Influence of Inelastic Collisions with Hydrogen Atoms on Non-LTE Oxygen Abundance Determinations

We present the results of our modeling of the O I line formation under non-LTE conditions in the atmospheres of FG stars. The statistical equilibrium of O I has been calculated using Barklem’s quantum-mechanical rates of inelastic collisions with hydrogen atoms. We have determined the non-LTE oxygen abundance from atomic O I lines for the Sun and 46 FG stars in a wide metallicity range, ?2.6 < [Fe/H] < 0.2. The application of accurate atomic data has led to an increase in the departures from LTE and a decrease in the oxygen abundance compared to the use of Drawin’s theoretical approximation. The change in the non-LTE abundance from the infrared O I 7771-5 Å triplet lines is 0.11 dex for solar atmospheric parameters and diminishes in absolute value with decreasing metallicity. We have revised the [O/Fe]–[Fe/H] relationship derived by us previously. The change in [O/Fe] is small in the [Fe/H] range from ?1.5 to 0.2. For stars with [Fe/H] < ?1 the [O/Fe] ratio has increased so that [O/Fe] = 0.60 at [Fe/H] = ?0.8 and rises to [O/Fe] = 0.75 at [Fe/H] = ?2.6.     

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

We have performed statistical equilibrium calculations for Ca I–Ca II, Ti I–Ti II, and Fe I–Fe II by taking into account the nonequilibrium line formation conditions (the non-LTE approach) in model atmospheres of giant stars with effective temperatures 4000 K ≤ T _eff ≤ 5000 K and metal abundances ?4 ≤ [Fe/H] ≤ 0. The dependence of departures from LTE on atmospheric parameters has been analyzed. We present the non-LTE abundance corrections for 28 Ca I lines, 42 Ti I lines, 54 Ti II lines, and 262 Fe I lines and a three-dimensional interpolation code to obtain the non-LTE correction online for an individual line and specified atmospheric parameters.     

Formation of Zr I and II lines under non-LTE conditions of stellar atmospheres

The formation of Zr I and Zr II lines in stellar atmospheres under non-LTE conditions has been considered for the first time. A model zirconium atom has been composed using 148 Zr I levels, 772 Zr II levels, and the ground Zr III state. Non-LTE calculations have been performed for model atmospheres with T _eff = 5500 and 6000 K, log g = 2.0 and 4.0, [M/H] = −3, −2, −1, 0. In the entire investigated range of parameters, the Zr I levels are shown to be underpopulated relative to their LTE populations in the line formation region. In contrast, the excited Zr II levels are overpopulated, while the ground state and lower excited levels of Zr II retain their LTE populations. Since the non-LTE effects cause the Zr I and Zr II spectral lines being investigated to weaken, the non-LTE corrections to the abundance derived from Zr I and Zr II lines are positive. For Zr II lines, they increase with decreasing metallicity and surface gravity up to 0.34 dex for the model with T _eff = 5500, log g = 2.0, and [M/H] = −2. The non-LTE effects depend weakly on temperature. The non-LTE corrections for Zr I lines reach 0.33 dex for solar-metallicity models. Zr I and Zr II lines in the solar spectrum have been analyzed. The non-LTE zirconium abundances derived from lines in the two ionization stages are shown to agree between themselves within the error limits, while the LTE abundance difference is 0.28 dex. The zirconium abundance in the solar atmosphere (averaged over Zr I and Zr II lines) is log ɛ_Zr,⊙ = 2.63 ± 0.07.     

Observational restrictions on sodium and aluminium abundance variations in evolution of the galaxy

In this paper we construct and analyze the uniform non-LTE distributions of the aluminium ([Al/Fe]-[Fe/H]) and sodium ([Na/Fe]-[Fe/H]) abundances in the sample of 160 stars of the disk and halo of our Galaxy with metallicities within ?4.07 ≤ [Fe/H] ≤ 0.28. The values of metallicity [Fe/H] and microturbulence velocity ξ _turb indices are determined from the equivalent widths of the Fe II and Fe I lines. We estimated the sodium and aluminium abundances using a 21-level model of the Na I atom and a 39-level model of the Al I atom. The resulting LTE distributions of [Na/Fe]-[Fe/H] and [Al/Fe]-[Fe/H] do not correspond to the theoretical predictions of their evolution, suggesting that a non-LTE approach has to be applied to determine the abundances of these elements. The account of non-LTE corrections reduces by 0.05–0.15 dex the abundances of sodium, determined from the subordinate lines in the stars of the disk with [Fe/H] ≥ ?2.0, and by 0.05–0.70 dex (with a strong dependence on metallicity) the abundances of [Na/Fe], determined by the resonance lines in the stars of the halo with [Fe/H] ≤ ?2.0. The non-LTE corrections of the aluminium abundances are strictly positive and increase from 0.0–0.1 dex for the stars of the thin disk (?0.7 ≤ [Fe/H] ≤ 0.28) to 0.03–0.3 dex for the stars of the thick disk (?1.5 ≤ [Fe/H] ≤ ?0.7) and 0.06–1.2 dex for the stars of the halo ([Fe/H] ≤ ?2.0). The resulting non-LTE abundances of [Na/Fe] reveal a scatter of individual values up to Δ[Na/Fe] = 0.4 dex for the stars of close metallicities. The observed non-LTE distribution of [Na/Fe]-[Fe/H] within 0.15 dex coincides with the theoretical distributions of Samland and Kobayashi et al. The non-LTE aluminium abundances are characterized by a weak scatter of values (up to Δ[Al/Fe] = 0.2 dex) for the stars of all metallicities. The constructed non-LTE distribution of [Al/Fe]-[Fe/H] is in a satisfactory agreement to 0.2 dex with the theoretical data of Kobayashi et al., but strongly differs (up to 0.4 dex) from the predictions of Samland.     

Non-LTE Effects of Helium Lines in Late-B and A Stars

A helium model atom that includes 55 He I levels and the He II ground level in a detailed consideration has been constructed to investigate the departures from local thermodynamic equilibrium (LTE) in the formation of helium lines in stars with effective temperatures from 9300 to 20 000 K. For eight stars with effective temperatures from 9380 to 17 500 K the helium abundance has been determined from He I lines. The neutral helium lines in B stars cannot be described under LTE conditions using the common helium abundance. Furthermore, the profiles of several lines cannot be described in terms of the LTE approach at all. In contrast, a satisfactory coincidence of the theoretical and observed profiles for the entire set of helium lines observed in a wide spectral range can be achieved using virtually the same helium abundance by taking into account the departures from LTE. The LTE and non-LTE helium abundances can differ by up to a factor of 2–3, depending on the stellar parameters. The higher the stellar temperature, the stronger the departures from LTE. As a rule, the lines in the blue spectral region are less affected by non- LTE effects. In the atmospheres of six stars the helium abundance corresponds, within the error limits, to the present-day solar value. A helium underabundance is observed in the atmospheres of Sirius and HD 72660 classified as hot Am stars.     

High-resolution optical spectroscopy of the sharp-lined B-type star HD 83206

Very-high-resolution ( R ∼160 000) spectroscopic observations are presented for the early B-type star, HD 83206. Because it has very sharp metal lines, this star affords an opportunity to test theories of model atmospheres and line formation. Non-LTE model atmosphere calculations have been used to estimate the atmospheric parameters and absolute metal abundances (C, N, O, Mg and Si); an LTE analysis was also undertaken to investigate the validity of this simpler approach and to estimate an iron abundance. For the non-LTE calculations, there is excellent agreement with observations of the Balmer lines H α and H δ and the lines of Si  ii and Si  iii for atmospheric parameters of T _eff≃21 700±600 K and log  g ≃4.00±0.15 dex. The agreement is less convincing for the LTE calculations, and a higher gravity is deduced. Careful comparison of the metal line profiles with non-LTE calculations implies that the projected rotational and microturbulent velocities have maximum values of ≃5 and ≃2 km s⁻¹, respectively. The latter value is smaller than has often been adopted in LTE model atmosphere analyses of main-sequence stars. Non-LTE absolute metal abundances are estimated, and a comparison with those for normal B-type stars (deduced using similar non-LTE techniques) shows no significant differences. A comparison of the abundances deduced using non-LTE and LTE calculations implies systematic differences of 0.1–0.2 dex, showing the importance of using a non-LTE approach when accurate absolute abundances are required. Its location in the Hertzsprung–Russell diagram and normal metal abundance lead us to conclude that HD 83206 is probably a main-sequence B-type star. As such, it is among the sharpest-lined young B-type star discovered to date.     

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

We have performed calculations by abandoning the assumption of local thermodynamic equilibrium (within the so-called non-LTE approach) for Al I and Si I with model atmospheres corresponding to stars of spectral types F–G–Kwith differentmetal abundances. To take into account inelastic collisions with hydrogen atoms, for the first time we have applied the cross sections calculated by Belyaev et al. using model approaches within the formalism of the Born–Oppenheimer quantum theory. We show that for Al I non-LTE leads to higher ionization (overionization) than in LTE in the spectral line formation region and to a weakening of spectral lines, which is consistent with earlier non-LTE studies. However, our results, especially for the subordinate lines, differ quantitatively from the results of predecessors. Owing to their large cross sections, the ion-pair production and mutual neutralization processes Al I(nl) + HI(1s) ? Al II(3s ²) + H^? provide a close coupling of highly excited Al I levels with the Al II ground state, which causes the deviations from the equilibrium level population to decrease compared to the calculations where the collisions only with electrons are taken into account. For three moderately metal-deficient dwarf stars, the aluminum abundance has been determined from seven Al I lines in different models of their formation. Under the assumption of LTE and in non-LTE calculations including the collisions only with electrons, the Al I 3961 ?A resonance line gives a systematically lower abundance than the mean abundance from the subordinate lines, by 0.25–0.45 dex. The difference for each star is removed by taking into account the collisions with hydrogen atoms, and the rms error of the abundance derived from all seven Al I lines decreases by a factor of 1.5–3 compared to the LTE analysis. We have calculated the non- LTE corrections to the abundance for six subordinate Al I lines as a function of the effective temperature (4500 K ≤ T _eff ≤ 6500 K), surface gravity (3.0 ≤ log g ≤ 4.5), and metal abundance ([M/H] = 0, ?1, ?2, and ?3). For Si I including the collisions with HI leads to the establishment of equilibrium populations in the spectral line formation region even in hot metal-deficient models and to vanishingly small departures from LTE in spectral lines.     

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

The non-LTE sodium abundance has been determined from the Na I 6154 and 6161 Å lines for 38 thin-disk stars (15 of them are Ba II stars), 15 thick-disk stars, 13 Hercules-stream stars, and 13 stars that cannot be attributed neither to the thick Galactic disk nor to the thin one. The Na I model atom has been constructed using the most accurate present-day atomic data. For the Na I 6154 and 6161 Å lines, the non-LTEabundance corrections are from ?0.06 to ?0.24 dex, depending on the stellar parameters. No differences in [Na/Fe] abundance between the thick and thin disks have been detected; the derived ratios are close to the solar ones. The existence of a [Na/Fe] overabundance in the Ba II stars has been confirmed. The Hercules-stream stars exhibit nearly solar [Na/Fe] ratios. The results obtained can be used to test the sodium nucleosynthesis models.     

High-precision stellar abundances of the elements: methods and applications

Efficient spectrographs at large telescopes have made it possible to obtain high-resolution spectra of stars with high signal-to-noise ratio and advances in model atmosphere analyses have enabled estimates of high-precision differential abundances of the elements from these spectra, i.e. with errors in the range 0.01–0.03 dex for F, G, and K stars. Methods to determine such high-precision abundances together with precise values of effective temperatures and surface gravities from equivalent widths of spectral lines or by spectrum synthesis techniques are outlined, and effects on abundance determinations from using a 3D non-LTE analysis instead of a classical 1D LTE analysis are considered. The determination of high-precision stellar abundances of the elements has led to the discovery of unexpected phenomena and relations with important bearings on the astrophysics of galaxies, stars, and planets, i.e. (i) Existence of discrete stellar populations within each of the main Galactic components (disk, halo, and bulge) providing new constraints on models for the formation of the Milky Way. (ii) Differences in the relation between abundances and elemental condensation temperature for the Sun and solar twins suggesting dust-cleansing effects in proto-planetary disks and/or engulfment of planets by stars; (iii) Differences in chemical composition between binary star components and between members of open or globular clusters showing that star- and cluster-formation processes are more complicated than previously thought; (iv) Tight relations between some abundance ratios and age for solar-like stars providing new constraints on nucleosynthesis and Galactic chemical evolution models as well as the composition of terrestrial exoplanets. We conclude that if stellar abundances with precisions of 0.01–0.03 dex can be achieved in studies of more distant stars and stars on the giant and supergiant branches, many more interesting future applications, of great relevance to stellar and galaxy evolution, are probable. Hence, in planning abundance surveys, it is important to carefully balance the need for large samples of stars against the spectral resolution and signal-to-noise ratio needed to obtain high-precision abundances. Furthermore, it is an advantage to work differentially on stars with similar atmospheric parameters, because then a simple 1D LTE analysis of stellar spectra may be sufficient. However, when determining high-precision absolute abundances or differential abundance between stars having more widely different parameters, e.g. metal-poor stars compared to the Sun or giants to dwarfs, then 3D non-LTE effects must be taken into account.     

High Resolution Optical Spectroscopy of an Intriguing High-Latitude B-Type Star HD119608

We present an LTE analysis of high resolution echelle optical spectra obtained with the 3.9-m Anglo-Australian Telescope (AAT) and the UCLES spectrograph for a B1Ib high galactic latitude supergiant HD119608. A fresh determination of the atmospheric parameters using line-blanketed LTE model atmospheres and spectral synthesis provided T_eff = 23 300 ± 1000 K, log g = 3.0 ± 0.3, and the microturbulent velocity ξ = 6.0 ± 1.0 kms^?1 and [Fe/H] = 0.16. The rotational velocity of the star was derived fromC, O, N, Al, and Fe lines as v sin i = 55.8 ± 1.3 kms^?1. Elemental abundances were obtained for 10 different species. He, Al, and P abundances of the star were determined for the first time. In the spectra, hot post-AGB status as well as the Pop I characteristics of the star were examined. The approximately solar carbon and oxygen abundances, along with mild excess in helium and nitrogen abundances do not stipulate a CNO processed surface composition, hence a hot post-AGB status. The LTE abundances analysis also indicates solar sulphur and moderately enriched magnesium abundances. The average abundances of B dwarfs of well studied OB associations and Population I stars show a striking resemblance to abundances obtained for HD119608 in this study. This may imply a runaway status for the star.     

Non-LTE effects in Al I lines

We present the theoretical analysis of the Al I line formation in the spectra of late-type stars ignoring the assumption of local thermodynamic equilibrium (LTE). The calculations were based on the 39-level aluminum atom model for one-dimensional hydrostatic stellar atmosphere models with the parameters: T _eff from 4000 to 9000 K, log g = 0.0–4.5, and metallicity [A] = 0.0;–1.0;–2.0;–3.0;–4.0. The aluminum atom model and the method of calculations were tested by the study of line profiles in the solar spectrum. We refined the oscillator strengths and Van-der-Vaals broadening constants C ₆ of the investigated transitions. We conclude that the Al I atom is in the overionization state: the 3p level is underpopulated in the line formation region. This leads to the line weakening, as compared with the LTE results. The overionization effect becomes more pronounced with increasing temperature and decreasing metallicity. We show that the use of various atomic data (ionization cross-sections) for the low levels of Al I does not change the behavior of non-LTE deviations, whereas the value of these deviations varies essentially. For nine selected Al I lines we calculated the grids of theoretical non-LTE corrections (ΔX _NLTE = logɛ _NLTE − log ɛ _LTE) to the Al abundances determinedwith the LTE assumption. The non-LTE corrections are positive and significant for the stars with temperatures T _eff > 6000 K. These corrections weakly depend on log g, and increase with declining stellar metallicity.     

Chemical enrichment by massive stars

Heavy element abundances derived from high-quality ground-based and Hubble Space Telescope (HST) spectroscopic observations of low-metallicity blue compact galaxies (BCGs) with oxygen abundances 12+log O/H between 7.1 and 8.3 are discussed. None of the heavy element-to-oxygen abundance ratios studied here (C/O, N/O, Ne/O, Si/O, S/O, Ar/O, Fe/O) depend on oxygen abundance for BCGs with 12+log O/H≤7.6 (Z≤Z_⊙/20). This constancy implies that all these heavy elements have a primary origin and are produced by the same massive (M≥10 M_⊙) stars responsible for O production. The dispersion of the C/O and N/O ratios in these galaxies is found to be remarkably small, being only ±0.03 dex and ±0.02 dex respectively. This very small dispersion is strong evidence against any time-delayed production of C and primary N in the lowest-metallicity BCGs, and hence against production of these elements by intermediate-mass (3 M_⊙≤M≤9 M_⊙) stars at very low metallicities, as commonly thought.In higher metallicity BCGs (7.6<12+log O/H<8.2), the Ne/O, Si/O, S/O, Ar/O and Fe/O abundance ratios retain the same constant value they had at lower metallicities. By contrast, there is an increase of the C/O and N/O ratios along with their dispersions at a given O. We interpret this increase as due to the additional contribution of C and primary N production in intermediate-mass stars, on top of that by high-mass stars. BCGs show the same O/Fe overabundance with respect to the Sun (∼0.4 dex) as galactic halo stars, suggesting the same chemical enrichment history.     

High Resolution Optical Spectroscopy of Hot Post-AGB Star Candidates LS IV-04 1 and LB3116

We present LTE analysis of high resolution optical spectra for B-type hot PAGB stars LS IV-04 1 and LB3116 (LSE 237). The spectra of these high Galactic latitude stars were obtained with the 3.9-m Anglo-Australian Telescope (AAT) and the UCLES spectrograph. The standard 1D LTE analysis with line-blanketed LTE model atmospheres and spectral synthesis provided fundamental atmospheric parameters of T_eff= 15 000±1000 K, log g= 2.5±0.2, ξ = 5.0±1.0 km s^?1, [M/H] = ?1.81 dex, and v sin i= 5 km s^?1 for LSIV-04 1 and T_eff= 16 000±1000 K, log g= 2.5±0.1, v sin i= 25 km s^?1, and [Fe/H] = ?0.93 dex for LB 3116. Chemical abundances of ten different elements were obtained. For LS IV-04 1, its derived model temperature contradicts with previous analysis results. The upper limits for its nitrogen and oxygen abundances were reported for the first time. The magnesium, silicon and calcium were overabundant (i.e. [Mg/Fe] = 0.8 dex, [Si/Fe] = 0.5 dex, [Ca/Fe] = 0.9 dex). With its metal-poor photosphere and V_LSR ≈ 96 km s^?1, LSIV-04 1 is likely a population II star and most probably a PAGB star. LTE abundances of LB 3116 were reported for the first time. The spectrum of this helium rich star shows 0.9 dex enhancement in the nitrogen. The photosphere of the star is slightly deficient in Mg, Si, and S. (i.e. [Mg/Fe] = ?0.2 dex, [Si/Fe] = ?0.4 dex, [S/Fe] = ?0.2 dex). The Al is slightly enhanced. The phosphorus is overabundant, i.e. [P/Fe] ≈ 1.7 ± 0.47 dex, hence LB3116 may be the first example of a PAGB star which is rich in phosphorus. With its high radial velocity (i.e.V_LSR = 73 km s^?1), and the deficiencies observed in C, Mg, Si, and S indicate that LB 3116 is likely a hot PAGB star at high galactic latitude.     

Effect of atomic parameters on determination of aluminium abundance in atmospheres of late-type stars

We study the effect of the photoionization cross sections for the ground state of Al I on the inferred aluminium abundance in stellar atmospheres. We match the theoretical and observed line profiles of the resonance λλ 3944.01, 3961.52 Å and subordinate λλ 6696.03, 6698.68 Å doublets in high-resolution spectra of the metal-poor solar-type stars HD22879 and HD201889. We determine the parameters of these stars from their photometric and spectroscopic data. Our computations show that the profiles can be matched and a single aluminium abundance inferred simultaneously from both groups of spectral lines only with low photoionization cross sections (about 10–12 Mb). Larger cross sections (about 58–65 Mb) make such fits impossible. We therefore conclude that small photoionization cross sections should be preferred for the determination of aluminium abundances in metal-poor stars. We redetermine the aluminium abundances in the atmospheres of halo stars. The resulting abundances prove to be lower by 0.1–0.15 dex than our earlier determinations which does not affect the conclusions based on our earlier estimates. In particular, the NLTE [Al/Fe]-[Fe/H] dependence, on the whole, agrees only qualitatively with the results of theoretical predictions. Therefore further refinement of the theory of nuclear synthesis of aluminium in the process of the chemical evolution of the Galaxy remains a task of current importance.     

Chemical abundance analysis of the Be star HD 171054

In this work the results of a spectroscopic study of the southern field narrow-line Be star HD 171054 are presented. High dispersion and signal-to-noise ratio spectra allowed the estimation of the fundamental photospheric parameters such as the projected rotational velocity, effective temperature and superficial gravity from non-LTE stellar atmosphere models. From these parameters and microturbulence, the abundances of He, C, N, O, Mg, Al and Si for this object are estimated. Results show that C is depleted whereas N is overabundant compared with the sun and OB stars in the solar vicinity. Oxygen and helium are close to the solar value. Magnesium is down by 0.43 dex and aluminium and silicon are overabundant.     

A NLTE model atmosphere analysis of the pulsating sdO star SDSS J1600+0748

We started a program to construct several grids of suitable model atmospheres and synthetic spectra for hot subdwarf O stars computed, for comparative purposes, in LTE, NLTE, with and without metals. For the moment, we use our grids to perform fits on our spectrum of SDSS J160043.6+074802.9 (J1600+0748 for short), this unique pulsating sdO star. Our best fit is currently obtained with NLTE model atmospheres including carbon, nitrogen and oxygen in solar abundances, which leads to the following parameters for SDSS J1600+0748 : T _eff=69060±2080 K, log?g=6.00±0.09 and log?N(He)/N(H)=?0.61±0.06. Improvements are needed, however, particularly for fitting the available He ii lines. It is hoped that the inclusion of Fe will help remedy the situation.     

Disentangling Metallicity and Age for Turnoff Stars

This is a progress report on calculations of near-ultraviolet spectrawith Ben Dorman at NASA/Goddard, for the ultimate purpose of extractingage and metallicity from extragalactic spectra. We are calculating fromfirst principles a grid of spectra covering 2200–3400 Å using theKurucz program SYNTHE, beginning with stars of metallicity less thanone-fifth solar ([Fe/H] < ?0.7). For these stars, LTE calculationsusing known opacities and line lists including only transitions measuredin the laboratory, coupled with standard line-blanketed LTE models, providea satisfactory match to the spectra of turnoff stars of temperaturesT _eff = 5750 K – 6250 K. For more metal-rich stars, two problemsarise: lines without a laboratory identification become increasinglyinfluential, and the cores of all strong lines become too strong. Theseproblems must be addressed to match near-UV spectra of turnoff stars ofsolar metallicity or higher.     

Spectroscopy of candidate metal-deficient galaxies with the 6-m telescope

We present the first results of our program of search for the most metal-deficient blue compact galaxies (BCGs) carried out with the 6-m Special Astrophysical Observatory telescope. The results of spectrophotometry are presented and discussed for ten galaxies from the Case and Hamburg/SAO surveys. The selection of candidates, observations, and data reduction are described in detail. For all the galaxies studied, we measured the intensity of the [O III] λ4363 Å emission line, which allows us to properly determine the temperatures of H II regions and to deduce elemental abundances. We measured the intensities of all the detected emission lines in H II regions of the galaxies under study and determined the abundances of oxygen and neon in them and in some of these galaxies, of other elements (N, S, He, Ar, and Fe). The oxygen abundance log (O/H)+12 in six galaxies was derived with an error ≤0.1 dex. Six of the ten galaxies studied turned out to be metal-poor with an oxygen abundance ≤1/10 of its solar value [i.e., 12+log(O/H)≤7.92]. HS 0837+4717 with 12+log(O/H) ≤7.7 is one of the most metal-poor galaxies in this sample and one of the candidates for young galaxies. Low-contrast, broad emission components of the nebular [O III]λ4959 and 5007 Å lines were detected in its spectrum, suggesting high velocities of gas motions in this galaxy.     

Microturbulence and the effect of departures from LTE on photospheric iron lines

It is shown that depth-dependent departures from LTE such as obtained by Athay and Lites (1972) will not notably affect the solar curve-of-growth of Fe i. This implies that both abundance and microturbulence may be determined from this curve-of-growth assuming LTE, and excludes that microturbulence is an artefact produced by non-LTE effects.