed depending on atmospheric parameters. We present the non-LTE abundance corrections for 28 lines of Ca I, 42 lines of Ti I, 54 lines of Ti II, and 262 lines of Fe I and a three-dimensional interpolation code to obtain the non-LTE correction online (http://spectrum.inasan.ru/nLTE/) for an individual spectral line and given atmospheric parameters.

Influence of inelastic collisions with hydrogen atoms on the formation of AlI and SiI lines in stellar spectra

The non-LTE line formation for Al I and Si I was calculated with model atmospheres corresponding to F-G-K type stars of different metallicity. To account for inelastic collisions with H I, for the first time we applied the cross sections calculated by Belyaev et al. using model approaches within the formalism of the Born-Oppenheimer quantum theory. For Al I non-LTE leads to overionization in the line formation layers and to weakened spectral lines, in line with earlier non-LTE studies. However, in contrast to the previuos studies, our results predict smaller magnitude of the non-LTE effects for the subordinate lines. Owing to large cross sections, the ion-pair production and mutual neutralization processes Al I(nl) + H I(1s) $\leftrightarrow$ Al~II(3s^2) + H^- provide a close coupling of high-excitation Al I levels to the Al II ground state, which causes smaller deviations from the TE populations compared to the case of pure electron collisions. For three metal-poor stars, the Al abundance was determined from seven lines in different models of their formation. In LTE and in non-LTE calculations with pure electron collisions, the Al I 3961 A resonance line gives a 0.25-0.45 dex lower abundance than the mean from the subordinate lines. The difference is removed by accounting for the collisions with H I, and the rms error of the abundance from all seven lines decreases by a factor of 1.5-3 compared to LTE. We calculated the non-LTE abundance corrections for six Al I lines depending on Teff (4500-6500 K), log g (3.0-4.5), and [Fe/H] (0, -1, -2, -3). For Si I including the collisions with H I leads to TE populations in the line formation layers and to minor departures from LTE in spectral lines.

Mg line formation in late-type stellar atmospheres

Mg is often traced in late-type stars using lines of neutral magnesium, which is expected to be subject to departures from LTE. The astrophysical importance of Mg as well as its relative simplicity from an atomic physics point of view, makes it a prime target and test bed for detailed ab initio non-LTE modelling in stellar atmospheres. For the low-lying states of Mg i, electron collision data were calculated using the R-matrix method. Calculations for collisional broadening by neutral hydrogen were also performed where data were missing. These calculations, together with data from the literature, were used to build a model atom. First, the modelling was tested by comparisons with observed spectra of benchmark stars with well-known parameters. Second, the spectral line behaviour and uncertainties were explored by extensive experiments in which sets of collisional data were changed or removed. The modelled spectra agree well with observed spectra. The line-to-line scatter in the derived abundances shows improvements compared to LTE. The observed Mg emission features at 7 and 12 microns in the spectra of the Sun and Arcturus are reasonably well reproduced. The modelling predicts non-LTE abundance corrections in dwarfs, both solar metallicity and metal-poor, to be very small (of order 0.01 dex), even smaller than found in previous studies. In giants, corrections vary greatly between lines, but can be as large as 0.4 dex. Our results emphasise the need for accurate data of Mg collisions with both electrons and H atoms for precise non-LTE predictions of stellar spectra, but demonstrate that such data can be calculated and that ab initio non-LTE modelling without resort to free parameters is possible. Grids of departure coefficients and abundance corrections for a range of stellar parameters are planned for a forthcoming paper.

RED SUPERGIANT STARS AS COSMIC ABUNDANCE PROBES. III. NLTE EFFECTS IN J-BAND MAGNESIUM LINES

Non-LTE calculations for Mg I in red supergiant stellar atmospheres are presented to investigate the importance of non-LTE for the formation of Mg I lines in the NIR J-band. Recent work using medium resolution spectroscopy of atomic lines in the J-band of individual red supergiant stars has demonstrated that technique is a very promising tool to investigate the chemical composition of the young stellar population in star forming galaxies. As in previous work, where non-LTE effects were studied for iron, titanium and silicon, substantial effects are found resulting in significantly stronger Mg I absorption lines. For the quantitative spectral analysis the non-LTE effects lead to magnesium abundances significantly smaller than in LTE with the non-LTE abundance corrections varying smoothly between -0.4 dex and -0.1 dex for effective temperatures between 3400 K and 4400 K. We discuss the physical reasons of the non-LTE effects and the consequences for extragalactic J-band abundance studies using individual red supergiants in the young massive galactic double cluster h and chi Persei.

Non-LTE sodium abundance in galactic thick- and thin-disk red giants

We evaluate non-local thermodynamical equilibrium (non-LTE) line formation for neutral sodium in model atmospheres of the 79 red giants using the model atom that incorporates the best available atomic data. The non-LTE abundances of Na were determined from Na I 6154, 6161 \AA\ for the 38 stars of the thin disk (15 of them the BaII stars), 15 stars of the thick disk, 13 stars of Hercules stream and 13 transition stars which can be identified with neither thin disk nor thick disk. For Na I 6154, 6161 \AA\ non-LTE abundance corrections amount to -0.06 to -0.24 dex depending on stellar parameters. We found no difference in [Na/Fe] abundance between the thick disk and thin disk and the obtained abundances are close to the solar one. We confirmed a weak excess of [Na/Fe] in BaII stars. Stars of the Hercules stream reveal [Na/Fe] abundances close to the solar one. The obtained results can be used to constrain the nucleosynthesis models for Na.

RED SUPERGIANT STARS AS COSMIC ABUNDANCE PROBES. II. NLTE EFFECTS INJ-BAND SILICON LINES

Medium-resolution J-band spectroscopy of individual red supergiant stars is a promising tool to investigate the chemical composition of the young stellar population in star-forming galaxies. As a continuation of recent work on iron and titanium, detailed non-LTE (NLTE) calculations are presented to investigate the influence of NLTE on the formation of silicon lines in the J-band spectra of red supergiants. Substantial effects are found resulting in significantly stronger absorption lines of neutral silicon in NLTE. As a consequence, silicon abundances determined in NLTE are significantly smaller than in local thermodynamic equilibrium (LTE) with the NLTE abundance corrections varying smoothly between −0.4 dex and −0.1 dex for effective temperatures between 3400 K and 4400 K. The effects are largest at low metallicity. The physical reasons behind the NLTE effects and the consequences for extragalactic J-band abundance studies are discussed.

RED SUPERGIANT STARS AS COSMIC ABUNDANCE PROBES: NLTE EFFECTS INJ-BAND IRON AND TITANIUM LINES

Detailed non-LTE calculations for red supergiant stars are presented to investigate the influence of NLTE on the formation of atomic iron and titanium lines in the J-band. With their enormous brightness at J-band red supergiant stars are ideal probes of cosmic abundances. Recent LTE studies have found that metallicities accurate to 0.15 dex can be determined from medium resolution spectroscopy of individual red supergiants in galaxies as distant as 10 Mpc. The non-LTE results obtained in this investigation support these findings. Non-LTE abundance corrections for iron are smaller than 0.05 dex for effective temperatures between 3400K to 4200K and 0.1 dex at 4400K. For titanium the non-LTE abundance corrections vary smoothly between -0.4 dex and +0.2 dex as a function of effective temperature. For both elements, the corrections also depend on stellar gravity and metallicity. The physical reasons behind the non-LTE corrections and the consequences for extragalactic J-band abundance studies are discussed.