Atomic oscillator strengths in the spectral domain of Gaia

Mon. Not. R. Astron. Soc. 372, 609 614 (2006) doi:10.1111/j.1365-2966.2006.10701.x Atomic oscillator strengths in the spectral domain of Gaia L. Bigot and F. Thévenin Département Cassiopée, Observatoire de la Côte d Azur, BP 4229, 06304 Nice Cedex 4, France Accepted 2006 June 13. Received 2006 June 9; in original form 2006 February 27 1 INTRODUCTION The ESA Gaia space mission aims at determining how the Galaxy was born and how it has evolved (Wilkinson et al. 2005). It will rely on a large variety of observables to classify and parametrize stars (Bailer-Jones 2003). It will have on board an astrometric and a photometric instrument giving proper motions, accurate positions and photometric data for a billion stars. A dedicated radial velocity spectrometer (RVS; Katz et al. 2004) with a resolving power of 11 500 working in a spectral band from 848 to 875 nm around the Ca II triplet, will help Gaia to achieve its goal by giving the radial velocity V r of several million stars with a precision of 1kms 1 up to the magnitude V = 14 for the F- or G-type stars and 0.2 dex for the chemical element abundances. Gaia will then provide a representative map of chemical composition throughout the Galaxy. This challenge forces us to prepare the best grid of synthetic spectra to be used to extract V r and to estimate accurate chemical abundances of elements like Ca, Fe, Mg or Si from late-type star spectra. In this respect, the best atmospheric modelling is absolutely necessary to avoid systematic effects in the determination of the stellar parameters. At present, the spectroscopic determination of the atmospheric parameters is based on 1D hydrostatic models, like ATLAS (Kurucz 1992). These models require the use of microturbulence and macroturbulence in order to compensate for their lack of realism since the velocity field and 3D inhomogeneities in the atmosphere are not taken into account. The presence of these adjustable parameters is a serious source of uncertainties in the diagnostic of stellar spectra because the results of the analysis (abundances) depend on the input parameters. These 1D approaches must be overcome. In this E-mail: lbigot@obs-nice.fr ABSTRACT This paper presents the results of a detailed investigation of the validity of oscillator strengths in the spectral domain of the Gaia spectrometer 848 875 nm. This analysis is performed by fitting the most significant Fe I and Si I solar lines in this spectral range with synthetic profiles calculated by 3D radiative hydrodynamical (RHD) simulations. Our main conclusion is that the laboratory oscillator strengths agree well (< 0.1 dex) with values derived from 3D simulations, whereas the semi-empirical values found in data bases like the Vienna Atomic Line Database are imprecise, with a disagreement that can be as large as 1 dex. We address this conclusion to laboratories to encourage new oscillator strength measurements in the infrared, especially in the Gaia region. Key words: atomic data convection hydrodynamics line: formation Sun: infrared Sun: photosphere. respect, the development of realistic 3D radiative hydrodynamical (RHD) simulations of stellar atmospheres in the last two decades (e.g. Stein & Nordlund 1989; Nordlund & Stein 1990; Stein & Nordlund 1998; Freytag, Steffen & Dorch 2002; Vögler et al. 2005) has considerably helped us to improve solar chemical abundance determination (Asplund, Grevesse & Sauval 2005b). This has led to impressive results on stellar chemical abundances, in particular, quite recently, for the lithium in very metal-poor star analyses (Asplund et al. 2006). The derived synthetic profiles are very close to the observed ones in terms of depths, shifts and asymmetries without the use of adjustable parameters. Another concurrent approach is to use multicomponent atmospheric models based on inversion of solar (Borrero et al. 2003) or stellar (Gray & Toner 1985; Dravins 1990; Frutiger, Solanki & Mathys 2005) lines. They are able to reproduce up and down convective flows and thereby the line profile asymmetry. Their main advantage emphasized by some authors lies in the fact that these approaches do not require heavy numerical simulations and are therefore easier to use for stellar diagnostics than 3D hydrodynamical simulations. However, nowadays the power ( Giga flops) of supercomputers is such that the time needed to perform RHD atmospheric models is very reasonable (a few days) and is not a limiting factor. The crucial ingredients used to compute accurate line profiles are the laboratory oscillator strengths (hereafter log gf) and central wavelengths of the transition. The accuracy of these atomic data is the Achilles heel of stellar parameter determinations because of a lack of accurate laboratory measurements. An error on the input oscillator strength or central wavelength will lead to an error on the line strength or on H shift that propagates to the atmospheric parameter determination and thereby the derived abundances and radial velocities. We emphasize that the near-infrared spectral domain of Gaia is a poorly known region: very few line transitions with log gf measurements are available in laboratory data bases like those of C 2006 The Authors. Journal compilation C 2006 RAS

610 L. Bigot and F. Thévenin the Oxford (Blackwell et al. 1986) and Hannover (Bard, Kock & Kock 1991; Bard & Kock 1994) groups. During many years, the log gf used for spectroscopic analyses were those obtained by inversion techniques based on the fit of the solar spectrum (e.g. Thévenin 1989, 1990). Another approach is to perform semi-empirical calculations (Kurucz & Peytremann 1975), but they are known to be imprecise. For astrophysical purposes all these sources of line data are compiled into useful data bases like the Vienna Atomic Line Database (VALD; Kupka et al. 1999), Kurucz (http://cfa-www. harvard.edu/amdata/ampdata/kurucz23/sekur.html) or the National Institute of Standards and Technology (NIST; http://physics.nist. gov/physref/asd/index.html). On the basis of these conclusions and in respect to the preparation of the Gaia mission, we explored the Gaia RVS wavelength range to check and to correct the log gf and central wavelengths proposed in the VALD data. The approach is based on a fit of solar line profiles in the region of Gaia by the use of realistic 3D RHD simulations. The derived log gf will be used in the near future to compute an extensive grid of new synthetic spectra for late-type stars, based on these 3D simulations. After a brief description of the 3D atmosphere used (Section 2), we present the result of the fit on 30 main lines present in the region 848 875 nm (Section 3). 2 THE 3D ATMOSPHERIC MODEL AND THE SYNTHETIC PROFILES The line profile calculations are performed in two steps. First, we compute a realistic time-dependent 3D RHD model of the solar surface. For each snapshot, we solve line transfer at the disc centre with state-of-the-art quantum physics. The final synthetic profile is obtained after time and spatial averages. Each selected line is then fitted to the observed solar spectrum by adjusting both oscillator strengths and central wavelengths. 2.1 The solar atmospheric model The numerical code used for this work belongs to a new generation of 3D atmospheric codes developed for the study of solar granulation (Stein & Nordlund 1998), line formations (Asplund et al. 2000a,b,c, 2004, 2005a) and helioseismology (Rosenthal et al. 1999). The code solves the non-linear, compressible equations of mass, momentum and energy conservation on a Eulerian mesh: ln ρ = u ln ρ u, (1) t u t = u u + g P ln P + σ, (2) ρ e t = u e P ρ u + Q rad + Q visc, (3) where the variables are u the vector field, ρ the density and e the internal energy per unit mass. The pressure P is obtained by the use of a realistic equation of state (Gustafsson et al. 1975 plus subsequent updates), which includes ionization, dissociation and recombination processes. The quantities σ and Q visc denote respectively the viscous stress tensor and the viscous dissipation. The radiative cooling/heating, Q rad = κ λ (I λ, S λ )d dλ, (4) λ is obtained by assuming local thermodynamic equilibrium (LTE), i.e. the source function equals the Planck function, S λ = B λ (T). The 3D radiative transfer is solved at each time-step along different inclined rays. We considered two latitudinal μ points and four longitudinal ϕ points, and checked that a finer grid in (μ, ϕ) does not change the properties of the model. The opacities κ λ are obtained through precalculated tables κ λ (ln ρ, e) using the Uppsala stellar atmosphere package (Gustafsson et al. 1975). The line blanketing was taken into account through the opacity binning technique (Nordlund 1982). We considered a Cartesian grid of sufficiently high resolution (x, y, z) = 253 253 163 points in order to get very accurate line profiles. The code is stabilized by a numerical viscosity that removes noise generated by spatial derivatives at the level of the mesh. It has then little influence on large-scale convective motions. The coefficients of the diffusion were adjusted by standard tests, like classical shock test tubes, and are never adjusted to fit the line profiles. The geometrical sizes are 6 6 Mm for the horizontal directions and 3 Mm for the vertical one. The dimensions of this domain are large enough to include a sufficiently large number of granules (n 20) simultaneously. A periodic boundary condition was applied for the horizontal directions, and transmitting vertical boundaries were used at the top and bottom of the domain. The bottom of the domain is placed to have a nearly adiabatic, isentropic and featureless convective transport for the incoming flow. The upper boundary was placed sufficiently high in the atmosphere at +0.5 Mm (log τ 5000 = 3.3) so it does not influence the properties of the atmospheric model. We note that our model does not include chromosphere. A detailed description of the current version of the code used in this paper may be found in (Stein & Nordlund 1998). The parameters that define the solar model are T eff = 5770 ± 20 K, and log g = 4.44, and the chemical element mixture is taken from Asplund et al. (2005b). We note that the effective temperature is not an input but rather an output slowly varying in time. Indeed, the input parameter is rather the entropy at the bottom of the domain of simulation. This quantity is adjusted so that the temporal average of T eff matches the desired value. We emphasize that, unlike 1D hydrostatic models that reduce all the hydrodynamics into a single adjustable (mixing length) parameter, the present simulations were done ab initio. The diagnosis made by such RHD simulations is therefore much more realistic than the 1D models, which suffer from an arbitrary choice of parameters. 2.2 Synthetic line profiles The RHD simulation ran for t = 1 h of solar time and the snapshots were stored every 30 s. For each of them, the radiative line transfer equation was solved at the disc centre μ = 0 for each horizontal (x, y) position I λ (x, y, t, μ = 0). Before comparison with observations, both time and horizontal averages of the 3D time-dependent line profile were performed. We used a state-of-the-art equation of state (Mihalas, Däppen & Hummer 1988) and opacities (Gustafsson et al. 1975 plus updates). We use the most recent quantum mechanical calculations of hydrogen collisions with neutral species (Anstee & O Mara 1995; Barklem & O Mara 1997; Barklem, O Mara & Ross 1998). The great improvement with quantum mechanical calculation compared with the traditional Unsöld (1955) recipe is to lead to line widths that agree well with the observed one without the need of an enhancement factor (e.g. Mihalas 1978; Thévenin 1989). Stark broadening was ignored in the present simulations. We emphasize that we have tried several numerical resolutions for the 3D atmospheric models. The final adopted mesh, i.e. 253 253 163, leads to the best fit with the observations. Higher resolution would be too CPU demanding and unnecessary for the present work

Atomic oscillator strengths 611 and desired precision for line profiles. The reader may see Asplund et al. (2000a) for discussions about effects of grid resolution. The synthetic profiles are convolved with a Gaussian function representing the instrumental profile of the spectrograph with a resolution λ/δλ 4 10 5. The calculated wavelengths are shifted by 633ms 1 to take into account the gravitational redshift. The adopted solar abundances of Fe and Si are taken from Asplund et al. (2005b) and are 7.45 and 7.51, respectively. In this work, we ignored non-local thermodynamic equilibrium (NLTE) effects. The solar Fe I lines have been extensively studied recently in 1D, 3D, LTE and NLTE conditions (Thévenin & Idiart 1999; Gehren, Korn & Shi 2001; Shchukina & Trujillo Bueno 2001; Collet, Asplund & Thévenin 2005). A recent review on NLTE line formation can be found in Asplund (2005). The main conclusion of these studies, based on different assumptions, is that NLTE effects on line formation in 1D or 3D solar atmospheres are relatively low, e.g. less than 0.1 dex. It results in a 3D NLTE abundance of Fe I similar to the meteoritic one (Shchukina & Trujillo Bueno 2001). 3 DETERMINATIONS OF ATOMIC PARAMETERS 3.1 Observations and line selection The observed solar spectrum used in this work is obtained by the Fourier Transform Spectrograph, hereafter FTS (Brault & Neckel 1987). It is particularly well adapted for the present work because of its high signal-to-noise ratio (S/N > 5000) and its large resolving power 4 10 5. Our selected lines were extracted from the Moore et al. (1966) catalogue. We selected lines with reasonably large equivalent widths of W λ 20 m Å among the Fe I and Si I lines. This selection resulted in a sample of 30 lines listed in Table 1. In our present work, we do not include the Ca II triplet, which will be treated in a separate forthcoming paper. The reason is that, at the time of the writing of this present paper, some new calculations of atomic constants are in progress and will be included in our 3D line profile calculation later. Moreover, some NLTE corrections will be necessary for these three lines, which are beyond the scope of this work. 3.2 Results The values of log gf are found by fitting the observed profiles. For each line, we compute a series of profiles with different values of log gf with a step of 0.01 dex around the value given in VALD. Regarding the precision on solar chemical abundances (±0.1 dex), a finer step in log gf would be unnecessary. As seen in Fig. 1, the agreement between the observed and computed line profiles from 3D RHD simulations is very satisfactory. The agreement with the solar FTS spectrum is generally of the order of 1 per cent, which demonstrates the realism of the 3D RHD simulations of the solar surface: both the temperature structure and Table 1. Corrections of oscillator strengths and central wavelengths of lines in the spectral domain of Gaia/RVS. The excitation potential χ is taken from VALD. The results of our inversion are λ 3D and (log gf) 3D. The equivalent widths W λ are from Moore et al. (1966). The symbols ( ) indicate some strong Fe I lines for which the core is not well fitted, probably due to NLTE effects. The lines for which the log gf come from laboratory measurements (Nave et al. 1994) are denoted by superscript lab in the table. Line W λ (må) χ (ev) λ VALD (nm) λ 3D (nm) (log gf) VALD (log gf) 3D Fe I 22 4.1860 848.198 20 848.198 53 1.631 2.097 Si I 34 5.8710 850.154 40 850.155 09 1.530 1.223 Si I 50 5.8710 850.221 90 850.222 42 1.260 0.943 Fe I 108 2.1980 851.407 21 851.406 82 2.229 lab 2.250 Fe I 79 3.0180 851.510 84 851.510 96 2.073 lab 2.033 Fe I 58 4.9130 852.666 90 852.666 76 0.760 lab 0.675 Si I 58 6.1810 853.616 40 853.616 33 0.910 0.730 Si I 134 5.8710 855.677 70 855.678 32 0.730 0.259 Fe I 36 5.0100 857.180 20 857.180 35 1.441 1.134 Fe I 86 2.9900 858.225 74 858.225 78 2.134 lab 2.198 Fe I 48 4.9560 859.294 50 859.295 10 0.968 0.891 Si I 54 6.1910 859.596 00 859.596 45 1.040 0.897 Si I 36 6.1910 859.705 00 859.706 29 1.370 1.122 Fe I 54 4.3860 859.883 02 859.882 89 1.089 lab 1.285 Fe I 19 5.0100 860.707 10 860.707 99 1.246 1.419 Fe I 99 2.8450 861.180 40 861.180 10 1.926 lab 1.900 Fe I 33 4.9880 861.393 50 861.393 93 1.384 1.121 Fe I 42 4.9130 861.627 60 861.627 98 0.405 0.935 Fe I 75 2.9490 862.160 07 862.160 14 2.321 lab 2.369 Si I 161 6.2060 864.846 50 864.845 98 0.300 0.020 Fe I 113 2.8310 867.474 65 867.47410 1.800 lab 1.780 Fe I 41 4.9660 867.963 80 867.963 88 1.445 1.040 Si I 54 6.2060 868.635 20 868.635 20 1.200 0.935 Fe I 268 2.1760 868.862 55 868.862 30 1.212 lab 1.249 Fe I 20 2.9900 869.870 70 869.870 57 3.483 3.464 Fe I 73 4.9550 869.945 40 869.945 31 0.380 lab 0.480 Fe I 82 4.9130 871.039 20 871.039 12 0.646 0.425 Si I 107 6.1810 872.801 00 872.801 14 0.610 0.300 Fe I 22 3.4150 872.914 80 872.914 69 2.954 2.933 Si I 97 5.8710 874.244 60 874.245 38 0.630 0.363

612 L. Bigot and F. Thévenin Figure 1. Comparisons between the synthetic (diamonds) and observed solar (full line) disc centre intensities. In each panel, the residual intensity is shown as an indicator of the goodness of the fit. The synthetic profiles match almost perfectly the observation for both shifts and asymmetries, with an overall agreement better than 1 per cent in most cases. velocity field are close to the real ones. The derived values of oscillator strengths (log gf) 3D and new central wavelengths λ 3D obtained by our fit are reported in Table 1. The differences with the VALD values are plotted in Fig. 2. In most cases, there is a significant disagreement between the derived log gf and the VALD data, which can be as large as 0.5 dex. Indeed, due to the lack of laboratory measurements, most of the (log gf) VALD come from semi-empirical calculations, which are relatively imprecise, especially for complex atoms, which strengthens our present work. Among our selection of lines, we focused our attention on the 10 Fe I lines for which laboratory measurements of oscillator strengths (log gf) labo are available (Nave et al. 1994, NIST). In these cases, the differences between the derived (log gf) 3D and the laboratory measurements (log gf) labo are smaller and less than ±0.1 dex, which is roughly the accuracy of laboratory measurements. This satisfactory agreement supports both laboratory measurements and 3D RHD simulations. We emphasize here that this work can only be done in the context of the 3D hydrodynamical approach, which does not contain any free parameter. Indeed, the same work with a 1D hydrostatic code

Atomic oscillator strengths 613 Figure 2. Results of the fit for the 30 selected lines. Left-hand panel: differences between (log gf) 3D and (log gf) VALD as a function of the fitted central wavelengths λ 3D :FeI (filled circles) and Si I (open circles). The lines represented by asterisks correspond to the Fe I lines for which (log gf) VALD come from laboratory measurements. Dashed lines indicate a reasonable level of accuracy ±0.1 dex for the log gf. Right-hand panel: same figure for the line shifts of the central wavelengths corrected by the gravitational redshift. Figure 3. Left-hand panel: close-up view of Fig. 2 for the 10 Fe I lines (asterisks) for which laboratory log gf are available (Nave et al. 1994). The dashed lines indicate ± 0.1 dex. The symbols (open triangles) correspond to the difference between (log gf) 1D derived from a 1D hydrostatic code (MOOG plus the Holweger Müller model) and (log gf) labo. For the 1D code, we assume a microturbulence ξ micro = 0.8 km s 1 and a macroturbulence ξ macro = 1.6 km s 1.A reason for the difference between (log gf) 3D and (log gf) 1D is that the line does not form at the same optical depth in the two approaches due to the difference in the model structure. Right-hand panel: comparison of the synthetic profiles calculated from 3D RHD (full line) and 1D MOOG plus Holweger Müller (dashed line) codes for the same value of log gf. The 1D approach cannot reproduce the observed line as well as the 3D RHD approach. would make the validity of the log gf impossible to check because the result of the analysis would depend on the microturbulence and macroturbulence parameters. The accuracy of the derived (log gf) 3D depend on the input accuracy of solar element abundances ( 0.1 dex), the observed solar spectrum and, even if small, the non-perfection of the 3D solar model, in particular the presence of NLTE effects. We estimate the final accuracy to be of the order of 0.1 0.2 dex. Regarding the resolving power of the Gaia spectrometer (R = 11 500), this precision on the (log gf) 3D is satisfactory. We note that we faced some problems to fit some of the strongest Fe I lines (W λ > 100 m Å and χ<3 ev) of our selection. The cores of these lines are slightly too deep compared with the observed ones (a few per cent). These lines are marked by a star ( ) in Table 1. They are formed very high in the atmosphere so we suspect the presence of NLTE and/or chromospheric effects. Further improvements in the modelling are needed for these peculiar lines. For comparison purposes, we also fit the same selection of solar lines using the 1D hydrostatic code MOOG 1 (Sneden 1973) in which we have injected the solar 1D model of Holweger & Müller (1974). The results are shown in Fig. 3. The agreement between the (log gf) 1D and (log gf) labo are slightly less satisfactory than those obtained from 3D. The differences between (log gf) 3D and (log gf) 1D are less than 0.15 dex. Finally, we adjusted the central wavelengths of our selected lines to those of VALD. The 1 http://verdi.as.utexas.edu/moog.html

614 L. Bigot and F. Thévenin corresponding line shifts are in a range of ±200ms 1 ( ±10mÅ) and are shown in Fig. 2. We emphasize that both results on log gf and lineshifts are similar (quantitatively) to those obtained by the inversion analysis of infrared (980 1570 nm) solar lines using the two-component solar atmospheric model of Borrero et al. (2003). 4 CONCLUSIONS We have performed 3D hydrodynamical simulations of the solar surface to obtain realistic synthetic line profiles, which have been compared with the observed solar spectrum for a selection of 30 lines of neutral species (Fe I,SiI) in the spectral range 848 875 nm of the Gaia space mission. The work has shown that the atomic data provided by VALD need to be corrected. Indeed, our derived values show differences that can be as large as ±0.5 dex. The agreement is much better for the lines that have log gf determined in laboratory. In those cases, the agreement is less than ±0.1 dex, which is roughly the accuracy of the laboratory measurements. The spectral domain of Gaia/RVS has been selected mainly for the presence of the Ca II triplet, which may be measurable even for metal-poor stars. However, we emphasize the need for significant improvements in the modelling of the external layers. That is why we did not include the synthetic profiles of the Ca II lines in the present paper. Indeed, 3D NTLE line formation and correct modelling of the chromosphere are necessary for a realistic fit of the Ca II triplet as well as for some Fe I lines (Recio-Blanco & Thévenin 2005). For the moment and because of these limitations, we claim that the extraction of stellar parameters (abundance, effective temperature, gravity) from the Ca II triplet region cannot be reasonably done. We also emphasize in this paper the lack of precise laboratory measurements in the near-infrared. 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