Lithium in the globular cluster NGC 6397 - Evidence for dependence on evolutionary status

J. I. González Hernández; P. Bonifacio; E. Caffau; M. Steffen; H.-G. Ludwig; N. T. Behara; L. Sbordone; R. Cayrel; S. Zaggia

doi:10.1051/0004-6361/200912713

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Volume 505 / No 2 (October II 2009)

A&A, 505 2 (2009) L13-L16

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Issue		A&A Volume 505, Number 2, October II 2009


Page(s)		L13 - L16
Section		Letters
DOI		https://doi.org/10.1051/0004-6361/200912713
Published online		15 September 2009

LETTER TO THE EDITOR

Lithium in the globular cluster NGC 6397^,^,

Evidence for dependence on evolutionary status

J. I. González Hernández^1,2 - P. Bonifacio^1,2,3 - E. Caffau¹ - M. Steffen⁴ - H.-G. Ludwig^1,2 - N. T. Behara^1,2 - L. Sbordone^1,2 - R. Cayrel¹ - S. Zaggia⁵

1 - Cosmological Impact of the First STars (CIFIST) Marie Curie Excellence Team, France
2 - GEPI, Observatoire de Paris, CNRS, Université Paris Diderot, Place Jules Janssen, 92190 Meudon, France
3 - Istituto Nazionale di Astrofisica - Osservatorio Astronomico di Trieste, via Tiepolo 11, 34143 Trieste, Italy
4 - Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
5 - INAF - Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, Padua 35122, Italy

Received 17 June 2009 / Accepted 3 September 2009

Abstract
Context. Most globular clusters are believed to host a single stellar population. They can thus be considered a good place to study the Spite plateau and to search for possible evolutionary modifications of the Li content.
Aims. We want to determine the Li content of subgiant (SG) and main sequence (MS) stars of the old, metal-poor globular cluster NGC 6397. This work was aimed not only at studying possible Li abundance variations but also to investigate the cosmological Li discrepancy.
Methods. Here, we present FLAMES/GIRAFFE observations of a sample of 84 SG and 79 MS stars in NGC 6397 selected in a narrow range of B-V colour and, therefore, effective temperatures. We determine both effective temperatures and Li abundances using three-dimensional hydrodynamical model atmospheres for all the MS and SG stars of the sample.
Results. We find a significant difference in the Li abundance between SG stars and MS stars, the SG stars having an abundance higher by almost 0.1 dex on average. We also find a decrease in the lithium abundance with decreasing effective temperature, both in MS and SG stars, albeit with a significantly different slope for the two classes of stars. This suggests that the lithium abundance in these stars is, indeed, altered by some process, which is temperature-dependent.
Conclusions. The lithium abundance pattern observed in NGC 6397 is different from what is found among field stars, casting some doubt on the use of globular cluster stars as representative of Population II with respect to the lithium abundance. None of the available theories of Li depletion appears to satisfactorily describe our observations.

Key words: stars: abundances - stars: atmospheres - stars: population II - stars: fundamental parameters - Galaxy: globular clusters: individual: NGC 6397

1 Introduction

The old, metal-poor dwarf stars of the Galactic halo share approximately the same Li abundance, irrespective of their metallicity or effective temperature (Spite & Spite 1982b,a). This plateau of lithium was believed to provide evidence of a primordial Li abundance. The WMAP satellite has been able to measure with high accuracy the baryonic density from the fluctuations of the cosmic microwave background (Spergel et al. 2007). This result implies a primordial Li abundance of $\log ({\rm Li}/{\rm H})+ 12 =2.72\pm0.06$ (Cyburt et al. 2008) whereas the observed Li abundances in metal-poor dwarfs are in the range 2.0-2.4 (see Charbonnel & Primas 2005; Asplund et al. 2006; Meléndez & Ramírez 2004; Sbordone et al. 2008; Bonifacio et al. 2007a, and references therein). This discrepancy may be trivially solved if the Spite plateau does not represent the primordial Li abundance. In this case the amount of lithium in the atmospheres of all ancient stars, of all masses and metallicities, must have been uniformly depleted by at least a factor of three.

Possible explanations of this difference are: (a) the first generation of stars, Population III stars, could have processed some fraction of the halo gas, lowering the lithium abundance (Piau et al. 2006); (b) the primordial Li abundance has been uniformly depleted in the atmospheres of metal-poor dwarfs by some physical mechanism (e.g. turbulent diffusion as in Korn et al. 2006; Richard et al. 2005; gravitational waves as in Charbonnel & Talon 2005, etc.); (c) the standard Big Bang nucleosynthesis (SBBN) calculations should be revised, possibly with the introduction of new physics (see e.g. Hisano et al. 2009; Jedamzik 2004; Jittoh et al. 2008; Jedamzik 2006). The observed Li abundances, A(Li), in metal-poor stars appear to show a very well defined plateau with very little dispersion at relatively high metallicities, whereas at low metallicities there seems to be an increased scatter, or perhaps even a sharp down turn in the Li abundances (González Hernández et al. 2008; Sbordone et al. 2008; Bonifacio et al. 2007a). The existence of a slope in A(Li) versus [Fe/H] would exacerbate the discrepancy between Li abundance in metal-poor stars and the WMAP predictions (Bonifacio et al. 2007a). The issue of the slope in the plateau is somewhat elusive and different groups reach different conclusions, depending on the adopted temperature scale (Meléndez & Ramírez 2004).

Globular clusters (GCs) were initially considered to be a good place to investigate the Spite plateau (Boesgaard et al. 1998; Pasquini & Molaro 1996,1997; Molaro & Pasquini 1994), since the classical paradigm was that GCs are made of a single stellar population. The discovery of correlations among elemental abundances in turn-off (TO) stars (Gratton et al. 2001) and in particular the presence of a Li-Na anti-correlation (Bonifacio et al. 2007b; Pasquini et al. 2005), showed the need for the presence of different stellar populations, capable of nucleosynthetic activity and variable amounts of pollution of the presently observable stars. Such signatures are not found among field stars and are peculiar to GCs. This makes the perspective of using GCs to investigate the Spite plateau meagre.

Among the observed GCs, NGC 6397 occupies a special role, in the sense that the Li abundance among non-evolved stars is very homogeneous (Bonifacio et al. 2002; Thévenin et al. 2001), at variance with what is observed in NGC 6752 (Pasquini et al. 2005) and 47 Tuc (Bonifacio et al. 2007b). More recent studies (Korn et al. 2007,2006) have claimed a tiny variation of A(Li) along the subgiant branch, in the sense of higher A(Li) being found for lower $T_{\rm eff}\;$ values. This variation is however quite small compared to what is observed in NGC 6752 and 47 Tuc.

In this Letter we present the result of the analysis of the first observations of Li in main sequence (MS) stars of a globular cluster.

2 Observations

We integrated NGC 6397 over 15 h with the multi-object spectrograph FLAMES-GIRAFFE (Pasquini et al. 2002) at the European Southern Observatory (ESO), using the 8.2-m Very Large Telescope, on 2007 April-July, covering the spectral range $\lambda\lambda$ 6400-6800 Å at a resolving power $\lambda/\delta\lambda\sim17~000$ . The targets were selected using our own calibrated Johnson-Cousins B, V photometry, based on public images (ESO program 163.O-0741(C)) obtained with WFI at the ESO/MPI 2.2 m telescope on 14 May 1999. We chose SG and MS stars in the colour range $B-V=0.6\pm0.03$ , thus ensuring a narrow $T_{\rm eff}\;$ range (see Fig. 3 online). By swapping the fibres on the SGs we managed to observe over 9 h for about 80 MS stars and 2.5 h for roughly the same number of SGs. The resulting S/N ratio $\sim$ 80-130 is the same for both sets of stars. The spectra were reduced using the ESO Giraffe pipeline, version 2.5.3. A combined spectrum of all sky fiber spectra in each night was properly subtracted from each individual spectrum. We then corrected each spectrum for the earth velocity and combined all the spectra of the same target (see the quality of the spectra in Fig. 4 online). Each star spectrum was corrected for its radial velocity, providing a mean cluster radial velocity of $V_{\rm r,c}=18.5$ ${\rm km}\:{\rm s}^{-1}$ . We removed all stars, considered as cluster non-members, with $\mid V_{\rm r}-V_{\rm r,c} \mid~> 3\sigma_{V_{\rm r,c}}$ , where $\sigma_{V_{\rm r,c}}$ is the radial velocity dispersion (3.7 ${\rm km}\:{\rm s}^{-1}$ ). We ended up with 79 MS (orginally 80) and 84 SG (88).

$\begin{figure} \par\includegraphics[width=8.5cm,angle=0.]{12713f1.eps} \end{figure}$	Figure 1: Histograms of observed equivalent width of the lithium doublet at 670.8 nm in MS and SG stars in the globular cluster NGC 6397. Histograms of the equivalent width of Li line are displayed in bins of 0.5 pm for MS stars (solid line) and SG stars (dashed-dotted line).
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3 Analysis and results

The narrow range in effective temperatures ensures that the uncertainty in the comparisons between MS and SG stars is dominated by the error on the measured equivalent width (EW) of the Li doublet line. These were measured by fitting the observed Li line profile with synthetic profiles of the Li doublet, as previously done for this cluster (Bonifacio et al. 2002). The EW measurements show (Fig. 1) that SGs have, on average, larger EWs of the Li doublet than MS stars (see the accuracy of our fitting procedure in Fig. 10 online). Although there is a slight dependence of the B-V colour on surface gravity, and a SG star of a given colour is indeed cooler than a MS star of the same colour ( $\sim$ 90 K at B-V=0.6), the difference displayed in Fig. 1 is too large to be explained in this way. The weighted mean of the EW is $2.97\pm0.02$ pm and $4.06\pm0.01$ pm for MSs and SGs, respectively. The difference in the mean EW values is of about 1.1 pm which would require a mean $T_{\rm eff}\;$ difference of $\sim$ 210 K. Prior to any model-dependent analysis, this clearly points towards the SGs having a higher Li abundance than the MSs. This is similar to what is found among field stars, where the Li abundance appears to be about 0.04 dex higher in turn-off and SG stars than in MSs (Charbonnel & Primas 2005).

$\begin{figure} \par\includegraphics[width=8.1cm,angle=0]{12713f2.eps} \end{figure}$

Figure 2:

3D NLTE Li abundances versus 3D effective temperatures of the observed MS (filled circles) and SG (open circles) stars together with Li isochrones for different turbulent diffusion models. The stars have been divided into five effective temperature bins. The error bar in A(Li) shows the dispersion divided by the square root of the number of stars in each bin. In each isochrone, the dashed and solid stretch of the line shows the Li abundance in MS and SG stars, respectively. The horizontal dashed line depicts the cosmological Li abundance.

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We derived $T_{\rm eff}\;$ by fitting the observed H $\alpha$ line profile with synthetic profiles, using 3D hydrodynamical model atmospheres computed with the CO⁵BOLD code (Wedemeyer et al. 2004; Freytag et al. 2002). The ability of 3D models to reproduce Balmer line profiles has been shown in Behara et al. (2009), where the H $\alpha$ profiles of the Sun, and the metal-poor stars HD 84937, HD 74000 and HD 140283 were investigated. From a purely theoretical point of view Ludwig et al. (2009) quantified the differences in using 1D or 3D models for Balmer line fitting (see the accuracy of our fitting procedure in Fig. 9 online). In the online Table 1 we provide information on the 3D model atmospheres used in this work. Self-broadening of the H $\alpha$ line was calculated according to Barklem's theory (Barklem et al. 2000). Stark broadening was calculated following Griem's theories (Griem 1960) with corrections to approximate the Vidal et al. profiles (Vidal et al. 1973). Fixed values for the surface gravity were adopted for both SG and MS stars in the sample, according to the values that best match the position of the stars on a 12 Gyr isochrone (Straniero et al. 1997). The adopted values were $\log (g/{\rm cm~s}^2)=4.40$ and 3.85 for MSs and SGs, respectively. This choice of the surface gravity is supported by the 1.6 mag difference in the V-filter between SGs and MSs in the sample. The Li abundances were derived using the same 3D hydrodynamical model atmospheres. The line formation of Li was treated in non-local thermodynamical equilibrium (NLTE) using the same code and model atom used in Cayrel et al. (2007). The model atom consists of 8 energy levels and 11 transitions. Full details will be given in Sbordone et al. (in prep.). To derive 3D-NLTE Li abundances we used the analytical fit as a function of stellar parameters and EW also provided in Sbordone et al. (in preparation). The analysis was also done with 1D model atmospheres, providing essentially the same picture, although $T_{\rm eff}\;$ in 1D show lower values. We also tried using the Carlsson et al. (1994) NLTE corrections, rather than our own, with no significant difference in the general picture.

In Fig. 2 we display the derived Li abundances versus the effective temperatures of MSs and SGs of the globular cluster NGC 6397. The Li abundance decreases with decreasing temperature, although more rapidly for MSs than for SGs. This Li abundance pattern is different from what is found among field stars (González Hernández et al. 2008; Meléndez & Ramírez 2004; Bonifacio et al. 2007a). The lithium-temperature correlations have a probability of 99.9% and 99.5% for MSs and SGs, respectively, according to the non parametric rank correlation test, Kendall's $\tau$ test. We performed a Kolmogorov-Smirnov test and obtained a probability of $8\times10^{-6}$ . Therefore, the possibility that the two sets (MSs and SGs) have been drawn from the same population (same Li abundance) can be rejected. Even ignoring the trend in A(Li) one can deduce that there is a real difference in the A(Li) of MSs and SGs by computing the mean A(Li) and the standard deviation of the mean for the two samples. For SGs we find $2.37\pm0.01$ , while for MSs $2.30\pm0.01$ . Such a result is also evident in the analysis of Lind et al. (2009) who find only a 0.03 dex difference between the mean A(Li) in MSs and SGs, which is still significant at 1 $\sigma$ . The signal is partly erased by the very narrow range of $T_{\rm eff}\;$ for MSs deduced by Lind et al. (2009) ( $\sim$ 80 K) compared to the wide range ( $\sim$ 450 K) for the SGs (see Fig. 7). Such a difference in the $T_{\rm eff}\;$ range spanned by MSs and SGs is inconsistent with the very similar B-V colours of the two sets of stars. In Fig. 8 online, the lack of correlation between colour and $T_{\rm eff}\;$ is fully compatible with the photometric and reddening uncertainties. The $T_{\rm eff}\;$ values adopted by Lind et al. (2009) for the MSs are on the lower $T_{\rm eff}\;$ side of the range spanned by the sample; this results in an artificial increase of the deduced A(Li) for the MSs, which reduces the difference with SGs, without totally erasing it. We conjecture that this is because the $T_{\rm eff}\;$ estimates of Lind et al. (2009) are derived by interpolating our V magnitudes onto the cluster fiducial sequence, ignoring any colour information. This necessarily compresses the $T_{\rm eff}\;$ scale into a range smaller than what is implied by the range in colour, when photometric errors and variations in reddening are taken into account.

4 Discussion and conclusions

Our results imply unambiguously that the Li surface abundance changes with evolutionary status. The fact that A(Li) is higher in SG stars suggests a scenario in which lithium sinks below the photosphere during the MS phase, but to a depth low enough to prevent Li distruction, so that it can be restored in the photosphere, when the stars evolve beyond the TO. The slope of A(Li) with $T_{\rm eff}\;$ among MS stars suggests that the amount by which Li is depleted in the atmospheres is different for stars of different mass ( $T_{\rm eff}\;$ on the MS). The similar slope found among SG stars suggests that after being restored in the atmosphere at the TO, lithium is then decreased by some other mechanism, possibly mixing linked to the convective motions which are more pronounced for the cooler $T_{\rm eff}\;$ of the SGs. Although the above described scenario is plausible, we have so far no detailed understanding of the physical processes that bring it about. Diffusive processes may alter the elemental composition of stars. Diffusion has been studied for decades (Michaud et al. 1984; Aller & Chapman 1960), but only a few years ago, detailed element-by-element predictions from models including effects of atomic diffusion and radiative accelerations have become available (Richard et al. 2002). These models produced strong abundance trends that are not compatible with the Spite plateau, and only with the recent inclusion of turbulent mixing, some of the model predictions roughly agree with observations (Richard et al. 2005).

Pure diffusion models (Richard et al. 2005), with no turbulence, predict A(Li) differences as large as 0.4 dex between MSs and SGs of the same age and temperature. The inclusion of turbulence can change this trend, and the SGs may exhibit a A(Li) which is higher, lower, or almost equal to that of the MSs, depending on the precise value of the turbulence parameter.

In Fig. 2 we show the Li isochrones for different turbulent diffusion models (Richard et al. 2005). These models have been shifted up by 0.14 dex in Li abundance to make the initial abundance of the models, $\log ({\rm Li}/{\rm H})=2.58$ , coincide with the primordial Li abundance predicted from fluctuations of the microwave background measured by the WMAP satellite (Cyburt et al. 2008).

The models assuming pure atomic diffusion, and, among those including turbulent mixing, T6.0 and T6.09, are ruled out by our observations. All such models predict that in MS stars Li should be either more abundant or the same as in subgiant stars. The only model that predicts a A(Li) pattern which is qualitatively similar to that observed, is the T6.25 model. For this model there is a trend of decreasing A(Li) with decreasing $T_{\rm eff}\;$ and at the cool side MSs show less Li than SGs. However, the model fails quantitatively because A(Li) of the warmest stars is about 0.05 dex lower than what is observed. The slope of A(Li) with $T_{\rm eff}\;$ is not perfectly reproduced. Models that include atomic diffusion and tachocline mixing (Piau 2008) do not seem to reproduce our observations, since they provide a constant A(Li) up to 5500 K. The sophisticated models that, besides diffusion and rotation, also take into account the effect of internal gravity waves (Talon & Charbonnel 2004), seem to accurately predict the A(Li) pattern in solar-type stars, at solar metallicity (Charbonnel & Talon 2005). However, Li isochrones have not yet been computed for Population II stars. Our observations call for new investigations into the stellar physics, including gravity waves, atomic diffusion, winds and turbulent mixing. The Li abundance pattern uncovered by our observations has not been observed in field stars and opens up the possibility that it may be peculiar to globular clusters, or, perhaps, to NGC 6397. The cosmological lithium problem still awaits a solution.

Our results indicate a decrease of Li abundance along the subgiant branch, as the stars become cooler and slightly more luminous. This is at variance with what was found by Korn et al. (2007,2006) and Lind et al. (2009), who find, instead, an increase in A(Li) in the same region of the colour-magnitude diagram. We note that the latter authors used our own data, as retrieved from the ESO archive. The difference is mainly in the different $T_{\rm eff}\;$ scales used by the different investigations. Lind et al. (2009) also estimate slightly different EWs for our sample. The difference between their and our weighted mean EWs is $-0.08\pm0.02$ pm and $-0.08\pm0.03$ pm for SG and MS stars, respectively (see also Fig. 5 online) The difference is smaller than the mean error in the EW measurements ( $\sim$ 0.2 pm in this work and $\sim$ 0.35-0.4 pm in Lind et al. 2009), suggesting that the two sets of measurements are fully consistent. To verify that the differences in EWs are irrelevant to our conclusions we adopted the Lind et al. EWs and our $T_{\rm eff}\;$ to compute A(Li): our main conclusions are unchanged. This reinforces our claim that the difference lies in the $T_{\rm eff}\;$ scale. The difference in A(Li) that Korn et al. (2006) find between turn-off (TO) and SG stars is driven by the very low $T_{\rm eff}\;$ they find at the TO. This is inconsistent with our H $\alpha$ fitting. Our stars are cooler than the TO but we find higher $T_{\rm eff}\;$ than the TO stars in Korn et al. (2006). We also determined 1D $T_{\rm eff}\;$ using H $\alpha$ profiles (see Fig. 6 online). 3D and 1D $T_{\rm eff}$ , Li abundances and EWs of the stars in our sample are given in Table 2 online. We compare these $T_{\rm eff}\;$ with the colour temperatures derived from our B-V photometry and the colour calibration, based on the infrared flux method (IRFM) from González Hernández & Bonifacio (2009). Adopting a mean reddening for the cluster of E(B-V)=0.186 (Gratton et al. 2003), we find that for our sample of MS stars the mean IRFM effective temperature is 6262 K, to be compared with 6047 K and 6296 K of our 1D and 3D H $\alpha$ temperatures, respectively. The temperature spread, using both 1D and 3D H $\alpha$ fitting, is also considerably larger, by a factor of two. That IRFM provides higher $T_{\rm eff}\;$ than 1D H $\alpha$ is well established (González Hernández & Bonifacio 2009). We repeated the analysis also with 1D model atmospheres, and the results are qualitatively similar: higher A(Li) for SG stars and decreasing A(Li) for decreasing $T_{\rm eff}$ . The first result is very robust, since it can be deduced directly from the distribution of Li EWs. The second relies on our ability to model stellar atmospheres. To the extent that our 3D hydrodynamical models are a good description of a stellar atmosphere, the second result is robust as well. The issue of the behaviour of A(Li) with $T_{\rm eff}\;$ ultimately depends on the $T_{\rm eff}\;$ scale adopted. This could be solved if we had a direct measure of the angular diameters of metal-poor MSs and SGs. This is probably beyond the reach of present-day interferometers.

NGC 6397 appears to have a higher Li content than field stars of the same metallicity. This needs to be confirmed by a homogeneous analysis of field stars, with the same models and methods. This may or may not be related to the fact that this cluster is nitrogen rich, compared to field stars of the same metallicity (Pasquini et al. 2008).

Acknowledgements

We wish to thank O. Richard for providing us his lithium depletion isochrones for different turbulent diffusion models. Special thanks to K. Lind for sending us her analysis of our data in advance of publication. J. I. G. H., P. B., H.-G. L., N. B. and L. S. acknowledge support from the EU contract MEXT-CT-2004-014265 (CIFIST). We acknowledge use of the supercomputing centre CINECA, which has granted us time to compute part of the hydrodynamical models used in this investigation, through the INAF-CINECA agreement 2006, 2007.

References

Aller, L. H., & Chapman, S. 1960, ApJ, 132, 461 [NASA ADS] [CrossRef]
Asplund, M., Lambert, D. L., Nissen, P. E., Primas, F., & Smith, V. V. 2006, ApJ, 644, 229 [NASA ADS] [CrossRef]
Barklem, P. S., Piskunov, N., & O'Mara, B. J. 2000, A&A, 363, 1091 [NASA ADS] (In the text)
Behara, N. T., Ludwig, H.-G., Steffen, M., & Bonifacio, P. 2009, AIP Conf. Ser., 1094, 784 [NASA ADS] (In the text)
Boesgaard, A. M., Deliyannis, C. P., Stephens, A., & King, J. R. 1998, ApJ, 493, 206 [NASA ADS] [CrossRef]
Bonifacio, P., Pasquini, L., Spite, F., et al. 2002, A&A, 390, 91 [NASA ADS] [CrossRef] [EDP Sciences]
Bonifacio, P., Molaro, P., Sivarani, T., et al. 2007a, A&A, 462, 851 [NASA ADS] [CrossRef] [EDP Sciences]
Bonifacio, P., Pasquini, L., Molaro, P., et al. 2007b, A&A, 470, 153 [NASA ADS] [CrossRef] [EDP Sciences]
Carlsson, M., Rutten, R. J., Bruls, J. H. M. J., & Shchukina, N. G. 1994, A&A, 288, 860 [NASA ADS] (In the text)
Cayrel, R. 1988, The Impact of Very High S/N Spectroscopy on Stellar Physics, IAU Symp., 132, 345
Cayrel, R., Steffen, M., Chand, H., et al. 2007, A&A, 473, L37 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
Charbonnel, C., & Primas, F. 2005, A&A, 442, 961 [NASA ADS] [CrossRef] [EDP Sciences]
Charbonnel, C., & Talon, S. 2005, Science, 309, 2189 [NASA ADS] [CrossRef] (In the text)
Cyburt, R. H., Fields, B. D., & Olive, K. A. 2008, J. Cosmology Astropart. Phys., 11, 12 [NASA ADS] [CrossRef] (In the text)
Freytag, B., Steffen, M., & Dorch, B. 2002, Astron. Nachr., 323, 213 [NASA ADS] [CrossRef]
González Hernández, J. I., Bonifacio, P., Ludwig, H.-G., et al. 2008, A&A, 480, 233 [NASA ADS] [CrossRef] [EDP Sciences]
González Hernández, J. I., & Bonifacio, P. 2009, A&A, 497, 497 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
Gratton, R. G., Bonifacio, P., Bragaglia, A., et al. 2001, A&A, 369, 87 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
Gratton, R. G., Bragaglia, A., Carretta, E., et al. 2003, A&A, 408, 529 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
Griem, H. R. 1960, ApJ, 132, 883 [NASA ADS] [CrossRef] (In the text)
Hisano, J., Kawasaki, M., Kohri, K., & Nakayama, K. 2009, Phys. Rev. D, 79, 063514 [NASA ADS] [CrossRef]
Jedamzik, K. 2004, Phys. Rev. D, 70, 083510 [NASA ADS] [CrossRef]
Jedamzik, K. 2006, Phys. Rev. D, 74, 103509 [NASA ADS] [CrossRef]
Jittoh, T., Kohri, K., Koike, M., et al. 2008, Phys. Rev. D, 78, 055007 [NASA ADS] [CrossRef]
Korn, A. J., Grundahl, F., Richard, O., et al. 2006, Nature, 442, 657 [NASA ADS] [CrossRef]
Korn, A. J., Grundahl, F., Richard, O., et al. 2007, ApJ, 671, 402 [NASA ADS] [CrossRef]
Lind, K., et al. 2009, A&A, in press (In the text)
Ludwig, H.-G., Behara, N. T., Steffen, M., & Bonifacio, P. 2009, A&A, 502, L1 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
Meléndez, J., & Ramírez, I. 2004, ApJ, 615, L33 [NASA ADS] [CrossRef]
Michaud, G., Fontaine, G., & Beaudet, G. 1984, ApJ, 282, 206 [NASA ADS] [CrossRef]
Molaro, P., & Pasquini, L. 1994, A&A, 281, L77 [NASA ADS]
Pasquini, L., & Molaro, P. 1996, A&A, 307, 761 [NASA ADS]
Pasquini, L., & Molaro, P. 1997, A&A, 322, 109 [NASA ADS]
Pasquini, L., Avila, G., Blecha, A., et al. 2002, The Messenger, 110, 1 [NASA ADS] (In the text)
Pasquini, L., Bonifacio, P., Molaro, P., et al. 2005, A&A, 441, 549 [NASA ADS] [CrossRef] [EDP Sciences]
Pasquini, L., Ecuvillon, A., Bonifacio, P., & Wolff, B. 2008, A&A, 489, 315 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
Piau, L. 2008, ApJ, 689, 1279 [NASA ADS] [CrossRef] (In the text)
Piau, L., Beers, T. C., Balsara, D. S., et al. 2006, ApJ, 653, 300 [NASA ADS] [CrossRef] (In the text)
Richard, O., Michaud, G., & Richer, J. 2002, ApJ, 580, 1100 [NASA ADS] [CrossRef] (In the text)
Richard, O., Michaud, G., & Richer, J. 2005, ApJ, 619, 538 [NASA ADS] [CrossRef]
Sbordone, L., Bonifacio, P., Hernández, J. I., et al. 2008, First Stars III Conference, AIP Conf. Proc., 990, 339
Spergel, D. N., Bean, R., Doré, O., et al. 2007, ApJS, 170, 377 [NASA ADS] [CrossRef] (In the text)
Spite, M., & Spite, F. 1982a, Nature, 297, 483 [NASA ADS] [CrossRef]
Spite, F., & Spite, M. 1982b, A&A, 115, 357 [NASA ADS]
Straniero, O., Chieffi, A., & Limongi, M. 1997, ApJ, 490, 425 [NASA ADS] [CrossRef] (In the text)
Talon, S., & Charbonnel, C. 2004, A&A, 418, 1051 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
Thévenin, F., Charbonnel, C., de Freitas Pacheco, J. A., et al. 2001, A&A, 373, 905 [NASA ADS] [CrossRef] [EDP Sciences]
Vidal, C. R., Cooper, J., & Smith, E. W. 1973, ApJS, 25, 37 [NASA ADS] [CrossRef] (In the text)
Wedemeyer, S., Freytag, B., Steffen, M., Ludwig, H.-G., & Holweger, H. 2004, A&A, 414, 1121 [NASA ADS] [CrossRef] [EDP Sciences]

Online Material

$\begin{figure} \par\includegraphics[width=8.50cm,clip]{12713f3.eps} \end{figure}$	Figure 3: Colour-magnitude diagram of the cluster NGC 6397. The stars studied in this work are depicted in small filled squares.
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Table 1: Details of the 3D hydrodynamical model atmospheres.

$\begin{figure} \par\includegraphics[width=8.5cm,angle=0]{12713f4.eps} \end{figure}$	Figure 4: Observed GIRAFFE/FLAMES spectra of a dwarf star MSS005634 ( bottom, S/N = 102) and a subgiant star SGB002930 ( top, S/N= 111)of the globular cluster NGC 6397.
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$\begin{figure} \par\includegraphics[width=8.5cm,angle=0]{12713f5.eps} \end{figure}$	Figure 5: Comparison between the equivalent widths derived in this work and those provided by Lind et al. (2009). Filled circles and open circles correspond to dwarf and subgiant stars, respectively.
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$\begin{figure} \par\includegraphics[width=8.5cm,angle=0]{12713f6.eps} \end{figure}$	Figure 6: Comparison between 3D and 1D effective temperatures of the observed stars. Filled circles and open circles correspond to dwarf and subgiant stars, respectively. The dashed line shows the one-to-one relationship.
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$\begin{figure} \par\includegraphics[width=8.5cm,angle=0]{12713f7.eps} \end{figure}$

Figure 7:

Comparison between 3D effective temperatures of the observed stars and the 1D effective temperatures derived from colors by Lind et al. (2009). Filled circles and open circles correspond to dwarf and subgiant stars, respectively. The dashed line shows the one-to-one relationship. Since our stars have been selected in a B-V range of 0.06 mag, their temperature range should be of, at least 250 K. It could be larger due to stars being moved into our selection box by photometric and reddening uncertainties. There is no plausible reason why this range should be as small as that implied by the Lind et al. (2009) effective temperatures $\sim$ 80 K.

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$\begin{figure} \par\includegraphics[width=8.5cm,angle=0]{12713f8.eps} \end{figure}$	Figure 8: Comparison between 3D effective temperatures and B-V colours of the observed stars. Filled circles and open circles correspond to dwarf and subgiant stars, respectively. The lack of correlation between B-V and effective temperature is consistent with photometric errors and reddening variations.
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$\begin{figure} \par\includegraphics[width=8.5cm,angle=0.]{12713f9a.eps}\includegraphics[width=8.5cm,angle=0.]{12713f9b.eps} \end{figure}$	Figure 9: Observed GIRAFFE/FLAMES H $\alpha$ profile fitted with a synthetic 3D profile for a dwarf star MSS005634 ( left panel, S/N = 102, $T_{\rm eff,3D}=6327$ K) and for a subgiant star SGB002930 ( right panel, S/N = 111, $T_{\rm eff,3D}=6126$ K).
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$\begin{figure} \par\includegraphics[width=8.5cm,angle=0.]{12713f10a.eps}\include... ...2713f10c.eps}\includegraphics[width=8.5cm,angle=0.]{12713f10d.eps} \end{figure}$	Figure 10: Observed spectra of two dwarf stars, MSS005634 ( top-left panel, S/N= 102, EW(Li) = 32.21 mÅ) and MSS006561 ( top-right panel, S/N=71, EW(Li) = 27.97 mÅ) and two subgiant stars, SGB002930 ( bottom-left panel, S/N=111, EW(Li) = 36.83 mÅ) and SGB004904 ( bottom-left panel, S/N =68, EW(Li) = 48.52 mÅ), showing the fit of the Li line with a synthetic profile.
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Table 2: Photometric data of the dwarf and subgiant stars of the globular cluster NGC 6397. We also provide the signal-to-noise of the spectra, the 3D and 1D H $\alpha$ -based effective temperatures, 3D Li abundances, and the equivalent widths and errors.

Footnotes

... 6397: Based on observations obtained with FLAMES/GIRAFFE at VLT Kueyen 8.2 m telescope in programme 079.D-0399(A).
...: Table and Figs. 3-10 are only available in electronic form at http://www.aanda.org
...: Table 2 is available in electronic form at http://www.aanda.org and at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/505/L13

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