NLTE effects on Fe I/II in the atmospheres of FGK stars and application to abundance analysis of their spectra
aa r X i v : . [ a s t r o - ph . S R ] S e p NLTE effects on Fe I/II in the atmospheres of FGKstars and application to abundance analysis of theirspectra
Maria Bergemann , Karin Lind , Remo Collet and Martin Asplund Max-Planck Institute for Astrophysics, Karl-Schwarzschild Str. 1, 85741, Garching, GermanyE-mail: [email protected]
Abstract.
We describe the first results from our project aimed at large-scale calculations ofNLTE abundance corrections for important astrophysical atoms and ions. In this paper, thefocus is on Fe which is a proxy of stellar metallicity and is commonly used to derive effectivetemperature and gravity. We present a small grid of NLTE abundance corrections for Fe I linesand discuss how NLTE effects influence determination of effective temperature, surface gravity,and metallicity for late-type stars.
1. Introduction
Iron is a key element in stellar astrophysics. The very complex atomic structure of its lowestionization stages, Fe I and Fe II, gives rise to a wealth of spectral lines all across the spectrumof a typical late-type star. This atomic property, coupled to a relatively large abundance makesFe a reference for spectroscopic estimates of stellar parameters using the method of excitation-ionization balance.The classical implementation of this method in spectrum analysis codes involves threeassumptions: local thermodynamic equilibrium (LTE), hydrostatic equilibrium, and 1Dgeometry. These approximations strongly reduce the complexity of the problem, thus permittinganalysis of very large stellar samples in short timescales. Yet, in the conditions when thebreakdown of 1D static LTE models occurs the inferred stellar parameters suffer from largesystematic biases. To assess the latter, more physically realistic modeling is necessary.Studies of NLTE effects on the Fe I/Fe II level populations for FGK stars trace back to Athay& Lites (1972). Since then, vast amount of work has been performed in this field demonstratingthat NLTE effects in the excitation-ionization balance of Fe I/Fe II are significant and can not beignored even in the analysis of solar-type stars (Mashonkina et al. 2011 and references therein).Yet, despite major efforts aimed at understanding how non-equilibrium thermodynamics affectsthe line formation of Fe, there has never been an attempt to accurately quantify these deviationsin a systematic manner across a wide range of stellar parameters, and to apply them to a largestellar sample.Here we present a new NLTE model atom of Fe I/Fe II to be applied in large-scale calculationsof NLTE abundance corrections for late-type stars. We discuss the NLTE effects influencingatomic level populations at the typical conditions in their atmospheres and provide a smallgrid of NLTE corrections for the Fe I lines. The model has been tested on a number ofell-studied stars with independently-determined parameters, including metal-poor giants andturnoff stars. These tests performed with classical 1D hydro-static model atmospheres andaverages of 3D hydrodynamical simulations of stellar convection will be presented in Bergemannet al. (in preparation). A complete grid of NLTE abundance corrections computed with multi2.3 statistical equilibrium code will be presented in Lind et al. (in preparation).
2. Methods
The calculations presented here were performed with 1D LTE plane-parallel mafags-odf models(Fuhrmann et al. 1997, Grupp 2004). In these models, convective energy transport is accountedfor using the mixing-length theory of B¨ohm-Vitense (1958) with the mixing length parameter α mlt set to 0 .
5. Line opacity is represented by all elements up to Ni, and various diatomicmolecules (H , CH, CO, TiO, etc). This accounts for nearly 20 million atomic and molecularlines. The reference solar abundances were compiled from various literature sources, givingpreference to the determinations by the Munich group. The model atmosphere provide partitionfunctions and partial pressures of all relevant atoms and molecules, which are then used indetailed line formation calculations.NLTE statistical equilibrium was computed with a revised version of the detail code (Butler& Giddings 1985), which solves multi-level NLTE radiative transfer with a given static 1D modelatmosphere. The last version of the code is based on the method of Accelerated Lambda Iteration(ALI). LTE and NLTE line formation calculations with departure coefficients from detail wereperformed with the revised version of the spectrum synthesis code SIU (Reetz 1999). The majorupdate in the code relates to the automated computation of NLTE abundance corrections ,which generally proceeds by constructing the grids of LTE and NLTE line equivalent widths fora range of stellar parameters and interpolating in the corresponding curves-of-growth for theinput observed equivalent widths or abundances. The NLTE model atom of Fe was constructed using all available atomic data from the Kurucz database, which also includes laboratory data from the NIST compilation . All predictedenergy levels of Fe I with the same parity above E low ≥ . gf ’s of individual transitions.Thus, in the final atomic model, the number of energy levels is 296 for Fe I and 112 for Fe II,with uppermost excited levels located at 0 .
03 eV and 2 .
72 eV below the respective ionizationlimits, 7 . .
19 eV. The model is closed by the Fe III ground state. The total numberof radiatively-allowed transitions is 16 207 (13 888 Fe I and 2 316 Fe II).Photoionization cross-sections for 136 states of Fe I were taken from Bautista (1997) andthe hydrogenic approximation was adopted for all other levels. The rates of transitions inducedby inelastic collisions with free electrons (e − ) and H I atoms were computed using differentrecipes. For the states coupled by permitted b-b and b-f transitions, we used the formula ofvan Regemorter (1962), respectively, Seaton (1962) for e − . To derive the rates of transitionsdue to inelastic collisions with H I atoms, we used the Drawins formula (Drawin 1969) in theversion of Steenbock & Holweger (1984). Also, the states are connected by forbidden transitionsinduced by inelastic collisions with e − and H I atoms. These are computed using the formulae NLTE abundance correction is defined to be the difference in abundance required to match NLTE and LTEline profiles or equivalent widths http://kurucz.harvard.edu/atoms.html .0 0.5 1.0 1.5 2.0 ∆ E (eV)−3−2−1012 l og RC ( Q M / A ll e n ) Fe II 0 − 1.7 eV, T = 5294
Figure 1.
Left panel: Grotrian diagram of the Fe I atom. Right panel: comparison of quantum-mechanical rate coefficients for e − -induced forbidden transitions between the lowest energy levelsof Fe II with the classical Allen’s (1973) recipe.of Allen (1973) and Takeda (1994). Quantum-mechanical calculations exist only for e − -inducedforbidden transitions between the 16 lowest Fe II energy levels (Ramsbottom et al. 2007). Thesedata are compared with the Allen’s (1973) recipe in Fig. 1.The influence of e − and H I collisions on the statistical equilibrium of Fe was carefullyinvestigated by performing test calculations with various scaling factors to the above-mentionedformulae. The NLTE synthetic profiles were furthermore compared with the observed stellarspectra to check how well the test model atoms satisfy the constraint of ionization-excitationbalance of Fe I/Fe II under restriction of different stellar parameters. The final choice of scalingfactors will be discussed in Bergemann et al. (in preparation).
3. Statistical equilibrium of Fe
Fig. 2 shows level departure coefficients, b i , as a function of continuum optical depth log τ for a number of model atmospheres computed with different stellar parameters. The latterare representative of stars typically used in Galactic chemical evolution studies. Only selectedenergy levels of Fe I and Fe II typical for their depth-dependence are included in the plot: a D(ground state of Fe I), z D ◦ (2 . e D (5 . t H ◦ , a D (ground state of Fe II), and z D ◦ (5 . b i <
1. The Fe II numberdensities remain close to LTE values, b i ≈
1, and a minor overpopulation of the Fe II groundstate develops only close to the outer atmospheric boundary.Deviations from LTE in the distribution of atomic level populations arise because meanradiation field, J ν , at different depths and frequencies is not equal to the Planck function, B ν [ T e ( τ )], which is defined by the local temperature T e ( τ ) at each depth. For Fe I, excess ofthe mean intensity over Planck function in the UV continua leads to over-ionization, which setsin as soon as the optical depth in the photoionization continua of low-excitation Fe I levelsfalls below unity, i.e. log τ ∼
0. In the outer layers, ionization balance is dominated by the Departure coefficient is defined to be the ratio of NLTE to LTE atomic level populations, b i = n NLTE i /n LTE i τ (500 nm)0.00.20.40.60.81.01.2 d e p a r t u r e c o e ff i c i e n t s z D o e D t H o a D z D o a D5000/2.20/+0.3 −4 −3 −2 −1 0 1 2log τ (500 nm)0.00.20.40.60.81.01.2 d e p a r t u r e c o e ff i c i e n t s z D o e D t H o a D z D o a D5000/2.20/−1.2 −4 −3 −2 −1 0 1 2log τ (500 nm)0.00.20.40.60.81.01.2 d e p a r t u r e c o e ff i c i e n t s z D o e D t H o a D z D o a D5000/2.20/−3.6 −4 −3 −2 −1 0 1 2log τ (500 nm)0.00.20.40.60.81.01.2 d e p a r t u r e c o e ff i c i e n t s z D o e D t H o a D z D o a D6200/2.20/−2.4 −4 −3 −2 −1 0 1 2log τ (500 nm)0.00.20.40.60.81.01.2 d e p a r t u r e c o e ff i c i e n t s z D o e D t H o a D z D o a D5800/4.60/−1.2 −4 −3 −2 −1 0 1 2log τ (500 nm)0.00.20.40.60.81.01.2 d e p a r t u r e c o e ff i c i e n t s z D o e D t H o a D z D o a D5800/4.60/−3.6
Figure 2.
Departure coefficients of selected Fe I and Fe II levels for a number of modelatmospheres from the grid; stellar parameters are indicated in each figure.e I levels with excitation energies at 4 − J ν < B ν leads toover-recombination, which is very efficient for our atomic model with only 0 .
03 eV energy gapof the upper Fe I levels from the Fe II ground state.Due to an extremely tight radiative and collisional coupling of atomic energy levels, excitationbalance of Fe I is also affected by radiative imbalances in line transitions. These include radiativepumping by super-thermal UV radiation field of non-local origin at the line frequencies, aswell as photon suction driven by photon losses in large-probability transitions between highly-excited levels. These processes leave a characteristic imprint on the behavior of b i -factors in theouter atmospheric layers. In Fig. 2, this is seen as the onset of deviations from the relativethermal equilibrium between the Fe I levels, which occurs, depending on the model metallicity,at log τ ∼ − ... −
2. The NLTE effects on the line formation are different for the strong andweak Fe I lines. The former are mostly shaped by deviations of their source function from thePlanck function, which makes a clear effect in the line cores. Weak lines are pre-dominantlycontrolled by their opacity, thus the major change is due to the shift of their optical depth scalein NLTE.
We computed NLTE abundance corrections, hereafter ∆
NLTE , to Fe I lines for a small grid ofmodel atmospheres covering metallicity range − . ≤ [Fe/H] ≤ +0 .
3. The results are presentedin Fig. 3 for the parameters representative of giants (left panel) and dwarfs (right panel).Our sample of Fe I lines includes transitions between 0 to 5 eV levels, and the line equivalentwidths range from 5 m˚A to few ˚A depending on stellar parameters. In the plot, each symbolcorresponds to a mean ∆
NLTE obtained by averaging individual NLTE corrections for all FeI lines in the sample, and the errors bars correspond to the line-to-line variations in ∆ foreach model atmosphere. The former quantity roughly demonstrates how much the Fe I/Fe IIionization balance, and, thus, determination of surface gravity, is affected by NLTE, whereasthe latter helps to assess the influence of NLTE on the excitation balance and determination ofeffective temperature. −4 −3 −2 −1 0 1[Fe/H]−0.20.00.20.40.6 ∆ ( N LTE − LTE ) average over all Fe I lines, ew λ > 5 mA5000 K, log g = 2.25000 K, log g = 3.4 −4 −3 −2 −1 0 1[Fe/H]−0.10.00.10.20.3 ∆ ( N LTE − LTE ) average over all Fe I lines, ew λ > 5 mA5000 K5400 K5800 K6200 K Figure 3.
NLTE abundance corrections for different stellar parameters. Right panel: all modelatmospheres adopt log g = 4 . g , thus ionization balance achievedassuming LTE leads to progressively underestimated gravities and metallicities. In particular,at T eff = 5000 K (Fig. 3, left panel), the mean NLTE corrections are twice as large in thelog g = 2 . g = 3 . . ∼ − . T eff . Fig. (right panel) shows that for the coolest models, T eff ∼ T >
NLTE amongFe I lines with different equivalent widths W λ and excitation potentials E low strongly increaseswith decreasing metallicity for giants, and less so for dwarfs. Furthermore, this scatter is notrandom, but corresponds to a trend of ∆ NLTE with E low , as shown in Fig. 4. The figuredemonstrates variation of NLTE corrections with lower level excitation potential for the modelswith parameters: T eff = 5000, log g = 2 .
2, [Fe/H] = − . T eff = 5800, log g = 4 . − . W λ >
60 m˚A, tend to experience smaller departuresfrom LTE compared to weaker lines, but they also demonstrate systematically increasing ∆
NLTE with increasing E low . No such effect is seen for the weak lines, W λ ≤
60 m˚A, which, for someexceptions, have very similar NLTE corrections independent of their excitation potential.Thus, our results suggest that LTE T eff determinations become very inaccurate at [Fe/H] < − T eff scale of dwarfs and giants. −1 0 1 2 3 4 5 6Excitation energy (eV)0.00.10.20.30.40.5 ∆ ( N LTE − LTE ) < 60 mA < −1 0 1 2 3 4 5 6Excitation energy (eV)−0.050.000.050.100.15 ∆ ( N LTE − LTE ) < 60 mA < Figure 4.
NLTE abundance corrections for the Fe I lines as a function of lower level excitationpotential. Red and blue colors separate the spectral lines with W λ greater and less than 60 m˚A,respectively. Stellar parameters are indicated in the plots.
4. Conclusions
We have constructed a new NLTE Fe model atom using the most up-to-date theoretical andexperimental atomic data. The model has been tested on a number of well-studied late-type starswith parameters determined by other independent methods (Bergemann et al, in preparation).Our preliminary results for the NLTE effects on Fe I and Fe II in the atmospheres of late-type stars are qualitatively consistent with other studies. Kinetic equilibrium of Fe, which is aminority ion at the typical conditions of these cool and dense atmospheres, favors lower numberdensities of Fe I compared to LTE. The number densities of Fe II are hardly affected by NLTE. Ingeneral, this leads to a weakening of Fe I lines compared to LTE, which, in turn, requires largerFe abundance to fit a given observed spectral line. The magnitude of departures and NLTEcorrections critically depends on stellar parameters. Whereas NLTE abundance corrections forthe Fe I lines do not exceed ∼ .
05 dex for solar metallicity dwarfs, they can be as large as 0 . g , thus ionization balancechieved assuming LTE leads to progressively underestimated gravities and metallicities. Onthe other side, Fe I levels are also not in thermal equilibrium with respect to each other, andfor the stronger lines NLTE abundance corrections show trends with line excitation potential.In particular, we find that LTE T eff determinations become very inaccurate at low metallicitiesand significant systematical effects in the T eff scale of dwarfs and giants can be expected.The NLTE abundance corrections will be publicly available through an interactive onlinedatabase, which is currently under construction. They can be used to retrieve NLTE abundancesand abundance corrections for input equivalent widths. We also consider an option to providefunctional dependency of NLTE corrections on line parameters for a grid of stellar parameters( T eff , log g , [Fe/H]). This is a more convenient solution for implementation in the automatedcodes used in large-scale spectroscopic studies, such as follow-up spectroscopy for Gaia targets. Acknowledgments
We would like to thank Luca Sbordone for the help with revision of the SIU code.
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