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.     

Model atmospheres of red giants

Techniques and results of computations of model atmospheres are discussed for M and C giants and for giants with abundance anomalies. The SAM12 code, a modification of the ATLAS12 code developed by Kurucz, is used. Blanketing effects due to atomic and molecular line absorption are taken into account using the opacity-sampling approach. The computed model atmosphere for the Sun (G2V) is used as a test of the SAM12 code. The model red-giant atmospheres are compared with models reported in other studies. Comparisons between the computed and observed spectral energy distributions are given for the C giant WX Cyg (C-J6) and Sakurai's object (V4334 Sgr).     

Collision-induced absorption of radiation in the atmospheres of late-type stars

Problems associated with taking into account absorption induced by collisions between hydrogen and helium atoms, helium atoms and hydrogen molecules, and hydrogen molecules, resulting in the formation of short-lived, quasi-molecular complexes are discussed, together with opacity in the atmospheres of late-type stars due to such absorption. There is good agreement between such opacities computed using codes developed by the author and by R. Kurucz. To demonstrate the importance of including collision-induced opacity, theoretical fluxes are compared to the observed spectral energy distribution of the metal-poor L subdwarf SDSS J125637.13-022452.4. The spectral energy distribution of this object can be reproduced with an effective temperature of T_eff = 2600 K only if collision-induced absorption is taken into account.     

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.     

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.     

Non-LTE analysis of the formation of KI lines in the spectra of A-K stars

The non-LTE formation of KI lines in the spectra of A-K stars is analyzed. The computations are based on a 36-level model of the neutral potassium atom for blanketed LTE Kurucz model atmospheres with T _eff=4000–10000 K, logg=0.0–4.5, and [M/H]=(0.0)–(?2.0). The KI atoms in the atmospheres of these stars are in states of moderate and strong “over-recombination.” A number of atomic parameters are refined using the profiles and equivalent widths of five lines in the solar spectrum. The classical van der Waals damping constants must be increased by factors of 2–60 to fit the observed profiles. The non-LTE solar potassium abundance—logε (K)=5.14—corresponds to the meteoritic abundance. Non-LTE corrections to the potassium abundance are important and equal to ?0.4...?0.7 dex for the λ7699 Å line and ?0.15...?0.3 dex for the λλ12522, 12432, and 11769 Å lines.     

The carbon abundance and <Superscript>12</Superscript>C/<Superscript>13</Superscript>C isotopic ratio in the atmosphere of Arcturus from 2.3 µm CO bands

We have modeled absorption lines of the ¹²CO and ¹³CO (Δυ = 2) molecular bands at λλ 2.29–2.45 µm in the spectrum of Arcturus (K2III). A grid of model atmospheres and synthetic spectra were computed for the red giant using T _eff = 4300, log g = 1.5, and the elemental abundances of Peterson et al. (1993), with the exception of the abundances of carbon, log N(C), and oxygen, log N(O) and the carbon isotopic ratio, ¹²C/¹³C, which were varied in our computations. The computed spectra were compared to the observed spectrum of Arcturus from the atlas of Hinkle et al. (1976). The best fit between the synthetic and observed spectra is achieved for log N(C) = ?3.78, ¹²C/¹³C = 8 ± 0.5. We discuss the dependence of ¹²C/¹³C on log N(C) and log N(O) in the atmosphere of the red giant.     

Determinations of high-precision effective temperatures for giants based on spectroscopic criteria

Spectral lines with high and low excitation potentials respond differently to changes of the effective temperature (T _eff), making the ratio of their depths (or equivalent widths) a very sensitive temperature indicator. We derive a set of 100 equations relating T _eff to the line-depth ratios, calibrated against accurate (to within 1%) published temperature determinations for giants. These relations are used to determine very accurate temperatures for a sample of 110 giants with nearly solar metallicities based on high-resolution (R = 42 000) échelle spectra with high signal-to-noise ratios (SNRs). The calibration relations are valid for temperatures of 4000–7000 K (F2III–K4III). The internal errors of each of the calibration relations are below 95 K, and applying all these relations together to spectra with SNR = 100 reduces the errors to 5–25 K (1 σ). A major advantage of this technique is that it is independent from interstellar reddening, spectroscopic resolution, and line broadening due to rotation and microturbulence.     

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.     

A model for the irradiative coloration of smoky feldspar and the inhibiting influence of water

Radiation-induced smoky color and associatedelectron paramagnetic resonance (EPR) signals develop only in potassium feldspar (KAlSi₃O₈) free of structurally bound molecular water. Fluid inclusion water does not influence coloration. The integrated intensity of each of the four bands (11,600, 16,200, 19,100, and 27,200 cm^?1) in the optical absorption spectra are linearly correlated with the doubly-integrated intensity of a broad, asymmetric first derivative atg _eff=2.027 in EPR spectra. In microcline, the EPR pattern is resolved into an asymmetric six-line pattern atg _eff=2.024 and a single derivative atg _eff=2.009 which, based on analogy to alkali-silicate glass, are due respectively to [SiO₄/K⁺]²⁺ and a hole shared between two nonbonding oxygens on Si. We propose that structural water inhibits formation of smoky centers in feldspar by releasing atomic hydrogen during irradiation which destroys centers while diffusing towards a stable site.     

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.     

Detection of spectral variability of the optical component of the IR source IRAS 20508+2011

Our high-resolution spectral observations have revealed variability of the optical spectrum of the cool star identified with the IR source IRAS 20508+2011. We measured the equivalent widths of numerous absorption lines of neutral atoms and ions at wavelengths 4300–7930 Å, along with the corresponding radial velocities. Over the four years of our observations, the radial velocity derived from photospheric absorption lines varied in the interval V _r⊙ = 15–30 km/s. In the same period, the Hα profile varied from being an intense bell-shaped emission line with a small amount of core absorption to displaying two-peaked emission with a central absorption feature below the continuum level. At all but one epoch, the positions of the metallic photospheric lines were systematically shifted relative to the Hα emission: ΔV _r = V _r(met) ? V _r(Hα, emis) ≈ ?23 km/s. The Na D doublet displayed a complex profile with broad (half-width ≈ 120 km/s) emission and photospheric absorption, as well as an interstellar component. We used model atmospheres to determine the physical parameters and chemical composition of the star’s atmosphere: T _eff = 4800 K, log g = 1.5, ξ_t = 4.0 km/s. The metallicity of the star differs little from the solar value: [Fe/H]_⊙ = ?0.36. We detected overabundances of oxygen [O/Fe]_⊙ = +1.79 (with the ratio [C/O] ≈ ?0.9), and α-process elements, as well as a deficit of heavy metals. The entire set of the star’s parameters suggests that the optical component of IRAS 20508+2011 is an “O-rich” AGB star with luminosity M _v ≈ ?3^m that is close to its evolutionary transition to the post-AGB stage.     

Structure energies of the alkali feldspars

Structural energetics of the alkali feldspars have been studied using a “lattice” or structure energy model. Electrostatic energies, U _e,for 20 well-refined, non-intergrown alkali feldspars were calculated using Bertaut's (1952) summation procedure and average about ?13,400 kcal/mol; the repulsive energies of the alkali site in each structure (～15 kcal/mol) were calculated using repulsive parameters for K-O and Na-O interactions estimated from bulk modulus data for NaF and KF and the exponential form of the repulsive potential. Using a procedure in which the position of the alkali cation was varied while the oxygen cage was kept fixed, structure energy gradients for the alkali sites of high albite and a hypersolvus Ab₄₂Or₅₈ structure were computed. In both cases, a broad structure energy well, elongated approximately parallel to c and subparallel to the observed split Na positions, was found. In both structures there is a single energy minimum corresponding closely with the observed single alkali positions. Comparison of U _e values for the alkali feldspars with different K/Na ratios shows that intermediate compositions are predicted to be less “stable” than either endmember and that the potassic end-member is predicted to be less “stable” than the sodic one, assuming that all other factors contributiong to the free energies of each phase are approximately the same. Comparison of U _e values for the high albite and low sanidine structures with different Al/Si distributions and a fixed tetrahedral framework indicates that the ordered charge distributions are 63.0 and 54.8 kcal/mol, respectively, more “stable” than the disordered distributions. Smaller, more realistic energy differences were obtained by using U _evalues averaged from four separate calculations with a +3 charge on a different T site in each and with +4 charges on the other T sites. If, in addition, the charges on cations and oxygen are reduced to half their nominal formal charges, in agreement with Pauling's electroneutrality principle and the results of recent molecular orbital calculations on silicates, the predicted electrostatic energy differences are reduced to 3.6 and 1.6 kcal/mol, respectively. These calculations also indicate that the T₁O site in the high albite structure energetically favors Al and that the Al/Si distribution determines the Na position within the alkali site.     

Evolutionary changes in the optical spectrum of the peculiar supergiant IRC+10420

We present new spectroscopic observations of the peculiar supergiant IRC+10420. In 1997–2000, we obtained three high signal-to-noise ratio spectra of the object at 4300–8000 Å with a spectral resolution of 15 000 (20 km/ s) using the 6-m telescope of the Special Astrophysical Observatory. From our 2000 spectrum, we estimate the spectral type of IRC+10420 to be A2, corresponding to a temperature of ～9200 K. Many emission lines were detected, identified with lines of Fe I; Fe II, Ti II, Cr II, and Sc II ions; and [O I], [Fe II], and [Ca II] forbidden lines. The radial velocity derived from absorption lines without obvious emission components (He I λ5876, O I, N I, Si II) and from absorption components of the Balmer lines is 93±1 km/s. The redshift of photospheric lines relative to the star’s center-of-mass velocity is interpreted as a consequence of scattering in the expanding, optically thick dust envelope. Both emission and absorption lines show a correlation between radial velocity and oscillator strength. We found variability in the relative intensities of the H _α and H _β emission components. We conclude that IRC+10420 is rapidly evolving towards a Wolf-Rayet stage; the current rate of the photospheric temperature increase is ～120 K per year. Based on the intensity of the O I (λ7773) triplet, we estimate the star’s luminosity to be M _bol=?9.5^m. In all 1997–2000 spectra of IRC+10420, the He I λ5876 line has a significant equivalent width of at least 200 mÅ; this may be possible in the presence of such a low temperature due to the star’s high luminosity and the enhanced helium abundance in the supergiant’s atmosphere.     

Non-stationary wind in the system of the infrared source RAFGL 5081

Based on long-term spectral monitoring with high spectral resolution, the optical spectrum of the weak central star of the IR source RAFGL 5081 has been studied for the first time. The spectral type of the star is close to G5–8 II, and its effective temperature is T_eff ≈ 5400 K. An unusual spectral phenomenon was discovered: splitting of the profiles of broad, stationary absorption lines of medium and low intensity. The heliocentric radial velocities V _r of all components of metal absorption lines, the Na I D lines, and the Hα line were measured for all the observation epochs. The constancy of the absorption lines rules out the possibility that the line splitting is due to binarity. The radial velocities of the wind components in the profiles of the Na I D and Hα lines reach ?250 and ?600 km/s, respectively. These profiles have narrow components, whose number, depth, and position vary with time. The time variability and multicomponent structure of the profiles of the Na I D and Hα lines indicates inhomogeneity and instability of the circumstellar envelope of RAFGL 5081. The presence of components with velocity V _r (IS) = ?65 km/s in the Na I (1) lines provides evidence that RAFGL 5081 is located behind the Perseus arm, i.e, no closer than 2 kpc. It is noted that RAFGL 5081 is associated with the reflection nebula GN 02.44.7.     

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.     

Soft X-ray spectroscopy of ferrous silicates

Energy gaps and electrical conductivities in the ferrous silicates, Fe₂SiO₄ and FeSiO₃, depend primarily on Fe-O bonding and may be studied by ultraviolet and soft X-ray spectroscopy. We have measured FeL_II–III X-ray band spectra under conditions of “minimal” (I₄, at 4.0 keV) and “high” (I₁₀, at 10.0 keV) self absorption to determine 3d orbital energy levels, to delineate d states in the valence band, and to construct band gap models. Absorption spectra, I₄/I₁₀, were computed to determine vacant orbital levels in the gap. A difference function (I₄–I₁₀) has been proposed to identify X-radiation at photon energies above the measured L_III absorption edge, including high-energy, double-vacancy satellites and radiative transitions involving the anti-parallel (spin-down) d ⁶ electron in the ground state. The proposed band gap model for Fe₂SiO₄ is consistent with that of Nitsan and Shankland (1976), including an intrinsic transition of 6.5 eV and an energy gap of 7.8 eV. The 3d orbital energy level electronic structures are in general agreement with levels computed by Tossell et al. (1974) for [FeO₆]^10? in FeO using an SCF Xα cluster MO method. A high-energy, double-vacancy satellite was found at ～710.7 eV, and is presumed to originate from an L_IIIM_II,III initial state. The intensity of these satellites for the ferrous silicates and other iron compounds, and corresponding Fe L_II/L_III intensity ratios are correlated with differences in band gap magnitudes and gap structure. Fe L_II/L_III intensity ratios are not well correlated with iron oxidation state.     

Lithium lines in the spectra of M dwarfs: UX Tau C

The results of numerical modeling of lithium lines in the spectra of M dwarfs are discussed. The behavior of the lithium lines relative to the local pseudocontinuum formed by molecular bands is analyzed as a function of model atmosphere parameters: effective temperature T _eff, gravity logg, and metallicity μ The molecular opacity was computed using the just overlapping line approximation (JOLA) and “line-by-line” methods. The pseudo-equivalent widths of lithium lines depend appreciably on metallicity μ and weakly on T{nteff}. The lithium abundance in the atmosphere of UX Tau C is redetermined. Previous studies underestimated the lithium abundance in this star as a result of the use of insufficiently accurate molecular-line lists. The new lithium abundance log N (Li)=3.2±0.3was derived by comparing the observed profiles of the 670.8 nm resonance doublet lines with profiles calculated using the new TiO line list of Plez.¹ The new abundance agrees with the atmospheric lithium abundances of the other two components in the stellar system, providing further evidence that the three stars in the UX Tau system have the same age. A comparison of the observed spectra of UX Tau C near the lithium resonance doublet (665–680 nm) with spectra computed using JOLA and line-by-line methods suggests that the list of Plez is the best currently available.     

Electron density and polarized absorption spectra of fayalite

The maxima of the electron difference densities of Fe²⁺ atM(1) andM(2) positions of fayalite, Fe₂SiO₄, determined by x-ray diffraction are considered to correspond to atomic dipoles. Provided the selection rules of dipole radiation are satisfied and the energy of the incident radiation lies within the appropriate range, the interaction of incident radiation with these atomic dipoles should lead to three absorption bands of which two originate from Fe²⁺ atM(1), one from Fe²⁺ atM(2). The relative intensities of the three bands, dependent on the polarization direction, are estimated. The result ist in excellent agreement with the interpretation of olivine spectra given by Burns (1970).