Non-LTE effects in Mg I lines for various types of stars

We have performed a detailed statistical-equilibrium analysis based on a 49-level model of the magnesium atom for the atmospheres of stars of various spectral types: T _eff=4500–12000 K, logg=0.0–4.5, and [M/H]=0 to ?3. In the atmospheres of stars with T _eff>5500 K, deviations from LTE for Mg I are due to photoionization by ultraviolet radiation from the 3p level; i.e., neutral magnesium is in a state of “superionization.” When T _eff<5500 K, the populations of the Mg I levels differ from their LTE values due to radiative processes in bound-bound transitions. We analyzed Mg I lines in the solar spectrum in order to empirically refine certain atomic parameters (the van der Waals broadening constant C ₆ and cross sections for photoionization and collisional interactions with hydrogen atoms) and the magnesium abundance in the solar atmosphere. We studied non-LTE effects for five Mg I lines for a wide range of stellar parameters. In the case of dwarfs and subdwarfs, the magnitude of non-LTE corrections to magnesium abundances does not exceed 0.1 dex for the λλ 4571, 4703, 5528, and 5711 Å lines but can be as large as ±0.2 dex for the λλ 3829–3838, 5172, and 5183 Å lines. The non-LTE corrections for giants and supergiants do not exceed 0.15 dex for the λλ 4571 and 5711 Å lines but can reach ±0.20 dex and even more for the λλ 4703, 5528, 3829–3838, 5172, and 5183 Å lines.     

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

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

Non-LTE effects in Na I spectral lines in stellar atmospheres

The paper examines the statistical equilibrium of Na I in stellar atmospheres with a wide range of parameters: T _eff=4000?12500 K, logg=0.0?4.5, and heavy element content [A] from 0.5 to ?4.0. The effect of the “overrecombination” of Na I (i.e., excess relative to the equilibrium number density of Na I) is present over the entire range of parameters considered, and increases with T _eff and luminosity. Na I lines are stronger than in the LTE case, so that non-LTE corrections to the sodium abundance, Δ_NLTE, are negative. Eight Na I lines commonly employed in abundance analyses are used to construct the dependences of the non-LTE corrections on T _eff, logg, and metallicity. The non-LTE corrections are small only for the Na I λλ615.4, 616.0 nm lines in main-sequence stars: |Δ_NLTE| ≤0.08 dex. In all other cases, Δ_NLTE depends strongly on T _eff and logg, and a non-LTE treatment must be applied if the sodium abundance is to be determined with an accuracy no worse than 0.1 dex. The profiles of solar Na I lines are analyzed in order to empirically refine two types of atomic parameters required for the subsequent analysis of the stellar spectra. In the solar atmosphere, inelastic collisions with hydrogen atoms influence the statistical equilibrium of Na I only weakly, and the classical Unsold formula underestimates the van der Waals constant C ₆. The empirical correction ΔlogC ₆ is from 0.6 to 2 for various Na I lines. The sodium abundance in the solar atmosphere is determined based on line-profile analyses, yielding different results depending on whether the model atmospheres of Kurucz (log?_Na=6.20±0.02) or Holweger and Muller (log?_Na=6.28±0.03) are applied.     

A method for modeling the formation of caii lines in the spectra of irradiated stellar atmospheres

We have developed a method for calculating deviations from LTE of level populations and profiles of selected spectral lines in stellar atmospheres in the presence of external radiation. The influence of Thomson scattering at the frequencies of the external radiation is considered. The method used to calculate model irradiated atmospheres in a semi-grey approximation has been improved. We have modified the NONLTE3 code used to determine the level populations to make it suitable for irradiated atmospheres. A model for the CaII atom including 42 energy levels of CaII, the ground state of CaIII, and 80 linearized transitions was constructed for these calculations. This atomic model takes into account the effect of all relevant collisional processes and radiative processes at the frequencies of the internal and external radiation. We investigated the correctness of the non-LTE calculations for the CaII ion by analyzing 16 lines of ionized calcium in the solar spectrum. The influence of uncertainties in the atomic data on the non-LTE level populations and CaII line profiles was also analyzed, and the van der Waals broadening coefficients C ₆ were refined. The scaling coefficient in the Dravin formula was taken to be 0.1. We found the non-LTE abundance corrections for most lines to be significant (Δlog?(Ca)=0.05?0.15dex), even under the conditions for the solar atmosphere. The lines of the λ=8498, 8542, 8662 Å infrared triplet can be adequately described. Differences in the mean calcium abundance obtained using different model atmospheres are smaller than 0.02 dex. Our final estimate of the mean calcium abundance in the solar atmosphere is log?(Ca)=6.31, in good agreement with the meteoritic abundance, log?(Ca)=6.32.     

Non-LTE analysis of the formation of EuII lines in the atmospheres of solar-type stars

A method to analyze the statistical equilibrium of the EuII ion based on a 36-level model atom has been developed. The formation of EuII lines without assuming local thermodynamic equilibrium (LTE) is considered for T _eff=5500–7000 K, logg=4.0, and metallicities [A] from 0 to ?1.5. Non-LTE effects in the level populations are primarily due to radiative pumping of excited states from the ground and low-lying levels, which leads to over-population of upper relative to lower levels. As a result, the studied λ4129 and λ6645 Å lines are weaker than in the LTE case. However, due to the small energy differences between even low-lying EuII levels, collisional coupling is strong, and deviations from LTE in EuII lines are modest: for the Sun, non-LTE corrections to the abundance are only 0.04 dex. The non-LTE effects grow with an increase in the effective temperature and with a decrease in the metallicity, so that non-LTE abundance corrections can reach 0.12 dex for T _eff=5500K, logg=4.0, [A]=?1.5 and 0.1 dex for T _eff=7000K, logg=4.0, [A]=0. The effect of inaccuracy in the atomic parameters for EuII on the non-LTE calculations is examined. Analysis of the profiles of the solar EuII λ4129 and λ6645 Å lines is used to empirically refine estimates of the efficiency of collisional processes in forbidden transitions in establishing the distribution of EuII ions over excited states.     

Effects of spot structure of lines of rare earths and non-LTE effects on lithium abundance estimates for two roAp stars

Taking into account blending of the lithium 6108 Å line profile by adjacent rare-earth lines together with their spotted surface structure does not appreciably affect lithium abundance estimates for the atmospheres of HD 83368 and HD 60435 but provides a better fit of the observed and stimulated line profiles. Our computed non-LTE corrections reduce the lithium abundance estimates by 0.1–0.2 dex for both stars. Given the uncertainties in the lithium abundances, it is not possible to be certain whether the lithium abundances in roAp stars, or at least in their spots, exceed the cosmic (primordial) value.     

The atmospheric lithium abundances of solar analogues

We have analyzed the lithium abundance in the atmospheres of 20 stars that are solar analogues based on high-resolution echelle spectra using model atmospheres in a non-LTE approach. In terms of their lithium abundances, the stars (which are located in a narrow range of temperatures of 5650–5900 K) can be divided into two groups: one with low lithium abundances, as in the solar atmosphere, and one with lithium abundances that are higher than the solar value by about 1 dex (with the accuracy of the lithium abundances being 0.15 dex).     

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

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

Revised magnesium abundances in galactic halo and disk stars

A differential analysis of the magnesium abundances in 61 F-K dwarfs and subgiants with metallicities ?2.6<[Fe/H]<+0.2 is performed based on published observational data. Fundamental parameters for 36 stars are determined: T _eff from V-K and V-R; logg from HIPPARCOS parallaxes, and [Fe/H] and ξ_t from Fe II lines. The computations allow for non-LTE effects in the formation of the Mg I lines. For most of the stars, the standard errors in the Mg abundances do not exceed 0.07 dex. The metallicity dependence of [Mg/Fe] is analyzed. Magnesium shows a constant overabundance relative to Fe of 0.46±0.06 dex for metallicities ?2.6<[Fe/H] $\overline {[Mg/Fe]} = + 0.22 dex$ ) compared to the [Mg/Fe] values for other stars with similar [Fe/H].     

CaII line formation in the spectra of irradiated atmospheres

We have studied the effect of external radiation on the formation of LTE and non-LTECaII lines in the spectra of A-M-star atmospheres. Three frequency distributions were chosen for the external radiation: X-ray radiation specified by the power law \(I_v^ + = I_{0^v } ^{ - 0.6} \) at 1–16.5 keV and UV radiation specified by blackbody distributions with the temperatures T_rad=50000 and 15000 K. We analyze the influence of variations in the irradiating flux and its angle of incidence on the profiles and equivalent widths of the λλ3933, 3968 Å resonance doublet and the λλ8498, 8542, 8662 Å infrared triplet. For any type of external radiation, allowing for deviations from LTE decreases the reflection effects for the CaII lines. We conclude that the CaII profiles do not display emission components in the spectra of optically thick stellar atmospheres irradiated by X-rays. Therefore, CaII emission lines observed in the radiation of cataclysmic variables must be formed in an optically thin plasma. CaII emission lines are likely to form in the spectra of stars with UV irradiation if CaII is the dominant ionization state in atmospheric layers close to the depths at which the continuum is formed. As a result, the spectra of symbiotic variables with hot primaries can contain CaII lines originating on the surfaces of the M-giants and supergiant secondaries due to reflection effects. These lines can be used to analyze the reflection effects and the temperature structure in the atmospheres of the secondaries only if non-LTE effects are included. In the spectra of close binaries with cool white dwarfs, CaII emission lines originate in the irradiated atmospheres of the secondaries under conditions close to thermalization. These lines can be used to study the reflection effects and calcium abundances even in an LTE approximation. We calculated the profiles and equivalent widths of CaII lines in the spectra of the four precataclysmic variables BE UMa, EG UMa, MS Peg, and HR Cam. The observed and theoretical reflection effects in the λλ3933, 8542 Å emission lines for the specified parameters of the systems and a solar calcium abundance in the atmospheres of the red dwarfs are in good agreement.     

The chemical composition of HR 1512, a peculiar helium-weak star

We have used high-resolution spectra to study the chemical composition of HR 1512, a star with effective temperature T _eff = 15 200 K, atmospheric gravity log g = 3.52, microturbulence parameter V _t = 1.5 km/s, and rotation rate v sin i = 17 km s^?1. We confirm the presence of a helium deficiency (?0.6 dex), indicating that HR 1512 is a helium-weak star. Its considerable phosphorus excess (1.6 dex) testifies that the star belongs to the PGa subtype. We suggest that the He and P abundances increase with height; i.e., that there is stratification of He and P in the star’s atmosphere. Among the CNO elements, nitrogen demonstrates an underabundance of ?0.4 dex, while the abundances of carbon and oxygen are solar. Deficits of about ?0.5 or ?0.6 dex were also found for Mg, Si, and S. A neon excess of 0.4 dex was derived from our non-LTE analysis of NeI lines. The largest excess among the iron-peak elements (Cr, Mn, Fe, and Ni) is 0.6 dex, for manganese; the abundances of chromium and nickel display excesses of 0.5 and 0.3 dex, respectively, while the iron abundance is almost normal. The chemical anomalies of HR 1512 generally agree with those for mercury-manganese stars. This supports the hypothesis that PGa stars represent an extension of HgMn stars to higher temperatures.     

Modeling the spectral energy distributions of L dwarfs

Mechanisms for the formation of the optical (λλ500–950 nm) spectra of L dwarfs—stars and sub-stellar objects with T _eff<2200 K—are discussed. Their spectral energy distributions are determined primarily by the K I and Na I resonance-doublet absorption lines. The equivalent widths of these absorption lines formally computed using the dusty model atmospheres of Tsuji can reach several thousand angstroms. In this case, the extended wings of these lines form a pseudo-continuum for weaker absorption lines and even molecular bands. Mechanisms for the broadening of alkali-element lines in the atmospheres of late-type stars due to interactions between neutral atoms and hydrogen molecules are analyzed. The computed optical spectral energy distributions of several L dwarfs are compared with their observed spectra.     

Resonance potassium and sodium lines in the spectra of ultracool dwarfs

We discuss the methodological problems and results of computations of the spectral energy distributions (SEDs) of L dwarfs. Over a wide wavelength interval (λλ4000–10 000 Å), the spectra of these stars are determined to a considerable extent by absorption in resonance lines of potassium (7666.961, 7701.031 Å) and sodium (5891.518, 5897.489 Å). We compute the extended wings of these lines using the theory of quasi-stationary broadening. We compute the cores and nearby wings (up to Δλ = 40 Å from the line center) of the KI and NaI lines in a collisional approximation (van der Waals theory). In our modeling of the SED of the ultracool dwarf 2MASS J15232263+3014562 (L8), we find that the observations agree best with the COND atmospheric models of Allard et al. with T _eff = 2200 K and log g = 6.0.     

Evolutionary status of the spectral variable BD + 48°1220 = IRAS 05040+4820

Based on high-resolution observations (R = 60 000 and 75 000), we have studied the optical spectral variability of the star BD + 48°1220, identified with the IR source IRAS 05040+4820. We have measured the equivalent widths of numerous absorption lines of neutral atoms and ions at wavelengths from 4500 Å to 6760 Å, as well as the corresponding radial velocities. We use model atmospheres to determine the effective temperature T _eff = 7900 K, surface gravity log g = 0.0, microturbulence velocity ξ _t = 6.0, and the abundances for 16 elements. The star’s metallicity differs little from the solar value: [Fe/H] = ?0.10 dex. The main peculiarity of the chemical composition of the star is a large helium excess, derived from the Hel λ 5876 Å absorption, [He/H] = +1.04, and the equally large oxygen excess, [O/Fe] = +0.72 dex. The carbon excess is small, [C/Fe] = +0.09 dex, and the ratio [C/O] < 1. We obtained an altered relation for the light-metal abundances: [Na/Fe] = +0.87 dex with [Mg/Fe] = ?0.31 dex. The barium abundance is low, [Ba/Fe] = ?0.84 dex. It is concluded that the selective separation of elements onto dust grains of the envelope is probably efficient. The radial velocity of the star measured from photospheric absorption lines over three years of observations varies in the interval V _⊙ = ?(7–15) km/s. Time-variable differential line shifts have been revealed. The entire set of available data (the luminosity M _v ≈ ?5 ^m , velocity V _lsr ≈ ?20 km/s, metallicity [Fe/H] = ?0.10, and peculiarities of the optical spectrum and chemical composition) confirms the status of BD + 48°1220 as a post-AGB star with He and O excesses belonging to the Galactic disk.     

Abundances of carbon,nitrogen, oxygen,and other elements in the atmosphere of the giant 30 LMi

We have studied the star 30 LMi using high-dispersion CCD spectra and photographic observations. We estimate the star's effective temperature T_eff=7210 K, gravity log g=3.34, and microturbulence velocity ξ_t=5.8 km/s. The carbon abundance, log ?(C)=8.57, is close to the solar value. Nitrogen (log ?(N)=7.81), oxygen (log ?(O)=8.76), and sulfur (log ?(S)=7.20) are slightly underabundant compared to the Sun, by ?0.16 dex, ?0.11 dex, and ?0.13 dex, respectively. A relatively large underabundance of ?0.27 dex was found for titanium (log ?(Ti)=4.75), whereas zinc shows an over-abundance by +0.21 dex (log ?(Zn)=4.81). Sodium (log ?(Na)=6.26), silicon (log ?(Si)=7.57), calcium (log ?(Ca)=6.38), chromium (log ?(Cr)=5.62), iron (log ?(Fe)=7.51), nickel (log ?(Ni)=6.34), and yttrium (log ?(Y)=2.34) exhibited abundances close to the solar values. We find no chemical anomalies characteristic of Am stars or δ Scuti stars in the spectrum of 30 LMi.     

Analysis of the spectral energy distributions of four cool R CrB stars near the brightness maximum

The effective temperatures T _eff and carbon and nitrogen abundances in the atmospheres of the cool R CrB stars ES Aql, SV Sge, Z UMi, and NSV 11154 have been determined by modeling their spectral energy distributions in the optical and near-infrared. The hydrogen-deficient model atmospheres were computed using the SAM12 code in the classical approximation, taking into account sources of opacity characteristic of the atmospheres of R CrB stars. The influence of the hydrogen deficiency on theoretical stellar spectra is analyzed. The resulting effective-temperature estimates for ES Aql, SV Sge, Z UMi, and NSV 11154 are in the range T _eff = 4600–5200 K. The carbon abundances log n(C) in the atmospheres of ES Aql, SV Sge, and Z UMi are 8.9–10.1, corresponding to [C/Fe] values typical of the atmospheres of R CrB stars. The nitrogen abundances are lower than those determined in other studies, and differ considerably from star to star. The mean [N/Fe] value for these three stars is ≈1.5 dex lowthan the mean [N/Fe] for known warm R CrB stars. Abnormally high estimates were obtained for the atmosphere of NSV 11154: log n(C) = 10.8 and log n(N) = 10.0. The approximate log g estimates agree with the conclusion from photometric observations that cool R CrB stars have lower luminosities than hotter R CrB stars.     

A study of rare earth elements in the atmospheres of chemically peculiar stars. Pr III and Nd III lines

We determine the abundances of Pr and Nd in the atmospheres of magnetic and non-magnetic chemically peculiar stars from the lines of rare earth elements in the first and second ionization states. The computations for the magnetic stars take into account the influence of the magnetic field on line formation. We studied the influence of errors in the stellar-atmosphere parameters and the atomic parameters of the spectral lines on the accuracy of abundance determinations. Within the derived accuracy, ionization equilibrium is satisfied in the atmospheres of non-pulsating magnetic and non-magnetic stars (so that abundances derived separately from lines of first and second ions agree). For all the pulsating magnetic (roAp) stars studied, the abundances derived from lines of second ions are 1.0 to 1.7 dex higher than those derived from first ions. The violation of ionization equilibrium in the atmospheres of pulsating stars is probably due to, first, considerable enrichment of Pr and Nd in the uppermost atmospheric layers, and second, a higher location for the layer of enhanced elemental abundance in roAp stars than in non-pulsating stars. Two objects from the list of non-pulsating magnetic stars, HD 62140 and HD 115708, exhibit anomalies of their Pr and Nd lines characteristic of roAp stars. The differences in the rare earth anomalies for the pulsating and non-pulsating peculiar stars can be used as a selection criterion for candidate roAp stars.     

Molecular bands in the spectra of M stars

The profiles of the main molecular bands in the spectral-energy distributions (SEDs) of M stars have been calculated. The calculations of the individual band profiles were performed using the just-overlapping-lines approximation. Information about the oscillator strengths and the sources of the spectroscopic data for specific transitions between electronic levels of molecules is provided. The calculations of theoretical SEDs for M stars were performed using available lists of molecular lines for sources of bound-bound opacity in the atmospheres of oxygen-sequence stars. The observed SEDs of the oxygen-sequence red giant HD 148783 (30 Her) and the M dwarf 2MASS J22424129?2659272 are reproduced. The dependence of the calculated SEDs of the M giant on the adopted metallicity and carbon abundance is studied. The observed SEDs of HD 148783 and 2MASS J22424129?2659272 are described well by theoretical spectra calculated for model atmospheres with T _eff/log g/[Fe/H] = 3250/ ? 0.4/0 and 3000/5.0/0, respectively.     

Abundances of carbon,nitrogen, oxygen,and other elements in the atmospheres of the giants 25 Mon and HR 7389

An analysis of high-resolution CCD spectra of the giant 25 Mon, which shows signs of metallicity, and the normal giant HR 7389 is presented. The derived effective temperatures, gravitational accelerations, and microturbulence velocities are T_eff = 6700 K, log g = 3.24, and ξ _t = 3.1 km/s for 25 Mon and T_eff = 6630 K, log g = 3.71, and ξ _t = 2.6 km/s for HR 7389. The abundances (log ε) of nine elements are determined: carbon, nitrogen, oxygen, sodium, silicon, calcium, iron, nickel, and barium. The derived excess carbon abundances are 0.23 dex for 25 Mon and 0.16 dex for HR 7389. 25 Mon displays a modest (0.08 dex) oxygen excess, with the oxygen excess for HR 7389 being somewhat higher (0.15 dex). The nitrogen abundance is probably no lower than the solar value for both stars. The abundances of iron, sodium, calcium (for HR 7389), barium, and nickel exceed the solar values by 0.22–0.40 dex for both stars. The highest excess (0.62 dex) is exhibited by the calcium abundance for 25 Mon. Silicon displays a nearly solar abundance in both stars—small deficits of ?0.03 dex and ?0.07 dex for 25 Mon and HR 7389, respectively. No fundamental differences in the elemental abundances were found in the atmospheres of 25 Mon and HR 7389. Based on their T_eff and log g values, as well as theoretical calculations, A. Claret estimated the masses, radii, luminosities, and ages of 25 Mon (M/M_⊙ = 2.45, log(R/R_⊙) = 0.79, log(L/L_⊙) = 1.85, t = 5.3 × 10⁸ yr) and HR 7389 (M/M_⊙ = 2.36, log(R/R_⊙) = 0.50, log(L/L_⊙) = 1.24, t = 4.6 × 10⁸ yr), and also of the stars 20 Peg (M/M_⊙ = 2.36, log(R/R_⊙) = 0.73, log(L/L_⊙) = 1.79, t = 4.9 × 10⁸ yr) and 30 LMi (M/M_⊙ = 2.47, log(R/R_⊙) = 0.73, log(L/L_⊙) = 1.88, t = 4.8 × 10⁸ yr) studied by the author earlier.     

Solar analogs: Spectral energy distributions and physical parameters of their atmospheres

The angular diameters, radii, and effective temperatures of 16 G0–G5 main-sequence stars with color excesses 0.60≤B-V≤0.68 and parallaxes derived from Hipparcos data have been determined using their infrared fluxes, obtained from JHKLM photometric observations. For all the stars except BS 483, these effective temperatures differ from the spectroscopic temperatures by no more than 1–2%. Such differences are within the uncertainties expected for the IR-flux method. The effective temperatures of BS 483 derived from its infrared fluxes are 3% higher than those indicated by spectroscopic observations; this may be due to the specific atmospheric structure of this star. Spectroscopic observations at 3400–7500 Å and JHKLM photometric observations are compared with analogous solar data and Kurucz models. The best agreement with the model with T _eff=5750 K and logg=4.5 in the interval 4400–7500 Å was obtained for BS 7503 and BS 7504 (16 Cyg A and 16 Cyg B). The infrared color indices H-K, K-L, and K-M for these stars differ from the corresponding solar indices, and their angular diameters grow with wavelength, which is not the case for the Sun. H-K for BS 6060, currently considered to be the closest analog to the Sun, is near the solar value. The vast majority of the stars studied (13 of 16) have higher luminosities than the Sun. These include 16 Cyg A, 16 Cyg B, and 51 Peg, which thus cannot be considered full “twins” of the Sun.