arXiv subjects

P. S. Barklem

Publications and source records attributed to P. S. Barklem.

At least 19 recordsLinked to original sources

arXiv2025

Revisiting inelastic Cu+H collisions and the non-LTE Galactic evolution of copper

The Galactic evolution of copper remains poorly understood, partly due to the strong departures from local thermodynamic equilibrium (LTE) affecting Cu I lines. A key source of uncertainty in non-LTE modelling is the treatment of inelastic Cu+H collisions. We present new rate coefficients based on a combined asymptotic LCAO and free electron model approach, which show significant differences from previous calculations. Applying these updated rates to non-LTE stellar modelling, we find reduced line-to-line scatter and improved consistency between metal-poor dwarfs and giants. Our non-LTE analysis reveals a strong upturn in the [Cu/Fe] trend towards lower [Fe/H] < -1.7. We show that this may reflect the interplay between external enrichment of Cu-rich material of the Milky Way halo at low metallicities, and metallicity-dependent Cu yields from rapidly rotating massive stars. This highlights the unique diagnostic potential of accurate Cu abundances for understanding both stellar and Galactic evolution.

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arXiv2024

The solar beryllium abundance revisited with 3D non-LTE models

The present-day abundance of beryllium in the solar atmosphere provides clues about mixing mechanisms within stellar interiors. However, abundance determinations based on the Be II 313.107 nm line are prone to systematic errors due to imperfect model spectra. These errors arise from missing continuous opacity in the UV, a significant unidentified blend at 313.102 nm, departures from local thermodynamic equilibrium (LTE), and microturbulence and macroturbulence fudge parameters associated with one-dimensional (1D) hydrostatic model atmospheres. Although these factors have been discussed in the literature, no study has yet accounted for all of them simultaneously. To address this, we present 3D non-LTE calculations for neutral and ionised beryllium in the Sun. We used these models to derive the present-day solar beryllium abundance, calibrating the missing opacity on high resolution solar irradiance data and the unidentified blend on the centre-to-limb variation. We find a surface abundance of 1.21 $\pm$ 0.05 dex, which is significantly lower than the value of 1.38 dex that has been commonly adopted since 2004. Taking the initial abundance via CI chondrites, our result implies that beryllium has been depleted from the surface by an extra 0.11 $\pm$ 0.06 dex, or 22 $\pm$ 11%, on top of any effects of atomic diffusion. This is in tension with standard solar models, which predict negligible depletion, as well as with contemporary solar models that have extra mixing calibrated on the abundances of helium and lithium, which predict excessive depletion. These discrepancies highlight the need for further improvements to the physics in solar and stellar models.

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arXiv2024

3D NLTE modelling of Y and Eu. Centre-to-limb variation and solar abundances

Context. Abundances of s- and r-process elements in Sun-like stars constrain nucleosynthesis in extreme astrophysical events, such as compact binary mergers and explosions of highly magnetised rapidly rotating massive stars. Aims. We measure solar abundances of yttrium (Y) and europium (Eu) using 3D non-local thermal equilibrium (NLTE) models. We use the model to determine the abundance of Y, and also explore the model's ability to reproduce the solar centre-to-limb variation of its lines. In addition, we determine the Eu abundance using solar disc-centre and integrated flux spectra. Methods. We developed an NLTE model of Eu and updated our model of Y with collisional data from detailed quantum-mechanical calculations. We used the IAG spatially resolved high-resolution solar spectra to derive the solar abundances of Y across the solar disc and of Eu for integrated flux and at disc centre using a set of carefully selected lines and a 3D radiation-hydrodynamics model of the solar atmosphere. Results. We find 3D NLTE solar abundances of A(Y)$_{\textrm{3D NLTE}}$=$2.30 \pm 0.03_{\textrm{stat}} \pm 0.07_{\textrm{syst}}$ dex based on observations at all angles and A(Eu)$_{\textrm{3D NLTE}}$=$0.57 \pm 0.01_{\textrm{stat}} \pm 0.06_{\textrm{syst}}$ dex based on the integrated flux and disc-centre intensity. 3D NLTE modelling offers the most consistent abundances across the solar disc, and resolves the problem of severe systematic bias in Y and Eu abundances inherent to 1D LTE, 1D NLTE, and 3D LTE modelling.

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arXiv2023

The molecular chemistry of Type Ibc supernovae, and diagnostic potential with the James Webb Space Telescope

We aim to investigate how the molecular chemistry in stripped-envelope supernovae (SESNe) affect physical conditions and optical spectra, and produce ro-vibrational emission in the mid-infrared (MIR). We also aim to assess the diagnostic potential of observations of such MIR emission with JWST. We coupled a chemical kinetic network including carbon, oxygen, silicon, and sulfur-bearing molecules into the nonlocal thermal equilibrium (NLTE) spectral synthesis code SUMO. We let four species - CO, SiO, SiS, and SO - participate in NLTE cooling of the gas to achieve self-consistency between the molecule formation and the temperature. We applied the new framework to model the spectrum of a Type Ic SN in the 100-600d time range. Molecules are predicted to form in SESN ejecta in significant quantities (typical mass $10^{-3}$ $M_\odot$) throughout the 100-600d interval. The impact on the temperature and optical emission depends on the density of the oxygen zones and varies with epoch. For example, the [O I] 6300, 6364 feature can be quenched by molecules from 200 to 450d depending on density. The MIR predictions show strong emission in the fundamental bands of CO, SiO, and SiS, and in the CO and SiO overtones. Type Ibc SN ejecta have a rich chemistry and considering the effect of molecules is important for modeling the temperature and atomic emission in the nebular phase. Observations of SESNe with JWST hold promise to provide the first detections of SiS and SO, and to give information on zone masses and densities of the ejecta. Combined optical, near-infrared, and MIR observations can break degeneracies and achieve a more complete picture of the nucleosynthesis, chemistry, and origin of Type Ibc SNe.

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arXiv2023

Titanium abundances in late-type stars I. 1D non-local thermodynamic equilibrium modelling in benchmark dwarfs and giants

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 influences the ionisation imbalance, but satisfactory non-LTE modelling for both dwarfs and giants has not been achieved in previous literature. The reliability of titanium abundances is reassessed in benchmark dwarfs and giants using a new non-LTE model and one-dimensional (1D) model atmospheres. 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. 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 HD84937 and HD140283. For the very metal-poor giant HD122563, 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 reduce the overall ionisation imbalance to $-0.17$ dex for HD122563. However, it also increases the imbalance for the very metal-poor dwarf and sub-giant to around $0.2$ dex. 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 the conclusions in earlier literature. To make further progress, consistent 3D non-LTE models are needed.

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arXiv2023

Detailed $α$ abundance trends in the inner Galactic bulge

In this paper, we aim to derive high-precision alpha-element abundances using CRIRES high-resolution IR spectra of 72 cool M giants of the inner Galactic bulge. Silicon, magnesium, and calcium abundances were determined by fitting a synthetic spectrum for each star. We also incorporated recent theoretical data into our spectroscopic analysis (i.e. updated K-band line list, better broadening parameter estimation, non-local thermodynamic equilibrium (NLTE) corrections). We compare these inner bulge alpha abundance trends with those of solar neighbourhood stars observed with IGRINS using the same line list and analysis technique; we also compare our sample to APOGEE DR17 abundances for inner bulge stars. We investigate bulge membership using spectro-photometric distances and orbital simulations. We construct a chemical-evolution model that fits our metallicity distribution function (MDF) and our alpha-element trends. Among our 72 stars, we find four that are not bulge members. [Si/Fe] and [Mg/Fe] versus [Fe/H] trends show a typical thick disc alpha-element behaviour, except that we do not see any plateau at supersolar metallicities as seen in other works. The NLTE analysis lowers [Mg/Fe] typically by $\sim$0.1 dex, resulting in a noticeably lower trend of [Mg/Fe] versus [Fe/H]. The derived [Ca/Fe] versus [Fe/H] trend has a larger scatter than those for Si and Mg, but is in excellent agreement with local thin and thick disc trends. With our updated analysis, we constructed one of the most detailed studies of the alpha abundance trends of cool M giants in the inner Galactic bulge. We modelled these abundances by adopting a two-infall chemical-evolution model with two distinct gas-infall episodes with timescales of 0.4 Gyr and 2 Gyr, respectively. Based on a very meticulous spectral analysis, we have constructed detailed and precise chemical abundances of Mg, Si, and Ca for cool M giants.

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arXiv2022

The solar photospheric silicon abundance according to CO5BOLD: Investigating line broadening, magnetic fields, and model effects

In this work, we present a photospheric solar silicon abundance derived using CO5BOLD model atmospheres and the LINFOR3D spectral synthesis code. Previous works have differed in their choice of a spectral line sample and model atmosphere as well as their treatment of observational material, and the solar silicon abundance has undergone a downward revision in recent years. We additionally show the effects of the chosen line sample, broadening due to velocity fields, collisional broadening, model spatial resolution, and magnetic fields. CO5BOLD model atmospheres for the Sun were used in conjunction with the LINFOR3D spectral synthesis code to generate model spectra, which were then fit to observations in the Hamburg solar atlas. We present a sample of 11 carefully selected lines (from an initial choice of 39 lines) in the optical and infrared, made possible with newly determined oscillator strengths for the majority of these lines. Our final sample includes seven optical Si I lines, three infrared Si I lines, and one optical Si II line. We derived a photospheric solar silicon abundance of $\log ε_\mathrm{Si} = 7.57 \pm 0.04$, including a $-0.01$ dex correction from Non-Local Thermodynamic Equilibrium (NLTE) effects. Combining this with meteoritic abundances and previously determined photospheric abundances results in a metal mass fraction Z/X = $0.0220 \pm 0.0020$. We found a tendency of obtaining overly broad synthetic lines. We mitigated the impact of this by devising a de-broadening procedure. The over-broadening of synthetic lines does not substantially affect the abundance determined in the end. It is primarily the line selection that affects the final fitted abundance.

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arXiv2022

The Gaia-ESO Public Spectroscopic Survey: Motivation, implementation, GIRAFFE data processing, analysis, and final data products

The Gaia-ESO Public Spectroscopic Survey is an ambitious project designed to obtain astrophysical parameters and elemental abundances for 100,000 stars, including large representative samples of the stellar populations in the Galaxy, and a well-defined sample of 60 (plus 20 archive) open clusters. We provide internally consistent results calibrated on benchmark stars and star clusters, extending across a very wide range of abundances and ages. This provides a legacy data set of intrinsic value, and equally a large wide-ranging dataset that is of value for homogenisation of other and future stellar surveys and Gaia's astrophysical parameters. This article provides an overview of the survey methodology, the scientific aims, and the implementation, including a description of the data processing for the GIRAFFE spectra. A companion paper (arXiv:2206.02901) introduces the survey results. Gaia-ESO aspires to quantify both random and systematic contributions to measurement uncertainties. Thus all available spectroscopic analysis techniques are utilised, each spectrum being analysed by up to several different analysis pipelines, with considerable effort being made to homogenise and calibrate the resulting parameters. We describe here the sequence of activities up to delivery of processed data products to the ESO Science Archive Facility for open use. The Gaia-ESO Survey obtained 202,000 spectra of 115,000 stars using 340 allocated VLT nights between December 2011 and January 2018 from GIRAFFE and UVES. The full consistently reduced final data set of spectra was released through the ESO Science Archive Facility in late 2020, with the full astrophysical parameters sets following in 2022.

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arXiv2022

Non-LTE abundance corrections for late-type stars from 2000Å to 3μm: I. Na, Mg, and Al

It is well known that cool star atmospheres depart from local thermodynamic equilibrium (LTE). Accurate abundance determination requires taking those effects into account, but the necessary non-LTE calculations are often lacking. Our goal is to provide detailed estimates of NLTE effects for FGK type stars for all spectral lines from the ultraviolet to the infrared that are potentially useful as abundance diagnostics. The first paper in this series focusses on the light elements Na, Mg and Al. The code PySME is used to compute curves-of-growth for 2158 MARCS model atmospheres in a wide parameter range. Nine abundance points 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 are selected from the ultra-violet to the near infrared wavelength range. 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, HD84937, HD140283 and HD122563. 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 ionization 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 a 0.6 dex ionization 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, except for strongly saturated lines.

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arXiv2022

The Gaia-ESO Public Spectroscopic Survey: Implementation, data products, open cluster survey, science, and legacy

In the last 15 years different ground-based spectroscopic surveys have been started (and completed) with the general aim of delivering stellar parameters and elemental abundances for large samples of Galactic stars, complementing Gaia astrometry. Among those surveys, the Gaia-ESO Public Spectroscopic Survey (GES), the only one performed on a 8m class telescope, was designed to target 100,000 stars using FLAMES on the ESO VLT (both Giraffe and UVES spectrographs), covering all the Milky Way populations, with a special focus on open star clusters. This article provides an overview of the survey implementation (observations, data quality, analysis and its success, data products, and releases), of the open cluster survey, of the science results and potential, and of the survey legacy. A companion article (Gilmore et al.) reviews the overall survey motivation, strategy, Giraffe pipeline data reduction, organisation, and workflow. The GES has determined homogeneous good-quality radial velocities and stellar parameters for a large fraction of its more than 110,000 unique target stars. Elemental abundances were derived for up to 31 elements for targets observed with UVES. Lithium abundances are delivered for about 1/3 of the sample. The analysis and homogenisation strategies have proven to be successful; several science topics have been addressed by the Gaia-ESO consortium and the community, with many highlight results achieved. The final catalogue has been released through the ESO archive at the end of May 2022, including the complete set of advanced data products. In addition to these results, the Gaia-ESO Survey will leave a very important legacy, for several aspects and for many years to come.

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arXiv2021

Diagnostic capabilities of spectropolarimetric observations for understanding solar phenomena I. Zeeman-sensitive photospheric lines

Future ground-based telescopes will expand our capabilities for simultaneous multi-line polarimetric observations in a wide range of wavelengths, from the near-ultraviolet to the near-infrared. This creates a strong demand to compare candidate spectral lines to establish a guideline of the lines that are most appropriate for each observation target. We focused in this first work on Zeeman-sensitive photospheric lines in the visible and infrared. We first examined their polarisation signals and response functions using a 1D semi-empirical atmosphere. Then we studied the spatial distribution of the line core intensity and linear and circular polarisation signals using a realistic 3D numerical simulation. We ran inversions of synthetic profiles, and we compared the heights at which we obtain a high correlation between the input and the inferred atmosphere. We also used this opportunity to revisit the atomic information we have on these lines and computed the broadening cross-sections due to collisions with neutral hydrogen atoms for all the studied spectral lines. The results reveal that four spectral lines stand out from the rest for quiet-Sun and network conditions: Fe I 5250.2, 6302, 8468, and 15648 A. The first three form higher in the atmosphere, and the last line is mainly sensitive to the atmospheric parameters at the bottom of the photosphere. However, as they reach different heights, we strongly recommend using at least one of the first three candidates together with the Fe I 15648 A line to optimise our capabilities for inferring the thermal and magnetic properties of the lower atmosphere.

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arXiv2020

The GALAH Survey: Non-LTE departure coefficients for large spectroscopic surveys

Massive sets of stellar spectroscopic observations are rapidly becoming available and these can be used to determine the chemical composition and evolution of the Galaxy with unprecedented precision. One of the major challenges in this endeavour involves constructing realistic models of stellar spectra with which to reliably determine stellar abundances. At present, large stellar surveys commonly use simplified models that assume that the stellar atmospheres are approximately in local thermodynamic equilibrium (LTE). To test and ultimately relax this assumption, we have performed non-LTE calculations for $13$ different elements (H, Li, C, N, O, Na, Mg, Al, Si, K, Ca, Mn, and Ba), using recent model atoms that have physically-motivated descriptions for the inelastic collisions with neutral hydrogen, across a grid of $3756$ 1D MARCS model atmospheres that spans $3000\leq T_{\mathrm{eff}}/\mathrm{K}\leq8000$, $-0.5\leq\log{g/\mathrm{cm\,s^{-2}}}\leq5.5$, and $-5\leq\mathrm{[Fe/H]}\leq1$. We present the grids of departure coefficients that have been implemented into the GALAH DR3 analysis pipeline in order to complement the extant non-LTE grid for iron. We also present a detailed line-by-line re-analysis of $50126$ stars from GALAH DR3. We found that relaxing LTE can change the abundances by between $-0.7\,\mathrm{dex}$ and $+0.2\,\mathrm{dex}$ for different lines and stars. Taking departures from LTE into account can reduce the dispersion in the $\mathrm{[A/Fe]}$ versus $\mathrm{[Fe/H]}$ plane by up to $0.1\,\mathrm{dex}$, and it can remove spurious differences between the dwarfs and giants by up to $0.2\,\mathrm{dex}$. The resulting abundance slopes can thus be qualitatively different in non-LTE, possibly with important implications for the chemical evolution of our Galaxy.

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arXiv2020

The 3D non-LTE solar nitrogen abundance from atomic lines

Nitrogen is an important element in various fields of stellar and Galactic astronomy, and the solar nitrogen abundance is crucial as a yardstick for comparing different objects in the cosmos. In order to obtain a precise and accurate value for this abundance, we carried out N i line formation calculations in a 3D radiative-hydrodynamic STAGGER model solar atmosphere, in full 3D non-local thermodynamic equilibrium (non-LTE), using a model atom that includes physically-motivated descriptions for the inelastic collisions of N i with free electrons and with neutral hydrogen. We selected five N i lines of high excitation energy to study in detail, based on their strengths and on their being relatively free of blends. We found that these lines are slightly strengthened from non-LTE photon losses and from 3D granulation effects, resulting in negative abundance corrections of around $-0.01$ dex and $-0.04$ dex respectively. Our advocated solar nitrogen abundance is $\logε_{\mathrm{N}} = 7.77$, with the systematic $1σ$ uncertainty estimated to be $0.05$ dex. This result is consistent with earlier studies after correcting for differences in line selections and equivalent widths.

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arXiv2019

Excitation and charge transfer in low-energy hydrogen atom collisions with neutral carbon and nitrogen

Low-energy inelastic collisions with neutral hydrogen atoms are important processes in stellar atmospheres, and a persistent source of uncertainty in non-LTE modelling of stellar spectra. We have calculated and studied excitation and charge transfer of C i and of N i due to such collisions. We used a previously presented method that is based on an asymptotic two-electron linear combination of atomic orbitals (LCAO) model of ionic-covalent interactions for the adiabatic potential energies, combined with the multichannel Landau-Zener model for the collision dynamics. We find that charge transfer processes typically lead to much larger rate coefficients than excitation processes do, consistent with studies of other atomic species. Two-electron processes were considered and lead to non-zero rate coefficients that can potentially impact statistical equilibrium calculations. However, they were included in the model in an approximate way, via an estimate for the two-electron coupling that was presented earlier in the literature: the validity of these data should be checked in a future work.

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arXiv2019

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 $ε_{\text{C}}$ = $8.44\pm0.02$, 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.

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arXiv2019

Carbon and oxygen in metal-poor halo stars

Carbon and oxygen are key tracers of the Galactic chemical evolution; in particular, a reported upturn in [C/O] towards decreasing [O/H] in metal-poor halo stars could be a signature of nucleosynthesis by massive Population III stars. We reanalyse carbon, oxygen, and iron abundances in thirty-nine metal-poor turn-off stars. For the first time, we take into account three-dimensional (3D) hydrodynamic effects together with departures from local thermodynamic equilibrium (LTE) when determining both the stellar parameters and the elemental abundances, by deriving effective temperatures from 3D non-LTE H$β$ profiles, surface gravities from Gaia parallaxes, iron abundances from 3D LTE Feii equivalent widths, and carbon and oxygen abundances from 3D non-LTE Ci and Oi equivalent widths. We find that [C/Fe] stays flat with [Fe/H], whereas [O/Fe] increases linearly up to $0.75$ dex with decreasing [Fe/H] down to $-3.0$ dex. As such [C/O] monotonically decreases towards decreasing [O/H], in contrast to previous findings, mainly by virtue of less severe non-LTE effects for Oi at low [Fe/H] with our improved calculations.

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arXiv2019

Ca line formation in late-type stellar atmospheres: I. The model atom

Context. Departures from local thermodynamic equilibrium (LTE) distort the calcium abundance derived from stellar spectra in various ways, depending on the lines used and the stellar atmospheric parameters. The collection of atomic data adopted in non-LTE (NLTE) calculations must be sufficiently complete and accurate. Aims. We derive NLTE abundances from high-quality observations and reliable stellar parameters using a model atom built afresh for this work, and check the consistency of our results over a wide wavelength range with transitions of atomic and singly ionised calcium. Methods. We built and tested Ca i and Ca ii model atoms with state-of-the-art radiative and collisional data, and tested their performance deriving the Ca abundance in three benchmark stars: Procyon, the Sun, and Arcturus. We have excellent-quality observations and accurate stellar parameters for these stars. Two methods to derive the LTE / NLTE abundances were used and compared. The LTE / NLTE centre-to-limb variation (CLV) of Ca lines in the Sun was also investigated. Results. The two methods used give similar results in all three stars. Several discrepancies found in LTE do not appear in our NLTE results; in particular the agreement between abundances in the visual and infra-red (IR) and the Ca i and Ca ii ionisation balance is improved overall, although substantial line-to-line scatter remains. The CLV of the calcium lines around 6165 Angs can be partially reproduced. We suspect differences between our modelling and CLV results are due to inhomogeneities in the atmosphere that require 3D modelling.

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arXiv2018

Inelastic O+H collisions and the OI 777nm solar centre-to-limb variation

The OI 777 nm triplet is a key diagnostic of oxygen abundances in the atmospheres of FGK-type stars; however it is sensitive to departures from local thermodynamic equilibrium (LTE). The accuracy of non-LTE line formation calculations has hitherto been limited by errors in the inelastic O+H collisional rate coefficients: several recent studies have used the so-called Drawin recipe, albeit with a correction factor $\mathrm{S_{H}}$ that is calibrated to the solar centre-to-limb variation of the triplet. We present a new model oxygen atom that incorporates inelastic O+H collisional rate coefficients using an asymptotic two-electron model based on linear combinations of atomic orbitals, combined with a free electron model, based on the impulse approximation. Using a 3D hydrodynamic stagger model solar atmosphere and 3D non-LTE line formation calculations, we demonstrate that this physically-motivated approach is able to reproduce the solar centre-to-limb variation of the triplet to 0.02 dex, without any calibration of the inelastic collisional rate coefficients or other free parameters. We infer $\logε_{\mathrm{O}}=8.69\pm0.03$ from the triplet alone, strengthening the case for a low solar oxygen abundance.

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