Fe I/Fe II ionization equilibrium in cool stars: NLTE versus LTE
Lyudmila Mashonkina, Thomas Gehren, Jianrong Shi, Andreas Korn, Frank Grupp
aa r X i v : . [ a s t r o - ph . S R ] O c t Chemical Abundances in the Universe: Connecting First Stars toPlanetsProceedings IAU Symposium No. 265, 2009K. Cunha, M. Spite & B. Barbuy, eds. c (cid:13) Fe I/Fe II ionization equilibriumin cool stars: NLTE versus LTE
Lyudmila Mashonkina , , Thomas Gehren , Jianrong Shi ,Andreas Korn , and Frank Grupp Institute of Astronomy, Russian Academy of Science,Pyatnitskaya 48, 119017 Moscow, Russiaemail: [email protected] Universit¨ats-Sternwarte M¨unchen,Scheinerstr. 1, 81679 M¨unchen, Germanyemail: lyuda, gehren, [email protected] National Astronomical Observatories, Chinese Academy of Sciences,A20 Datun Road, Chaoyang District, Beijing 100012, PR Chinaemail: [email protected] Department of Physics and Astronomy, Uppsala University,Box 515, 75120 Uppsala, Swedenemail: [email protected]
Abstract.
Non-local thermodynamic equilibrium (NLTE) line formation for neutral and singly-ionized iron is considered through a range of stellar parameters characteristic of cool stars. Acomprehensive model atom for Fe I and Fe II is presented. Our NLTE calculations support theearlier conclusions that the statistical equilibrium (SE) of Fe I shows an underpopulation of Fe Iterms. However, the inclusion of the predicted high-excitation levels of Fe I in our model atomleads to a substantial decrease in the departures from LTE. As a test and first application of theFe I/II model atom, iron abundances are determined for the Sun and four selected stars withwell determined stellar parameters and high-quality observed spectra. Within the error bars,lines of Fe I and Fe II give consistent abundances for the Sun and two metal-poor stars wheninelastic collisions with hydrogen atoms are taken into account in the SE calculations. For theclose-to-solar metallicity stars Procyon and β Vir, the difference (Fe II - Fe I) is about 0.1 dexindependent of the line formation model, either NLTE or LTE. We evaluate the influence ofdepartures from LTE on Fe abundance and surface gravity determination for cool stars.
Keywords. atomic data, line: formation, stars: atmospheres
1. Introduction
Iron plays an outstanding role in studies of cool stars thanks to quite numerous lines inthe visible spectrum, which are easy to detect even in very metal-poor stars. Iron servesas a reference element for all astronomical research related to stellar nucleosynthesis andchemical evolution of the Galaxy. Iron lines are used to determine the surface gravity,log g, and the microturbulence ξ of stellar atmospheres. In the atmosphere with T eff > et al. (2001)). However, a consensus on the expectedmagnitude of the NLTE effects was not reached.In this study, we update the model atom of Fe I-II treated by Gehren et al. (2001)1 Mashonkina et al.(hereafter Paper I) and apply it to analysis of the Fe spectrum in the Sun and selectedcool stars with the aim of empirically constraining the role of inelastic collisions withhydrogen atoms in the SE of Fe I-II.
2. The Fe model atom
In all previous NLTE calculations, the model atom of Fe I was build using measuredenergy levels. The experimental analysis of Nave et al. (1994) with later updates provided965 energy levels for Fe I. A comparison with the calculated Fe I atomic structure (Kurucz(2007)) reveals that the system of measured levels is nearly complete below excitationenergy, E exc , 5.6 eV, however, laboratory experiments do not see most of the high-excitation levels with E exc > E exc up to 7.83 eV, in total, 2970 levels. Multiplet fine structurewas neglected for all terms. The predicted and measured levels with close energies werecombined resulting in 233 terms. In addition, six super-levels were made up from theremaining predicted levels. For 11958 radiative transitions occurring in this atom ofFe I, gf -values were taken from the Nave et al. (1994) compilation, where available, andKurucz (2007) calculations. Photoionization cross-sections of the IRON project (Bautista(1997)) have been used for 149 levels and a hydrogenic approximation for the remaininglevels. The collisional rates were computed as in Paper I.For Fe II, we rely on the reference model atom treated in Paper I. In this study, it wasreduced and includes now the levels with E exc up to 10 eV. The main uncertainty of theNLTE calculations for Fe I and II is the treatment of the poorly known inelastic collisionswith hydrogen atoms. We employ the formula of Steenbock & Holweger (1984) for allowedtransitions and a simple correlation between hydrogen and electron collisional rates, C H = C e p ( m e /m H ) N H /N e , for forbidden transitions. Calculations were performed withthe hydrogen collision enhancement factor S H , which was varied between 0 and 3.
3. Results
The coupled radiative transfer and statistical equilibrium equations are solved withan improved version of the DETAIL program (Butler & Giddings (1985)) based on theaccelerated lambda iteration. All calculations are performed with plane-parallel, homo-geneous, LTE, and blanketed model atmospheres computed with the MAFAGS-OS code(Grupp et al. (2009)).For comparison with observed data, a total of 43 lines of Fe I and 18 lines of Fe IIwere chosen. For the Sun and HD 84937, the analysis was extended to a larger line listincluding 271 lines of Fe I and 34 lines of Fe II. The Sun is also used as a referencestar for a line-by-line differential analysis of stellar spectra. Solar flux observations weretaken from the Kitt Peak Solar Atlas (Kurucz et al. (1984)). The absolute solar ironabundances were determined using gf -values from O’Brian et al. (1991) and Mel´endez& Barbuy (2009) for Fe I and Fe II, respectively. We find that virtually all models ofline formation, whether LTE or NLTE with S H > .
1, lead to acceptable solar ionizationequilibria within their 1 σ error bars. To show the maximal NLTE effect on abundance AUS 265. Fe I/Fe II ionization equilibrium: NLTE versus LTE Table 1.
Stellar parameters and iron abundances obtained for selected starsHD T eff log g V mic , [Fe/H] I [Fe/H] II km s − NLTE LTE NLTE LTESun 5777 4.44 0.9 7.63 ± ± ± ± − ± − ± − ± − ± ± − ± − ± − ± − ± ± − ± − ± − ± − ± ± ± ± ± ± determination, Table 1 presents the average abundances for both ionization stages derivedfrom the NLTE with S H = 0 (denoted as NLTE ) and LTE calculations.Four stars with effective temperature and surface gravity measured from the model-independent methods were chosen to investigate the ionization equilibrium between Fe Iand Fe II for various S H values. They are listed in Table 1 together with the T eff andlog g values taken from Di Folco et al. (2004) for HD 10700 ( τ Cet), Allende Prieto et al. (2002) for HD 61421 (Procyon), Korn et al. (2003) for HD 84937, North et al. (2009) forHD 102870 ( β Vir). Observational data were obtained with the FOCES spectrograph atthe 2.2m telescope of the Calar Alto Observatory during a number of observing runsbetween 1997 and 2005, with a spectral resolution of R ≃
60 000 and a signal-to-noiseratio
S/N > S H = 0 and LTE abundances obtained from the lines of Fe I (denotedas [Fe/H] I ) and Fe II ([Fe/H] II ) are presented in Table 1. It is worth noting that, withthe updated model atom of Fe I-II, the departures from LTE are substantially smallercompared to those from the previous studies. For example, with S H = 0, we obtainan average NLTE abundance correction ∆ NLTE = log ε NLTE − log ε LTE = 0.22 dex forthe Fe I lines in HD 84937, while the corresponding value amounts 0.40 dex in Korn et al. (2003). Figure 1 displays the abundance difference between Fe I and Fe II forvarious assumptions for the hydrogen collisions. We find that NLTE with pure electroniccollisions ( S H = 0) is not acceptable for HD 84937 and τ Cet. This indicates the need
Figure 1.
The difference in abundance between Fe I and Fe II in selected stars from calculationswith various line formation models. For each star, the error bars is indicated in the upper partof panel.
Mashonkina et al.for thermalizing processes not involving electrons in the atmosphere of metal-poor stars.For each object, the NLTE effect on abundance determination is small (within the errorbars) when hydrogen collisions are included with S H >
1. For Procyon and β Vir, themean Fe abundance from Fe I lines is about 0.1 dex lower compared to that from Fe IIlines. The origin of such a discrepancy will be investigated in a forthcoming paper. Forthe Fe I/Fe II ionization equilibrium in two metal-poor stars, LTE seems to be as goodas NLTE with S H > S H = 1 for the small grid of modelatmospheres with T eff = 5000 and 6000 K, [M/H] = − −
3, and log g rangingbetween 2 and 4 in order to inspect the departures from LTE depending on stellarparameters. Negligible NLTE effects were obtained for Fe II. Fe I is subject to significantNLTE effects for low gravity (log g <
3) and very metal-poor models. An importantconsequence is that surface gravities of giants and very metal-poor stars derived by LTEanalysis are in error with a magnitude strongly depending on log g/[Fe/H]. For example,LTE leads to a 0.26 dex lower gravity for T eff = 5000 K, log g = 2, and [Fe/H] = −
4. Conclusions • Completeness of model atom for Fe I is important for a correct calculation of theFe I/Fe II ionization equilibrium in the atmosphere of cool stars. • Thermalizing processes not involving electron collisions have to be included in theSE calculations for Fe I-II. Collisions with hydrogen atoms could be good candidates forsuch processes. • Fe I is affected by significant NLTE effects for giants and very metal-poor stars. • Only minor departures from LTE are obtained for Fe II.
Acknowledgements.
L.M. acknowledges a partial support from the International As-tronomical Union, the Russian Foundation for Basic Research (08-02-92203-GFEN), andthe Russian Federal Agency on Science and Innovation (02.740.11.0247) of the partici-pation at the IAU XXVII General Assembly. This study is supported by the DeutscheForschungsgemeinschaft (GE 490/34.1). A.K. acknowledges support by the Swedish Re-search Council (VR).
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