3D non-LTE Research Articles

Titanium abundances in late-type stars

Context. Rapidly growing datasets from stellar spectroscopic surveys are providing unprecedented opportunities to analyse the chemical evolution history of our Galaxy. However, spectral analysis requires accurate modelling of synthetic stellar spectra for late-type stars, for which the assumption of local thermodynamic equilibrium (LTE) has been shown to be insufficient in many cases. Errors associated with LTE can be particularly large for Ti I, which is susceptible to over-ionisation, particularly in metal-poor stars. Aims. The aims of this work are to study and quantify the 1D non-LTE effects on titanium abundances across the Hertzsprung-Russell diagram for a large sample of stars. Methods. A large grid of departure coefficients, βν, were computed on standard MARCS model atmospheres. The grid extends from 3000 K to 8000 K in Teff, −0.5 dex to +5.5 dex in log g, and −5.0 to +1.0 in [Fe/H], with non-LTE effects in this grid reaching up to 0.4 dex. This was used to compute abundance corrections that were subsequently applied to the LTE abundances of over 70 000 stars selected from the GALAH survey in addition to a smaller sample of literature Keck data for metal-poor dwarfs. Results. The non-LTE effects grow towards lower [Fe/H], lower log g, and higher Teff, with a minimum and maximum ΔA(Ti)Ti I of 0.02 and 0.19 in the GALAH sample. For metal-poor giants, the non-LTE modelling reduces the average ionisation imbalance (ΔI−II) from −0.11 dex to −0.01 dex at [Fe/H] = −1.7, and the enhancement in titanium abundances from Ti I lines results in a [Ti/Fe] versus [Fe/H] trend that more closely resembles the behaviour of Ti II at low metallicities. At higher metallicities, the results are limited by the precision of the GALAH DR3 LTE abundances and the effects are within the errors. For the most metal-poor dwarfs from the Keck sample, the average ionisation imbalance increases from −0.1 dex to +0.2 dex, a shortcoming that is consistent with previous 1D non-LTE studies and which we speculate could be related to 3D effects. Conclusions. Non-LTE effects on titanium abundances are significant. Neglecting them may alter our understanding of Galactic chemical evolution. We have made our grid of departure coefficients publicly available, with the caveat that the Ti abundances of metal-poor dwarfs need further study in 3D non-LTE.

1D non-LTE corrections for chemical abundance analyses of very metal-poor stars

ABSTRACT Detailed chemical abundances of very metal-poor (VMP; [Fe/H] < −2) stars are important for better understanding the first stars, early star formation, and chemical enrichment of galaxies. Big on-going and coming high-resolution spectroscopic surveys provide a wealth of material that needs to be carefully analysed. For VMP stars, their elemental abundances should be derived based on the non-local thermodynamic equilibrium (non-LTE = NLTE) line formation because low metal abundances and low electron number density in the atmosphere produce the physical conditions favourable for the departures from LTE. The galactic archaeology research requires homogeneous determinations of chemical abundances. For this purpose, we present grids of the 1D-NLTE abundance corrections for lines of Na i, Mg i, Ca i, Ca ii, Ti ii, Fe i, Zn i, Zn ii, Sr ii, and Ba ii in the range of atmospheric parameters that represent VMP stars on various evolutionary stages and cover effective temperatures from 4000 to 6500 K, surface gravities from $\rm log g$ = 0.5 to 5.0, and metallicities −5.0 ≤ [Fe/H] ≤ −2.0. The data is publicly available, and we provide the tools for interpolating in the grids online.

3D non-LTE iron abundances in FG-type dwarfs

Iron is one of the most important elements in-stellar astrophysics. However, spectroscopic measurements of its abundance are prone to systematic modelling errors. We present three dimensional non-local thermodynamic equilibrium (3D non-LTE) calculations across 32 STAGGER-grid models with effective temperatures from 5000 K to 6500 K, surface gravities of 4.0 dex and 4.5 dex, and metallicities from −3 dex to 0 dex, and we study the effects on 171 Fe i and 12 Fe ii optical lines. In warm metal-poor stars, the 3D non-LTE abundances are up to 0.5 dex larger than 1D LTE abundances inferred from Fe i lines of an intermediate excitation potential. In contrast, the 3D non-LTE abundances can be 0.2 dex smaller in cool metal-poor stars when using Fe i lines of a low excitation potential. The corresponding abundance differences between 3D non-LTE and 1D non-LTE are generally less severe but can still reach ±0.2 dex. For Fe ii lines, the 3D abundances range from up to 0.15 dex larger to 0.10 dex smaller than 1D abundances, with negligible departures from 3D LTE except for the warmest stars at the lowest metallicities. The results were used to correct 1D LTE abundances of the Sun and Procyon (HD 61421), and of the metal-poor stars HD 84937 and HD 140283, using an interpolation routine based on neural networks. The 3D non-LTE models achieve an improved ionisation balance in all four stars. In the two metal-poor stars, they removed excitation imbalances amounting to 250 K to 300 K errors in effective temperature. For Procyon, the 3D non-LTE models suggest [Fe/H] = 0.11 ± 0.03, which is significantly larger than literature values based on simpler models. We make the 3D non-LTE interpolation routine for FG-type dwarfs publicly available, in addition to 1D non-LTE departure coefficients for standard MARCS models of FGKM-type dwarfs and giants. These tools, together with an extended 3D LTE grid for Fe ii from 2019, can help improve the accuracy of stellar parameter and iron abundance determinations for late-type stars.

Titanium abundances in late-type stars

Context. The titanium abundances of late-type stars are important tracers of Galactic formation history. However, abundances inferred from Ti I and Ti II lines can be in stark disagreement in very metal-poor giants. Departures from local thermodynamic equilibrium (LTE) have a large impact on the minority neutral species and thus influence the ionisation imbalance, but satisfactory non-LTE modelling for both dwarfs and giants has not been achieved in the literature. Aims. The reliability of titanium abundances is reassessed in benchmark dwarfs and giants using a new non-LTE model 1D model atmospheres. Methods. A comprehensive model atom was compiled with a more extended level structure and newly published data for inelastic collisions between Ti I and neutral hydrogen. Results. In 1D LTE, the Ti I and Ti II lines agree to within 0.06 dex for the Sun, Arcturus, and the very metal-poor stars HD 84937 and HD 140283. For the very metal-poor giant HD 122563, the Ti I lines give an abundance that is 0.47 dex lower than that from Ti II . The 1D non-LTE corrections can reach +0.4 dex for individual Ti I lines and +0.1 dex for individual Ti II lines, and they reduce the overall ionisation imbalance to −0.17 dex for HD 122563. However, the corrections also increase the imbalance for the very metal-poor dwarf and sub-giant to around 0.2 dex. Conclusions. Using 1D non-LTE reduces the ionisation imbalance in very metal-poor giants but breaks the balance of other very metal-poor stars, consistent with conclusions drawn in the literature. To make further progress, consistent 3D non-LTE models are needed.

Improving spectroscopic lithium abundances

Context. Accurate spectroscopic lithium abundances are essential in addressing a variety of open questions, such as the origin of a uniform lithium content in the atmospheres of metal-poor stars (Spite plateau) or the existence of a correlation between the properties of extrasolar planetary systems and the lithium abundance in the atmosphere of their host stars. Aims. We have developed a tool that allows the user to improve the accuracy of standard lithium abundance determinations based on 1D model atmospheres and the assumption of local thermodynamic equilibrium (LTE) by applying corrections that account for hydrodynamic (3D) and non-LTE (NLTE) effects in FGK stars of different metallicity. Methods. Based on a grid of CO5BOLD 3D models and associated 1D hydrostatic atmospheres, we computed three libraries of synthetic spectra of the lithium λ 670.8 nm line for a wide range of lithium abundances, accounting for detailed line formation in 3D NLTE, 1D NLTE, and 1D LTE, respectively. The resulting curves-of-growth were then used to derive 3D NLTE and 1D NLTE lithium abundance corrections. Results. For all metallicities, the largest corrections are found at the coolest effective temperature, Teff = 5000 K. They are mostly positive, up to + 0.2 dex, for the weakest lines (lithium abundance A(Li)1DLTE = 1.0), whereas they become more negative towards lower metallicities, where they can reach − 0.4 dex for the strongest lines (A(Li)1DLTE = 3.0) at [Fe/H] = − 2.0. We demonstrate that 3D and NLTE effects are small for metal-poor stars on the Spite plateau, leading to errors of at most ± 0.05 dex if ignored. We present analytical functions evaluating the 3D NLTE and 1D NLTE corrections as a function of Teff [5000…6500 K], log g [3.5…4.5], and LTE lithium abundance A(Li) [1.0…3.0] for a fixed grid of metallicities [Fe∕H] [ − 3.0…0.0]. In addition, we also provide analytical fitting functions for directly converting a given lithium abundance into an equivalent width, or vice versa, a given equivalent width (EW) into a lithium abundance. For convenience, a Python script is made available that evaluates all fitting functions for given Teff, log g, [Fe∕H], and A(Li) or EW. Conclusions. By means of the fitting functions developed in this work, the results of complex 3D and NLTE calculations are made readily accessible and quickly applicable to large samples of stars across a wide range of metallicities. Improving the accuracy of spectroscopic lithium abundance determinations will contribute to a better understanding of the open questions related to the lithium content in metal-poor and solar-like stellar atmospheres.

Observational constraints on the origin of the elements

Context. The pursuit of more realistic spectroscopic modelling and consistent abundances has led us to begin a new series of papers designed to improve current solar and stellar abundances of various atomic species. To achieve this, we have begun updating the three-dimensional (3D) non-local thermodynamic equilibrium (non-LTE) radiative transfer code, MULTI3D, and the equivalent one-dimensional (1D) non-LTE radiative transfer code, MULTI 2.3. Aims. We examine our improvements to these codes by redetermining the solar barium abundance. Barium was chosen for this test as it is an important diagnostic element of the s-process in the context of galactic chemical evolution. New Ba II + H collisional data for excitation and charge exchange reactions computed from first principles had recently become available and were included in the model atom. The atom also includes the effects of isotopic line shifts and hyperfine splitting. Methods. A grid of 1D LTE barium lines were constructed with MULTI 2.3 and fit to the four Ba II lines available to us in the optical region of the solar spectrum. Abundance corrections were then determined in 1D non-LTE, 3D LTE, and 3D non-LTE. A new 3D non-LTE solar barium abundance was computed from these corrections. Results. We present for the first time the full 3D non-LTE barium abundance of A(Ba) = 2.27 ± 0.02 ± 0.01, which was derived from four individual fully consistent barium lines. Errors here represent the systematic and random errors, respectively.

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.

3D non-LTE corrections for Li abundance and6Li/7Li isotopic ratio in solar-type stars

Context. Convective motions in solar-type stellar atmospheres induce Doppler shifts that affect the strengths and shapes of spectral absorption lines and create slightly asymmetric line profiles. One-dimensional (1D) local thermodynamic equilibrium (LTE) studies of elemental abundances are not able to reproduce this phenomenon, which becomes particularly important when modeling the impact of isotopic fine structure, like the subtle depression created by the6Li isotope on the red wing of the Li Iresonance doublet line.Aims. The purpose of this work is to provide corrections for the lithium abundance,A(Li), and the6Li/7Li isotopic ratio that can easily be applied to correct 1D LTE lithium abundances in G and F dwarf stars of approximately solar mass and metallicity for three-dimensional (3D) and non-LTE (NLTE) effects.Methods. The corrections forA(Li) and6Li/7Li are computed using grids of 3D NLTE and 1D LTE synthetic lithium line profiles, generated from 3D hydro-dynamicalCO5BOLDand 1D hydrostatic model atmospheres, respectively. For comparative purposes, all calculations are performed for three different line lists representing the Li Iλ670.8 nm spectral region. The 3D NLTE corrections are then approximated by analytical expressions as a function of the stellar parameters (Teff, logℊ, [Fe/H],νsini,A(Li),6Li/7Li). These are applied to adjust the 1D LTE isotopic lithium abundances in two solar-type stars,HD 207129andHD 95456, for which high-quality HARPS observations are available.Results. The derived 3D NLTE corrections range between −0.01 and +0.11 dex forA(Li), and between −4.9 and −0.4% for6Li/7Li, depending on the adopted stellar parameters. We confirm that the inferred6Li abundance depends critically on the strength of the Si I670.8025 nm line. Our findings show a general consistency with recent works on lithium abundance corrections. After the application of such corrections, we do not find a significant amount of6Li in any of the two target stars.Conclusions. In the case of6Li/7Li, our corrections are always negative, showing that 1D LTE analysis can significantly overestimate the presence of6Li (up to 4.9% points) in the atmospheres of solar-like dwarf stars. These results emphasize the importance of reliable 3D model atmospheres combined with NLTE line formation for deriving precise isotopic lithium abundances. Although 3D NLTE spectral synthesis implies an extensive computational effort, the results can be made accessible with parametric tools like the ones presented in this work.

Revisiting the Iron Abundance in the Hyper Iron-poor Star HE 1327–2326 with UV COS/HST Data*

Abstract We present a new iron abundance analysis of the hyper metal-poor star HE 1327−2326, based on Fe ii lines detected in its UV spectral range for the first time. In a Cosmic Origins Spectrograph (COS) spectrum, five new Fe ii lines could be measured. A Si i line was also detected for the first time. We determine a 1D local thermodynamic equilibrium (LTE) Fe ii abundance of [Fe ii/H] = −5.99 ± 0.25. We also investigate departures from LTE for both Fe i and Fe ii lines. Guided by 3D non-LTE (NLTE) analyses of other well-studied metal-poor stars, we identify potential “residual” 3D effects in HE 1327−2326 arising from the absence of full 3D NLTE Fe calculations. Accordingly, we employ measurements of 10 weak Fe i lines previously detected in an optical spectrum of HE 1327−2326, as no Fe i lines are detectable in our UV spectrum. Following our previous work, we adopt the 1D NLTE Fe i abundance of = −5.20 ± 0.12 for HE 1327−2326. Adopting a value based on the optical Fe i rather than UV lines was heavily informed by our extensive investigation of model atmosphere and radiative transfer effects on different lines across the entire UV–optical wavelength range. An iron abundance of = −5.20 ± 0.12 is only 0.2 dex higher than what was used in previous studies. Accordingly, no previous conclusions regarding the nature of the star are affected.

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.

Non-LTE oxygen line formation in 3D hydrodynamic model stellar atmospheres

The OI 777 nm lines are among the most commonly used diagnostics for the oxygen abundances in the atmospheres of FGK-type stars. However, they form in conditions that are far from local thermodynamic equilibrium (LTE). We explore the departures from LTE of atomic oxygen, and their impact on OI lines, across the Stagger-grid of three-dimensional hydrodynamic model atmospheres. For the OI 777 nm triplet we find significant departures from LTE. These departures are larger in stars with larger effective temperatures, smaller surface gravities, and larger oxygen abundances. We present grids of predicted 3D non-LTE based equivalent widths for the OI616nm, [OI] 630 nm, [OI] 636 nm, and OI 777 nm lines, as well as abundance corrections to 1D LTE based results.

The barium isotopic fractions in five metal-poor stars

We provide measurements of the Ba isotopic fractions for five metal-poor stars derived with an LTE analysis using 1D model stellar atmospheres. We use high resolution (R\equiv{\lambda}/\Delta{\lambda}=90000-95000), very high signal-to-noise (S/N>500) spectra to determine the fraction of odd Ba isotopes (fodd) by measuring subtle asymmetries in the profile of the Ba ii line at 4554 {\AA}. We also use two different macroturbulent broadening techniques, Gaussian and radial-tangential, to model the Fe lines of each star, and propagate each technique to model macroturbulent broadening in the Ba 4554 {\AA} line. We conduct a 1D non-LTE (NLTE) treatment of the Fe lines in the red giant HD122563 and the subgiant HD140283 in an attempt to improve the fitting. We determine [Ba/Eu] ratios for the two giants in our study, HD122563 and HD88609, which can also be used to determine the relative contribution of the s- and r-processes to heavy-element nucleosynthesis, for comparison with fodd. We find fodd for HD122563, HD88609 and HD84937, BD+26\circ3578 and BD-04\circ3208 to be -0.12\pm0.07, -0.02\pm0.09, and -0.05\pm0.11, 0.08\pm0.08 and 0.18\pm0.08 respectively. This means that all stars examined here show isotopic fractions more compatible with an s-process dominated composition. The [Ba/Eu] ratios in HD122563 and HD88609 are found to be -0.20\pm0.15 and -0.47\pm0.15 respectively, which indicate instead an r-process signature. We report a better statistical fit to the majority of Fe profiles in each star when employing a radial-tangential broadening technique during our 1D LTE investigation. We have shown that, from a statistical point of view, one must consider using a radial-tangential broadening technique rather than a Gaussian one to model Fe line macroturbulences when working in 1D. No improvement to Fe line fitting is seen when employing a NLTE treatment.

Convection and 6Li in the atmospheres of metal-poor halo stars

AbstractBased on 3D hydrodynamical model atmospheres computed with the CO5BOLD code and 3D non-LTE (NLTE) line formation calculations, we study the effect of the convection-induced line asymmetry on the derived 6Li abundance for a range in effective temperature, gravity, and metallicity covering the stars of the Asplund et al. (2006) sample. When the asymmetry effect is taken into account for this sample of stars, the resulting 6Li/7Li ratios are reduced by about 1.5% on average with respect to the isotopic ratios determined by Asplund et al. (2006). This purely theoretical correction diminishes the number of significant 6Li detections from 9 to 4 (2σ criterion), or from 5 to 2 (3σ criterion). In view of this result the existence of a 6Li plateau appears questionable. A careful reanalysis of individual objects by fitting the observed lithium 6707 Å doublet both with 3D NLTE and 1D LTE synthetic line profiles confirms that the inferred 6Li abundance is systematically lower when using 3D NLTE instead of 1D LTE line fitting. Nevertheless, halo stars with unquestionable 6Li detection do exist even if analyzed in 3D-NLTE, the most prominent example being HD 84937.

Multi-level 3D non-LTE computations of lithium lines in the metal-poor halo stars HD 140283 and HD 84937

The lithium abundances in metal-poor halo stars are of importance for cosmology, galaxy evolution and stellar structure. In an attempt to study possible systematic errors in the derived Li abundances, the line formation of Li i lines has been investigated by means of realistic 3D hydrodynamical model atmospheres of halo stars and 3D non-LTE radiative transfer calculations. These are the first detailed 3D non-LTE computations reported employing a multi-level atomic model showing that such problems are now computationally tractable. The detailed computations reveal that the Li i population has a strong influence from the radiation field rather than the local gas temperature, indicating that the low derived Li abundances found by Asplund et al. (1999) are an artifact of their assumption of LTE. Relative to 3D LTE, the detailed calculations show pronounced over-ionization. In terms of abundances the 3D non-LTE values are within 0.05 dex of the 1D non-LTE results for the particular cases of HD 140283 and HD 84937, which is a consequence of the dominance of the radiation in determining the population density of Li i. Although 3D non-LTE can be expected to give results rather close (≈ dex) to 1D non-LTE for this reason, there may be systematic trends with metallicity and effective temperature.